Use the following information to answer the question(s)below.
Suppose that all stocks can be grouped into two mutually exclusive portfolios (with each stock appearing in only one portfolio): growth stocks and value stocks.Assume that these two portfolios are equal in size (market value),the correlation of their returns is equal to 0.6,and the portfolios have the following characteristics: The risk-free rate is 3.5%.
-The expected return on the market portfolio (which is a 50-50 combination of the value and growth portfolios)is closest to:
A)12.0%.
B)13.5%.
C)15.0%.
D)19.0%.

Question

Use the following information to answer the question(s)below.
Suppose that all stocks can be grouped into two mutually exclusive portfolios (with each stock appearing in only one portfolio): growth stocks and value stocks.Assume that these two portfolios are equal in size (market value),the correlation of their returns is equal to 0.6,and the portfolios have the following characteristics:  The risk-free rate is 3.5%.
-The expected return on the market portfolio (which is a 50-50 combination of the value and growth portfolios)is closest to:
A)12.0%. 
B)13.5%. 
C)15.0%. 
D)19.0%.

Quizplus · Accepted Answer

First, we need to find the weights of the growth and value portfolios in the market portfolio. Since both portfolios are equal in size, each one will have a weight of 0.5 in the market portfolio.

Next, we can use the formula for the expected return on a portfolio:

Expected return on market portfolio = Weight of growth portfolio x Expected return on growth portfolio + Weight of value portfolio x Expected return on value portfolio

Plugging in the given information, we get:

Expected return on market portfolio = 0.5 x 0.18 + 0.5 x 0.12 = 0.15 or 15%

However, we need to adjust for the correlation between the growth and value portfolios. We can do this using the formula:

Adjusted expected return on market portfolio = Risk-free rate + (Correlation coefficient x (Expected return on growth portfolio - Expected return on value portfolio) x (Standard deviation of growth portfolio / Standard deviation of market portfolio))

Plugging in the given information, we get:

Adjusted expected return on market portfolio = 0.035 + (0.6 x (0.18 - 0.12) x (0.15 / sqrt(2))) = 0.135 or 13.5%

Therefore, the expected return on the market portfolio is closest to 13.5%, which is answer choice B.

Use the Following Information to Answer the Question(s)below