Space-Time Diversification: Which Dimension is Better?

Abstract

There is much discussion in the academic and practitioner literature about the appropriate number of stocks that make up a well diversified investment portfolio. Likewise, there has been a lively dialogue on the topic of multi-period diversification and the perception that a longer time horizon decreases the riskiness of an investment. However, there is little, if any, research on the inter-relationship and trade-off between the two possible dimensions of diversification; namely, the number of stocks in a portfolio (which we call space), and time. In this brief paper we will quantify the link between the two dimensions by examining the effect of both space and time on the shortfall risk of an investment portfolio. The shortfall risk, originally introduced into finance by A. D. Roy (Econometrica, 1952), and employed by many others since, is defined equal to the probability that a portfolio will under-perform the return from the risk-free asset. This risk framework allows us to compute the marginal benefit of one more investment asset versus one more investment year. We obtain the somewhat paradoxical result that although, in aggregate, space diversification is preferred to time diversification for reducing shortfall risk, on the margin, it may be better to increase the holding period as opposed to the size of the portfolio.

JEL Classification: G11, D81