the portfolio. The certainty equivalent rate of return is a value that, if it is received with certainty, would yield the same utility as the risky port- folio. 5. Hedging is the purchase of a risky asset to reduce the risk of a portfolio. The negative correlation between the hedge asset and the initial portfolio turns the volatility of the hedge asset into a risk-reducing feature. When a hedge asset is perfectly negatively cor- related with the initial portfolio, it serves as a perfect hedge and works like an insurance contract on the portfolio.     KEY TERMS risk premium risk averse utility certainty equivalent rate risk neutral risk lover mean-variance (M-V) criterion indifference curve hedging diversification expected return variance standard deviation covariance correlation coefficient     PROBLEMS 1. Consider a risky portfolio. The end-of-year cash flow derived from the portfolio will be either $70,000 or $200,000 with equal probabilities of .5. The alternative risk-free investment in T-bills pays 6% per year. a. If you require a risk premium of 8%, how much will you be willing to pay for the portfolio? b. Suppose that the portfolio can be purchased for the amount you found in (a). What will be the expected rate of return on the portfolio? II. Portfolio Theory 6. Risk and Risk Aversion The McGraw−Hill Companies, 2001           168 PART II Portfolio Theory     c. Now suppose that you require a risk premium of 12%. What is the price that you will be willing to pay? d. Comparing your answers to (a) and (c), what do you conclude about the relationship between the required risk premium on a portfolio and the price at which the portfo- lio will sell? 2. Consider a portfolio that offers an expected rate of return of 12% and a standard devi- ation of 18%. T-bills offer a risk-free 7% rate of return. What is the maximum level of risk aversion for which the risky portfolio is still preferred to bills?