Chapter 7: Asset Pricing Models

Question 1

Assumptions of the CAPM

Answer 1

ALL ASSUMPTIONS FROM MODERN PORTFOLIO THEORY PLUS:

All investors:

• have the same 1-period horizon
• can borrow/lend unlimited amounts at the same risk-free rate.
• have the same estimates of the expected returns, standard deviations and covariances of securities over the one-period horizon.
• measure in the same “currency” or in “real”/”money” terms.
• The market for risky assets are perfect

Question 2

4 Results of CAPM

Answer 2

• All investors have same efficient frontier of risky assets
• Efficient frontier collapses to a straight line in E-σ space in the presence of a risk-free asset.
• All investors hold a combination of the risk free asset and the same portfolio of risky assets, M.
• M is the market portfolio - it consists of all assets held in proportion to their market cap.

Question 3

Limitations of basic CAPM

Answer 3

Empirical studies do not provide strong support for the model.

It does not account for

• taxes,
• inflation or
• where there is no riskless asset.

It does not consider

• multiple time periods or
• optimisation of consumption over time.

Question 4

Strength of Arbitrage pricing theory

Answer 4

Based on no-arbitrage conditions.

- It allows us to describe equilibrium in terms of any multi-index model.

Question 5

Weaknesses of APT

Answer 5

• Gives no evidence as to what might be an appropriate multi-index model
• Tells nothing about the size or signs of the λs

Question 6

7 Requirements for a perfect market

Answer 6

• Many buyers and sellers, so that no one individual can influence the market price
• All investors are perfectly informed
• Investors all behave rationally
• Large amount of each type of asset
• Assets can be bought / sold in very small quantities (perfect divisibility)
• No taxes
• No transaction costs

Question 7

Separation Theorem

Answer 7

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 (of their liabilities).

Question 8

2 Main assumptions underlying Arbitrage Pricing Theory

Answer 8

• Principle of no arbitrage applied

- The returns on any stock can be linearly related to a set of factors.

Question 9

Principle of no arbitrage

Answer 9

It is not possible to make risk-free profits by exploiting anomalies in prices.
Any 2 assets that have identical payoff profiles must have the same price.

Question 10

Perfect market

Answer 10

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.

Question 11

3 features of security returns in practice which appear to contradict the implications of the lognormal model.

Answer 11

• Skewness and fat tails
• Varying volatility
• Mean reversion and momentum

Question 12

Suggest an alternative to the lognormal distribution to better cater for:
- Skewness and fat tails

Answer 12

Alternative distribution (e.g. t-distribution)
or Levy jump-diffusion process

Question 13

Suggest an alternative to the lognormal distribution to better cater for:
- varying volatility

Answer 13

ARCH models or Markov models

Question 14

Suggest an alternative to the lognormal distribution to better cater for:
- mean reversion and momentum

Answer 14

Autoregressive models