Following is information for the required returns and standard deviations of ret
ID: 2787020 • Letter: F
Question
Following is information for the required returns and standard deviations of returns for A, B, and C. Here are the expected returns and standard deviations for stocks A, B, and C: Stock ri si A 7.0% 33.11% B 10.0% 53.85% C 20.0% 89.44% Here is the correlation matrix: A B C A 1.0000 0.1571 0.1891 B 0.1571 1.0000 0.1661 C 0.1891 0.1661 1.0000 a. Suppose a portfolio has 30 percent invested in A, 50 percent in B, and 20 percent in C. What are the expected return and standard deviation of the portfolio? wA = 30% wB = 50% wC = 20% rp = Portfolio variance = sp = b. The partial model lists 66 different combinations of portfolio weights. For each combination of weights, find the required return and standard deviation. If you would like a return of 10.50 percent, what is the smallest standard deviation that you must accept? Why? Portoflio # wA wB wC Variance sp rp 1 0.0 0.0 1.0 2 0.0 0.1 0.9 3 0.0 0.2 0.8 4 0.0 0.3 0.7 5 0.0 0.4 0.6 6 0.0 0.5 0.5 7 0.0 0.6 0.4 8 0.0 0.7 0.3 9 0.0 0.8 0.2 10 0.0 0.9 0.1 11 0.0 1.0 0.0 12 0.1 0.0 0.9 13 0.1 0.1 0.8 14 0.1 0.2 0.7 15 0.1 0.3 0.6 16 0.1 0.4 0.5 17 0.1 0.5 0.4 18 0.1 0.6 0.3 19 0.1 0.7 0.2 20 0.1 0.8 0.1 21 0.1 0.9 0.0 22 0.2 0.0 0.8 23 0.2 0.1 0.7 24 0.2 0.2 0.6 25 0.2 0.3 0.5 26 0.2 0.4 0.4 27 0.2 0.5 0.3 28 0.2 0.6 0.2 29 0.2 0.7 0.1 30 0.2 0.8 0.0 31 0.3 0.0 0.7 32 0.3 0.1 0.6 33 0.3 0.2 0.5 34 0.3 0.3 0.4 35 0.3 0.4 0.3 36 0.3 0.5 0.2 37 0.3 0.6 0.1 38 0.3 0.7 0.0 39 0.4 0.0 0.6 40 0.4 0.1 0.5 41 0.4 0.2 0.4 42 0.4 0.3 0.3 43 0.4 0.4 0.2 44 0.4 0.5 0.1 45 0.4 0.6 0.0 46 0.5 0.0 0.5 47 0.5 0.1 0.4 48 0.5 0.2 0.3 49 0.5 0.3 0.2 50 0.5 0.4 0.1 51 0.5 0.5 0.0 52 0.6 0.0 0.4 53 0.6 0.1 0.3 54 0.6 0.2 0.2 55 0.6 0.3 0.1 56 0.6 0.4 0.0 57 0.7 0.0 0.3 58 0.7 0.1 0.2 59 0.7 0.2 0.1 60 0.7 0.3 0.0 61 0.8 0.0 0.2 62 0.8 0.1 0.1 63 0.8 0.2 0.0 64 0.9 0.0 0.1 65 0.9 0.1 0.0 66 1.0 0.0 0.0 Following is information for the required returns and standard deviations of returns for A, B, and C. Here are the expected returns and standard deviations for stocks A, B, and C: Stock ri si A 7.0% 33.11% B 10.0% 53.85% C 20.0% 89.44% Here is the correlation matrix: A B C A 1.0000 0.1571 0.1891 B 0.1571 1.0000 0.1661 C 0.1891 0.1661 1.0000 a. Suppose a portfolio has 30 percent invested in A, 50 percent in B, and 20 percent in C. What are the expected return and standard deviation of the portfolio? wA = 30% wB = 50% wC = 20% rp = Portfolio variance = sp = b. The partial model lists 66 different combinations of portfolio weights. For each combination of weights, find the required return and standard deviation. If you would like a return of 10.50 percent, what is the smallest standard deviation that you must accept? Why? Portoflio # wA wB wC Variance sp rp 1 0.0 0.0 1.0 2 0.0 0.1 0.9 3 0.0 0.2 0.8 4 0.0 0.3 0.7 5 0.0 0.4 0.6 6 0.0 0.5 0.5 7 0.0 0.6 0.4 8 0.0 0.7 0.3 9 0.0 0.8 0.2 10 0.0 0.9 0.1 11 0.0 1.0 0.0 12 0.1 0.0 0.9 13 0.1 0.1 0.8 14 0.1 0.2 0.7 15 0.1 0.3 0.6 16 0.1 0.4 0.5 17 0.1 0.5 0.4 18 0.1 0.6 0.3 19 0.1 0.7 0.2 20 0.1 0.8 0.1 21 0.1 0.9 0.0 22 0.2 0.0 0.8 23 0.2 0.1 0.7 24 0.2 0.2 0.6 25 0.2 0.3 0.5 26 0.2 0.4 0.4 27 0.2 0.5 0.3 28 0.2 0.6 0.2 29 0.2 0.7 0.1 30 0.2 0.8 0.0 31 0.3 0.0 0.7 32 0.3 0.1 0.6 33 0.3 0.2 0.5 34 0.3 0.3 0.4 35 0.3 0.4 0.3 36 0.3 0.5 0.2 37 0.3 0.6 0.1 38 0.3 0.7 0.0 39 0.4 0.0 0.6 40 0.4 0.1 0.5 41 0.4 0.2 0.4 42 0.4 0.3 0.3 43 0.4 0.4 0.2 44 0.4 0.5 0.1 45 0.4 0.6 0.0 46 0.5 0.0 0.5 47 0.5 0.1 0.4 48 0.5 0.2 0.3 49 0.5 0.3 0.2 50 0.5 0.4 0.1 51 0.5 0.5 0.0 52 0.6 0.0 0.4 53 0.6 0.1 0.3 54 0.6 0.2 0.2 55 0.6 0.3 0.1 56 0.6 0.4 0.0 57 0.7 0.0 0.3 58 0.7 0.1 0.2 59 0.7 0.2 0.1 60 0.7 0.3 0.0 61 0.8 0.0 0.2 62 0.8 0.1 0.1 63 0.8 0.2 0.0 64 0.9 0.0 0.1 65 0.9 0.1 0.0 66 1.0 0.0 0.0Explanation / Answer
Here, Portfolio Returns = wa x Ra + wb x Rb + wc x Rc = 11.10%
where, w - weight and R - Returns
Portfolio Variance = (wa x SDa)^2 + (wb x SDb)^2 + (wc x SDc)^2 + (2 x wa x wb x SDa x SDb x corr(ab)) + (2 x wb x wc x SDb x SDc x corr(bc)) + (2 x wc x wa x SDc x SDa x corr(ca))
= 14.55%
where, w - weight, SD - Standard Deviation and corr - correlation between two stocks
Portfolio Standard Deviation = Square Root of Variance = (14.55%)^(1/2) = 38.14%
A B C Portfolio Returns 7% 10% 20% 11.10% SD 33.11% 53.85% 89.44% 38.14% Weights 30% 50% 20% Correlation AB BC CA 0.1571 0.1661 0.1891