Question

Suppose we have the following information about two stocks: Beta Expected Return 11% 6% 1.6 Stock 1 Stock 2 0.5 If the CAPM holds, what is the risk-free interest rate, the expected stock market return, and the market risk premium? (hint: Use CAPM equation for each separately; plug in known values and see if you can find unknown parameters through the two equations. Question #5 (30 points) Download monthly price data for Cigna (CI) and Amazon.com (MNZ) for the period of Jan. 1, 2000 through Feb. 1, 2016 (use Finance.Yahoo.com). Use Excel for this question. 1. Assume that you allocate 40% of your wealth to Cigna and 60% to Amazon at the beginning of the investment period (i.e. Jan. 2000). If you have $10,000 to invest, how many shares of each would you buy of each stock? 2. Create a column in Excel and apply a range of weights between -1 and +1 to Cigna to construct a portfolio consisting of the two shares (remember that the sum of weights should be one; so you can easily calculate the weight for Amazon. Don't worry if a weight is negative; this is due to "short-selling"). Construct a scatter-plot graph showing the average return and standard deviation of the portfolio. 3. Now apply a constraint on weights: eliminate negative values and allow the weights to range between 0 and 1 only, and re-plot the scatter plot of average returns and variance of portfolio. 4. Eliminating negative weights is called short sales constraints. Compare the results of parts (1) and (2) and discuss the effects of imposing short-sales constraints on a market. 6

Answer 1

Ques-).

As per CAPM,

R_f = Risk Free Rate

R_m = market Return

R_MP = Market risk Premium = (R_m - R_f)

So, (R_m - R_f) = R_MP

Stock-1

Expected/Required Return = 11%

Beta = 1.6

11% = R_f + 1.6(R_MP)

R_f = 11%- 1.6(R_MP) ....Eq(1)

Stock-2

Expected/Required Return = 6%

Beta = 0.5

6% = R_f + 0.5(R_MP)

R_f = 6%- 0.5(R_MP) ....Eq(2)

Taking Eq(1) equal to Eq(2)

11%- 1.6(R_MP) = 6%- 0.5(R_MP)

11%-6% = 1.6(R_MP) - 0.5(R_MP)

5% = 1.1(R_MP)

(R_MP) = 4.55%

Now, putting (R_MP) in eq(1)

R_f = 11%- 1.6(R_MP)

R_f = 11%- 1.6(4.55%)

R_f = 3.72%

(R_m - R_f) = R_MP

R_m = 4.55% + 3.72%

R_m = 8.27%

So, R_f = Risk Free Rate = 3.72%

R_m = market Return = 8.27%

R_MP = Market risk Premium = 4.55%

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