EC3114 - Financial Economics Vinay P NUNDLALL Problem Set 2 Question 1 The table below gives the monthly (adjusted) closing value of a stock market index over the period December 2016 through to August 2018 (twenty one months). The closing price given has already been adjusted for dividends paid throughout the period. Assume the monthly risk-free rate is 0.1% throughout the period. Date 12/3/2016 1/2/2017 5879.8 2/1/2017 5884.3 3/3/2017 5702.1 4/1/2017 6087.3 5/1/2017 6053.5 6/2/2017 5625.9 7/1/2017 5411.9 8/1/2017 5636.6 9/1/2017 4902.5 10/1/2017 4377.3 11/3/2017 4288 12/1/2017 4434.2 1/2/2018 4149.6 2/2/2018 3830.1 3/2/2018 3926.1 4/1/2018 4243.7 5/1/2018 4417.9 6/1/2018 4249.2 7/1/2018 4608.4 8/3/2018 4908.9 Adjusted Close 6456.9 Preferably, use Excel to do the following calculations: (a) The one-month Holding Period Return (HPR) for each month. (b) Calculate the Expected one-month HPR. (c) Calculate the level of risk incurred by holding the index over this period. (d) If you were to invest £100 at the beginning, what would be your final wealth at the end of the period? (e) What is the monthly risk premium obtained from holding this security? (f) Using the one-month statistics, calculate the Sharpe Ratio. (g) Would investing in the index at the beginning of the period be considered a gamble or a speculation? (h) What could influence the decision behind such an investment? 1
Question 2 You are an investor with a utility function U = 6 + 0.5W1/3 where W is your level of wealth, and U is utility. You are faced with the following gamble: Probability Payoff (£) Win 0.2 1,000 Lose 0.8 -512 (a) Calculate the expected payoff of the gamble. (b) Calculate the expected utility of the gamble. (c) Calculate the utility of expected payoff of the gamble. (d) Determine this investor's attitude to risk. (e) Determine which type of marginal utility of wealth this utility function exhibits. (f) Calculate the certainty equivalent of this gamble. (g) Calculate the Markowitz risk premium for this gamble. Interpret the risk premium in this particular case. (h) Explain the difference between a risk-loving investor and a risk-neutral investor. Question 3 Suppose Financia chooses to invest half of her wealth in a stock market fund with expected return of 10% and the other half in a risk-free asset with return of 2%. (a) What is the expected return on her portfolio? (b) Now, suppose she could borrow, at the risk-free rate, in order to invest in the stock market fund, an amount equal to: 1. half of her wealth 2. twice her wealth 3. ten times her wealth What is the portfolio's expected return in each case? Additional problems for Practice: these will not be covered in the Seminar, but you should attempt them to gain familiarity with the concepts. Question 4 Bodie, Kane, and Marcus, Global Edition, Chapter 6, Problem 4 Question 5 Bodie, Kane, and Marcus, Global Edition, CFA Problems, Problems 1 to 3 2