Problem: Stockholder Risk This table summarizes the performance of four mutual f

Question

Problem: Stockholder Risk

This table summarizes the performance of four mutual funds over a three-year period.

______ A) What is the risk premium on the “market portfolio” (represented here by the Stock Market Index)?

______ B) According to the Capital Asset Pricing Model, what rate of return must the Aggressive Growth Fund earn to adequately compensate fund holders for market risk?

   C) Suppose that you held only two investments in your portfolio, Treasury bills and the Aggressive Growth Fund. If you earned a return of 16% over the past year,

______ 1. What proportion of your portfolio was invested in the AGF?

______ 2. What was your portfolio BETA?

   D) Consider two funds, the Emerging Markets Fund and the Value Fund.

______ 1. Estimate alpha for each fund. (Alpha = actual return – required return)

______

______ 2. On a return/risk basis, which fund has posted the most impressive performance?

______ 3. Is either fund “outperforming” the market? If so, which one(s)?

   E) Compare the Value Fund and the Aggressive Growth Fund.

______ 1. Which fund is likely to perform better in a “bear” (declining) market? Briefly explain.

______ 2. Which fund probably exposes its fund holders to larger capital gains taxes? Briefly explain.

Explanation / Answer

A )risk premium on the “market portfolio” = market return - t bill yield = 13.5 - 4.5 = 9%

B)  rate of return for Aggressive Growth Fund = t bill rate + beta *(market risk premium) = 3.5 + 1.33*9 = 15.47%

C)

I) let x be proportion of investment in aggressive growth fund and 1-x be proportion invested in t bills

return on growth fund * x + t bill yield * (1 - x) = 16

20.1 * x + 4.5 ( 1-x) = 16

there fore x= 0.737

and 1-x = .2628

II) Portfolio beta = x* aggresive fund beta + (1-x) tbill beta

= .737 * 1.33 + .2628*0

= 0.98021

D)

I) required rate of return for: emerging markets fund ,re= t bill rate + beta *(market risk premium) = 3.5 + 1.5*9 = 17%

Value fund rv= t bill rate + beta *(market risk premium) = 3.5 + 0.84*9 = 11.06%

emerging markets fund alpha = actual return - re = 14.7 - 17 = -2.3%

value fund alpha = actual return - rv= 16.8 - 11.06 = 5.74%

II) Return/risk for emerging markets fund = 14.7/22 = .6681

Return/risk for value fund = 16.8/9.6 = 1.75

value fund is performing better as it has greater return/risk ratio

III) Both funds are outperforming the market as their returns are more than the market return

E) 1)In a bear market the market portfolio has low or negative returns. Fund with low correlation to the market portfolio should perform better in the bear market. Thus global stock fund should perform better as it has the lowest beta.

2) aggresive growth fund should have highest capitals gains tax as it has highest return of all funds thus greatest capital gains and thus highest taxes paid out on the capital gains

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