6 Risk and Risk Aversion 157     p .5 to each outcome. In that case the expected profit to both is zero and each has entered one side of a gambling prospect. What is more likely, however, is that the bet results from differences in the probabilities that Paul and Mary assign to the outcome. Mary assigns it p .5, whereas Pauls assess- ment is p .5. They perceive, subjectively, two different prospects. Economists call this case of differing beliefs "heterogeneous expectations." In such cases investors on each side of a financial position see themselves as speculating rather than gambling. Both Paul and Mary should be asking, "Why is the other willing to invest in the side of a risky prospect that I believe offers a negative expected profit?" The ideal way to resolve het- erogeneous beliefs is for Paul and Mary to "merge their information," that is, for each party to verify that he or she possesses all relevant information and processes the information properly. Of course, the acquisition of information and the extensive communication that is required to eliminate all heterogeneity in expectations is costly, and thus up to a point het- erogeneous expectations cannot be taken as irrational. If, however, Paul and Mary enter such contracts frequently, they would recognize the information problem in one of two ways: Ei- ther they will realize that they are creating gambles when each wins half of the bets, or the consistent loser will admit that he or she has been betting on the basis of inferior forecasts.       CONCEPT C H E C K ☞ QUESTION 2 Assume that dollar-denominated T-bills in the United States and pound-denominated bills in the United Kingdom offer equal yields to maturity. Both are short-term assets, and both are free of default risk. Neither offers investors a risk premium. However, a U.S. investor who holds U.K. bills is subject to exchange rate risk, because the pounds earned on the U.K. bills eventually will be exchanged for dollars at the future exchange rate. Is the U.S. investor engaging in speculation or gambling?     Risk Aversion and Utility Values   We have discussed risk with simple prospects and how risk premiums bear on speculation. A prospect that has a zero risk premium is called a fair game. Investors who are