The Term Structures of Loss and Gain Uncertainty

We investigate the uncertainty around stock returns at different investment horizons. Since a return is either a loss or a gain, we categorize return uncertainty into these two components. Loss uncertainty is the uncertainty surrounding negative returns, and gain uncertainty is the uncertainty surrounding any future gain. Investment opportunities can be evaluated by looking at these components.

Using data from a large panel of S&P 500 Index options with time to maturity ranging from 1 month to 12 months, we measure both types of uncertainty at different investment horizons. We also look at whether existing reduced-form option pricing models can generate similar measures.

We find that, on average, investors expect the potential for loss to decrease as the time to maturity increases. However, in the market, hedging the long-term loss potential of stocks is more expensive than hedging the short-term loss potential. Likewise, on average, investors expect the potential for gain to increase as the time to maturity increases. However, in the market, speculating on the short-term gain potential of stocks is almost as costly as speculating on the long-term gain potential.