Realized Rates of Return Stocks a and B Have the Following Historical Returns

Realized rates of return Stocks A and B have the following historical returns: Year Stock A's Returns, rA Stock B's Returns, rB 2001 (18.00%) (14.50%) 2002 33.00 21.80 2003 15.00 30.50 2004 (0.50) (7.60) 2005 27.00 26.30 a. Calculate the average rate of return for each stock during the period 2001 through 2005. b. Assume that someone held a portfolio consisting of 50 percent of Stock A and 50 percent of Stock B. What would the realized rate of return on the portfolio have been in each year? What would the average return on the portfolio have been during this period? c. Calculate the standard deviation of returns for each stock and for the portfolio. d. Calculate the coefficient of variation for each stock and for the portfolio. e. Assuming you are a risk-averse investor, would you prefer to hold Stock A, Stock B, or the portfolio? Why? a,b,c, & d)

kA kB Portfolio 2001 (18.00%) (14.50%) (16.25%) 2002 33.00 21.80 27.40 2003 15.00 30.50 22.75 2004 (0.50) (7.60) (4.05) 2005 27.00 26.30 26.65

Mean 11.30 11.30 11.30 Std. Dev. 20.79 20.78 20.13 Coef. Var. 1.84 1.84 1.78

e. A risk-averse investor would choose the portfolio over either Stock A or Stock B alone, since the portfolio offers the same expected return but with less risk. This result occurs because returns on A and B are not perfectly positively correlated (rAB = 0.88).

Expected returns Stocks X and Y have the following probability distributions of expected future returns: Probability X Y 0.1 (10%) (35%) 0.2 2 0 0.4 12 20 0.2 20 25 0.1 38 45 a. Calculate the expected rate of return, rˆY, for Stock Y. (rˆX _ 12%.) b. Calculate the standard deviation of expected returns, _X , for Stock X. (_Y _ 20.35%.) Now calculate the coefficient of variation for Stock Y. Is it possible that most investors might regard Stock Y as being less risky than Stock X? Explain.

n ˆ  a. k  Piki . i  1

ˆ kY = 0.1(-35%) + 0.2(0%) + 0.4(20%) + 0.2(25%) + 0.1(45%) = 14% versus 12% for X.

n  ˆ 2 b.  = (ki k) Pi . i 1

2 2 2 2 σX = (-10% - 12%) (0.1) + (2% - 12%) (0.2) + (12% - 12%) (0.4) + (20% - 12%)2(0.2) + (38% - 12%)2(0.1) = 148.8%.

X = 12.20% versus 20.35% for Y.

CVX = X/kˆ X = 12.20%/12% = 1.02, while

CVY = 20.35%/14% = 1.45.

If Stock Y is less highly correlated with the market than X, then it might have a lower beta than Stock X, and hence be less risky in a portfolio sense.

7-8 Yield to call Six years ago, the Singleton Company issued 20-year bonds with a 14 percent annual coupon rate at their $1,000 par value. The bonds had a 9 percent call premium, with 5 years of call protection. Today, Singleton called the bonds. Compute the realized rate of return for an investor who purchased the bonds when they were issued and held them until they were called. Explain why the investor should or should not be happy that Singleton called them.

The rate of return is approximately 15.03 percent, found with a calculator using the following inputs: N = 6; PV = -1000; PMT = 140; FV = 1090; I = ? Solve for I = 15.03%.