Business Finance Answers_Part_62

Business Finance Answers_Part_62 - CHAPTER 13 B-245 22. We...

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CHAPTER 13 B-245 22. We know that the reward-to-risk ratios for all assets must be equal. This can be expressed as: [E(R A ) – R f ]/ A = [E(R B ) – R f ]/ß B The numerator of each equation is the risk premium of the asset, so: RP A / A = RP B / B We can rearrange this equation to get: B / A = RP B /RP A If the reward-to-risk ratios are the same, the ratio of the betas of the assets is equal to the ratio of the risk premiums of the assets. 23. a. We need to find the return of the portfolio in each state of the economy. To do this, we will multiply the return of each asset by its portfolio weight and then sum the products to get the portfolio return in each state of the economy. Doing so, we get: Boom: E(R p ) = .4(.24) + .4(.36) + .2(.55) = .3500 or 35.00% Normal: E(R p ) = .4(.17) + .4(.13) + .2(.09) = .1380 or 13.80% Bust: E(R p ) = .4(.00) + .4(–.28) + .2(–.45) = –.2020 or –20.20% And the expected return of the portfolio is: E(R p ) = .35(.35) + .50(.138) + .15(–.202) = .1612 or 16.12% To calculate the standard deviation, we first need to calculate the variance. To find the variance, we find the squared deviations from the expected return. We then multiply each possible squared deviation by its probability, than add all of these up. The result is the variance. So, the variance and standard deviation of the portfolio is: 2 p = .35(.35 – .1612) 2 + .50(.138 – .1612) 2 + .15(–.202 – .1612) 2 2 p = .03253 p = (.03253) 1/2 = .1804 or 18.04% b. The risk premium is the return of a risky asset, minus the risk-free rate. T-bills are often used as
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Business Finance Answers_Part_62 - CHAPTER 13 B-245 22. We...

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