Winter 2011 Assignment 1 solutions.S11

Winter 2011 Assignment 1 solutions.S11 - AP/ADMS 3531,...

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AP/ADMS 3531, Winter 2011 Solutions to homework assignment #1 Guidelines for rounding: If you are using percents, for example 1.23%, then you should use two decimal places for your calculations. If the same number is converted to decimal form, as 0.0123, then use four decimal places throughout your calculations. Dollar amounts, for example a share price of $12.34, should be rounded to the nearest cent. However, if there are no pennies, such as 100 shares worth $12 per share, then use integer dollar amounts. 1. (15 points) You are provided with the following probability distributions on the returns on three stocks: B, U and Y. State of Economy Probability of State (%) Return on Stock B (%) Return on Stock U (%) Return on Stock Y (%) Excellent 20 50 35 25 Good 35 20 30 20 Moderate 25 16 -10 8 Poor 20 -30 0 5 (a) Calculate the expected return and the standard deviation of returns of each stock. E (R B ) = 0.20(50%) + 0.35(20%) + 0.25(16%) + 0.20(-30%) = 15% σ 2 B = [0.20(0.50-0.15) 2 + 0.35(0.20-0.15) 2 + 0.25(0.16-0.15) 2 + 0.20(-0.30-0.15) 2 ] = 0.0659 σ B = (0.0659 ) ½ = 0.659 or 25.67% E (R U ) = 0.20(35%) + 0.35(30%) + 0.25(-10%) + 0.20(0%) = 15% σ 2 U = [0.20(0.35-0.15) 2 + 0.35(0.30-0.15) 2 + 0.25(-0.10-0.15) 2 + 0.20(0-0.15) 2 ] = 0.0360 σ U = (0.0360) ½ = 0.1897 or 18.97% E (R Y ) = 0.20(25%) + 0.35(20%) + 0.25(8%) + 0.20(5%) = 15% σ 2 Y = [0.20(0.25-0.15) 2 + 0.35(0.20-0.15) 2 + 0.25(0.08-0.15) 2 + 0.20(0.05-0.15) 2 ] = 0.0061 σ Y = (0.0061) ½ = 0.0781 or 7.81% (b) Suppose you want to invest in any one of the three stocks listed above. Which one should you select? Why? Invest in Stock Y: lowest risk for the same expected return.
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(c) Now, you are familiar with the benefits of investing in a diversified portfolio. You are evaluating three portfolios. Portfolio (1) is invested equally in Stock B and in Stock U. Portfolio (2) consists of 30% in B and the rest in Y. Portfolio (3) consists of 80% in U and the rest in Y. Assume that the correlations of the returns between B and U, B and Y and U and Y are 0.00, -0.60 and 0.60, respectively. (Use these assumed correlation values to answer the question, even though they are different from correlations which could be calculated from the data above.) Which portfolio should you invest in? Why? E (R 1 ) = 0.50(15%) + 0.50(15%) = 15% σ 2 1 = (0.5) 2 (0.0659) + (0.5) 2 (0.0360) + 2(0.5) (0.5) (0.2567) (0.1897) (0) = 0.0255 σ 1 = (0.0255) ½ = 0.1597 or 15.97% E (R 2 ) = 0.30(15%) + 0.70(15%) = 15% σ 2 2 = (0.3) 2 (0.0659) + (0.7) 2 (0.0061) + 2(0.3) (0.7) (0.2567) (0.0781) (-0.60) = 0.0039 σ 2 = (0.0039) ½ = 0.0624 or 6.24% E (R 3 ) = 0.80(15%) + 0.20(15%) = 15% σ 2 3 = (0.8) 2 (0.0360) + (0.2) 2 (0.0061) + 2(0.8) (0.2) (0.1897) (0.0781) (0.60) = 0.0 261 σ 3 = (0.0261) ½ = 0.1616 or 16.16% Invest in Portfolio (2): lowest risk for the same expected return. 2. (15 points) Consider three of the portfolios presented in Table 2.9 on page 52 of the textbook,
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Winter 2011 Assignment 1 solutions.S11 - AP/ADMS 3531,...

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