# Econometric Analysis of Capm

**Topics:**Capital asset pricing model, Financial markets, Stock market

**Pages:**31 (6596 words)

**Published:**October 12, 2009

Lok Kin Gary Ng,

contact email: gary_ng_@hotmail.com

May, 2009

School of Economic

Introduction

The analysis of this paper will derive the validity of the Fama and French (FF) model and the efficiency of the Capital Asset Pricing Model (CAPM). The comparison of the Fama and French Model and CAPM (Sharpe, 1964 & Lintner, 1965) uses real time data of stock market to practise its efficacy. The implication of the function in realistic conditions would justify the utility of the CAPM theory. The theory suggests that the expected return demanded by investors on a risky asset depends on the risk-free rate of interest, the expected return on the market portfolio, the variance of the return on the market portfolio, and the covariance of the return on the risky asset with the return on the market portfolio. (Peirson et al, 2007)

CAPM can be express as a function;

rprf = ∫(rmrf)

There is an anticipate relationship between the expected return and risk for the portfolio; a risk factor, observed based on finance and economic theory (Peirson et al, 2007). This relationship can explain the demand on investing in the financial market; under the economic principle of profit maximization; if the return on investment is greater then interest rate, then people would favor investment (Peirson et al, 2007).

Under the CAPM theory, the expected return on investment can be express as;

E(Rp) = Rf + (E(Rm) –Rf) Cov(Rp,Rm)

((m)2

The CAPM risk factor can be estimated with this empirical equation. The risk associate with the CAPM can be divided into two categories; company specific factors (unsystematic risk) and market-wide factors (systematic risk). In order to minimise the risk and fluctuation effect on market, a portfolio of five stocks are choose to stabilise the flux effect and eliminate the unsystematic risk (Peirson et al, 2007).

In 1996, Fama and French (1996) suggested an alternative asset pricing model (AAPM) that extended the application of CAPM. The alternative asset pricing model allows expected returns to be linked to more than a single source of risk. According to Peirson (2007), the returns were related to firm size, leverage, the ratio of the company’s earnings to its share price (E/P) and the ratio of the company’s book value of equity to its market value (BV/MV) (Peirson et al, 2007). This provides further insight to the CAPM methodology for forecasting. Review of Previous Literature

The logic of the CAPM is derived from Markowitz’s (1959) “mean – variance – model”, a model interested in mean and variance of portfolio return with respect to risk. The model acted upon the assumption of all investors as risk averse. The model speculated the minimisation of the variance of portfolio return, given expected return and the maximisation of expected return, given variance. (Fama & French, 1996)

Furthermore, the rise of Sharpe – Lintner CAPM provides an algebraic condition in Markowitz model to predict the relationship between risk and expected return (Perison et al, 2007). This risk relationship is presented as market Beta term ((i) that takes the market variance into account (assumed that market variance is the frontier variance) (Fama & French, 1996).

According to Sharpe (1964) and Lintner (1965), the CAPM’s expected return is completely explained by the Beta, meaning to say, other variables should add nothing to the explanation of expected return. In contrast, Basu’s (1977) evidence that other variables (such as the P/E ratio) has a significant affect on CAPM theory, other scholars (such as Fama and French) developed new methodology to extend the application of the CAPM, called Alternative Asset Pricing Model (AAPM) (Peirson et al, 2007).

The rises of an AAPM reflects the inefficiency of the Beta assumption, this is based on the evidence that stock’s price depends not only on the expected cash flows, but also on earnings-price, debt – equity and book-to-market (Peirson et...

References: Ball, R, (1978). ‘Anomalies in Relationships Between Securities ' Yields and Yield-Surrogates.’ Journal of Financial Economics, Vol. 6, No. 2, p103-26, viewed 16th April, 2009,

Basu, S, (1977)

Fama, EF, and. French, KR, (1996), ‘Multifactor Explanations of Asset Pricing Anomalies’, Journal of Finance, Vol. 51, No. 1, March, p55-84. Viewed 25th of March, 2009,

Fama, EF, and

HKSAR, (1999), ‘HKSAR – The Key Issues 1998/99’, viewed 5th May, 2009,

Lintner, J

Markowitz, H. (1959). ‘Portfolio Selection: Efficient Diversification of Investment’. Cowles Foundation Monograph No. 16. New York: John Wiley & Sons, Inc.

Peirson, G, et al (2007), ‘Chapter 7 Portfolio Theory and Asset Pricing’, Business Finance, 9th ed., McGraw-Hill, Australia, p186-219

Sharpe, WF

Verbeek, M., (2008), A Guide to Modern Econometrics, 3rd ed., Chichester UK and New York, Wiley.

Data Sources

French, KR, (2009) ‘Country Portfolios formed on B/M, E/P, CE/P, and D/P [ex

RBA, (2009) ‘Cash Rate - Overnight - Interbank - Securities and Interbank Overnight Cash Rate’ viewed 14th of April, 2009,

Yahoo7, (2009a) ‘^ALFI: Historical Prices for S&P/ ASX 50 – Yahoo!7 Finance’, viewed 14th of April, 2009,

Yahoo7, (2009b) ‘^AORD: Historical Prices for ALL ORDINARIES – Yahoo!7 Finance’, viewed 14th of April, 2009,

Yahoo7, (2009c) ‘^AXSO: Historical Prices for S&P/ ASX SMALL ORDINARIES – Yahoo!7 Finance’, viewed 14th of April, 2009,

Yahoo7, (2009d) ‘MEO.AX: Historical Prices for MEO AUST FPO – Yahoo!7 Finance’, viewed 14th of April, 2009,

Yahoo7, (2009e) ‘NXS.AX: Historical Prices for NEXUS FPO – Yahoo!7 Finance’, viewed 14th of April, 2009,

Yahoo7, (2009f) ‘PRT.AX: Historical Prices for PRIME TV FPO – Yahoo!7 Finance’, viewed 14th of April, 2009,

Yahoo7, (2009g) ‘SGM.AX: Historical Prices for SIM METAL FPO – Yahoo!7 Finance’, viewed 14th of April, 2009,

Yahoo7, (2009h) ‘UGL.AX: Historical Prices for UNITED GRP FPO – Yahoo!7 Finance’, viewed 14th of April, 2009,

Appendices

|rmrf |1.554 |(0.3738)* |

|constant |0.0176 |(0.0098) |

|rmrf |1.6402 |(0.3843)* |

|smb |0.6994 |(0.4070) |

|hml |0.2195 |(0.3115) |

|constant |0.0154 |(0.0098) |

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