The market has three risky assets. The variance-covariance matrix of the risky assets are as follows: r1 r2 r3 r1 0.25 0 -0.2 r2 0 4 0.1 r3 -0.2 0.1 1 Assume the market portfolio is M = 0.2 ◦ r1 + 0.5 ◦ r2 + 0.3 ◦ r3. Further assume E(rM) = 0.08. (1) What is the variance of M? (2) What is the covariance of r2 and M? (3) What is β2? (4) If the rate of return of the risk-free asset is 0.02. Then what is the fair expected rate of return of security 2? (5) An investor wants to invest in a portfolio P = 0.4◦r1+0.6◦r3. What is its “fair” expected rate of return?
Risk and return
Before understanding the concept of Risk and Return in Financial Management, understanding the two-concept Risk and return individually is necessary.
Capital Asset Pricing Model
Capital asset pricing model, also known as CAPM, shows the relationship between the expected return of the investment and the market at risk. This concept is basically used particularly in the case of stocks or shares. It is also used across finance for pricing assets that have higher risk identity and for evaluating the expected returns for the assets given the risk of those assets and also the cost of capital.
The market has three risky assets. The variance-covariance matrix of the risky assets are as follows:
| r1 | r2 | r3 | |
| r1 | 0.25 | 0 | -0.2 |
| r2 | 0 | 4 | 0.1 |
| r3 | -0.2 | 0.1 | 1 |
Assume the market portfolio is M = 0.2 ◦ r1 + 0.5 ◦ r2 + 0.3 ◦ r3. Further assume E(rM) = 0.08.
(1) What is the variance of M?
(2) What is the covariance of r2 and M?
(3) What is β2?
(4) If the
(5) An investor wants to invest in a portfolio P = 0.4◦r1+0.6◦r3. What is its “fair” expected rate of return?
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