Fill This Form To Receive Instant Help
Fill This Form To Receive Instant Help
Homework answers / question archive / You are given the following data on return, risk (i
You are given the following data on return, risk (i.e., standard deviation) and correlations of the assets A, B and C. Return Risk A B ? 22.50000% 11.000000% 18.1000% 22.16416% 17.578396% 15.1225% A 1.0000 B -0.4787 ? Correlations B ? A -0.4787 -0.7107 1.0000 -0.2774 -0.7107 -0.2774 1.0000 1. Which asset is inefficient? Plot the three assets in a graph in order to determine this. (Use the Excel spreadsheet, HW12-Excel.xls, uploaded with this assignment) 2. Compute the variance-covariance matrix for the three assets. (Use the Excel spreadsheet, HW12-Excel.xls, uploaded with this assignment) 3. By varying the weights of A and C in a portfolio that only consists of these two assets, find the corresponding values for the portfolio's return (E (Tp)) and risk (op). (Use the Excel spreadsheet, HW12-Excel.xls, uploaded with this assignment) Weight of A Weight of C E() 1.0 0.0 % % ?? 0.9 0.1 ..% : . : 0.0 1.0 % 4. Plot the efficient frontier by using the result in question 3. (i.e., plot the risk-return combinations that you obtained in part (c).)
2. Correlation (A,B)= Covariance(A,B)/ ( standard deviation of A* standard deviation of B)
or,-0.4787= Covariance(A,B)/ 22.16416% * 17.578396%
Covariance(A,B)= -1.8651
Correlation (A,C)= Covariance(A,C)/ ( standard deviation of A* standard deviation of C)
or, - 0.7107= covariance(A,C) / 22.16416% * 15.1225%
Covariance(A,C)= -2.3821
Correlation (C,B)= Covariance(C,B)/ ( standard deviation of C* standard deviation of B)
or,-0.2774= Covariance(B,C)/17.578396%*15.1225%
Covariance(B,C)= -0.73741
Covariance of portfolio or asset with itself is variance.
Correlation (A,A)= Covariance(A,A)/ ( standard deviation of A* standard deviation of A)
or, 1= Covariance(A,A) / 22.16416% * 22.16416%
Covariance(A,A) = 4.9125
Similarly, Covariance(B,B)= 17.578396% * 17.578396%= 3.09
Covariance (C,C)= 15.1225% * 15.1225%= 2.2869
| A | B | C | |
| A | 4.9125 | -1.8651 | -2.3821 |
| B | -1.8651 | 3.09 | -0.73741 |
| C | -2.3821 | -0.73741 | 2.2869 |
3. Return of protfolio= Wa*Ra + Wc * Rc
standard deviation of portfolio= (Wa2* Standard deviation of a2 + wc2 * standard deviation of c2 + 2WaWc* standard deviation of A * standard deviation of C* correlation (a,c))1/2
| weight of A (Wa) | weight of C(Wc) | Return of portfolio | Standard deviation of portfolio |
| 1 | 0 | 22.5% | 22.16416% |
| 0 | 1 | 18.10% | 15.1225% |
| 0.9 | 0.1 | 22.06% | 16.015% |
| 0.8 | 0.2 | 21.62% | 8.2493% |
| 0.7 | 0.3 | 21.18% | - |
| 0.6 | 0.4 | 20.74% | - |
| 0.5 | 0.5 | 20.3% | - |
| 0.4 | 0.6 | 19.86% | - |
| 0.3 | 0.7 | 19.42% | - |
| 0.2 | 0.8 | 18.98% | - |
| 0.1 | 0.9 | 18.54% | - |
Since standard deviation cannot be negative.
please see the attached file for the complete solution
1.
