Question #168703

**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.

Expert's answer

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

"\u03c3=(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"

"\u03c3=(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

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