Question

Stock A and Stock B produced the following returns during the past five years (Year -1 is one year ago, Year -2 is two years ago, and so forth):

Year Stock A's Returns Stock B's Return

-1	-16.00%	-13.00%
-2	31..40	28.00
-3	14.00	28.00
-4	-1.20	-7.40
-5	25.00	26.30

a. Calculate the average rate of return for each stock during the past five years.

b. Assume that someone held a portfolio consisting of 50 percent Stock A and 50 percent Stock B. What would have been the realized rate of return on the portfolio in each year for the past five years? What would have been the average return on the portfolio 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. If you are a risk-averse investor, would you prefer to hold Stock A, Stock B, or the portfolio? Why?

e. Assume a third stock, Stock C, is available for inclusion in the portfolio. Stock C produced the following returns during the past five years: Year Stock C’s Return -1 30.00% -2 –2.50 -3 11.28 -4 29.30 -5 –15.00 Input these values and calculate the average return, standard deviation, and coefficient of variation for Stock C.

f. Assume that the portfolio now consists of 33.33 percent Stock A, 33.33 percent Stock B, and 33.34 percent Stock C. How does this composition affect the portfolio return, standard deviation, and coefficient of variation versus when 50 percent was invested in A and in B?

g. Make some other changes in the portfolio, making sure that the percentages sum to 100 percent. For example, enter 25 percent for Stock A, 25 percent for Stock B, and 50 percent for Stock C. Notice that P r ˆ remains constant and that sp changes. Why do these results occur?

h. In part b, you should see that the standard deviation of the portfolio decreased only slightly because Stocks A and B were highly positively correlated with each other. The addition of Stock C causes the standard deviation of the portfolio to decline dramatically, even though sC = sA = sB. What does this change indicate about the correlation between Stock C and Stocks A and B?

i. Would you prefer to hold a portfolio consisting only of Stocks A and B or a portfolio that also includes Stock C? If others react similarly, how might this fact affect the stocks’ prices and rates of return?

Answer 1

a)

average=sum of returns/no. of returns

Stock A:

=> (-16+31.4+14-1.20+25)/5

=> (53.2)/5

=> 10.64%

Stock B:

=> (-13+28+28-7.4+26.3)/5

=> (61.9)/5

=> 12.38%

b) realized rate of return

year -1: (-16.00 – 13.00) / 2 = -14.5%

year -2: (31.40 + 28.00) / 2 = 29.70%

year -3: (14.00 + 28.00) / 2 = 21%

year -4: (-1.20 – 7.40) / 2 = -4.3%

year -5: (25.00 + 26.30) / 2 = 25.65%

average return on the portfolio:

Avg = (-14.5 + 29.70 + 21 – 4.3 + 25.65) / 5 = 11.51%

c) standard deviation of returns for each stock and for the portfolio:

Stock A:

=>

s= 9.67

Stock B:

=>

s= 10.35

Portfolio:

s= 9.83

d) coefficient of variation for each stock and for the portfolio:

Stock A: CV = 9.67 / 10.64= 0.9088

Stock B: CV = 10.35 / 12.38 = 0.83602

Portfolio: CV = 9.83 / 11.51 = 0.8149

Assuming you are a risk-averse investor, would you prefer to hold Stock A, Stock B, or the portfolio? Why?

A risk-averse investor would prefer to hold the portfolio as it has the lowest coefficient of variation. The coefficient of variation measures the risk assumed per unit of return. In this case, the average rate of return is the same for all three options, but the portfolio has a smaller standard deviation, leading to a smaller coefficient of variation, thereby indicating that the portfolio carries less risk compared to either Stock A or Stock B.

e)Stock C:

average return=(30-2.50+11.28+29.3-15)/5

=> avg=10.616

standard deviation=

s= 9.85

CV=9.85/10.61=0.9283