1. Theoretical assumptions and implications of Capital Asset Pricing Model (CAPM) derived from Sharpe (1964) and Lintner (1965)

The Capital Asset Pricing Model established by Sharpe (1964) and Lintner (1965) specifies that expected return on a particular stock is developed by considering the risk premium and risk free interest rate. Early practical analysis of different models have supported the main prediction that beta is the sole explanatory factor, which tends to explain the cross-sectional variation in stock. It is observed in recent empirical tests that the asset pricing model comprise a number of variables, which helps in explaining cross-sectional variations in stock returns, apart from the market risk. The model had initiated the idea of asset pricing theory (Roll, 1997). Prior to that, there was no asset pricing models and the same was generated by considering the nature and taste of investment opportunities available in the stock market. The model clearly tested predictions that are made with respect to return and risk of the stock. The models are used presently for estimating cost of equity and examining performance of portfolios that are developed in the stock market. It states that there is always a linear relation between expected return of a stock, risk associated with the stock and beta. Here, beta is defined as the variable, which focuses on explaining the cross-sectional return of stocks. The model was initially devised by Harry Markowitz. However, it was later modified by Sharpe and Lintner. Initially, the model explained that if an investor is selecting a particular portfolio for a particular period of time and receiving a return, he is risk averse. The model is based on algebraic statement, which predicts the relation between risk and return of the portfolio. The modified version of Sharpe (1964) and Lintner (1965) has the following assumptions:

1. The security markets are expected to be perfectly competitive.
a) There are many small investors. 
b) The investors are regarded as the price takers.

2. The markets are not expected to encounter any friction or disturbance.
a) The markets transactions do not bear any taxes or other costs.

3. Investors are very narrow-minded as well as risk averse.  
a) The investors count only one and the same holding period (Lakonishok, Shleifer and Vishny, 1994)

4. The investments are restricted to publicly traded assets. The assets bear unlimited lending and borrowing at risk-free rates.
a) The assets, like, human capital, does not form the part of opportunity set of the investment plan.

5. All investors are regarded as rational beings (Mitchell and Stafford, 2000). They optimize the mean-variance before investing. 
a) Investors are using the Markowitz portfolio method for selecting their investment plan.

6. Perfect information is collected by investors in order to get a clear idea regarding the security market and risk associated with it (U.S. Department of Treasury, 2013)
a) The investors have good access to the information that is provided to them.
b) The investors are expected to analyse the information in the same way (Fama and French, 2003).

The equation for the model can be written as the following:
E(Ri) = Rf + ?(E(Rm) - Rf)
Rm = Return from the market
E(Ri) = Expected return on the asset in which investment is made
Rf = risk-free rate of interest i.e. interest arising from government bonds
?= sensitivity of the expected excess asset returns to the expected excess market returns
The regression version of the model can be written as:
Rpt- Rft = ?+ ?*(Rmt - Rft) + ?t
Rpt-Rft = excess return of the portfolio (taken as dependent variable for solving the problem)
Rmt?Rft = excess return of the market (taken as independent variable for solving the problem)
? = estimated vales of the parameters
? = estimated vales of the parameters
?t = error at time t (Roll, 1997)
The value of beta depends on the type of assets and it gauges volatility of same, in terms of market risk. The following are the interpretation of beta with respect to different assets:



Greater than 1

Performance of the shares is aggressive. They outperform the market, which implies that the stocks with ?> 1 provide higher return than the market.

Equals to 1

Performance of the share is neutral. The performance of the stocks is in line with that of the average return of the market.

Less than 1

Performance of the shares is noticed to be conservative and is less risky than the market returns.

Apart from the above explanation, it is observed that every market has a beta factor of 1. For example, if the beta factor is 2, then return of the stock varies twice as much as the market return. If market return (Rm) is 5% more the risk free return, then the expected return of the company stocks with beat factor 2 is 10% above risk free rate of return.

2. Validity of the assumptions

The model was considered by taking time period as one year.  The validity of model is approved only by expanding the time period to multiple years. It, thus, measures whether the return of the market is stable or not. The changing market conditions and company’s cost structure indicate the fact that beta of the security market will not remain the same over years. Beta is regarded as risk associated with the stock returns. The estimation of these betas is subject to statistical variability. The betas related to the industry are more reliable than individual betas of the company.

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