The Case for Market Neutral

Part I: The Case for Market Neutral

by Jason Lejonvarn and Claes Lekander

Next Issue: Part II: The Mechanics of Market Neutral in the BARRA Aegis System™ Suite

The well-publicized reversal of fortune suffered by several prominent hedge funds has moved many to fear any investment strategy that advertises the word "hedge." Not all hedge strategies deserve such a stigma.

Two recent examples highlight why investors should understand the nuances of and distinctions between different hedge strategies. An article on Long-Term Capital stated, "These bets required the strategists to buy one thing and sell short another, so that they maintained a Swiss-like neutrality to the market." ¹ In 1996, David Shaw pointed out that his firm’s proprietary strategies were "market neutral, meaning the goal is finding these little profit pockets without actually betting on the direction of the market." ²

This article discusses the merits of market neutral hedge strategies, particularly as they are practiced by institutional portfolio managers.

Definitions

A hedge strategy involves the inclusion of both long and short positions in a portfolio. The short positions allow the manager to achieve leverage, which can also be achieved through the use of derivatives. Leverage is an absolute exposure to risky assets which is greater than 100% of invested capital. A strategy’s leverage can be expressed as a ratio; for example, a strategy that is long two dollars and short one dollar for every dollar of invested capital has a leverage of 3:1.

A market neutral hedge strategy takes long and short positions in such a way that the impact of the overall market is minimized. Market neutral can imply dollar neutral, beta neutral or both. A dollar neutral strategy has zero net investment (i.e., equal dollar amounts in long and short positions).

A beta neutral strategy targets a zero total portfolio beta (i.e., the beta of the long side equals the beta of the short side). Does dollar neutrality alone make a fund market neutral? While dollar neutrality has the virtue of simplicity, beta neutrality better defines a strategy uncorrelated with the market return.

To refer to hedge funds as a group is not instructive since they do not conform to a single definition. However, institutional market neutral managers implement a more or less standardized hedge strategy that is often dollar and beta neutral with a fixed 2:1 leverage. This strategy, for the purposes of this article, will be referred to as institutional market neutral.

Basic Theory

A review of portfolio theory further illustrates the differences between dollar neutral and beta neutral strategies. It also emphasizes the theoretical underpinnings of the market neutral approach and describes its inherent advantages.

Notation:
r excess return
residual return
m market return
h absolute fraction of invested capital
l the long portfolio
s the short portfolio
p the total portfolio or l + s

In the general context of a hedge strategy, EQUATION 1 defines excess return. equation 2 separates out market related return and residual return.

(1) r_p = h_l r₁ + h_s r_s
(2) r_p = h₁ (₁ m + ₁) + h_s(-_s m + _s )

In the case of a dollar neutral strategy, EQUATION 1 can be reduced to EQUATION 3. A dollar neutral strategy that fixes leverage at 2:1 is defined by EQUATION 4.

(3) r_p = h₁ (r₁ + r_s)
(4) r_p = (r₁ + r_s)

The excess return of a beta neutral strategy is given by EQUATION 5. The condition ₁= -_s neutralizes the effect of the market, leaving only residual returns. EQUATION 6 defines a strategy that is both dollar and beta neutral. Finally, if a strategy also employs a fixed 2:1 leverage, as in the institutional market neutral strategy, then the portfolio’s excess return can be expressed by EQUATION 7.

(5) r_p = h_{1 1}+ h_{s s}
(6) r_p = h₁ (₁+ _s)
(7) r_p = ₁+_s

EQUATION 7 is the "double-alpha" argument that institutional market neutral managers frequently use to promote their strategy. EQUATION 8 extends EQUATION 7 to the residual risk dimension. The more general formula for the risk of hedge strategies is given by EQUATION 9.

(8)
(9)

Portfolio theory reinforces how one can reduce risk by taking advantage of low correlations among assets’ returns. In this regard, the market neutral portfolio is similar to any other portfolio. What makes it unique is the opportunity to exploit the correlation between the longs and shorts. This diversification benefit for the institutional market neutral manager is depicted in graph 1.3 If the correlation 1, is less than 1, then the increase in residual risk is less than the increase in residual return.

EQUATION 10, by combining EQUATION 7 and 8, defines the information ratio, IR, for an institutional market neutral manager.

(10)

If E[₁] = E[_s] and 1 = 1, then EQUATION 11 demonstrates the improvement in IR with the addition of the short side.

(11)

An institutional market neutral portfolio with a high residual correlation between the longs and shorts1 attains double the return (al + as), but also double the risk (2). On the other hand, if the manager can construct long and short portfolios with uncorrelated residual returns (1,= 0), as illustrated in GRAPH 1, then the return is double but the risk increases by 1.4 . Consequently, the effectiveness of the institutional market neutral strategy improves by approximately 40%, as expressed in EQUATION 11.

Graph 1: Correlation (al, as) and Risk

Efficient Frontier Analysis

A picture is worth more than 11 equations. GRAPH 2 makes a succinct theoretical case for market neutral by plotting three ex-ante residual efficient frontiers:

Graph 2: Ex-Ante Risk/Return Frontier

Long =	Traditional long-only strategy
M/N =	Market neutral strategy with unconstrained leverage
M/N (2:1) =	Market neutral strategy with leverage 2:1

All three strategies use the same information set. Random alphas for all stocks in the S&P 500 were fed to the BARRA optimizer. The area under each frontier represents each strategy’s opportunity set. At low risk levels, the frontiers are almost indistinguishable from one another. For example, a market neutral fund with a risk of 1% does not do much better than a long-only portfolio with the same risk.

For a risk level above 1%, the opportunity set of the long-only strategy becomes increasingly inferior to those of the market neutral strategies. Beyond the 4% risk level, the market neutral strategy with leverage of 2:1 starts to lose ground to its sibling with unconstrained leverage.

How can one explain the divergence between the efficient frontiers? The answer lies in the strategies’ implicit constraints. As is suggested by its name, a long-only portfolio consists only of long positions (and by extension, has no leverage). The manager therefore cannot take full advantage of negative information. The most a long-only manager can under-weight a stock is the stock’s weight in the benchmark. Even worse, if the stock is not in the benchmark, it cannot be under-weighted. In a low risk strategy, which tends to hold the portfolio’s weights close to those of the benchmark, the efficiency loss is not great because the optimal solution is largely unaffected by the implicit lower asset bounds. For aggressive portfolios, however, the loss can be substantial, as the efficient frontiers show.

With no implicit lower bound on asset holdings, the market neutral manager can fully exploit negative information and more efficiently diversify risk. In the unconstrained case (i.e. M/N), the highest attainable information ratio can be infinitely leveraged with no change in the composition of the portfolio. Therefore, the straight-line frontier defines the upper limit of all opportunity sets.

If leverage is constrained (i.e. M/N (2:1)), then the market neutral manager cannot maintain the same information ratio for all levels of risk. At the point where maximum leverage is reached, the optimizer can increase expected return only by changing the composition of the portfolio, which is less efficient than leverage.

This theoretical efficient frontier analysis supports market neutral strategies at intermediate and high levels of risk. In fact, the analysis endorses leverage for aggressive strategies. But recent hedge fund losses highlight an important caveat — hedge managers should ensure that their risks are accurately measured and consistent with the investor’s risk tolerance.

Monte Carlo

Theory is a good starting point, but does the case for market neutral hold up in the real world? While a Monte Carlo simulation does not entirely answer this question, it does provide a significant intermediate step between theory and practice.

A Monte Carlo study was done to compare the performance of four strategies: institutional market neutral, long-only conservative, long-only moderate, and long-only aggressive.⁴ Each strategy is emulated by 100 managers, all operating in the same environment. The effectiveness of each strategy is measured by the average "realized" residual information ratio.

In this study, optimal portfolios are formed on a monthly basis given a set of alphas and a covariance matrix, without controlling for turnover or transaction costs. In the first set of simulations, the managers know the covariance matrix and need only to estimate an IC for each asset. In the second, the managers must also estimate the covariance matrix.

At the start of each simulation, 20 months of data is available to estimate the required parameters. Over the course of the simulation, the estimation errors gradually decline as a longer history becomes available.

Each manager’s signals (raw forecasts) are drawn from a normal distribution ~N[0,1] and are uncorrelated by design. Each manager possesses a different information coefficient (correlation between signal and actual return) that is drawn from a uniform distribution with a range of [0, .2] and a mean of 0.105 for each asset. To produce alphas, the manager scales the signals using the fundamental law of active management.5

Results of the first set of simulations, presented in TABLE 2, show that the institutional market neutral strategy comfortably beats all three long-only strategies in the case where the covariance matrix is known. The risk levels chosen to define the strategies are shown in addition to the information ratios. While all strategies improve as the simulation period is extended, their relative performance remains largely the same. Notice that for the long strategies, there is a strong inverse relationship between the risk level and the information ratio. This finding is consistent with the preceding efficient frontier analysis.

Table 2: Average Simulated Performance: Estimation Error on IC

	After 5 Years	After 10 Years	After 20 Years

		RT		RT		RT
Inst. Market-Neutral	5.54 %	2.08	5.54 %	2.22	5.54 %	2.29
Long-Only Conservative	0.66 %	1.87	0.66 %	1.97	0.66 %	2.03
Long-Only Moderate	2.32 %	1.39	2.32 %	1.45	2.32 %	1.47
Long-Only Aggressive	8.80 %	0.42	8.80 %	0.48	8.80 %	0.52

TABLE 3 shows the results of the second set of simulations, where both IC and risk are nknown and must be estimated. Note that the presence of estimation error on risk impacts alphas as well as risk because volatility is used in the scaling of the raw signals. This scenario more closely emulates the realities of portfolio construction.

Table 3: Average Simulated Performance: Estimation Error on IC and

	After 5 Years	After 10 Years	After 20 Years

		RT		RT		RT
Inst. Market-Neutral	8.92 %	1.34	7.34 %	1.65	6.46 %	1.96
Long-Only Conservative	0.78 %	1.5	0.72 %	1.68	0.69 %	1.89
Long-Only Moderate	2.48 %	1.2	2.39 %	1.31	2.38 %	1.45
Long-Only Aggressive	8.34 %	0.45	8.69 %	0.48	8.75 %	0.53

The introduction of estimation error on risk impacts the market neutral strategy more negatively than the long-only strategies. The long-only conservative strategy outperforms the market neutral strategy after 5 years, but after 20 years, the risk estimation error is sufficiently reduced that market neutral is again the superior strategy. These results reinforce the notion that market neutral investing is difficult to justify at low levels of risk but clearly outperforms when compared to aggressive long-only strategies.

Empirical Study

Ideally, the merits of a portfolio strategy could be entirely defined by observed performance. Unfortunately performance data can contain many biases, such as sample bias, time period bias, and survivorship bias. Furthermore, the short statistical history of investment funds and the nuances between investment techniques often prevent the statistically significant identification of a superior strategy. Despite these caveats, empirical comparisons can be instructive, especially in light of the strong theoretical arguments for market neutral.

A study that compares the realized information ratios of institutional market neutral managers to several hundred institutional and mutual fund managers who represent long-only strategies is summarized inTABLE 4.⁶ The market neutral strategy is represented by fourteen BARRA clients who provided their performance histories.

Table 4: Realized information ratios for different investment strategies.

Percentile	14 Market-Neutral 1/90-12/90	Heuristic Long Only	367 Institutional Portfolios Q4/93 – Q4/96	300 Mutual Funds 10/88 – 9/94
90	1.45	1.00	1.01	1.08
75	1.24	0.50	0.48	0.58

In this study, the market neutral managers out performed institutional and mutual fund managers. Focusing on the skillful managers, as represented by those in the 90^th and 75^th percentiles, the market neutral strategy shows a markedly superior IR to both institutional and mutual fund managers.

This performance gap could be due to sample and selection biases, but for two reasons, it is not a surprising result. First, the inherent advantages of institutional market neutral strategies, other things equal (including skill), imply that they should do better than long-only strategies. Second, for its inherent advantages, skillful managers should gravitate toward market neutral strategies. Consequently, the skill level of market neutral managers becomes higher than that of long-only managers.

This empirical comparison lends credence to market neutral strategies and builds on the already compelling theoretical case for market neutral strategies.

Drawbacks and Limitations

Market neutral strategies have steadily increased in popularity over the past decade.⁸ But surely there must be some potential pitfalls otherwise every active manager would be market neutral. Here are some common arguments against market neutral investing.

Transaction costs To maintain market neutrality, frequent re-balancing is necessary as differential returns between the long and short sides create an imbalance. The "up-tick" rule also adds to the transaction cost on the short side. In addition, a futures overlay (to regain a desired market exposure) creates an additional source of transaction cost that is incurred when contracts have to be rolled over.

Liquidity The short side of the market contains a potential shortage of liquidity. Every stock is not available to short. If a stock is available, the quantity one can obtain may be limited. The capacity of a long-short strategy is clearly constrained for this reason.

Unlimited downside risk The strategy can conceivably lose more than its invested capital, as proved recently by some hedge funds. For strategies with fixed leverage, beta neutrality and sound diversification, this risk is not of practical significance.

Risk measurement As demonstrated in the Monte Carlo study, optimized market neutral strategies tend to exploit estimation errors in risk forecasts. If the estimation errors are large, the true risk of the portfolio could be substantially underestimated. The same bias could be present even if an optimizer is not used, as long as risk was a consideration in the portfolio construction process.

Capacity to absorb capital If a market neutral fund doubles its capital, the fund may accept large positions in thinly traded assets, positions in assets with lower absolute alphas or return the capital to investors for lack of opportunities. If a long-only fund doubles its capital, the fund may double its positions and, purposely or inadvertently, increase exposure to the market.

Conclusion

Contrast these pitfalls with the arguments in favor of market neutral investing:

double alpha, flexibility to diversify risk, increased opportunity sets, and superior information ratios.

The case for institutional market neutral investing is supported by a clear and persuasive theoretical framework and empirical evidence. For low risk strategies, there is little to gain from market neutral investing. Aggressive, skillful managers, on the other hand, should take a close look at market neutral strategies. Are they discarding an important opportunity to enhance their performance? N

¹ Michael Lewis, "How the Eggheads Cracked." New York Times, January 24, 1999.

²James Aley, "Wall Street’s King Quant," Fortune, February 5, 1996.

³ Assume hl = hs or dollar neutrality and sa1 = sas.

⁴ Stan Beckers, "Manager Skill and Investment Performance: How Strong is the Link?," presented at BARRA’s European Research Seminar in 1997.

⁵ ai = (signal)i (information coefficient)manager (volatility)i . See R. Grinold and R. Kahn, Active Portfolio Management, 1995.

⁶ Andrew Rudd and Ron Kahn, "What’s the Market for Market Neutral," presented at BARRA’s 1997 Research Seminar. The study includes US equity funds only.

⁸ The watershed market neutral event for institutions was the Internal Revenue Service’s private letter ruling issued in 1988. On behalf of the Common Fund, this private letter clarified that short sales did not constituent Unrelated Business Taxable Income (UBTI).