The capital asset pricing model (CAPM) and its beta calculation have long been used to determine expected returns on assets and to determine the "alpha" generated by active managers. But this calculation may be misleading â€“ active managers touting positive alpha strategies may be taking excessive risk that is not captured in their analysis and attribution of returns. Investors should understand the intertemporal capital asset pricing model (ICAPM) and its extension of efficient markets theory in order to avoid the surprise caused by risks they did not even know they were taking. (For a primer on CAPM, refer to *The Capital Asset Pricing Model: An Overview.*)

**The CAPM Fails to Explain Returns**The CAPM is a widely-known model of asset pricing that implies that, in addition to the time value of money (captured by the risk-free rate), the only factor that should affect the calculation of an asset's expected return is that asset's co-movement with the market (i.e. its systematic risk). By running a simple linear regression using historical market returns as the explanatory variable and the asset's returns as the dependent variable, investors can easily find the coefficient - or "beta" - that shows how sensitive an asset is to market returns, and determine an expected future return for the asset, given an assumption of future market returns. While this is an elegant theory that should simplify investors' risk/return trade-off decisions, there is considerable evidence that it simply does not work - that it does not fully capture expected asset returns. (For more reasons why some investors think CAPM is full of holes, see

*Taking Shots At CAPM.*)

The CAPM is based on a number of simplifying assumptions, some of which are reasonably made, while others contain significant deviations from reality which lead to limitations of its usefulness. While the assumptions were always defined in the academic literature on the theory, for many years after the introduction of the CAPM, the full extent of the effects resulting from these assumptions were not understood. Then in the 1980s and early 1990s, research uncovered anomalies to the theory: by analyzing historical equity returns data, researchers found that small-cap stocks tended to outperform large-cap stocks in a statistically significant way, *even after accounting for differences in beta*. Later, the same type of anomaly was found using other factors, for example value stocks appeared to outperform growth stocks. To explain these effects, researchers went back to a theory developed by Robert Merton in his 1973 paper, "An Intertemporal Capital Asset Pricing Model."

**The ICAPM Adds More Realistic Assumptions About Investor Behavior**The ICAPM contains many of the same assumptions found in the CAPM, but recognizes that investors may wish to construct portfolios that help hedge uncertainties in a more dynamic way. While the other assumptions embedded in the ICAPM (such as complete agreement among investors, and a multivariate normal asset return distribution) should continue to be tested for validity, this extension of the theory goes a long way in modeling more realistic investor behavior, and allows more flexibility in what constitutes efficiency in markets.

The word "intertemporal" in the theory's title refers to the fact that, unlike the CAPM, which assumes investors only care about minimizing variance in returns, the ICAPM assumes investors will care about their consumption and investment opportunities over time. In other words, the ICAPM recognizes that investors may use their portfolios to hedge uncertainties relating to future prices of goods and services, future expected asset returns, and future employment opportunities, among other things.

Because these uncertainties are not incorporated into the CAPM's beta, it will not capture the correlation of assets with these risks. Thus, the beta is an incomplete measure of the risks investors may care about, and thus will not allow investors to accurately determine discount rates and, ultimately, fair prices for securities. In contrast to the single factor (beta) found in the CAPM, the ICAPM is a multi-factor model of asset pricing - allowing additional risk factors to be incorporated into the equation.

**The Problem of Defining Risk Factors**While the ICAPM gives a clear reason why the CAPM does not fully explain asset returns, unfortunately it does little to define exactly what should go into the calculation of asset prices. The theory behind the CAPM unequivocally points to co-movement with the market as the defining element of risk that investors should care about. But the ICAPM has little to say on specifics, only that investors may care about additional factors that will influence how much they are willing to pay for assets. What these specific additional factors are, how many there are, and how much they influence prices is not defined. This open-ended feature of the ICAPM has led to further research by academics and professionals trying to find factors by analyzing historical pricing data.

Risk factors are not observed directly in asset prices, so researchers must use proxies for underlying phenomena. But some researchers and investors contend that risk factor findings may be nothing more than data-mining. Rather than explaining an underlying risk factor, the outsized historical returns of particular types of assets are simply flukes in the data - after all, if you analyze enough data, you will find some results that get past the tests of statistical significance, even if the results are not representative of *true* underlying economic causes.

So researchers (particularly academics) tend to continually test their conclusions using "out of sample" data. Several results have been thoroughly vetted and the two most famous (the size and value effects) are contained in the Fama-French three factor model (the third factor captures co-movement with the market - identical to that of the CAPM). Eugene Fama and Kenneth French have explored economic reasons for underlying risk factors, and have suggested that small-cap and value stocks tend to have lower earnings and greater susceptibility to financial distress than large cap and growth stocks (above that which would be captured in higher betas alone). Combined with thorough exploration of these effects in historical asset returns, they contend that their three factor model is superior to the simple CAPM model because it captures additional risks that investors care about.

**The ICAPM and Efficient Markets**The quest to find factors affecting asset returns is big business. Hedge funds and other investment managers are constantly seeking ways to outperform the market, and discovering that certain securities outperform others (small cap vs. large cap, value vs. growth, etc.) means that these managers can build portfolios with higher expected returns. For example, since research appeared which showed that small cap stocks outperform large caps, even after adjusting for beta risk, many small cap funds have opened as investors try to cash in on better-than-average risk adjusted returns. But the ICAPM and the conclusions drawn from it presume efficient markets. If the ICAPM theory is correct, the outsized returns of small cap stocks are not as good a deal as they initially appear. In fact, the returns are higher because investors demand greater returns to compensate for an underlying risk factor found in small cap stocks; higher returns compensate for greater risk than that which is captured in these stocks' betas. In other words, there is no free lunch.

**Using the ICAPM when Making Investment Decisions**Many active investors deplore efficient markets theory - partly due to its underlying assumptions that they view as unrealistic, and partly due to its inconvenient conclusion that active investors cannot outperform passive management - but individual investors can be informed by the ICAPM theory when building their own portfolios.

**Conclusion**

The theory suggests that investors should be skeptical of alpha generated by various systematic methods, since these methods may simply be catching underlying risk factors that represent justifiable reasons for higher returns. Small-cap funds, value funds and others that tout excess returns may, in fact, contain additional risks that investors should consider. (Learn more about efficient markets in our article *Working Through the Efficient Market Hypothesis.*)