Chapter 6 - Asset Pricing Models (CAPM)

Question 1

What does the CAPM model tell us?

Answer 1

The Capital Asset Pricing Model tells us about the relationship between risk and return in the security market as a whole, assuming that investors act in accordance with mean-variance portfolio theory and that the market is in equilibrium.

Question 2

What are the 5 additional assumption for CAPM (on top of those of MPT)?

Answer 2

Assumption from MPT and

• All investors have the same one-period horizon.
• All investors can borrow or lend unlimited amounts at the same risk-free rate.
• The markets for risky assets are perfect. Information is freely and instantly available to all investors and no investor believes that they can affect the price of a security by their own actions.
• Investors have the same estimates of the expected returns, standard deviations and covariances of securities over the one-period horizon.
• All investors measure in the same ‘currency’ eg pounds or dollars or in ‘real’ or ‘money’ terms

Question 3

What does it mean to have a perfect market?

Answer 3

• There are many buyers and sellers, so that no one individual can influence the market price.
• All investors are perfectly informed.
• Investors all behave rationally.
• There is a large amount of each type of asset.
• Assets can be bought and sold in very small quantities, ie perfect divisibility.
• There are no taxes.
• There are no transaction costs.

Question 4

Explain why CAPM implies that all investors will arrive at the same efficient frontier.

Answer 4

If investors:
- have the same estimates of the expected returns, standard deviations and covariances of securities over the one-period horizon and
-are able to perform correctly all the requisite calculations

then they will all arrive at the same opportunity set and hence the same efficient frontier of risky securities

Question 5

Does CAPM require every investor to have the same attitude towards risk?

Answer 5

The model does not require that investors all have the same attitude to risk, only that their views of the available securities are the same – and hence that the opportunity set is identical for all investors.

Question 6

True or False: All rational investors will hold a combination of risky assets and the risk free portfolio.

Answer 6

True

Question 7

Why is the old efficient frontier (with just risky assets) tangential to the new efficient front (with the risk free asset)?

Answer 7

It has to be tangential as
- if it was above, there are no portfolios that exist here i.e. not within the opportunity set
- if it was below then these portfolio are inefficient

Question 8

Why is the point where old efficient frontier (with just risky assets) tangential to the new efficient front (with the risk free asset)?

Answer 8

The point where it is tangential represents the Market Portfolio.

The systematic risk i.e. related to the market, is equal to one.

Question 9

If I put all money in ONLY the risk free asset, is this still efficient?

Answer 9

Yes, as you cant get more expected return for 0 risk.

Question 10

Define the Market Portfolio

Answer 10

It is the portfolio where all the assets held in proportion to their market capitalisation.

e.g. if someone hold 1% is Tesco, then tesco must be 1% of the market.

Question 11

What’s is the formula of the Capital Market line?

Answer 11

Ep = r + ((E_M-r)/(sigmaM))*sigmaP

Question 12

What is the formula for Market Price of Risk?

Answer 12

((E_M-r)/(sigmaM))

0.6% for market price of risks means for every increase of sigma p by 1, you need to be compensated by an increase in Ep by 0.6%

Question 13

Explain how Market Price of Risk if it 5%?

Answer 13

For an increase in sigmaP by 1% (i.e. risk increases by 1%) then you will need an increase in 5% in Ep (expected returns)

Question 14

What is the gradient of the Capital Market line?

Answer 14

The market price of risk.

Question 15

What is the formula for the Beta factor?

Answer 15

For an individual asset:
B_i=cov(R_i,R_m)/V_m

For a portfolio:
B_p=cov(R_p,R_m)/V_m

Question 16

What is the formula for the Security Market Line?

Answer 16

E_p = r + B_i*(E_m-r) (Note: in E-B (x,y) space)

E_p- expected return on portfolio
r - return on risk free asset
E_m - expected return on the market portfolio
B_i - beta factor of security i which measures systematic risk of an asset wrt the market portfolio

Question 17

What is the B_m for the Market Portfolio?

Answer 17

1

Question 18

What are the Limitation of CAPM?

Answer 18

• Unrealistic assumptions
  -Impossible to get the whole market as this would include paints, property etc.

However there is some evidence to suggest a linear relationship between expected return and systematic risk

Question 19

How would you calculated the Beta of a portfolio?

Answer 19

You would take the weight averaged of the Betas for each individual share.

Question 20

What is the separation theorem?

Answer 20

The fact that the optimal combination of risky assets for an investor can be determined without any knowledge of their preferences towards risk and return (or their liabilities) is known as the separation theorem.

The separation theorem doesn’t tell us whereabouts on the new efficient frontier an individual investor’s portfolio will be. For this we need to know the investor’s attitude towards risk and return, or equivalently the investor’s utility function, in order to determine their preferred split between risky assets and the risk-free asset, ie the value of a.
However, we no longer have to make thousands of estimates of covariances in order to determine the portfolio of risky assets, because we know that it is always the market portfolio, M.