Question

You currently hold $50,000 investment in Sancour Company’s stock with 9% expected return and 18% volatility. The market portfolio has 15 % expected return and 10% volatility. The risk free rate is 5%.

1. Based on the CAPM assumptions, how would you switch your Sancour stock investment to the CML portfolio with the lowest possible volatility while having the same expected return as the Sancour stock?

1. Invest $30,000 in the market portfolio and $20,000 in a risk-free security

2. Invest $20,000 in the market portfolio and $30,000 in a risk-free security

3. Set up and equally-weighted portfolio of the market portfolio an the risk-free security

4. None of the above

2. What would be the debt-equity ratio of the levered CML portfolio that would have the highest possible expected return while having the same volatility as the Sancour stock?

1. 1/5

2. 2/5

3. 3/5

4. 4/5

5. None of the above

3. Which CML portfolio’s would have both a higher expected return and lower volatility than the Sancour stock

1. Portfolios with less than $20,000 invested in the market portfolio

2. Portfolios with more than $90,000 invested in the market portfolio

3. Portfolio with any amount between $20,000 and $90,000 invested in the market portfolio

4. None of the above

4. Based on your answer to question 1 above, how much volatility of Sancour stock was reduced?

1. 4%

2. 14%

3. 18%

4. 20%

5. None of the above

Answer 1

1). Requirement is that the new portfolio return should be 9% and volatility should be lowest.

Let the weight invested in the market be x. Then, weight invested in the risk free asset will be 1-x

Portfolio return = sum of weighted returns = (x*15%) + (1-x)*5%

Portfolio volatility (or standard deviation) = x*volatility of market = x*10%

Using the options given, we see that if x = 0.4 and 1-x = 0.6 then

portfolio return = (0.4*15%)+(0.6*5%) = 9%

portfolio volatility = 0.4*10% = 4% (Conversely, this can also be solved using Solver).

If x = 0.4 then amount invested in the market = 0.4*50,000 = 20,000 and amount invested in the risk free asset is 50,000-20,000 = 30,000 (Option B is correct).

2). For the levered CML portfolio, debt will be the risk free security and equity will be the market portfolio.

Again, using Solver, for the highest portfolio return with volatility of 18% (same as Sancour stock), the weight of the riskfree security has to be -0.8 and weight of market portfolio has to be 1.8, so D/E ratio becomes -0.8/1.8 = -0.444 (basically, in order to increase volatility to more than market volatility, the risk free security has to be short sold.) Option E - none of the above is correct.

3). A CML portfolio with an investment between 20,000 and 90,000 in the market portfolio will have a portfolio return greater than Sancour return (9%) and volatility less than Sancour volatility (18%). Option C is correct.

This is so because from Ans.1 we know the portfolio return will start increasing as investment in market portfolio goes beyond 20,000. From Ans.2, we know that portfolio volatility will start increasing beyond 18% once investment in market portfolio exceeds 90,000.

4). In Ans.1, volatility of the Sancour stock was reduced from 18% to 4% so reduction of 14% happened. Option B is correct.