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Question: Consider the monthly returns of Ford Motor Company and General Electric shown on the next page. A...

Consider the monthly returns of Ford Motor Company and General Electric shown on the next page. An Excel spreadsheet with the data is also attached. Assume an economy where only these two stocks exist.
a. Calculate their average return, standard deviation and correlation?

b. What is the standard deviation of a mean-variance efficient portfolio that targets an expected return of 0.015?

c. What is the expected return of a mean-variance efficient portfolio whose standard deviation is 0.05?

DATE	FORD	GE
12-Jul	-0.0365	-0.0043
12-Aug	0.0162	-0.0019
12-Sep	0.0557	0.1048
12-Oct	0.1369	-0.0727
12-Nov	0.026	0.0033
12-Dec	0.131	0.0024
13-Jan	0.0077	0.0615
13-Feb	-0.0263	0.0507
13-Mar	0.0428	-0.0043
13-Apr	0.0426	-0.0359
13-May	0.151	0.0462
13-Jun	-0.0134	0.0026
13-Jul	0.0976	0.0509
13-Aug	-0.0409	-0.0505
13-Sep	0.042	0.0406
13-Oct	0.0202	0.0942
13-Nov	-0.0018	0.0199
13-Dec	-0.0966	0.0596
14-Jan	-0.0224	-0.1035
14-Feb	0.0287	0.0223
14-Mar	0.0136	0.0165
14-Apr	0.0433	0.0386
14-May	0.018	-0.0037
14-Jun	0.0487	-0.0108
14-Jul	-0.0055	-0.043
14-Aug	0.0229	0.033
14-Sep	-0.1505	-0.0054
14-Oct	-0.0389	0.0074
14-Nov	0.1164	0.0263
14-Dec	-0.0146	-0.0374

Answer 1

a) Average return and std deviation of the returns of Ford and GE are:

FORD	GE
0.0205	0.0102
0.0652	0.0458

Correlation of the returns, $\rho$ = 0.1007

b) Let the weights of Ford and GE in the portfolio be w1 and w2 respectively.

We need 0.015 = w1 * 0.0205 + w2 * 0.0102, where w1 + w2 = 1

=> 0.015 = w1 * 0.0205 + (1-w1) * 0.0102  

=> w1 = 0.466, w2 = 1 - 0.466 = 0.534

Now, variance of the portfolio,

$\sigma_p^2$ = w1² * $\sigma_1^2$ + w2² * $\sigma_2^2$ + w1w2
01
$\sigma_2$$\rho$

= 0.001596

=> Std deviation of the portfolio = = 0.0399

P

c) Std deviation of the new portfolio = 0.05

=> 0.05 = w1² * $\sigma_1^2$ + w2² * $\sigma_2^2$ + w1w2
01
$\sigma_2$$\rho$

=> 0.05 = w1² * $\sigma_1^2$ + (1-w1)² * $\sigma_2^2$ + w1(1-w1)
01
$\sigma_2$$\rho$ ------- (i)

Solving for w1, we get w1 = 0.735

=> w2 = 1 - 0.735 = 0.265

Hence, expected return of the portfolio,

$\mu_p$ = w1 * 0.0205 + w2 * 0.0102 = 0.01778