15.4. You have developed the following information about two stocks, whose corre

Question

15.4. You have developed the following information about two stocks, whose correlation coefficient is 0.5:

Name                            E(R)                                 (R)                             B

Burroughs Corp             14%                                   20%                          0.85

Chandler Corp                16%                                  23%                           1.10

(A) Make a portfolio that simulates the market. Find the expected return on the market, E(Rm), and the standard deviation of this return, (Rm). Answer is E(Rm) = .152, (Rm) = .191
(B) Find the probability that the actual return on the market is more than 20%. Answer is 40.08%.

Explanation / Answer

(A) To simulate market the beta of the portfolio should be equal to one. Let the weightage of Burroughs Corp be 'x' and subsequently weightage of Chandler Corp be '(1-x)'.

1.00 = 0.85 * x + 1.10 * (1-x)

=> x = 0.40

Therefore, Expected return of the portfolio E (Rm) = 14% * 0.40 + 16% * (1 - 0.40)

= 15.20%

Standard deviation of portfolio = [(20% * 0.4)2 + (23% * 0.6)2 + 2 * 20% * 23% * 0.4 * 0.6 * 0.5]1/2

= 19.10%

(B) z = (20% - 15.20%) / 19.10%

= 0.2513

Probability = 1 - NORM.S.DIST(0.2513,TRUE)........................ Excel function

= 40.08%

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