Monday, February 12, 2007

Reducing Downside Risk

The following three papers provide perspective on maximizing downside risk protection in the asset allocation decision. In our first paper, Benjamin Cotton considers the effects of uncertainty on the question of asset allocation:

The Uncertain Science of Asset Allocation

Cotton, Benjamin L., "The Uncertain Science of Asset Allocation" (September 16, 1999)

Descriptive statistics for asset class return distributions are compared to inferential statistics produced by Monte Carlo simulations to illustrate that the assumption of normality and constant correlation can understate the risk associated with a given portfolio. Results are presented in a form accessible to students, investors, and practitioners alike. This working paper is to be part of a larger work illustrating investment uncertainty and the methods by which to deal with such uncertainty.

Factors such as skewness, kurtosis, and inconsistent asset class correlations result in downside risk roughly double that suggested by mean variance optimization. Stabilizing the portfolio with investment grade bonds can reduce this downside risk. However, Cotton notes:

"However, the table also illustrates that a 75% allocation to fixed income would be required to bring the portfolio’s worst case within the expectations set by the simulation. Even a 50/50 allocation between fixed income and equities underestimates our actual worst case by over 80% relatively. This is quite disturbing when you consider that most advisors consider a 60/40 allocation between equities and fixed income to be conservative."

A second paper, examining asset allocation under value-at-risk measures, comes to similar conclusions:

Asset Allocation in a Value-at-Risk Framework

Huisman, Ronald, Koedijk, Kees C.G. and Campbell, Rachel A.J., "Asset Allocation in a Value-at-Risk Framework" (April 27, 1999).

In this paper we develop an asset allocation model which allocates assets by maximising expected return subject to the constraint that the expected maximum loss should meet the Value-at-Risk limits set by the risk manager. Similar to the mean-variance approach a performance index like the Sharpe index is constructed. Furthermore it is shown that the model nests the mean-variance approach in case of normally distributed expected returns. We provide an empirical analysis using two assets: US stocks and bonds. The results highlight the influence of non-normal characteristics of the expected return distribution on the optimal asset allocation.

At the 99% confidence level mandated by Basel for commercial bank value-at-risk use, the optimal portfolio under realistic non-normal distributions consists of 23.93% stock; 35.59% bonds; and 40.68% cash.

Finally, Lingfeng Li takes a look at the macroeconomic factors driving stock and bond correlations. He finds the primary driver to be unexpected changes in inflation expectations:

Macroeconomic Factors and the Correlation of Stock and Bond Returns

Li, Lingfeng, "Macroeconomic Factors and the Correlation of Stock and Bond Returns" (November 2002). Yale ICF Working Paper No. 02-46; AFA 2004 San Diego Meetings

This paper examines the correlation between stock and bond returns. It first documents that the major trends in stock-bond correlation for G7 countries follow a similar reverting pattern in the past forty years. Next, an asset pricing model is employed to show that the correlation of stock and bond returns can be explained by their common exposure to macroeconomic factors. The link between the stock-bond correlation and macroeconomic factors is examined using three successively more realistic formulations of asset return dynamics. Empirical results indicate that the major trends in stock-bond correlation are determined primarily by uncertainty about expected inflation. Unexpected inflation and the real interest rate are significant to a lesser degree. Forecasting this stock-bond correlation using macroeconomic factors also helps improve investors' asset allocation decisions. One implication of this link between trends in stock-bond correlation and inflation risk is the Murphy's Law of Diversification: Diversification opportunities are least available when they are most needed.

This suggests that the fixed income portfolio allocation would be best filled by short term bonds and inflation indexed bonds, both of which are hedges against unexpected inflation.

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