Within these components of the portfolio, unsystematic risk can be eliminated by increasing the portfolio size, the reason being these risks (which are specific to an individual security such as business or financial risk) can be eliminated by constructing a well-diversified portfolio. Meanwhile, systematic risks are associated with overall movements in the general market or economy and are often referred to as the market risks. Market risks are the components of the total risk that cannot be eliminated through portfolio diversification of a company.

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CAOM was introduced independently by Jack Treynor (1961, 1962), William Sharpe (1964), John Lintner (1965) and Jan Mossin (1966). All of them built on the earlier work regarding diversification and modern portfolio theory of Harry Markowitz. The Nobel Memorial Prize in Economics was jointly received by Sharpe, Markowitz and Merton Miller for this contribution to the field of financial economics. The CAPM discussed in the following section, relates the expected rate of return of an individual security to a measure of its systematic risk. Since then, a variety of models have been developed to predict asset returns
According to CAPM, the securities are priced such that the expected returns will compensate its investors for the expected risks involved.
The main assumption of CAPM is that the risk-return profile of a portfolio can be optimized. An optimal portfolio displays the lowest level of risk that is possible for its level of return.
An optimal portfolio includes every asset and each of these assets is value-weighted to achieve the above (assuming no trading costs and that any asset is infinitely divisible). This is because each additional asset introduced into a portfolio further diversifies the portfolio. The efficient frontier comprises of all such optimal portfolios, i.e., one for each level of return.
Because the unsystematic risk is diversifiable, the total risk of a portfolio can be viewed as beta β
Capital Asset Pricing Model (CAPM) is the most preferred risk/return model used by the finance fraternity. This model is used to calculate the expected return on investment (also known as the hurdle rate). However as argued by its critiques, it places very high reliance on one variable – the beta. If CAPM with all its assumptions is right, then the difference in the expected rate of return between two stocks is attributed solely to the difference in β of the stocks.
Expected rate of return = Rf + β (Rm – Rf)
Where Rf = Risk-free rate (Government bond yield).
β = Beta
Rm = Market return ( of a broad based index)
Since the risk -free rate and the market return in CAPM for two stocks can be similar (assuming the same index for calculating market return has been considered), the difference in the expected return between two stocks would entirely depend on the beta of the stocks. Therefore while estimating the hurdle rate, the accuracy -of beta is of utmost importance.
Basic assumptions made by this model are
Maximizing economic utility is the aim of all investors.
Investors should be rational and risk-averse.
Asset prices cannot/ should not be influenced by investors
There should be a risk-free asset in zero net supply.
Demand of assets equals supply in equilibrium
Transaction or taxation costs are not involved in trade
Perfectly competitive markets should be present
Investors should be able to lend as well as borrow unlimitedly ( provided this is under a risk free rate of interest).
There should be a risk-free asset paying interest rate
Investors should agree on the asset returns distribution
Information should be provided at the same time to all investors.
Derivations of CAPM – (numerical + formal)
There are 2 models that are the building blocks for deriving the CAPM
capital market line
security market line
Capital Market Line
The capital market line (CML) gives the return to be received on a portfolio that an individual investor expects. It is a linear relationship between risk and return on efficient portfolios that can be represented as:
Where ,
Rp = Return on portfolio
Rf = Return on risk-free asset
Rm= Return on market portfolio
σp = standard deviation of returns on portfolio
σm = standard deviation of returns on market portfolio
The sum of the return for delaying consumption and a premium for bearing risk inherent in the portfolio can be defined as the expected return on a portfolio. The CML expresses investors’ behaviour regarding the market portfolio and their behaviour regarding their own investment portfolios. It is valid only for efficient portfolios.
Security market line
Security market line (SML) describes the return that an individual investor should expect in terms of a risk-free rate and the relative risk of a security or portfolio held by him. With respect to security, SML can be written as:
where
and Ri= the correlation between security return Ri, and market portfolio return.
The βi can be represented as the amount of non-diversifiable risk inherent in the security which is relative to the risk of the market portfolio.
Following are the set of assumptions that are sufficient to derive the CAPM of:
(i) the investor’s utility functions can be either normal or quadratic,
(ii) elimination of all diversifiable risks has taken place
(iii) the opportunity set of risky assets should dominated by market portfolio and the risk-free assets.
SML can be used in portfolio analysis to test whether the given securities are priced fairly, or not.
CAPM essentially includes the comparison of all the present and future cost implications of an investment decision, along with the expected returns. So it is an important tool for investment management.
The exercise of comparing the present and future cost implications of an investment decision, involves discounting of all future cash flows to their present net value. It is necessary to carry out this discounting in order to honour the concept of ‘Time Value of Money’. According to the concept of ‘Time Value of Money’, a rupee in the present is worth more than the rupee earned sometime later in the future. Cost of Capital is the rate at which the future cash flows are discounted.
Traditionally calculation of the Cost of Capital has been through the use CAPM. The process of calculation is:
1. Determination of a rate of return that is risk free. This risk free rate of return is typically the yield on government bonds or long-term treasury.
2. Addition of a premium to the risk free rate to reflect the risk of the investment option. Normally the premium that is taken for the above calculation is equal to the difference between the risk free rate and the return offered by the stock market. This difference is then multiplied by an adjusting number to show the volatility of a stock (with respect to the stock market in general).
Volatility of a stock measures the expected change in price of a stock for a given change in the index value. Correlation determines both the direction as well as the strength of relationship between stock & index volatility.
Beta
The most common method of calculating beta is through regression analysis.
Beta of the stock = Covariance of stock with market portfolio/ Variance of the market portfolio
Even though this method of calculating beta is extensively used, it is not the most accurate. It has been observed that the regression beta, especially in emerging markets like India, has a high standard error attached to it. If the standard error is abnormally high, then the value of the beta maybe erroneous and not be fit for valuation purpose
For example, if the beta of the stock is 1.2 with a standard error of 0.5 then this data is flawed to the extent that it could be anywhere in the range of 0.7-1.7.
There are also circumstances when the regression beta is not available. This situation can arise in the case of a private firm. The data for calculating regression beta may not be available even after the company has gone public due to lack of sufficient historic data.
As an alternative the bottom-up approach of calculating beta is available. Although this approach includes additional workings as against a relatively simple calculation of top-down (regression) beta, the beta arrived from this method is more reliable
The business of the company plays a fundamental role in determining the beta of the stock. If the company’s products are discretionary nature i.e., if the consumer can live without the product or can delay its purchase, the beta of such a company will usually be on the higher side. On the other hand, a company which is engaged in the business of providing basic necessities such as food and clothing will generally have a lower beta for its stock.
Example: Calculation of Beta
The beta of the stock reflects the risk embedded in the firm. This risk can be due to many reasons – due to business of company, its operating leverage structure or the financial leverage balance (in its balance sheet). The focus now is to first delineate from the industry beta the effect of financial and operating leverage. This would result in a number which is purely indicative business risk. This can be termed as unlevered industry beta.
CAPM assumes that stock markets are efficient and the prices prevailing at any point of time are based on all available information. However, there are people with varying exposure to information and hence differing perceptions regarding the risk and return associated with a particular stock. Had this not been the case, then there would have been no concept on insider trading, which essentially refers to a state where certain people make investment decisions on the basis of information that is not available to the public at large. Also assuming market efficiency would be denying the role of all those people who actively deal in stocks and securities without having the will, resources or the ability to acquire and interpret all the information that might have a bearing on their investment decisions
Investors are risk averse:
The model assumes that all invest-ors are essentially risk averse and seek an optimum portfolio which maximises the return for an acceptable level of risk. However, this cannot be the common motive for all invest-ors. In fact investment considerations can be seen as a spectrum of opportunities falling between the profit maximisation & risk minimisation. Investors choose to place themselves on the basis of the returns they desire & their ability and tolerance to take risks.
Homogeneous expectations:
CAPM assumes that all investors have homogeneous or similar assumptions regarding the returns associated with a stock. However, to accept this assumption would be a rejection of the fundamental of stock markets wherein every transaction happens because of difference in investor opinion & expectation. For every transaction there is a person who sees a gain in selling and the other who expects a gain in buying at the same point. This is due to the varying expectations that they have regarding future returns from the stock.
Calculating Beta:
The second important reason for the problems associated with the use of CAPM involves calculation of the Beta which has often been accused of being an unreliable measure of a stock’s riskiness. This is on account of the following reasons:
Historical Data:
Beta is expe-cted to serve as a measure of a stock’s future risk. However, the calculation of Beta itself is based on historical data. Given this Beta can be a reliable measure only if its value remains stable over a period of time for future projections. However research has proved that Beta values of stocks vary significantly over a period of time. This implies that historic Beta values are a poor indicator of the future risk of stocks.
Subjectivity:
Calculation of Beta value always involves an element of subjectivity. This is because for determining Beta the volatility & correlation of the stock with respect to the chosen index is compared over a certain time period. However different investors can choose different time periods for comparison thus arriving at difference Beta values for evaluating an investment option.
Skewed Index:
Often the benchmark or the index used for Beta calculation is highly skewed or concentrated which can distort Beta calculations. This means that any particular stock might actually be benchmarked against a few stocks rather than a comprehensive index. For example, in the Indian context stocks like HLL, Reliance and Infosys together account for nearly 40 per cent of the total weight age.
Combination of volatility and correlation:
Bringing correlation into the equation affe-cts the estimates and hence the perception of risk associated with a particular stock.
Do all these pitfalls imply that CAPM is an ineffective tool? Certainly not. Over the years several investors have benefited from making conscious and calculated investment using CAPM. It is important for investors to realise that while CAPM does give some useful direction, it cannot be seen as the ultimate guide for investment decisions as the model has its constraints and more importantly because risks and returns associated with any investment are subject to so many variables that no model can possibly provide an accurate & comprehensive picture to the investors.
Imperfections in the Indian Capital Market
The result of several studies indicates that the risk return relations present in the Indian capital market cannot be explained by CAPM.
There can be several reasons for the failure of this model. One of the shortcomings of CAPM is its inability to define the market’s portfolio. The assumptions of CAPM imply that any market portfolio shows the universally preferred combination of assets. Ideally the CAPM market portfolio should include all assets. On the other hand, only a reasonable proxy should be used for the market portfolio. Therefore, if the market proxy hasn’t been properly defined, CAPM tests can give misleading results.
Many studies have made the use of BSE Sensitive Index, RBI Index and Economic Times Index as market proxy. Thus the possibility that the results are distorted (because of problems in the market index construction) is quite low and there is no need to explore other more probable causes.
The “efficient market” assumption of CAPM is unlikely to be valid in India (compared to the developed country markets). In India, securities trading is much less efficient in terms of transparency in transactions, speed and availability of information related to the market, periods of settlement, transaction cost, liquidity, depth of the market, etc.
Some of these important factors are :
Non Diversified Portfolio Holding
Indian investors normally hold undiversified portfolio. For example,
Indian households have share portfolios of median size 4.7. The average Indian investor possesses very few scrips in his/her portfolio. This violates CAPM where investors are expected to hold a combination of zero beta assets (risk free) and market portfolio. In CAPM, investors are not rewarded for undertaking unsystematic risk. Hence holding few securities or portfolios that are undiversified will add to market inefficiency.
Liquidity
SEBI states poor liquidity situation at Indian stock exchanges in one of its recent consultative papers. The trading is highly concentrated on a few scrips. The trading velocity at BSE (total trading volume in the year divided by market capitalization) if far less than the figures of developed countries (if top 50 shares by trading volume are excluded). Lack of liquidity violates CAPM. It results in a transaction cost for investors, which leads to a price band around the SML in which the scrips will lie. It will not be profitable for investors to trade shares within this band.
Insider Trading
This practice is rampant in India because of lack of transparency in the trading system. In a market infiltrated by inside traders, investors can never have homogeneous expectations as assumed in CAPM. It also means that the market price will not reflect all information.
Inadequate Infrastructure
Inadequacies in infrastructure affect the quality of investor service. This leads to violation of CAPM due to higher transaction cost of investors and low operational efficiency.
Weak Database
India needs to strengthen its database to perform a thorough analysis of the capital market. There are no tapes containing historical data (compared to U.S. where data dating back to 1920’s is available). We also don’t possess data that has been adjusted for rights/bonus, etc over a long period of time.
Thus India needs to strengthen infrastructure, minimize inside trading, improve liquidity, and usher in transparency to reduce the intricacies of the imperfections in the Indian market.
Conclusion
CAPM theoretical convenience:
It is relatively easy to implement.
It is simple and sensible:
• is built on modern portfolio theory
• distinguishes systematic risk and non-systematic risk
• provides a simple pricing model.
CAPM practical controversiality:
It is difficult to test:
• difficult to identify the market portfolio
• difficult to estimate returns and betas.
Empirical evidence is mixed.
Alternative pricing models might do better.
• Multi-factor CAPM.
• Consumption CAPM (C-CAPM).
• APT.