Friday, April 16, 2010

When the risk free rate is not risk free, CAPM musings

Much of modern finance and pricing theory rests upon the firm bedrock of a "risk free" asset from which all other prices and returns derive.

This has to do with the ramifications of the CAPM pricing model. The risk free asset or rate has zero volatility and zero covariance with market returns or the systemic risk associated with market returns.

But the CAPM (and its extensions by Tobin, et al.) also has the unfortunate property of not working in reality. How can this be?

Let's look at "Beta", defined as the covariance of an asset and a portfolio in terms of the variance of the market portfolio (all assets, but typically for stocks this is taken to be the S&P 500). This is a nice and tidy way to say an asset is less risky if it tracks market returns, since the market is broad and efficient.

But there are problems.

Over what period of time are we measuring? The beta of an asset with the market can vary between time periods (would a measurement including only the returns from 2006-2009 be an accurate indication of an assets "Beta"?) Since time is a non-fungible item (every second that passes this world is unique given the activity of all matter at that time), assigning a discrete value to a continuous series of events is not helpful.

Saying "this asset has a Beta of x, and thus, its behavior with respect to the market at future point T1 will be Y" is fallacious. Post hoc ergo propter hoc.

As for the "risk free" rate. This should in theory always be zero (risk=return). But since we rarely see this, all assets contain some risk. Treasuries contain a massive number of risks (most of them collapse into results like "inflation" and "devaluation" or "ceasing to exist").

Thus, the two major assumptions of the CAPM, the risk free rate and Beta, are not very helpful when attempting to assess the relationship between risk and return. It is no surprise then that prices according to CAPM formations have simply not conformed to its rules. It is a dead theory and we should all move on instead of creating epicycles explaining "anomalies".

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