Conclusions
Diversification effect is a potential result of asset allocation and a function of imperfect correlation coefficients between the returns of portfolio assets. Meaningful diversification effect may not result from asset allocation alone, so it follows that active risk management requires measurement. This article illustrates how a direct diversification effect metric provides useful information about important portfolio properties.
The first illustration started with a three-asset portfolio. When we added the fourth asset, less imperfect correlation coefficients yielded a negative incremental diversification effect. The fourth asset’s relatively high correlations with existing assets diminished any risk-attenuating benefit that might have been gained by adding the asset. A secondary lesson in this second illustration reminds us that adding nominally different assets does not necessarily increase diversification effect.
Replacing the original fourth asset with a low-correlated asset enabled a positive incremental diversification effect. In this example, the values of other important portfolio properties improved.
DE metrics presented here directly measure diversification effect and do not require any inference or dependence upon theoretical assumptions. They also do not duplicate the information value of other metrics.
Diversification effect measurement should not be confused with total risk measurement. If an investor wants to change a portfolio’s total risk level, the standard deviation is the correct metric. However, if an investor wants to capitalize on diversification effect or evaluate the extent to which a certain allocation of certain assets reduces risk as a function of imperfect correlation coefficients, DE provides necessary and sufficient information because it directly measures diversification effect. Likewise, if an investor wants to evaluate the impact of changing portfolio assets on diversification effect, IDE provides necessary and sufficient information.
One perspective might hold that the variability of correlation coefficients diminishes the information value of DE and IDE. Research on the relationship between real estate investment trusts (REITs) and the S&P 500 Index suggests that correlations increase after REIT down months and decrease after REIT up months [Chandrashekaran, 1999]. Correlations among stocks increase during market downturns [Campbell, Koedijk and Kofman, 2002]. Also during stock market downturns, stock-bond correlations turn negative, but they approach unity during stock market upturns [Gulko, 2002]. Speidell and Sappenfield (1992) report rising correlations among developed markets due to economic convergence and interdependence. We would expect similar variability in other modern portfolio statistics such as returns, standard deviation of returns, beta and Sharpe ratios.
Yet all of these caveat examples provide evidence that favors actively measuring and managing diversification effect. None of these facts concerning variability of markets compromises the value of measuring diversification effect any more than uncertainty about the future compromises the value of planning. These facts are all the more reason to directly measure diversification effect.
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