Consumption CAPM: Cyclical Risk, Insurance Payoffs, and Expected Returns
Summary
The document poses questions about asset pricing in a consumption CAPM setting with quadratic utility and consumption growth whose mean and volatility vary with the business cycle. It asks how securities tied positively to consumption should be priced, how a security that pays more during bad consumption states should behave, and how to compare expected returns across industries and company types. The suggested intuition is that investors require compensation for assets that perform poorly when consumption is weak, while insurance-like payoffs can help smooth consumption.
It also raises the possibility that additional return factors, including the Fama–French factors, would affect the rankings. The document does not supply answers or calculate consumption betas for the examples, so it leaves the industry ordering unresolved. Any comparison would require evidence about each asset’s covariance with consumption growth and, in a multifactor setting, its exposure to the relevant priced factors; sector labels alone do not determine those exposures.
Key ideas
- The consumption CAPM relates expected returns to how asset payoffs covary with consumption risk.
- An asset that performs poorly in bad consumption states may require greater expected compensation, all else equal.
- A security that pays more during adverse consumption shocks can provide insurance and help smooth consumption.
- Expected-return rankings across industries require estimates of their consumption exposures rather than labels alone.
- Additional priced factors can change comparisons, but the document does not estimate exposures or provide a ranking.
Tags
Full text
# Some basic questions using consumption CAPM
# Some basic questions using consumption CAPM
Say we are in a world described by the consumption CAPM. All investors in this world have quadratic utility. Also, assume that consumption is as follows: $$c_{t+1} = (1+m_t)c_t + s_t c_t e_{t+1} $$ where the shocks $e_t$ are iid with $E_t(e_{t+1})=0$ and $V_t(e_{t+1}) = 1$. Now $m_t$ and $s_t$ depend on the business cycle so that in down times $m_t$ and $s_t$ are high, but in boom periods $m_t$ and $s_t$ are low. Assume that the risk-free rate is independent of time.
I have a few questions as follows and was wondering if my answers make sense or if someone can correct me.
> Say there is a company (e.g., luxury goods) that is very sensitive to the business cycle. Will this company have high or low returns?
My answer: Investors don't like uncertainty about consumption. You consume more luxury good in good times and less in bad times. Since it varies positively with consumption, you will require a low price and hence luxury goods will have high returns. Is my explanation right here?
> Now consider a security that provides insurance against bad consumption shocks so that in down periods it pays off more. What can we say about the price of this security? Will it have a high/low price when consumption is high? Will it have high/low price during a down period?
My answer: This security would smooth consumption since it varies negatively with consumption. It pays off good in bad times and does not pay off in good times. As a result during a recession/down period, this security would have a high price and during a boom (when consumption is high), it will have a low price. Is my explanation right here?
> Using the consumption CAPM, rank the expected returns on the following types of companies: i) computer software; ii) luxury goods; iii) basic consumer products; iv) oil and gas; v) high-growth company.
We need to compare the consumption beta of each company. The higher the consumption beta, the higher the expected return, all else equal. But I'm not quite sure how to roughly compare the betas of the above companies. Could anyone help?
> Now for the above ranking, consider other risk factors that could explain expected returns, e.g., Fama-French 3 factors etc. How would the rankings change?
Again, I know I need to think about the covariance between the returns of the companies and how they co-vary with the risk factors, but I am unsure of the direction of the covariance. Could someone help here?Shown in full with attribution under the source's licence. Licence: CC BY-SA 4.0 (Stack Exchange)
This summary was written by Stratmill's research agent from the original; it is not a copy of the source.