Target Volatility: Equity Hedge Funds’ Real Source of Alpha?

The argument over the value of active versus passive investing is never ending. Here, we make the case for active hedge funds and deliver a passive solution in Target Volatility. 

According to BarclayHedge, the Hedge Fund Industry, excluding Managed Futures, has grown from $500 billion to $3.5 trillion during the 15-year period from 2002 through 2017. Here, we will analyze the major source of returns that comprise the Barclay Hedge Fund Index (BHFI) during that time. 

There are 14 different categories of benchmarks that are listed by BarclayHedge. The risk-adjusted returns of the index are primarily determined by equity hedge fund strategies and strategies correlated to equity hedge funds. We estimate the index has 80% to 90% of its risk allocated to equity strategies or strategies that are highly correlated to equity strategies. Hedge funds, as represented by the BHFI, can effectively be viewed as equity replacements. Further, we also believe that the proper benchmark for Equity Hedge Funds are Target Volatility strategies. We will use the BHFI, and two of its categories, Barclay Equity Long Bias Index (BELBI) and Barclay Equity Long Short Index (BELSI), to represent equity hedge funds.

There are three issues we will address in this essay. First, the BHFI provides little diversification to traditional long-only equity indexes due to its high correlation. Second, equity hedge fund managers outperform traditional equity indexes on a risk-adjusted basis (this may or may not be surprising to some, but it was surprising to us). And third, we hypothesize that the reason for this outperformance is that hedge funds engage in a risk premia strategy called “intertemporal risk parity.” Other terms for this are Target Volatility and Constant Volatility. 

In other words, this outperformance by BHFI over long-only equities can also be matched by using Target Volatility strategies. That is, Target Volatility equity strategies outperform long-only equity strategies by a similar amount, just as equity hedge fund strategies outperform long-only equity strategies (once fees are equalized). When lower fees are applied to Target Volatility strategies they, therefore, outperform Hedge Funds. Hence, the proper benchmark for equity hedge funds are not long-only equity indexes but Target Volatility equity strategies. 

We are not aware of any studies that have discussed these three topics in an integrated fashion. If our combined hypotheses are accurate, this can have a significant impact on how one should view the performance of hedge funds.

Index Correlation

It is generally assumed that hedge funds create diversification. This can be true, of course, depending on what investors combine them with. What surprises us, however, is how highly correlated the BHFI is with long-only equities. 

We first compared the MSR Global Equity Dollar Weighted Total Return Index (GEDWTR) to the BHFI. The GEDWTR consists of seven equally notionally weighted futures contracts (SPX, NDX, DOW30, FTSE, EUROSTOXX30, DAX and Nikkei). These are the most traded equity futures indexes and they represent about 43% U.S. equities, 43% European equities and 14% Japanese equities. The GEDWTR is a traditional long-only equally weighted total return index that reinvests dividends and is rebalanced daily to maintain equal notional weightings among the seven equity futures markets. The monthly correlation between GEDWTR and BHFI is 0.84 and the annual correlation is 0.94. “GEDWTR vs. BHFI” (above) provides a variety of performance statistics, some of which may be unfamiliar. Calmar ratio means annualized return divided by maximum drawdown over the timeframe measured; excess return is the total return less the risk-free rate; and CPS is the sum of the Calmar ratio and Sharpe ratio. We also use the term “true” Calmar. All that True Calmar does is use excess returns above the risk-free rate in the numerator rather than total return.

Beating Long Equities on Risk-adjusted Basis 

We have asserted that the BHFI is virtually an equity replacement. That is from an analytical perspective as one cannot invest in the BHFI. However, there are practical implications of this we will discuss. Most essays that compare hedge funds to mutual fund performance, or any long-only equity strategy such as the S&P 500, tend to emphasize absolute returns rather than risk-adjusted returns. Many articles have been written about the underperformance of hedge funds to equities, but they are not often discussed in risk-adjusted terms. However, a recent essay by Pensions & Investments references a study by Preqin and the Alternative Investment Management Association (AIMA) shows that hedge funds have outperformed equities on a risk-adjusted basis. While we agree with their conclusion, we believe that Target Volatility is the cause of this outperformance. 

Before we make that case, we first want to discuss how to properly compare risk-adjusted performance.

It is extremely unusual that every hedge fund index and individual hedge funds calculate their Sharpe ratios as if the returns of hedge funds follow the equivalent of Burton Malkiel’s famous “random walk.” Sharpe ratios convey misleading information when this is done. Hedge fund returns do not follow a random walk. The BHFI and its components have very high positive serial correlations, typically about 0.30. A random walk return profile has zero serial correlation. We use the term “Adjusted Sharpe,” or “True Sharpe” to account for serial correlation and to differentiate the way we quote Sharpe ratios from how all the various index data providers as well as hedge funds quote them. 

This is a topic that has been written about for at least 25 years by many academics and practitioners (including by William Sharpe), and yet, with all the quantitative talent in the industry, this continues to be ignored. It is not a coincidence that Sharpe ratios are higher when a random walk is assumed. The Calmar ratio is an intuitive and helpful way to understand why the True Sharpe is a better measure of risk-adjusted returns. True Sharpe ratios also account for large left tail results (and, perhaps more importantly, left tails yet to come) as do Calmar ratios. 

Strategies with higher Calmar ratios tend to have lower comparative random walk Sharpe ratios, but higher comparative True Sharpe ratios. In “GEDWTR vs. BHFI,” the True Sharpe ratio for the BHFI is 0.61 and 0.52 for GEDWTR. The True Calmar ratio is 0.20 for BHFI and 0.16 for GEDWTR. So, even when we calculate the risk-adjusted returns accounting for serial correlation in hedge funds, long-only equities still underperform hedge funds. Further, GEDWTR has no fees attached to it, while hedge funds tend to charge about a 1% management fee and 20% incentive fee on average. If we were to charge the same 1 and 20 to the GEDWTR, the Sharpe ratio of the latter would be 0.38 vs. 0.61 for the BHFI. This is significant outperformance by the BHFI. Now that we have plowed through how to look at risk-adjusted returns, should we be surprised at this outperformance? 

When we thought about this at first, we were surprised. After all, this would seem to be prima facie evidence that when adjusted for equal fees, equity hedge funds provide pure alpha, even if they keep a large part for themselves. Yet, think of all the essays that have been written demonstrating that passive index funds outperform actively managed funds. Vanguard in “The case for low-cost index fund investing,” and S&P/Dow Jones in “Persistence Scorecard: December 2017” both make compelling cases that passive indexes outperform actively managed portfolios. Equity hedge fund managers are nothing if not active managers. While higher fees tend to be part of Vanguard’s and S&P’s arguments for passive index outperformance, it is not the sole reason. But as we have shown, equity hedge funds clearly outperform equity indexes. We believe this performance is explainable and not merely prima facie evidence of Alpha implied by Preqin and AIMA. Outperformance is very likely the result of a definable risk resulting from Target Volatility strategies. 

Target Volatility & Risk Premium 

A Target Volatility portfolio seeks to maintain a constant standard deviation of returns. For example, assume we use a simple rolling six-month look back period to implement target volatility. As the underlying volatility of the market rises over time to maintain the desired target volatility, we will need to reduce the absolute dollar or notional size of the portfolio. Conversely, if the volatility of the market declines, we would need to increase the absolute notional size of the portfolio to maintain the constant volatility of a portfolio. In short, the portfolio will get smaller in size as volatility rises and larger in size as volatility declines. Interestingly, as a general matter, we do not observe a significant difference in risk-adjusted returns in most asset classes when using either method. However, the one exception appears to be in the equity markets. 

Target Volatility is likely the cause of equity hedge fund benchmark outperformance versus long-only equities. While it is not possible to directly calculate the risk weighting through time of equity portfolios in the BHFI, our experience tells us that equity traders likely de facto engage in this activity purely as a function of risk management. The use of value-at-risk (VAR) limits provides an example of how this can happen. If a trader has a certain VAR limit, this will incentivize them to increase their position sizes as volatility declines and decrease their positions as volatility rises, which is exactly what Target Volatility strategies do. But regardless of the precise cause, equity hedge fund outperformance is very similar to the outperformance one would expect if they did directly engage in Target Volatility strategies. 

We need not merely speculate, however. Target Volatility is a well-known phenomenon. It is a type of risk parity strategy (called intertemporal risk parity) that has been used in various ways since the early days of the over-the-counter derivative markets. In addition, there are many studies which have documented its relative performance to traditional long-only indexes. In “Equity Investing with Targeted Constant Volatility Exposure,” a paper written by Nicolas Papageorgiou, Jonathan J. Reeves and Michael Sherris, the authors conducted an empirical analysis comparing a constant volatility-weighted (or intertemporal risk parity) S&P 500 portfolio and a constant dollar-weighted S&P 500 portfolio (the normal S&P portfolio) and demonstrated that the former portfolio outperformed on a risk-adjusted basis. 

The authors found the results consistent throughout sub-periods of time as well. The timeframe covered was from 1929 through 2013. They calculated the annualized daily information ratio (annualized daily returns/annualized daily volatility) of the two portfolios, which were 0.65 for the constant volatility portfolio and 0.51 for the constant dollar-weighted portfolio. Under the assumption of equal average volatility for both portfolios, the constant risk portfolio outperformed by 200-basis-points per year. 

In 2017, AQR Capital Management produced the paper “AQR - Portfolio Rebalancing: Common Misconceptions,” performing a similar analysis on 17 equity markets beginning in 1975. Fifteen of the 17 markets had a higher Sharpe ratio when using Target or Constant Volatility than did those same markets when dollar weighted. They also found this phenomenon primarily worked only in equity markets. Perchet, Corvalho, Heckel and Moulin seek to explain why this phenomenon occurs in their paper, “Predicting the success of volatility targeting strategies: Application to equities and other asset classes.” 

The primary reason they site is that volatility clustering, when combined with an inverse relationship between volatility and returns, will create higher risk-adjusted returns. This is the case only in equity markets. 

“GEDWTR vs. the GETV15TR” (above) compares the performance of the GEDWTR and the Global Equity Target Vol 15 Total Return index (GETV15TR) from Jan. 1, 2003 through Feb. 28, 2018. Recall, the GEDWTR is a traditional long-only total return index, which reinvests dividends and is rebalanced daily to maintain equal notional weightings among seven equity futures markets. The GETV15TR is a constant Target Volatility portfolio of the same instruments (while 15% is the average monthly volatility of the equity markets, the choice of Target Volatility 15 versus Target Volatility 10 or 20 does not impact risk-adjusted returns). 

The GETV15TR is rebalanced daily to maintain a constant risk weighting as described above. The Sharpe ratio of the GEDWTR vs. the GETV15TR is 0.50 vs. 0.73; the monthly correlation is 0.88; the comparative Calmar ratios are 0.16 vs. 0.30; the comparative excess returns are 8.11% vs. 10.08% and the comparative maximum drawdowns are 50.7% vs. 31.78%. These results confirm the results documented in the studies we referenced. We also got comparable results when comparing dollar-weighted U.S. equities and dollar-weighted non-U.S. equities to each of their Target Volatility equivalents. The dollar-weighted S&P versus the Target Volatility S&P from 1983 through Feb. 28, 2018 also gets similar results. Constant Volatility equity portfolios do outperform traditional dollar-weighted portfolios.

What is the risk that Target Volatility portfolios assume that creates this outperformance? It is primarily volatility risk. The volatility risk is the potential of a sudden spike in volatility after an extended period of lower volatility when Target Volatility traders are likely to be more leveraged. This is a risk because spikes in volatility are usually associated with a decline in returns. The result of taking this risk has been earning a risk premium, which has created outperformance. The willingness to potentially suffer sharp short-term declines in prices when one is leveraged (or to underperform when one is de-levered) is the risk one takes when one uses Target Volatility. Yet, over the long run, this strategy has paid off with lower maximum drawdowns, higher Calmar ratios and higher True Sharpe ratios than long-only indexes, just as equity hedge fund indexes, have. This is a simplified version of the phenomenon that Perchet, Corvalho, Heckel and Moulin discuss in greater detail in their paper. 

Hedge Fund vs. Target Volatility Returns

What we demonstrated here so far is simply confirming the research that we referenced earlier. Constant Volatility portfolios do outperform traditional long-only portfolios. We will now compare hedge fund returns to Constant Volatility portfolios. Recall that our hypothesis is that hedge funds’ (i.e., BHFI) Sharpe ratios will outperform dollar-weighted portfolios (e.g., GEDWTR) by a similar amount as Target Volatility portfolio Sharpe ratios (e.g., GETV15TR) will outperform dollar-weighted portfolios (i.e., GEDWTR) once adjusted for fees. A little simple algebra tells us that we should expect the fee-adjusted Sharpe ratios and Calmar ratios of the BFHI and the GETV15TR to be approximately equal. 

We will test the hypothesis by assuming the BHFI has average fees of 1 and 20. We will then compare that to the GEDWTR portfolio (see “GEDWTR vs. BHFI,” above). Then, we will charge 1 and 20 to the GETV15TR and compare that to GEDWTR (see “GEDWTR vs. GETV15TR+ fees,” above). For the hypothesis to be correct, we should expect the difference between the two pairs of Sharpe ratios and Calmar ratios of the BHFI vs. GEDWTR and the GETV15TR vs. GEDWTR to be approximately the same, once the fees have been equalized. 

When we compare the difference in Sharpe ratios and the difference in Calmar ratios in the BHFI vs. GEDWTR and the GETV15TR vs. GEDWTR, we discover the differences are very close when fees are made the same. What this all means is that our hypothesis appears to hold up. The BHFI outperforms the GEDWTR by a little more than the GETV15TR outperforms the GEDWTR. The relative Sharpe outperformance is 0.04 for the BHFI (0.59 vs. 0.55), but the relative True Calmar ratios are better for the GETV15TR (0.21 vs. 0.20). The relative correlations of the BHFI vs. GEDWTR and the GETV15TR vs. GEDWTR are 0.84 and 0.89. 

Finally, we directly compare the GETV15TR to both the BHFI (see “BHFI vs. GETV15TR with equal fees,” below) and the combination of the Barclay Equity Long Bias Index and the Barclay Equity Long Short Index (“BELBI+BELSI”) assuming equal fees (see “BELBI + BELSI vs. GETV15TR with equal fees,” below). 

The direct comparison of the GETV15TR vs. the Barclay indexes show the Calmar ratios to be almost identical and the Sharpe ratios of the Barclay indexes to be about 0.05 higher when we assume the fees are 1 and 20 for the BHFI and GETV15TR. 

Why this matters 

We do not believe it is coincidental that equity hedge funds outperform dollar-weighted indexes by virtually the same amount Target Volatility indexes outperform dollar-weighted indexes. This means that equity hedge funds and Target Volatility indexes have virtually the same results when fees are made equal. We have also demonstrated this through a direct comparison of hedge funds vs. Target Volatility indexes. But Target Volatility indexes are indexes. They are transparent and easily implemented. It would be impossible to charge 1 & 20 for a transparent index. Target Volatility strategies can be viewed as a replacement for equity hedge fund strategies. Target Volatility strategies not only outperform long-only equities, but they also outperform equity hedge funds when fees are fixed below hedge fund fees. 

In the same way that Vanguard and S&P/Dow Jones factor in fees when comparing active and passive strategies, we should also factor in fees when comparing Target Volatility strategies to equity hedge fund strategies. A transparent Target Volatility index should charge the same as other transparent liquid alternative strategies, or no higher than 50- to 100-basis points. We use a 75-basis point fee (which is high for an index strategy) for a GETV10TR index and compare it to the “BELBI+BELSI” portfolio. 

This result should be an excellent benchmark for equity hedge funds. We can use the same argument that Vanguard and S&P/Dow Jones makes when comparing passive and active long-only funds, except apply it to Target Volatility vs. Equity Hedge Funds. “BELBI + BELSI vs. GETV10TR with adjusted fees,” below), compares a 10% Volatility Global Equity Index to the BELBI+BELSI portfolio assuming a 75-basis point fee. 

The GETV10TR is an example of a potential benchmark for equity hedge funds. It is also an excellent liquid alternative replacement investment for equity hedge funds. More importantly, we have introduced the idea that any alpha one thinks that equity hedge funds provide is derived from exposure to the risk premia strategy described in this paper – Target Volatility. 

We are not aware of anyone coming to the same conclusion regarding Target Volatility being the main alpha driver for equity hedge funds. However, every component idea in this article is known and well documented. Technicians can test it for themselves.  

* This essay was adapted from a White Paper by Michael S. Rulle Jr. that one can access under “third-party research” on the BarclayHedge Website.