Question

Stocks A and B have the following historical returns:

Year –rA   –r

2009 −18% −24%
2010 44 24
2011 −22 −4
2012 22 8
2013 34    56

a. Calculate the average rate of return for each stock during the 5-year period. Assume
that someone held a portfolio consisting of 50% of Stock A and 50% of Stock B.
What would have been the realized rate of return on the portfolio in each year?
What would have been the average return on the portfolio for the 5-year period?

b. Now calculate the standard deviation of returns for each stock and for the portfolio.
Use Equation 6-5.

2 Σ (Ft--Avg) t-l (6-5) Estimated σ n- 1

c. Looking at the annual returns data on the two stocks, would you guess that
the correlation coefficient between returns on the two stocks is closer to 0.8
or to −0.8?

d. If you added more stocks at random to the portfolio, which of the following is
the most accurate statement of what would happen to σp?

(1) σp would remain constant.
(2) σp would decline to somewhere in the vicinity of 20%.
(3) σp would decline to zero if enough stocks were included.

Answer 1

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