Finance Research Paper



Finance Research Paper

Finance Research代写 Capital Asset Pricing Model (CAPM), numerous studies have been developed working for and against its empirical soundness.



When Sharpe (1964) propounded Capital Asset Pricing Model (CAPM), numerous studies have been developed working for and against its empirical soundness. That notwithstanding, CAPM built the foundation on which asset pricing models were developed to measure the relationship risk and the returns.

Finance Research代写
Finance Research代写

However, researchers observed that explaining the market behaviour using market beta as the single factor was the undoing of the whole model objective. According to Lakonishok, Shleifer, and Vishny (1994) the model has limitations in the return patterns yielding earnings/price, cash flow/price, and sales growth. In the light of the numerous anomalies associated with the single factor model, scholars have tried to come up with a model to replace it, thus, Fama and French (1993) came up with three-factor model. The model added two factors, that is, size and value, in the previous single factor model. Finance Research代写

The Fama and French three-factor model demonstrated that the additional two factors accounted for both the size and value effects after sorting stocks by size and book-to-market equity. The size effect according to Banz (1981) is where the small stocks have higher average excess returns. On the other hand, the value effect it was explained by Rosenberg, Reid, and Lanstein (1985) is where stocks have higher average excess returns than growth stocks.

The three-factor model apply time-series regression formula  Finance Research代写

Rit–RFt = ai + bi(RMt – RFt) + siSMBt + hiHMLt + eit


i. Rit– return on security is i for time

ii. RFtas the risk-free return

iii. RMtas the value-weight market portfolio

iv. SMBtas the return on a diversified portfolio of small stocks minus the return on a diversified portfolio of big stocks

v. HMLt give the difference between the return on diversified portfolios of high and low B/Mstocks

vi. eitis a zero-mean residual.

Despite the Fama and French model being a success from 1992 to 2012, it developed some anomalies in explaining momentum, profitability, and investment. In 1997 Carhart (1997), added a factor related to momentum to compensate for the failure of the three-factor model in finding the momentum. As per the documentation by Jagadeesh and Titman (1993), the momentum effect is where the stocks have high returns over the few months, they tend to outperform other stocks.  Finance Research代写

Although, Fama and French were reluctant to incorporate the identified changes, in 2015 they introduce the two more variables into the previous model to form the current five-factor model. They profitability and investment to be incorporated into the three-factor model. The two were related to the average returns in dividend discounts model.

Adding profitability and investment, five-factor model formula is derive to be:  Finance Research代写

Rit – RFt = ai + bi(RMt – RFt) + siSMBt + hiHMLt + riRMWt + ciCMAt + eit


i. RMWtas the difference between the returns on diversified portfolios of stocks with robust and weak profitability

ii. CMAtis the difference between the returns on diversified portfolios of the stocks of low and high investments

Given that bi, si, hi, ri, and ci, accounts for deviations in stock returns, they intercept at ai, thus securities and portfolios are zero at i.

The zero-intercept hypothesis is interpreted using two perspectives.  Finance Research代写

First, was done by Huberman and Kandel (1987) who proposed that the mean-variance-efficiency tangency portfolios be used to price all risk-free assets, market portfolio, SMB, HML, RMW, and CMA. Merton (1973) proposed the second perspective as the most ambitious regression equation was proposed by. He gave four unspecified state variables not in the market factor. In the light of this, Size, B/M, OP, and Inv are not state variables as well as SMB, HML, RMW, and CMA are not state variable mimicking portfolios. In essence, these factors are just diversified portfolios of various combinations of exposures to the unspecified state variables.

Various other studies have proceeded the five-factor model.  Finance Research代写

Such studies conducted by Choe and Yang (2008) and Hahn and Yoon (2016), have explained how liquidity as a factor has extensive explanatory in the analysis of the cross-section variations of stocks. Also, according to Jung, Lee, and Park (2009), a model constituting investor heterogeneity-based factor is better than the Fama and French three-factor model. As a Korean researcher, Jung and Kim (2011) reported the need for innovation in changes in money growth and pricing in the stock market are needed.

This research paper at investigating the applicability of five-factor model  Finance Research代写

According to Fama and French (2015) in the interpretation of various investment returns as collected from the archive. The previous studies have not been conclusive in providing empirical evidence on the applicability and the use of Fama and French three-factor model (1993). This notwithstanding, the model was still widely used as the benchmark model in risk-adjusted returns.

Finance Research代写
Finance Research代写

The data analysis in this paper endeavour to test the applicability of the Fama and French five-factor model (2015) as a better model than the previous ones in explaining cross-sectional variation of stock returns. As such, the paper mimics the model application in the analysis to determine how the additional factors have made it more reliable than the three-factor model, that is profitability and the investment factors.  Finance Research代写

Following the methods in the Fama and French (2015), before others, the size, B/M, profitability and investment patterns in average returns are analyzed. The regression method will be applied to individual data to determine the performance over the period as shown in the data throughout the data set. The results will then be discussed to have a conclusive statement about the finding of the study as well as the recommendation and the future work intended for more in-depth understanding of the model.

References  Finance Research代写

Carhart, M. M. (1997). On persistence in mutual fund performance. The Journal of finance, 52(1), 57-82.

Choe, H. & Yang, C.W. (2009). Liquidity risk and asset returns: the case of the Korean stock market. Kor. J. Finance. 26. 103-140.

Fama, E. F., & French, K. R. (1993). Common risk factors in the returns on stocks and bonds. Journal of financial economics, 33(1), 3-56.

Fama, E. F., & French, K R. (2015). A five-factor asset pricing model. Journal Of Financial Economics, 116(1), 1-22. doi: 10.1016/j.jfineco.2014.10.010

Hahn, J., & Yoon, H. (2016). Determinants of the cross-sectional stock returns in Korea: evaluating recent empirical evidence. Pacific-Basin Finance Journal, 38, 88-106. doi: 10.1016/j.pacfin.2016.03.006

Huberman, G., & Kandel, S. (1987). Mean-Variance Spanning. The Journal Of Finance, 42(4), 873-888. doi: 10.1111/j.1540-6261.1987.tb03917.x

Jung, C., Lee, D., & Park, K. (2008). Can investor heterogeneity be used to explain the cross-section of average stock returns in emerging markets?. SSRN Electronic Journal. doi: 10.2139/ssrn.1084825

Jung, H., & Kim, D. (2011). Innovations in the Future Money Growth and the Cross-Section of Stock Returns in Korea. Asia-Pacific Journal Of Financial Studies, 40(5), 683-709. doi: 10.1111/j.2041-6156.2011.01054.x

Jegadeesh, N., & Titman, S. (1993). Returns to Buying Winners and Selling Losers: Implications for Stock Market Efficiency. The Journal Of Finance, 48(1), 65-91. doi: 10.1111/j.1540-6261.1993.tb04702.x

Lakonishok, J., Shleifer, A., & Vishny, R. (1994). Contrarian Investment, Extrapolation, and Risk. The Journal Of Finance, 49(5), 1541-1578. doi: 10.1111/j.1540-6261.1994.tb04772.x

Merton, R. C. (1973). Theory of rational option pricing. The Bell Journal of economics and management science, 141-183.

Rosenberg, B., Reid, K., & Lanstein, R. (1985). Efficient Capital Markets: II. Persuasive Evidence of Market Inefficiency, 11(3), 9-16.

Sharpe, W. (1964). Capital asset prices: A theory of market equilibrium under conditions of risk*. The Journal of Finance, 19(3), 425-442. doi: 10.1111/j.1540-6261.1964.tb02865.x


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