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Investors’ ability to capitalize on the benefits of the diversification effect seems threatened:
- Economic globalization has reduced international asset return independence [Dunis and Shannon, 2005].
- Economic shocks spill over international borders at precisely the times investors most need the diversification benefits of asset allocation [Longin and Solnik, 1995; Calvo and Mendoza, 1999; Kodres and Pritsker, 2002].
- Correlations between asset classes and subclasses vary across time [Krein, 2007].
Observations surrounding the equity-market slide that accelerated in September 2008 reinforce these findings. These phenomena diminish the diversification effect, which is the reduction in portfolio risk attributable to imperfect correlations between the returns of different portfolio assets [Markowitz, 1991; Adair et al., 2006]. Because the diversification effect is central to the portfolio management process [Israelsen, 2007], these threats to the diversification effect underscore the importance of a valid, reliable and direct measure of diversification effect that portfolio managers can use to aid decision making.
This article describes a parsimonious diversification effect metric and a related metric of incremental diversification effect. These metrics require no inferences about the diversification effect because they are direct measures. The results, expressed as percentages, are easy for investors to understand. As this article illustrates, portfolio managers can apply these diversification effect metrics to portfolio construction and management.
Why Asset Allocation Alone Is Not Sufficient
Investors apply asset allocation mainly to help reduce portfolio risk. Part of the asset allocation rationale rests on the common sense underlying the familiar idiom, “Don’t put all your eggs in one basket.” This process allocates resources to at least nominally different asset classes. Unfortunately, asset allocation’s idiomatic rationale is overrated: Nominal asset allocation alone fails to confer a meaningful effect on one important form of risk—portfolio volatility.
That’s not to say that asset allocation is useless or harmful. Asset allocation’s greatest benefit is its capacity to mitigate concentration risk. Also, if the investor gets lucky, maybe one or more of the selected asset classes will outperform a benchmark. This potential return benefit of asset allocation is not a risk management strategy at all; it’s a seat-of-the-pants attempt at increasing the rate of return.
Concentration risk is easy to manage because asset allocation is its simple solution. The greatest risk threat comes from portfolio volatility. Volatility is rapid price change. It creates havoc with investors whether prices go up or down. We can improve the effectiveness of asset allocation as a risk-reducing process by measuring the diversification effect in the process of planning asset allocation and evaluating portfolio performance.
A Review Of Diversification Effect Metrics And Their Shortcomings For Practical Applications
Diversification effect measurement is not new. Research articles (e.g., Conover et al., 2002; Abraham et al., 2001, among many others) and some commercial investment analytics programs publish correlation coefficient matrices to help gauge the diversification effect. These matrices list the correlation coefficients of all assets in a given portfolio, and they can be onerous. For example, a modest 10-asset portfolio yields 45 different correlation coefficients. How are we to draw confident conclusions about a portfolio’s diversification effect by poring over a table with so many coefficients?
Correlation coefficient matrices and correlations in general present another problem when we use them to gauge portfolio risk in an applied setting: Correlation is not a direct measure of the diversification effect. It measures covariance. Measuring covariance as a proxy for the diversification effect is somewhat like measuring absolute price change as a proxy for rate of return. Certainly, price change is a critical input for rate of return. But a direct rate-of-return measure is better. Likewise, a direct measure of diversification effect is better than its proxies.
Researchers often apply more-complicated measures of the diversification effect that surely serve their specific purposes well. Sharpe [1992], among others, applied factor models and the coefficient of determination to quantify the diversification effect. Mills [1996] used co-integration to measure the tendency for two stationary time series to move together in a long-term equilibrium state. From an applied perspective, these are indirect metrics because they only permit inference about risk reduction as a function of imperfect correlations.
Another approach to diversification measurement quantifies the gain in expected returns by allocating from a benchmark portfolio to a portfolio located at the same risk level on the efficient frontier [Li, et al., 2003; Kandel et al., 1995]. This tactic depends on the efficient frontier component of Modern Portfolio Theory. Yet, for practical applications, we need not appeal to theory if we can directly measure the diversification effect.
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