**ABSTRACT**<?xml:namespace prefix = o ns = "urn:schemas-microsoft-com:office:office" />

This paper aims to review the concept of long-short investing and to discuss the ability to take market exposure as the main difference between the long short and market neutral investing styles. We demonstrate the theoretical result for the information ratio as a function of the market exposure and other main parameters as we believe this has important implications on management of a long short investment strategy.

**INTRODUCTION**

In its broadest sense, long short equity investing involves taking simultaneously long and short positions in equities or equity related securities (e.g. equity index). The resulting net market exposure may vary as it can be either negative, zero, or positive. Indeed, investment strategies are often defined in terms of how this net market exposure is constrained. For example, a market neutral strategy always has zero net market exposure whilst a long short strategy is often associated with various levels of net market exposure.

In this paper we are concerned with this particular feature - the flexibility of long short strategies to take market exposure.

Before we start to explore this additional flexibility of long short investing it is helpful to remind us of other flexibilities that also apply to market neutral investing. The following table summarises five "degrees of freedom" that apply to these strategies.** Table 1**

**Degree of freedom**

**Flexibility of Long-short Strategies**

**Market-neutral**

**Long Short**

DF 1

Flexibility to short any stocks

Yes

Yes

DF 2

No constraint on short portfolio

Yes

Yes

weights

DF 3

No constraint on proportion

Yes

Yes

actively invested

DF 4

Flexible benchmark can be re-

Yes

Yes

engineered

DF 5

Flexibility to take net long/short

Yes

The first four degrees of freedom have been introduced and explained in another paper1 and are useful to differentiate market neutral and long short investing from long only investing. One of the most important consequences of the first four "degrees of freedom" is the potential to increase the portfolio alpha and to improve the portfolio risk/reward trade-off. In this paper we aim to investigate the fifth one as it is only available to long short and so it is a key difference between the long short and market neutral strategies.

**THE LONG-SHORT INFORMATION RATIO SENSITIVITY ANALYSIS**

For a long short strategy, the additional "degree of freedom" enables us to consider stock selection and market timing decisions separately. This means that in addition to selling short stocks we expect to under-perform, and buying stocks we expect to out-perform, at the same time a decision needs to be made about the long and the short side portfolio weights. The formula presenting this point is in the appendix to this report. It shows that the information ratio2 depends on five key parameters: manager skill (alpha), market return, market volatility, long short correlation (by which we mean correlation between the long and short side returns) and the net market exposure.

As the structure of the relationship is rather complex, we investigate the impact of each of these parameters on the information ratio separately. Each time we allow only one of the parameters to vary whilst we keep all the other ones constant at the single assumption level. Table 2 summarises the assumptions made.

Table 2

**Parameter**

**Min**

**Max**

**Main Assumption**

á (alpha)

0% p.a.

30% p.a.

15% p.a.

*R *(market return)

-10% p.a.

20% p.a.

5% p.a.

ó (market volatility)

10% p.a.

30% p.a.

20% p.a.

^{ñ}* _{ls}* (long short correlation)

0.5

0.99

0.75

*k* (Net market exposure)

-100%

+100%

-100%,0,100%

**EFFECTS OF ALPHA, MARKET RETURN, MARKET VOLATILITY AND THE LONG SHORTCORRELATION ON THE INFORMATION RATIO**

The sensitivity analysis with respect to the first four parameters is shown below. First we consider the effects of alpha and the market return on the information ratio.

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_{1 }"Market Neutral Investing" by Jelicic and Munro published in the AIMA Newsletter in June 2000. (Available upon request)_{2} The long short strategy return divided by the long short strategy return volatility**Fig 1: Sensitivity Analysis -Information ratio as a function of alpha and the market return for various net market exposures [1]**

*Impact of alpha*

The information ratio is positively affected by alpha in a linear fashion. The information ratio for a net short portfolio (Net market exposure of -1) is worse than for a market neutral or a net long portfolio due to our positive market return assumption. The market neutral portfolio starts to dominate net long portfolio at higher alphas (higher than 7% in this case) as the effect of increased volatility starts to dominate positive return contribution from the market.*Impact of market return*The information ratio has a linear relationship with the market return, however the slope depends entirely on the sign of net market exposure. The slope is negative for a net short portfolio, zero for a market neutral and positive for a net long portfolio. The information ratio for a net long and a net short is the same when market return equals 0; however this is inferior to the market neutral case as additional volatility is not being rewarded.

*Impact of market return volatility*

The information ratio has a decreasing relationship with the market volatility. The lower the volatility, the better the information ratio. The strongest information ratio is provided for a market neutral case whilst the net long case dominates the net short case.

*Impact of the long short correlation*

The information ratio has an increasing relationship with the correlation. As the correlation increases, the information ratio increases as well. However, for a market neutral strategy, the rate of the increase goes up dramatically at high levels of correlation (above 0.9). It follows that when the long and the short portfolio are highly correlated as in pairs based statistical arbitrage programs, at least in theory, very high information ratios can be achieved.**EFFECT OF THE NET MARKET EXPOSURE ON THE INFORMATION RATIO**

The information ratio has also a quadratic relationship with the net market exposure. We first show the effect of the market exposure for four cases where market neutral return equals -10%, 0%, 5% and 20% respectively.

**Fig 3: Sensitivity Analysis -Information ratio as a function of the net market exposure [3]**

** **

In all cases the information ratio is first an increasing function of the net market exposure until a maximum is reached after which the information ratio declines with market return. In the case where the market return is zero, the maximum information ratio is reached when net market exposure is also zero (market neutral case is also optimal), when the market return is less than zero, the optimal net exposure is negative and when the market return is greater than zero, the optimal net exposure is positive.

It is also interesting to note that all the curves have a unique point at zero market exposure. This is because market return makes no difference for the market neutral strategy.

We also show interaction between net exposure, market return and the information ratio in three dimensions.

We can see how the information ratio envelope varies as a function of the market return in a rather different way as the net exposure changes.**Fig 4: Sensitivity Analysis -Information ratio as a function of the market return and the net market exposure [4]**

As highlighted above, the information ratio is declining with the market return for positive net exposure and increasing for negative net exposure. Best information ratio is achieved when market return and net exposure are at the highest. However this is only marginally better than the more stable information ratio area that is available at zero market exposure regardless of the market return.

Given the very strong sensitivity of the information ratio to correlation we want to investigate further this relationship by also considering the correlation. We show the information ratio as a function of net exposure and correlation when the market return equals 5%.**Fig 5: Sensitivity Analysis: Information ratio as a function of the long short correlation and the net market exposure [5]**

The maximum information ratio is in all cases when the long side exposure is greater than the short side exposure, the higher the correlation the higher the maximum information ratio and also the lower the net market exposure. We observe again a dramatic impact of increasing correlation as the information ratio exceeds 3 for correlation of 0.95 and above (Net exposure between 0 and 10%).

Continued in Part II [6]