Frustrated Worker

Option Theory Does Not Refute Time Diversification

Frustrated Worker

This is the self-explanatory title of an article by Keith Redhead of Coventry University Business School in the UK. It is an answer to the academics who have proffered the argument that since put option prices increase with the length of the time period, the risk of equities must increase with time. Recall that a put option bestows upon the owner the right to sell the underlying asset at a given price (the strike price). Certainly, if you buy a 6-month put option on the S&P 500 at a given strike price, you are going to pay more than if you buy a 3-month option with the same strike price. Another way to think about it is that it costs more to insure your car for 6 months than for 3 months—not exactly rocket science.

Naturally, the crux of the argument on both sides is how we define risk. If risk is defined as the standard deviation of the total cumulative return, then risk definitely increases with time. However, many if not most investors would define risk as the chance of losing money or purchasing power by the end of their time horizon. Redhead demonstrates that when this definition of risk is combined with the assumption that equities have a positive real expected return, then stock market risk declines with the length of the investment horizon.  The primary reason that the market prices of put options increase with time is that they allow early exercise which automatically means that a longer term option is worth more than a shorter term option.

A few years ago at Index Fund Advisors, we ran our own simulations based on bootstrapping of historical monthly equity returns, and we calculated the fair cost of an option to hedge against the loss of purchasing power. We reached the same conclusion as Redhead—that option theory does not refute time diversification of risk.