wk 5 ans for Q25 - Homework Assignment 6: Answers Financial...

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Homework Assignment 6: Answers Financial Management Ning Gong Part 1: The questions you can do it after Week 8’s lecture. 1: Challenge questions 1(a,b,c) and 2 (actually this is a pretty easy question. It is the Capital Allocation Line) on page 178 of Chapter 7. _________________________ 1. a. In general: Portfolio variance = σ P 2 = x 1 2 σ 1 2 + x 2 2 σ 2 2 + 2x 1 x 2 ρ 12 σ 1 σ 2 Thus: σ P 2 = (0.5 2 )(0.530 2 )+(0.5 2 )(0.475 2 )+2(0.5)(0.5)(0.72)(0.530)(0.475) σ P 2 = 0.21726 Standard deviation = σ P = 0.466 = 46.6% b. We can apply the formula for a portfolio of three securities. One of these securities, T-bills, has zero risk and, hence, zero standard deviation. σ P 2 = x 1 2 σ 1 2 + x 2 2 σ 2 2 + x 3 2 σ 3 2 2x 1 x 2 ρ 12 σ 1 σ 2 + 2x 1 x 3 ρ 13 σ 1 σ 3 + 2x 2 x 3 ρ 23 σ 2 σ 3 Thus: σ P 2 = (1/3) 2 (0.530 2 )+(1/3) 2 (0.475 2 )+2(1/3)(1/3)(0.72)(0.530)(0.475) σ P 2 = 0.09656 Standard deviation = σ P = 0.311 = 31.1% Another way to think of this portfolio is that it is comprised of one-third T-Bills and two-thirds a portfolio which is half Dell and half Microsoft. Because the risk of T-bills is zero, the portfolio standard deviation is two- thirds of the standard deviation computed in Part (a) above: Standard deviation = (2/3)(0.466) = 0.311 = 31.1% c. With 50 percent margin, the investor invests twice as much money in the portfolio as he had to begin with. Thus, the risk is twice that found in Part (a) when the investor is investing only his own money: Standard deviation = 2 × 46.6% = 93.2% 2. For a two-security portfolio, the formula for portfolio risk is: Portfolio variance = x 1 2 σ 1 2 + x 2 2 σ 2 2 + 2x 1 x 2 ρ ρ 12 σ 1 σ 2
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If security one is Treasury bills and security two is the market portfolio, then σ 1 is zero, σ 2 is 20 percent. Therefore: Portfolio variance = x 2 2 σ 2 2 = x 2 2 (0.20) 2 Standard deviation = 0.20x 2 (Note: In my lecture slide 7.6, I give the above expression right away.) The second asset has a risk premium
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This note was uploaded on 02/22/2011 for the course FIN 535 taught by Professor Edward during the Spring '11 term at Chaminade University.

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wk 5 ans for Q25 - Homework Assignment 6: Answers Financial...

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