Levine Inc. is considering an investment that has an expected return of 15% and

Question

Levine Inc. is considering an investment that has an expected return of 15% and a standard deviation of 10%. What is the investment's coefficient of variation?

Desreumaux Inc's stock has an expected return of 12.25%, a beta of 1.25, and is in equilibrium. If the risk-free rate is 5.00%, what is the market risk premium?

Jim Angel holds a $200,000 portfolio consisting of the following stocks:

Stock Investment Beta
A $ 50,000 0.95
B 50,000 0.80
C 50,000 1.00
D 50,000 1.20
Total $200,000

What is the portfolio's beta?

Company A has a beta of 0.70, while Company B's beta is 1.20. The required return on the stock market is 11.00%, and the risk-free rate is 4.25%. What is the difference between A's and B's required rates of return? (Hint: First find the market risk premium, then find the required returns on the stocks.)

Explanation / Answer

Part 1: What is the coefficient of variation? CV is equal to the standard deviation over expected return. I think of it as a measure that shows you how much standard deviation you have to take on for a given expected return. It's helpful for comparing stock's with different expected returns and different standard deviations. Here the answer is 10/15 or 2/3 or .66. This measure would be useful if we were comparing it to another stock with a say a Standard Deviation of 12% and Expected return of 16.5%... this would have a CV of 12/16.5 or .72... we would rather take this stock even though it has a higher standard deviation because it gives us more return for our "standard deviation buck" so to speak.

Part 2: This is a CAPM type question... the formula is CAPM = RFrate + MRP*Beta

We know the answer to the CPAM is 12.25%, Beta 1.25, and risk free rate is given as 5%...

So we have to solve for the MRP using a little algebra.

12.25% = 5% + MRP*1.25... 7.25%=MRP*1.25 ... 7.25%/1.25= MRP ... 6% = MRP

Part 3: Portfolio Beta

Stock a b c d

Weight .25 .25 .25 .25

Beta .95 .80 1.0 1.2 Add together

Multiply .24 .2 .25 0.3 .9875 is the portfolio Beta

Part 4: What is the difference between A and B's required return.

Company A required return = RFrate + MRP*Beta

4.25% + 6.75%*0.7 = 8.975

Company B required return = RFrate + MRP*Beta

4.25 + 6.75%*1.2 = 12.35

Difference = 12.35-8.975 ... 3.375

Hope this helps!

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