It is widely accepted among investment professionals that, while portfolio optimization has compelling theoretical merit, it is not useful in practice. Practitioners are concerned that optimization is an “error maximizing”^{1 }process fraught with insurmountable estimation issues. The abstract of an early academic critique of mean-variance optimization, (Michaud 1989) states:

The indifference of many investment practitioners to mean-variance optimization technology, despite its theoretical appeal, is understandable in many cases. The major problem with mean-variance optimization is its tendency to maximize the effects of errors in the input assumptions. Unconstrained mean-variance optimization can yield results that are inferior to those of simple equal-weighting schemes.

Many nay-sayers selectively quote the above passage as reason to dismiss optimization altogether. However, this same abstract continues with the following thoughts:

Nevertheless, mean-variance optimization is superior to many ad hoc techniques in terms of integration of portfolio objectives with client constraints and efficient use of information. Its practical value may be enhanced by the sophisticated adjustment of inputs and the imposition of constraints based on fundamental investment considerations and the importance of priors. The operating principle should be that, to the extent that reliable information is available, it should be included as part of the definition of the optimization procedure.

It’s clear that portfolio optimization is a powerful tool that must be used thoughtfully and responsibly. However, even the critics agree that optimization is the only mechanism to make best use of all the information available to investors.

In this paper, we will first build a theoretical framework that will enable us to determine the most appropriate method of portfolio construction for most situations. We’ll introduce the Portfolio Optimization Machine^{TM }and suggest how an investor might decide which type of optimization is most consistent with the qualities, beliefs, and assumptions he holds about the assets under consideration.

¹ Michaud (1989)

In his 1998 second edition of ** “Stocks for the Long Run^{1}”**, Jeremy Siegel added a chapter called “Technical Analysis and Investing with the Trend”, where he explored simple trend rules to time the U.S. stock market. In the chapter, Dr. Siegel revealed that the simple trend following strategy produced similar returns to a strategy of buying the index and re-investing dividends over the very long run, but with less portfolio volatility and smaller maximum peak-to-trough losses.

To this day, many novice investors and advisors make use of simple trend rules to try to time exposure to stock markets. The 200 day moving average that Dr. Siegel explored (and many other market timers and trend traders have been using for decades) is perhaps the most closely watched indicator. With the introduction of liquid ETFs tracking major equity indexes, it’s a simple matter for any investor to own stocks when the major indexes trade above this simple moving average, but cut and run when they break.

While novice investors typically stumble onto the concept of trend-following in the context of stock-market timing, professionals know that trend-following is not about using trends to time one or two individual markets. Modern professional trend-followers often trade dozens of futures markets across equities, bonds, currencies, commodities, and more obscure markets like carbon offsets.

In fact, professionals have long understood that the key to success with trend following, which most novice investors overlook, is **diversification**. In the preface to Michael Covel’s classic book,** “ Trend Following^{2} ”**, Larry Hite, one of the original

In my early days, there was only one guy I knew who seemed to have a winning track-record year after year. This fellow’s name was Jack Boyd. Jack was also the only guy I knew who traded lots of different markets. If you followed any

oneof Jack’s trades, you never really knew how you were going to do. But, if you were like me and actually countedallof his trades, you would have made about 20 percent a year. So, that got me more than a little curious about the idea of trading futures markets “across the board.” Although each individual market seemed risky, when you put them together, they tended to balance each other out and you were left with a nice return with less volatility.

Larry’s insight was that the only way to achieve consistent results is to trade markets “across the board”. At the time, Larry was referring to the Chicago Board of Trade, which housed trading for most major commodity futures. Now futures are traded on a wide variety of exchanges, and investors are no longer constrained to trading commodity futures. But the same lesson holds today as it did four decades ago when Larry Hite began his trading career. That is, if you trade just one market “you never really know how you are going to do”, but if you trade markets across the board, you have a good chance of earning “a nice return with less volatility”.

Many novice investors and advisors choose to apply trend following concepts to time stock indices. More than anything this probably reflects the public’s pre-occupation with stocks. But some analysts also argue that investors should focus on equities because they have the largest risk premium.

**This completely misses the point.**

The highest risk premium argument only holds for small investors who, despite overwhelming headwinds, insist on managing their own portfolios^{4}, and for investors who do not understand the Capital Market Line (CML).

Remember, the goal for most investors is to maximize their return at a level of risk that they can bear. Investors have many options to achieve different rates of return. Typically, as an investor seeks higher levels of return he is encouraged to take on greater exposure to the equity risk premium. However, this is not the only way to achieve higher returns.

Following on the work of Harry Markowitz and Jack Treynor, Bill Sharpe published a 1964 treatise titled ** “Capital Asset Prices: A Theory of Market Equilibrium under Conditions of Risk^{5}”**, which described a method for investors to achieve higher returns without sacrificing diversification. He proposed that an investor with typical preferences regarding tradeoffs between risk and return would prefer to hold an efficient diversified portfolio at all times.

Investors who can tolerate higher risk in pursuit of higher returns would borrow money to invest in more units of this diversified portfolio. This is preferable to moving out the efficient frontier into portfolios with increasing concentration in stocks.

Consider Figure 1 which describes an efficient frontier (in dark blue) and CML (in red) derived from recently published asset return premia and correlation estimates from a major institution^{6}. Emerging Stocks are expected to produce the highest returns, while Foreign Bonds have the lowest expected return. The portfolio that is expected to produce the maximum return per unit of risk, the maximum Sharpe ratio portfolio, is highlighted with a red point on the chart, and is found at the point where the CML intersects the efficient frontier.

**Figure 1: Capital Market Line vs. Efficient Frontier**

*Source: ReSolve Asset Management. For illustrative purposes only.*

Let’s examine a case where a “Growth” investor wishes to maximize his rate of return given that he can tolerate 15% annual volatility, consistent with the historical risk character of a 70/30 global stock/high grade bond portfolio. Under typical conditions, this investor would be forced to push out the efficient frontier and take on a concentrated portfolio of equity markets. Figure 2 describes the composition of this portfolio.

Figure 2: **Mean-Variance Optimal Portfolio at 15% Target Volatility Along Efficient Frontier**

*Source: ReSolve Asset Management. For illustrative purposes only.*

Given the capital market assumptions above, to achieve the highest return possible at no more than 15% volatility would require that he hold 29.4% Long Treasuries, 18% Asian Stocks, 52.6% Emerging Stocks, since this is the most efficient portfolio at 15% volatility.

This portfolio would be expected to earn 4.8% annual excess return, highlighted with a gold point on the efficient frontier in Figure 1.

Now consider an investor who is liberated from the no-leverage tyranny imposed by the efficient frontier. He can choose to own the more diversified mean-variance optimal portfolio described in Figure 3, and borrow (with margin or futures or other derivatives) to purchase more units of the portfolio using leverage until he achieves his target volatility. Again given our working capital market assumptions, this portfolio would be dominated by Emerging Bonds, Long Treasuries, and Asian Stocks.

Figure 3: **Maximum Sharpe Ratio Portfolio**

*Source: ReSolve Asset Management. For illustrative purposes only.*

Leverage is a foreign concept for many novice investors. But readers with an open mind will recognize that by using a prudent^{7} amount of leverage to invest in the maximum Sharpe ratio portfolio, they can now take advantage of investments that earn their premium during very different market environments, and from diverse economic regions.

The concentrated equity investor would only expect to earn attractive returns during periods of sustained economic growth, benign inflation, and abundant liquidity. However, the maximum Sharpe ratio portfolio in Figure 3 contains Treasury bonds, which are designed to benefit during deflationary growth shocks; emerging bonds, which would benefit from an increase in credit quality among emerging countries, as well as potential currency tailwinds; and equity markets from around the world.

Aside from the benefits of broader diversification, the choice to leverage the maximum Sharpe ratio portfolio in Figure 3 provides an opportunity to earn 6.45% excess return, a full 1.65 percentage points more per year than the investor can expect to achieve by moving out the frontier. This point is also highlighted on the CML in Figure 1.

To close the loop, investors who focus their trend trading on equity indexes because the equity risk premium is of a larger magnitude than other premia are missing the point. Under reasonable assumptions about the general relationship between risk and return, a diversified portfolio will produce considerably greater return *per unit of risk*. When scaled up the CML using prudent amounts of leverage, this leads to a higher absolute return, *period*, than a concentrated position in equities.

Of course, the benefits of diversification grow in proportion to the number of alternative sources of return that are available. Diversification is the key.

Notwithstanding the benefits of diversifying into uncorrelated markets outside of equities, many investors start their investment journey with a myopic focus on equities. Upon discovering the benefits of trend following, they often spend years applying the techniques to time a major stock index, such as the S&P 500 or their local market.

In this section we will continue to focus on equity market trend following. We’ll examine the performance of a representative trend-following strategy applied to fifteen global stock index futures.

First we’ll observe the performance of the trend strategy when applied to the individual markets. Then we’ll demonstrate the monstrous advantage that is available from trading a diversified strategy of all equity indexes. Finally, we’ll expand our horizon to include assets outside of equities, and unleash the true potential of diversified multi-asset trend-following.

We first examine the distribution of trend-following performance when applied to individual equity index futures, relative to the performance that can be achieved by trading a diversified basket of equity index futures. To keep things simple, we examine the performance of a simple moving-average trend trading strategy, based on a 200 day (~10 month) lookback horizon. The strategy will hold a market long when its price is above its moving average, and exit when price falls below.

Let’s first observe the growth profile of our toy trend strategy when it is applied to futures tracking several major equity markets around the world.

Figure 4 plots the growth trajectories for each equity index futures market. S&P 500 futures started trading in 1983, and other markets were introduced over time. To account for the fact that some markets have less time to compound (because they come into existence later), we bring each market into existence at the current level of the S&P 500 strategy. Thus, the terminal value for each strategy in Figure 4 offers a meaningful indication of relative performance.

Figure 4: **Growth of $1: Simple 200 Day Moving Average Long/Flat Trend Strategy Applied to Futures on Major Equity Indices**

*Source: Calcuations by ReSolve Asset Management. Data from CSI Data. Growth of $1 from executing long/flat 200-day moving-average trend strategies on equity index futures scaled to ex post 20% volatility.*

There is a large dispersion in results across markets. Japanese investors trading the TOPIX or the Nikkei fared much worse than Finnish or Swiss investors trading exactly the same strategy. In fact, the worst strategy grew $1 to just over $2 in 35 years, while the best strategy turned $1 into over $16.

Perhaps surprisingly, while the trend strategy improved risk-adjusted performance relative to a buy and hold strategy for the majority of equity indexes, investors in Commonwealth countries (UK, Canada and Australia) experienced lower absolute and risk-adjusted returns by following trends.

In our toy example, if the investor chooses to run a trend-following strategy on just one equity index, he has equity assets to choose from. Assuming the investor chose one equity index to trade at random, the best estimate of the investor’s performance is the median performance among all strategies.

Importantly, it is the median that matters to one investor who chooses just one strategy, not the mean, because the investor can live just one life, and has chosen not to take advantage of the law of large numbers^{8}.

What many investors miss is that, absent extremely confident views about which market will outperform in the future, investors are better off trading all of the markets at once.

Let’s consider a more humble investor that is focused on investing in equities, but cannot decide which market(s) to trade. Instead, he chooses to trade all of the equity index assets as part of one diversified strategy.

The “Portfolio” quantity in Figure 5 reflects the performance of this diversified strategy relative to the median strategy. Critically, the diversified strategy benefits from the fact that the returns from each of the individual strategies are not perfectly correlated. In other words, they diversify one another.

Figure 5 compares the Sharpe ratio of a diversified trend strategy, which trades all equity markets, against the median performance of trend strategies over the 15 equity index futures.

An investor choosing a market to trade at random would have expected to experience a Sharpe ratio of 0.45, while an investor who traded all markets as a diversified trend strategy would have achieved a Sharpe ratio of 0.76. The difference between the “Median” and the “Portfolio” performance is the bonus that an investor accrued from taking advantage of this diversification.

Astonishingly, investors who chose to diversify would have produced 1.69x the return per unit of risk relative to an investor trading one random market. This diversification bonus is so large that the “Portfolio” strategy surpasses the risk adjusted performance of all but one of the individual strategies^{9}. Which means an investor would have had to be better than 93% accurate in choosing which index to trade *in advance* in order to achieve better performance than one could generate from simply diversifying across all of them.

**For those focused on U.S. stocks, it’s worth noting that the diversified strategy dominated trend trading on the S&P 500, with a Sharpe ratio of 0.51, by almost 50%. ^{10}**

Figure 5: **Marginal Sharpe Contribution from Diversified Long/Flat Trend Trading Across Equity Markets vs. Median Performance by Individual Market**

*Source: Calcuations by ReSolve Asset Management. Data from CSI Data. “Median” is the median Sharpe ratio of long/flat 200-day moving-average trend strategies applied to individual equity index futures. “Portfolio” is the Sharpe ratio of a strategy that trades all of the equity index futures markets as one aggregate strategy. Diversification Bonus is the improvement in performance from trading all equity index futures as a diversified strategy instead of choosing one market to trade. Performance does not account for fees, transacation costs, or other factors which may impact performance. For illustrative purposes only.*

We mentioned above that the concept of diversification extends (obviously) to other asset classes besides equities. The fact is, it rarely pays to focus your efforts on any one market, in any asset class.

Let’s expand our domain of analysis to include six bond futures, seven currency futures, and twenty commodity futures. Figure 6 describes the diversification bonus from choosing to trade all markets in each category, rather than trading any single one.

The commodity asset category provides a particularly interesting case study. Long/flat trading based on a simple 200 day moving average has not been a particularly profitable strategy for individual commodity markets over the past few decades. The median Sharpe ratio for trend strategies across twenty commodities is just 0.24.

However, commodity markets are generally uncorrelated with one another. Which means that there is a large advantage to running even relatively ineffective strategies “across the board.” Incredibly, an investor would have achieved 2.29x the return per unit of risk relative to an investor trading any one random commodity market.

Figure 6: **Marginal Sharpe Contribution from Diversified Long/Flat Trend Trading Across Major Asset Categories vs. Median Performance by Individual Market Within Each Asset Category**

*Source: Calculations by ReSolve Asset Management. Data from CSI Data. “Median” is the median Sharpe ratio of long/flat 200-day moving-average trend strategies run on each individual market in each asset category. Markets are weighted using ex post inverse volatility. “Portfolio” is the Sharpe ratio of a strategy that trades all of the markets in the asset category as one aggregate strategy. “Diversification Bonus”” is the improvement in performance from trading all markets in the category instead of choosing one market to trade. Performance does not account for fees, transacation costs, or other factors which may impact performance. For illustrative purposes only.*

Now that we’ve quantified the diversification bonus for investors who are concentrated in any one asset category, we conclude by expanding the trend strategy to trade all assets from all categories at once. This is obviously where the rubber hits the road, since professional trend followers use all the instruments at their disposal to achieve the largest divesification bonus possible.

Figure 7 describes the gargantuan bonus available to investors who understand the power of combining trend-following with diversification across all major asset categories. It’s shocking to see that diversification alone can transform many independent strategies with low Sharpe ratios on their own into a diversified strategy with long-term performance that rivals even the most successful markets and hedge funds.

Figure 7: **Marginal Sharpe Contribution from Diversified Long/Flat Trend Trading Across All Markets vs. Median Performance by Individual Market**

*Source: Calculations by ReSolve Asset Management. Data from CSI Data. “Median” is the median Sharpe ratio of long/flat 200-day moving-average trend strategies run on each individual market across all asset categories. Markets are weighted using ex post inverse volatility. “Portfolio” is the Sharpe ratio of a strategy that trades all markets in all categories as one aggregate strategy. “Diversification Bonus”” is the improvement in performance from trading all markets as one aggregate strategy instead of choosing one asset to trade. Performance does not account for fees, transacation costs, or other factors which may impact performance. For illustrative purposes only.*

For natural reasons, many novice investors and advisors try to harness the power of trend following to trade their favorite equity index. But this misses the point. By trend-trading a single index investors are extremely vulnerable to the probability of choosing an equity market with low forward returns, unproductive trends, or both.

The true benefit of trend following is only realized when investors take advantage of the extreme liquidity and diversity of global futures markets to trade a wide range of markets across all major asset categories. Our analysis shows that an investor would have achieved more than double the risk-adjusted performance of a median equity trend strategy by trading a diversified strategy across many diverse markets.

Traditionally, many diversified futures funds were only availble to Qualified Investors. This barrier has lifted over the past few years with the introduction of liquid alternatives, as several private funds have been “converted” to traditional mutual funds. Catalyst and Rational Funds have been especially active in making top futures strategies available to everyone. Even better, gains on futures receive favourable tax treatment, and futures funds are often extremely capital efficient.

- Siegel, Jeremy J. “Stocks for the Long Run, 2nd ed.”, McGraw-Hill (1998)↩
- Covel, Michael W. “Trend Following: Learn to Make Millions in Up or Down Markets”, FT Press (2009)↩
- Schwager, Jack D. “Market Wizards”, HarperCollings (1989)↩
- Small investors may have skill and certain advantages (i.e. liquidity, mandate flexibility, portfolio agility, long-term thinking, etc.), but they also pay egregious fees for margin, typically cannot effectively access futures and swaps markets, and either a) pay onerous commissions or b) trade for “free” but get killed on execution because the broker sells their flow for rebates. Remember, the broker has to get paid somehow…↩
- Paper can be found here↩
- NOT official ReSolve estimates.↩
- Some readers might wonder about the term “prudent” referring to leverage. For context, the average leverage ratio for the S&P 500 is 1.7x since 1995, which means there is $1.7 of debt for ever $1 of equity.↩
- To gain a deeper understanding of the concept of ergodicity and the difference between ensemble mean and finite time mean, please see this article: https://aip.scitation.org/doi/full/10.1063/1.4940236 .↩
- I know, I know, you all would have known to trade Finnish index futures in advance, so this point is moot.↩
- Many investors have probably examined the performance of a 200 day moving average strategy on the S&P 500 using index data. It may surprise aspiring quants to learn that the exact same strategy run on the S&P 500 total return cash index produces a substantially higher Sharpe ratio over the same period. Please do not learn the wrong lesson! Given very small changes in the exact path of returns, we could just have easily have seen that the futures strategy outperformed the cash index strategy. This dispersion in performance highlights the extreme fragility of this type of strategy run on just one index, and the sensitivity to path dependence.↩

Last week we were jazzed to have Dr. Kathryn Kaminski deliver a comprehensive presentation on Managed Futures Trend Following: The Ultimate Diversifier, where she covered the role of convergent and divergent strategies, and introduced other important themes like:

- The role of managed futures in institutional portfolios
- Diversifiers vs. crisis alpha

- Return based style analysis to differentiate between managed futures funds, and build optimal portfolios
- Identifying and managing the drivers of managed futures returns

- Sources of “craftsmanship alpha” in managed futures
- The qualities to look for and what to avoid

Yes, post 2008 hasn’t been an easy period for Managed Futures. In all fairness, it has also been one of the easiest periods for Equity investors in the past 100 years or more.

There are several things to consider:

- Low interest rates are a drag for Managed Futures.If 80% or more of your assets are in T-bills and cash management accounts, this doesn’t help. In the 70s and even in the 80s Managed Futures had an 8% tail wind from interest on collateral. That would be nice right now.Put simply, low rates aren’t good for Managed Futures in pure carry terms. In addition, low rates may also create less movement in futures prices (Remember – the futures price includes the time value of money). Alex Greyserman and I examined this issue in our book. We considered the amount of market divergence in recent years and couldn’t find any evidence that prices are more efficient and less divergent than before. (See Chapter 5)
- No-crisis equals less divergence in prices equals less trend to capture. Hutchinson and O’Brien (2014) examine this issue in a paper entitled “Is this time different? Trend Following and Financial Crises” https://papers.ssrn.com/sol3/papers.cfm?abstract_id=2375733

They show that when there is a sustained period without crises things are not so easy for Trend Following. I also have a whitepaper on “Crisis Alpha Everywhere” discussed in PIOnline that shows that it is the amount of crisis in different assets, not just equities, that matters. Equity crisis is a bigger driver, but it is crisis in general that drives divergence/dislocation that creates tradable trends.

http://www.pionline.com/article/20170330/ONLINE/170329884/crisis-alpha-everywhere

To put it more simply, there has been less crisis since 2008. There are some exceptions: 2014 was a rough year in commodities and currencies, CTAs did very well as we would expect. If there are no more serious crises in the next 10 years, I would expect this to be a headwind for Managed Futures returns.

Trend following should still be a main allocation for managed futures. The only difference is that they can consider a wide range of strategies as long as they don’t have them already. For example, if an investor buys a multi-strategy CTA this could help smooth some of the difficult periods for trend following. Since managed futures trade mostly in futures, the key strategies to consider are those that could provide risk premiums: things like carry, macro, short term strategies, and possibly volatility strategies.

One major red flag for me as a former allocator was manager discretion. If a trend following manager is changing their portfolios based on the heat of the moment and going against the system – that is not ideal. Trend following often works its best when things are uncomfortable for investors, and it is the “rule based” approach that lets the strategy take positions that aren’t always comfortable.

Take the example of oil in 2014. No macro trader wanted to short oil because it seemed impossible that the price could keep going down. A trend system should short oil because it is going down. If the manager is willing to come in and make a discretionary decision, this is going against the approach – put in the words of the talk – adding convergent to the divergent approach. This often can backfire.

Another red flag is style drift – if the manager is moving their strategy around too much they are most likely suffering from hindsight bias. A simple example would be speeding up or slowing down the trend system due to recent performance. When slow trend systems have worked, if they move their system to be slower they are chasing past performance, which is not a great plan.

Carry is a good fit for trend – as long as it isn’t too big and as long as it is multi-asset class. Macro strategies are also good because they have similar positions but they tend to get into positions at different times.

For a global perspective, CRO is not really a new concept but in the US the term and concept is new. In 2012, one of the largest Swedish Pension funds discussed a similar objective and they built what they called a “protection portfolio” which has a similar mandate to the CRO mandates in the US. Pension funds in Europe, the Middle East, and Japan have been investing in Managed Futures with a similar objective for many years. US pensions have been somewhat newer to investing in Managed Futures.

How does CRO shift the conversation about Managed Futures? Historically Managed Futures has been bucketed in with “convergent” strategies in hedge funds. In this case, when compared with these strategies they came up short as a stand-alone investment. The Sharpe ratios are lower than the typical hedge fund.

On the other hand, from a “global” portfolio perspective they are one of the best global risk reducers. Hedge funds tend to have higher Sharpe ratios, but while they are generally uncorrelated they tend to correlate during periods of crisis, or when credit or liquidity risk are an issue. In this case, they are “locally optimal” in a hedge fund portfolio but not always globally optimal from the entire portfolio perspective.

A CRO strategic class is meant to put strategies like managed futures (in particular trend following) into a different bucket with a different strategic objective than hedge funds. Given this, investors have understand that if they are looking for risk mitigation they may make different choices than if they are looking for something that is just uncorrelated.

**No offence, but trend following on equity indexes is not good at all as a stand-alone.**

I would estimate the Sharpe ratio about 0.08 over long horizons (see our book on trend). This doesn’t mean you shouldn’t do it but it’s not generally that fun to do. It is a part of a trend system but I wouldn’t advise doing it alone. Timing seems to be more difficult in equities, traditionally trends on short rates and fixed income have had the best Sharpe ratios.

**If the S&P goes down, CTAs will tend to short the S&P, but it will depend on how quickly the S&P goes down and what happened prior to the S&P going down.**

Most CTAs who focus on longer-term trends may reduce their long positions but not start shorting until some time after the S&P goes down. This is why Q1 has been hard for CTAs even in an equity correction. Since the long term trend in equities was up up up, they were long equities, but when this trend reverted they lost on the correction and had to reduce equity positions.

**A key thing to remember is that CTAs tend to have long term signals it can take some time for them to go from long to short in any asset.**

Great question, I would suggest a 20% allocation but I do agree that it requires the right framing for an investor. The investor needs to see the investment as complementary to the remainder of the portfolio, not necessarily just crisis alpha. This is precisely why a CRO or strategic class for pensions is a big step for understanding managed futures. If they are less comfortable with hugging their peers or a benchmark, a lower allocation may be more appropriate. I often focus on also telling them with this investment it is important to not buy high and sell low. Many investors invest after a big “divergent event” and then they get frustrated that it doesn’t repeat. If they want to reduce an allocation, reduce after, not at the bottom. This is why framing the investment is so important.

Historically shorts do not preform as well as longs. This is simply because over the long run many assets with a risk premium tend to up-trend.

But since most investors hold long assets, being able to be short from time to time can have great complimentary properties. Without doing any analysis, I would suggest that the contribution is 80/20 or 70/30.

In our book, Alex and I look at the long bias in equities in Chapter 13 of our book using the equity bias factor. You can see there that most of the time it is better to have more long bias, but sometimes when it really matters being short can really add value.

I would suggest Robert Carver’s book “Systematic Trading” and Andreas Clenow’s book “Following the Trend.”

**The article below illustrates how capital efficiency, taxes, and fees impact portfolio choices given what we feel to be reasonable assumptions.**

However, we recognize that **you** may have different views on these variables.

That’s why we prepared a simple online application so that you can generate a bespoke report based on your own assumptions.

Returns to the simplest domestic capitalization weighted indexes have dominated virtually all active strategies over the nine years since the Global Financial Crisis. It’s not hard to understand why many investors have opted to eschew active strategies altogether, and instead have migrated *en masse* to the lowest cost index products. And for most investors, when considering traditional active long-only equity or bond mutual funds, it is prudent to place a high priority on fees. After all, most equity mutual-funds and smart-beta index products will have a correlation of 0.8 or higher to a traditional 60/40 portfolio^{1}. As a result, they are likely to produce only small marginal benefit in terms of portfolio efficiency.

However, the equation changes somewhat when investors start to consider allocations to alternatives.

Alternatives are constructed to capture returns from sources that are structurally uncorrelated with equities and bonds. Therefore, they may be expected to be uncorrelated to core portfolios, and substantially improve portfolio efficiency by increasing returns, reducing volatility, or both. However, many investors in alternatives evaluate these products using the same criteria that they use to compare traditional funds.

This is a mistake.

The evaluation of alternatives introduces an extra dimension into the equation that investors don’t need to think about with traditional equity funds. It’s the concept of capital efficiency.

Capital efficiency measures the amount of market exposure one can achieve with an investment per unit of capital invested. This has become a central theme for many institutional investors, who understand that they may face low expected returns on capital in their core portfolios over the next few years.

Capital efficiency can be best understood as “bang for your buck”.

Consider two funds, A and B, with similar expected Sharpe ratios, fees and taxes. In other words, the Funds are equally efficient. However, Fund A is run at 6% volatility while Fund B is run at 12%. This is possible in the world of alternatives because they often involve leverage or the use of derivatives like futures.

Given that Fund B runs at 2x the volatility of Fund A, Fund B should be expected to produce 2x the excess returns. In other words, an investor who carves out 20% of their portfolio to invest in liquid alternatives would gain 2x the marginal improvement in returns and Sharpe ratio on their portfolio by investing in Fund B instead of Fund A.

To help illustrate the point, imagine an investor owns a traditional portfolio consisting of 60% in a US equity index ETF and 40% in a bond index ETF. Acknowledging that expected returns are low for both stocks and bonds at the current time, the investor wishes to diversify with a 20% allocation to alternative investments. His objective is to raise his expected returns with minimal risk.

He evaluates his options and identifies three attractive funds:

- A market-neutral equity fund with an expected gross Sharpe ratio of \(1.1\), targeting 7% annualized volatility on up to 300% gross exposure, with a gross expense ratio of 2.24%, and 0 correlation with the current portfolio
- A managed futures mutual fund with an expected gross Sharpe ratio of \(1.1\), targeting 12% annualized volatility on up to 300% gross exposure, with a gross expense ratio of 2%, and 0 correlation with the current portfolio
- A GTAA ETF of ETFs with an expected gross Sharpe ratio of 0.8, expected
*long-term average*annualized volatility of 8.25% on a maximum of 100% gross exposure, with a gross expense ratio of 0.8%, and a correlation of 0.5 with the current portfolio.

Let’s dig a little deeper into how we arrived at these assumptions.

The market neutral fund is, by definition, hedged against market beta. Thus, it’s reasonable to assume it will have a consistent correlation of zero to the market. If the fund has equal risk exposure to five uncorrelated styles (say size, value, quality, investment, and momentum) with average Sharpe ratios of 0.5, the expected Sharpe ratio of a well-crafted portfolio is about \(0.5 \times \sqrt{5}=1.1\)^{2}.

A quick glance at larger equity market neutral funds shows that they tend to exhibit between 5% and 7% volatility, so we chose an estimate near the top of the range to give this option the benefit of the doubt (you’ll see why below). We used a fee estimate from a fund managed by a very large quantitative shop that is known for competitive fees in the alternative space.

Market-neutral funds typically turn-over greater than 100% of their portfolio per year, and all gains are taxable as ordinary income.

A managed futures fund typically allocates to a large basket of global asset classes across equities, bonds, currencies, and commodities, and sometimes to more esoteric markets like carbon credits.

A study by Hurst, Ooi and Pedersen (2017)^{3} found that a diversified trend-following strategy produced excess returns of 11% annualized, net of estimated trading costs, on volatility of 9.7% over 126 years from 1880-2016, for a Sharpe ratio of \(11\%/9.7\%=1.1\).

In its worst decade (1910-1919) the strategy produced net returns of 4.1%, while it produced over 20% annualized returns in its best decade (1970-1979).

Many managed futures strategies combine trend signals with carry signals, and this combination has improved the results to trend strategies in historical testing^{4}. When managed futures funds are properly constructed, 60% of gains on trading would typically be taxed as long-term capital gains, while 40% would be taxed as regular income.

The website Allocate Smartly has taken the time to replicate over forty global tactical asset allocation (GTAA) strategies using a common data set over similar time horizons.

We examined data from the site and found that the average strategy produced 8.6% annualized returns net estimated trading costs on 8.25% annualized volatility. Excess returns were 6.6% annualized after subtracting a 2% risk-free rate. The average of pairwise correlations for all strategies with a U.S. 60/40 portfolio was 0.5, and the strategies produced an average Sharpe ratio of 0.8.

A survey of GTAA ETFs listed on U.S. exchanges indicated a range of fees between about 0.8% and 1.7%, so we chose a fee estimate near the bottom of the range. In many cases, trading within Exchange Traded Funds does not produce taxable gains until the fund is sold, at which time an investor pays capital gains on the difference between sale and purchase prices.

How might the investor analyze the relative benefits of these funds to a portfolio over a 10-year evaluation horizon, given his objective to add a 20% allocation to these funds? For our analysis, we assume the core 60/40 allocation is held indefinitely (ignoring tax implications of periodic rebalancing), but the alternative fund is sold after 10 years.

Let’s assume the 60/40 portfolio has an expected net after-tax annualized return of 4% with average 12% annualized volatility. For the purpose of our analysis, it’s simpler to deal with *excess* returns, net of the expected risk-free rate^{5}. If we assume a 2% expected risk-free rate over the next 10 years, the 60/40 portfolio is expected to produce 2% *excess* annualized returns, with an expected Sharpe ratio of \((4\%-2\%)/12\%=0.17\). We assume zero fees on the core portfolio to reflect the costless options available to investors at Schwab, Fidelity, and other dealers, and the near-zero fees on many core ETFs.

We assume a tax rate of 39.6% on ordinary income and 23.8% on long-term capital gains^{6}. Table 1 summarizes the impact of adding a 20% allocation to each of our three hypothetical funds to the 60/40 portfolio, while Figure 1 illustrates the potential difference in ending portfolio value.

We present a detailed breakdown of the analysis that led to the values in Table 1 in an Appendix below.

Table 1: **Hypothetical Impact of Adding a 20% Alternative Fund Allocation to a Core 60/40 Allocation: Summary Statistics**

100% Core 60/40 | 80% Core + 20% Market Neutral Fund | 80% Core + 20% Managed Futures Fund | 80% Core + 20% GTAA ETF | |
---|---|---|---|---|

Weighted Average Fee | 0% | 0.45% | 0.4% | 0.16% |

Expected Net After-Tax Portfolio Return | 4% | 4.26% | 5.17% | 4.54% |

Expected Portfolio Volatility | 12% | 9.7% | 9.9% | 10.5% |

Expected Portfolio Net After-Tax Sharpe ratio | 0.17 | 0.23 | 0.32 | 0.24 |

$1 Grows To | 1.48 | 1.52 | 1.66 | 1.56 |

Source: Calculations by ReSolve Asset Management. For illustrative purposes only.

Figure 1: **Impact of Adding a 20% Alternative Fund Allocation to a Core 60/40 Allocation: Hypothetical Growth**

Source: Calculations by ReSolve Asset Management. For illustrative purposes only.

From Table 1 it’s clear that a 20% allocation to the alternative mutual funds adds up to 0.45% in weighted average portfolio fees, compared with just 0.16% in fees from the addition of the GTAA ETF. However, despite these higher fees and less advantageous tax status, a hypothetical 20% position in the managed futures fund increases expected wealth creation after 10 years by 1.37 times what would be expected from the core 60/40 portfolio on its own. This compares to improvements of just 1.08 times and 1.17 times the wealth creation that would be expected when capital is allocated to the market neutral fund and GTAA ETF, respectively.

**The key point is that the improvement in capital efficiency from managed futures overwhelms all other considerations.**

In addition, due to the low correlation between the managed futures fund and the core portfolio, the improvement in hypothetical returns is achieved with just slightly higher portfolio volatility than what we’d expect from an investment in the market neutral fund, and **less** volatility than an investment in the more highly correlated GTAA ETF.

As a result, an investment in the hypothetical managed futures fund could boost portfolio Sharpe ratio by 1.88x, representing a much larger boost than what one could achieve from the other funds.

The evaluation of alternatives introduces an extra dimension into the equation that investors don’t need to think about with traditional equity funds. Capital efficiency measures the amount of market exposure one is able to achieve per unit of capital invested. In other words, it quantifies “bang per buck” of an investment.

All things equal, it is often more advantageous to a portfolio’s performance, from an **after-fee, after-tax** perspective, to allocate capital within the alternative sleeve to strategies with low correlation and high target volatility, especially if the strategy trades futures. This is true **even if** these funds have higher fees and less favorable tax treatment. Focusing exclusively on fees and taxes misses the forest for the trees.

Note that the advantages of allocating to capital-efficient alternatives may be magnified through thoughtful “asset location”. In other words, investors with retirement accounts have the opportunity to hold less tax-efficient investments in IRAs or 401ks in order to defer or perhaps even eliminate the tax drag.

**The article above illustrates how capital efficiency, taxes, and fees impact portfolio choices given what we feel to be reasonable assumptions.**

However, we recognize that **you** may have different views on these variables.

That’s why we prepared a simple online application so that you can generate a bespoke report based on your own assumptions.

Just set your variables and generate your report – Go to the app now!

First, it’s critical to standardize the expected return across funds, after fees and taxes.

The market-neutral fund is expected to produce gross *excess* returns of \(1.1 \times 7\% = 7.7 \%\). Now let’s subtract fund fees of 2.24% for net returns of 5.46%. The fund returns are considered 100% ordinary income for tax purposes, so if we assume a tax rate of 39.6%, expected net after-tax return would be \(5.46\% \times (1-39.6\%)=3.3\%\). As a result, the new portfolio would be expected to produce an excess return of \(80\% \times 2\% + 20\% \times 3.3\%=2.26\%\) with annualized volatility of \(9.7\%\)^{7}, so that the expected net after-tax portfolio Sharpe ratio would be \(\frac{2.26\%}{9.7\%}=0.23\). All gains are crystallized each year.

The managed futures mutual fund is expected to produce gross *excess* returns of \(1.1 \times 12\% = 13.2 \%\) less fund fees of 2% for net returns of 11.2%. Since the fund trades futures, gains should be taxed at 60% long-term capital gains and 40% ordinary income. If we assume long-term gains are taxed at 23.8% and ordinary income is taxed at 39.6%, we can estimate a combined tax rate on gains of approximately \(60\%\times23.8\%+40\%\times39.6\%=30.12\%\), so expected net after-tax return would be \(11.2\% \times (1-30.12\%)=7.83\%\). As a result, the new portfolio would be expected to produce an excess return of \(80\% \times 2\% + 20\% \times 7.83\%=3.17\%\) with annualized volatility of \(9.9\%\)^{8}, so that the expected net after-tax portfolio Sharpe ratio would be \(\frac{3.17\%}{9.9\%}=0.32\). Again, all gains are crystallized each year.

Finally, the GTAA ETF is expected to produce gross *excess* returns of \(0.8 \times 8.25\% = 6.6 \%\). Now let’s subtract fund fees of 0.8% for net returns of \(5.8\%\). Because of the unique tax treatment of trading inside certain ETFs, we will assume the fund crystallizes zero capital gains each year.

However, while taxes on the market neutral and managed futures funds are crystallized in full each year, the ETF structure simply defers capital gains until the ETF is sold. Assuming the ETF is sold at the termination of our 10-year holding horizon, the investor would expect to pay 23.8% long-term gains tax on the compounded gains at termination. If we assume a net growth rate of \(5.8\%\) after fees, the fund should turn \(\$1\) into \(\$1.76\) after 10-years. The investor would pay 23.8% on the gain of \(\$0.76\), which reduces the net gain to \(\$0.76\times(1-23.8\%) = \$0.58\). Thus, the net expected annualized return actually works out to \((1+0.58)^{(1/10)}-1=4.7\%\).

Therefore, the new portfolio would be expected to produce an excess return of \(80\% \times 2\% + 20\% \times 4.7\%=2.54\%\) with annualized volatility of \(10.5\%\)^{9}, so that the expected net after-tax portfolio Sharpe ratio would be \(\frac{2.54\%}{10.5\%}=0.24\).

- Author’s estimates based on a small survey of U.S. equity mutual funds and smart-beta ETFs.↩
- The volatility of a portfolio with N assets and average pairwise correlations of \(\theta\) is \(s_p=\bar{s_a}\sqrt{1/N +\bar{\theta}}\). Note that for any \(\bar\theta<1\) portfolio volatility will be lower than the average volatility of the constituent assets, while portfolio expected return is constant, resulting in a higher Sharpe ratio.↩
- See https://dx.doi.org/10.2139/ssrn.2993026 Exhibit 1.↩
- For example the paper “Time-Series Momentum, Carry and Hedging Premium” by Molyboga, Qian, and He (2017) suggests that adding carry to trend improves the Sharpe ratio by 0.17. See https://dx.doi.org/10.2139/ssrn.3075650 .↩
- Note that we use annualized returns rather than average returns when translating between Sharpe ratios, returns and volatilities. There are some issues with this, but it was important to compare expected compound growth, which requires annualized returns. The use of arithmetic means rather than annualized (geometric) means should not have any material impact on the economic interpretation of the results.↩
- Assumes the highest federal tax bracket for ordinary income (~39.6%), with commensurate federal tax rate on capital gains and dividends and including Medicare Contribution Tax of 3.8% (total of ~23.8%). Source↩
- \(\sqrt{80\%^2\times12\%^2+20\%^2\times7\%^2+2\times80\%\times20\%\times12\%\times7\%\times0}=9.7\%\) .↩
- \(\sqrt{80\%^2\times12\%^2+20\%^2\times12\%^2+2\times80\%\times20\%\times12\%\times12\%\times0}=9.9\%\) .↩
- \(\sqrt{80\%^2\times12\%^2+20\%^2\times8.25\%^2+2\times80\%\times20\%\times12\%\times8.25\%\times0.5}=10.5\%\) .↩

Confidential and proprietary information. The contents hereof may not be reproduced or disseminated without the express written permission of ReSolve Asset Management Inc. (“ReSolve”). ReSolve is registered as an investment fund manager in Ontario and Newfoundland and Labrador, and as a portfolio manager and exempt market dealer in Ontario, Alberta, British Columbia and Newfoundland and Labrador. Additionally, ReSolve is an SEC registered investment adviser. ReSolve is also registered with the Commodity Futures Trading Commission as a commodity trading advisor and a Commodity Pool Operator. This registration is administered through the National Futures Association (“NFA”). Certain of ReSolve’s employees are registered with the NFA as Principals and/or Associated Persons of ReSolve if necessary or appropriate to perform their responsibilities.

PAST PERFORMANCE IS NOT NECESSARILY INDICATIVE OF FUTURE RESULTS.

The information contained herein are of an illustrative nature and for informational purposes only and does not constitute financial, investment, tax or legal advice. These materials reflect the opinion of ReSolve on the date of production and are subject to change at any time without notice due to various factors, including changing market conditions or tax laws. Where date is presented that is prepared by third parties, such information will be cited, and these sources have deemed to be reliable. Any links to third party websites are offered only for use at your own discretion. ReSolve is a separate and unaffiliated from any third parties listed herein and is not responsible for their products, services, policies or content of their website. All investments are subject to varying degrees of risk, and there can be no assurance that the future performance of any specific investment, investment strategy or precut referenced directly or indirectly in this website will be profitable, perform equally to any corresponding indicated historical performance level(s), or be suitable for your portfolio. Past performance is not an indicator of future results.

#### Calendar 2017 was an exemplary year for ReSolve strategies.

#### Strategies targeting long-term equity-like volatility produced almost double the return of U.S. stocks, with some mandates achieving over 40% growth.

#### Strong results are a function of proven process + relentless discipline + favourable conditions. We offer a comparative analysis to cement the point.

Statistics | Return | Volatility | Max Drawdown |
---|---|---|---|

AAA 16% | 42.37% | 16.30% | -5.72% |

AAA 12% | 29.57% | 11.63% | -4.40% |

AAA 8% | 17.67% | 7.62% | -3.08% |

AAA 8% Un-Levered | 15.47% | 5.73% | -1.78% |

Risk Parity 12% | 24.06% | 8.78% | -4.39% |

Risk Parity 6% Un-Levered | 12.66% | 4.44% | -2.13% |

Tactical Equity | 17.66% | 7.50% | -2.74% |

SOURCE: ReSolve Asset Management. PAST PERFORMANCE IS NOT NECESSARILY INDICATIVE OF FUTURE RESULTS. See disclaimer.

Calendar 2017 was an exemplary year for ReSolve strategies. Per Table 1, at a 12% annualized volatility target, consistent with the long-term risk of a traditional 60/40 global balanced portfolio^{1}, performance of Adaptive Asset Allocation (AAA) and Global Risk Parity (RP) mandates rivaled most global equity benchmarks^{2}. Adaptive Asset Allocation mandates targeting a volatility closer to the long-term profile of global equities (16%-20%) produced almost double the return of U.S. stocks, with some mandates achieving over 40% return.

Figure 1: Live geometrically linked net daily returns to ReSolve USD mandates in 2017. SOURCE: ReSolve Asset Management. See disclaimer.

Figure 1 compares the net total return trajectories of ReSolve’s Adaptive Asset Allocation, Risk Parity, and Tactical Equity mandates against global equities^{3}.

Long-time investors know that ReSolve takes an ensemble approach to strategy design to minimize the risk of specifying the exact wrong model for the current market environment. The current version of Adaptive Asset Allocation uses resampling to draw many combinations of lookback and weighting parameters to estimate momentum, correlations, and volatilities, each time we create an optimal portfolio. In addition, the Strategy uses four techniques to measure momentum and trend; three transforms of momentum data; and five portfolio optimization methods.

One of these methods is thematically consistent with the toy model we described in our seminal whitepaper, Adaptive Asset Allocation: A Primer (2012 rev 2015), where assets are ranked on average momentum, and the top half of assets are held in minimum variance weights. But we also apply forty other combinations of momentum measures, transforms, and optimization methods when we form portfolios. Final portfolios represent a thoughtful combination of all forty-one sub-strategies. While the long-term performance profiles of these sub-strategies are statistically indistinguishable, we observe fairly wide dispersion in performance from year-to-year.

Figure 2: Return trajectory of Adaptive Asset Allocation sub-strategies in 2017. Live aggregate strategy performance is highlighted in gold. SOURCE: ReSolve Asset Management. See disclaimer.

Figure 2 illustrates how each of the forty-one sub- strategies that comprise ReSolve’s Adaptive Asset Allocation approach performed this year, without any volatility targeting. The worst strategy produced less than 9%, while the best generated almost 21%. This is quite a range given that the strategies all seek to maximize momentum and trend while minimizing portfolio volatility. Meanwhile, the live aggregate strategy^{4} delivered net returns of 15.5%.

Some investors may be wondering why the unlevered version of Adaptive Asset Allocation lagged global stocks. After all, global equities produced one of the best trends ever in 2017. The reason is that ReSolve’s strategies, in contrast with many other ostensibly similar strategies, explicitly account for the fact that adding assets with lower expected Sharpe ratio, but low correlation to other portfolio assets, will improve the expected risk-adjusted performance of the portfolio.

Take the case of a two asset portfolio, where one asset has twice the expected Sharpe ratio of the other asset. If the two assets are perfectly correlated, an investor should simply choose to invest all her capital in the asset with the best expected performance. However, if the assets are uncorrelated, the investor is always better off, in terms of expected risk-adjusted performance, to invest in a combination of the two assets rather than simply investing all her funds in the asset with the best expected performance^{5}.

Figure 3: Optimal risk budget for a lower Sharpe asset given different correlation assumptions. SOURCE: ReSolve Asset Management.

Figure 3 considers the case of a two asset portfolio, and quantifies the risk budget^{6} that should be allocated to an asset with a lower expected Sharpe ratio (with the remainder in the higher Sharpe asset), to maximize the portfolio’s expected risk-adjusted performance. Given the example where one asset has half the expected Sharpe ratio of the other asset, the violet line in the chart shows that the most efficient portfolio would combine about 63% in the higher Sharpe asset with a 37% position in the lower Sharpe asset, when the correlation between the two assets is zero. Indeed, assets with negative Sharpe ratios may improve the efficiency of a portfolio given sufficient negative correlation. The light blue line tracks the optimal allocation to a lower Sharpe asset given a correlation of -0.5 with the higher Sharpe asset. You can see that an asset with a Sharpe ratio that is negative and 0.25 times as large as the higher Sharpe asset would still deserve a risk budget allocation of almost 30%!

Why does this matter? Many popular Global Tactical Asset Allocation strategies simply emphasize assets with favorable characteristics, which often leads to portfolios that are fully allocated to just one asset class. In years like 2017, this approach works well, because there are no trend reversals, and the best approach in retrospect was simply to hold 100% in emerging stocks all year. However, under conditions of uncertainty, portfolios that account for correlations will hold more diverse assets, which positions them to capture a smaller proportion of losses on reversals, and to transition into alternate asset classes more quickly.

This is one of the reasons why even a simple Adaptive Asset Allocation strategy is the top ranked strategy by Sharpe ratio, and second-best strategy by annualized total return, over the past twenty years (in simulation) according to a popular GTAA portal^{7}.

PERFORMANCE ATTRIBUTION ANALYSIS

The relatively strong performance of ReSolve’s strategies this year accrued from a confluence of factors. First, most global assets delivered positive returns on the year, and several markets produced spectacular growth. Indeed, the top performing assets produced their returns with low volatility and high Sharpe ratios, so that it was possible to amplify returns using the Capital Market Line. Second, there was a large disparity between the top and bottom- performing assets, which made it easy for our momentum indicators to separate the wheat from the chaffe. In addition, the best performing assets outperformed the worst performing assets very consistently all year, with few rank-reversals.

At the end of 2015, we produced a report to explain some of the reasons why ReSolve’s strategies had struggled that year. We described the necessary conditions for long-only active asset allocation strategies to thrive, and compared the conditions that prevailed in 2015 with conditions during other calendar years over the previous two decades. The analysis made clear just how extraordinarily challenging that year was relative to other years on a wide variety of dimensions. We thought that this year it would be interesting and instructive to contrast conditions in the current year with conditions that prevailed in calendar 2015, using the same analytical tools.

This exercise is useful because, while we have made incremental improvements to our strategies over the past few years, the fundamental mechanics that inform our strategies have not changed materially. By revisiting the metrics that we used to explain the unexciting performance in 2015, and demonstrating how current conditions would have predicted strong performance this year, it will become clear that results in any one year do not reflect on the value of our strategies, but rather reflect the role of luck on short term investment results.

To kick-off our analysis, let’s first examine just how amazing the current year was for equity investors. While investors in U.S. equities have enjoyed outstanding returns for the past nine years, 2017 rewarded investors from virtually every corner of the globe. Moreover, per Figure 4, equities produced their mouth-watering returns with vanishingly low monthly volatility, leading to stratospheric Sharpe ratios at monthly scale.

Figure 4: Rolling 12-month annualized Sharpe ratio. SOURCE: Global Financial Data from 1926 – 2015, CSI Data for VT ETF from 2015 – 2017. PAST PERFORMANCE IS NOT NECESSARILY INDICATIVE OF FUTURE RESULTS. See disclaimer.

In fact, 2017 was the only calendar year since 1926 that global equities offered investors positive returns in every single month^{8}.

Recall that ReSolve’s Adaptive Asset Allocation and Risk Parity mandates are long-only. These strategies will produce positive returns only if one or more markets are rising. In most years, this is not an issue, as there is almost always a strong bull market somewhere. During periods of strong global growth surprises, equity markets should produce good returns. In other years characterized by negative growth or outsized inflation shocks, other assets, like high grade bonds or commodities, should do well. But there are usually good opportunities for dynamic, long-only strategies to prosper, as evidenced by the top row of Figure 5.

Figure 5: Total returns to major asset classes in calendar years 2000 – 2017, sorted from highest to lowest. SOURCE: Calculations by ReSolve Asset Management. Data from CSI, S&P Dow Jones, Deutsche Bank. PAST PERFORMANCE IS NOT NECESSARILY INDICATIVE OF FUTURE RESULTS. See disclaimer.

Most years present good opportunities for long-only active asset allocation strategies to prosper, but some years, like 2001 and 2015, conspire to produce few profitable opportunites.

A historical case study will help cement the point. Imagine that on January 1st of each year, we knew in advance which major global asset classes9 would deliver returns above the group’s average, as well as positive returns, in the coming year. Of course, knowing the future in this way is impossible, but it helps to illustrate the available opportunity set for an active long-only global asset allocation strategy. Perhaps unsurprisingly, an investor with this type of perfect foresight – who allocated capital equally among the top half of positively performing assets each year – would have produced average annual returns of 21.5% since 1991.

Moreover, as can be seen in Figure 6, this strategy would have generated returns over 15% in 21 out of 27 years, and gains of more than 10% in 23 of the years. Fully 26% of years provided returns of greater than 25%! Any investor in his right mind would gleefully invest in this ‘crystal ball’ strategy…

**Continued in the report…**

*Footnotes*

*1. A portfolio consisting of 60% MSCI Global All-Cap World Index, 20% U.S. Aggregate, and 20% S&P/Citigroup International Treasury Ex-US total return indexes exhibited an annualized daily volatility of 11.7% since 1990.* * 2. The Vanguard Total U.S. Stock Market ETF (VTI) returned 21.28%, and the global Vanguard Total Market ETF (VT) returned 24.57%.* * 3. Total return index of the Vanguard Total Stock Market ETF (VT)* * 4. ReSolve Adaptive Asset Allocation: 8% Volatility (USD) unlevered mandate.* * 5. Note the repeated emphasis of the word expected. Obviously if an investor has perfect information about which asset will outperform in the coming period, they should invest all their capital in that asset, with maximum leverage. Unfortunately, markets rarely present investors with perfect information, so investors must act to optimize their expected future wealth under conditions of uncertainty, which supports diversification.* * 6 .If the assets have equal expected volatility then risk budget is the same as portfolio weight.* * 7. See the “Strategies” page in the member’s section at Allocate Smartly https://allocatesmartly.com* * 8. Actually, the twelve months ending November and December 2017 represent two of just sixteen twelve-month rolling periods in the past 1075* * months where global equities offered investors positive returns in every single month.*

In most parts of Canada we have very distinct seasons. Some months of the year are temperate and relatively dry, while other months are cold and snowy. As a result, most Canadian towns of any size have stores that sell skis and bikes. Of course, they don’t inventory both skis and bikes at the same time. Rather, in the spring they sell off all their ski related inventory and set out their bike gear, and in the fall they clear out the bike gear to make room for skis. Pretty creative, right? Let’s observe a simplified example of bike sales and ski sales over several years.

Figure 1. Sales of skis and bikes

Source: ReSolve Asset Management. For illustrative purposes only.

As winter approaches, ski sales accelerate while bike sales drop off. As summer approaches people stop buying skis, but ramp up their purchases of bikes. One line of business is thriving while the other is flat. In some years, winter might come late and produce very little snow, stifling ski sales.

But the subsequent spring might be warm and dry, and encourage bumper bike sales. This is the nature of diversification.

This same effect plays out in markets. Economic news that is good for one type of investment is often bad news for another. In fact, the hallmark of a diversified portfolio is the observation that one or more investments is disappointing you most of the time. A portfolio that consists of assets that all produce gains at similar times for similar reasons will probably produce their worst losses at the same time too.

The skis and bikes example above shows how deriving cash-flows from two independently profitable businesses, which produce returns at different times, reduces the variability of cash- flows throughout the year. This is helpful because it makes it easier for the business owner to manage investments in the business, and stabilizes the owner’s income. In other words, diversifying across two return sources – skis and bikes – lowers the overall risk of the business. Let’s examine why this is so important.

If the business owner simply wanted to reduce his risk, he could have abandoned the business altogether, and kept his savings in safe bonds or cash. But the business owner needs to take some risks to earn a higher income. Both the ski business and the bike business are risky enterprises on their own, with highly fickle cash-flows. Either one might have been too risky for the shop owner to earn a stable income. But when the businesses are combined, the resulting ‘portfolio’ of businesses is much more stable.

The skis and bikes example extends quite intuitively to the domain of investment portfolios. In investing, it is a simple thing to build a low-risk portfolio by holding lower risk assets, like short- term government bonds. Unfortunately, this portfolio would not be expected to generate much in the way of returns. Remember, the reason investors own higher risk assets like stocks instead of clinging to the safety of short-term bonds or cash is that higher risk assets are expected to produce higher returns. Figure 2 illustrates this relationship for a broad universe of global asset classes.

Figure 2. Return vs. risk for global asset classes Source: Bridgewater Associates

The long-term return we can expect to earn from any one investment is proportional to that investment’s risk. If we seek to lower portfolio risk by investing a large portion of capital in lower risk assets, this will necessarily lower the expected return on the portfolio.

In order to generate returns above cash, investors need to take on risk.

Diversification in Theory

The central advantage of diversification is that it allows investors to hold many risky assets, while maintaining a tolerable level of portfolio risk. But many investors express confusion about how two investments can both be expected to rise in value, even while they are uncorrelated. After all, if they are uncorrelated, shouldn’t we expect them to move in different directions? The skis and bikes example offers some perspective on this apparent contradiction. The revenues accumulated from both skis and bikes are rising over time. But they are rising at precisely opposite times. As a result, the shop owner can even out his revenue streams across the different seasons of the year.

Now let’s apply this same phenomenon to two investments. In Figure 3. below both Market 1 and Market 2 grow at the same rate of 10% per year for three years. We know this is true because the assets’ prices begin and end in the same place. In addition, the assets fluctuate the exact same average amount from day to day – that is, they have the same “volatility”. However, Market 1 and Market 2 take a very different path to the same final destination. Market 1 shoots up early on but then returns flatten out and become choppy. Market 2 endures a steady decline over the first half of the period, but then shoots higher. Market 1 inflicts a 26% maximum peak-to-trough loss while Market 2 forces investors to endure an even steeper decline of 34% before recovering.

Figure 3. Two uncorrelated markets

Market 1 | Market 2 | |
---|---|---|

Compound Return | 10.0% | 10.0% |

Volatility | 20.0% | 20.0% |

Return-Risk Ratio | 0.5 | 0.5 |

Maximum Peak-to-Trough Loss | -26% | -34% |

Source: ReSolve Asset Management. For illustrative purposes only. Simulated results.

To make this example more real, assume that the markets in Figure 3. represent the returns to a long-duration bond index [Market 1] and a diversified stock index [Market 2] over the three-year period from April 2013 through March 2016. By the middle of the period, investors in the stock index are extremely anxious, as their wealth has declined by 25%. They are also envious of investors in bonds, who have outperformed them by over 50%. Meanwhile investors in bonds are convinced that their outperformance was inevitable in retrospect, given their superior talent and good sense. Of course, by the end of the period those investors in stocks who kept faith with their investment ended with exactly the same wealth as investors in bonds.

Remember that both Market 1 and Market 2 have the same expected average returns over the long-term. However, they move in different directions at different times for different reasons. In other words, they are uncorrelated. If we expect the same average outcome from both markets, and they are different, then we should take advantage of the opportunity for diversification. Consider the experience of an investor that places half of her capital in Market 1 and half in Market 2 over the same period.

Figure 4. Combining two uncorrelated markets

Market 1 | Market 2 | Combo | |
---|---|---|---|

Compound Return | 10.0% | 10.0% | 10.0% |

Volatility | 20.0% | 20.0% | 13.7% |

Return-Risk Ratio | 0.5 | 0.5 | 0.73 |

Maximum Peak-to-Trough Loss | -26% | -34% | -18% |

Source: ReSolve Asset Management. For illustrative purposes only. Simulated results.

When we examine the full three-year experience of a diversified investor relative to investors with concentrated investments in just one market, it’s clear that diversification produces a gentler ride. While the diversified portfolio produced the same return, it did so with about 1/3 less volatility. Even better, because the declines in the two markets occurred at different times, the diversified portfolio achieved its returns with a 40% smaller peak-to-trough loss than that endured by investors in either of the individual markets.

However, while it’s clear with the benefit of perfect hindsight that diversified investors were better off over the entire period, it’s illustrative to revisit how each investor might have felt half-way through. At that time, investors who chose to diversify were probably regretting their decision, as Market 1 had produced about 25% in extra returns. They were wishing that they had never even heard of Market 2! Only after the completion of the period, once Market 1 experienced its own 26% decline, would diversified investors finally have felt vindicated.

What makes investing so incredibly challenging is that we can’t know for sure in advance whether two investments will produce the same returns, or whether one investment will produce higher returns than another. And even if there is a high degree of confidence that one investment will beat another in the long term, there is no guarantee that returns will converge over a time horizon that investors can live with. For example, over the two decades from 1981 through 2001, safe U.S. government Treasury bonds produced higher returns than stocks, without inflicting the pain and anxiety of two major bear markets1.

Ironically, this uncertainty about the true average return is actually a good thing. If investors knew the true average return of their investments in advance, it’s likely that these investments would attract a lot more capital. This would drive the price of the investments so high that future investors would necessarily earn a much lower return.

As a thought experiment, it’s interesting to see how introducing more uncorrelated investments can make the experience even smoother. For example, in the event an investor could construct five uncorrelated investments with the same 10% expected compound return and 20% volatility, an equally weighted portfolio would have the same return, but less than half the volatility, of any of the individual investments. Even better, while the average peak-to-trough loss of each individual investment is close to 30%, the peak-to-trough loss of the portfolio is well under 10%.

Figure 5. Combining 5 uncorrelated sources of return

Market 1 | Market 2 | Market 3 | Market 4 | Market 5 | Combo | |
---|---|---|---|---|---|---|

Compound Return | 10.0% | 10.0% | 10.0% | 10.0% | 10.0% | 10.0% |

Volatility | 20.0% | 20.0% | 20.0% | 20.0% | 20.0% | 8.7% |

Return-Risk Ratio | 0.5 | 0.5 | 0.5 | 0.5 | 0.5 | 1.14 |

Maximum Peak-to-Trough Loss | -26% | -34% | -30% | -27% | -25% | -7.2% |

Source: ReSolve Asset Management. For illustrative purposes only. Simulated results.

As you can see, the “Holy Grail” of diversification is the ability to introduce streams of investment returns from many diverse sources. The emphasis here is on the word ‘diverse’, as it is unhelpful, from a diversification standpoint, to add many investments that are highly correlated. However, the diversification advantage from adding many uncorrelated investments to a portfolio is indistinguishable from magic.

Skipping to the Punch-Line

So far this is just theory. Let’s face it, few investors care about esoteric objectives like maximizing the diversification opportunity in a portfolio. Investors care about results.

Specifically, they want to maximize the probability that they will achieve their financial objectives. But the fact is, expected risk-adjusted performance is a good proxy for this probability where investors have reasonable goals. In Figure 6, we examine the historical character of the global 60/40 portfolio and a maximally diversified global portfolio over the past quarter century to see what diversification means in terms of real dollars and cents.

Figure 6. Global Risk Parity vs. Global 60/40 portfolio, scaled to 10% volatility, 1991 – 2017

Global 60/40 | Strategic Global Risk Parity | |
---|---|---|

Compound Return | 8.32% | 10.97% |

Sharpe Ratio | .62 | .86 |

Volatility | 10.00% | 10.00% |

Max Drawdown | -40.95% | -34.40% |

Beta to US Balanced | 74.33 | 48.34 |

Alpha to US Balanced | 2.05% | 6.33% |

Source: ReSolve Asset Management. Data from CSI, MSCI, S&P Dow Jones Indices, Deutsche Bank. The Strategic Global Risk Parity portfolio allocates to four regional equity market indexes, U.S., international developed and government bonds, global REITs, a broad commodity index, gold, U.S. TIPs. The portfolio is weighted such that assets contribute equal risk to the portfolio based on pairwise complete covariances over the life of the assets since 1991. Simulated results.

This is where theory meets economic reality. The enhanced diversification properties of the Global Risk Parity portfolio produce higher returns when scaled to the same level of risk as the Global 60/40 portfolio. In fact, over a quarter century the Global Risk Parity portfolio produces almost twice as much wealth at the same level of volatility, and with a smaller peak-to-trough loss (Max Drawdown) along the way.

In 2008 Warren Buffett proposed a public bet that actively managed investment products, plagued by high fees, would not live up to the goal of beating a passive investment in the Vanguard S&P 500 ETF over the subsequent decade. Only one person had the intellectual conviction to represent the active management side of the bet. Ted Seides at Protégé Partners LLC, a fund-of-hedge-funds firm, placed a $1 million bet that a diversified basket of hedge funds (in fund-of-fund structures) would outperform U.S. stocks from January 1, 2008 through December 31, 2017.

In a letter posted to Bloomberg earlier this year, Seides acknowledged that, with just 8 months to go in the bet, “for all intents and purposes, the game is over. I lost.”

But the outcome wasn’t always so certain. Over the first 14 months after Buffett and Seides sealed the wager the S&P 500 lost over half its value. In fact, U.S. stocks lagged Seides’ fund-of-funds portfolio for almost 5 years before finally pulling ahead in 2014.

Why would anyone bet against Warren Buffett? Seides cited some very good reasons for why he felt such a bet was skewed in his favor at the time. But his primary reasoning was based on market valuations. When Seides agreed to the bet, U.S. stocks were trading at valuations that had only been observed about 10% of the time over the previous 140 years. That 10% included the months before the Great Depression, and a few years toward the end of the technology bubble in the late 1990s. Both periods subsequently saw stocks produce returns well below their long-term average. Seides felt the historical precedent stacked the odds in his favor.

Of course, Seides’ forecast turned out to be wrong over the bet’s ten-year horizon. U.S. stocks have produced 8% compound returns per year from January 1st, 2008 through September 30, 2017. At last check (May 2017) Seides’ fund-of-funds portfolio had generated less than 3% per year net of fees.

It’s important to recognize that Seides’ rationale for taking the bet was reasonably sound at the time. Markets were very expensive, and history would have guided toward lower future returns. In fact, after enduring one of the worst bear markets in history soon after the bet was struck, it took a run back up to nosebleed levels of valuation at the end of the period to pull Buffett’s side of the bet so far ahead. According to some of the more useful valuation metrics, such as the Shiller CAPE, markets are currently 50%-75% overvalued relative to long-term trend valuations. Moreover, while U.S. markets fully recovered from the epic collapse in 2008 (and more), other major markets were not nearly so fortunate. For example, the Vanguard FTSE All-World ex-US Index fund generated just 1.2% per year over the same horizon.

Figure 1. Vanguard S&P 500 Index fund vs. Vanguard FTSE All-World Index fund total returns, January 1, 2008 – September 30, 2017

*Source: ReSolve Asset Management. Data from CSI.*

Seides faced one other major headwind with his bet. While we don’t have access to the specific constitution of his portfolio, we can be confident that his diversified portfolio of hedge-funds had a volatility well below that of the S&P 500. In fact, the volatility of the fund-of-funds portfolio was probably about 5% annualized, about one-fifth of the volatility observed in the S&P 500 over the same period. Had Seides scaled exposure to his portfolio so that it approximated the same risk as U.S. stocks, it’s likely that the competition would have been much tighter. In fact, there’s a good chance Seides might have won his bet after all.

Earlier this year I raised the prospect with my partners of issuing a new Bet with Buffett based on a portfolio oriented around risk parity and factors. As mentioned above, U.S. stocks have pushed well into the same nosebleed valuation territory as Seides identified in 2007. For investors to achieve the same results as they achieved over the past 10 years in the next decade, we will have to experience a third major bubble in a row. As a result, we believe that investors with material allocations to U.S. equity-linked strategies are going to be disappointed with their returns over the next decade or so.

We aren’t alone with this view; there is a broad consensus across many credible sources, including AQR, Research Affiliates, and even Jack Bogle at Vanguard, that traditional U.S.-oriented portfolios will have low returns over the next decade or more. We expect U.S. bonds to produce about 2% nominal returns over the next ten years, while stocks are likely to generate between 2% and 5% nominal through 2030. Meanwhile, the duration of U.S. bonds, a common measure of bond risk, is near the top of its historical range, while stocks are known to be more susceptible to the type of crashes we saw in 2000 and 2008 when they are trading at such expensive valuations.

As a result, we are going on record with a portfolio framework based on global risk parity and academic factor strategies, which offers a greater likelihood of producing the returns investors need, with less risk than they would be taking with a concentrated investment in the S&P 500 index. Remember, we define risk as the probability of not achieving financial objectives. We believe our proposed portfolio, described below, does a pretty good job of minimizing this risk over the next ten or fifteen years, given the tools at our disposal in the current environment.

As usual, our approach starts with a comprehensive focus on diversification. Remember, diversification requires a thoughtful combination of both diversity and balance. A diverse universe of investments will have assets that are designed to thrive in all of the major economic environments, not just environments that are favorable to stocks. That means we need to complement the investments that are typically found in portfolios with assets like commodities and gold; global government bonds; inflation protected securities like TIPS and; emerging market securities.

Fortunately, while developed market stocks and bonds are expensive, emerging market stocks, bonds, and currencies may be priced for significantly better returns at the current time. It is not our intention to make a formal call on the relative merits of some assets over others, but we want to ensure all major asset classes are represented, including those that are often ignored. We aren’t in the business of forecasting, we are in the business of being prepared.

Of course, some of these diverse asset classes are much more volatile than others, so we need to be thoughtful about how we bring them together in a portfolio. Our objective will be to ensure each major asset class has an equal ability to express its unique character, so that the portfolio is designed to be resilient to any economic future. The portfolio strategy that optimizes the benefits of diversification by maximizing both diversity and balance is called Risk Parity. Thus Risk Parity funds will form a large part of our fund-of-funds portfolio.

The concept of diversification can extend to other sources of return that behave differently than the major asset classes themselves. It is well documented that investors in most countries around the world have a strong preference to own the stock and debt of their own domestic companies. This home bias is one of the strongest and most pervasive effects in markets. Many investors also express a preference for “lottery ticket”-type investments, and investments that are popular or appear to have a good “story.” Investors also take comfort in holding portfolios that are consistent with their peer group because the pain of underperforming their friends is much more intense than the joy of outperforming them. Investors are often slow to adapt to new information, and are prone to extrapolate intermediate-term trends, while underestimating the tendency of corporate or economic prospects to revert to the mean. Most investors are also averse to the use of leverage; avoid taking short positions; and chase performance at precisely the wrong horizon. They also overpay for insurance against large short-term losses.

These behaviors are universal, and are observed at the highest ranks of the most sophisticated organizations. Most investment capital is still guided by humans, and humans can be counted on to consistently behave in certain ways.

It turns out that the systematic errors above manifest in economically large effects across global markets. These effects, which academics call “factors” and many practitioners call “style premia” explain a very large portion of the differences in returns across groups of securities. If a large portion of investors can be counted on to behave in ways that leave profits on the table, then there is an opportunity for other investors – factor investors – to earn excess profits by taking the other side of those trades. And these excess profits can be very attractive. Figure 2 describes the long-term gross excess returns to these factors based on the literature.

Figure 2. Excess annualized historical returns to long-short factor portfolios formed from individual securities (Equities) and asset classes (Multi-Asset) scaled to 10% ex post volatility.

*Source: Value and Momentum data from Asness, Moskowitz & Pedersen “Value and Momentum Everywhere” (2013). Carry (dividend) equity factor is for U.S. only from Ken French database (long top decile value-weighted, short bottom decile value-weighted for stocks in top 30% by market capitalization). Carry factor is from Koijen et al., “Carry” (2013). Defensive factor data from Frazzini & Pedersen, “Betting Against Beta” (2014). Equity trend data from “The Enduring Effect of Time-Series Momentum on Stock Returns over nearly 100-Years” by D’Souza et al. (2015). Multi-asset trend data from Hurst, Ooi, and Pedersen, “A Century of Evidence on Trend-Following Investing” (2017).*

Many investors will be familiar with some of these investment factors or “styles”. The value investing style is especially popular, made famous by such lionized investors as Benjamin Graham and his protégé, Warren Buffett (though neither Graham nor Buffett invested according to contemporary systematic value methods). Other styles are more obscure, but no less powerful in terms of their historical results. Momentum, also known as “relative strength”, is the tendency for assets with high returns over the past few months to outperform assets with low returns. Several behavioural phenomena contribute to this effect, including the tendency for investors to herd; the fact that it takes investors some time to adjust prices to account for new information; and behavioral biases that compel investors to dispose of assets with gains too soon, while failing to dispose of assets with losses. The momentum strategy takes a long position in assets with the strongest returns, and shorts assets with the worst returns over the past 12 months (with a skip month).

The low-beta or low-volatility premium arises from the tendency for investors to avoid leverage, and overprice lottery type investments. As a result, lower volatility assets tend to outperform higher volatility assets on a risk-adjusted basis. “Carry” is the return that an investor would earn on an asset if the price didn’t change. For example, an equity investor might receive dividends, and a bond investor would receive a coupon. Commodities and currencies also offer carry, in the form of futures “roll yield” and interest rate differentials. Finally, the trend factor capitalizes on the tendency for assets with rising (falling) prices over the past few months to continue moving higher (lower) over the subsequent few weeks. This strategy goes long assets with positive excess returns over the past few months, and short assets with negative excess returns.

Unfortunately, most investors attempt to harvest exposure to these factors using severely diluted “smart beta” products, like the iShares Russell 1000 Value ETF (IWD), or the Vanguard Value Index fund (VIVAX). The returns to these funds are over 90% explained by simple exposure to the S&P 500, which means their “value” exposure is almost meaningless to long-term returns. Even the popular DFA Small-Cap Value fund is over 70% explained by the returns to broad U.S. stocks (Source: PortfolioVisualizer.com). Investors need access to new products that isolate the true uncorrelated opportunities afforded by these powerful premia.

While certain hedge funds have been profiting from long-short exposure to these alternative premia for decades, it has been challenging for most investors to take advantage. Fortunately, flattering returns from passive indexing strategies have compelled the traditional active management industry to innovate and focus on strategies with the most differentiated value. As a result, investors now have at their disposal a rich array of reasonably priced, accessible strategies that offer pure exposure to the most persistent, pervasive, and significant alternative return premia.

A handful of other firms (including ReSolve) run strategies that allocate to diversified sleeves of the most persistent, pervasive and economically significant long-short style premia. One such strategy run by AQR allocates to value, momentum, low beta, and carry. The strategy achieves this exposure by forming market-neutral long and short portfolios on both individual securities and global stock, bond, commodity and currency indexes consistent with the underlying factor definitions. Since the strategy exclusively uses long-short portfolios in global assets classes, it is completely uncorrelated with traditional asset class premia, like stocks, bonds and commodities.

Many diversified style premia strategies separate out exposure to trend, because investors typically like to customize their exposure to this factor. Trend is particularly attractive as a diversifier for other sources of return, because it has a history of producing some of its best days, months and years when other strategies are struggling. Figure 3. shows the cumulative returns to the global trend factor during the eight worst equity market declines since 1926. The mean return to equities during the eight worst periods is negative 46%, while the mean return to the trend factor is +42%. While there is no guarantee the trend factor will serve the same hedge function in the future, history strongly suggests that trend is an attractive exposure to have in your portfolio during crisis periods.

Figure 3. Trend factor returns during the eight worst U.S. equity market declines, Monthly 1926 – 2017

*Source: U.S. equity returns sourced from Ken French data library (Mkt + Rf). Multi-asset trend data from Hurst, Ooi, and Pedersen, “A Century of Evidence on Trend-Following Investing” (2017)*

This is where the rubber hits the road. To reiterate, our overarching objective is to maximize diversification across as many independent, persistent, pervasive, economically significant sources of return as we can access in public markets. In short, we are advocating a portfolio based on risk parity and factors. Specifically, we want exposure to diversified funds of global asset classes, as well as style premia and trend. We want to hold these sources of return so that they all contribute approximately the same total risk to the portfolio. If we hold assets with similar expected Sharpe ratios in equal risk, this portfolio will have the highest ex ante Sharpe ratio; in other words, it is the most mean-variance efficient portfolio that we can construct.

Our portfolio will combine exposure to traditional asset classes in a global risk parity framework, and diversified factor premia. Specifically, we will allocate 40% to global risk parity, 40% to a combination of market-neutral style premia including value, momentum, low-volatility and carry factors; and 20% to the global trend factor. We are choosing to emphasize the trend factor for two reasons. First, as mentioned above, trend is particularly attractive due to its history of delivering its best returns when other markets are in crisis. Second, because the trend factor is currently as “cheap” as it’s ever been in terms of its rolling 10-year annualized Sharpe ratio. Per Figure 4, the Sharpe ratio for the trend factor over the current decade ending September 2017 is lower than what has been observed over 98% of periods since 1903. We like to allocate to proven strategies that have fallen out of favor, and trend is a perfect example at the moment.

Figure 4. Percentile of diversified trend factor rolling 10-year Sharpe, 1900 – 2017

*Source: Calculations by ReSolve Asset Management. Data from Hurst, Ooi, and Pedersen, “A Century of Evidence on Trend-Following Investing” (2017) for period 1903 – 2012, and Moskowitz, Ooi and Pedersen, “Time-Series Momentum” (2012) for period 2013 – 2017.*

One challenge to our approach, which seeks to maximize diversification across many uncorrelated sources of return, is that the final portfolio will have very low volatility. Despite this low volatility, the expected returns from un-levered exposure to the diversified portfolio are considerably higher than what we expect from traditional stocks and bonds over the next decade or two. However, since our strategy is explicitly competing with an all-stock benchmark (the S&P 500), we will use leverage to target a volatility that is more consistent with the long-term volatility of stocks. This will help us to avoid one of the challenges that Mr. Seides faced with his portfolio. Specifically, we will borrow the same value as the portfolio to achieve a total of 200% exposure, and 12% volatility. To finance the leverage, we will assume borrowing costs at T-bills + 1%.

For illustrative purposes, Figure 5 through 9 describe the hypothetical constitution, historical risk contributions, and performance character of our proposed strategy. The global “Risk Parity” strategy is based on a diversified basket of global asset classes reconstituted monthly to achieve “Equal Risk Contribution” assuming a 1% fee. Volatilities and correlations are calculated using the RiskMetrics (2006) methodology described here. The market-neutral “Style Premia” portfolio is proxied by a heavily discounted version of the strategy described in the paper “Investing with Style” (2012) by Ilmanen, Israel and Moskowitz, with data provided by the authors. The returns data also include a 1.5% fee. The diversified “Trend” strategy is proxied by the strategy in “A Century of Evidence on Trend-Following Investing” (2017) by Hurst, Ooi and Pedersen (data provided by the authors) and supplemented by data from “Time-Series Momentum” (2012) by Moskowitz, Ooi and Pedersen (data here), less a 1.5% annualized fee. We use data from 1990 through September 2017, with a 1 year data priming period, which gives us monthly data from 1991 – August 2017.

Figure 5. Proposed portfolio weights

*Source: Calculations by ReSolve Asset Management. Data for Risk Parity from CSI and S&P Down Jones Indices. Data for Style Premia furnished by the authors, and based on the strategy described in ”Investing with Style” (2012) by Ilmanen, Israel and Moskowitz. Data for Trend furnished by the authors, and based on the strategy described in”A Century of Evidence on Trend-Following Investing” (2017) by Hurst, Ooi and Pedersen from 1990 – 2012, and “Time-Series Momentum” (2012) by Moskowitz, Ooi and Pedersen from 2013 – 2017. **This material has been prepared for informational purposes only and is not intended to provide, and should not be relied on for, accounting, legal, investment or tax advice.*

Figure 6. Proposed proportional risk contributions

*Source: Calculations by ReSolve Asset Management. Data for Risk Parity from CSI and S&P Down Jones Indices. Data for Style Premia furnished by the authors, and based on the strategy described in ”Investing with Style” (2012) by Ilmanen, Israel and Moskowitz. Data for Trend furnished by the authors, and based on the strategy described in”A Century of Evidence on Trend-Following Investing” (2017) by Hurst, Ooi and Pedersen from 1990 – 2012, and “Time-Series Momentum” (2012) by Moskowitz, Ooi and Pedersen from 2013 – 2017. **This material has been prepared for informational purposes only and is not intended to provide, and should not be relied on for, accounting, legal, investment or tax advice.*

Figure 7. Proposed portfolio volatility contributions

*Source: Calculations by ReSolve Asset Management. Data for Risk Parity from CSI and S&P Down Jones Indices. Data for Style Premia furnished by the authors, and based on the strategy described in ”Investing with Style” (2012) by Ilmanen, Israel and Moskowitz. Data for Trend furnished by the authors, and based on the strategy described in”A Century of Evidence on Trend-Following Investing” (2017) by Hurst, Ooi and Pedersen from 1990 – 2012, and “Time-Series Momentum” (2012) by Moskowitz, Ooi and Pedersen from 2013 – 2017. **This material has been prepared for informational purposes only and is not intended to provide, and should not be relied on for, accounting, legal, investment or tax advice.*

Figure 8. Constituent strategies and Diversified Premia performance 1991 – Aug 2017. SIMULATED PERFORMANCE

*Source: Calculations by ReSolve Asset Management. SIMULATED PERFORMANCE. **Global Diversified Premia is 40% Risk Parity, 40% Style Premia, 20% Trend. **Data for Risk Parity from CSI and S&P Down Jones Indices. Data for Style Premia furnished by the authors, and based on the strategy described in ”Investing with Style” (2012) by Ilmanen, Israel and Moskowitz. Data for Trend furnished by the authors, and based on the strategy described in”A Century of Evidence on Trend-Following Investing” (2017) by Hurst, Ooi and Pedersen from 1990 – 2012, and “Time-Series Momentum” (2012) by Moskowitz, Ooi and Pedersen from 2013 – 2017. This material has been prepared for informational purposes only and is not intended to provide, and should not be relied on for, accounting, legal, investment or tax advice.*

After borrowing costs and assumed fees, the simulated Diversified Premia portfolio produced almost 18% annualized returns since 1991, with a Sharpe ratio of 1.27. We are targeting a long-term Sharpe ratio of about 1.0, so we expect the portfolio to produce 12% excess returns at our target 12% volatility, which is about twice the long-term U.S. equity risk premium of about 6%. Of course, we could have levered the portfolio to a volatility target of 16%, consistent with the long-term volatility of global equities, but we don’t think we’ll need anywhere close to that amount of risk to dominate U.S. stock returns over the next decade or so.

Importantly, we expect our Diversified Premia portfolio to produce returns with very little help from U.S. equities or bonds. A regression of the historical simulated Diversified Premia returns on the Vanguard Balanced Index fund (VBINX) yields an r-squared value of 0.084, suggesting that traditional U.S. stock and bond exposure explains just 8.4% of the returns to our Diversified Premia portfolio. In addition, over 25 years in simulation, and after discounting and fees, the strategy produced 1.2% per month in pure alpha, or about 14% per year. This alpha is a function of exposure to a wider variety of traditional and alternative risk premia.

Figure 9. Regression of proposed Diversified Premia returns on Vanguard Balanced Index Fund (VBINX), 1992 – Aug 2017

*Source: Calculations by ReSolve Asset Management. VBINX data from CSI. Data for Risk Parity from CSI and S&P Down Jones Indices. Data for Style Premia furnished by the authors, and based on the strategy described in”Investing with Style” (2012) by Ilmanen, Israel and Moskowitz. Data for Trend furnished by the authors, and based on the strategy described in”A Century of Evidence on Trend-Following Investing” (2017) by Hurst, Ooi and Pedersen from 1990 – 2012, and “Time-Series Momentum” (2012) by Moskowitz, Ooi and Pedersen from 2013 – 2017. This material has been prepared for informational purposes only and is not intended to provide, and should not be relied on for, accounting, legal, tax, investment or tax advice.*

At ReSolve we believe risk is the probability that an investor will not meet his financial objectives. In the context of this definition of “risk”, and given current historically rich developed-market stock and bond valuations, we think traditional portfolios are extremely risky. Our objective is to propose a publicly available, alternative portfolio filled with a much wider variety of return sources, that we believe will help close the gap. In particular, we believe our proposed Diversified Premia strategies based on risk parity and factors is well positioned to deliver considerably higher returns than traditional portfolios over the next 10-20 years, with less risk. If you have questions about how to access strategies like this, feel free to contact us.

Note: this is Part two of a two-part article series. Please see article one here.

Michael Edesess’ article, The Trend that is Ruining Finance Research, makes the case that financial research is flawed. In this two-part article series, we examine the points that Edesess raised in some detail. His arguments have some merit. Importantly however, his article fails to undermine the value of finance research in general. Rather, his points serve to highlight that finance is a real profession that requires skills, education, and experience that differentiates professionals from laymen.

Edesess’ case against evidence based investing rests on three general assertions. There is a very real issue with using a static t-statistic threshold when the number of independent tests becomes very large. Financial research is often conducted with a universe of securities that includes a large number of micro-cap and nano-cap stocks. These stocks often do not trade regularly, and exhibit large overnight jumps in prices. They are also illiquid and costly to trade. Third, the regression models used in most financial research are poorly calibrated to form conclusions on non-stationary financial data with large outliers.

This article will tackle the “p-hacking” issue in finance, and propose a framework to help those who embrace evidence based investing to make judicious decisions based on a more thoughtful interpretation of finance research.

When Fama, French, Jegadeesh, et al. published the first factor models in the early 1990s, it was reasonable to reject the null hypothesis (no effect) with an observed t-statistic of 2. After all, the computational power and data at the time did not afford very much in the way of data mining. Moreover, these early researchers were careful to derive their models very thoughtfully from first principles, lending economic credence to their results.

However, as Cam Harvey has so assiduously noted, the relevant t-statistic to signal statistical significance must expand through time to reflect the number of independent tests. He suggests that, based on several different approaches to the problem, current finance research should seek to exceed a t-statistic threshold of at least 3 to be considered significant. If the results are derived explicitly through data mining, or through multivariate tests, the threshold should be closer to 4, while results derived from first principles based on economic or behavioral conjecture, and with a properly structured hypothesis test, may be considered significant at thresholds somewhat below 3.

Cam Harvey’s recommendations make tremendous sense. The empirical finance community – like so many other academic communities such as medicine and psychology – are guilty of propagating “magical thinking” for the sake of selling journal subscriptions and advertising. With few exceptions, journals only publish papers with interesting and significant findings. As a result, the true number of tests of significance in finance likely vastly exceeds the number of published journal articles.

Finance professionals should be cautioned by the fact that researchers are performing more and more tests each year, while journals only report a fraction of the tests that are performed. But these issues are amplified by the fact that many papers are never independently verified. Where researchers do attempt to verify results and find errors, journals just publish corrections that are often buried at the bottom of issues many months or years in the future. This is unsatisfactory.

The Merriam-Webster dictionary defines “profession” as “a calling requiring specialized knowledge and often long and intensive academic preparation”. Incumbent in this definition is the idea that professionals are responsible for understanding and validating research that they use to inform their recommendations to clients. But far too few advisers – even those of the “evidence based” variety – take the time to thoroughly investigate the papers they rely on to form client portfolios. Far fewer have the skills, resources, or inclination to independently validate the strategies they endorse.

My team has identified several major errors in research published in some of the most prestigious finance periodicals. In August we questioned the results of a paper on volatility published in one of the most popular practitioner journals. The author – shaken and contrite – confirmed that he had miscalculated the effect, and overstated the results by more than a factor of two. I genuinely believe the author did his best to present the facts, but errors happen. That’s why it is incumbent on practitioners to verify results before making allocations with other peoples’ money.

Cam Harvey and his co-authors are not alone in their desire to bring statistical rigor to the financial research process. Many respected practitioners share their concerns and apply similar methods in their own practices.

One way for practitioners to gain greater confidence in prospective factors is through out-of-sample testing. Fortunately, there is an abundance of out-of-sample analysis validating the most robust factors. One obvious out-of-sample test involves testing the factor on a brand new universe. For example, if a method worked on U.S. stocks, it should also work on stocks in other international stock markets. In addition, if a factor was identified in 1993, then tests over the 20-year period from 1994 – 2013 are also considered out-of-sample. One might also ‘perturb’ a factor’s specification to test for robustness, say by changing the definition of ‘value’ from price to book value to price to cash-flow or price to earnings.

In “Finding Smart Beta in the Factor Zoo”, Jason Hsu and Vitali Kalesnik at Research Affiliates performed tests of the value, momentum, low beta, quality and size factors on stocks across U.S. and international markets. For tests on U.S. markets they used data back to 1967, while international tests were run from 1987. Recall that the size, value and momentum factors were first documented in the early 1990s, and the low beta anomaly was first catalogued by Haugen in the mid-1970s. In addition, all factors were first identified using exclusively U.S. stocks. As such, by testing in international markets over the period 1987-2013 their analysis was legitimately ‘out of sample’. That is, they tested on out-of-sample universes, and over a 26 year horizon where 20 years were out of sample in time. Results in international markets were consistent with the results of the seminal papers.

In addition, Hsu and Kalesnik tested using different definitions of the factors. For example, they tested ‘value’ as defined by dividends-to-price, cash-flow-to-price, and earnings-to-price as well as the original book-to-price metric. They also varied the lookback horizons and skip-months for momentum, and tested both beta and volatility for the low-beta factor, again with different lookback horizons. As you can see from Figure 1., the value, momentum and low beta factors all proved robust to alternative definitions.

Figure 1. Value, low beta and momentum factors prove robust to alternative specifications

Source: Research Affiliates

Clearly Jason Hsu at Research Affiliates takes seriously the concerns raised by Cam Harvey, and has taken steps to increase empirical rigour of their solutions, but they are not alone in their quest. The principals at AQR, principally Cliff Asness and colleagues, performed their own analysis of the value and momentum factors across both a universe of global stocks and a universe of global asset class indexes. Their tests span the period 1972-2011, so about 40% of their analysis period is out of sample in time. Of course, about half of their global stock universe, and the entire global asset class universe, is also out of sample for the entire period. Their results are summarized in Figure 2. below.

Figure 2. Statistical significance of value and momentum factors across global stocks and asset classes, 1972-2011

Source: Asness, Moskowitz and Pedersen, “Value and Momentum Everywhere“

Highlighted in green, note the statistical significance of risk-adjusted excess returns from the value and momentum factors in global stocks (top) and global asset classes (bottom). This analysis validates the persistence of the value and momentum factors across a largely out of sample data set. Even better, the t-scores exceed the higher thresholds proposed by Cam Harvey, and tests on the asset class universe overcome higher hurdles with substantial margin to spare (full disclosure: ReSolve investment solutions rely largely on the asset class momentum and low beta factors).

Edesess asserts that, in the absence of reliable research, investment professionals should make life-changing decisions for clients based on “common sense”. But common sense is just a narrow data sample – one’s own experience – filtered through an often imperfect, emotionally charged, heavily biased cognitive prism. Further, there is no mention of “common sense” in the dictionary – or any practical – definition of the word “professional”. The fact is, to call ourselves professionals, investment practitioners must make judicious decisions based on finance research. There are many reasons why this may be challenging, but the alternative is unacceptable.

To be successful in empirical finance requires a mosaic of experience, mental models, data, humility, and a fundamental understanding of how decisions are made in markets. For example, my framework considers that investors are corrupted by the following forces when faced with making decisions in uncertain markets:

- incentives
- agency issues
- behavioral biases (prospect theory, herding, overreaction, underreaction)
- non-wealth-maximizing preferences (i.e. lottery preferences, leverage aversion, home-bias)
- structural challenges (i.e. siloed decision making, regulation, compliance, information diffusion)

A dense body of literature in behavioral finance, and my own experience with clients, advisors, and investment managers, supports the view that these forces drive investors to make decisions that are not purely in the interest of their own wealth. These inefficiencies manifest in investable sources of excess return for those investors with the capacity to take the other side of the trade. As I seek to interpret the empirical literature, and innovate in pursuit of sustainable premia, there must be a clear connection between these forces and the premia under investigation.

Evidence based investment professionals should also have a healthy understanding and respect for complex adaptive systems. Even where an investor is satisfied that an effect is rooted in the factors above, and economically significant, she must be honest with herself about whether there are sustainable barriers to arbitrage that would allow it to persist. A solid risk-based explanation is a wide moat that suggests an effect should persist. As Michael Edesses asserts, the ERP is solidly rooted in risk. The volatility risk premium is also obviously rooted in risk, as is the duration premium. Some other commonly cited risk premia have plausible risk explanations, but also might be explained by behavioral biases or alternative preferences.

Most investors think about risk in terms of loss, but I would argue that tracking error, regulatory risk, liability risk, career risk, and other types of risk play an integral role in investor decision making. Most investors find it very difficult to underperform their home market index, or miss out on bubble-like investments for any length of time. Regulators impose constraints on leverage and concentration. The new fiduciary standards may subject advisers to liability from making recommendations that deviate from other “prudent investors”. Institutional investors face career risk from recommending investments that may underperform in the short term. These forces result in non-wealth-maximizing decision making, and are real risks that manifest in persistent anomalies.

For example, equity mutual fund managers are typically incentivized on the basis of assets in their funds, and investment performance relative to their benchmark. Benchmark-centric performance metrics such as Information Ratio penalize managers based on tracking error. Yet outperformance necessarily requires managers to take bets that are different from the index.

If there were no leverage constraints, a manager could overlay diversified beta exposure to complement their active bets. But regulatory constraints prevent 40-Act mutual funds from taking on leverage, except in certain narrow circumstances. In practice, this leads managers to place concentrated bets on certain stocks with large active risk.

To balance this risk, managers often lower portfolio tracking error by investing in a basket of high-beta stocks with their remaining capital. Thus, due to regulatory constraints and incentive structure, mutual fund managers place a premium on high-beta stocks that is independent of expected returns. This lowers the ex-ante expected return on these stocks, and is a strong candidate for the source of the low-beta anomaly. A few other commonly cited alternative premia have equally valid explanations rooted in similar forces. [Please see discussion of multi-asset strategies below, as an example of strong barriers to arbitrage].

The framework above is not perfect. It is an organic concept, which evolves over time with my own experience in markets. I invite you to append your own belief systems to make it your own. But it is a way forward. Ultimately, our goal as a profession should be that all advisers have the “specialized knowledge, and long and intensive academic preparation” to deliver informed, robust advice to clients. “Common sense” is a necessary, but profoundly insufficient, foundation for a professional code of conduct. Investors deserve better.

The framework above presents a compelling case for multi-asset strategies. Multi-asset anomalies arise from the same forces as securities-based anomalies, are even more economically significant, and may have larger barriers to arbitrage. Most institutional portfolios are structured along asset-class silos, where each silo is charged with seeking alpha within its own narrow sandbox. As a result the equity team at one institution competes with very little friction against the equity teams at every other institution.

However, there are large barriers to arbitrage at the multi-asset level. The asset allocation is set by a policy committee, and guided by long-term capital market expectations. Institutions rarely take on material active risk at this level of the portfolio. Some institutions are bound by rigid actuarial rules, and are able to tolerate very little deviation from policy weights. Committee level decisions are typically slow, incremental, and reactive. And peer-oriented compensation schemes heavily and asymmetrically penalize short-term tracking error relative to long-term alpha generation. These are large and persistent barriers to arbitrage that suggest multi-asset anomalies like trend and carry have a long shelf-life.

Moreover, for all the reasons stated above investors have been slow to embrace active multi-asset strategies. According to the Blackrock research department (whom I queried on this very subject last year), active multi-asset strategies like GTAA, managed futures, risk parity, global macro, and slower-moving asset allocation strategies in managed accounts, account for just 13% of global liquid market capitalization. This stands in stark contrast to the proportion of active in stocks and bonds, where 65% and 87% of these markets are dominated by active mandates, respectively. And this does not count assets tracking active indexes, like “smart-beta” ETFs, etc.

Figure 3. Proportion of actively managed assets by mandate

Source: Blackrock

This gap does not exist for lack of evidence. As shown in Figure 4 below, global multi-asset carry and trend strategies exhibit historical Sharpe ratios roughly twice what is observed in historical tests of traditional equity-based factors like cross-sectional momentum and value. Admittedly, some multi-asset factor strategies have struggled in the current central-banking dominated cycle, alongside many traditional equity factors. Stock momentum and value have had a very rough decade indeed.

It’s noteworthy that the period 1932 – 1942 was also a very difficult decade for most systematic strategies, as central banks were also active during that period, distorting the natural price-discovery process. And more generally, factor based investors should expect to have long periods of “famine”; if factor investors feasted every night, the feast would quickly dwindle to a thin gruel as arbitrage would be risk-free.

Figure 4. Sharpe ratios: global equities vs. global asset classes

Sources: Value and Momentum data from Asness, Moskowitz & Pedersen “Value and Momentum Everywhere” (2013). Carry (dividend) equity factor is for U.S. only from Ken French database (long top decile value-weighted, short bottom decile value-weighted for stocks in top 30% by market capitalization). Carry factor is from Koijen et al., “Carry” (2013). Defensive factor from Frazzini & Pedersen, “Betting Against Beta” (2014). Equity trend data from “The Enduring Effect of Time-Series Momentum on Stock Returns over nearly 100-Years” by D’Souza et al. (2015). Multi-asset trend data from Hurst, Ooi, and Pedersen, “A Century of Evidence on Trend-Following Investing” (2017).

Michael Edesses’ article, “The Trend that is Ruining Finance Research” makes the case that financial research is flawed. In this two-part article series, we will examine the points that Michael raises in some detail. We find his arguments have some merit. Importantly however, his article fails to undermine the value of finance research in general. Rather, his points serve to highlight that finance is a real profession, that requires skills, education, and experience that differentiates professionals from laymen.

Thoughtful, educated finance professionals equipped with the right tools can use evidence based finance to make much better decisions.

Michael’s case against evidence based investing rests on three general assertions. First, there is a very real issue with using a static t-statistic threshold when the number of independent tests becomes very large. Second, financial research is often conducted on a universe of securities that includes a large number of micro-cap and nano-cap stocks. These stocks often do not trade regularly, and exhibit large overnight jumps in prices. They are also illiquid and costly to trade. Third, the regression models used in most financial research are poorly calibrated to form conclusions on non-stationary financial data with large outliers.

This article will explore the issues around the latter two challenges. Our next article will tackle the “p-hacking” issue in finance, and propose a framework to help those who embrace evidence based investing to make judicious decisions based on a more thoughtful interpretation of finance research.

A large proportion of finance studies perform their analysis on a universe of stocks that is practically un-investable for most investors. That’s because they include stocks in their analysis with very small market capitalizations. In fact, the top 1000 stocks by market capitalization represent over 93% of the total aggregate market capitalization of all U.S. stocks. This means the bottom 3000 or so stocks account for just 7% of total market capitalization. The median market cap of a stock in the bottom half of the market capitalization distribution is just over $1billion.

Figure 1. Cumulative proportion of U.S. market capitalization

Source: Blackrock

Mathematically, only a very small portion of investment capital can be deployed outside the top 1000 or so stocks. These smaller stocks are also much less liquid, with less frequent trading, high bid-ask spreads, and larger overnight jumps. Moreover, these companies tend to trade at low prices, which means trading costs are larger for institutions who pay commissions on a per share basis.

For these reasons, practitioner oriented studies should include sections on how inefficiencies manifest among larger and smaller companies in isolation. And many do. In particular, many of the papers from AQR break down the performance of anomalies into effects among large (top 30% by market cap), mid (middle 40% by market cap) and small (lowest 30% by market cap) companies. The paper “The Role of Shorting, Firm Size, and Time on Market Anomalies” by Israel and Moskowitz at AQR focuses specifically on this topic. Figure 2 below shows the results for traditional value and momentum factor portfolios for five different market capitalization buckets from 1926 – 2011.

Figure 2. Performance of value and momentum factor portfolios conditioned on market capitalization

Source: Israel, R., and T. Moskowitz. “The Role of Shorting, Firm Size, and Time on Market Anomalies.” *Journal of Financial Economics*, Vol. 108, No. 2 (2013)

Many readers may be surprised at the results. Notable effects in Figure 2 are highlighted in circles of different colors. Red circles show the long-short factor returns for the largest 20% of firms by market capitalization. The value factor implemented on the largest capitalization bucket produced 3.7% excess average annual returns, which produces a t-stat of just 1.9, which is not quite statistically significant. On the other hand momentum produced 7.49% average annual excess returns with a highly significant t-stat of 2.95 (more on t-stats below). Regression alphas were more grim for large-cap value, with a t-stat of just 1.14, while large-cap momentum has produced over 10% average annual alpha with a very significant t-stat of 4.23 (more on regression below).

The blue circles in Figure 2 examine whether the difference in factor alphas between the lowest and highest market capitalization buckets are statistically significant. The value factor produced over 10% greater average annual alpha in the smallest capitalization stocks than in large cap stocks. This is a highly statistically significant effect, with a t-statistic of 3.21 (top blue circle). In contrast, the difference in alphas between the lowest and highest capitalization buckets was relatively small (2.88%) and insignificant (t-stat = 1.31) for the momentum factor.

It’s worth noting that the analysis in Figure 2 did not account for trading frictions. After accounting for the cost of liquidity, which might be substantial for small-cap stocks, but inconsequential for large-cap stocks, the gap between large- and small-cap factor performance would almost certainly close, perhaps significantly. In addition, those practitioners who are fond of small- or mid-cap value should feel well validated, as value factor performance is strong and significant for every market capitalization quintile other than the largest cap stocks.

To summarize this section, investors must be aware of the practical implications of the universe chosen for investment research. Practitioners should focus on observed effects among mid- and large-capitalization stocks, where results in practice may be expected to align more closely with academic findings.

Researchers in empirical finance use linear regression to determine whether, and to what extent, an effect that they are investigating is already explained by previously documented effects. For example, academics use linear regression to determine how well a factor model explains differences in the cross-section of securities prices. Researchers in search of novel return premia use linear regression to determine how much value a newly proposed factor adds above what is explained by already well-known factors. Advisors, consultants and investors use regression to determine if an active investment product or strategy has delivered significant excess risk-adjusted performance, above what they could achieve through inexpensive exposure to factor products.

Unfortunately, linear regression is a very blunt tool when it comes to dealing with complex financial data. The following example will highlight one important reason why. Note that I poached this example from Larry Swedroe, because it is so perfect and surprising.

Consider two strategies A and B, and their returns over a 10-year period. Their return series is depicted in the table below.

Period 1.

Strategy | Year 1 | Year 2 | Year 3 | Year 4 | Year 5 | Year 6 | Year 7 | Year 8 | Year 9 | Year 10 |

A | 12% | 8% | 12% | 8% | 12% | 8% | 12% | 8% | 12% | 8% |

B | 8% | 12% | 8% | 12% | 8% | 12% | 8% | 12% | 8% | 12% |

Both strategies have an annual average return of 10. Whenever A’s return is above its average of 10, B’s return is below its average of 10. And whenever A’s return is below its average of 10, B’s return is above its average of 10. Thus, regressing strategy A’s returns on strategy B’s returns over this period will conclude they are negatively correlated. Note that they are negatively correlated even though they both always produced positive returns.

Now imagine that the same strategies produced the following returns in a different 10-year period.

Period 2:

Strategy | Year 1 | Year 2 | Year 3 | Year 4 | Year 5 | Year 6 | Year 7 | Year 8 | Year 9 | Year 10 |

A | 2 | -2 | 2 | -2 | 2 | -2 | 2 | -2 | 2 | -2 |

B | -2 | 2 | -2 | 2 | -2 | 2 | -2 | 2 | -2 | 2 |

Over this period, the same strategies have an average annual return of 0 percent. Perhaps the styles went out of favor. However, whenever A’s return is above its average of 0, B’s return is below its average of zero. And whenever A’s return is below its average of 0, B’s return is above its average of zero. Thus, regressing A on B will render the conclusion that they are negatively correlated.

Now let’s string together the two 10-year periods so that we have a 20-year period. Thus, the return series looks like this:

**Asset A: 12, 8, 12, 8, 12, 8, 12, 8, 12, 8, 2, -2, 2, -2, 2, -2, 2, -2, 2, -2.**

**Asset B: 8, 12, 8, 12, 8, 12, 8, 12, 8, 12, -2, 2, -2, 2, -2, 2, -2, 2, -2, 2.**

Recall that both A and B had average returns in the first 10 years of 10 percent, and average returns of 0 percent in the second 10 years. Thus, their average return for the full 20 years in both cases is 5 percent. Now: Are A and B positively or negatively correlated?

A closer inspection reveals that, over the full 20-year period whenever A’s return was above its average of 5, B’s return was also above its average of 5. And whenever A’s return was below its average of 5, B’s return was also below its average of 5. Thus, we see that __despite the fact that A and B were negatively correlated over each of the two 10-year periods independently, over the full 20-year period they were positively correlated__.

This example highlights an omnipresent by rarely discussed challenge with financial time-series. Specifically, that the measured relationship between variables will almost always change dramatically across time. This effect is not isolated to observations over two distinct periods of time; rather, we observe similar dynamics at play when time series are observed at different frequencies. In fact, variables can appear to be negatively correlated at one frequency – say daily – and yet be positively correlated at another frequency – say monthly!

There are other reasons to be skeptical of results from financial time-series regression analysis. One reason relates to factor specification. Most regression analyses in the finance literature use a common set of risk factors like the Fama French 3-Factor model; the Fama-French-Carhart 4-Factor model; the Fama-French 5-Factor Model, or; a few other variations that include factors like quality, low volatility, and term structure.

Let’s unpack the most common 3-Factor model from Fama and French. This model seeks to explain returns using a combination of a market factor (MKT), a size factor (SMB) and a value factor (HML). Fama and French define the value factor using the Book-to-Price ratio. Specifically, each July 31st they sort stocks based on the Book-to-Price ratio observed on December 31^{st} of the previous year. So when a value oriented investment strategy is regressed on the 3-Factor model, if the strategy employs the Book-to-Price ratio, and rebalances on the same dates as the value strategy in the Fama French model, the regression will show a strong value tilt[1].

However, “value” can be defined in many ways. Some practitioners use Book-to-Price; others use Earnings-to-Price, or Sales-to-Price, or Cash-Flow-to-Price, or other metrics. Portfolios have different numbers of holdings and are rebalanced at different times. Many managers use several factors at once to measure value. All of these deviations from the traditional value factor specification will lead the regression model to observe weak exposure to the “value” factor, even though the other value specifications and methods are equally useful.

The AQR Alternative Style Premia Fund offers an informative case study. The fund purports to invest in pure, market neutral value, momentum, carry, and “defensive” factor strategies applied to individual stocks and bonds, as well as stock and bond indexes and other asset classes around the world.

Using the fantastic PortfolioVisualizer web application, we ran a linear regression analysis to determine the fund’s exposures to the ubiquitous Fama French factors. We started with the three-factor model (market beta (Mkt), small-cap (SMB), value (HML)), then proceeded to the 4-factor model (adding momentum (UMD), and finally to the 5-factor model (removing UMD and adding profitability (RMW) and investment (CMA). The results are shown in Figure 3.

Figure 3. Linear regression factor attribution analysis of AQR Style Premia Fund (QSPIX) using Fama-French factor models

- Regression on Fama French 3-Factor Model
- Regression on Fama-French-Carhart 4-Factor Model
- Regression on Fama-French 5-Factor Model

Source: PortfolioVisualizer

Unpacking the results in Figure 3 we see that when the fund returns were regressed on the 3-Factor model (part 1), the fund had no meaningful loading on the HML value factor (t-statistic of 0.5, p-value of 0.617). However, when the fund returns were regressed on the 4-factor model in part 2, adding momentum (UMD), the analysis surfaced an extremely significant loading on the exact same value factor, along with a very significant loading on momentum. Then when momentum was replaced with profitability and investment factors in part 3, value disappears again. In fact, the fund returns appear not to load meaningfully on any of the factors!

Finally, we ran a regression using AQRs own factor specifications. Specifically, we regressed on the market, AQRs value factor (HML-Devil), momentum, and quality (QMJ). Per Figure 4, this regression surfaced very statistically significant loadings on all of the factors that one might expect given the fund’s mandate. (Note: when we included the Betting Against Beta (BAB) factor, neither the QMJ or BAB factors were statistically significant, because these factors are highly cointegrated).

Figure 4. Linear regression factor attribution analysis of AQR Style Premia Fund (QSPIX) using AQR factor model

Source: PortfolioVisualizer

Given the challenges described above with the use of linear regression models, many practitioners may be tempted to abandon the process altogether. Worse, investors may resort to comparing simple returns, with no awareness of the exposures to risk factors beneath the hood. However, those investors who persist in finding better tools for analysis are likely to be richly rewarded with better calibrated models, and a clearer understanding of the factors that drive investment returns.

To address the challenges raised above, specifically the fact that relationships between variables change over time (non-stationarity), and issues around how explanatory variables are specified, researchers should employ more robust regression methods. For example, k-fold cross-validation, where linear regression is performed on a subset of the data and applied to several out-of-sample subsets, helps control for the non-stationarity issue. Constrained regressions like LASSO, sequential, and ridge regression allow researchers to include many correlated variables in their analyses – like different specifications of “value”, or both the QMJ and BAB factors – which would otherwise corrupt a linear regression analysis. Admittedly, these tools require technical knowledge and advanced education, but this is the nature of a true profession. Those who wish to learn more about these methods could do a lot worse than this book (h/t to Dave Cantor for the book reference).

Finance research suffers from a variety of challenges that make it difficult for practitioners to make informed decisions. Many papers examine financial effects by including in their analysis stocks with very small market capitalizations, which would probably not be tradable in practice. When the same studies are conducted on a larger capitalization universe of stocks, which investors could trade with reasonable costs and scale, researchers often arrive at different results. We highlighted one example, which showed that, while the popular “value” factor exhibits a large and significant effect when applied to mid- and small-cap U.S. companies, it renders a statistically insignificant result when applied to a large-cap investment universe. Thus there appears to be little value in exposing investors to value tilts in large-cap portfolios.

Another important consideration for evidence-based investors is that the most common tool for investigation – linear regression – is not well designed to deal with noisy and evolving financial data. As a case study, we performed several factor attribution regression analyses on a pure factor-oriented product, the AQR Alt Premia Fund (QSPIX). Our results show that these types of regression analyses can be highly sensitive to which factors are included as explanatory variables, and how those factors are specified. We suggested several advanced regression methods that address the key challenges of traditional regression analysis, but warned that meaningful research will require a greater depth of knowledge about advanced statistical techniques.

In our next article, we will explore the issue of scalability in financial research. Advances in computational power and an explosion of new data sources makes it easy to test thousands of potential relationships among financial variables. Just as a billion monkeys typing randomly for thousands of years will eventually produce a Shakespearean sonnet, thousands of researchers running tests on millions of combinations of economic variables will inevitably stumble onto spurious relationships. We take this issue head-on, and show that the most robust factors easily survive this statistical challenge. We also propose a framework to help investment __professionals__ make judicious decisions based on finance research.

[1] Fama and French performed other machinations to create their factor portfolios which confound regression analysis for attribution on real investment strategies. For example to create the value factor returns they perform the sort on large cap stocks, and again on small-cap stocks, and average the results from the two sorts.

To be crystal clear, our discussion will NOT focus on trying to identify which signals or parameters, or combinations of signals and parameters, are better or worse than others. While most quants – being tinkerers at heart – waste most of their time fine-tuning the parameters of their strategies to maximize performance in backtests, we are acutely aware of the futility of these efforts. The few decades of data that most quants have at their disposal for simulation are nowhere near enough to tease out differentiating features given the vast dimensionality of this exercise.

Rather, our discussion of optimization will focus on how to use the signals at our disposal to assemble a portfolio of assets that is most likely to deliver the maximum return with minimal risk. We will begin our discussion with an exploration of whether the magnitude of the momentum signal itself provides useful information for building portfolios. To begin, we will examine the strength of this signal by constructing portfolios such that asset weights are in proportion to the magnitude of their momentum relative to other assets.

First, let’s look at what happens when we don’t incorporate any momentum tilts in the portfolio: a base portfolio where all 12 assets are held in equal weight (see article 1 for our investment universe). This base portfolio will serve to gauge the benefit of our optimization efforts. Consistent with the process we applied in previous posts, we will iterate over holding periods of 5, 10, 15, and 20 days, including all different trading days. For example, for simulations with 5 day holding periods, we will run 5 independent tests, which rebalance on day 1, day 2, day 3, day 4 and day 5.

*Table 1: Equal weight portfolio.*

*Source: ReSolve Asset Management. Data from CSI data and underlying index providers where data for investable funds have been extended prior to their date of inception. The results are hypothetical results and are NOT an indicator of future results and do NOT represent returns that any investor actually attained.*

**METHODOLOGY**

Now let’s investigate the performance of portfolios that are tilted toward the assets with the highest momentum. First, we rank our assets from weakest to strongest at each lookback according to our various momentum metrics (discussed in detail here and here). The lowest scoring asset at each lookback will receive a 1 and the highest will receive a 12 (the total number of assets in our universe). The ranks are then averaged across lookbacks, and then percentile-ranked for a final score. We detail the steps below.

**Formula 1: Rank**

Where is the vector of ranks of, , the proportional momentum scores at lookback . For Excel, assume the scores at lookback horizon , for assets 1 through 12, are in cells A1 through A12 (the first lookback). We’ll use the RANK.EQ function as we’re not concerned with tied scores here.

=RANK.EQ(A1,A12

Now that we have vectors of rank averages we will convert them into a percentile rank, from 0 to 1, by applying the percentile rank formula from our second article, . We will use this final transformation as a means of weighting (and eventually filtering) – a heuristic optimization processes.

**Formula 2: Percentile transform**

Where is the percentile ranks of the vector of averaged rank scores . The following Excel code assumes that the vector of averaged ranks is stored in cells F13:F24.

=PERCENTRANK.INC(13:24,F13)

**MOMENTUM WEIGHTING**

Our first test will be to use our percentile ranks as a means of weighting the portfolio. This is accomplished by dividing each asset’s percentile score at time by the sum of the scores at time . The result is a vector which distributes portfolio capital in proportion to an asset’s momentum rank score at each rebalance period. Note that for this test the portfolio will always hold some positive weight in every asset, with highest momentum assets earning the most weight.

**Formula 3: Non-parametric momentum weight**

**RESULTS**

*Tables 2 and 3: Momentum-weight performance of aggregate models.*

*Source: ReSolve Asset Management. Data from CSI data and underlying index providers where data for investable funds have been extended prior to their date of inception. The results are hypothetical results and are NOT an indicator of future results and do NOT represent returns that any investor actually attained.*

Momentum weighting markedly improves upon our equal-weight baseline, enhancing every metric across all 21 indicators. We observe an average boost of about 1.5% per year in annualized returns, an almost 40% improvement in Sharpe ratio, and a 25% reduction in maximum drawdown. Clearly there is some signal in the rank order of assets by momentum.

**CONCENTRATING ON THE BEST ASSETS**

You may recall from our previous posts that we held the top 2-5 assets at each lookback as a way to filter the strongest from the weakest. This is a reasonable approach, but it does not account for changes in the distribution of momentum across assets through time. Sometimes many assets will have strong returns, while just one or two will have extreme negative returns that drag the cross-sectional average down. At such times, it may be useful to hold all of the assets that are doing relatively well, and simply ignore the ones in extreme negative trends. Many other situations are possible.

For these next tests we are going to filter by 50^{th} percentile (0.5), so that we will hold all assets that exhibit momentum scores above the median momentum score. This will allow the number of assets that we hold in our portfolios to change dynamically, in consideration of the changing cross-sectional distribution of momentum.

First let’s have a look at the results when each asset is held in __equal weight__ given that it is above the 0.5 cutoff.

*Tables 4 and 5: Percentile-filtered, equal weight performance of aggregate models.*

*Source: ReSolve Asset Management. Data from CSI data and underlying index providers where data for investable funds have been extended prior to their date of inception. The results are hypothetical results and are NOT an indicator of future results and do NOT represent returns that any investor actually attained.*

As with our first two articles, removing the laggards provides a powerful way to enhance portfolio performance. There is incremental outperformance of the percentile filtering versus the unfiltered momentum-weighting across all tests. Both strategies seek to respond dynamically to the distribution of momentum across assets, however it appears that allowing the portfolio to “breathe” given the percentile rank cutoff offers an additional adaptive ability, which improves results at the margin.

Finally, let’s see if there’s any benefit in momentum weighting our percentile-filtered portfolios. We’ll use Formula 3 to convert our *filtered* assets to momentum weights at each rebalance.

*Tables 12 and 13: Percentile-filtered, momentum weight performance of aggregate models.*

Further concentration of our portfolio towards favorable assets leads to marginal improvement in CAGR and maxDD, with only commensurate improvements in Sharpe and volatility.

**MEASURING THE ENSEMBLE**

Remember, the purpose of running tests using a wide variety of momentum metrics is to illustrate that momentum is robust to many different specifications. We do not want to lead readers to the conclusion that they should favor the single metric that seems to deliver the best results in backtests.

Rather, we believe all of these metrics have (for the most part) statistically indistinguishable merit, as they all capture the momentum effect from slightly different angles. As such, and consistent with previous articles in this series, we want to examine the performance of ensemble (aggregate) systems to observe the portfolio effect of using many different types of signals. First let’s examine the correlation relationships between the unfiltered momentum weight, percentile filter, and momentum-weighted percentile filter methods. We have distinguished between results for aggregate systems of raw signals and risk-adjusted signals because of their slightly different characters.

*Tables 14 and 15: Cross correlation of individual, aggregate strategies:*

*Raw Momentum*

*Risk-Adjusted Momentum*

As expected, the three methods are highly correlated for both raw and risk-adjusted methods, ranging from a low of 0.84 to a high of 0.98. However, we still expect to observe a diversification benefit when we allocate equally to the three different methods. We expect the ensemble of all model iterations to be greater than the simple average of their performances. Even iterations which are decidedly worse can contribute positively to the aggregate if they are sufficiently uncorrelated with other systems, giving us confidence that consistency and intelligent, dynamic diversification will ultimately deliver more stable results out of sample.

*Table 15: Performance comparison of ensemble models versus the simple average performance of all model iterations. The difference arises from diversification between the sub-systems.*

*Raw Momentum*

*Source: ReSolve Asset Management. Data from CSI data and underlying index providers where data for investable funds have been extended prior to their date of inception. Results reflect a strategy equally invested in all raw momentum based strategies, rebalanced monthly back to equal weight. The results are hypothetical results and are NOT an indicator of future results and do NOT represent returns that any investor actually attained.*

*Risk-Adjusted Momentum*

*Source: ReSolve Asset Management. Data from CSI data and underlying index providers where data for investable funds have been extended prior to their date of inception. Results reflect a strategy equally invested in all risk-adjusted momentum strategies, rebalanced monthly back to equal weight. The results are hypothetical results and are NOT an indicator of future results and do NOT represent returns that any investor actually attained.*

*Figure 1. Growth of $1 from 1991 – 2017*

*Source: ReSolve Asset Management. Data from CSI data and underlying index providers where data for investable funds have been extended prior to their date of inception. Results reflect a strategy equally invested in all raw momentum based strategies, and all risk-adjusted momentum based strategies, as indicated. Sub-strategies are equally weighted and rebalanced back to equal weight on a monthly basis. The results are hypothetical results and are NOT an indicator of future results and do NOT represent returns that any investor actually attained.*

**CONCLUSION AND NEXT STEPS**

The purpose of this article was to introduce, and perform some simple tests to determine whether the magnitude of the momentum signature is a useful signal for the relative expected returns over the ensuing period. The results of the first test lend credence to the idea that the strength of momentum signal is correlated with better performance. However, when we compare the filtered equally-weighted results with the filtered momentum-weighted results, we see that momentum weighting is unhelpful. A more nuanced conclusion might be that it is advantageous to overweight the assets in the top half of the distribution, and underweight the assets in the bottom half. However, once we have identified the top assets, the magnitude of momentum does not provide meaningful information about relative returns between them.

We also introduced the idea of identifying the “top” assets based on a percentile filter that accounts for the cross-sectional distribution of returns, rather than using a fixed cut-off threshold for the number of assets to hold in the portfolio. This allows the size of the portfolio to “breathe” based on the distribution of momentum. The nature of the current tests does not allow for an “apples-to-apples” comparison with previous strategies, but the approach seems to have merit.

Follow-on posts will focus more specifically on the problem of portfolio optimization to target higher returns given leverage constraints, and eventually on heuristic and formal optimization methods that incorporate covariance relationships between the assets.