Fundamentals of Finance FIN 300 1 Homework #4 Due on 4/26 Instructions: Please upload your answers to Blackboard as a pdf file (either scan your handwritten answers or type them in a document). The...

Need help on question 2,3, and 4



Fundamentals of Finance FIN 300 1 Homework #4 Due on 4/26 Instructions: Please upload your answers to Blackboard as a pdf file (either scan your handwritten answers or type them in a document). The grade of this assignment will take into account the neatness of the presentation, the clarity of the analysis and the exactness of computations. All answer must be your own. 1. Suppose your expectations regarding the stock price are as follows: State of the Market Probability HPR (including dividends) Boom 0.35 44.50% Normal growth 0.3 14.00% Recession 0.35 -16.50% Compute the mean and standard deviation of the HPR on stocks. 2. Derive the probability distribution (i.e. fill up the table below) of the 1-year HPR on a 30-year U.S. Treasury bond with an 8% coupon if it is currently selling at par and the probability distribution of its price a year from now is as follows: Economy Probability YTM Price HPR Boom 0.2 11% Normal Growth 0.5 8% Recession 0.3 7% Assume that the entire 8% coupon is paid at the end of the year rather than every 6 months over a principal of $100. Compute the expected return and standard deviation of returns of the bond. 3. Suppose the economy can only be in one of the following two states: (i) Boom or “good” state and (ii) Recession or “bad” state. Each of the states can occur with an equal probability. At the beginning of a month, you can purchase the following two securities in the market: • Security 1: It is currently trading at $4. At the end of the month, the stock price is expected to increase by $10 in the good state and expected to remain unchanged in the bad state. • Security 2: It is also currently trading at $5. This asset has payoffs that are like an insurance contract. It yields a positive return when the economic conditions are poor. At the end of the month, the price of security 2 is expected to remain unchanged in the good state and expected to increase by $10 in the bad state. a) Compute the expected returns (not prices) of securities 1 and 2. b) Compute the standard deviations of returns for securities 1 and 2. c) Compute the covariance and the correlation between the returns of two securities. d) Why does the second security have a higher price? Please explain briefly. Fundamentals of Finance FIN 300 2 4. A pension fund manager is considering three mutual funds. The first is a stock fund, the second is a long-term government and corporate bond fund, and the third is a T-bill money market fund that yields a rate of 8%. The probability distribution of the risky funds is as follows: Fund Expected Return Standard Deviation Stock fund (S) 20% 30% Bond fund (B) 12% 15% The correlation between the returns of S and B is 0.10. a) Tabulate the investment opportunity set of the two risky funds: Proportion in Stock Fund Proportion in Bond Fund Expected Return Standard Deviation 0% 100% 20% 80% 40% 60% 60% 40% 80% 20% 100% 0% b) Using the table above, what are the investment proportions in the minimum-variance portfolio of the two risky funds? 5. The average annual rate of return on the S&P 500 portfolio over the past 85 years has averaged roughly 8% more than the Treasury bill return, and the S&P 500 standard deviation has been about 20% per year. Assume these values are representative of investors' expectations for future performance and that the current T-bill rate is 5%. Calculate the expected return, variance and standard deviation of portfolios invested in T-bills and the S&P 500 index with weights as follows: WBills WIndex Expected Return Variance Standard Deviation 0.0 1.0 0.2 0.8 0.4 0.6 0.6 0.4 0.8 0.2 1.0 0.0 Fundamentals of Finance FIN 300 3 6. Suppose that there are many stocks in the security market and that the characteristics of stocks A and B are given as follows: Stock Expected Return Standard Deviation A 10% 5% B 15% 10% The correlation between the stock returns is -1. Suppose that it is possible to borrow at the risk-free rate, ????. What must be the value of the risk-free rate? (Hint: Think about constructing a risk-free portfolio from stocks A and B.) 7. Consider an economy spanned by two risky assets A and B that have the following characteristics: • ??(????) = 0.08; ????2 = 0.04 • ??(????) = 0.15; ????2 = 0.10 • ????,?? = − 1 a) Suppose that you aim for an expected return of 20%, what should be the composition of your portfolio? What is the risk of that portfolio? Explain how this strategy can be possible. b) Draw the investment opportunity set and clearly identify the minimum variance portfolio, its composition and its characteristics. c) Is there a risk-free asset in this economy? If so, what is its return?