When does ‘All Eggs in One Risky Basket’ Make Sense?

Abstract

In an important paper comparing expected utility and mean-variance analysis, Feldstein (1969) examined a simple portfolio problem involving just two assets, one riskless and one risky. He concluded there could easily be ‘plunging’, that is, investment in the risky asset alone. His background assumptions were that the risky asset’s yield was log normally distributed and that the investor’s attitude to risk was expressible by a logarithmic utility. We look at how conclusions are affected by choice of distribution and utility function. While conclusions can depend on choice of distribution, they are remarkably robust to choice within the range of plausible positive distributions. In contrast, conclusions are sensitive to choice of utility function and we find the key determinant to be how much the investor’s relative risk aversion differs from unity and in what direction. Based on historical stock market returns, our analysis implies that the prevalence of diversification that is observed is consistent with a relative risk aversion coefficient of about 2.5.