Beyond Mean Variance: A New World of Risk Management

Beyond Mean Variance:
A New World of Risk Management
Tristram S. Lett - Vice-President, Quantitative Investment Products, YMG Capital Management Inc.
 
Absolute return strategies create return distributions that are decidedly non-normal.

Because the Capital Asset Pricing Mode (CAPM) is so widely embraced by institutional investors, it is important to be aware that it assumes that the underlying distributions of returns incorporated into it are standard normal. In addition, the covariance matrix is assumed to be relatively stable, when in reality it is considerably more volatile than most investors expect, and this volatility often occurs when it is least helpful.

The appeal of absolute return strategies lies both in their higher returns and in a higher incidence of positive returns, but what really makes them work in an investment portfolio is their low correlation to conventional asset classes. This attaches very strong diversification properties to absolute return strategies. However, given the inherent instability of the covariances and non-normality of their return distributions, one must be careful and use this information appropriately in the CAPM analytics.

You can create combinations of absolute return managers that minimize the impact of fat tail issues, particularly in the left-hand tail. Non-normal distributions can be skewed, kurtotic or both. Skew is the standardized third moment of a distribution and has a value of zero if it is normal. Negative values indicate a fat tail on the undesirable left-hand side. Kurtosis is the standardized fourth moment of a distribution and has a value of three if it is normal. Values less than three indicate a platykurtic distribution with fat right and left tails. Investors should be wary of any fat left tails in symmetric or asymmetric distributions.

Due to the non-normality of absolute return strategies, investors should look to fund of funds structures that seek, in part, to create a normal distribution of returns from non-normal components and to stabilize the pairwise correlations of the constituents.

It is possible to stress-test the correlations at points when the market has undergone a major shock such as the Long Term Capital incident in August 1998 or the attack of September 11th. Management combinations should be structured to be as "all weather" as possible. Market stress has the curious ability to make historical correlations suddenly diverge to +1 or -1, thereby creating the fat tail events investors wish to avoid. This behaviour, called phase-locking, is particularly pernicious when it is positive, causing correlation to a negative event. However, it can be beneficial if the correlation is negative to a negative event. Consequently, it is senseless to simply rely on historical correlations to carefully structure investment diversification when the diversification fails miserably during a stressful event. Investors, once aware of phase-locking behaviour, can take advantage of it to create management combinations that are less susceptible to undesired fat tail events.

I won't go into detail on other stress-testing activities, except to point out that Monte Carlo simulations using GARCH (Generalized Autoregressive Conditional Heteroscedasticity) methodology are very useful because GARCH creates fatter tails than Gaussian methods. Observations in fat tails are scarce in the performance histories, so it is vitally important that this kind of testing be undertaken. One might also mention the Jarque-Berra test for normality, which is an asymptotic test based on sample measures of skew and kurtosis.

Using these testing procedures will help investors create management combinations of absolute return managers that fit into the mean-variance framework so familiar to them. This will give institutional investors and others the needed confidence to engage absolute return strategies in their overall investment policy. *

 

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