Published On: Sun, Jan 21st, 2018

Capm and fama french three factor model finance essay

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Shortly following the ground-breaking job of Markowitz on modern portfolio theory (1952) a fresh branch in Finance developed trying to clarify the expected return on any economical asset. Soon the unit with probably largest impact on the financial industry was born, the Capital Asset Pricing Model. Possibly after many different analyses questioning the validity of the model, it really is still the most employed by practitioners. A lot of other products were subsequently developed on a single reasoning. Fama & French Three-Factor Model is considered the most promising and consistent.

We begin this paper briefly explaining the CAPM and its own shortcomings. On those grounds, we explain the Fama & French style. In that case, we test both designs in US info from 1967 till now. Diverse portfolios were used, tests for the effect of size, book-to-market ratios, and the specific industry.

We wrap up drawing conclusions on the results found.


The Capital Asset Prices Model (henceforth CAPM) includes a very curious background, being built independently by Jack Treynor (1965), William Sharpe (1964), John Lintner (1965) and Jan Mossin (1966), all in the same time span of the early sixties. This function was based on the earlier groundbreaking theory of Markowitz and also on Tobin’s Separation Theorem.

The CAPM has some strong assumptions inherited from the stated projects of mean variance performance that essentially create a perfect market environment. Investors are rational and risk averse, can borrow and lend unlimited sums at the risk-free charge and also have homogenous expectations and information regarding all possessions returns. There happen to be no taxes, inflation, transaction costs, no short advertising restrictions and all resources are infinitely divisible and properly liquid.

The assumptions constrain the environment for the CAPM universe. They set a stage that only non-diversifiable dangers are rewarded with extra returns, and since each additional asset introduced right into a portfolio further diversifies the portfolio, the perfect portfolio must comprise every asset with each asset value-weighted. All such optimum portfolios comprise the successful frontier. This creates the expected return of any asset or portfolio to alter linearly with the returns of the market portfolio, based on the following formula:

Beta may be the key measure as it provides sensitivity of the excess returns of a secured asset or portfolio compared to the excess returns of the market portfolio. Because the unsystematic risk is normally diversifiable, the chance of a portfolio can be viewed as beta.

The CAPM is most beneficial described by Sharpe (1988) as a "simple, yet powerful description of the relationship between risk and return in an efficient market". This is a very intuitive way of thinking. The level of returns one expects to get is directly linked to the contact with market volatility. Stock particular error is diversified aside when choosing the efficient portfolio, and therefore the only source of return comes from picking the relation your portfolio offers with the marketplace.

The CAPM is so important that the standard deviation of a share return no longer was the normally used risk measure, but rather its relation to the marketplace returns. Additionally it is the main tool to find special discounts for organization valuation and for portfolio control. Nonetheless it has not been free of criticism.

CAPM criticism

After it was proposed, empirical tests were executed normally working the following regression:

Where a proxy of unwanted market returns is used and regressed against a particular asset come back. The Alpha of the regression signifies the excess return (either great or negative) that is not explained by the CAPM. Regarding to CAPM, as the correlation with marketplace should completely make clear its come back, the apha of the prior regression should be 0.

First of all, the use of a market proxy contributes to Richard Roll’s critique (1976). It is pretty simple but revealing and it basically states the CAPM can never be tested as the actual composition of the market portfolio is not known. All proxies used might be mean variance efficient but the market might not, resulting in all tests becoming inherently biased. Besides, the interpretation of Beta applying market proxies contributes to relative measures of risk, as the Beta obtained depends on the marketplace proxy used.

Besides Roll’s judgment on the theory, a variety of anomalies were found on the model. Characteristics such as for example size, earnings/price, Money flow/price, book-to-market-equity, earlier sales growth had results on average returns of stocks. These are called anomalies as they are not really explained by CAPM, resulting in the theory that risk is normally multidimensional and as such the CAPM is definitely fundamentally incorrect in its core bottom line.

Eugene Fama and Kenneth French (1996) made the best stride, when stating that anomaly variables add a risk premium contained in the characteristics of these variables. These anomalies will be largely divided by two primary factors. Size, which they make clear theoretically, and relative distress, moving through the E/P and book to market as measures.

Fama French Three-Factor Model

Eugene Fama and Kenneth French since expanded the CAPM to the Fama-French (FF) tri-factor unit (1992), which gives two variables to capture the cross-sectional variation in average stock returns connected with industry: Beta, size, leverage, e book to advertise and earnings-cost ratio. This creates the next model:

, which is often transformed into

Where the factors added to the CAPM are the SMB (Compact minus Big), a measure of the historic excess go back of small caps over big caps, and HML (Superior minus Low), the same difference for returns of worth stocks over growth shares. This model isn’t as trusted as the CAPM, but we will check empirically if it performs better than the initial one-factor model.


After introducing the theoretical bases of these models, we will make clear the methodology we used on our testing. We used info from Kenneth French´s website, comprising market extra returns from NYSE, AMEX, and NASDAQ firms and the ideals of returns from all those companies split into size and book to advertise quintiles and also split into five parts of industries – Consumer Goods, Making (strength and utilities), High-tech, Health care and Service industry. The data is monthly from 1967 to 2010. Our variables of interest comprise the alphas of each regression (i.e., returns unexplained by the unit) and the altered, which adjusts for the amount of explanatory terms in a model – unlike the regular, the adjusted increases only if new variables enhance the model. We used all this data to run the standard empirical evaluation regression expressed in (2).

We will ignore Roll’s critique in the exams and use a particular market proxy as inside our opinion data on returns of a certain index representative of the country where investors negotiate is pretty representative of marketplace returns, as that data is certainly amply divulged and influences all possessions related.


These are the results in regression web form and the values of the alphas obtained with double standard error bands:

Table 1 – Regression Results from Size Portfolios

(Values in parenthesis refer to the t-stat of the variable above)

Looking at the alpha values of the regressions beneath the CAPM, the 4th quintile may be the only 1 significant on a 95% confidence interval. All of the beta ideals are significant and different than zero. Alpha values decrease as we go from portfolios of smaller to bigger businesses, as does indeed the of the regressions. As for the Fama French model,

the values of factors are significant in every the size regressions, and the alpha value is only significant in the 5th quintile of major companies. The follows an identical behavior.

These results seem to be to favour the tri-factor approach, as including the SMB variable appears to improve the quality of match of smaller corporations. The difference in the modified of the cheapest 20% quintile between the CAPM and Fama French designs is an impressive 30%, indicating that some unsystematic dangers, captured by the difference between big and tiny firms, affect returns. Basically, these outcomes favor Fama and French´s model in explaining returns over the CAPM.

Chart 1 – Plot of CAPM alpha with dual standard error band

Chart 2 – Plot of FF alpha with double standard error band

These charts tell a more interesting report. The alpha values of the CAPM diminish a lot when going from little cap quintiles to large cap ones, from relatively high alphas to near zero. Everything changes when working with FF three-factor model where the alpha values are harmful for tiny caps and go to positive when moving to greater companies.

The larger selection of alphas in the CAPM over FF, specifically in smaller companies, once again indicates that returns aren’t fully captured by measuring just correlation with the market. Accordingly, with the addition of SMB this spectrum is considerably reduced, especially in the portfolios based on the lowest 20% companies in proportions.

Table 2 – Regression Outcomes from Book-to-Market Portfolios

(Values in parenthesis refer to the t-stat of the adjustable above)

Here the Betas of most regressions are significant. The 4th and fifth quintiles on the CAPM present a higher alpha rejecting the null hypothesis that they are not significant, with a 95% confidence level. However, the FF model rejects only the cheapest 20% B/M portfolios, and by the littlest of margins.

These results show proof that Fama and French were indeed correct by taking into consideration the HML element in their regression. In fact, the presence of significant alphas in the two highest quintiles in the CAPM, combined with the substantial distinctions in the adjusted – 13% for the 4th quintile, almost 20% in the 5th – again demonstrate that CAPM isn’t considering important variables in determining returns.

Chart 3 – Plot of CAPM alpha with dual standard error band

Chart 4 – Plot of FF alpha with dual standard error band

As the B/M ideals increase, CAPM’s results are ever before worse regarding alpha. With the addition of double standard error bands, CAPM’s portfolios based on the highest 20% benefit have alphas which range from 0.1 and 0.6, very substantial ideals. FF performs far better, with alphas not really moving far away from 0.

Table 3 – Regression Results from Industry Portfolios

(Values in parenthesis refer to the t-stat of the variable above)

Chart 5 – Plot of CAPM alpha with dual standard error band

Chart 6 – Plot of FF alpha with double standard error band

Contrary to the prior analysis, the three-factor style only displays marginal advancements in the adjusted to the single-factor model when dealing with industry-based portfolios. Actually, the FF model has got significant alphas in two several industries – HEALTHCARE and Others – while the CAPM has none. Furthermore, the SMB variable appears to be irrelevant in the buyer Goods and in other industries. We should certainly not be shocked by these results, as the FF model was made around two tips: small companies and the ones with great B/M ratios were undervalued by the marketplace. Thus, when analyzing portfolios based on different restraints (like market) the model won’t perform much better compared to the CAPM.

A take note on Fama-French Three-Factor Model

The FF model can be an expansion of the CAPM style in the feeling that it uses two extra factors: SMB and HML. The initial one increases the modulation of distinct size portfolios. The next one addresses the difference in publication values of companies included in several portfolios.

We suspect that SMB is actually important whenever we want to predict the different overall performance of portfolios split using size as the standards. The same reasoning works extremely well to portfolios split applying book-to-market ratio as the requirements.

We made a decision to apply this notion to the info, computing the common contribution of every factor to the full total excess return of each portfolio. The resulting table is presented below.

Table 4 – Issue Contribution to Excess Return

We can easily see that, as we suspected, SMB is actually very relevant (19% normally) to explain the surplus return of several portfolios split with industry size criteria. That’s even more critical whenever we are thinking about portfolios of smaller shares. In those portfolios, the issue HML isn’t particularly important.

When we proceed to book-to-market value unique portfolios, it really is HML that contributes substantially (14%), especially to substantial book-to-value stocks and shares, and SMB can be neglected.

Finally, when the criterion to split portfolios is certainly neither size nor book-to-market, the two extra factors of the Fama-French version have no explanatory power typically. We can see the average weights are very near to standard CAPM. We can speculate on the difference across sectors: for example, hi-tech and health care stocks tend to have higher book-to-market ratios, and so the HML factor is pertinent. It is possible a aspect like "high dividend yield much less low dividend yield" could be robust to clarify performance distinctions among portfolios split according to dividend yield level.

We aren’t questioning the applicability of the Fama-French version. What we will be addressing here is that each factor does not have a generalized relevant contribution to clarify excess returns. Using situations, like tiny cap portfolios and expansion stocks, each factor in turn becomes very crucial. Beyond these "native environments", the factors do not contribute to describe or predict extra returns.

Final Remarks

Throughout this work we’ve proven that Fama and French’s tri-factor style is more advanced than the CAPM in capturing some non-systematic anomalies not considered by the simple one-factor approach. These anomalies include the undervaluation of small firms and those with excessive B/M ratios. Adding variables that reflect this impact considerably improves the standard of fit of the unit and eliminates loose ends as reflected by the significant alphas within some portfolios employing the CAPM. However, we must absorb data, as accomplishing a FF regression on data that does not reflect these variables, – as industry – will not increase the models.

References and Other Bibliography

Fama, E. F., & French, K. R. (1992). The Cross-Section of Expected Stock Returns. The Journal of Financing, 47(2), 427-465.

Fama, E. F., & MacBeth, J. D. (1973). Risk, Come back, and Equilibrium: Empirical Testing. The Journal of Political Overall economy, 81(3), 607-636.

Lintner, J. (1965). The Valuation of Risk Assets and the Selection of Risky Investments in Share Portfolios and Capital Budgets. The Review of Economics and Statistics, 47(1), 13-37.

Markowitz, H. (1952). Portfolio Collection. The Journal of Finance, 7(1), 77-91.

Mossin, J. (1966). Equilibrium in a Capital Asset Market. Econometrica, 34(4), 768-783.

Roll, R. (1977). A critique of the asset prices theory’s tests Component I: On past and potential testability of the idea. Journal of Financial Economics, 4(2), 129-176.

Sharpe, W. F. (1964). Capital Asset Rates: A Theory of Market Equilibrium under Circumstances of Risk. The Journal of Financing, 19(3), 425-442.

Treynor, Jack L. (1965). How exactly to Rate Management of Expense Funds. Harvard Business Analysis, 43(1), 63-75.

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