Question

Q3. Jamie Wong is considering building an investment portfolio containing two stocks, L and M. Stock L will represent 40% of the dollar value of the portfolio, and stock M will account for the other 60%. The expected returns over the next 6 years, 2013–2018, for each of these stocks are shown in the following table.

a. Calculate the expected portfolio return, rp, for each of the 6 years.

 b. Calculate the expected value of portfolio returns, , over the 6-year period.

 c. Calculate the standard deviation of expected portfolio returns, over the 6-year period.

 d. How would you characterize the correlation of returns of the two stocks L and M?

e. Discuss any benefits of diversification achieved by Jamie through creation of the portfolio.  

Answer 1

Let the expected returns be as follows

1 2 3 4 5 6

L 5 6 7 2 2 8

M 4 8 5 7 3 6

a.

expected return on each share:

$L=\frac{5+6+7+2+2+8}{6}=5$

$M=\frac{4+8+5+7+3+6}{6}=5.5$

b.

 expected value of portfolio returns

$EVp=0.4\times5+0.6\times5.5=5.30$

c.

the standard deviation is the square root of the variance

$σ=(w1\times w2\times covLM)^{0.5}$

$covLM=\frac{\sum_{(ri-\tilde{ri})(rj-\tilde{rj})}}{n-1}=\frac{\sum_{(5-{5})(4-5.5)}}{6-1}=1.2$

$σ=(w1\times w2\times covLM)^{0.5}=(0.4\times 0.6\times 1.20)^{0.5}=0.54$

d. $\frac{5.5}{5}=1.1$

the yield M is greater than the yield L

e.

the yield of M is greater than the yield of L, so the portfolio needs to include more securities of M