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Investment Management Tutorial

You are faced with the probability distribution on the stock market index fund given below. Suppose the price of a put option on a share of the index fund with an exercise price of $110 and maturity of one year is $12. The current share price is $100 and a cash dividend of $4 per share is expect

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Investment Management Tutorial

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    1. Investment Management Tutorial October 10, 2008 James Kozyra

    2. You are faced with the probability distribution on the stock market index fund given below. Suppose the price of a put option on a share of the index fund with an exercise price of $110 and maturity of one year is $12. The current share price is $100 and a cash dividend of $4 per share is expected to be paid during the year. Chapter 5 Problem 16

    3. What is the probability distribution of the HPR on the put option Chapter 5 Problem 16

    4. What is the probability distribution of the HPR on a portfolio consisting of one share of the index fund and a put option? The cost of one share and a put is $112 ($110 + $12). Chapter 5 Problem 16

    5. Chapter 5 Problem 16

    6. Two investment advisors are comparing performance. One averaged a 19% rate of return and the other a 16% rate of return. However, the beta of the first investor was 1.5, whereas the that of the second was 1. a) Can you tell which investor was a better predictor of individual stocks (aside from the issue of general movements in the market)? Chapter 8 Problem 14

    7. a) To determine which investor was the better predictor we look at their abnormal return, which is the ex-post alpha. This means that the abnormal return is the difference between the actual return and the return predicted by the SML. Without the parameters of the equation (risk-free rate and market rate of return) we cannot determine which investor was more accurate. Chapter 8 Problem 14

    8. b) If the t-bill rate were 6% and the market return during the period were 14%, which investor would be the superior stock selector? Investor 1 = 19 [6 + 1.5(14-6)] = 19 18 = 1% Investor 2 = 16 [6 + 1(14-6)] = 16 14 = 2% Chapter 8 Problem 14

    9. c) What if the t-bill rate were 3% and the market return were 15%? Investor 1 = 19 [3 + 1.5(15-3)] = 19 21 = -2% Investor 2 = 16 [3 + 1(15-3)] = 16 15 = 1% Chapter 8 Problem 14

    10. First case the second investor has the larger abnormal return and appears to be the superior stock selector. He appears to have done a better job finding underpriced stocks. Second case the second investor again is the superior stock selector. The first investors predictions appear to be worthless. Chapter 8 Problem 14

    11. You manage a risky portfolio with an expected rate of return of 18% and a standard deviation of 28%. The t-bill rate is 8%. A passive portfolio has an expected rate of return of 13% and a standard deviation of 25%. Your client ponders whether to switch the 70% that he has invested in your risky portfolio to the passive portfolio. Chapter 6 Problem 21

    12. a) Explain to your client the disadvantages of the shift. Current Portfolio E(r) = (.3 x 8%) + (.7 x 18%) = 15% Std Dev = .7 x 28% = 19.6% Portfolio after the shift E(r) = (.3 x 8%) + (.7 x 13%) = 11.5% Std Dev = .7 x 25% = 17.5% Chapter 6 Problem 21

    13. a) Therefore, the shift entails a decline in the expected return from 14% to 11.5% and a decline in the standard deviation from 19.6% to 17.5%. The disadvantage is that the client could achieve an 11.5% expected return in my portfolio, with a lower standard deviation. Chapter 6 Problem 21

    14. We first must write the mean of the complete portfolio as a function of the proportions invested in my portfolio, y: E(r) = 8 + y(18-8) E(r) = 8 + 10y Given the target 11.5% return, the proportion that must be invested in the fund is determined as follows: 11.5 = 8 + 10y Chapter 6 Problem 21

    15. 11.5 = 8 + 10y 10y = 11.5 8 10y = (11.5 8) / 10 y = 0.35 The standard deviation of the portfolio would thus be 9.8% (.35 x 28%). Achieving the 11.5% return can be done with a standard deviation of 9.8% in my portfolio as opposed to 17.5% in the passive portfolio. Chapter 6 Problem 21

    16. b) Show your client the maximum fee you could charge that would still leave him/her at least as well off investing in your fund. (Hint: the fee will lower the slope of the CAL by reducing E(r) net of the fee. The fee would reduce the reward-to-variability ratio (CAL slope). Clients will be indifferent if the slope of the after-fee CAL and the CML are equal. Chapter 6 Problem 21

    17. Let f denote the fee Slope of the CAL with the fee = (18 8 f) / 28 = (10 f) / 28 Slope of the CML (no fee required) = (13 8) / 25 = .20 We must set the slopes to be equal. Chapter 6 Problem 21

    18. (10 f) / 28 = 0.20 (10 f) = 28 x 0.20 (10 f) = 5.6 f = 10 5.6 f = 4.4 Therefore the maximum fee that can be charged to make the client indifferent between portfolios is 4.4% per year. Chapter 6 Problem 21

    19. You are considering investing $1,000 in a T-bill that pays 0.05 and a risky portfolio, P, constructed with two risky securities, X and Y. The weights of X and Y in P are 0.6 and 0.4, respectively. X has an expected rate of return of 0.14 and variance of 0.01, and Y has an expected rate of return of 0.10 and a variance of 0.0081. Portfolio Selection Problem

    20. If you want to form a portfolio with an expected rate of return of 10%, what percentages of your money must you invest in the t-bill, X, and Y respectively if you keep X and Y in the same proportions to each other as in portfolio P (60:40). E(r) Portfolio = (0.6 x 14%) + (0.4 x 10%) E(r) T-bill = w x 5% Portfolio Selection Problem

    21. Portfolio Selection Problem

    22. Portfolio Selection Problem

    23. What would be the dollar value of your position in X, Y, and the t-bills, respectively if you decide to hold a portfolio that has an expected outcome of $1,120 HPR = ($1,120 - $1,000) / $1,000 HPR = 12% Portfolio Selection Problem

    24. Portfolio Selection Problem

    25. Portfolio Selection Problem

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