A portfolio consists of 40% in Security A and 60% in Security B. The covariance matrix for A is 144, 225; for B is 225, 81. The standard deviation for the portfolio is.

a. 11.2.

b. 12.

c. 14.9.

d. 12.7.

e. 10.

A portfolio consists of 40% in Security A and 60% in Security B. The covariance matrix for A is 144, 225; for B is 225, 81. The standard deviation for the portfolio is 12.7

Option D is correct

Explanation:

Wa: 0.4

Wb: 0.6

a^2: 144

b^2: 81

Cov(a,b): 225

Portfolio Variance:

: (0.4*0.4*144) + (0.6*0.6*81) + (2*0.4*0.6*225)

: 160.2

Portfolio Standard Deviation: 12.7

Option d. Is the correct answer.

Explanation:

We are given

Wa = 40/100

Wa = 0.4

Wb = 60/100

Wb = 0.6

We are also give given the covariance as a,b

a² = 144

b² = 81

Therefore, the covariance will be

Cov(a,b) = 225

Portfolio Variance:

Variance =

(0.4×0.4×144) + (0.6×0.6×81) + (2×0.4×0.6×225)

Variance = 23.04 + 29.16 + 108

Variance = 160.2

Remember that, standard deviation is the square root of variance which we have has

Standard Deviation of the portfolio =√160.2

Standard Deviation of the Portfolio = 12.7

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