in a risk-free asset paying an annual interest rate of 6%. There is a probability of .001 that your house will burn to the ground and its value will be reduced to zero. With a log utility of end-of-year wealth, how much would you be willing to pay for in- surance (at the beginning of the year)? (Assume that if the house does not burn down, its end-of-year value still will be $200,000.) 2. If the cost of insuring your house is $1 per $1,000 of value, what will be the certainty equivalent of your end-of-year wealth if you insure your house at: a. 1⁄2 its value. b. Its full value. c. 11⁄2 times its value.     SOLUTIONS TO CONCEPT C H E C K S B.1. a. U(W) W U(50,000) 50,000 223.61 U(150,000) 387.30 b. E(U) (.5 223.61) (.5 387.30) 305.45 c. We must find WCE that has utility level 305.45. Therefore WCE 305.45 WCE 305.452 $93,301 d. Yes. The certainty equivalent of the risky venture is less than the expected out- come of $100,000. e. The certainty equivalent of the risky venture to this investor is greater than it was for the log utility investor considered in the text. Hence this utility func- tion displays less risk aversion. II. Portfolio Theory 7. Capital Allocation between the Risky Asset and the Risk−Free Asset The McGraw−Hill Companies, 2001         C H A P T E R S E V E N       CAPITAL ALLOCATION BETWEEN THE RISKY ASSET AND THE RISK-FREE ASSET     Portfolio managers seek to achieve the best possible trade-off between risk and re- turn. A top-down analysis of their strategies starts with the broadest choices con- cerning the makeup of the portfolio. For example, the capital allocation decision