Question

You are given the following information on two securities.

Security	Expected Return	Standard Deviation of Returns
A	10.0%	14.0%
B	16.0%	12.0%

The correlation between the returns on the two securities is +0.6. The standard deviation of returns of a portfolio earning an expected return of 14.0 percent is closest to:

Group of answer choices

A 11.4%.

B 9.3%.

C 27.1%.

D 12.7%.

Answer 1

Given that,

Expected return on a security A Ra = 10%

Expected return on a security B Rb = 16%

Expected return on portfolio E(r) = 14%

Weight of security A in portfolio be Wa = W

Weight of security B in portfolio be Wb = (1-W)

So, Expected return on portfolio is weighted average return on its portfolio

=> E(r) = Wa*Ra + Wb*Rb

=> 14 = W*10 + (1-W)*16

=> 14 + 10W + 16 - 16W

=> W = 2/6 = 1/3 or 33.33%

So, Weight of security A Wa = 1/3 or 0.3333

and weight of security B is Wb = 1 - 1/3 = 2/3 or 0.6667

Standard deviation of security A SDa = 14%

Standard deviation of security B SDb = 12%

Correlation between two security Corr(a,b) = 0.6

So, standard deviation of portfolio is calculated as

SDp = SQRT(((Wa*SDa)^2) + ((Wb*SDb)^2) + 2*Wa*Wb*SDa*SDb*Corr(a,b))

=> Standard deviation of portfolio = SQRT(((0.3333*14)^2) + ((0.6667*12)^2) + 2*0.3333*0.6667*14*12*0.6) = 11.4%

So, option A is correct.