This paper presents a three-factor model as a tool that can be used by financial advisors to structure and analyze portfolios. Additionally, the tool can be used to evaluate mutual fund performance and measure style drift among active managers. The three-factor model facilitates the development of a consistent investment philosophy and enables the analysis of portfolios based on the most recent scientific advances in portfolio management.
Alejandro Murguía, Ph.D., is the director of investment research for McLean Asset Management Corporation (MAMC).
Dean T. Umemoto, CFP, ChFC, CLU, founded MAMC in 1984. MAMC provides comprehensive financial and investment advisory and management services for clients located primarily in the Washington, D.C., metropolitan area.
As financial planners become increasingly responsible for managing client investment holdings, portfolio management has undertaken an integral role within the planner’s workplace. A planner may be expected to perform an analysis of a prospective client’s current holdings and suggest appropriate changes. A planner also may receive additional funds from an existing client that may merit a new analysis of the client’s holdings.
As planners, we have been exposed to the many truisms with regard to portfolio management. These may include popular adages such as “don’t put all your eggs in one basket” and tables from which a planner derives a client’s equity to fixed-income allocation based on an algorithm of age or investment time horizon. Although these are prudent suggestions, we are generally unaware of how these tables are constructed and become somewhat dependent on others for any changes in these broadly defined allocation parameters.
Moreover, planners are exposed to a myriad of financial software systems and subscription services that offer a black box approach to evaluating and designing clients’ portfolios. While these services provide broad guidelines for constructing a portfolio, their shortcomings can outweigh their benefits. Such programs often are based on assumptions that may change every year and subsequently cause frequent rebalancing in order to attain the ever-elusive “efficient portfolio.” A planner may unintentionally become too reliant on these systems for monitoring a client’s portfolio.
A financial planner wanting to break free of this current landscape may want to explore incorporating the available scientific research of portfolio management into practical applications. This may seem like a daunting task when one considers the cryptic nature of many scientific journals. Another deterrent is a belief that the halls of academia are filled with many theories that are philosophically interesting but void of practical use. The purpose of this paper is to present planners with one of those scientific tools, the Fama/French three-factor model, which can be personalized and effectively used for analyzing and structuring portfolios, as well as evaluating mutual fund performance on a greater level of sophistication than offered by many packaged analytical tools.
Brief Review of the Research
Building on the work developed by Harry Markowitz (1952), several researchers worked independently of one another in the development of the basic construct for what is recognized as the capital asset pricing model (CAPM). Co-winner of the Nobel prize in 1990 with Harry Markowitz and Merton Miller, William Sharpe conveyed his findings in a seminal essay, “Capital Asset Prices: A Theory of Market Equilibrium Under Conditions of Risk.”1 The capital asset pricing model conveys that the expected return for a given portfolio is determined by its overall exposure to market risk.
If all investors are able to combine a market portfolio of all risky assets with a risk-free asset, the only risk that an investor would be compensated for is investing in the market as opposed to the risk-free asset (such as Treasury bills). Hence, investors get paid for taking risk associated with the market. Furthermore, the CAPM posits that the expected return of any risky asset is a function of its relationship with the market portfolio—its beta.
Currently, the CAPM is the backbone of modern portfolio theory. It is commonly used in practical research and included in financial Web sites and software packages used for analyzing mutual funds and portfolios. But academic research has shown that other risk factors play a significant role in stock market equity returns.
Other Risk Factors
Basu (1977)2 showed that stocks with low price/earnings (P/E) ratios earned significantly higher returns than stocks with high P/E ratios. Moreover, his investigation indicated that these differences in returns were not due to differences in beta. If beta is the only risk factor associated with returns, then the P/E ratio should not lead to statistically significant findings. Banz (1981)3 was able to show that small-capitalization stocks have a higher rate of return than large-capitalization stocks. Although smaller stocks exhibited higher betas than larger stocks, their return differences were significantly more than what would be explained by beta. In other words, there should not be a small-cap premium beyond what can be explained by beta.
Research by other investigators adds weight to the body of evidence that contradicts the conclusions drawn from the single-factor CAPM. The variables that led to differences in returns among market portfolios include price/book ratio (Rosenberg, Reid and Lanstein, 1985),4 leverage (Bhandari, 1988),5 and momentum (Jegadeesh, 1990).6 These investigators spurred the development of the three-factor model.
The Fama/French Three-Factor Model
Eugene Fama and Kenneth French (1992)7 brought together the market, size,
price/earnings, price/book and leverage factors in a single cross-sectional investigation of market returns. When controlling for all these factors, they wanted to study what variables remained statistically significant predictors of stock market returns. They found that a combination of three factors—market beta, firm size and price/book—explained approximately 95 percent of the variability of stock market returns. Follow-up investigations applying the three-factor model to other time periods and to international equity markets found similar results.8, 9
Even though the single-factor model does not seem to work as previously thought, the main contribution of the risk/reward concept remains a lynchpin in investment theory. One’s reward should be commensurate with one’s risk. Adding the size and price/book factors increases our understanding of investment returns. Most people can easily understand that investing in the stock market is riskier than holding Treasury bills. Investors are compensated through higher returns for taking extra market risk. If not, there would not be a market premium. Similarly, small-cap stocks have more risk than large-cap stocks and should reward the investor with greater returns to justify their risk. Low price/book stocks are riskier than high price/book stocks and thus have an expected return premium. For example, a company that is valued in the stock market for less than book value is usually experiencing a high level of distress. An investor has incentive to undertake this form of risk if there is an expected return premium. If the expected return on a distressed company were similar to a financially stable company, there would be no incentive to take the added value factor risk.
Fama and French also proposed a five-factor model for measuring balanced portfolios and other hybrid strategies.10 The additional two factors, “term” and “default,” are applied to fixed-income securities. The term factor is the risk of long-term bonds over Treasury bills and the default factor is the risk of corporate bonds over long-term government bonds. For the purpose of U.S. equity analysis, the three-factor model is sufficient.
Table 1 shows the historical returns of different asset classes from 1964–2001. In the large-cap category, large-cap value is the highest returning asset class and large-cap growth is the lowest. Additionally, large-cap value has a lower standard deviation than the market and growth asset classes. A similar relationship is observed in the small-cap asset classes. The small-cap value index is the highest returning asset class. It has a higher return than both the Center for Research in Securities Prices (CRSP) 9–10 Index, which represents the smallest two deciles of equity securities ranked by market cap and the small-cap growth index. And the small-cap value index achieves this return premium with a lower standard deviation than small growth. Although the value indexes exhibit less variance in their returns than the growth indexes as measured by the standard deviation of returns, the stocks that make up the value indexes exhibit significantly greater per-share earnings volatility than the growth stocks.11
Table 2 reveals that one can only expect to receive these premiums over the long term. For example, the S&P 500 outperformed one-month Treasury bills 85 percent of the time over ten-year rolling periods from 1926–2001. For any single year, however, this expectation declines to 68 percent of the time. The same pattern is observed for the size and value risk factors.
Table 3 shows the historical average returns for the three risk factors from 1964–2001. This is how much a portfolio can expect to return for taking an incremental exposure to each type of risk. For example, a portfolio exposed to 100 percent of the size premium during this period would have received the full-size premium of 3.54 percent annualized. This concept is very similar to the beta concept in the single-factor CAPM.
How do we use the three-factor model? By identifying the three independent factors of risk, the model allows us to measure their role in portfolio returns. A planner can use this tool to assess the extent to which portfolios are exposed to these risk premiums. Additionally, the model can be used for a wide variety of functions that can truly give the planner a level of sophistication not present in many advising or investment firms. It can be used to analyze current portfolios and reallocation strategies, structure proposed portfolios to obtain a premium over market returns, analyze mutual fund performance, and track style drift.
The statistical test for using the three-factor model requires knowledge of multiple regression analysis. The method for conducting this type of analysis is presented in many introductory statistical textbooks. Additionally, the statistical function is included in many spreadsheet packages. Multiple regression analysis is an extension of correlation analysis, which involves the use of one independent variable, such as market risk, to measure corresponding changes in one dependent variable (the outcome, such as stock price returns). This method, however, ignores the possible influence of other independent variables (size and value risk, for example) to the dependent variable—that is, stock price returns. Accounting for these other variables enables the acceptance of valid relationships because other possible influences are controlled for in the analysis.
An analogy used to convey this idea is that there is a statistically positive correlation between ice cream consumption and drownings. When another variable, seasonality, is added in this analysis, through multiple regression, the relationship between drownings and ice cream consumption becomes insignificant and the relationship between drownings and seasonality becomes significant. In essence, time of year is more significantly related to drownings than ice cream consumption. The relationship between ice cream consumption and the dependent variable was more a function of its relationship to the season.
It is important to remember that correlation does not imply causation. Multiple regression analysis attempts to analyze which independent variables, such as factors in returns, are significantly related to the dependent variable when accounting for other independent variables. As with all statistical techniques, certain assumptions need to be met in order to engage in the regression analysis.
Analyzing Portfolios with the Three-Factor Model
As an investment advisor, it can be difficult to arrive at an effective set of recommendations for a prospective client whose portfolio consists of multiple accounts with a varied menu of equity and fixed-income holdings. Often an advisor does not have the resources and time to conduct a thorough fundamental analysis of the many stock and mutual fund holdings in such a portfolio. Analyzing the securities with a standard investment research data service is usually the primary resource available to an advisor for determining asset characteristics. Although such programs are convenient, we all have been frustrated to find securities mislabeled as to their asset class or when the fundamental data is inaccurate. This makes it extremely difficult to monitor funds and analyze portfolios in a consistent manner.
Since the three-factor model explains approximately 95 percent of the variability of stock price returns, we can use this analytical tool to measure a portfolio’s performance to its exposure to these risk factors rather than relying on a simplistic comparison of a portfolio’s performance to an arbitrary and, perhaps, inappropriate benchmark.
Figure 1 represents the entire U.S. equity landscape. The crosshairs represent two axes. The size dimension is on the vertical axis and the value dimension (as expressed through book-to-market) is on the horizontal axis. These axes represent exposure to the factors. Movement from the left to right on the horizontal axis represents an increased exposure to the value factor. Movement from the bottom to the top of the vertical axis represents an increased exposure to the size factor. There is not a third axis for the market factor because all equities have similar market risk when accounting for the two other factors. The market portfolio sits at the intersection of size and value. This intersection is the equity market average. The CRSP Universe Index, a proxy for the entire U.S. equity market, represents this average. The intersection of the crosshairs lies toward the bottom of the graph because the index is market-weighted.
Figure 1 also describes a hypothetical client’s portfolio. The portfolio consists of a combination of four evenly divided mutual funds. They consist of the largest small-cap growth, small-cap value, large-cap growth and large-cap value mutual funds with at least five years of data ending in 2001. A multiple regression analysis of the combined portfolio’s monthly returns from 1997–2001 was analyzed using the three-factor model. Although the portfolio consisted of four mutual fund holdings in different asset classes, its returns were very similar to a mid-cap market portfolio. Conceptually this makes sense, considering each of the four funds is evenly divided among the four asset classes.
Results indicate that the three-factor model is able to account for 92.53 percent of the portfolio’s return variability. Based on its total exposure to the risk premiums, it is currently structured to perform very similar to an extended market portfolio on an annualized basis.
This number was achieved by performing the following calculations: The beta of the portfolio is .78 and the annual market risk premium is 6.07—.78 multiplied by 6.07 equals a market premium of 4.73. The portfolio’s exposure to the size premium (.33 x 3.54) is 1.17. The value premium (.04 x 5.07) is .20. These premiums (4.73 + 1.17 + .20) add up to 6.10. Finally, the general market premium is subtracted (6.10 – 6.07), because all portfolios in the equity market should, by default, receive that premium. This indicates that, based on the portfolio’s current risk exposure, it can be expected to perform in line with the market on an annualized basis.
The portfolio is designed to capture 33 percent of the size premium and 4 percent of the value premium. With a market beta of .78, however, the portfolio was not maximizing its entire market risk premium. A possible reason for such a low beta is that the mutual fund managers may have been holding large cash positions. Morningstar Principia indicates that the portfolio funds have had 12 percent cash positions for the last three years ending September 30, 2001. Such large cash positions can hinder a portfolio’s performance if a planner chooses a mutual fund with the expectation that the funds will be invested in an equity asset class. Moreover, a low beta can raise several questions about the fund manager’s investment behavior. This may indicate that the manager may be trying to time the market, having difficulties meeting redemptions, or managing new money. Whatever the reason, implementation of the three-factor model facilitates detection of problems that may not be obvious when using other methods of analysis.
The portfolio’s positive exposure to the size premium was mitigated by a negligible exposure to value. In other words, investing in equities with low value risk compromised the positive exposure to the size premium. Even though having a market portfolio is a perfectly acceptable strategy, the portfolio should efficiently capture the market premium. Based on the portfolio’s location on the crosshairs plot and a client’s tolerance for risk, the planner can recommend an increasing exposure to the value and size premium in order to provide an expected return over the market.
Although the previous example simplistically used a hypothetical portfolio consisting of four mutual funds, a client may have a portfolio of 20 mutual funds in various asset classes that is similar in performance to an extended market index fund with more expenses. The plot provides a snapshot of where the portfolio is with regard to size and value, but unlike other available programs, it also gives the planner an idea of the portfolio’s expected long-term return based on its exposures to these risk premiums. With this descriptive information, a planner can recommend a portfolio that takes advantage of the risk premiums.
The degree to which a planner increases a portfolio’s allocation to risk factors should be approached with caution. There are many years where value does not outperform growth and small cap does not outperform large cap. It is important for the investor to remember that he or she is compensated for taking on more risks and a long-term investment horizon is the best way to fully capture the return premiums. Additionally, the planner must consider the extent to which clients are sensitive to market tracking error. If an investor is going to be disappointed with performance that differs from a market portfolio on a yearly basis, then a planner may want to reconsider an increased exposure to these risk factors.
Structuring a Portfolio to Obtain Market Premiums
A planner can use the three-factor model for structuring portfolios to obtain above-average returns based on the client’s willingness to take risks. Figure 2 identifies another hypothetical portfolio. This portfolio is allocated among passive U.S. indexes composed of micro cap (14 percent), small-cap value (26 percent), large-cap value (40 percent) and large-cap (20 percent) asset classes. It is over-weighted toward value to take advantage of the value premium. Based on the three-factor model and using monthly returns from 1973 through 2001, the portfolio is exposed to 38 percent of the size premium, 40 percent of the value premium and 3 percent over the market premium. In aggregate, the portfolio is structured to capture a 3.56 percent annualized premium over the market.
Historical results indicate that compared with the CRSP Universe index, this hypothetical portfolio outperformed the market index by 3.37 percent annualized (15.22 percent versus 11.85 percent) over a period from 1973–2001. Given this disciplined approach, one can reasonably expect a similar long-term premium of about 300 basis points annualized, barring significant changes in the risk premiums. These results are dependent on a strict and consistent adherence to the asset class styles over the long term. Additionally, the risk premiums can be adjusted to reflect the planner’s own expectations of the market. For example, although the market risk premium has been approximately six percent since 1964, many articles have been written about the declining market equity risk premium.12 With this tool, a planner can accurately structure portfolios for an investor commensurate with how much risk he or she is willing to tolerate.
Analyzing Mutual Funds from a Value Added Perspective
The model also can be used to analyze individual mutual fund performance. A fund’s performance is compared with a combination of exposures to the three risk factors. Alpha measures the return that a manager has significantly provided beyond what is explained by these risk factors. For example, a large-cap manager may frequently outperform the S&P 500 index because the fund was exposed to more value and small-cap risk relative to the benchmark. To justify their fees, active fund managers strive to provide returns above and beyond what can be achieved by a passively structured portfolio. But if the added return can be achieved by simply structuring a combination of passive indexes, the performance is not due to manger’s stock picking skill—that is, he’s not adding alpha.
Assuming the hypothetical portfolio in Figure 2 is an actively managed fund, a planner might reasonably interpret the long-term annualized outperformance for 29 years of the portfolio compared with a market-wide index (15.22 percent versus 11.85 percent) as convincing evidence of manager stock picking skill. Attributing this performance to skill, however, is not correct. By passively overweighting the size and value risk premiums, the portfolio should have attained a 3.56 percent premium over the market. Additionally, the three-factor model explained 97.4 percent of the variability of the portfolio’s returns. The manager’s value-added effect should not be measured by simply outperforming a benchmark but rather by outperforming the expected equity risk premiums. Of course, achieving a 15.22 percent return annualized over 29 years would be very appealing to most advisors and their clients. It would be extremely difficult, however, to attain these results from a combination of active managers. Although such a portfolio can be initially structured, manager style drift will most likely occur over a period of 29 years and cause constant shifting in the portfolio’s allocation to the detriment of long-term returns. The returns are dependent on a consistent exposure to the three risk factors.
Measuring Style Drift
Another use of the three-factor model is to track manager style drift in a portfolio. Style drift is a very important issue if a planner considers selecting a mutual fund based on the fund’s exposure to a particular asset class. This drift can inadvertently distort portfolio allocations among asset classes at inopportune moments. For example, Figure 3 shows where a highly successful “value” fund was positioned on the three-factor plot based on monthly returns from 1986–1990. The chart indicates that the fund was essentially a small to mid-cap value fund. However, returns over the last five years ending in 2001 indicate the fund has become a large-cap fund with similar risk exposures to the S&P 500 index.
This drift may be acceptable to a planner, but usually a planner is the individual responsible for structuring a client’s portfolio allocation according to the client’s risk/return profile. This is generally achieved through a combination of different asset class funds. If the selected asset class managers all decide to deviate from their original investment objective, the portfolio will likely randomly develop into a combination of misappropriated asset classes.
At the start of 2001, a planner may have chosen the aforementioned fund to represent the mid-cap value asset class of a new client’s portfolio. At the end of the year, the fund’s actual performance was similar to the large-cap market index. The S&P 500 index had a return of –11.88 percent and the S&P Mid-Cap Value index gained 7.14 percent. Ultimately, this resulted in a double loss for the portfolio. Although this may be a manager with a very good long-term track record, the fund would not be an appropriate selection for the mid-cap value asset class in a diversified portfolio. Moreover, style drift may have caused an unintended change to the risk factors that may run counter to the client’s risk tolerance.
The three-factor model is a very powerful tool for a planner to harness. This model brings an increased level of structure to the way portfolios are managed. Additionally, it provides a level of sophistication for portfolio analysis that does not require a planner to hire a staff that pours over financial statements to assess whether a holding is a value or growth asset. By focusing on the factors of risk within a portfolio, the planner can obtain a more cohesive strategy for developing, maintaining and evaluating portfolios. It provides solutions to many portfolio management problems in a simple yet effective manner.
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