Introduction

This report has aim to highlight the limitations of an important portfolio theory i.e. Capital Asset Pricing Model (CAPM) and will compare it with other portfolio theories that are based on the multifactor approach. The report intends to assess how effectively the practicality in the implementation and empirical testing of CAPM model has been addressed by multifactor models.

The data that have been used for the purpose of carrying out required comparison is related to various researches performed subsequent to the implementation of CAPM and the outcomes or suggestions of the researchers that agree or oppose the CAPM concept for measuring market and portfolio return. Further, some of the required information has also been obtained through the internet where online articles have been reviewed. Majorly, this report refers to the renown journals articles and books about CAPM and its limitations.

1.A Review of CAPM

Financial independence is a major factor that determines the pattern of life of a person and an organization. Individuals and corporations undertake various steps that involve taking multiple risks in order to achieve the desired prosperity. One of the key tools that are used for this purpose is investment in the stock market where the investor needs a reward as a compensation for providing funds to the firm in the form of investment in shares. However, this approach for attainment of affluence comes with a price i.e. risk of uncertainty that is associated with returns from the stock market.Every investor wants to create a portfolio that has an expected level of standard deviation and highest return as compared to other portfolios. In order to create a balance between expected return and investment risk, Capital Asset Pricing Model (CAPM) has been used as a generic tool by investors for many years and it has helped them a great deal in the decision making process (Barberis et al., 2015).

Sharpe (1965) introduced CAPM which was further developed during the 1960s by Jack Treynor, John Lintner and Jan Mossin (Perold, 2004).It calculates expected return of a portfolio by adding risk free return with the beta adjusted difference between the expected market return and risk free return.

r_a = r_f + B_a (r_m – r_f)

The simplicity of CAPM and reasonable accuracy in analysing the portfolio returns made it a preferred choice for investors. CAPMcovers basic areas related to portfolio pricing and manages investment risk by splitting portfolio’s risks into two broad categories i.e. systematic risk and specific risk.It helps the investors in mitigating the investment risk without corresponding reduction in return (Zabarankin et al., 2014).One of the most effective means to reduce the investment risk is to select a mix of stocks in the portfolio that either contains negatively correlated returns or where there is no or very little correlation between assets’ returns. CAPM supports the assumption that the specific risks related to a portfolio can be minimized by making it efficient throughtaking measures such as portfolio diversification. The systematic risk on the other hand is denoted by beta (Risk Encyclopedia, n.d.).A Beta value that is less than 1 means that a portfolio is less risky than the market and vice versa. Further, it assumes that preferences, expectations and market knowledge of all investors are more or less the same and they make informed decisions relating to their portfolio management. Further, risk free investments are available in the market and are used invariably by the investors as a part of their portfolio diversification arrangement.

 

2.1.Limitations of CAPM

CAPM has been in use for many years by investors for analysing risks associated with investment in the stock market on the basis of assumptions related to accuracy of Beta, availability of risk free investment and homogenous understanding of the market by all investors.The above-referred assumptions related to CAPM, however, have been questioned by many researchers and some of the assumptions used in CAPM model have been declared incorrect by them (Dempsey, 2013).

One of the most noticeable objections is related to the overall understanding of investors about market risks and expected returnsfrom a portfolio.Specifically, factors such as non-availability of risk free rate of return, expected market return and gaps in the calculation of Beta point to anomalies in the model. Practically, it is not possible for every investor to fully capture the market trends, understand covariance between different assets and underlying assumptions that have a far greater bearing on the ultimate return of an individual or group of assets. Furthermore, CAPM does not take dividends and market price of a stock in consideration while calculating expected return from the portfolio (Ward and Muller, 2012).

Roll (1977) has stated that no testing for checking the accuracy of CAPM has been carried out that could confirm its assumptions. It is further stated that the only point related to CAPM that can be tested reasonably is its mean variance efficiency and that it is very difficult to measure the market return.

Further, Banz (1981) opined that smaller firms have shown the potential of a higher or abnormal return on assets as compared to the medium and large size organizations (referred to as size effect). This again contests the assumptions used by the CAPM model that presents a scenario where market trends and expected returns can be predicted with considerable accuracy on the basis of portfolio diversification and systematic risk management. It has been suggested that other factors also contribute towards market performance and returns from an asset / portfolio. According to a study carried out by Litzenberger and Ramaswamy (1982) relating to common stocks for the 1936-1977 period, a positive correlation can be recognized between dividend yield and the return of an asset. Further, it was also highlighted that Price Earning (P/E) ratio has been observed to have a strong impact on the overall performance, i.e. return from an asset. However, this paper does not seem to point out any fault on part of CAPM in this regard and suggests that this trend is attributed to the market inefficiency factor. Contrary to this opinion, other researchers have noted that the abnormal change in an asset’s return is due to the fact that CAPM fails to recognize the importance of its P/E ratio, i.e. relationship of a company’s earnings with the market price of its stock. Banz (1981) suggests that gamma (one term accounting for firm market size) needs to be incorporated in the CAPM model with an aim to eliminate this anomaly.

Reinganum (1981) has also mentioned that results of research have shown that earnings of organizations along with their size can be effectively used by analysts and investors to form portfolios that provide more than the expected return on assets. This idea was based on review of profitability of companies during the period 1976-77 suggested that abnormal earning from a portfolio can be made through diversification of portfolio and analysis of P/E ratio of companies.

Basu (1983) has pointed out that impact created by stocks with low earning P/E ratio is ignored by the CAPM model. Further, DeBondt and Thaler (1985) found that stocks with abnormally low returns during previous three years tend to provide unusually high returns during next three years; a fact that has not been covered by CAPM.

In addition to above, there can be other factors such as economic growth, rise in inflation, law and order situation, introduction of enhanced regulatory framework etc. that can have a significant impact on the return of individual stocks as well as overall market performance. Not all stocks respond in a similar manner to say interest rate changes, technological advancements, crime rate etc. Although critical, these factors have however been ignored in the CAPM model (Andriotto and Teti, 2014). Furthermore, CAPM ignores taxation and transaction costs which can turn out to be the decision changing factors in a market. Carhart (1997) has also pointed out that transaction costs, portfolio turnover and the investment costs of expense ratios have a negative impact on the short term returns of mutual funds. The paper also describes how investment in last year’s top performing stocks and selling worst performing ones improved overall return by 8%. The breakup of this 8% improvement showed that 4.6% was due to the difference in the market value and momentum of stocks held, 0.7% due to variation in expense ratios and 1% because of transaction costs.In particular, the concept of investing in the high performing stocks of the previous year for benefitting from one-year momentum strategy (Jegadeesh & Titman, 1993) has been observed to be successful in the short term. These concepts / factors seem critical for making both short term and long term investments in the stock market, however, these have not been included in CAPM model, which shows another anomaly in this concept.

Beta has also been found to be inconsistent as it is always considered to be positive when the market index is positive irrespective of the general perception of investors about market risk. Further, Beta calculation involves comparing returns of a particular asset with market returns over a specified period of time (Ramachandaran, 2012). The issue arises when a different time period is used by the investors as it results into the difference in the outcome, thereby increasing the chance of a misinterpreted stock performance with reference to the market trends.Moreover, Bhandari (1988) has stated that average returns are related to leverage.

2.Discussion

The above referred anomalies in the CAPM model and empirical failure led to the emergence of more complex and detailed models for ascertaining the pricing and return of assets. These models have been conceived as an effort to consider additional factors for the purpose of calculating expected return from the market with greater accuracy, thereby aiming to overcome the limitations of CAPM especially related to uncertainty. As a result, researchers came up with some theories as an alternative to CAPM to eliminate the above referred limitations. The most notable of these models are appended hereunder.

 

3.1.Arbitrage Pricing Theory

The Arbitrage Pricing Theory (APT) is an important finding in the field of asset pricing and it provides answers to many questions that have been raised against CAPM model. APTwas presented by Stephen Ross in 1976 and was considered as areplacement of CAPM (Connor and Korajczyk, 1992) that used the mean variance theory for determining price of a portfolio. APT is based on the idea that returns from an asset can be forecasted by analysing it against associated risk factors that include but are not limited to capital and labour. These economic shocks or statistical factors play an important role in determining the return of an asset.

 

As per InvestingAnswers (n.d.) the APT formula is:

 

E(r_j) = r_f + b_j1R_P1 + b_j2R_{P2 +} b_j3R_{P3 + …… +} b_jnR_Pn

 

Where,E(r_j) is expected rate of return, r_fis risk free rate, b_jis sensitivity of asset’s return to the particular factor and R_Pis risk premium associated with the particular factor.

 

The above formula shows that risk factors and risk premium that impact the return of the asset have been included in APT equation which covers these missing links inthe CAPM concept.

The testing carried out using APT helps in ascertaining particular risks that impact the price of a stock e.g. increase in inflation causes a company’s stock price to decrease, increase in crime rate in US leads to increase in stock price of ammunition manufacturing companies etc (Huberman, 2005).

Therefore, APT is known to have more wide ranging parameters as compared to CAPM. APT compares macro-economic factors of individual assets against its expected return for the purpose of concluding the return from an asset. It thus helps the investors in covering the impact of unexpected return and assessing the overpriced and under-priced stocks that ultimately leads to realization of required profit for the investor (Lehmann and Modest, 1988).Hence, cumulative return from individual assets is taken into consideration while calculating a portfolio’s return. The theory also suggests that stocks with similar risk and return patterns (such as banking industry) should have the same market value. However, as APT leads to estimation of a stock price, it may result in trading for prompt profit taking in the stock market. APT has some similar limitations as CAPM such as investors have similar expectations from the market, absence of tax and transaction costs and reliance on Beta etc. (Connor and Korajczyk, 1986). In particular, APT assumes that a number of known factors impact the return from an asset (Connor and Korajczzzyk, 1992) and additional assumptions are taken into consideration in order to obtain the precise price of an asset which serves as a limitation of this model as well.

Overall, APT improves understanding of the market return and has opened door for many researchers to analyse impact of other factors for asset pricing with improved accuracy.

 

3.2.Fama and French Factors Model

Fama and French (1992) pointed out that little relation could be established between Beta used in CAPM and average return of assets in the USA market. The researchers evaluated role of Beta, firm size, P/E and market capitalization of average returns of companies in New York Stock Exchange, American Stock Exchange and NASDAQ. The results showed that firm size and market capitalization impact upon the average portfolio returns. Therefore, Fama and French Three Factors Model was developed which covered the aspects of firm size and market capitalization that were not previously covered by CAPM.

 

According to Moneychimp (n.d.) Fama and French Three Factors Model formula is:

 

r – R_f = beta₃ x (K_m – R_f) + b_s x SMB + b_v x HML + alpha

 

Where, r is rate of return, R_fis risk free rate, K_mis market return, SMB is small (cap) minus big and HML is high (book/price) minus low. SMB and HML multiplied with their beta coefficients incorporate effect of abnormal returns of small cap and value stocks in the formula that is missing in CAPM model.

Fama and French (1992) further explained that the positive relation between Beta and market returns as presented by CAPM has not been validated and can only be applied to a comparatively previous period of 1926-1968 however it was not reflected in the market return during 1963-1990.

Fama and French also found out that value stocks (a stock that is traded at a price lower than its actual value) (Investopedia, n.d.)performed better than the growth stocks during the period 1975 to 1995. This model has made the researchers to realize that single factor (i.e. Beta) model does not reflect true or entire picture of an asset or a market.They have therefore added size factor and value stocks factor in the CAPM model in addition to beta in order to improve its outcome. Jain (2013) suggests that application of Fama French Three Factors has explained over 90% of diversified portfolio returns as compared to 70% for CAPM.

However, there has also been some criticism from researchers on the theory presented by Fama and French. For example, Kothari et al., (1995) checked this theory using data collected from S&P’s industry level data related to the period 1947 to 1987 and reported that many companies that did not survive due to low market capitalization were excluded from the data by Fama and French. Further, factors such as similarity between investors’ understanding of the market, availability of risk free return, external factors such as inflation, technological risks, incremental crime etc. have not been covered in this model as is the case with the CAPM model. However, various researchers have supported their theory after successful validation and it has opened broader vision into predicting the trends of the stock markets with more accuracy.

 

3.Conclusion

The CAPM was successfully used by investors over quite a long period of time for analysing expected performance of a portfolio with the help of Beta and by including factors of risk free return and market return in the formula. It is also used for calculating the cost of fund of securities being traded in the stock markets. However,there were many factors such as non-availability of risk free rate of return, expected market return and gaps in the calculation of Beta that have been considered as weaknesses in the CAPM model. Further, uncertainties in market trends and unexpected or abnormal returns in the stocks led to additional researches. These studies concluded that a single factor model is insufficient to cover all the aspects of a market and its individual stocks.

As a result, multi-factor models have emerged that cover other important risk factors such as inflation, GDP growth, the size of a firm, its market capitalization, P/E ratio etc. that have not been covered by CAPM. Specifically, size factor has emerged as an important element for determining market behaviour, especially related to abnormal returns. These models provide prospective investors and other stakeholders an important insight into the expected return from a single asset as well as a portfolio, keeping in view all known factors. Although, multi-factor models are also not perfect, they have been found to be more accurate and consistent as compared to CAPM for ascertaining reasons for determining the market and assets’ behaviour. It is pertinent to mention that multi-factor models have been tested against the data of many countries in addition to the USA and its findings, as presented by Fama and French, have been validated to a great extent.

 

 

 

References

 

1. Andriotto, M. and Teti, E., 2014. Beyond CAPM: an innovative factor model to optimize the risk and return trade-off. Journal of Business Economics and Management, 15(4), pp.615-630

 

2. Banz, Rolf W. (1981), The Relationship between Return and Market Value of Common Stocks, Journal of Financial Economics (1981) 3318.

 

3. Barberis, N., Greenwood, R., Jin, L. and Shleifer, A., 2015. X-CAPM: An extrapolative capital asset pricing model. Journal of Financial Economics,115(1), pp.1-24.

 

4. Basu S. (1977) Investment performance of common stocks in relation to their price- earnings ratios. A test of market efficiency. Journal of Finance 32, June 663 - 682

 

5. Bhandari, Laxmi Chand (1988), Debt / Equity Ratio and Expected Common Stock Returns: Empirical Evidence, Journal of Finance 43, 507 - 528

 

6. Carhart, M. M. (1997). "On Persistence in Mutual Fund Performance". The Journal of Finance 52: 57 – 82

 

7. Connor, Gregory and Korajczyk, Robert A. (1992), The Arbitrage Pricing Theory and Multifactor Models of Asset Returns

 

8. Connor, G. and Korajczyk, R.A., 1986. Performance measurement with the arbitrage pricing theory: A new framework for analysis. Journal of financial economics, 15(3), pp.373-394.

 

9. DeBondt, W. and R. H. Thaler (1985). Does the stock market overreact? Journal of Finance 40: 793 - 805

 

10. Dempsey, M., 2013. The capital asset pricing model (CAPM): the history of a failed revolutionary idea in finance?. Abacus, 49(S1), pp.7-23.

 

11. Fama, E. F. and K. R. French. 1992. The cross-section of expected stock returns. Journal of Finance 47: 427 – 465

 

12. Huberman, G., 2005. Arbitrage pricing theory (No. 216). Staff Report, Federal Reserve Bank of New York

 

13. InvestingAnswers (n.d.), Available through InvestingAnswers website

<http://www.investinganswers.com/financial-dictionary/stock-valuation/arbitrage-pricing-theory-apt-2544> [Accessed Dec 31, 2015]

 

14. Investopedia (n.d.), DEFINITION of 'Value Stock'. Retrieved December 25, 2015 from http://www.investopedia.com/terms/v/valuestock.asp

 

15. Jain, sahil (2013), Fama French Three Factor Model in Indian Stock Market, The Current Global Trends, Vol. 2 Issue 1

 

16. Jegadeesh, Narasimham and Sheridan Titman (1993), Returns to buying winners and selling losers: Implications for stock market efficiency, Journal of Finance 48, 65 - 91

 

17. Kothari, S. P., Jay Shanken, and Richard P. Sloan (1995). Another look at the cross-section of expected stock returns. Journal of Finance 50: 185 – 224

 

18. Lehmann, B.N. and Modest, D.M., 1988. The empirical foundations of the arbitrage pricing theory. Journal of Financial Economics, 21(2), pp.213-254.

 

19. Litzenberger, Robert H. and Ramaswamy, Krishna (1982), The Effects of Dividends on Common Stock Prices: Tax Effects or Information Effects? The Journal of Finance, Vol. XXXVII, No.2
19.  
20. Moneychimp (n.d.). Available through Moneychimp website

<http://www.moneychimp.com/> [Accessed Dec 31, 2015]

 

21. Perold, Andre’ F. (2004), The Capital Asset Pricing Model, Journal of Economic Perspectives—Volume 18, Number 3—Summer 2004—Pages 3–24

 

22. Ramachandaran, Anish (2012), A Discussion of Beta – Its limitations and Usefulness. Available through Ken Stern & Associates website

<http://www.kenstern.com/wp-content/uploads/2012/03/AlphaAdvisor-4Q2012.pdf> [Accessed December 26, 2015]

 

23. Reinganum, Marc R. (1981), Misspecification of Capital Asset Pricing: Empirical Anomalies based on Earnings Yields and Market Values, Journal of Financial Economics 9 (1981) 19 - 46.

 

24. Risk Encyclopedia, n.d., Capital Asset Pricing Model. Available through Risk Encyclopediawebsite

<http://www.riskencyclopedia.com/articles/capital_asset_pricing_model/> [Accessed December 25, 2015]

 

25. Roll, Richard (1976), A Critique of the Asset Pricing Theory’s Tests, Journal of Financial Economics 4 (1977) 129-176.

 

26. Sharpe, William F. (1964), Capital Asset Prices: A Theory of Market Equilibrium under Conditions of Risk. The Journal of Finance, Vol. 19, No. 3 (Sep., 1964), pp. 425 - 442

 

27. Ward, M. and Muller, C., 2012. Empirical testing of the CAPM on the JSE.Investment Analysts Journal, (76), pp.1-12.

 

28. Zabarankin, M., Pavlikov, K. and Uryasev, S., 2014. Capital asset pricing model (CAPM) with drawdown measure. European Journal of Operational Research, 234(2), pp.508-517.