We introduce ambiguity in conjunction with risk to study the relation between risk, ambiguity, and expected returns. Distinguishing between ambiguity and attitudes toward ambiguity, we develop an empirical methodology for measuring the degree of ambiguity and for assessing attitudes toward ambiguity from market data. The main findings indicate that ambiguity in the equity market is priced. Introducing ambiguity alongside risk provides stronger evidence on the role of risk in explaining expected returns in the equity markets. The findings also indicate that investors’ level of aversion to or love for ambiguity is contingent on the expected probability of favorable returns.

We examine the practice of resetting the terms of previously-issued executive stock options. We identify properties of reset options, develop a model for valuing resettable options, and characterize the firms that have reset options. We find the vast majority of options are reset at-the-money, resulting, on average, in the strike price dropping 40%. Our valuation model suggests that resetting has only a small impact on the ex-ante value of an option award, but the ex-post gain can be substantial. Finally, we find resetting has a strong negative relation with firm performance even after correcting for industry performance.

We examine the relation between the prices of Japanese stocks traded on the Tokyo Stock Exchange (TSE) as reflected in the Nikkei Stock Average (NSA) stock index and the prices of the NSA futures contract traded on the Singapore International Monetary Exchange (SIMEX). Since the inception of trading in September 1986, the NSA futures contract has generally sold at a discount relative to its theoretical value. Trading restrictions and transaction costs may explain some of this mispricing, which has been declining over time, as in the U.S. markets.