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# expected returns

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A. In order for you to be indifferent between the after tax returns on a corporate bond paying 8.5% and a tax-exempt municipal bond paying 6.12%, what would your tax bracket need to be?

b. What is the bond equivalent yield of a T-Bill that is selling for \$9,453 and has 173 days remaining until maturity?

2) You purchased 100 shares of ABC common stock on margin at \$70 per share. Assume the initial margin is 50% and the maintenance margin is 30%. Below what stock price level would you get a margin call? Assume the stock pays no dividend; ignore interest on margin.

3) Discuss the consistency of mutual fund performance results, as studied by Goetzmann and lbbotson (1994) and Malkiel (1995).

4) You have been given this probability distribution for the holding period return for XYZ stock:

State of the Economy Probability HPR

Boom .30 18%
Normal growth .50 12%
Recession .20 -5%

Requirement: Calculate the expected returns and standard deviation for XYZ stock.
Prob HPR(%) Prob×HPR HPR-Exp.Ret (HPR-Exp.Ret)2 Prob×(HPR-Exp.Ret)2
0.30 18 5.4 7.6 57.76 17.328
0.50 12 6.0 1.6 2.56 1.28
0.20 -5 -1.0 .-15.4 237.16 47.432
Exp. Ret. = 10.4% Variance = 66.04
Std. Dev.= 8.13

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#### Solution Preview

a. In order for you to be indifferent between the after tax returns on a corporate bond paying 8.5% and a tax-exempt municipal bond paying 6.12%, what would your tax bracket need to be?

The after tax return on the bond is R = Rb*(1-t). To make it equal to the tax-exempt bond, we need the following equation:
Rb*(1-t) = 6.12%
8.5%*(1-t) = 6.12%
(1-t) =6.12% /8.5%
t = 0.28
so your tax bracket needs to be 28%

b. What is the bond equivalent yield of a T-Bill that is selling for \$9,453 and has 173 days remaining until maturity?

PV = -9453
FV = 10000
Number of period = 173 / 365 = 0.474
By a financial calculator, or EXCEL command "=RATE(0.474,,-9453,10000)", we can compute interest rate = 12.6%, which is the bond equivalent yield (assuming there is no coupon payment during the 173 days).

2) You purchased 100 shares of ABC common stock on margin at \$70 per share. Assume the initial margin is 50% and the maintenance margin is 30%. Below what stock price level would you get a margin call? Assume the stock pays no dividend; ignore interest on margin.

Number of shares is N = 100
P ...

#### Solution Summary

The expert calculates the expected returns and standard deviation.

\$2.19