*There is obviously something in the water in California that has led to uncommonly large cerebral cortexes in some of its citizens. This is partly evidenced by the flood of financial innovation coming from the Left Coast for over a generation â€“ from Barr Rosenberg to Bill Sharpe, BGI/Wells Fargo, Analytic, and Wilshire. Even Harry Markowitz loved the place so much, he recently conducted a presentation in Boston by satellite so he wouldn’t have to leave (see posting).*

*Today, we are pleased to bring you a guest posting from one of the homes of the large-brained Financialus Californius: Jia Ye of First Quadrant L.P. In this summary of a yet-to be-published First Quadrant white paper, Ye warns us that not all managers can benefit from removing the so-called short constraint. And what she has found may surprise you.*

**Do Short Extensions Benefit All Managers?**

By **Jia Ye,** Director & Chief Investment Strategist, First Quadrant L.P., Special to AllAboutAlpha.com

Contrary to popular belief, the ability to take short positions in equity portfolios does not necessarily lead to superior performance for all managers. When we take into account the positive skew in stocks returns, only managers who can maintain a stable correlation between forecast and realized returns (captured by the manager’s information coefficient or IC) can take full advantage of the efficiency gains from short extensions. In other words, the ability to short stocks will not necessarily help managers with an unstable IC.

As the volume of articles here at AllAboutAlpha.com clearly illustrates, there has been a lot written recently about short extension (1X0/X0) strategies. But there is little mention, here and elsewhere, that studies of this topic are based on one or both of the following implicit assumptions:

- The correlation between managers’ forecast and realized return (the information coefficient, or IC) is constant over time.
- Stock returns are symmetric.

**Volatility in the Information Coefficient (IC)**

While information coefficients are often assumed to be stable, the reality is that IC’s of active managers tends to vary over time. For example, if market inefficiencies are caused by short-term liquidity shocks, they will fade away as more investors enter the market to exploit them. Or, if market inefficiencies relate to human cognitive biases or risk preference, they will likely fluctuate with changes in overall economic conditions.

According to the fundamental law of active management, IC of active managers is a key component of expected portfolio returns. So when IC varies over time, the returns of the active portfolio are drawn from slightly different distributions in each period. In other words, there are two determinants of active risk: the variation in return of assets in the portfolio, and the variation in IC.

The impact of IC volatility can be significant. For example, if a manager has an investment universe of 100 stocks and a variation in IC of 0.2, the total active risk is 2.36 times as much as the risk estimate based on holdings alone (for details on this calculation and empirical evidence of this phenomenon, see this paper by First Quadrant). Commercial risk models rely only on portfolio holdings and ignore the variation in IC over time. As a result, tools from such firms as Barra and RiskMetrics have a tendency to understate the tracking error of active strategies.

**Right-Skewed Returns**

Another feature of equity returns that investment scholars routinely ignore in the interests of simplicity is the asymmetric distribution in stock returns. Stock returns have a positive skew due to the limited liability of equity holders. Technically, they can go up an infinite amount, but they can only go down to zero.

Figure 4 (below) from a recent paper of this topic plots the difference between the positive and negative tails of return distribution for stocks in the S&P 500 Index and in the MSCI Developed World Index. All of the data points in the exhibit are greater than zero, indicating that the likelihood of large positive returns exceeds the likelihood of large negative returns. In other words, the graph illustrates a fatter positive tail and right-skewed returns distribution.

So how do right-skewed returns affect active strategies? When returns are not symmetrically distributed, the traditional mean-variance framework leads to incorrect results. For example, if active equity managers use the mean-variance framework to construct a market-neutral portfolio, the long portfolio will have slightly better information ratio (IR) than the short portfolio. This portfolio is sub-optimal because we can improve risk-adjusted performance by simply allocating slightly more risk to the long portfolio and less risk to the short portfolio.

Even in the absence of short positions, a mean-variance optimization leads to a sub-optimal risk allocation as long as returns are right-skewed like this. Additionally, the requirement that more risk should be assigned to the overweight (long) segment is even more important when IC volatility rises.

A direct implication from the analysis is that active portfolios with short-constraints may be desirable for managers with unstable IC, because a larger amount of risk is allocated to the overweight segment of these portfolios. For these managers, the optimal risk ratio between the overweight and underweight segments of their portfolios is much larger than one, and therefore an increase in risk-taking on the short side may potentially hurt performance. In contrast, managers with stable IC will benefit from the loosening of short constraints because their optimal risk allocation is close to symmetrical.

The figure below, also taken from First Quadrant’s paper on this topic, shows that the information ratio (IR) rises when short positions are added only if the IC has a low standard deviation (e.g. 0.05). However, when the standard deviation is increased to 0.20 adding short positions actually reduces the information ratio.

**Conclusion**

For managers who have large swings in IC, taking full advantage of the ability to short does not generate better performance. The benefit of short extension can only be realized by managers who have the ability to generate stable IC over time.

The investment community should be aware of the impact IC volatility has on active strategies. Variation in IC is an important source of active risk; it reduces the IR of active managers; it amplifies the misallocation of risk in a mean-variance framework when asset returns are asymmetric; and it is an important determinant of optimal portfolio structure. Armed with this knowledge, investors and managers can make informed decisions about the optimal level of shorting they should take and improve investment performance.

*– Jia Ye, First Quadrant, October 30, 2007*

**Note:** First Quadrant’s Rick Roberts will be expanding on this idea at Terrapinn’s Portable Alpha & 130/30 Strategies conference in New York next Wednesday through Friday (Nov. 7-9).

## 2 Comments

November 27, 2007 at 12:33 pm## Joe