Solutions+Problem+Set+8

Solutions+Problem+Set+8 - E 120 Problem Set 8 Solutions...

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Unformatted text preview: E 120 : Problem Set 8 Solutions - Fall 2010 Problem 1 Return from 1 / 2 / 03 to 2 / 5 / 03 given by R 1 = 30 . 67 + 0 . 17 33 . 88- 1 =- . 08973 Return from 2 / 5 / 03 to 5 / 14 / 03 given by R 2 = 29 . 49 + 0 . 17 30 . 67- 1 =- . 03293 Return from 5 / 14 / 03 to 8 / 13 / 03 given by R 3 = 32 . 38 + 0 . 17 29 . 49- 1 = 0 . 10376 Return from 8 / 13 / 03 to 11 / 12 / 03 given by R 4 = 39 . 07 + 0 . 17 32 . 38- 1 = 0 . 21186 Return from 11 / 12 / 03 to 1 / 2 / 04 given by R 5 = 41 . 99 39 . 07- 1 = 0 . 07474 Return for the year is: (1 + R 1 )(1 + R 2 )(1 + R 3 )(1 + R 4 )(1 + R 5 )- 1 = 26 . 55% Problem 2 a. E [ R ] = 0 . 15(0 . 6)- . 1(0 . 4) = 0 . 05 Standard Deviation = p . 6(0 . 15- . 05) 2 + 0 . 4(- . 1- . 05) 2 = 0 . 12247 Because all S firms in the portfolio move together there is no diversification benefit. So the standard deviation of the portfolio is the same as the standard deviation of the stocks - 12 . 25%. b. E[R] = 0 . 15(0 . 6)- . 1(0 . 4) = 0 . 05 Standard Deviation = p . 6(0 . 15- . 05) 2 + 0 . 4(- . 1- . 05) 2 = 0 . 12247 Type I stocks move independently. Hence the standard deviation of the portfolio is SD(Portfolio of 20 Type I stocks) = . 12247 √ 20 = 2 . 74% 1 Problem 3 (a) The average return of Stock A is given by (- 8 + 20 + 5- 5- 2) 5 = 2% The average return of Stock B is given by (21- 5- 3 + 1- 4) 5 = 2% The variance of Stock A’s return is given by (- . 08- . 02) 2 + (0 . 20- . 02) 2 + (0 . 05- . 02) 2 + (- . 05- . 02) 2 + (- . 02- . 02) 2 4 = 0 . 01245 Volatility of A = Standard deviation of Stock A’s return = √ . 01245 = 11 . 16%....
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Solutions+Problem+Set+8 - E 120 Problem Set 8 Solutions...

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