The Theory Behind The Capital Asset Pricing Model Finance Essay

The Capital Asset Pricing Model ( CAPM ) is being used since the 1960s to mensurate portfolio public presentation and to cipher the cost of capital. In the 1990s Eugene Fama and Kenneth French tried to better the public presentation of the CAPM by adding two factors to the theoretical account. The first factor is the book-to-market ratio of stocks in the portfolio and the 2nd factor is the stock ‘s implicit in company size. This theoretical account was to be superior to the CAPM. However, Graham and Harvey ( 2001 ) proved that in 2001 the CAPM was still used by 73,5 % of the U.S. CFO ‘s to cipher the cost of capital and portfolio public presentation. In Europe, Brounen, de Jong and Koedijk ( 2004 ) showed that this per centum was still 45 % . Why do CFO ‘s still rely on an inferior theoretical account, or is n’t the Fama French Three Factor Model superior to the CAPM? The end of this paper is to find whether the CAPM or the Fama French Three Factor Model is superior to one another in size and book-to-market portfolios.

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2. Theory

2.1 The Capital Asset Pricing Model

The Capital Asset Pricing Model is a theoretical account that describes the relationship between hazard and expected return. It is chiefly used by investors to value assets and to find expected returns. The chief thought behind the theoretical account is that investors need to be compensated for their exposure to systematic hazard, because non all of the investings are genuinely hazardous. By diversifying a portfolio, it is possible to cut down hazard. The hazard reduced is called the Risk Free Rate. In other words, the expected return of a security or a portfolio is formed by the hazard free rate plus a hazard premium.

The CAPM by Sharpe ( 1964 ) and Lindtner ( 1965 ) is in fact an extension of the one period mean discrepancy portfolio theoretical accounts of Tobin ( 1958 ) and Markowitz ( 1959 ) . It builds on the theoretical account of portfolio pick, where an investor selects a portfolio that minimizes the discrepancy of portfolio return and maximizes the expected return, given this discrepancy. This is frequently referred to as the “ average discrepancy theoretical account ” . The CAPM is in fact a anticipation trial about the coherency between hazard and expected return and identifies a portfolio that is efficient if plus monetary values are to unclutter the market of all assets. The two added premises to this average discrepancy theoretical account place a mean-variance-efficient portfolio are “ complete understanding ” and “ adoption and loaning at hazard free rate ” . Complete understanding stands for the understanding amongst investors on the joint distribution of plus returns from which the returns we use to prove the theoretical account are drawn. Borrowing and loaning at a hazard free rate exists and is equal for all investors and does non depend on the sum borrowed or Lent. The relationship between hazard and the expected return for portfolios is evident. The higher the hazard, the higher the final payment and frailty versa harmonizing to Fama and French ( 2004 ) .

The Sharpe-Lindtner CAPM equation:

E ( Ri ) = Rf + i??im * ( E ( Rm ) – Releasing factor )

Where E ( Ri ) is the expected return on plus I, Rf is the riskless rate, i??im is the market beta of plus I, E ( Rm ) is the expected return on the market. Where i??im consists of the undermentioned factors:

i??im = cov ( Ri, Rm ) /i??2 ( Rm )

Where cov ( Ri, Rm ) is the covariance hazard of plus I in m and i??2 ( Rm ) is the discrepancy of the market return. In words, the expected return on plus I is the riskless rate ( Rf ) times the unit premium of beta hazard, E ( Rm ) – Releasing factor.

The expected return on an investing portfolio is equal to the leaden norm of all of the assets ‘ expected returns in the portfolio, therefore is linearly combined. The standard divergence of a portfolio is nonlinearly combined, because of the variegation of hazard that takes topographic point when a portfolio is formed as seen in Figure 1[ 1 ]. For illustration, when a portfolio of two every bit hazardous assets is formed, with every bit expected returns, the expected return on the portfolio will be equal to the expected return of one of the assets, though the standard divergence of the portfolio will be lower than the standard divergence of each of the implicit in assets because of the variegation consequence. In other words, variegation leads to a hazard decrease without decreasing the expected return.

Figure 1 describes the assorted portfolio possibilities and explains the CAPM farther. On the horizontal axis portfolio hazard is set and on the perpendicular axis expected return is set. The curve is called the minimal discrepancy frontier, and is a line that describes the minimal discrepancy at different hazard degrees of multiple hazardous portfolios, when there is no chance of hazard free adoption. For illustration, when an investor is looking for a high expected return, this automatically brings a high hazard along with it. The optimum pick of a portfolio for an investor lies on the minimal discrepancy frontier, since it maximizes the expected return for a given volatility. By adding the chance to borrow at a hazard free rate, the average discrepancy efficient frontier comes into being. This is now the efficient set, in position of the minimal discrepancy frontier harmonizing to Fama and French ( 2004 ) .

Graph 1 thesis.jpg

Figure

2.2 The Pro ‘s and Con ‘s of the Capital Asset Pricing Model

The chief advantage of the CAPM over any other pricing manner is its simpleness to utilize. However, there are some anomalousnesss. During the 80 ‘s and 90 ‘s, several divergences in the CAPM were discovered which show anomalousnesss in the CAPM and inquiry it ‘s rightness. Harmonizing to Basu ( 1977 ) hereafter returns on high Net incomes to Price ratios are in world higher than the ratios predicted by the CAPM. Banz ( 1981 ) finds that the low market value stocks really had a higher return than predicted by the CAPM. Bhandari ( 1988 ) showed that purchase high debt equity stocks had returns that were excessively high relation to their betas harmonizing to the CAPM. He besides shows that there is a positive relation between between purchase and mean return in the CAPM. Leverage could be associated with hazard and expected return, but harmonizing to Bhandari ( 1988 ) , the purchase hazard should be explained by the market i?? .

2.3 The Fama French Three Factor Model.

Fama and French ( 1992 ) knock the empirical adequateness of the CAPM and claim to better the theoretical account by adding two through empirical observation based factors. The factors are a merchandise of empirical informations research and there is no underlying theory to explicate these factors. Of all the researched factors, these turn out to be the most effectual. Fama and French ( 1992 ) used the cross-sectional arrested development attack of Fama and MacBeth ( 1973 ) to demo that i?? does n’t do to explicate mean return. Size gaining controls differences in mean stock returns where i?? misses them. To better the prognostic value of the CAPM they added two factors to the theoretical account. Harmonizing to the theoretical account the hazard premium or extra return above the hazard free rate is a composing of three factors, viz.

The hazard premium on the market portfolio ( Rm – Releasing factor ) .

The difference in returns between the little stock portfolios and the large stock portfolios ( SMB ) .

The difference in returns between the high book to market stock portfolios and the low book to market stock portfolios ( HML ) .

The Fama and French Three Factor Model:

E ( Ri ) – Rf = Bi * ( E ( Rm ) – Releasing factor ) + si E ( SMB ) + hi E ( HML )

Where:

E ( Rm ) is the expected return on the market, Rf is the hazard free rate, E ( SMB ) and E ( HML ) are the expected premiums and Bi, Si and hello are the arrested development inclines.

The first factor is Small Minus Big ( SMB ) which is designed to mensurate the extra return investors have historically received by puting in company stocks with little market capitalisation. This extra return is most normally known as the ‘size premium ‘ . Fama and French ( 2006 ) compose six value weight portfolios, SG, SN, SV, BG, BN, and BV. They province that: “ The portfolios are intersections stocks of NYSE, AMEX ( after 1962 ) and Nasdaq ( after 1972 ) into two size groups, Small and Big and three book to market ( B/M ) equity groups Growth ( houses in the bottom 30 % of NYSE B/M ) , Neutral ( in-between 40 % of NYSE B/M ) and Value ( high 30 % of NYSE B/M ) .[ 2 ]“ The SMB factor is the mean returns on the little stock portfolios minus the mean returns on the large portfolios harmonizing to Fama and French ( 2006 ) and is computed as follows:

SMB =1/3 ( Small Value + Small Neutral + Small Growth ) A – 1/3 ( Big Value + Big Neutral + Big Growth )

Where:

Small Value are the houses with the June market cap below the NYSE median that are at the high 30 % of NYSE B/M.

Small Neutral are the houses with the June market cap below the NYSE median that are at the in-between 40 % of NYSE B/M.

Small Growth are the houses with the June market cap below the NYSE median that are at the bottom 30 % of the NYSE B/M.

Large Value are the houses with the June market cap value above NYSE median that are at the high 30 % of NYSE B/M.

Large Neutral are the houses with the June market cap value above NYSE median that are at the in-between 40 % of NYSE B/M.

Large Growth are the houses with the June market cap value above NYSE median that are at the bottom 30 % of NYSE B/M.

When this value is positive, the little caps have outperformed the big caps in the peculiar month and frailty versa. The 2nd is High Minus Low ( HML ) which is designed to mensurate the ‘value premium ‘ investors get for puting in high book-to-market companies. The HML factor is the mean returns on value portfolios minus the mean returns on growing portfolios harmonizing to Fama and French ( 2006 ) and is computed as follows:

HML =1/2 ( Small Value + Big Value ) A – 1/2 ( Small Growth + Big Growth )

When this value is positive, the growing stocks outperformed the value stocks in that peculiar month and frailty versa.

The market hazard premium ( Rm-Rf ) that is used is the value to burden return on all NYSE, AMEX and Nasdaq stocks diminished by the one-month Treasury measure rate.

2.4 The Pro ‘s and Con ‘s of the Three Factor Model

The extra two factors in the Fama and French Three factor theoretical account are strictly empirical. There is no underlying theory as there exists in the CAPM. Though the three factor theoretical account needs extra day of the month compared to the CAPM ( the SMB factor and the HML factor ) the higher costs in utilizing the three factor theoretical account compared to the CAPM is non justified harmonizing to Bartholdy ( 2002 ) , because the three factor theoretical account does n’t look to surpass the CAPM significantly on single stock returns appraisal.

2.5 The Momentum factor

Carhart ( 1997 ) adds another factor to the equation, making his Four Factor Model. This 4th factor describes the consequence of Jegadeesh and Titman ‘s ( 1993 ) one twelvemonth impulse anomalousness. This theoretical account is a market equilibrium-based four-risk factor theoretical account. Carhart ‘s factor ( PR1YR ) brings the annual impulse return to the equation, which enlarges the account of the theoretical account compared to the three factor theoretical account, so the 4th factor well improves the public presentation of the theoretical account harmonizing to Carhart ( 1997 ) . In the three factor theoretical account, mistakes refering last twelvemonth ‘s stock portfolios are perceptibly reduced. Carhart managed to cut down most of the forms in pricing mistakes. This indicates a good executing theoretical account on depicting transverse sectional fluctuation in mean stock returns.

The Carhart four factor theoretical account:

E ( Ri ) – Rf = Bi * ( E ( Rm ) – Releasing factor ) + si E ( SMB ) + hi E ( HML ) + pi E ( PR1YR )

3. Research Questions and Hypotheses

Which of the two theoretical accounts, the CAPM or the Three Factor Model, is superior to one another for the different portfolios of size and book-to-market in the clip period between 1993 and 2009?

Hypothesiss:

The Three Factor theoretical account is superior in foretelling the value of securities in the portfolio size in the clip period 1993-2009.

The Three Factor theoretical account is superior in foretelling the value of securities in the portfolio book-to-market in the clip period 1993-2009.

Not all the factors of the three factor theoretical account are lending to the adequateness of the theoretical account in valuing the portfolios size and book-to-market in the clip period 1993-2009.

The momomentum factor helps explicate returns.

4. Methodology and Data Collection

4.1 Datas

This paper uses the informations gathered by Fama and French and published on the web site[ 3 ]of Kenneth R. French. Harmonizing to Fama and French ( 1992 ) this information consists of all non-financial houses in the intersection of the NYSE, AMEX and NASDAQ files and the merged COMPUSTAT one-year industrial files of income statement and balance sheet informations, maintained by the Center for Research in Security Prices ( CSRP ) . They have excluded the fiscal houses from their dataset because high purchase in these houses is rather normal in resistance to high purchase in non-financial houses. In non-financial houses this high purchase could perchance bespeak hurt. In the Small-Minus-Big factor in the Three Factor Model, accounting variables play a function, and to guarantee that these accounting variables are known before the returns they are used to explicate, the accounting informations for all financial year-ends T, are calculated after a lower limit of 6 months has passed the financial year-end.

4.2 Estimating market i??

This paper uses the market i?? provided by Fama and French and published on the web site of Kenneth R. French. The plus pricing trials performed in this paper use the cross sectional arrested development attack of Fama and MacBeth ( 1973 ) . The market i?? ‘s for portfolios are more precise than the single i?? ‘s, so the attack of Fama and MacBeth ( 1973 ) is to gauge the portfolio ‘s i?? and so delegate this i?? to each stock in the implicit in portfolio. By utilizing this method, the useage of single stocks in the asset-pricing trials of Fama and MacBeth is enabled.

4.3 Methodology

SPSS 15 will be used for the information analysis in this paper, which will dwell of multivariate arrested development analysis to reply the research inquiry and hypotheses. To find whether the two extra factors of the Three Factor Model add excess prognostic value to the CAPM, this paper uses multiple additive arrested development in SPSS to see if the R-squared value increases with these extra factors for each of the portfolios. . In the informations library subdivision on their site[ 4 ], Fama and Gallic provide informations about portfolios formed on size and portfolios formed on book-to-market. To look into the size and book-to-market factors in the Three factor theoretical account, the informations of these portfolios are used in the arrested development analysis.

5. Literature

Brounen, D. Abe de Jong and K. Koedijk, 2004, “ Corporate Finance in Europe Confronting Theory with Practice ” , Financial Management 33, 71- 101.

Graham, J.R. and C.R. Harvey, 2001, “ The Theory and Practice of Corporate Finance: Evidence from the Field ” , Journal of Financial Economics 60, 187-243.

Litner, J. , 1965, “ The Evaluation of Risk Assets and the Selection of Risky Investments in Stock Portfolios and Capital Budgets ” , Review of Economics and Statistics 47, 13-37.

Sharpe, W.F. , 1964, “ Capital Asset Monetary values: A Theory of Market Equilibrium under Conditions of Risk ” , Journal of Finance 19,425-442.

Tobin, J. , 1958, “ Liquidity Preference as Behaviour Toward Risk ” , Review of Economic Studies 25, 65-86.

Fama, E.F. and K.R. French, 2006, “ The Value Premium and the CAPM ” , Journal of Finance 61, 2163-2185.

Fama, E.F. and K.R. French, 2004, “ The Capital Asset Pricing Model: Theory and Evidence ” , Journal of Economic Perspectives 18, 25-46.

Fama, E.F. and K.R. French, 1996, “ The CAPM is Wanted, Dead or Alive ” , Journal of Finance 51, 1947-1958.

Fama, E.F. and K.R. French, 1992, “ Common hazard factors in the returns on stocks and bonds ” , Journal of Financial Economics 33, 3-56.

Fama, E.F. and K.R. French, 1992 “ Cross-section of expected stock returns ” , Journal of Finance 47, no 2, 427-465.

Fama, E.F. and K.R. French, 1997 “ Industry cost of equity ” , Journal of Financial Economics 43, 153-193.

Markowitz, H. 1952. “ Portfolio Selection. ” Journal of Finance.7:1, pp. 77-99.

Markowitz, Harry. 1959. Portfolio Choice: “ Efficient Diversification of Investings ” Cowles Foundation Monograph No. 16. New York, John Wiley & A ; Sons Inc.

Fama, E.F. and K.R. French, 2010 “ Data Library ” hypertext transfer protocol: //mba.tuck.dartmouth.edu/pages/faculty/ken.french/data_library.html

Basu, S. , 1977, “ Investment Performance of Common Stocks in Relation to Their Price-Earnings Rations: A Trial of the Efficient Market Hypothesis ” , Journal of Finance 12, 129-156.

Banz, R.W. , 1981, “ The Relationship between Return and Market Value of Common Stocks ” , Journal of Financial Economics 9, 3-18

Bhandari, L. , 1988, “ Debt/Equity Ratio and Expected Common Stock Returns: Empirical Evidence ” , Journal of Finance 43, 507-528

Bartholdy, J. 2002, “ Appraisal of Expected Tax return: CAPM V Fama and Gallic ” , Working paper series hypertext transfer protocol: //ssrn.com/abstract=350100

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