Chapter 8: Asset Pricing Models

Question 1

What are the extra assumptions under the CAPM model?

Answer 1

• Investors are all on the same time horizon
• Investors can borrow and lend in unlimited amounts at the same risk discount rate
• The market for risky assets is perfect (there is perfect information, investors are well informed, investors behave rationally, no transactional costs, investors can hold a large amount of each asset, no single firm affects the price)
• Investors have the same estimations for expected return, variance and covariance
• All investors are using a single currency

Question 2

What are the consequences of the extra assumptions

Answer 2

• If investors have homogeneous expectations then they are all faced with the same efficient frontier or risky assets
• if in addition, they are all subject to the same risk-free rate of interest. The efficient frontier collapses to the straight line in E- sigma space which passes through the risk-free rate of return on the E - axis. And is tangential to the efficient frontier for risky assets
• All rational investors will hold a combination of risk-free assets and M, the portfolio of risky assets at the point where the straight line through the risk assets at the point where the straight line through the risk - free return touches the original efficient frontier
• Because this is the portfolio held in different quantities by all investors it must consist of all risky assets in proportion to their market capitalisation. It is commonly called the ‘market portfolio’. The proportion of a particular investor’s portfolio consisting of market portfolio will be determined by their risk-return preference ( indifference curves)

Question 3

State the Separation theorem

Answer 3

the fact that the optimal combination of risky assets for an investor can be determined without any knowledge of the preferences towards risk and return( or their liabilities)

Question 4

Define the Capital Market line

Answer 4

• It passes through (0,r) and (sigma_m, E_m)
• Gradient (E_m -r/sigma_m), market price of risk
• the formula of an efficient portfolio:
  E_p = r+(E_m-r)/sigma_m * sigma_p

Question 5

Define the security market line

Answer 5

• E_i = r + beta_i (E_m - r), which can be interpreted as the risk free rate plus risk premium
  where beta_i= cov(R_i, R_m)/ Var(R_m)
  beta_i can be interpreted as the sensitivity of the market