BUAD 306 Fall 2015 Professor Kenneth Ahern Practice Problems 6 Answers 1 Define and explain the three forms of market efficiency ANSWER The current stock price reflects the following information for each form of efficiency 2 Shawn earned an average return of 14 6 percent on his investments over the past 20 years while the S P 500 a measure of the overall market only returned an average of 13 9 percent Explain how this can occur if the stock market is efficient ANSWER An investor can purchase securities that have a higher level of risk than the overall market In an efficient market these securities will earn a higher return over the long term as compensation for the assumption of the increased risk This is the first lesson of the capital markets There is a reward for bearing risk 3 Describe the difference between systematic and unsystematic risk and give an example of each type of risk ANSWER Systematic risk is risk that cannot be avoided through diversification Unsystematic risk or idiosyncratic risk is risk that can be avoided through diversification An example of systematic risk is a worldwide panic which causes prices to fall An example of an unsystematic risk is the death of a CEO 4 You want your portfolio beta to be 0 90 Currently your portfolio consists of 4 000 invested in stock A with a beta of 1 47 and 3 000 in stock B with a beta of 0 54 You have another 9 000 to invest and want to divide it between an asset with a beta of 1 74 and a risk free asset How much should you invest in the risk free asset ANSWER BetaPortfolio 0 90 4 000 16 000 1 47 3 000 16 000 0 54 x 16 000 1 74 9 000 x 16 000 0 Investment in risk free asset 9 000 3 965 52 5 034 48 5 You recently purchased a stock that is expected to earn 30 percent in a booming economy 9 percent in a normal economy and lose 33 percent in a recessionary economy There is a 5 percent probability of a boom and a 75 percent chance of a normal economy What is your expected rate of return on this stock ANSWER E r 0 05 0 30 0 75 0 09 0 20 0 33 1 65 percent 6 What is the variance of the returns on a portfolio comprised of 5 400 of stock G and 6 600 of stock H ANSWER E r Boom 5 400 5 400 6 600 0 21 6 600 5 400 6 600 0 13 0 166 E r Normal 5 400 5 400 6 600 0 13 6 600 5 400 6 600 0 05 0 086 E r Portfolio 0 36 0 166 0 64 0 086 0 1148 VarPortfolio 0 36 0 166 0 1148 2 0 64 0 086 0 1148 2 0 001475 7 Your portfolio is comprised of 40 percent of stock X 15 percent of stock Y and 45 percent of stock Z Stock X has a beta of 1 16 stock Y has a beta of 1 47 and stock Z has a beta of 0 42 What is the beta of your portfolio ANSWER BetaPortfolio 0 40 1 16 0 15 1 47 0 45 0 42 0 87 8 The risk free rate of return is 3 9 percent and the market risk premium is 6 2 percent What is the expected rate of return on a stock with a beta of 1 21 ANSWER E r 0 039 1 21 0 062 11 40 percent 9 A stock has an expected return of 11 percent the risk free rate is 5 2 percent and the market risk premium is 5 percent What is the stock s beta ANSWER E Ri 0 11 0 052 i 0 04 i 1 16