Problem 11-17 Using CAPM [LO 4] A stock has a beta of 1.23 and an expected retur
ID: 2646954 • Letter: P
Question
Problem 11-17 Using CAPM [LO 4]
A stock has a beta of 1.23 and an expected return of 12.1 percent. A risk-free asset currently earns 3.95 percent.
What is the expected return on a portfolio that is equally invested in the two assets? (Do not round intermediate calculations. Enter your answer as a percentage rounded to 2 decimal places (e.g., 32.16).)
If a portfolio of the two assets has a beta of 0.83, what are the portfolio weights? (Do not round intermediate calculations. Round your answers to 4 decimal places (e.g., 32.1616).)
If a portfolio of the two assets has an expected return of 11.3 percent, what is its beta? (Do not round intermediate calculations. Round your answer to 2 decimal places (e.g., 32.16).)
If a portfolio of the two assets has a beta of 2.43, what are the portfolio weights? (Negative amounts should be indicated by a minus sign. Do not round intermediate calculations. Round your answers to 4 decimal places (e.g., 32.1616).)
A stock has a beta of 1.23 and an expected return of 12.1 percent. A risk-free asset currently earns 3.95 percent.
Explanation / Answer
CAPM is acronym for Capital Asset Pricing Model which is a measure of return of the stock considering the its beta in relation to the market and returns of the market and risk free assets. This is an expectation of the result from an investment made considering the systematic risk of the stock that is beta.
Here, expected return of the stock is given already and risk free returns are provided we are asked to calculate the following:
1. Expected Portfolio return using the equally weighted assets
Portfolio return = W1 * Return of stock + W2 * Return of risk free security
W1 = 50% (weight)
W2 = 50% (weight)
Return of stock = 12.1%
Return of risk free security = 3.95%
= 12.1% * 0.5 + 3.95% *0.5 = 8.03%
2. Beta of the portfolio is given we need to find the portfolio weights
Beta of the portfolio = W1 * Beta of the stock + W2 * Beta of the risk free security
W1 = Let it be X
W2 = ( 1 - X) (because both the weights if added will give 1, weights cannot be more than 1 in the present case)
Beta of stock = 1.23 given in question
Beta of risk free security = 0 since risk free assets donot have any systematic risk
0.83 = 1.23 * X + 0 * (1-X)
X = 0.83 / 1.23
X = 67.48%
Weight of stock = 67.48%
Weight of Risk free security = 32.52%
3. Portfolio return is given we need to find the beta of the portfolio
When the Beta of the portfolio is required but return of the portfolio is provided this means that we need to find weights for finding the beta of the portfolio.
Expected Return of the Portfolio = W1 * Return of the stock + W2 * Return of the risk free asset
W1 = Let this be X
W2 = ( 1 - X) (As the total of both the weights will be = 1 )
11.3% = X * 12.1% + (1-X) * 3.95%
11.3% = X12.1% + 3.95% - X3.95%
11.3% - 3.95% = X8.15%
7.35% = X 8.15%
X = 90.18%
Weight of stock = 90.18%
Weight of risk free asset = 9.82%
Beta = 90.18% * 1.23 + 0*9.82%
= 1.11
4. Beta of the portfolio is given we need to find the portfolio weights
Beta of the portfolio = W1 * Beta of the stock + W2 * Beta of the risk free security
W1 = Let it be X
W2 = ( 1 - X) (because both the weights if added will give 1, weights cannot be more than 1 in the present case)
Beta of stock = 1.23 given in question
Beta of risk free security = 0 since risk free assets donot have any systematic risk
2.43 = 1.23 * X + 0 * (1-X)
X = 2.43 / 1.23
X = 197.56%
Weight of stock = 197.56%
Weight of Risk free security = - 97.56%
This indicates that the investor has borrowed in the risk free asset and invested in the stock