The market portfolio is assumed to be composed of four securities. Their covaria
ID: 2708460 • Letter: T
Question
The market portfolio is assumed to be composed of four securities. Their covariance with the market and their proportions follow.
Security Covariance with Market Proportion
A 242 .2
B 360 .3
C 155 .2
D 210 .3
Given these data, calculate the market portfolio
The market portfolio is assumed to be composed of four securities. Their covariance with the market and their proportions follow. Given these data, calculate the market portfolio's standard deviation.Explanation / Answer
Recall that the standard deviation of the market portfolio is equal to
square root of a weighted average of the covariance of all securities
with it, where the weights are equal to the proportions of the
respective securities in the market portfolio, in this case:
STD_M = sqrt(pA*cov_A + pB*cov_B + pC*cov_C + pD*cov_D) =
= sqrt(0.2*242 + 0.3*360 + 0.2*155 + 0.3*210) =
= sqrt(250.4) =
= 15.82
The market porfolio's standard deviation is 15.82
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