Assume that security returns are generated by the single-index model, Ri = alphai + BetaiRM + ei where Ri is the excess return for security i and RM is the market's excess return. The risk-free rate is 2%. Suppose also that there are three securities A, B, and C, characterized by the following data. Security Betai E(Ri) sigma(ei) A 1.4 15% 28% B 1.6 17% 14% C 1.8 19% 23% a. If simaM = 24%, calculate the variance of returns of securities A, B, and C (round to whole number). Variance Security A Security B Security C b. Now assume that there are an infinite number of assets with return characteristics identical to those of A, B, and C, respectively. What will be the mean and variance of excess returns for securities A, B, and C (enter the variance answers as a whole number decimal and the mean as a whole number percentage)? Mean Variance Security A ?% Security B ?% Security C ?%
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.
Assume that security returns are generated by the single-index model,
Ri = alphai + BetaiRM + ei
where Ri is the excess return for security i and RM is the market's excess return. The risk-free rate is 2%. Suppose also that there are three securities A, B, and C, characterized by the following data.
| Security | Betai | E(Ri) | sigma(ei) |
| A | 1.4 | 15% | 28% |
| B | 1.6 | 17% | 14% |
| C | 1.8 | 19% | 23% |
a. If simaM = 24%, calculate the variance of returns of securities A, B, and C (round to whole number).
| Variance | |
| Security A | |
| Security B | |
| Security C |
b. Now assume that there are an infinite number of assets with return characteristics identical to those of A, B, and C, respectively. What will be the mean and variance of excess returns for securities A, B, and C (enter the variance answers as a whole number decimal and the mean as a whole number percentage)?
| Mean | Variance | |
| Security A | ?% | |
| Security B | ?% | |
| Security C | ?% |
Trending now
This is a popular solution!
Step by step
Solved in 2 steps with 2 images
