Hi,

I need help with problems 1-6, especially with #1 part A and #4 part B where it ask to draw the opportunity investment set.

Thanks!

Assignment 2, FIN 310 Prof. Hanh Le Due at the start of class, Wednesday, March 2, 2016 Fill in the following information on the rst page of your submission: Name: Class section and time: Students you work with on this assignment: Follow these instructions: Write all your answers on a separate sheet. Show all workings except for questions 2 and 3. Write legibly. Hand in individual work, even if you work in a group. 1. (1.5 pt) The expected return on the S&P 500 index is 12%. The return on the T-bill is 5%. The standard deviation of return on the S&P 500 index is 18%. Investors can form portfolios from these 2 securities. Suppose investors have a utility function of the following form: 1 U = E(Rp ) A 2 (Rp ) 2 where Rp is the return on the portfolio. Suppose that the coecients of risk aversion for George and Ann are 1 and 2, respectively. Answer the following questions: (a) Draw the investment opportunity set (b) What are the optimal portfolios for the two investors? (In other words, what are the optimal portfolio weights they put in the risk free asset and the S&P 500 index?) Calculate the utility level these investors obtain from these portfolios. (c) Suppose we are told that an investor invests optimally and that he puts 20% in the S&P 500 and 80% in the T-Bill. What must be his coecient of risk aversion? 1 2. (0.25 pt) A portfolio is composed of two stocks, A and B. Stock A has a standard deviation of return of 25% while stock B has a standard deviation of return of 5%. Stock A comprises 20% of the portfolio while stock B comprises 80% of the portfolio. If the variance of return on the portfolio is .0050, the correlation coecient between . the returns on A and B is (a) -.225 (b) -.474 (c) .474 (d) .225 3. (0.25 pt) A portfolio is composed of two stocks, A and B. Stock A has a standard deviation of return of 5% while stock B has a standard deviation of return of 15%. The correlation coecient between the returns on A and B is .5. Stock A comprises 40% of the portfolio while stock B comprises 60% of the portfolio. The variance of . return on the portfolio is (a) .0035 (b) .0085 (c) .0094 (d) .0103 4. (1 pt) The expected returns and standard deviation of returns for two securities are as follows: Security Z Security Y Expected Return 15% 28% Standard Deviation 20% 30% The correlation between the returns is + .5. (a) Calculate the expected return and standard deviation for the following portfolios: i. ii. iii. iv. v. all in Z 0.5 in Z and 0.5 in Y .35 in Z and .65 in Y .25 in Z and .75 in Y all in Y (b) Draw the investment opportunity set. (c) Which portfolios might be held by an investor who likes high expected return and low standard deviation? 2 5. (0.5 pt) Consider the following data: Expected Return Russell Fund 18% Windsor Fund 15% S&P Fund 9% Standard Deviation 12% 10% 6% The correlation between the returns on the Russell Fund and the S&P Fund is .7. The rate on T-bills is 6%. Which of the following portfolios would you prefer to hold in combination with T-bills and why? (a) Russell Fund (b) Windsor Fund (c) S&P Fund (d) A portfolio of 30% Russell Fund and 70% S&P Fund. 6. (1.5 pt) Bob and Ann both make optimal portfolio allocations. Bob has $ 1000 to invest, Ann has $ 2000 to invest. There are 3 assets that they can invest in: a risk free asset with a rate of return of 5%, and two risky assets with the following properties: Asset A has expected return of 10% and standard deviation of return of 12%. Asset B has expected return of 17% and standard deviation of return of 20%. The correlation between the return on asset A and return on asset B is 0.2. Assume now that Bob's optimal portfolio is $ 300 in the risk free asset, $ 300 in asset A and $ 400 in asset B. Ann's optimal portfolio has $ 900 invested in asset B, answer the following questions: (a) How much does Ann invest in the risk free asset? How much does Ann invest in asset A? (b) Which investor is more risk averse? Why? (c) Compute the expected return and standard deviation of return on Bob's and Ann's optimal portfolios. 3