# Capital Efficiency Trumps Fees

in the Search for Portfolio Diversifiers

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**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.

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# Capital Efficiency

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.

## Three Alternative Funds Walk Into a Bar

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.

## Market neutral fund

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.

## Managed futures fund

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.

## Global Tactical Asset Allocation (GTAA) ETF

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.

# A Horserace Between Funds

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.

## Take-aways

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.

### Build your own report!

**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!

## Appendix: Detailed fund by fund analysis

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

#### Market neutral fund

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.

#### Managed futures fund

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.

#### Global Tactical Asset Allocation ETF

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 \(\frac{2.54\%}{10.5\%}=0.24\).

#### Footnotes

- 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↩
- \(\sqrt{80\%^2\times12\%^2+20\%^2\times7\%^2+2\times80\%\times20\%\times12\%\times7\%\times0}=9.7\%\) .↩
- \(\sqrt{80\%^2\times12\%^2+20\%^2\times12\%^2+2\times80\%\times20\%\times12\%\times12\%\times0}=9.9\%\) .↩
- \(\sqrt{80\%^2\times12\%^2+20\%^2\times8.25\%^2+2\times80\%\times20\%\times12\%\times8.25\%\times0.5}=10.5\%\) .↩

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