Option Theory, Time Diversification, and Index Funds

Abstract

Some academics have suggested that stock market risk increases as the investment horizon lengthens thus refuting the concept of time diversification. That argument has been based on an apparent increase in the cost of hedging stock price risk as indicated by theoretical put-option prices, which appear to increase when the investment horizon extends. The present article argues that those views are based on a restrictive use of the Black–Scholes option pricing model. When the model is used less restrictively, put-option prices are found to decrease as the investment horizon lengthens so long as investment growth is sufficiently high and/or volatility is sufficiently low. Risk, as measured by the cost of hedging, may decline as the holding period lengthens. Dependent upon expected investment growth and volatility, option theory supports time diversification rather than refuting it.

One implication is that index funds may be more likely to provide time diversification than actively managed funds. Index funds offer higher returns because of their lower costs, and offer lower volatility because of the absence of active risk.