Aurora Borealis
1 November 2013 CFA Institute Journal Review

Volatility, Correlation, and Diversification in a Multi-Factor World (Digest Summary)

  1. Peter Eickelberg, CFA

Traditional correlation measures obscure true factor exposures across and within portfolios. By estimating factors that drive returns and selecting nonoverlapping investments that encompass each factor, managers can attain better diversification.

What’s Inside?

The author presents a conceptual argument around the idea that standard correlation measures leave out important data regarding factor exposures. Because the latter ultimately drive portfolio returns, de-emphasizing traditional correlation and focusing instead on factor exposures allows a portfolio manager to diversify more effectively. The author presents several ways to estimate factors before identifying targeted exchange-traded funds (ETFs) as the most likely practical solution for investors.

How Is This Research Useful to Practitioners?

Many investment professionals learned to diversify by combining assets with low correlations. But despite imperfect correlations, assets can, at times, move together more than expected because common factors within each asset class actually drive the returns. Mathematically, low correlations can occur simply as a result of differences in proportionality.

Common factors within asset classes explain why even highly diversified portfolios of similar assets show significant volatility. Different factors across asset classes explain why these assets often show low correlations with each other. Given the experience in 2008 and 2009, managers need to provide true diversification across scenarios and thus should look beyond correlations to the actual return factors so that portfolio decisions incorporate true risk exposures.

The author’s conceptual examples remain simple, but the implications affect portfolio management broadly. In particular, managers cannot rely on simple correlations to diversify but instead need to estimate return factors accurately and select investment vehicles carefully to express their views. Although a statistical approach to factor estimation offers computational soundness, nonstationarity becomes a problem. Macroeconomic approaches rest on a strong theoretical foundation, but observational frequency presents another challenge. Therefore, the use of nonoverlapping ETFs strongly associated with each factor probably represents the best practical way to build a truly diversified portfolio.

How Did the Author Conduct This Research?

The author presents portfolio return–generating models for two hypothetical portfolios that are not perfectly correlated. Their separate returns depend entirely on their different sensitivities to two uncorrelated factors. The author demonstrates how rearranging the second portfolio’s asset weights until its factor exposures match those of the first portfolio removes any diversification benefit from combining the portfolios. In other words, the return drivers present in the second portfolio were already present in the first, just in different proportions.

It follows that combining the portfolios would provide a diversification benefit only if the second portfolio carried a higher expected return or retained some idiosyncratic volatility, and neither of these alternatives depends on the correlation. Even adding a single asset whose returns were fully described by the first portfolio’s factor exposures would bring nothing new, in contrast to Treynor and Black’s (Journal of Business 1973) conclusions about the value of adding an imperfectly correlated asset to a portfolio.

Of course, specifying factors to manage risk presents significant challenges. Macroeconomic factors do not fully account for market movements because of changing expectations among investors and the low frequency of data points. Managers also cannot practically perform mean–variance analysis as well as build a correlation matrix for every asset in a well-diversified portfolio. And even if performed, the specifications would not remain stationary. Other models present their own problems as well. Therefore, the author suggests using ETFs (or ETF derivatives) that reflect the desired factor exposures. Provided that the markets covered by each ETF do not overlap, a manager could target factor exposures accurately and avoid nonstationarity problems in the data because the ETFs would simply change composition as their underlying markets changed.

Abstractor’s Viewpoint

The author’s argument assumes that managers can easily rearrange the asset weights in a low-correlated second portfolio and thus wipe out its diversification benefit. Of course, in reality, managers do not do this. Combining imperfectly correlated portfolios at least changes the risk–return characteristics of a blended portfolio because factor sensitivities change and the portfolios still carry some idiosyncratic risk. But given correctly specified factors and an intelligent understanding of how these relate to one another, managers using the author’s factor-based diversification approach could most likely do a better job diversifying risk and reflecting expected scenarios within an investment portfolio.

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