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Unformatted text preview: UNIVERSITY OF TORONTO Joseph L. Rotman School of Management Dec. 21, 2008 Ezer/Kan/Florence RSM332 FINAL EXAMINATION Pomorski/Zhou SOLUTIONS 1. (a) In a year, bond A will have one year to maturity and bond B will have two years to maturity. If the economy is strong, bond A ’s YTM will be 11.1% and its price will be P strong A, 1 = $1000 / (1+0 . 111) = $900 . 09. If the economy is weak, bond B ’s YTM will be 6.3% and its price will be P weak B, 1 = $1000 / (1 + 0 . 063) 2 = $884 . 98. (b) The expected next year’s price of bond A is E [ P A, 1 ] = 0 . 4 × 1000 1 + 0 . 111 + 0 . 6 × 1000 1 + 0 . 037 = 938 . 628 . The expected holding period return on bond A is E [ R A ] = E [ P A, 1 ] P A, P A, = 938 . 628 856 . 80 856 . 80 ≈ 9 . 55% . (c) The current value of your portfolio is $856.80+$800.00=$1,656.80. The value of this portfolio next year will depend on the economic conditions: Portfolio value Portfolio return Strong economy 900.09+713.34=1613.43 1613 . 43 1656 . 80 1 ≈  2 . 618% Weak economy 964.32+884.98=1849.30 1849 . 30 1656 . 80 1 ≈ 11 . 619% Thus, the expected return of the portfolio is μ p = 0 . 4 ×  . 02618 + 0 . 6 × . 11619 ≈ . 05924 . The variance of portfolio returns is σ 2 p = 0 . 4 × ( . 02618 . 05924) 2 + 0 . 6 × (0 . 11619 . 05924) 2 = 0 . 004865 . 1 The standard deviation is the square root of the variance, or about 6.97%. Note: you can also solve this question by computing portfolio weights of bonds A and B and then using the formulas for portfolio mean and standard deviation. Keep in mind that the portfolio is not equalweighted: the weight of bond A is about 52% and the weight of bond B is about 48%. (d) Bond C will deliver exactly $1,000 next year. We know the payoff up front, so this bond is riskfree in a oneyear portfolio: the standard deviation of returns on bond C is 0. Denote the weight of bond C in your new portfolio by w (the weight of your portfolio from part (c) is 1 w ). We want w to satisfy: σ p = q w 2 × 0 + (1 w ) 2 × . 004865 =  1 w  × . 0697 = 0 . 03227 . While this equation has two solutions ( w = 0 . 537 and w = 1 . 463), we need to choose the solution with w < 1. This is because we are already holding bonds A and B in our portfolio, so we have 1 w > 0 which implies w < 1. Thus, your holdings of bond C should account for 53.7% of the overall value of your portfolio. (e) Denote the number of units of bond C by x . The value of your position in bond C is 915 x . The total value of your portfolio is then 1656 . 8 + 915 x and the weight of bond C is w = 915 x/ (1656 . 8 + 915 x ). We need to solve: w = 915 x 1656 . 8 + 915 x = 0 . 537 ⇒ x = 2 . 1 ....
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This note was uploaded on 04/26/2011 for the course RSM 332 taught by Professor Raymondkan during the Spring '08 term at University of Toronto.
 Spring '08
 RAYMONDKAN

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