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Subject 10. The CAPM and the APT

The CAPM provides a simple, yet elegant framework for us to think about the question of reward and risk.

  • In market equilibrium, investors are only rewarded for bearing systematic risk -the type of risk that cannot be diversified away.
  • They should not be rewarded for bearing idiosyncratic risk, since this uncertainty can be mitigated through appropriate diversification.
  • For a risky asset ri, the right measure of the rewardable risk is not its variance var (ri), but its covariance cov (ri,rM) with the market.

    • For one unit exposure to the market risk, the reward is the same as the market: E(rM) - rf.
    • For β unit of exposure to the market, the reward is: β (E(rM) - rf).
    • For zero exposure to the market risk, the reward is zero, no matter how risky the asset is.

    In summary, the risk and reward relation in the CAPM is a linear relation.

Like the CAPM, the basic concept of the APT is that differences in expected return must be driven by differences in non-diversifiable risk. That is, the returns of a security are based on the systematic risk exposure of the security, as opposed to the total risk. However, the APT is not an equilibrium concept. It does not rely on the existence of a market portfolio. It is based purely on no-arbitrage conditions.

  • APT applies to well diversified portfolios and not necessarily to individual stocks.
  • With APT it is possible for some individual stocks to be mispriced - not lie on the SML.
  • APT is more general in that it gets to an expected return and beta relationship without the assumption of the market portfolio.
  • APT can be extended to multifactor models.

There are a number of limiting assumptions regarding the CAPM. Candidates should remember that the model assumes a perfect market that is unaffected by considerations such as transactions costs or undue influence by a single investor. Consequently, in a perfect market there would be no transactions costs, numerous investors with homogeneous expectations and the ability to borrow and lend at the risk-free rate.

Compared to CAPM, Arbitrage pricing theory (APT) is a broader based theory which states that all of the systematic factors may not be represented in the single market factor represented by the CAPM. The APT model requires fewer assumptions and considers multiple factors to help explain the risk of an asset.

The APT is a useful tool for building portfolios adapted to particular needs. For example, suppose a major oil company wanted to create a pension fund portfolio that was insulated against shock to oil prices. The APT allows the manager select a diversified portfolio of stocks that has low exposure to inflation shocks (oil prices are correlated to inflation). If the CAPM is a "one size fits all" model of investing, the APT is a "tailor-made suit." In the APT world, people can and do have different tastes and care more or less about specific factors.

The CAPM can be considered as a special case of the APT where there is only one risk factor, the market portfolio.

Practice Question 1

The drawback of the CAPM is that it:

A. Ignores the return on the market portfolio.
B. Requires a single measure of systematic risk.
C. Ignores risk-free return.

Correct Answer: B

Practice Question 2

Compared to CAPM, APT:

I. allows more risk factors.
II. assumes the investors are risk-averse.
III. assumes a normal distribution of returns.
IV. has fewer restrictive assumptions.

Correct Answer: I and IV

Practice Question 3

If there is only one factor (market risk) in an APT mode, the APT then equals


Correct Answer: A

APT does not identify the risk factors to be included in the model. If the market risk is used as the only factor, the APT would equal CAPM.

Practice Question 4

Which is not a major assumption in the Arbitrage Pricing Theory (APT)?

A. Investors always prefer more wealth to less wealth with certainty.
B. Capital markets are perfectly competitive.
C. A market portfolio that contains all risky assets and is mean-variance efficient.
D. The stochastic process generating asset returns can be represented as a K factor model.

Correct Answer: C

Practice Question 5

A similarity between the APT and CAPM model is that both models assume that:

A. the unique effects are independent and will not be diversified away in a large portfolio.
B. the unique effects are dependent and will be diversified away in a large portfolio.
C. the unique effects are independent and will be diversified away in a large portfolio.

Correct Answer: C

Practice Question 6

The feature of arbitrage pricing theory (APT) that offers the greatest potential advantage over the CAPM is the:

A. identification of anticipated changes in production, inflation, and term structure of interest rates as key factors explaining the risk-return relationship.
B. variability of coefficients of sensitivity to the APT factors for a given asset over time.
C. use of several factors instead of a single market index to explain the risk-return relationship.

Correct Answer: C

The security market line equation is called the CAPM. The CAPM is a single risk factor model which attempts to predict the expected return on an asset given the expected market return and a stock's beta coefficient.

APT is a competing asset valuation model that assumes that many risk factors, other than market risk, drive stock returns. A multi-factor model, the APT relies on the assumptions: that capital markets are competitive, investors prefer more wealth to less and zero arbitrage exists. APT does not identify the risk factors to be included in the model and if only market risk is used, the APT would equal CAPM.

Practice Question 7

In contrast to the Capital Asset Pricing Model, Arbitrage Pricing Theory:

A. uses risk premiums based on micro variables.
B. specifies the number and identifies the specific factors that determine expected returns.
C. does not require the restrictive assumptions of the market portfolio.

Correct Answer: C


Practice Question 8

The APT differs from the CAPM because the APT

I. places more emphasis on market risk.
II. recognizes multiple systematic risk factors.
III. recognizes multiple unsystematic risk factors.
IV. minimizes the importance of diversification.

A. II only
B. II and IV
C. I and III

Correct Answer: A

Practice Question 9

Which assumption best links the theories of the CAPM and the APT?

A. Once a portfolio is well diversified, all risk factors that are unique to a security will be diversified away.
B. All investors will hold the market portfolio.
C. Security prices are only affected by movements in the market.

Correct Answer: A

Both models assume that security returns will be dependent upon some "macro" or systematic factors. Consequently, when securities are added to a portfolio, the risk factors that are unique to specific securities will offset each other until they are all diversified away.

Practice Question 10

Which of the following statements is (are) true with respect to the comparison drawn between the arbitrage pricing model and CAPM?

I. Both models assert that there is a linear relationship between risk and return.
II. Both models define equilibrium as a state where all securities have the same reward to risk ratio.
III. The fundamental factors for the APT model are not known, whereas for CAPM, there is only one fundamental factor, the market portfolio.
IV. CAPM is based upon less restrictive assumptions than the APT model.

A. I and III only
B. I and IV only
C. II only

Correct Answer: A

II is incorrect because only CAPM defines equilibrium as a state where all securities have the same reward to risk ratio. APT, on the other hand, defines equilibrium as a state where no riskless profit may be had.

IV is incorrect because it's the other around; the APT model is based upon less restrictive assumptions than CAPM.

Practice Question 11

Which of the following statements with respect to CAPM and APT is true?

A. Both models state the market as a whole is a factor that will influence specific security returns.
B. The APT model has far more restrictive assumptions than CAPM.
C. CAPM would have a greater predictive power in forecasting individual security returns than would an APT model.

Correct Answer: A

In general, while the CAPM states that the market portfolio only influences the security return, the APT model considers that many more factors, other than the market portfolio, can influence security returns. CAPM then can be though of as a subset version of the APT model. Furthermore, because APT considers many more factors that influence security returns, it would have a greater predictive power in forecasting individual security returns than would CAPM.

Study notes from a previous year's CFA exam:

10. The CAPM and the APT