Consider two stocks: a large manufacturer of automobiles ("Colonel Motors") and an electric utility company operating in a large eastern city ("Separated Edison"). Assume the stocks have the following characteristics:

Expected Return Colonel Motors (C) 14% Separated Edison (S) 8%

Standard deviation 6% 3%

As you might suspect, the car manufacturer has higher expected return and more risk than the electric utility. Consider a portfolio, P, in which the proportion of wealth (weight) invested in C and S are w and 1 w , respectively, with 0 w 1, so short- selling is prohibited.

home / study / business / finance / questions and answers / 2. in addition to the two risky securities, c and ...

Your question has been answered! Rate it below.

Let us know if you got a helpful answer.

Question

a. Assume the correlation in the returns of the two stocks, cs, is +1. Plot the efficient frontier, mean return vs. standard deviation for P, as w is varied between 0 to 1. You can plot this relationship in Excel or any other software package for multiple w values and then connect the dots. Are there any gains to diversification?

b. Repeat the above exercise for cs = -1, 0, and 0.5. In each case, also identify the minimum variance portfolio. You can identify this portfolio by taking a simple derivative of the portfolio variance with respect to w and setting it equal to 0 or you can use Solver.

c. In addition to the two risky securities, C and S, noted , suppose there is also a third security, Unique Oil (U), with expected return of 20% and standard deviation of return of 15%. Further, assume the correlation between the security returns is as follows: cs = 0.5, cu = 0.2, and su = 0.4. Assume there are no constraints on short selling.

Plot the efficient frontier spanned by the three risky portfolios.

Add a fourth security, a risk-free security 0, to the mix with r0 = 5%. Plot the efficient frontier spanned by the four securities.

Explicitly identify the market portfolio, M. Write down the equation of the efficient frontier, i.e., the capital market line.

A risk-averse investor has $500 to invest. How should this investor allocate his wealth in the four securities if he wants to earn an expected return of 9 65 %?

Given the market portfolio M in part (c), calculate c = cM / M2 for Colonel Motors. Substitute this beta value in the right-hand-side of the CAPM, i.e., in r0 + c[rM r0 ], and verify that doing so indeed yields the expected return of the security that was given to you to begin with. This relationship of course must hold

for all three stocks.