Uncertainty premia for small and large risks

We develop a model showing that the effect of smooth ambiguity aversion on large risks, those that are independent of the holding period, is of first-order importance, in contrast to risks that are proportional to the holding period. To test this hypothesis, we construct an ex-ante measure of the price of uncertainty based on changes in the option-implied concavity of preferences. As predicted by our model, we find that such concavity increases ahead of scheduled macroeconomic announcements, which represent large risks. We also provide an estimate of the coefficient of relative ambiguity aversion and show how uncertainty varies across different announcements. Our results suggest that the macroeconomic announcement premium arises at least partly because of an increase in the price of uncertainty. One implication is that a fundamental benefit of securities markets is that they break large risks into small ones by allowing frequent trading, thereby reducing discount rates.