Optimal diversification and risk-taking: a theoretical and empirical analysis

Among the justifications for capital property income received by private households is that it is a 'return to risk-taking'. However, portfolio diversification provides an obvious means toward the reduction of risk. Moreover, it is widely believed that the wealthier the household, the more diversification it practices: the larger tends to be the proportion of its total portfolio allocated to publicly traded stock, and the larger tends to be the number of individual stock issues included in its portfolio. Using a simple 'homogeneous securities' model, explicit functional forms are obtained for both the optimal proportion of the portfolio allocated to stocks, and the optimal number of individual stock issues in the portfolio. Empirical evaluation of these theoretical results, using a dataset derived from the 2004 Survey of Consumer Finances (SCF), lends substantial support to the model. Applying these empirical results, it is found that as household capital wealth increases, expected capital income increases while simultaneously a reasonable risk indicator (the probability of incurring a negative return on the capital portfolio) decreases owing to the higher level of portfolio diversification. This indication casts significant doubt on the 'return to risk-taking' justification for capital property income received by wealthy private households.