Question

Consider the following information for the Alachua Retirement Fund, with a total investment of $4 million. The market required rate of returnis 12%, and the risk-free rate is 6%. What is its required rate of return?

a. 9.98%
b. 12.56%
c. 11.01%
d. 10.45%
e. 11.5%

Stock Investment Beta
A $500,000 1.2
B 500,000 -0.4
C 1,000,000 1.5
D 2,000,000 0.8
Total 4,000,000

Answer 1

The required rate of return for the Alachua Retirement Fund is calculated using the CAPM formula after determining the portfolio beta by finding the weighted average of the individual stock betas. Then, the CAPM formula incorporates the risk-free rate, the market required rate of return, and the portfolio beta to determine the return required by the fund.

Step-by-step explanation:

The calculation of the required rate of return for the Alachua Retirement Fund can be done by first calculating the weighted average beta of the portfolio, and then applying the Capital Asset Pricing Model (CAPM).


The formula for CAPM is Ri = Rf + βi(Rm - Rf), where Ri is the required return on the asset, Rf is the risk-free rate, βi is the beta of the asset, and Rm is the market required rate of return.

To use this formula, we first calculate the portfolio beta by taking the sum of the product of each stock's beta and its proportion to the total investment.


This gives us a beta for the portfolio as follows:

• (500,000/4,000,000) * 1.2 + (500,000/4,000,000) * (-0.4) + (1,000,000/4,000,000) * 1.5 + (2,000,000/4,000,000) * 0.8
  
  

Once the portfolio beta is determined, it's substituted into the CAPM to find the retirement fund's required rate of return.