Question

1. We observe the following annual returns on a stock in the past three years. The annual risk- free rate is 5%. Year 2016 2016 | Realized Return | 10% - 2017 300% 2018 -10% 2018 | (a) What is the arithmetic average stock return? (4%) (b) What is the geometric average stock return? (4%) (c) What are the sample mean and standard deviation of the stock return? (8%) (d) What is the stock's Sharpe ratio? (4%) (e) Jessica invests 50% of her money in stocks and 50% of her money in the risk-free asset. What are the expected return, standard deviation, and Sharpe ratio of her portfolio? (10 %) (f) Jessica plans to invest $1 million in the stock and the risk-free asset. If her risk aversion A=5, how many dollars will she invest in the stock and how many dollars will she invest in the risk-free asset in her optimal portfolio? (10%)

Answer 1

157 5% 158 Risk-free rate 159 160 YEAR 161 2016 2017 163 2018 164 165 (a) Arithmetic average retun RETURN 10% 30% -10% 10% 166 8.77% 15.00% 167 (b) Geometric average return 168 169 (c) 170 Sample Mean 171 172 Standard deviation 173 174 (d) 175 Sharpes Ratio 20.00% 0.50

157 CALCULATIONS 158 0.05 RETURN 0.1 0.3 -0.1 =AVERAGE(C161:C163) Risk-free rate 159 160 YEAR 161 2016 162 2017 163 2018 164 165 (a) Arithmetic average retun 166 (167(b) Geometric average return 168 169 (c) 170 Sar Sample Mean 171 172 Standard deviation 173 174 (d) 175 Sharpes Ratio =((1+C161)*(1+C162)*(1+C163))^(1/3)-1 =(C161+C162+C163)/(3-1) ESTDEV.S(C161:C163) =(C170-C158)/C172