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by Jeffrey Mortimer, CFA, and Seunghee Han, Hui Hui Huang, and Arbi Rizo It is common practice to evaluate active fund managers by simply comparing their returns to a specified benchmark. This focus on relative return is intuitive and implicitly accepts the risk of the benchmark as the appropriate level of risk. What this fails to do, however, is provide any formal evaluation of the true whether a fund manager’s return is the result of skill or risk taking. In addition to standard attribution methodologies, the J.P. Morgan Investment Analytics & Consulting group utilizes proprietary factor attribution models to measure the risk/return profile of equity and fixed income portfolios. For U.S. equity, we utilize a four-factor model. For fixed income portfolios, we utilize a three-factor model. The U.S. equity attribution model is an extension of Sharpe’s Capital Asset Pricing Model (CAPM). We incorporate the three-factor work of Eugene Fama and Kenneth French and add a fourth factor covering the work of Mark Carhart around momentum investing. Under our four-factor model, the sources of risk in U.S. equity investments are characterized as having market-related (systematic) and security-specific (unsystematic) components. The main goal of this attribution model is to decompose or strip out the effects of the market-related factors in an effort to identify the alpha, or value added or subtracted, as a result of the investment manager’s stock selection ability. Through this quantitative process, the portfolio’s exposures or factor betas are identified. The factor betas are multiplied by the average factor returns to assess the portfolio’s realized return. The alpha in this case is the security-specific component or the residual that remains after the factors and risk-free rate have been accounted for. As noted, alpha can be positive or negative, with the latter implying the investment manager has done a poor job selecting securities. This last point is important since all active managers will at some point experience periods of underperformance. The model helps us determine if this is a result of bad luck or poor stock picking ability. Additional advantages of using the four-factor model for analysis include a higher R-squared in explaining a security’s return stream than that of the CAPM alone and greater accuracy in determining a proper “normal” benchmark for a portfolio by defining a portfolio’s risk exposures relative to the exposures of potential benchmarks. Also, the model has the ability to define the manager’s true style, evaluate tracking error, and aid in identifying worthy candidates when performing manager searches. J.P. Morgan's Four Factors From a market-related or systematic standpoint, the risk and return sources in our equity attribution model are attributable to four common factors. The factors are:
The market risk factor is the risk associated with investing in the broad stock market as opposed to a risk-free investment such as T-Bills. This is Sharpe’s CAPM market factor, through which he introduced the notion of an asset’s sensitivity to systematic risk as well as unsystematic risk. Stock market indices are frequently used as proxies for the market and therefore have a beta close to one. Betas exceeding one indicate more than average “riskiness”, and betas below one indicate that risk is lower than average. Some portfolio characteristics that may lead to betas greater than one may be the result of holding a portfolio of volatile securities (as measured by beta), highly concentrated portfolios, or security holdings outside of the relevant index. Size is the risk related to the market capitalization of a firm. The belief is that small firms tend to be less profitable than large firms because their earnings are less certain. As a result, small firms are regarded as riskier investments and therefore should expect to earn higher rate of returns. The size beta measures the exposures of the portfolio to small cap, mid cap and large cap securities. A positive size beta indicates an exposure to smaller capitalization stocks. Large cap portfolios will have size betas close to or less than zero. Style is the risk associated with the financial distress of a firm. The measure of distress is analyzed by using the ratio of a firm’s book value to its market value of equity, which is otherwise known as the book-to-market ratio. A firm with a high book-to-market ratio is considered more risky or distressed because they have lower earnings, resulting in a lower stock price versus the book value per share. These firms are labeled as value stocks. Investors purchasing shares of value stocks should expect to earn a higher return than firms with low book-to-market ratios, known as growth stocks. A positive book-to-market beta indicates an exposure to value stocks whereas a beta close to or less than zero would represent a portfolio of more core-like or growth holdings. Momentum reflects the belief that stocks that have recently outperformed (underperformed) will continue to outperform (underperform) in the near future. The momentum factor returns some of the rapid change when markets move abruptly. Factor Returns and Betas The factor returns are computed from all publicly traded issues for which market data is available on the NYSE, Amex and NASDAQ exchanges. From this universe of stocks, sub-portfolios are created in order to isolate the returns due to size (small size sub-portfolio minus large size) and style (high book-to-market or value sub-portfolio minus low book-to-market or growth). The market factor is a value-weighted return of all the stocks less the one month T-bill. The momentum factor is based on the difference between two equally weighted portfolios of the top 30% and bottom 30% performing stocks over a specified holding period. Factor returns are common to all the stocks and benchmarks; in other words, benchmarks are treated as separate portfolios. The portfolio’s exposure, or beta, to the four factors is derived after obtaining the factors returns. In our model, a multiple regression of 48 months of rolling portfolio returns is run against each of the factor returns to obtain the portfolio’s sensitivity to each factor. All portfolios have their own unique set of betas for each factor, and this set of betas explains the portfolio’s style. Exhibit 1 charts the historical betas of the style factor for a sample small cap value portfolio. The green line indicates that the manager’s beta lies below the beta of the Russell 2000 value index (blue line). This implies that over the period in review, the portfolio had less of a value bias and more of a core-like exposure. This type of insight can be helpful when meeting with investment managers or performing due diligence to ensure that managers are following the strategies they claim to. The value/growth boundary lines are dynamic. Over time, they have generally moved in a range of about 10 points. We now incorporate the betas with our factor returns to analyze how successful the manager has been in adding value. Multiplying the portfolio’s average beta by the average factor returns produces the portfolio’s expected factor-driven returns. The sum of these expected factordriven returns plus the risk-free rate equals the expected return of the portfolio. The difference between the portfolio’s actual return and this expected return is the alpha or the ‘unexplained’ residual of the model. Analyzing a portfolio this way allows us to define the manager’s sources of return while measuring the risks taken to achieve that return. Exhibit 1: Style Beta (book to market)
The overall portfolio return is -1.27%, and from a relative return standpoint, the portfolio’s excess return is 139 basis points. From an attribution standpoint, we can see how the portfolio return is decomposed. The largest detractor from return comes from the market factor (-5.15%). The size and book-to-market factors provide some positive return influence. It is important to note that the alpha is positive, which indicates the manager is adding value after stripping out the effects of the factors. Exhibit 2: Components of Excess Return
In conclusion, the four-factor model is a powerful tool for manager evaluation. It provides analysis of how excess returns are achieved and aids in determining and quantifying the merits of active over passive management. The four factor model provides a picture of the manager’s investment style and can assist in constructing a diversified portfolio across size and style mandates. This is important since empirical studies indicate that approximately 90% of the differences in returns among institutional portfolios can be attributed to asset allocation differences. The four-factor attribution model provides clients with a tool to analyze their managers and formulate suitable questions.
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