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Sisyphean industries is seeking to raise capital from a large group of investors to fund a new project.Suppose that the efficient portfolio has an expected return of 14% and a volatility of 20%.Sisyphean's new project is expected to have a volatility of 40% and a 70% correlation with the efficient portfolio.The risk-free rate is 4%.
-The required return for Sisyphean's new project is closest to:
A)24%.
B)14%.
C)18%.
D)10%.

Question

Quizplus · Accepted Answer

To find the required return for Sisyphean's new project, we can use the capital asset pricing model (CAPM):

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

Since we are given the volatility and correlation of Sisyphean's new project with the efficient portfolio, we can use these to calculate the beta:

beta = (volatility of the new project / volatility of the efficient portfolio) * correlation with the efficient portfolio
beta = (0.4 / 0.2) * 0.7
beta = 1.4

We are also given the expected return of the efficient portfolio and the risk-free rate, so we can plug these values into the CAPM:

required return = 0.04 + 1.4 * (0.14 - 0.04)
required return = 0.04 + 1.4 * 0.1
required return = 0.04 + 0.14
required return = 0.18

Therefore, the required return for Sisyphean's new project is closest to 18%, which is answer choice C.

Use the Information for the Question(s)below