Consumption CAPM

When we recently examined Intertemporal Capital Asset Pricing Model (I-CAPM), we understood it to be an extension of CAPM in which investors establish additional portfolios to hedge specific risks representing short-term idiosyncratic tastes and preferences. Typical examples of these specific risks include inflation, job loss, economic downturn, etc. The model is somewhat incomplete, in that it doesn’t specify how to arrive at the proper factors to quantify these additional hedges.  Another approach, called the Consumption CAPM (C-CAPM) posits a single additional hedge portfolio based on consumption risk, which is a hedge against future consumption rates.  Let’s see how that works.

C-CAPM assumes that investors are not interested in maximizing their portfolio, but rather in maximizing over their lifetimes the consumption they get from their portfolio.  Therefore, there is a tradeoff between current and future consumption. The model assumes that investors will sell assets during bad economic times and buy them when times are good. That means that, say, a yacht, will have to have a very high future expected return (a high risk premium) to induce the owner to hold onto it when times are bad. Therefore the systematic risk of the asset (the yacht) is tied to the state of the economy.

An illustration will clarify.

Each person has their own set of utility functions. For instance, if I buy an asset (such as a yacht) today, it will cost me $X.    If I am to hold off on buying the asset, it had better be worth it to me to wait.  In other words, I should receive a return on the amount, $X, that I didn’t consume today.  If that return, which we’ll call the consumption premium, is high enough, I’ll wait; if not, I’ll buy the asset today. At some rate of return (let’s call it r0) I am indifferent to waiting or consuming. If my return on $X is expected to exceed r0, I’ll wait. If it is expected to be less than r0, I’ll consume today.

Now, if I expect a rosy economic future, I will assign a higher risk premium to the yacht; conversely, if I see the future economy tanking, I lower risk premium on the yacht, making it more likely to consume the asset now rather than waiting.  Of course, if I’m anticipating a severe depression, I just might keep the $X in Treasury bonds and adjust my utility function accordingly.  Since the price of my current Treasury bonds will rise during a depression (because of their relatively high interest rates), they are a good hedge against bad times – something that cannot be said about a yacht. In terms of C-CAPM theory, the returns on the Treasury bonds have a negative correlation with consumption, and are thus are worth more during times of depressed consumption. The yacht’s returns have a positive correlation with consumption (yachts sell for more in times of consumption growth), and are therefore worth less during low-consumption periods.

Bottom line: hedge your portfolio with assets that will do well when economic consumption rates drop.

In C-CAPM, one has to measure the consumption premium accurately in order to have a valuable model. One problem that arises is that of satisfice:  are consumers really looking to optimize consumption, or are they merely satisfied with achieving some minimum constraint? This will have considerable impact on the rate at which future consumption is discounted to arrive at its value today.

Now that we’ve looked at CAPM and several alternatives, we want to next explore the topic of specific risk premia, which we’ll loosely define as the return (above the risk-free rate) that can be associated with taking on certain systematic risks.  We want to see whether, for any given hedge fund strategy, returns can be ascribed solely to the systematic risks (i.e. beta) of the strategy, or whether some portion of the return is due to a superior fund manager (alpha).  This will lead to our ultimate topic: hedge fund replication.

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Copyright 2011 Eric Bank, Freelance Writer

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