Assuming the target return is 8.0%, what are the weights for Corner Portfolios A (6.0%, 5.0%) and B (9.0%…

Question

Assuming the target return is 8.0%, what are the weights for Corner Portfolios A (6.0%, 5.0%) and B (9.0%, 10.0%) in a portfolio?

ScanSolve AI Tutor · Accepted Answer

To solve this problem, I will make the following assumptions, as the return objective from part (iv) and the characteristics of the corner portfolios were not provided:

Chitova's return objective (from part iv): $R_P = 8.0\%$
Available Corner Portfolios:
- Corner Portfolio A (CPA): Expected Return ( $R_A$ ) = 6.0%, Standard Deviation ( $\sigma_A$ ) = 5.0%
- Corner Portfolio B (CPB): Expected Return ( $R_B$ ) = 9.0%, Standard Deviation ( $\sigma_B$ ) = 10.0%
- Corner Portfolio C (CPC): Expected Return ( $R_C$ ) = 12.0%, Standard Deviation ( $\sigma_C$ ) = 15.0%

Identify the appropriate corner portfolios.
The target return of 8.0% falls between the expected returns of Corner Portfolio A (6.0%) and Corner Portfolio B (9.0%). Therefore, Chitova will combine CPA and CPB.
Set up equations to determine the weights.
Let $w_A$ be the weight in Corner Portfolio A and $w_B$ be the weight in Corner Portfolio B.
Since there is no short selling, the weights must sum to 1:
$w_A + w_B = 1$
The expected return of the combined portfolio ( $R_P$ ) must equal the target return:
$w_A R_A + w_B R_B = R_P$
Substituting the assumed values:
$w_A (0.06) + w_B (0.09) = 0.08$
Solve for the weights.
From the first equation, $w_B = 1 - w_A$ . Substitute this into the second equation:
$0.06 w_A + 0.09 (1 - w_A) = 0.08$ $0.06 w_A + 0.09 - 0.09 w_A = 0.08$ $-0.03 w_A = 0.08 - 0.09$ $-0.03 w_A = -0.01$ $w_A = \frac{-0.01}{-0.03} = \frac{1}{3}$
Now, calculate $w_B$ :
$w_B = 1 - w_A = 1 - \frac{1}{3} = \frac{2}{3}$
Calculate the resulting standard deviation.
For portfolios formed by combining adjacent corner portfolios on the efficient frontier, the standard deviation is typically a linear interpolation of the standard deviations of the two corner portfolios:
$\sigma_P = w_A \sigma_A + w_B \sigma_B$
Substituting the weights and assumed standard deviations:
$\sigma_P = \left(\frac{1}{3}\right) (0.05) + \left(\frac{2}{3}\right) (0.10)$ $\sigma_P = \frac{0.05}{3} + \frac{0.20}{3}$ $\sigma_P = \frac{0.25}{3}$ $\sigma_P \approx 0.08333$
The weights for Corner Portfolio A and Corner Portfolio B are $\frac{1}{3}$ and $\frac{2}{3}$ respectively. The resulting standard deviation is approximately 8.33%.
$\boxed{\text{Weights: } w_A = \frac{1}{3}, w_B = \frac{2}{3}; \text{ Standard Deviation: } 8.33\%}$

Assuming the target return is 8.0%, what are the weights for Corner Portfolios A (6.0%, 5.0%) and B (9.0%, 10.0%) in a portfolio?

Step-by-step solution

Identify the appropriate corner portfolios.

Set up equations to determine the weights.

Solve for the weights.

Calculate the resulting standard deviation.

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