What's new

Nicole Seaman

Director of FRM Operations
Staff member
Learning objectives: Describe multifactor models, and compare and contrast multifactor models to the CAPM. Explain how stochastic discount factors are created and apply them in the valuation of assets. Describe efficient market theory and explain how markets can be inefficient.


701.1. In introducing multifactor models, Andrew Ang explains that "to capture the composite bad times over multiple factors, the new asset pricing approach uses the notion of a pricing kernel. This is also called a stochastic discount factor (SDF). We denote the SDF as (m)." This allows him to write the risk premium of an asset as a function of β(i,m) and the price of risk, λ(m), as follows:

About the relationship and its implications, each of the following statements is true EXCEPT which is false? Reminder hint: the β(i,m) here is not exactly the same CAPM's traditional beta exposure to the market risk premium, this is a generalized, different beta.

a. The expected return for the asset can be negative if this β(i,m) is high enough
b. The (m) denotes a pricing kernel or stochastic discount factor (SDF) and (m) is an "index of bad times"
c. A higher cov[r(i),m] corresponds to a higher β(i,m) which implies a higher risk premium and a higher expected return for the asset
d. The stochastic discount factor (SDF) can depend on a vector of factors, F = [f(1), f(2), ...f(k)] where each of the (K) factors defines different bad times; e.g., high inflation, low economic growth

701.2. Ang says "The $64,000 question with multifactor pricing kernel models is: how do you define bad times?" With respect to the multifactor model, among the following choices which is the BEST definition of "bad times?"

a. Low wealth level
b. Low happiness level
c. High marginal utility of the representative agent
d. Low marginal utility among heterogeneous agents

701.3. According to Ang's theory of factor risk, which of the following statements is TRUE?

a. There should never be rational deviations from efficiency
b. The financial crisis was consistent with the multifactor model
c. The financial crisis demonstrated the failure of diversification
d. Factor theory implies that active management does not add value; ie., factor strategies should fail to "beat the market"

Answers here:
Last edited by a moderator: