EC3114 - Financial Economics 1 Fall 2020 Vinay P NUNDLALL Problem Set 2 Solutions Question 1 Date 12/3/20 16 1/2/201 7 2/1/201 7 3/3/201 7 4/1/201 7 6087.3 0.067554059 5/1/201 7 6/2/201 7 5625.9 -0.070636822 0.929363178 7/1/201 7 8/1/201 7 5636.6 0.041519614 1.041519614 9/1/201 7 10/1/20 17 11/3/20 17 12/1/20 17 1/2/201 8 2/2/201 8 3830.1 -0.076995373 0.923004627 3/2/201 8 4/1/201 8 5/1/201 8 6/1/201 8 7/1/201 8 8/3/201 8 Adjusted Close 6456.9 5879.8 -0.089377255 5884.3 5702.1 -0.030963751 6053.5 -0.005552544 5411.9 -0.038038358 0.961961642 4902.5 -0.130238087 0.869761913 4377.3 -0.107129016 0.892870984 4288 -0.020400704 0.979599296 4434.2 4149.6 -0.064182942 0.935817058 3926.1 4243.7 4417.9 4249.2 -0.038185563 0.961814437 4608.4 0.084533559 4908.9 Returns (discrete g) 0.000765332 0.034095149 1.034095149 0.02506462 1.02506462 0.080894526 1.080894526 0.041049085 1.041049085 0.065207013 1.065207013 Gross HPR (1+HPR) 21 month HPR 0.910622745 1.000765332 0.969036249 1.067554059 0.994447456 1.084533559 -0.23974 1
Expected 1 month HPR -0.011550873 Risk (std deviation) 0.065217091 If we invest 100 at the beginning, end wealth = Risk Free Rate 0.001 Risk Premium = Expected Return - Risk Free Rate -0.01255087 -0.1924476 Sharpe Ratio 76.02564698 a. The one-month HPR for each month is the monthly return in each month from holding the index - see column 'Returns'. There should be 20 of them, given that there are 21 monthly prices. b. Expected 1-month HPR = Average of 1-month HPR's = - 0.0116 or -1.16% c. Level of risk incurred is the standard deviation of returns = 0.0652 or 6.52% d. If you invest £100 at the beginning of the period in the index at the price of 6,456.9, given that the last period price is 4,908.9, the final wealth will be £100*(4908.9/6456.9) = £76.026 e. Risk Premium obtained = Expected HPR - Risk-Free Rate = - 0.0116 - 0.001 = - 0.0126 or - 1.26% 0.0652 -0.1924 f. Sharpe Ratio = Risk Risk Premium -0.0126 g. Investing in a financial asset is speculation, as opposed to a gamble. The index is a financial asset; the expected return over this period is negative, but this is only a small window in the whole history of the index. h. The investment in such an asset is usually influenced by the investor's level of risk aversion (or attitude towards risk). 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 gamblefi Probability Payoff (£) Win 0.2 1,000 Lose 0.8 -512 (a) Calculate the expected payoff of the gamble. 2
E(Payoff) = 0.2*1,000 + 0.8* (-512) = 200 - 409.6 = - £209.6 (b) Calculate the expected utility of the gamble. Utility at $1,000 = 6 + 0.5(1,000)1/3 = 6 + 0.5(10) = 11 Utility at -$512 = 6 + 0.5(-512)1/3 = 6 + 0.5(-8) = 2 E(Utility) = 0.2*(11) + 0.8(2) = 2.2 + 1.6 = 3.8 (c) Calculate the utility of expected payoff of the gamble. U{E[Payoff]} = 6 + 0.5 (-209.6)1/3 = 3.03 (d) Determine this investor's attitude to risk. At the point where