The **Capital Asset Pricing Model (CAPM),** which estimates the return on an asset by its co-varying relationship (its **beta**) with the market portfolio, has spawned a whole field of study devoted to improving upon the original model. We have already explored **D-CAPM**, which modified beta to measure downside risk rather than total risk. Our attention now turns to another alternative theory, the **Intertemporal CAPM (I-CAPM)**. As in previous discussions, we omit the complicated mathematics.

I-CAPM was first introduced in 1973 by Merton. It is an extension of CAPM which recognizes not only the familiar time-independent CAPM beta relationship, but also additional factors that *change over time* (hence “intertemporal”). Specifically, Merton posited that investors are looking to hedge risks based on current and projected **factors**, such as changes in inflation, employment opportunities, future stock market returns, etc. Thus, an I-CAPM portfolio contains a core investment tied to the market portfolio, plus one or more hedge portfolios that mitigate an investor’s currently-perceived risks. Since each investor has his/her own perceptions of risk, I-CAPM is hard to generalize to a population of investors. Also, the correct factor to use for any given hedge is *ambiguous*: if you think you might be unemployed 3 years from now, which factor do you choose to hedge?

So, I-CAPM is a multi-factor model that attempts to capture more determinants of risk than just beta, but does not provide concrete guidance for identifying which additional factors to use, or even how many of them to include.

A popular “fix” to this problem has been to employ the **Fama-****French**** Three-Factor Model (FF)**, which states that the two additional factors beyond beta should be used to improve CAPM. These two factors relate to specific **investment styles**:

**Liquidity**: small capitalization stocks outperform large-cap stocks**Value**: value stocks outperform growth stocks

FF speculates that these two stock groupings, small cap and value stocks, are inherently more risky to macroeconomic downturns and thus are required by investors to provide higher returns (hence portfolios built on these factors should have betas higher than 1.0, the market beta). However, FF posits that the risk premia provided by these two factors *exceeds* that provided by a higher beta alone – that there is an **alpha** component (representing *non-systematic risk*) to the returns generated by portfolios built on these factors. But I-CAPM requires **efficient markets,** which would mean that each factor’s risk premium is due *only* to its beta. Hence, I-CAPM argues *against* alpha-based returns, which indeed is the overall conclusion we have been seeking to evaluate over the past months. We will keep returning to this question, as it has serious implications for our ultimate topic: alternative beta strategies and hedge fund replication.

Copyright 2011 Eric Bank, Freelance Writer