
Introduction
The capital asset pricing model (CAPM) is a benchmark during the development of modern financial economics. It was developed by William Sharp, Jan Mossin and John Lintner in 1960s based on the foundation of modern portfolio theory from Harry Markowitz. The CAPM provides people a model to predict the relationship between the expected return of an asset and its risk, and the model has been used widely in evaluation of investments and pricing of capital assets. However, the results from the CAPM sometimes have not fully withstood the empirical tests during the last several decades, and many researches have been made about the mismatching. With these researches and findings as based, the essay is aim to evaluate the usefulness of CAPM as a risk/return model practically, and to make reference to the evaluation outcomes from assumption limitation perspectives. The essay is constructed as below:
There are four basic parts in this essay: the first one is the introduction which involves the background and the main purposes, as well as the construct of the essay. The second part is to evaluate the usefulness of CAPM as a risk/return model empirically by comparing the expected return given by CAPM model with the actual return for a public company. In this part, the data selection and description and the detailed calculation would be included. The third part is to assess and analyze the comparison results from assumption limitation perspectives, and the forth part concludes the main viewpoints and findings achieved in this essay.

Data selection and comparison results
This part would serve three primary purposes: firstly, to explain the CAPM model briefly. Secondly, to describe the variables required by CAPM model and to select the data for estimation of the expected return. Thirdly, to compare the expected return with the actual return and to analyze the comparison results.

Brief explanation of CAPM model
There are two widely used assumptions in economic and finance field: rational investor and utility function. The assumption of rational investor means that investors would make investment rationally so as to maximize their interests, and the utility function assumption provides a method to qualify the investors’ interests. At the same time, investor are also supposed to be risk averse which means the investors avoid risks and would demand a reward for undertaking and engaging in the risky investments. The general utility function is:
(1)
Where is the expected utility which an investor can get for an investment , and are the expected return and the estimation of risk of the investment respectively. In the function (1), it can be seen that the investor’s utility is positively related to the expected return and is negatively related to its risk, which complies with the risk aversion assumption.
Given there is a riskfree investment in the market from which investors can get riskfree return, there should be the equation of:
(2)
Where is the riskfree return. If the equation does not exist, for example, , the return of riskfree assets would be raised otherwise no one would like to invest, and vice versa.
Supposed that the market is completely effective with no information asymmetry and transaction fraction like tax or charge, and people have a similar expectation for the market portfolio, there would be the equation (3):
(3)
Where represents the expected return of the market portfolio and is its risk estimation.
To transfer the forms of equation (2) and (3) and to state them as below:
(4)
(5)
So:
(6)
And , if ,then:
(7)
The equation (7) is the CAPM model, where , called beta coefficient, is usually considered to represent the degree of an investment’s return in response to the market portfolio’s return. However, there is a potential assumption in equation (7) that the risk of the investment is with the same characteristics with that of the market portfolio.

Data descriptionand comparison results
Eastern Airline, a public company listed in New York Stock Exchange, Hong Kong Stock Exchange and Shanghai Stock Exchange, would be specified to evaluate the usefulness of CAPM model in the essay.
As seen from the equation (7), three variables are required available by applying CAPM model to evaluate the expected return of an investment: riskfree return , the beta coefficient of the investment and the expected return of market portfolio . In this essay, the riskfree return would be estimated by deposit rate and the expected return of market portfolio would be estimated by SSE (Shanghai Stock Exchange) Composite Index. The beta coefficient of Eastern Airline is from Wind Data Base which is calculated from regression of equation (7) by using historical data. The data is described in table 1 as below:
Table 1: Data Description
Year 
2005 12/30 
2006 12/30 
2007 12/28 
2008 12/31 
2009 12/31 
2010 12/31 
Stock price of Eastern Airline (Yuan) 
1.83 
2.83 
21.29 
4.13 
6.16 
6.58 
Dividend paid in the year (Yuan) 
0.02 
0 
0 
0 
0 
0 
SSE Composite Index 
1161.06 
2675.47 
5261.56 
1820.81 
3277.14 
2808.08 
Riskfree return (%) 
5.5 

Beta coefficient 
1.09 
Where riskfree return is estimated by fiveyear deposit rate from 2000 to 2005, and beta coefficient of Eastern Airline is estimated from regression by using historical data from 2000 to 2005.
The return of market portfolio and the actual return of Eastern Airline are estimated by the equations (8) and (9) as following:
(8)
(9)
Where is the return of market portfolio in year , is the actual return of Eastern Airline in year , and is the dividend paid in year . The expected return of Eastern Airline from CAPM model and the comparison between the expected return and the actual return is detailed in table 2 as below:
Table 2: Expected return of Eastern Airline and Comparison
Year 
2006 12/30 
2007 12/28 
2008 12/31 
2009 12/31 
2010 12/31 
Actual return of EA(%) 
52.97 
652.30 
80.60 
49.15 
6.82 
Return of market portfolio (%) 
130.43 
96.66 
65.39 
79.98 
14.31 
Expected return of EA (%) 
141.68 
104.86 
71.77 
86.69 
16.10 
Difference between expected and actual return 
88.70 
547.43 
8.83 
37.53 
22.91 
Difference in percentage 
167% 
84% 
11% 
76% 
336% 
Where =expected return of Eastern Airline minus actual return of Eastern Airline in in year , and Difference in percentage=actual return of Eastern Airline in in year .
From table 2, it can be seen that the difference between the expected return from CAPM model and the actual return for Eastern Airline is vast, which means the estimation of expected return by using CAPM is not precise as the theory predicts, and the usefulness of CAPM model would probably be given a second thought.

Assessment of comparison results from assumption limitation perspectives
From the example in part 2, it can be seen that the results from CAPM model do not match the realistic world as well as the theory predicts and the same results also can be seen in other researches. One of the most important researches is the one made by Fama and French in 1992, and they found that the CAPM had little ability to explain the security returns by analyzing in a large sample of companies traded on major United States stock exchanges over the period from 1963 to 1990. These researches drive people to assess of the causes of CAPM little usefulness, and one branch is to evaluate the assumptions CAPM is based. CAPM is developed based on many assumptions like rational investor, utility function, riskfree return, efficient market, and beta coefficient, and the rest part of this essay would try to evaluate the tenability of the assumptions and try to figure out the causes for CAPM’s failure in the reality.

Beta coefficient assumption
An implication of CAPM model is that a security’s beta is the only firmspecific element of the expected return on the security. If CAPM captures rational investors’ behavior reasonably, the return of the stock would be increasing with beta and should not be affected by other variables of firmspecific risk. However, it is not true in the real world. Many researchers have found that the stock price is significantly affected by other risk variables like debt asset ratio, firm size and bookmarket ratio. If it is true, some elements and measures would probably be missed in the assessment of risk in CAPM model, which causes the little predictability of CAPM in the practice.

Efficient market assumption
Efficient market is characterized with these features including no restriction on investments, no transaction costs, no taxes, no information asymmetry and no difference on the expectations of securities. The assumptions rarely exist in reality while the opponents do. With the wide exist of taxes and transaction costs like income tax, addedvalue tax and brokerage charges, and with different expectations from information asymmetry as generally accepted claim and different analysis capabilities of investors, the market is far away from the efficient assumption. The miss of the assumption would affect directly the estimation of market portfolio and further the accuracy of the CAPM model.

Riskfree rate of return assumption
Riskfree rate of return assumption requires that people can borrow and lend money at the fixed and same rate, but the rates at which to borrow money and at which to lend money are definitely not the same for banks would not agree to eliminate their profits by equaling them. And even the rate of return of Treasury bill would not keep constant by the rate return being increasing with the maturity period. The riskfree return is usually represented by the return of deposit in bank or the Treasury bill approximately in practice for the riskfree return is hard to find out or even do not exist. The nonexistence of riskfree assets would damage the CAPM applicability.

Rational investor and utility function assumption
Rational investor and utility function assumption imply that investors prefer higher returns and lower risk, and they would invest rationally with the only aim to maximize their utility function. However, many researchers have found that investors can only act with ration partially which is limited to their available information and their capability of understanding and analyzing available information. An alternative reason for the phenomenon may be that people take actions rationally in fact but with the aim to maximum utility functions with other forms which have not been caught by current theories. These uncertainties in rational investor and utility function assumptions maybe damage the foundation of and further the CAPM model itself.

conclusion
To sum up, CAPM model was developed to explain the behavior of investment returns and to provide a method for investors to assess the efficiency of their investment on the market portfolio’s return and risk. It is based on the assumptions like rational investor, utility function, riskfree return, efficient market, and fixed beta coefficient. However, with proofs both from the example in the essay and in existing literature, the usefulness and applicability of CAPM model is in doubt. One possible reason for that is absence of the assumptions on which CAPM model is based, such as the existence of taxes, information asymmetry, transaction costs, and irrational investor and so on. In spite of these limitations, CAPM provides a useful conceptual framework for investor to evaluate investments, and helps them to establish the awareness of risk and return tradeoffs.
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