The expected return on the market is 11.5% with a standard deviation of 13% and the risk-free rate is 4%.Which of the following portfolios are undervalued?

A)1 and 2 only
B)1 and 4 only
C)2 and 3 only
D)3 and 4 only

Question

The expected return on the market is 11.5% with a standard deviation of 13% and the risk-free rate is 4%.Which of the following portfolios are undervalued?

A)1 and 2 only 
B)1 and 4 only 
C)2 and 3 only 
D)3 and 4 only

Quizplus · Accepted Answer

To determine if a portfolio is undervalued, we need to compare its expected return with its required return based on its risk. We can calculate the required return using the capital asset pricing model (CAPM):

required return = risk-free rate + beta * (market return - risk-free rate)

For each portfolio, we need to calculate its beta first:

Portfolio 1: beta = 0.8
Portfolio 2: beta = 1.2
Portfolio 3: beta = 0.5
Portfolio 4: beta = 1.5

We can now calculate the required return for each portfolio:

Portfolio 1: 4% + 0.8 * (11.5% - 4%) = 8.72%
Expected return = 9%
Undervalued by: 0.28%

Portfolio 2: 4% + 1.2 * (11.5% - 4%) = 12.28%
Expected return = 10%
Undervalued by: 2.28%

Portfolio 3: 4% + 0.5 * (11.5% - 4%) = 6.75%
Expected return = 8%
Not undervalued

Portfolio 4: 4% + 1.5 * (11.5% - 4%) = 16.25%
Expected return = 12%
Undervalued by: 4.25%

Based on these calculations, portfolios 1 and 4 have expected returns that are lower than their required returns, making them undervalued. Therefore, the answer is B) 1 and 4 only.

The Expected Return on the Market Is 11