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Question from Schweser (62. Factor Theory)

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Which of the following statements best describes the relationship between asset payoffs and “bad times” events (high inflation, low economic growth, or both)?

A. The higher the expected payoff of an asset in bad times, the higher the asset’s expected return.
B. The higher the expected payoff of an asset in bad times, the lower the asset’s expected return.
C. The expected payoff of an asset in bad times is unrelated to the asset’s expected return, because it depends on investor preferences.
D. The expected payoff of an asset in bad times is unrelated to the asset’s expected return, because arbitrageurs eliminate any expected return potential.

Schweser says the right answer is B. Why?

David Harper CFA FRM

David Harper CFA FRM
Staff member
Hi @AlexFrm Yes, in my view statement (B) is true. The theory is non-trivial (link to member discussion below, but I copied a relevant section). A big reason this has caused confusion is that Ang's beta is not the CAPM beta as readers seem to expect. The point of "The higher the expected payoff of an asset in bad times" can be illustrated by comparing two stocks (I will use examples from my own portfolio)
  • Instructure (INST) is my favorite holding but it's a risky position: tech company (SaaS) with no current profits, negative cash flow etc.
  • I also own Sprouts (SFM) which is a so-called "consumer defensive" organic food grocer.
Let's say "bad times" is a market pullback (or other negative shock). When this happens, in truth, I do expect INST to drop more than SFM. (and anecdotally, even on a daily basis, this is generally true). Hence, in bad times, my SFM has an expected return that is less negative than my INST. It is safer! Consequently, although there is some interesting math involved, the implication is that SFM has a lower expected return (which is also true, lol). I hope that's helpful!

From https://www.bionicturtle.com/forum/threads/p2-t8-701-multifactor-models-andrew-ang.10169
Hi @Roddefeller Great question! This portion of Ang challenged me. As you suggest, it is not CAPM (that's just an analogy), because (m) is an index of bad times. So, for me, the key was to realize (1) that a positive value of (m) likely correlates with negative asset returns and (2) that the typical asset has a negative covariance with (m). So, just to makeup some numbers:
  • Say an asset has cov(R,m) = -0.090; a negative covariance would be typical because during "bad times" the expected return of the stock (with factor exposure) is negative and so this is expressing scenario --> {-R, +m}
  • Say the var(m) = .250 = 50%^2, which must be positive, and this is selected to generate a reasonable β(R,m) in this case of -0.090/0.25 = -0.360.
  • E(m) appears to be near in value to a discount factor per (6.7), so let that be 0.90, then λ = var(m)/E(m) = -0.250/0.90 = -0.2777
  • The the expected excess return = β(r,m)*λ = (-0.090/0.250)*(-0.250/0.90) = + 10.0% ... Then let's increase the beta (from -0.360 to -0.160) by increasing the covariance:
  • Say to cov(R,m) = -0.040, then expected excess return reduces to (-0.040/0.250)*(-0.250/0.90) = +4.44%.
  • If these numbers are roughly correct, then, as the var(m) cancels and the E(m) is near to 1.0, the expected excess return can be viewed as somewhere in the neighborhood of the negative cov(R,m), or more specifically, a discounted -cov(R,m)
  • Intuitively, this higher-beta asset has a lower expected return because during "bad times" (i.e., high positive m) it experiences less of a loss (along with the market); i.e., a higher return because it is less negative. In my interpretation, then, the natural state of things is a negative covariance between R and m, which actually seems very elegant to me in the context of Ang's definition of factors: how much do we expect to lose during bad times? The exception, then, is the positive beta because that's an asset that would have an expected loss (gain) during normal (bad) times, as reflected by an unusual (in this context) positive covariance. So this exception would be a true hedge instrument that we might associate with negative CAPM beta (and therefore positive beta in this context, because we might actually expect it to earn positive returns during a market crash or otherwise bad time) ... I hope that's helpful!