10. You are an investment advisor at PT Securities Lad. You are considering two equity stocks for recommendation to Mr. Dela-Brown, a client of PT Securities. You assessed the risk profile of Mr. Dela- Brown and found that his risk-aversion index is negative 1.5. Below is information about the two equity stocks you are considering. 1. Masophe Corporation: The expected retum on this stock is 25% with a variance of 0.36. 2. Jul-Tech Ltd: The expected return on this stock is 15% with a standard deviation of 10%. Required: (a) Distinguish between speculation and gambling. (b) Would you say that Mr. Dela-Brown is a risk-averse investor? Explain (c) Compute the expected utility from each stock. Considering the expected utility, which of the two stocks would Mr. Dela-Brown be more motivated to invest in 11. You are an investment analyst. HH Hozokawa mutual fund engages you to analyse risk associated with investments of the fund and advise its fund managers accordingly. The value of assets currently held by the fund is GHS200,000. You gather the following historical rates of return on the portfolio for each quarter of the last 2 years. Quarter 1. Yr1 2. Yril 3. Yr1 4. Yr1 1. Yr2 2. Yr2 4. Yr2 HPR 0.200 0.168 0.172 0.208 0.220 0.176 0.248 0.140 Required: (a) Calculate the arithmetic average return (b) Calculate the geometrie average retum. (c) Calculate the standard deviation of the distribution of returns. (d) Suppose the annual simple interest rate on the GoG 91-day Treasury bill is 18 percent. Estimate the Sharpe ratio for the fund. What can you say about the performance of the fund? 3 Page (e) In testing the normality of the distribution of returns on the fund, you run descriptive analysis in Excel, which returned the output displayed below: HPR Mean 0.2165 Standard Error 0.020078 Median 0.204 Mode WN/A Standard Deviation 0.056788 Sample Variance 0.003225 Kurtosis 3.2048:49 Skewness 1.707022 Range 0.172 Minimum 0.168 Maximum 0.34 Sum 1.732 Count 8 Confidence Level (95.0%) 0.047476 Required: 1. Comment on the kurtosis of the distribution of retums. 11. Comment on the skewness of the distribution of returns. What can you say about the variance of the distribution and the corresponding standard deviation as estimators of risk associated with the fund? 12. You work with an investment company that manages a mutual fund. The mutual fund invests in equity stocks listed on the Ghana Stock Exchange. Currently the expected retum on the fund is 18% with standard deviation of 12%. The risk-free rate of return is 14%. Required: (a) Dr. Olufunmi has GHS20,000 to invest in both your fund and the risk-free asset. He demands a required rate of retum of 16% on the complete portfolio i) How much of his funds must be put into the risky portfolio and how much must be put into the risk-free asset? ii) Considering your answer in i) above and the earlier assumptions, what is the standard deviation of the complete portfolio? (b) If his risk-aversion index is 4, what is the maximum amount of his funds should be put into the risky portfolio? Explain in a few words. 13. Ms Tonia Anderson buys 182-day treasury bills at the price of GHS8,800 today. She expects to receive GHS10,000 at end of the investment period. Inflation is expected to be 17% in the coming year. Required: (a) Compute the holding period return on the investment. (b) Compute the annualised nominal rate of return on the investment. (c) Compute the annual real rate of retum on the investment. 10. You are an investment advisor at PT Securities Lad. You are considering two equity stocks for recommendation to Mr. Dela-Brown, a client of PT Securities. You assessed the risk profile of Mr. Dela- Brown and found that his risk-aversion index is negative 1.5. Below is information about the two equity stocks you are considering. 1. Masophe Corporation: The expected retum on this stock is 25% with a variance of 0.36. 2. Jul-Tech Ltd: The expected return on this stock is 15% with a standard deviation of 10%. Required: (a) Distinguish between speculation and gambling. (b) Would you say that Mr. Dela-Brown is a risk-averse investor? Explain (c) Compute the expected utility from each stock. Considering the expected utility, which of the two stocks would Mr. Dela-Brown be more motivated to invest in 11. You are an investment analyst. HH Hozokawa mutual fund engages you to analyse risk associated with investments of the fund and advise its fund managers accordingly. The value of assets currently held by the fund is GHS200,000. You gather the following historical rates of return on the portfolio for each quarter of the last 2 years. Quarter 1. Yr1 2. Yril 3. Yr1 4. Yr1 1. Yr2 2. Yr2 4. Yr2 HPR 0.200 0.168 0.172 0.208 0.220 0.176 0.248 0.140 Required: (a) Calculate the arithmetic average return (b) Calculate the geometrie average retum. (c) Calculate the standard deviation of the distribution of returns. (d) Suppose the annual simple interest rate on the GoG 91-day Treasury bill is 18 percent. Estimate the Sharpe ratio for the fund. What can you say about the performance of the fund? 3 Page (e) In testing the normality of the distribution of returns on the fund, you run descriptive analysis in Excel, which returned the output displayed below: HPR Mean 0.2165 Standard Error 0.020078 Median 0.204 Mode WN/A Standard Deviation 0.056788 Sample Variance 0.003225 Kurtosis 3.2048:49 Skewness 1.707022 Range 0.172 Minimum 0.168 Maximum 0.34 Sum 1.732 Count 8 Confidence Level (95.0%) 0.047476 Required: 1. Comment on the kurtosis of the distribution of retums. 11. Comment on the skewness of the distribution of returns. What can you say about the variance of the distribution and the corresponding standard deviation as estimators of risk associated with the fund? 12. You work with an investment company that manages a mutual fund. The mutual fund invests in equity stocks listed on the Ghana Stock Exchange. Currently the expected retum on the fund is 18% with standard deviation of 12%. The risk-free rate of return is 14%. Required: (a) Dr. Olufunmi has GHS20,000 to invest in both your fund and the risk-free asset. He demands a required rate of retum of 16% on the complete portfolio i) How much of his funds must be put into the risky portfolio and how much must be put into the risk-free asset? ii) Considering your answer in i) above and the earlier assumptions, what is the standard deviation of the complete portfolio? (b) If his risk-aversion index is 4, what is the maximum amount of his funds should be put into the risky portfolio? Explain in a few words. 13. Ms Tonia Anderson buys 182-day treasury bills at the price of GHS8,800 today. She expects to receive GHS10,000 at end of the investment period. Inflation is expected to be 17% in the coming year. Required: (a) Compute the holding period return on the investment. (b) Compute the annualised nominal rate of return on the investment. (c) Compute the annual real rate of retum on the investment