diversification - the capital asset pricing model and the required rate return for risk

Question 1

what is the primary use of primary use of the CAPM?

Answer 1

The primary use of the CAPM is in determining the appropriate discount rate to use in computing net present value (NPV) and valuing shares

Question 2

CAPM can be used to

Answer 2

take account of risk and uncertainty by developing a risk-adjusted discount rate.

•In other words, instead of having to be given discount rates for use in valuations, we will learn how to calculate them

Question 3

what does CAPM calculate?

Answer 3

calculates an expected return an investor should anticipate given the level of risk of the investment opportunity.

Question 4

investors are? what does this mean?

Answer 4

1. investors are risk averse.
2. A risk averse investor has to be paid to take on risk, that is, a risk averse investor will demand a risk premium for every unit of risk they take on. The higher the risk, the higher the return.

Question 5

because investors are risk averse, they will?

Answer 5

Because investors are risk averse, they want to maximize expected returns for a given level of risk and minimize risk for a given level of return. They will, therefore, choose to diversify their investments by combining assets that are not perfectly positively correlated.

Question 6

how to derive CAPM?

Answer 6

• Investors will diversify their portfolios until they are efficient
• These portfolios will be efficient portfolios in the sense that they maximize expected return for a given level of standard deviation
• Using this key result, the CAPM can be derived

Question 7

Deriving the CAPM

Investors prefer high returns

Answer 7

We know that investors prefer more wealth to less. Therefore, other things being equal, investors will invest in assets that promise high returns.

Question 8

deriving the CAPM

individuals are risk averse

Answer 8

Since investors are risk averse (they prefer a certain outcome) and prefer high returns, they may forego some expected return in order to reduce risk.

Moreover, because individuals are risk averse, they will demand to be paid to take on risk. That is, for every unit of risk that they take on, they will demand to be paid a risk premium.

Question 9

Deriving the CAPM

Investors Diversify in Order to Reduce Risk:

Answer 9

process of diversification allows an investor to reduce the risk of his/her portfolio without sacrificing any expected return

Since investors are risk averse, they will seek to do this. Indeed, the traditional CAPM assumes that they will continue to do this until they are fully diversified, that is, until they have spread their wealth across all assets in the economy, attaining *well-diversified efficient portfolios.*

Question 10

Deriving the CAPM

Investors are Concerned About the Risk of their Portfolios:

Answer 10

The fact that investors are concerned about the risk of their portfolio follows immediately from the fact that investors are risk averse and hold a portfolio of risky assets.

Since the portfolio they hold is the market portfolio, in assessing an individual asset, investors will be concerned about how this individual asset contributes to (OR ‘covaries with’) the risk of the market portfolio.

Question 11

. Deriving the CAPM

In a Large Portfolio, Covariance Risk Dominates

Answer 11

is how an individual asset contributes to the risk of the market portfolio. The variance of a well-diversified portfolio like the market portfolio is equal to the average covariance of all the assets in the portfolio.

That is, the variance of a large portfolio is simply the average covariance between the pairs of individual stocks. Therefore, the contribution of an individual asset to the risk of the portfolio will be through its contribution to the average covariance of the portfolio. Thus the appropriate measure of the risk of an individual asset i is σ_i,m (the covariance of the asset with the market portfolio).

Question 12

. Deriving the CAPM

In a Large Portfolio, Covariance Risk Dominates

what does this say?

Answer 12

when investors hold well-diversified portfolios, the riskiness of an asset can be measured by the covariance of the returns of the individual asset with the returns of the well-diversified portfolio.

It is not the individual asset variance, but the covariance, that matters as all other asset-specific risks can be diversified away in an efficient portfolio.

Question 13

deriving the CAPM

Investors Will Demand a Premium for Covariance Risk:

Answer 13

E(r_i)=r_f + σ _i,m[Risk premium per unit of risk]

that investors will demand a premium for bearing risk and that the relevant measure of risk is the covariance of the asset’s returns with those of the market portfolio, the required return on asset i will be equal to the risk free rate plus a risk premium per unit of risk, where risk is measured by the covariance of asset i with the market portfolio

Question 14

deriving the CAPM

. Appropriate Measure of the Risk Premium

Answer 14

To determine an appropriate measure of the risk premium, we begin by considering how many units of covariance risk are involved in holding the market portfolio that we are assumed to be holding already. Recall that the relevant risk measure is the covariance of the asset with the market:

•for asset i: σ_i,m
•for the market portfolio m: σ_m,m = σ_m²
–the covariance of the market with itself is equal to the variance of the market

Question 15

deriving the CAPM

appropriate measure of the risk premium

the relevant measure of the risk premium per unit of risk is

Answer 15

Question 16

what is the CAPM equation?

Answer 16

Question 17

what is where Beta?

Answer 17

is a measure of the sensitivity of asset returns to changes in the market return

Question 18

what is the CAPM model?

Answer 18

model is known as the Sharpe Lintner CAPM.

The model states that the expected return on a risky asset follows a linear relationship equal to the risk free rate plus a risk premium based on the riskiness of the asset relative to the market portfolio

Question 19

what does the CAPM model relate a security’s expected return to?

Answer 19

the model relates a security’s expected return to its level of exposure to market risk represented by the beta.

Question 20

what does the CAPM model relate a security’s expected return to?

the model relates a security’s expected return to its level of exposure to market risk represented by the beta.

what can beta be interpreted as?

Answer 20

as a measure of systematic or market-wide risk that cannot be diversified away as it is common to all assets in an efficient portfolio

Question 21

The CAPM

the model relates a security’s expected return to its level of exposure to market risk represented by the beta.the model relates a security’s expected return to its level of exposure to market risk represented by the beta. as a measure of systematic or market-wide risk that cannot be diversified away as it is common to all assets in an efficient portfolio

what does the CAPM not provide?

Answer 21

CAPM does not provide any compensation for diversifiable risk. It is important to note that the beta of the market is 1, since

This provides a useful reference point against which the risk of other assets can be directly compared

Question 22

The CAPM

Example: Beta of a Portfolio

You invest in two stocks, A and B. These stocks have betas of 1.5 and 1.2 respectively. If you hold an equally weighted portfolio of the two stocks, the beta of your portfolio is simply the weighted average of the betas for each asset, or:

Answer 22

Question 23

The CAPM

Example: Required Rate of Return Using CAPM

If a stock has a beta of 1.5, the return on the market is 15% and the risk free rate is 5% (therefore, the market risk premium is 10%), then the required rate of return on the stock can be calculated using the CAPM

Answer 23

Question 24

Example: Required Rate of Return Using CAPM

What is the required rate of return on a stock whose covariance with the market is 0.015 given the variance of the market is 0.02 (therefore, stock’s beta is 0.015/0.02 = 0.75). The expected return on the market is 8% and the risk free rate is 5%. Using the CAPM:

Answer 24

Question 25

Answer 25

Question 26

Uncertainty and Investment Decisions

firm’s beta cannot be used if

Answer 26

the firm is considering a project with a risk different to that of its existing projects.

• Imagine the new project under consideration is riskier than the firm’s existing projects. This means that the required rate of return on the new project will be higher than on the firm’s existing projects.
• The reverse is true if the project being considered has a lower risk than that of the firm’s existing projects.

Question 27

If the magnitude of risk of the new project relative to existing projects is known

Answer 27

the firm’s beta can and must be adjusted to account for this change in risk.

Question 28

Answer 28

Question 29

If it was 40% less risky?

Answer 29

We commence consideration of the project by calculating the required rate of return given its risk. Since the investment is 40% riskier than the normal investments of the firm, the beta of the investment equals (1-0.4)x 1.5 = 0.9. Therefore, the required rate of return for the project is:

E(r_p ) =0.08 + 0.9(0.12-0.08)= 11.6%

Question 31

determine the NPV

Answer 31

Question 32

Deriving the CAPM

investors diversify in order to reduce risk

investors are assumed to hold?

Answer 32

investors are assumed to hold the market portfolio (a portfolio of all assets) in some proportion. For the sake of developing the intuition behind the CAPM, we assume that all investors fully diversify until they hold the market portfolio