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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

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, = 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, = w12 * + w22 * + w1w2   = 0.001596

=> Std deviation of the portfolio = = 0.0399

c) Std deviation of the new portfolio = 0.05

=> 0.05 = w12 * + w22 * + w1w2   => 0.05 = w12 * + (1-w1)2 * + w1(1-w1)   ------- (i)

Solving for w1, we get w1 = 0.735

=> w2 = 1 - 0.735 = 0.265

Hence, expected return of the portfolio, = w1 * 0.0205 + w2 * 0.0102 = 0.01778

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