### Introduction

Hedge funds are a tool designed in theory to serve two primary purposes: increase expected returns and/or lower portfolio volatility. At Numeric, our focus in this area has historically been on the equity market neutral category. Over the last several years, we have made many enhancements to our hedge fund offerings, which we believe have strengthened our ability to produce positive returns with lower volatility. However, some investors have questioned the benefit of a hedge fund product that delivers ‘low’ levels of returns. Though market neutral strategies are generally used to reduce portfolio volatility, today they may also be used to potentially raise anticipated returns under the assumption that the fixed income returns of the last 30 years are unlikely to be repeated.

We hope to address the utility of hedge funds as a vehicle to potentially generate returns higher than the low returns currently anticipated for cash and fixed income. We will consider the characteristics of hedge funds in general, and more specifically, long-short and market neutral strategies. It is important to place the return, volatility, and correlation expectations of hedge funds in the context of realistic expectations for both equities and fixed income. We believe that even modest return expectations for hedge funds suggest they can play an important role in a portfolio. Based on one’s risk appetite, the substitution of a market neutral strategy for an allocation to fixed income may be attractive.

### I. STARTING ASSUMPTIONS

Before we delve into our assumptions for hedge funds, let us first describe our expectations for equities and fixed income (**Table 1**).

#### Table 1: Starting Assumptions for Equities and Fixed Income

Return Assumptions | Volatility Assumptions | Expected equity correlation ρ(EQ) | Expected fixed income correlation ρ(FI) | |
---|---|---|---|---|

Equities | 0-12% | 16% | 1.0 | (0.2) |

Fixed Income | 3% | 3.5% | (0.2) | 1.0 |

Sources of data and methods used to calculate assumptions are described below.

We vary return assumptions for equities from 0 to 12%, while holding constant both the expected volatility and correlation to fixed income. This may not be entirely accurate, but is intended to minimize the number of moving parts for ease of comprehension.

The fixed income assumptions are based on a slight premium to the current yield of the Barclays US Aggregate Bond Index (which was 2.36% as of September 30, 2014)^{1}. This index is fairly ‘high quality’ and has a duration of approximately five years, so the assumption is that one could achieve a 3% expected return by assuming more credit and duration risk.

As of September 30, the correlation between the MSCI World Index and the Barclays US Aggregate Bond Index was 0.00, -0.29, and +0.02 over 3, 5, and 10 year periods, respectively^{1}. We assume a modest negative correlation, which we believe is a ‘conservative’ assumption for hedge funds because it makes equities and fixed income more diversifying to each other; thus, more likely to crowd out target hedge fund allocations.

For hedge funds, we vary return assumptions from 0 to 8%, and will discuss the effect of volatility and correlation on optimization later in this paper. The breadth of hedge fund strategies makes a precise estimate of expectations difficult.

In our discussion, we focus on three primary categories of hedge funds: the broad index, equity long-short, and equity market neutral. We assume equity market neutral has the lowest return projections, lowest volatility, and least correlation to other asset classes, while equity long-short has the highest return expectations, highest volatility, and high correlation to equities.

The broad index category refers to larger multi-strategies, many of which have diversified bets across investment strategies. **Table 2** and **Table 3** below display the realized volatility and correlations of the most comparable Hedge Fund Research indices (‘HFRI’). The typical realized volatility for an individual fund will generally be notably higher than that of the index.

#### Table 2: HFRI Realized Volatility

3 YR Realized | 5 YR Realized | 10 YR Realized | |
---|---|---|---|

HFRI Fund Weighted | 4.20% | 5.18% | 6.36% |

HFRI Equity Hedge | 6.51% | 7.61% | 8.72% |

HFRI Equity Market Neutral | 1.84% | 2.61% | 2.82% |

Source: Hedge Fund Research, Inc. www.hedgefundresearch.com, © 2014 Hedge Fund Research, Inc. All rights reserved. Periods ending September 30, 2014. **Past performance is not indicative of future results.**

#### Table 3: HFRI Realized Correlations

3 YR ρ(EQ) | 5 YR ρ(EQ) | 10 YR ρ(EQ) | 3 YR ρ(FI) | 5 YR ρ(FI) | 10 YR ρ(FI) | |
---|---|---|---|---|---|---|

HFRI Fund Weighted | 0.91 | 0.93 | 0.9 | 0.08 | -0.18 | 0.00 |

HFRI Equity Hedge | 0.94 | 0.95 | 0.93 | -0.01 | -0.25 | -0.03 |

HFRI Equity Market Neutral | 0.82 | 0.82 | 0.59 | 0.09 | -0.27 | -0.26 |

Source: Hedge Fund Research, Inc. www.hedgefundresearch.com, © 2014 Hedge Fund Research, Inc. All rights reserved and Bloomberg. MSCI World Index has been used as a proxy for equities, fixed income data is based on Barclays Capital US Aggregate Bond Index. Periods ending September 30, 2014. **Past performance is not indicative of future results.**

One point that is striking is the level of correlation of the various hedge fund indices with equities during the post-crisis era; this is a source of frustration for some investors. We note that correlations can be fairly sensitive to the time period. As can be seen from the preceding table, the correlation of the equity market neutral index drops significantly between the 5-year and 10-year periods shown above. Indeed, over the last 15 years^{2}, the equity correlation falls to 0.34 notwithstanding the high alignment during the recent period. Moreover, in Section III, we briefly discuss the difference between correlation and beta; generally hedge funds are more diversifying than their correlations suggest because their betas are much lower than their correlations.

### II. RESULTS

Target portfolio allocations will be partly driven by risk aversion, so let us introduce four types of investors: *Return Maximization (‘RM’), Low Risk Aversion (‘LRA’), High Risk Aversion (‘HRA’), and Minimum Volatility (‘MV’).* For reference purposes, **Table 4** displays the weights of four portfolios that may invest only in equities and fixed income.

#### Table 4: Starting Assumptions for Equities and Fixed Income

RM | LRA | HRA | MV | |
---|---|---|---|---|

% Equities | 100% | 65% | 37% | 12% |

% Fixed Income | 0% | 35% | 63% | 88% |

Source: Numeric Investors LLC.

We will focus on Low Risk Aversion investors, as this group should be more sensitive to the return expectations of hedge funds. We optimize by solving the following equation: Maximize {Expected Return – λ x Expected Variance} where λ, the risk aversion scalar, equals 1.5.

**Figures 1-3** display target weights for equities, fixed income, and hedge funds while varying expected returns for both equities and hedge funds (assuming fixed income returns of 3%). We assume hedge fund volatility is 6%, and has a 0.7 correlation to equities, so this would be a ‘market neutral’ like case study.

#### Figure 1: Target Fixed Income Weight Surface

Under this scenario, fixed income is not attractive unless expected equity and hedge fund returns are both low. In fact, if hedge funds are expected to return 5% or more (with 6% volatility), no exposure to fixed income would be preferable **(Figure 1)**. There are two primary reasons for this. The first is the low return expectations for fixed income, and the second is that the modest negative correlation of fixed income to equities is insufficient to compensate the investor for the poor prospective return.

Target equity allocations are highly dependent on expected equity returns, with very high equity allocations when expected returns are 7-8% or greater **(Figure 2)**. But most interesting is the target allocation for a hedge fund with 6% volatility and a 0.7 correlation to equities. With an expected return of only 5%, this hedge fund dominates equities and fixed income if the expected return for equities is 8%. In fact, this hedge fund would comprise 1/3 of the target portfolio even if annual equity returns of 9% are expected **(Figure 3)**. Indeed, an 8% returning hedge fund would still constitute the majority of the target portfolio unless expected equity returns are 12%.

#### Figure 2: Target Equity Weight Surface

#### Figure 3: Target Hedge Fund Weight Surface (6% Vol, 70% Correlation)

The effect of correlation depends on the exact circumstances. In **Figure 4**, we look at the target allocations of a Low Risk Aversion investor, assuming equities have an 8% expected return with 16% volatility, and hedge funds have a 6% expected return with 6% volatility. In this situation, regardless of the correlation between equities and hedge funds, fixed income is completely dominated. As the correlation increases, the Low Risk Aversion investor prefers hedge funds because of the substantially higher information ratio (1.0 vs 0.5). Correlation does not matter for the Return Maximization investor, who would simply invest in the asset class with the highest expected return (in this case, equities).

#### Figure 4: Varying Expected Correlation Between Equities and Hedge Funds

#### Figure 5: Target Hedge Fund Weight Surface (10% Vol, 90% Correlation)

Even if we consider a higher correlation, higher volatility hedge fund (think equity long-short), the target weight surface for hedge funds in **Figure 5** is similar to what we see in **Figure 3**. Rather than 6% volatility and a 0.7 correlation to equities, this surface assumes 10% volatility and a 0.9 correlation to equities.

The surface is less than or equal to the prior hedge fund surface at every point, because we have only raised the volatility and correlation assumptions. So a 5% hedge fund return with 10% volatility is significantly less interesting unless equity returns are expected to be 6% or less. But unless double-digit returns for equities are anticipated, a hedge fund with 7% expected returns and 10% volatility may still be attractive.

A general theme that arises here is that, because fixed income expectations today are so low and sentiment towards equity markets appears to be becoming progressively less bullish, any hedge fund that satisfies the following criteria is likely to be attractive: 1) produces a level of return higher than fixed income, and 2) has either a low correlation with equities or a higher information ratio than equities. Ideally, the hedge fund would accomplish both.

### III. CAVEATS AND FURTHER CONSIDERATIONS

Our results suggest that low volatility return streams in the 5-10% range may be attractive in an environment where cash pays close to zero, fixed income generates low-to-mid single digit returns, and equities generate mid-to-high single digit returns (prospectively). There are several additional points to consider.

Correlations are an important variable for a variety of reasons, not least because they can (and do) change over time and often increase during crises. Moreover, the huge breadth of hedge fund strategies makes generalization more difficult since many hedge funds that seek to provide uncorrelated returns fail to do so.

The common complaint that hedge funds tend to be quite correlated to equities appears justified, given that the 10 year correlations of the HFRI Fund Weighted Index and Equity Hedge Index to global equities are 0.81 and 0.86, respectively. Even the HFRI Equity Market Neutral Index has displayed correlations to equities of 0.85 and 0.52 over a 3 and 10-year time frame respectively. However, certain strategies can generate much lower correlations than those quoted above and it is important to note that, even when correlations are higher than one would hope, an allocation to hedge funds can still be beneficial if they achieve their outcomes with significantly lower volatility than conventional equity exposure.

We would be remiss to not discuss 2008 in this context. Hedge funds generally disappointed investors in terms of delivering uncorrelated returns during the crisis. Though many hedge funds outperformed the equity market in 2008, they would have been a poor substitute for fixed income. This is a very unique data point that partially challenges our thesis. It is hard to generalize across the industry, but we used this period as a learning experience and an opportunity to improve our risk management and portfolio construction processes. Our expectation is that generally hedge funds are better positioned to face a crisis now than they did in 2008.

Another important consideration is the relatively higher fees of hedge funds compared to more traditional beta approaches (either active or passive). In this analysis, we have built fees into our expectations for hedge funds, so we have specified net return expectations. Nevertheless, some may still question the advisability of paying a hedge fund 2 or 3% to generate 7% net returns, when an 8% equity return can be obtained for a nominal fee. This is not a part of our analysis as we feel it is more important to focus on the net-of-fee outcome, but where aversion to high fees is an issue, this can be built into a utility function.

### IV. CONCLUSIONS

The attractiveness of hedge funds in general depends on many factors, including one’s expectations for equities, fixed income, the ability to select and invest in productive hedge funds, and comfort with higher levels of fees. In the current environment, where prospective fixed income returns are muted, we believe low volatility hedge funds that can produce returns in excess of fixed income can be an important tool in a portfolio. Even though market neutral strategies may have higher risk than high quality fixed income instruments, they may still be an effective substitute with respect to expected returns of a portfolio, or as a substitute for equities to reduce portfolio volatility.

1. Source: Bloomberg.

2. Hedge Fund Research, Inc. www.hedgefundresearch.com, © 2014 Hedge Fund Research, Inc. All rights reserved. Period ending September 30, 2014.