# Financial Modeling: Capital Asset Pricing Model

## Theoretical Hypotheses of CAPM

The Capital Asset Pricing Model (CAPM) identifies the connection between risk and the rate of return on assets. Normally, the assets are in well-diversified portfolios. It assumes that investors are rational and they choose among alternative portfolios based on each portfolio’s expected return and standard deviation. In addition, the model presupposes that investors do not like risk. Additionally, such investors have homogeneous expectations with regard to asset return. In this case, all assets are marketable and divisible. In other words, it is believed under this model that the capital market is efficient and perfect.

According to “Separability Theorem”, all investors, regardless of their attitude towards risk, should hold the same risk assets in their portfolios. The crucial differences in portfolios held by investors of different psychologies are in the in-between the risky stocks and the non-risk stocks. Different investors will choose different points on the capital market line. In the above figure, point M represents the market portfolio and R_{f }is the rate of return on the riskless asset. All investors combine R_{f and} M, but in different proportions (Oster, 1994). The market portfolio is the ‘same mix of risky stocks’. Investor A for example prefers to play safe with emphasis on riskless assets. Person B has most funds in the market portfolio. Person C could have had leveraged portfolios that were added to his original funds by borrowing at R_{f and} putting all of them into the market portfolio (Levich, 2001).

The interior decorator school of thought suggest that different portfolio of risky assets should be prepared for differing investors to suit their tastes. In other words, points other than M on the all risky portfolio should be taken. This will clearly lead to inefficiencies in the presence of riskless asset if all the assumptions of CAPM hold. If the assumptions do not hold, in particular the borrowing assumption, then the “Separability Theorem” falls. The Separability Theorem therefore maintains that investors borrow the money to be invested (Reilly & Brown, 2007).

In the above figure, person A combines the riskless asset with risky portfolio M. Person B selects his own interior decorator policy, while C combines yet another risky portfolio by borrowing at R_{b.} According to the above, it is then possible to say that risk and return are directly proportional. The higher the risk, the higher is the return on investment and vice versa (Dempsey, 2013).

The CAPM is given as follows:

- R
_{i}= R_{F}+ [E (R_{M}– R_{F})] ß - Where R
_{i}is required return of security i - R
_{F}is the risk free rate of return - E (R
_{M}) is the expected market rate of return - ß denote Beta.

## Validity of CAPM Assumptions

All assets with correct prices will lie on the security market line. The security market line, therefore, shows the pricing of all assets if the market is at equilibrium. It is a measure of the required rate of return if the investor were to undertake a certain amount of risk. The investor has the option of reducing her risk of exposure by going for the less risky assets such as treasury bills and bonds in order to reduce this risk. The data indicates that as long as you need additional returns, there is an additional risk that is associated with it. The investor can decide to take calculated risk by just investing along the security market line. Any portfolio or asset on the security market line is less risky and worthy. Treasury bills and bonds are considered less risky since they have a fixed rate of return and a fixed period of investment and every investor is assured of this return. The risk-averse investors mostly undertake this kind of investment.

## Empirical Test of the CAPM

The Pearson coefficients of biasness usually range between negative three and positive three. These are extreme values, that is, negative 3 and positive 3, which therefore indicate that a given frequency is negatively skewed and the amount of biasness is quite high. Similarly, if the coefficient of biasness is negative, it can be concluded that the amount of biasness of deviation from the normal distribution is quite high and the degree of frequency distribution is positively skewed. It therefore follows that the above case is one of the positive skewed distributions as indicated by the figures (Eraslan 2013). A portfolio consisting of one share of index fund and a put option takes a positively skewed distribution since it is very uncertain (Elton, Gruber, & Brown, 2006). It is not possible to tell which direction the share price might take because shares are considered very risky always. Since investment is often a risky venture, many investors take steps to ensure that they do not lose their money during investment. They try as much as possible to minimize such risks or otherwise hedge against such potential risk. Insurance is purchased to guard an investor against loss arising due to price fluctuations in the market. The distribution is less skewed since the risk factor has been minimized or taken into consideration by the investor who acquires this investment (Perold, 2004). A normal distribution is usually the ideal condition within which an investor can make a decision since the returns here are uniform and take a particular direction, which is at least known or predictable to the investor. Although in a real investment, there is no ideal condition, thus investors are forced to hedge or reduce their risks. This is why acquisition of insurance is necessary to guard the investor against losing his or her money, as well as investments (Bodie, Kane, & Marcus, 2008).

## Background and Importance of the Fama French Model

The Fama French model offers a very useful tool for understanding performance of a given portfolio. It also helps in the measurement of the effect of active management, construction of portfolio and estimation of future returns (Sharma & Mehta 2013). The 3-factor model is slowly replacing the CAPM since it is becoming among the most widely accepted and used explanation of prices of stock taken together investor returns (Bornholt 2013). The contribution of Fama was crowned by his collaborative work with French – his colleague. Together, they developed the 3-factor model that tends to extend the single market premium factor of the conventional theories of pricing assets. The model shows that the sensitivity to both value and size offers a sufficient model for the movements of share price. The first factor is usually denoted as SMB,which stands for ‘small minus big’. This is typically the difference between the returns portfolios (small capitalisation stocks) that have been diversified as well as a portfolio of large stocks that are designed to be neutral with regard to book equity to market equity denoted as BE/ME (Dempsey 2013). HML that means high minus low is the second element of the model. The difference between returns on diversified portfolios of low and high book equity to market equity shares developed regardless of their size. Evidently, the betas are slopes found in the regression. The three-factor model of Fama is described using the following equation:

Where R_{i }represents return on asset *I*, R_{m} is the return on the value-weight market portfolio, and R_{f} is the risk-free interest rate (Guthmann et al. 1966).

At any given time, none of the market factors is ever confident. It is, therefore, important to understand that value and volume risks are different compared to market risk. However, they do not necessarily increase the total risks of the portfolio. In that regard, an investment portfolio that is tilted away from the heart of the market will usually act differently from the rest of the market but without having more risks.

## Empirical Test of the Fama French 3 Factor Model

The results in appendices disprove the Fama French 3 Factor Model hypothesis. Therefore, we reject the null hypothesis. The explanatory variable for Y is quite small and statistically insignificant. Given that CAPM works very well only on theory, Fama-French model might be a useful alternative. The Fama-French Model’s way of inputting is highly controversial. Nevertheless, one of the clearest things about the model is that it usually does an excellent job providing explanations for the variability of returns- that is quite difficult from what happens in the CAPM model (Guermat 2014). For instance, Fama French (1993) explains that their three-factor model provides explanations for more than 90 percent variability in returns. On the other hand, APM only reveals 70 percent variability of returns. Largely, the FF model seems to be a better alternative to the capital asset pricing model (Eikseth & Lindset 2012).

## Reference List

Bodie, Z Kane, A & Marcus, A 2008, *Investments*, McGraw-Hill Irwin, New York.

Bornholt, G 2013, ‘The Failure of the Capital Asset Pricing Model (CAPM): An Update and Discussion’, *A Journal of Accounting, Finance and Business Studies*, Vol. 49, no. 1 pp 3-10.

Bornholt, G 2013, ‘The Failure of the Capital Asset Pricing Model (CAPM): An Update and Discussion’, *Abacus*, vol. 49, pp 36-43.

Das, S Markowitz, H & Scheid, J 2010, ‘Portfolio optimization with mental accounts’ *Journal of Financial and Quantitative Analysis, *vol. 45 no. 1, pp 311-334.

Dempsey, M 2013, ‘The Capital Asset Pricing Model (CAPM): The History of a Failed Revolutionary Idea in Finance?’, *Abacus*, Vol. 49, pp 36-48.

Dempsey, M 2013, *The Capital Asset Pricing Model (CAPM): The History of a Failed Revolutionary Idea in Finance?* McGraw-Hill, New York.

Eikseth, H & Lindset, S 2012, ‘Are taxes sufficient for CAPM rejection?’, *Applied Economics Letters*, vol. 19 no. 18, pp 1813-1816.

Elton, E Gruber, M & Brown, S 2006, *Modern Portfolio Theory and Investment Analysis*, John Wiley, New York.

Eraslan, V 2013, ‘Fama and French Three-Factor Model: Evidence from Istanbul Stock Exchange’, *Business & Economics Research Journal*, vol. 4 no. 2, pp 11-22.

Fama, E & French, K 2004, ‘The capital asset pricing model: Theory and evidence’, *Journal of Economic Perspectives*, Vol. 18, no. 3, pp 25-46.

Fama, E 1970, ‘Efficient capital markets: A review of theory and empirical work’, *Journal of Finance,* vol. 25 no. 2, pp 383-417.

Guermat, C 2014, ‘Yes, the CAPM is testable’, *Journal of Banking & Finance*, vol. 46, pp 31-42.

Guthmann, H Bakay, A Rangarajan, G Severn, A Scherer, J Beazer, W & Lintner, J 1966, ‘The Journal Of Finance December 1965’, *Journal Of Economic Abstracts*, vol. 4 no. 1, pp 96-100.

Levich, M 2001, *International Financial Market*, McGraw-Hill, New York.

Oster, S 1994, *Modern Competitive Analysis*, Oxford University Press, Nueva.

Perold, A 2004, ‘The Capital Asset Pricing Model’, *Journal of Economic Perspectives*, Vol. 18 no. 3, pp 3-24.

Reilly, K & Brown, C 2007, *Investment Analysis and Portfolio Management*, Southwestern Thomson, New York.

Sharma, R & Mehta, K 2013, ‘Fama and French: Three Factor Model’, *SCMS Journal Of Indian Management*, vol. 10 no. 2, pp 90-105.