Problem 3.
The following are the monthly rates of return for Madison Cookies and for Sophie Electric during a six-month period.
Madison Sophie
Month Cookies Electric
1 -0.04 0.07
2 0.06 -0.02
3 -0.07 -0.1
4 0.12 0.15
5 -0.02 -0.06
6 0.05 0.02
Compute the following:
a. Average mnthly rate of return Ri for each stock
b. Standard deviation of returns for each stock
c. Covariance between the rates of return
d. The correlation coefficient between the rates of return
What level of correlation did you expect? How did your expectations compare with the computed
correlation? Would these two stocks be good choices for diversification? Why or Why not?

The following are monthly percentage price changes for four market indexes.

Month DJIA S&P 500 Russell 2000 Nikkei
1 0.03 0.02 0.04 4.00
2 9.07 0.06 0.10 (0.02)
3 (0.02) (0.01) (0.04) 0.07
4 0.01 0.03 0.03 0.02
5 0.05 0.04 0.11 0.02
6 (0.06) (0.04) (0.08) 0.06

Compute the following:
a. Average monthly rate of return for each index.
b. Standard deviation for each index
c. Covariance between the rates of return for the following indexes:
DJIA – S&P500
S&P 500 – Russell 2000
S&P 500 – Nikkei
Russell 2000 – Nikkei
d. The correlation coefficients for the same four combinations
e. Using the answers from parts (a), (b), and (d), calculate the expected return and standard deviation of a portfolio consisting of equal parts of:
(1) the S&P and the Russell 2000, and
(2) the S&P and the Nikkei.
Discuss the two portfolios.

The standard deviation of Shamrock Corp. stock is 19 percent. The standard deviation of
Cara Co. stock is 14 percent. The covariance between these two stocks is 100. What is the
correlation between Shamrock and Cara Stock?

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