Question

An investor owns a portfolio consisting of two mutual funds, A and B, with 50% invested in A. The following table lists the inputs for these funds.

Measures	Fund A		Fund B
Expected value	10			7
Variance	68			43
Covariance	25

a. Calculate the expected value for the portfolio return. (Round your answer to 2 decimal places.)

Expected Value:

b. Calculate the standard deviation for the portfolio return. (Round intermediate calculations to at least 4 decimal places. Round your final answers to 2 decimal places.)

Standard Deviation:

Answer 1

SOLUTION:

From given data,

An investor owns a portfolio consisting of two mutual funds, A and B, with 50% invested in A. The following table lists the inputs for these funds.

Measures	Fund A	Fund B
Expected value	10	7
Variance	68	43
Covariance		25

a. Calculate the expected value for the portfolio return

The expected value of the portfolio return is obtained below:

From the information, the expected return for A is 10 and the expected return for B is 7. Moreover, the investment on A is 50%.

The expected return is,

EV = 1 x ER
-(0.5 x 10) + (0.5 x 7)
=5+3.5
= 8.50

The expected value of the portfolio return is 8.50.

b. Calculate the standard deviation for the portfolio return.

The standard deviation of the portfolio return is obtained as shown below:

From the information, the variance for fund A is 68 and the variance for fund B is 43.

The variance is,

Var(0.5 X + 0.5 Y ) = 0.5^2 Var(X)+0.5^2 Var(Y)+2 x 0.5 × 0.5 × Cov (X,Y)
Var(0.5 X + 0.5 Y ) = (0.5^2 x 68^2)+(0.5^2 x 43^2)+(2 x 0.5 x 0.5 x (25))
Var(0.5 X + 0.5 Y ) = 11 56 + 462.25 + 12.5

Var(0.5 X + 0.5 Y ) = 1630.75

The standard deviation is,

σ = sqrt( Var(0.5 X + 0.5 Y) )
σ = sqrt( 1630.75)

σ = 40.3825
σ = 40.38

The standard deviation of the portfolio return is 40.38.