PS 4 Solutions.pdf - Solutions to Problem Set 4 Corporate...

This preview shows 1 out of 3 pages.

Solutions to Problem Set 4 Corporate Finance, Prof. William Diamond 1. Because the proceeds from Year 1 are reinvested in Year 2 etc., the proper summary measure for returns is the geometric average of the annual returns. Thus, the geometric average returns are: Fund A = (1 . 16 × 1 . 10 × 1 . 14 × 1 . 02 × 1 . 04) 1 / 5 - 1 = . 090631 Fund B = (1 . 3 × . 9 × 1 . 28 × 1 . 17 × . 98) 1 / 5 - 1 = . 114196 The amount of money at the end can be calculated in either of 2 ways for each fund: Fund A = $100(1 . 16 × 1 . 10 × 1 . 14 × 1 . 02 × 1 . 04) = $154 . 308 or $100(1 . 090631) 5 = $154 . 308. Fund B = $100(1 . 3 × . 9 × 1 . 28 × 1 . 17 × . 98) = $171 . 715 or $100(1 . 114196) 5 = $171 . 715. 2. (a) The general formula for expected return for a two-security portfolio is: ¯ R p = X 1 ¯ R 1 + X 2 ¯ R 2 Also, the variance of return for a two-security portfolio is: σ 2 p = X 2 1 σ 2 1 + X 2 2 σ 2 2 + 2 X 1 X 2 σ 1 σ 2 ρ. Recall that X 2 = 1 - X 1 . Substituting the numerical values given in the question into these equations pro- duces the following results (remember to square terms or take the square root as necessary). Expected Standard Return Deviation i) .15 .200 ii) .20 .200 iii) .25 .245 iv) .30 .316 v) .35 .400 1
Image of page 1

Subscribe to view the full document.

3. Using the formulas ¯ R p = X 1 ¯ R 1 + X 2 ¯ R 2 and σ 2 p = X 2 1 σ 2 1 + X 2 2 σ 2 2 + 2 X 1 X 2 σ 1 σ 2 ρ we calculate ρ = - 1 ρ = 0 ρ = . 2 ρ = . 5 ρ = 1 ¯ R p . 142 . 142 . 142 . 142 . 142 σ p . 102 . 158 . 166 . 179 . 198 Note that the mean does not depend on the correlation. On the other hand, the higher is the correlation, the higher is the portfolio standard deviation. For stocks that move closely together, there are fewer gains from diversification from combining them into a portfolio. The standard deviation when ρ = 1 represents the highest standard deviation for this portfolio. Notice from the formula that the portfolio variance is increasing in ρ . Therefore σ p = ( X 2 1 σ 2 1 + X 2 2 σ 2 2 + 2 X 1 X 2 σ 1 σ 2 ρ ) 1 2 ( X 2 1 σ 2 1 + X 2 2 σ 2 2 + 2 X 1 X 2 σ 1 σ 2 ) 1 2 = X 1 σ 1 + X 2 σ 2 4. (a) i. The investor should choose security 2 because security 2 has a higher expected return than security 1 ( ¯ R 2 = . 16 while ¯ R 1 = . 10).
Image of page 2
Image of page 3
You've reached the end of this preview.

{[ snackBarMessage ]}

What students are saying

  • Left Quote Icon

    As a current student on this bumpy collegiate pathway, I stumbled upon Course Hero, where I can find study resources for nearly all my courses, get online help from tutors 24/7, and even share my old projects, papers, and lecture notes with other students.

    Student Picture

    Kiran Temple University Fox School of Business ‘17, Course Hero Intern

  • Left Quote Icon

    I cannot even describe how much Course Hero helped me this summer. It’s truly become something I can always rely on and help me. In the end, I was not only able to survive summer classes, but I was able to thrive thanks to Course Hero.

    Student Picture

    Dana University of Pennsylvania ‘17, Course Hero Intern

  • Left Quote Icon

    The ability to access any university’s resources through Course Hero proved invaluable in my case. I was behind on Tulane coursework and actually used UCLA’s materials to help me move forward and get everything together on time.

    Student Picture

    Jill Tulane University ‘16, Course Hero Intern