CAPM

Question 1

Covariance

Answer 1

Cov(r_L,r_U) = SUM: probability_e*[(r_L,_e - E(r_L))]*[(r_U,e - E(r_U))]

Question 2

What does β equal?

Answer 2

Cov(R_i,R_M)/σ²_M

Question 3

What does Cov(R_i,R_M) equal?

Answer 3

Corr(R_i,R_M)σ_iσ_M

Question 4

What are the assumptions of CAPM?

Answer 4

• Investors hold diversified portfolios
• Perfect capital market assumptions
• single period transaction horizon
• Investors have homogeneous expectations

–this means that:

–if investors have homogeneous expectations, they will all hold the tangent portfolio (of risky securities)

Question 5

What are the assumptions of a perfect capital market? (5)

Answer 5

–no individual dominates the market

–investors are rational and risk averse

–investors have perfect information

–all investors can borrow or lend at the risk free rate

–no transaction or taxation costs

Question 6

What are the limitations of CAPM?

Answer 6

-Unrealistic assumptions:

–Many investors are not well diversified

–perfect capital market assumptions are unrealistic

• model looks at a single period while in reality investment can take years
• Beta uses historical data without considering the future

Question 7

What is the beta of a levered firm?

Answer 7

For N assets:

∑wiβi

e. g. if you invest equally in assets X and Y, your beta is:
0. 5βx + 0.5βy

Similarly:

βasset = [w_equity * β_equity] + [w_debt * β_debt]

βasset = [w_equity * β_equity] because β_debt is assumed to be 0

Question 8

How do we calculate βequity given βasset?

Answer 8

βequity = βasset(1+D/E)

Note: βequity must be used to calculate CAPM

Question 9

What’s usually higher, βdebt or βequity?

Answer 9

βdebt is usually very low (zero) because beta is a measurement of how a stock reacts to market changes

Question 10

What should we do for beta of a project that has different risk than the firm?

Answer 10

Use the beta of another company in an industry specific to the project

Remember: if the comparable company uses debt, convert the beta to the pure beta β_asset

Question 11

What is the Weighted Average Cost of Capital?

Answer 11

If a firm uses both debt and equity, we weight the returns (R_equity and R_debt) to create a required cost of capital. This is given as: R_equity*w_equity + R_debt*w_debt

Question 12

What is the formula for WACC with tax?

Answer 12

R_equity*w_equity + R_debt*w_debt*(1-t)