Q6 through Q10 are based on the following given data. A universe of securities i
ID: 2787445 • Letter: Q
Question
Q6 through Q10 are based on the following given data.
A universe of securities includes a risky stock X, a stock-index fund M, and T-bills whose expected return and standard deviation are:
Universe
E(r)
X
15%
50%
M
10
20
T-bills
5
0
The correlation coefficient between X and M is -0.2.
6. Use the formula in footnote 1, p. 156 in your textbook, to find the minimum-variance portfolio’s weights, i.e., wX = ___.1818_____ and wM = ______.8182_____. Use 4 decimal places of accuracy.
7. Use formula 6.10 in p. 160 in your textbook to find the weights of the tangency portfolio, i.e., wtX = ____.2564_______, and wtM = ____.7436__________. Use 4 decimal places of accuracy.
8. Estimate the Sharpe ratio. S = _______34.64__________. Use 2 decimal places.
9. Express the capital allocation line, CAL, in y = a + bX form where “a” and “b” are numbers.
Answer: ____________________
10. Suppose an investor places 2/9 of her complete portfolio in the risky tangency portfolio, and the remaining in T-bills. Calculate her complete portfolio’s expected return, std dev, and Sharpe ratio.
E(rp) = _________; p = ___________; and S = ____________. Use 2 decimal places & % when needed.
(Use the reverse side of the printed page to show handwritten workings for Q6 through Q10).
PLEASE SHOW ALL WORK!
Universe
E(r)
X
15%
50%
M
10
20
T-bills
5
0
Explanation / Answer
8)
Portfolio Returns Rp = 25.64% x 15% + 74.36% x 10% = 11.28%
Standard Deviation SDp = [(wX x SDX)^2 + (wM x SDM)^2 + (2 x wX x wM x SDX x SDM x corrXM)]^(1/2)
= [(25.64% x 50%)^2 + (74.36% x 20%)^2 + (2 x 25.64% x 74.36% x 50% x 20% x -0.2)]^(1/2)
= 17.59%
Sharpe Ratio = (Rp - Rf) / SDp = (11.28% - 5%) / 17.59% = 0.3572
9) Capital Allocation Line demonstrates the relationship between returns and risk as measured by standard deviation
y = Risk-free rate + Sharpe Ratio * X
=> y = 5% + 0.3572 * X
10) E(rp) = 2 / 9 x 11.28% + 7 / 9 x 5% = 6.396%
p = 2/ 9 x 17.59% = 3.908%
S = (E(rp) - rf) / p = (6.396 - 5) / 3.908 = 0.3572
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