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Risk Management

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Estimation of expected return for individual stocks is central to many financial decisions such as those relating to portfolio management, capital budgeting, and performance evaluation. The two main alternatives available for this purpose are a single factor model (or Capital Asset Pricing Model (CAPM)) and the three factor model suggested by Fama and French. The CAPM’s simplicity helps to build intuition around the concept of modeling return as a function of risk, under this model beta is a catch-all proxy for systematic risk.

The CAPM’s simplicity is also its greatest shortcoming, as the underlying assumptions limit its ability to explain and predict actual returns. It is obvious that there are a myriad of risk factors facing companies today. Some of these factors are market risk, bankruptcy risk, currency risk, supplier risk, etc. ; and given that the CAPM uses a single factor to describe aggregate risk, it seems logical that a model including more sub-factors might provide a more descriptive and predictive model.

Furthermore, from a statistical perspective, the addition of independent variables to a regression often improves the explanatory power of a model. For these reasons, multifactor models relax the assumption and constraint of a single risk factor and look for other factors that affect expected return to assets. The Fama-French Three-Factor Model expands the capabilities of the CAPM model by adding two company specific risk factors – SMB and HML. The three factors in concert explain most of the returns due to risk exposure.

SMB, which stands for Small Minus Big, is designed to measure the additional return investors have historically received by investing in stocks of companies with relatively small market capitalization.

This additional return is often referred to as the “size premium. ” In practice, the SMB monthly factor is computed as the average return for the smallest 30% of stocks minus the average return of the largest 30% of stocks in that month. A positive SMB in a month indicates that small cap stocks outperformed large cap stocks in that month.

A negative SMB in a given month indicates the large caps outperformed. HML, which is short for High Minus Low, has been constructed to measure the “value premium” provided to investors for investing in companies with high book-to-market values. Constructed in a fashion similar to that of SMB, HML is computed as the average return for the 50% of stocks with the highest B/M ratio minus the average return of the 50% of stocks with the lowest B/M ratio each month.

A positive HML in a month indicates that value stocks outperformed growth stocks in that month. A negative HML in a given month indicates the growth stocks outperformed. BA measures of the exposure an asset has to market risk (although this beta will have a different value from the beta in a CAPM model as a result of the added factors), SA measures the level of exposure to size risk and HA measures the level of exposure to value risk. The coefficients SA and HA take values on a scale of 0 – 1.

By comparing the realized returns with that predicted by the CAPM model, we find that the model is often incorrect. We find that CAPM models usually achieve R square (coefficient of determination)1 measure of only about 0. 85. While this relatively high R Square value is one of the main reasons for the popularity of the CAPM, it also highlights the fact that roughly 15% of the variation in observed returns still remains unexplained. Whereas, with the SMB and HML factors the model provides a better R Square fit with R Square value of 0.95. (Tuck School of Business at Dartmouth, Case 03-111)

The intuition for SMB, which is a measure of “size risk”, is that small companies logically should be expected to be more sensitive to many risk factors as a result of their relatively undiversified nature and their reduced ability to absorb negative financial events. On the other hand, the HML factor suggests higher risk exposure for typical “value” stocks (high B/M) versus “growth” stocks (low B/M).

This appeals to intuition because companies need to reach a minimum size in order to execute an Initial Public Offering; and if we later observe them in the bucket of high B/M, this is usually an indication that their public market value has plummeted because of hard times or doubt regarding future earnings. Since these companies have experienced some sort of difficulty, it seems plausible that they would be exposed to greater risk of bankruptcy or other financial troubles than their more highly valued counterparts.

A primary implication of the Three Factor Model is that investors (unlike the single factor model) can choose to weight their portfolios such that they have greater or lesser exposure to each of the specific risk factors, and therefore can target more precisely different levels of expected return. It is interesting to note that Fama and French still see high returns as a reward for taking on high risk; in particular that means that if returns increase with book/price, then stocks with a high book/price ratio must be more risky than average – this is in contrast to traditional analyst’s beliefs.

The difference arises from whether or not one believes in the efficient market theory. The analyst doesn’t believe it, so he is opined that high book/price indicates a buying opportunity. But if an individual believes in efficient market theory then one might believe cheap stocks can only be cheap for a good reason, namely that investors think they are risky(http://www. moneychimp. com/articles/risk/multifactor. htm). The French and Fama model has many effective uses. The first being the ability to categorize investments depending on how their returns vary with different risk factors.

In practice, this characterization is executed through multivariate regression. The historical returns of a particular portfolio are regressed against the historical values of the three factors, generating estimates of the coefficients. Secondly, it helps to evaluate an active manager’s performance independent of her fund’s risk exposure. For this, funds are often plotted on a 3×3 matrix, demonstrating the relative amount of risk represented by the different strategies. With these tools, investors are able to make more informed investment decisions with respect to personal preference regarding the risk/reward tradeoff.

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