Capital Asset Pricing Model: Assumptions, Relationship Between SML And CML, Critique, And Alternatives

1.Describe the Capital Asset Pricing Model, including the assumptions underlying the theory?

2.Explain the relationship between the Security Market Line and the Capital Market Line, using diagrams and examples to illustrate your explanation?

3.Briefly set out arguments in favour of – and against - the theory, outline its uses and make a critique of its underlying assumptions?

4.Identify any alternatives which have been suggested in place of CAPM?

This essay carries out discussion on the capital assets pricing model (CAPM), which was developed in the early 1960s by the great economist William Sharpe (Fischer and Wermers, 2012). The CAPM mode has been an evolutionary work in the field of finance. It provided analysis of the risk with the expected return of the securities. Analyzing and incorporating the risk of securities with the expected return was a crucial work which was made possible with the evolution of the CAPM model. In this context, this essay provides discussion on the CAPM model with the coverage in depth in regards to relationship between security market line and capital market line. Moreover, the discussion extends to the critique of assumptions of CAPM model.                      

The capital asset pricing model provides for computation of expected return of security or the portfolio of securities. The expected return computed by applying the CAPM model incorporates the risk of the security which is an essential feature of the CAPM model. However, the CAPM model only incorporates the systematic risk because the unsystematic risk is treatable. The expected return by CAPM model is computed by the following formula (Fischer and Wermers, 2012):

CAPM=          R_f+Beta (R_m-R_f)

Where   R_f=      Risk free rate of return

            R_m=     Market rate of return

            Beta = Beta is the measure of systematic risk

It could be observed that the model computes the expected return by adding market risk premium multiplied by the beta of security to the risk free rate. Thus, eventually the risk free rate is increased by the premium for the risk taken by the investor (Fischer and Wermers, 2012). The CAPM model is based on certain assumptions as outlined below:

• The CAPM model assumes that the investors base their decisions in regards to investment only on two factors such as expected return and the risk (Focardi and Fabozzi, 2004).
• Further, it assumes that the investors are rational and they do not tend to take more risk.
• The investments made by all the investors are for same time period (Focardi and Fabozzi, 2004).
• The investors can borrow and lend unlimited amount at the risk free rate.
• There exists perfect competition in the capital market (Focardi and Fabozzi, 2004).

The use of CAPM model has been greatly admired in the field of finance. The investors may use the CAPM model in computing the desired rate of return based on which they may work out the current prices of the securities. Further, the CAMP return could also be used as the discount rate for discounting the cash flows of a project in evaluating its net present value (Sharifzadeh, 2010). 

Relationship between the Security Market Line and the Capital Market Line

There are two elements of the CAPM model such as capital market line and security market line. The capital market line and security market line both are used in finding out the efficient portfolios. However, difference between the two is that CML usages standard deviation to denote the risk while SML usages beta. The capital market line is drawn by taking standard deviation on the X-axes and expected returns on the Y-axes (Cvitanic and Zapatero, 2004). The diagram as shown below depicts the graphical presentation of the CML return:

Figure 1: CML Chart (Cvitanic and Zapatero, 2004)

From the chart shown above, it could be observed that the efficient frontier on the CML chart is drawn with reference to the expected return and the standard deviation. Thus, the slope of CML becomes:

R_m-R_f/ σ

Further, the security market line is nothing but just the graphical representation of the CAPM returns of different securities. The SML is drawn by taking beta of securities on the X-axes and expected returns on the Y-axes. The slope of SML becomes:

R_m-R_f/ β

The graph showing SML return is presented below:

Figure 2: SML Presentation (Lee and Su, 2014)

The slope of security market line is drawn based on the premise that the systematic risk is the only concern of the investors because the unsystematic risk can be diversified. Therefore, in computing the risk and return trade off, the beta which represents the systematic risk is considered. On the other hand, the risk and return trade off is computed with reference to the standard deviation in the case of CML (Lee and Su, 2014).  

The capital asset pricing model has been applied in the field of finance since many years and it has been considered as one of the most valuable finance theories. The theory establishes a linear relationship between the risk and the return. The proponents of the theory claims that the principles establish in the CAPM theory are still valid (Sharifzadeh, 2010). The theory provides a reasonable estimation of the required rate of return. Further, the proponents claim that the theory takes into account the systematic risk only which is justified because the unsystematic risk can be avoided and hence does not require any consideration. Further, it is claimed that the CAPM model is easy to use and it is widely accepted. The CAPM model provides a strong basis for computation of cost of equity. The proponents of the model claim that the CAPM model is more relevant and better than any other method for computation of cost of equity (Sharifzadeh, 2010).

Arguments for and against the Theory and Critique of its Underlying Assumptions

However, there are arguments against the CAPM model also. The opponents claim that the CAPM model is based on the unrealistic assumptions. The CAPM model takes into account only the systematic risk assuming that the investors already hold diversified portfolio and hence there does not exist unsystematic risk (Sharifzadeh, 2010). This assumption of the CAPM model does not seem to be valid because it is not possible that in all cases the investor would be holding perfectly diversified portfolios. Further, the CAPM model measures the systematic risk only based on one factor that is relative volatility of the stock to the market index. However, in order to assess the systematic risk in a detailed manner, it is essential to relate it to different factors such as gross domestic product, inflation, and beta. Thus, it is argued that the single factor model as adopted by the CAPM model for risk assessment is not adequate for the purpose; a multifactor model should be adopted (Sharifzadeh, 2010).                         

The assessment of systematic risk in the CAPM model has been based on the single factor. It has been argued by the economists that measurement of the systematic risk based on the single factor is not appropriate. Therefore, an alternative to the CAPM model has been found out which is known as arbitrage pricing theory (Elton et al., 2009). The arbitrage pricing theory provides for computation of systematic risk based on the multi factor model. It is also called the multi beta model. In this model, the assessment of systematic risk is linked to multiple factors such as GDP, inflation, interest rates, and relative volatility to the market index (Elton et al., 2009).     

Conclusion and Recommendation

The essay presented here covers a critical analysis of the capital asset pricing model. From the discussion in this essay, it has been articulated that the CAPM model provides a good basis for computation of desired rate of return. However, it has also been observed that CAPM model makes many assumptions which might be unrealistic in practical situations. Further, it could be articulated that the CAPM model does not assess the systematic risk appropriately and an alternative for this purpose has been found out as the arbitrage pricing theory (APT). The APT provides a multi factor model for computation of the systematic risk.        

Initial outflows
Cost of new machine	320000
Realizable value of old machine	-90000
Net outflows	230000

 

Loan amount	$      320,000.00
Interest	8%
Period	5
EMI	$80,146.07

 

Loan schedule: Assumed that the loan is repayable in 5 equal installments
Year	Opening balance	Installment	Interest	Closing balance
1	320000	$80,146.07	25600	$265,453.93
2	$265,453.93	$80,146.07	21236.315	$206,544.18
3	$206,544.18	$80,146.07	16523.535	$142,921.65
4	$142,921.65	$80,146.07	11433.732	$74,209.32
5	$74,209.32	$80,146.07	5936.7456	$0.00

 

Depreciation per year
Cost of machine	$      320,000.00
Depreciated to prime cost	$        50,000.00
Period	5
Depreciation	$        54,000.00

 

Yearly cash outflows and inflows
	Cash inflows				Cash outflows			Net cash flows
Year	Saving in cooling costs	Tax savings on interest	Tax savings on depreciation	Working capital	Loss of existing sales	Working capital	Interest
1	80,000.00	7,680.00	16,200.00		10,000.00	27,000.00	25,600.00	41,280.00
2	80,000.00	6,370.89	16,200.00		10,000.00		21,236.31	71,334.58
3	80,000.00	4,957.06	16,200.00		10,000.00		16,523.53	74,633.53
4	80,000.00	3,430.12	16,200.00		10,000.00		11,433.73	78,196.39
5	80,000.00	1,781.02	16,200.00	27,000.00	10,000.00		5,936.75	109,044.28

 

 

Calculation of present value
Year	Cash flows	PVF@10%	Present value
0	-230000	1.000	(230,000.00)
1	41,280.00	0.909	37,527.27
2	71,334.58	0.826	58,954.20
3	74,633.53	0.751	56,073.27
4	78,196.39	0.683	53,409.18
5	109,044.28	0.621	67,707.92
Net present value			43,671.85

Harry should purchase the new machine because it will provide additional benefits of $43,671.85. The net present value of replacing old machine with the new one is 43,671.85 which depicts that the alternative is advantageous

References

Cvitanic, J. and Zapatero, F. 2004. Introduction to the Economics and Mathematics of Financial Markets. MIT Press.

Elton, E.J., Gruber, M.J., Brown, S.J., and Goetzmann, W.N. 2009. Modern Portfolio Theory and Investment Analysis. John Wiley & Sons.

Fischer, B.R. and Wermers, R. 2012. Performance Evaluation and Attribution of Security Portfolios. Academic Press.Focardi, S.M. and  Fabozzi, F.J. 2004. The Mathematics of Financial Modeling and Investment Management. John Wiley & Sons.Lee, M.C. and Su, L. 2014. Capital Market Line Based on Efficient Frontier of Portfolio with Borrowing and Lending Rate. Universal Journal of Accounting and Finance, 2(4), pp. 69-76.Sharifzadeh, M. 2010. An Empirical and Theoretical Analysis of Capital Asset Pricing Model. Universal-Publishers.