The Efficiency Gains of Long–Short Investing

Abstract

Long–short strategies have generated controversy and institutional interest for more than 10 years. We analyzed the efficiency gains of long–short investing, where we defined efficiency as the information ratio of the implemented strategy (the optimal portfolio) relative to the intrinsic information ratio of the alphas. The efficiency advantage of long–short investing arises from the loosening of the (surprisingly important) long-only constraint. Long–short and long-only managers need to understand the impact of this significant constraint. Long–short implementations offer the most improvement over long-only implementations when the universe of assets is large, asset volatility is low, and the strategy has high active risk. The long-only constraint induces biases (particularly toward small stocks), limits the manager's ability to act on upside information by not allowing short positions that could finance long positions, and reduces the efficiency of traditional (high-risk) long-only strategies relative to enhanced index (low-risk) long-only strategies.

Long–short strategies have generated controversy and institutional interest for more than 10 years. In the study reported here, we analyzed the efficiency gains of long–short investing, where we defined efficiency as the information ratio of the implemented strategy (the optimal portfolio) relative to the intrinsic information ratio of the alphas. The efficiency advantage of long–short investing arises primarily from the loosening of the (surprisingly important) long-only constraint. Moreover, long–short strategies also avoid the small-cap bias induced by the long-only constraint.

Our discussion begins with a simple model characterized by a set of assets with uncorrelated residual risks that make up an equal-weighted benchmark. The long-only constraint affects assets with negative alphas below a threshold that depends on the portfolio's risk, the asset-level risk, and the number of assets in the benchmark. The impact of the constraint increases with portfolio risk and the number of assets and decreases with the riskiness of the individual assets. This model also identifies how the long-only constraint limits even an investor's ability to act on upside information by not allowing short positions that could finance long positions.

To analyze more realistic models accounting for cap-weighted benchmarks, we next discuss the distribution of market capitalization. We used Lorenz curves to capture this distribution. We fit a one-parameter lognormal distribution of market capitalization to the assets that constitute several popular (cap-weighted) indexes. Doing so allowed us to model typical benchmarks and analyze how the impact of the long-only constraint changes as the parameter of fit varies over a realistic range.

Armed with these results, we extended the simple model to account for cap-weighted benchmarks and we numerically simulated results as we varied portfolio risk, the number of assets in the benchmark, and asset-level risk. For each set of parameters (risks, asset numbers), we ran 900 simulations. Each simulation generated a set of alphas and built an optimal portfolio. We summarize these results by displaying the mean alpha and mean portfolio risk level from each set of simulations.

The results clearly show that for long-only strategies, expected return does not increase linearly with active risk. Instead, each unit of additional risk generates less and less expected return. Viewed another way, long-only information ratios (and efficiencies) decrease with increasing active risk.

This decrease in efficiency can be significant. A long-only strategy with a 500-asset universe and 4.5 percent active risk loses half its information ratio (efficiency = 49 percent) relative to a long–short strategy using the same information (same alphas). The impact is less severe at low risk levels: We found that an enhanced index strategy with the same universe but only 2 percent active risk has an efficiency of 71 percent.

Our analysis also demonstrates a second significant effect of the long-only constraint—a bias toward small stocks. This bias arises because the constraint affects mainly the smaller-cap stocks that have less weight in the benchmark. The bias increases with the level of portfolio risk. For a strategy with a 500-asset universe and 4.5 percent active risk, this bias would have generated a loss of 235 basis points over the 10-year period ending September 1998 (when large-cap stocks outperformed small-cap stocks).

In summary, long–short implementations offer the greatest advantage over long-only implementations when the universe of assets is large, asset volatility is low, and the strategy has high active risk. Among long-only strategies, enhanced index (low-risk) strategies offer better efficiency and less size bias than traditional higher-risk strategies.

The preliminary empirical results we provide on U.S. equity managers demonstrate that, at the very least, long–short managers can achieve market neutrality.

We thank Naozer Dadachanji, Uzi Levin, Bruce Jacobs, and Bill Jacques for helpful comments and suggestions. Andrew Rudd contributed to the section on the appeal of long–short investing.