Similarities And Differences Between The Single Index Model And Capital Asset Pricing Model

With Reference to this statement, describe, discuss and illustrate the principles of portfolio theory. Your essay should include coverage of the Markowitz Efficient Frontier and the Capital Market Line.

In this literate review the most important papers about explaining stock returns from 1952, when Markowitz came up with Modern Portfolio Theory, till around 2011 will be discussed. As stated in Chapter 2, Jack Treynor was one of the first economists that started to work on the CAPM model. When he developed the CAPM in 1961, there was no way yet to fully test it. Because there were no samples large enough or of sufficient quality, the real testing of the CAPM started in 1970. In 1973, the world was shown the famous Black and Scholes options pricing model. One of the first studies that gave a different answer than the CAPM was the research by Basu (1977). While he agrees with the Efficient Market Hypothesis, Basu reaches another

Given these approximations, the CAPM model would total the risk-free rate and the market risk premium times beta to arrive at a cost of equity of 9.68%, which reflects the investors’ expected return from investing in shares of the company.

The CAPM is a single factor model because it based on the hypothesis that required rate of return can be predicted using one factor that being systematic risk. It looks at risk and rates of returns, compares then to the stock market providing a usable measure of risk to help investors determine what return they will get for risking their money in an investment. There are a lot of assumptions and drawbacks of CAPM that lead to the conclusion that those investors utilizing this

The Capital Assets Price Model (CAPM), is a model for pricing an individual security or a portfolio. Its basic function is to describe the relationship between risk and expected return, which is often used to estimate a cost of equity (Wikipedia, 2009). It serves as a model for determining the discount rate which is used in calculating net present value. The CAPM says that the expected return of a security or a portfolio equals the rate on a risk-free security plus a risk premium. The formula is:

In order to find the optimal portfolio allocation, the group needs to find the portfolio structured with lowest risk under a given return. This can be achieved by applying Mean-Variance Theory and Markowitz model find the efficient frontier, which yields the most optimal portfolio under given returns. It can be expressed in mathematical terms and solved by quadratic programming. [Appendix A]

CAPM results can be compared to the best expected rate of return that investor can possibly earn in other investments with similar risks, which is the cost of capital. Under the CAPM, the market portfolio is a well-diversified, efficient portfolio representing the non-diversifiable risk in the economy. Therefore, investments have similar risk if they have the same sensitivity to market risk, as measured by their beta with the market portfolio.

Investors hold diversified portfolios : One of the assumptions of CAPM model is that investors are holding only portfolios which are subjected to systematic risk , the unsystematic risk can be ignored , therefore the unsystematic risk has been ignored (Lakonishok & Shapiro , 1986)

Using time series regression on the monthly returns we have estimated the beta coefficient for each stock. Using the market model of CAPM i.e., regressing each stock’s monthly returns against the market index (Nifty100) we have estimated individual stock beta’s.

According to the CAPM model:R_i=α+βR_m+ε, α represent the abnormal return gained by the portfolio. If the market is efficiency, the α has to be zero.

Even though there are flaws in the CAPM for empirical study, the approach of the linearity of expected return and risk is readily relevant. As Fama & French (2004:20) stated “… Markowitz’s portfolio model … is nevertheless a theoretical tour de force.” It could be seen that the study of this paper may possibly justify Fama & French’s study that stated the CAPM is insufficient in interpreting the expected return with respect to risk. This is due to the failure of considering the other market factors that would affect the stock price.

A market model states the return generated by a security is dependent on that generated by the market portfolio and the degree to which the security responds .Market model basically outlines the customer’s position in the industry and net worth.

CAPM model builds on the model by Markowitz(1959).Markowitz assumes investors to be rational and risk averse. The model is one period model in which investor chooses portfolio at time t-1 in anticipation of stochastic return in period t. He uses mean variance criterion that states that investor will either choose highest expected return portfolio for given level of variance or lowest variance for a given level of expected returns

Richard Roll, and University and Auburn, University of Washington, and University of Chicago educated economist, began his career researching the effect of major events of stock prices. This experience likely helped him reach the two conclusions he makes in his 1977 “A Critique Of The Asset Pricing Theory’s Tests”, one of the earliest and most influential arguments against CAPM. In the paper, Roll makes two major claims: that CAPM is actually a redundant equation that just further proves the concept of mean-variance efficiency, and that it is impossible to conclusively prove CAPM. His first claim relates to mean-variance efficiency: the idea that mathematically one must be able to create a portfolio that offers the most return for a given amount of risk. Roll claims that all CAPM is doing is testing a portfolio’s mean variance efficiency, and not actually modeling out projected future returns. The second claim in the paper is that there is not enough data about market returns for CAPM to ever prove conclusive. Even if modern technologies could help alleviate some of the burden of testing market returns for publicly traded equities, there is still no way to account for the returns of less liquid markets, where there is less public information. This means it is impossible for

Since CAPM was accepted and admitted in fundamental concepts by most people in financial economics, factor model researching becomes a popular topic in finance. In 1992, Eugene Fama and Ken French established the empirical foundations for the Fama & French Three-Factor Model. It is designed to capture the relation between average return and size and the relation between average return and B/M (price ratios).