Question

You can form a portfolio of two assets, A and B, whose retums have the following characteristics Expected Retum 9% Standard 29% 45 .3 17 a. lf you demand an expected return of 15%, what are the portfolio wei hts? Do not round intermediate calculations. Round your answers to 3 decimal places.) Stock" "Portfolio Weight- b. What is the portfolio's standard deviation? (Use decimals, not percents, in your calculations. Do not round intermediate calculations. Enter your answer as a percent rounded to 2 decimal places Standard deviation

Answer 1

Let the weight on stock A be "x", so weight on stock B will be 1-x
Now, the portfolio should give a return of 15%.
Expected return on A=9%
Expected return on A=17%
So, the equation will be: x*9%+(1-x)*17%=15%
9x+17-17x=15
-8x=-2
x=2/8=.25 or 25%
1-x=.75 or 75%
To get an expected return of 15% on the portfolio of A and B stocks, we need to give .25 weight to stock A and .75 to stock B.

Part b:

In a two asset portfolio Var(RiRj) = wi^2σi^2 + wj^2σj^2 + 2wiwjCov(Ri,Rj)
wi = the portfolio weight of the asset i
wj = the portfolio weight of the asset j
σi = the standard deviation of returns on asset i
σj = the standard deviation of returns on asset j
Var(RiRj) = Variance of the two asset portfolio returns.
Cov(Ri,Rj) = the covariance between the returns on the two assets
This covariance can be further simplified as Cov(Ri,Rj)=σiσj*corr(Ri,Rj)

corr(Ri,Rj) = the correlation between the returns on asset i and j
σi = the standard deviation of returns on asset i
σj = the standard deviation of returns on asset j

On simplifying variance equations by substituting the value of Cov(Ri,Rj) with σ(i)σ(j)*corr(Ri,Rj), we get
Var(RiRj) = wi^2σi^2 + wj^2σj^2 + 2wiwjσ(i)σ(j)*corr(Ri,Rj)

Given that the correlation between the two stocks is .3
Weight on stock A=25%=.25
Weight on stock B=75%=.75
Stock A has a standard deviation of 29%=.29
Stock B has a standard deviation of 45%=.45

Now, portfolio variance= .25^2*.29^2 +.75^2*.45^2+2*.25*.75*.29*.45*.3

=.0625*.0841 + .5625*.2025 + 0.01468125
=.00525625 + .11390625 + 0.01468125
= .13384375
This is the variance, to find standard deviation, we need to take square root of .13384375 which is equal to .36584 or .37 (rounded to 2 decimal places)