of the risky portfolio over investing in safe T-bills is   $22,000 $5,000 $17,000   meaning that one can earn a risk premium of $17,000 as compensation for the risk of the investment. The question of whether a given risk premium provides adequate compensation for an investments risk is age-old. Indeed, one of the central concerns of finance theory (and much of this text) is the measurement of risk and the determination of the risk premiums that investors can expect of risky assets in well-functioning capital markets.     CONCEPT C H E C K ☞ QUESTION 1 What is the risk premium of the risky portfolio in terms of rate of return rather than dollars?     Risk, Speculation, and Gambling   One definition of speculation is "the assumption of considerable business risk in obtaining commensurate gain." Although this definition is fine linguistically, it is useless without first specifying what is meant by "commensurate gain" and "considerable risk." By "commensurate gain" we mean a positive risk premium, that is, an expected profit greater than the risk-free alternative. In our example, the dollar risk premium is $17,000, the incremental expected gain from taking on the risk. By "considerable risk" we mean that the risk is sufficient to affect the decision. An individual might reject a prospect that has a positive risk premium because the added gain is insufficient to make up for the risk involved. To gamble is "to bet or wager on an uncertain outcome." If you compare this definition to that of speculation, you will see that the central difference is the lack of "commensurate gain." Economically speaking, a gamble is the assumption of risk for no purpose but en- joyment of the risk itself, whereas speculation is undertaken in spite of the risk involved be- cause one perceives a favorable risk-return trade-off. To turn a gamble into a speculative prospect requires an adequate risk premium to compensate risk-averse investors for the risks they bear. Hence, risk aversion and speculation are not inconsistent. In some cases a gamble may appear to the participants as speculation. Suppose two in- vestors disagree sharply about the future exchange rate of the U.S. dollar against the British pound. They may choose to bet on the outcome. Suppose that Paul will pay Mary $100 if the value of £1 exceeds $1.70 one year from now, whereas Mary will pay Paul if the pound is worth less than $1.70. There are only two relevant outcomes: (1) the pound will exceed $1.70, or (2) it will fall below $1.70. If both Paul and Mary agree on the probabilities of the two possible outcomes, and if neither party anticipates a loss, it must be that they assign