expected profit on the $100,000 investment portfolio is $22,000: 122,000 - 100,000. The variance, 2, of the portfolios payoff is calculated as the expected value of the squared deviation of each possible outcome from the mean:   2 p[W1 E(W)]2 (1 p) [W2 E(W)]2 .6(150,000 122,000)2 .4(80,000 122,000)2 1,176,000,000   The standard deviation, , which is the square root of the variance, is therefore $34,292.86. Clearly, this is risky business: The standard deviation of the payoff is large, much larger than the expected profit of $22,000. Whether the expected profit is large enough to justify such risk depends on the alternative portfolios.       1 Chapters 6 through 8 rely on some basic results from elementary statistics. For a refresher, see the Quantitative Review in the Appendix at the end of the book. II. Portfolio Theory 6. Risk and Risk Aversion The McGraw−Hill Companies, 2001           156 PART II Portfolio Theory     Let us suppose Treasury bills are one alternative to the risky portfolio. Suppose that at the time of the decision, a one-year T-bill offers a rate of return of 5%; $100,000 can be in- vested to yield a sure profit of $5,000. We can now draw the decision tree.         $100,000   A. Invest in risky prospect p .6 profit $50,000   1 p .4 profit $20,000 B. Invest in risk- profit $5,000 free T-bill