Expected returns, correlations, and optimal asset allocations

Abstract With increasing uncertainties in financial markets, individual investors now face difficult asset allocation choices. This article provides a framework for this deliberation by examining the marginal effects of the key input variables in the asset allocation for a portfolio of stocks, bonds, and bills. Expected stock returns are positively related to the optimal weight on stocks, but we show that the magnitude of this relation depends upon both the expected stock-bond correlation and the investor's attitude toward risk. We also find that an increase in the expected stock-bond correlation leads to shifts from bonds to bills for more risk-averse investors. © 2005 Academy of Financial Services. All rights reserved. Jel classification: GIl Keywords: Asset allocation; Stock-bond relationship; Individual investor decisions 1. Introduction Mean-variance analysis is one of the cornerstones of finance theory, allowing investors to select optimal portfolio combinations of assets to maximize return for given risk levels or minimize risk for given return levels. Mean-variance analysis is most useful when considering broad asset classes, such as stocks, bonds, and cash. The decision-making process requires expectations of asset class returns, standard deviations, and correlations as inputs. Given that we cannot predict the future with any certainty, the historical values of these input parameters are often employed as expected values. Currently, there is a particularly wide divergence of opinions regarding these mean-variance inputs and a strong sentiment that history will not repeat itself, at least in the near future. A great deal of attention has been focused specifically on stock returns and the correlation between the returns of stocks and bonds. Differences in expectations regarding these items will certainly affect asset allocation decisions, but to what degree? Many analysts believe that the historical returns experienced with equity over the past eighty years cannot continue. Investors have become accustomed to double-digit stock returns, but several recent studies have suggested that the equity premium compared to bonds will be noticeably smaller in the coming years. Philips (1999) forecasts long-run stock returns of a mere 6.5% per year. Hmanen (2003) offers a pessimistic forecast for equity of 5-6% per year, while his optimistic view is for equity to earn only 7-8% per year. Amott and Bernstein (2002) show that the "normal" risk premium of stocks is only 2.4% and suggest that a negative premium is a real possibility. Hunt and Hoisington (2003) and Bernstein (1997b) likewise expect lower return prospects for stocks in the future. Mehra (2003) and Jones and Wilson (1999), however, argue that the equity risk premium is alive and well. The view that the stock-bond correlation is stationary over time has been challenged by the likes of Bernstein (1997a) who suggests that covariances are "maddeningly unstable. " Dopfel (2003) notes that while the correlation between the returns of stocks and bonds is typically assumed to be a constant value between +0.30 and +0.50, his examination of 36-month rolling correlations from 1929 through June 2003 shows four periods, including the most recent period since 2000, where the correlation was negative. In fact, the correlation between the returns from stocks and bonds was negative for a full 10-year period, averaging -0.23 from 1955 to 1964. Wainscott (1990) studies these correlations from 1925 through 1988 using rolling one, three, five, and 10-year periods. Not surprisingly, the one-year periods show that correlations are very unstable, while the results are smoothed out over longer time periods. Ziering and Mclntosh (1997) note that the returns and correlations of stocks, bonds, REITs, and real estate vary considerably over subperiods from 1972 to 1995. Gulko (2002) observes the decoupling phenomenon whereby the correlation between stocks and bonds breaks down during market crashes. …