Question

1. There are two mutual fund managers. Manager 1 earned 15% in the past year, whereas manager 2 earned 10% in the past year. The beta of the first manager is 1.1, whereas the beta for the second manager is 0.8. Assume CAPM is the correct model. Which manager is a better stock selector (i.e. who performed better on a risk-adjusted basis)?

2. There are two mutual fund managers. Manager 1 earned 18% in the past year, whereas manager 2 earned 7% in the past year. The beta of the first manager is 2.1, whereas the beta for the second manager is 0.9. Assume the expected market risk premium is 12% and the risk-free rate is 5%. Assume CAPM is the correct model. Which manager is a better stock selector (i.e. who performed better on a risk-adjusted basis)?

3. A discount bond has a quoted yield to maturity of 10% and a par amount of $1000. What do you know about a) the price of the bond, and b) the coupon?

Answer 1

Answer (1)

Let us assume,if Risk free rate is 3%, and the Market risk premium is 8%. (This is common for both the managers).

Now,

CAPM for Manager 1 = 3% + 1.1 (8%) = 11.8%

CAPM for Manager 2 = 3% + 0.8 (8%) = 9.4%

On a risk adjusted basis, Manager 1 and Manager 2 were required to earn 11.8% and 9.4% respectively.

Risk Adjusted Actual Excess Return = Actual Return - CAPM requried return

Manager 1 = 15% - 11.8% = 3.20%

Manager 2 = 10% - 9.4% = 0.60%

Answer : Manager 1 earned higher excess return on risk adjusted basis, therefore Manager 1 is a better stock selector.

Answer (2)

CAPM for Manager 1 = 5% + 2.1 (12%) = 30.20%

CAPM for Manager 2 = 5% + 0.9 (12%) = 15.80%

Risk Adjusted Actual Excess Return = Actual Return - CAPM requried return

Manager 1 = 18% - 30.20% = -12.20%

Manager 2 = 7% - 15.80% = -8.80%

Answer : Manager 2 earned lower negative excess return on risk adjusted basis, therefore Manager 2 is a better stock selector.

Answer (3)

Discount Bond

YTM = 10%

Par Amount = $1000

(a) The price of the bond:

~ The price of the bond is less than $1000.

~ Because the bond is mentioned as a "discount bond", it means that it is trading at a price which is less than the par value, that is, less than $1000.

(b) The coupon:

~ The coupon of the bond is less than 10%.

~ When the bond is a discount bond, that is, when the bond is trading at less than par value, it means that the bond's YTM > bond's coupon. Therefore, the coupon rate will be less than the YTM, that is, less than 10%.