The New Arsenal of Risk Management - Research Paper Example

Critically compare the Arbitrage Pricing Theory (APT) with the Capital Asset Pricing Model (CAPM) for use by a fund manager in the UK. Table of Contents 1.0Introduction 1.1 Problem Statement and Objectives of Study 1.2 Structure of work 2.0Review of Related Literature 2.1 The Capital Assets Pricing Model 2.2 The Arbitrage Pricing Theory 2.3 Uses of the Two Models 3.0 Findings and Conclusion 3.1 Uses of CAPM and AP to the UK fund Manager 3.2 Conclusion and recommendation References 1.0Introduction This paper attempts to review and compare briefly the current position of capital asset pricing theory and testing with the Arbitrage pricing theory, and to consider the implications for the United Kingdom (UK) fund managers. Inevitably in a paper of this length, it is not possible to include all the material that is relevant in such a large and important area, but most of the important matters will hopefully be covered. The capital asset pricing model (CAPM) is a model that establishes the equilibrium relationship between the risk and return on a risky asset. (Bodie et al., 2005). The model has often been used by corporations during capital budgeting decisions to establish the appropriate discount rate for evaluating investments. In this paper, an explanation of how the CAPM can be used to determine the rate of return or discount rate to be used in evaluating an investment will be given. In addition considering that the theory of the CAPM is based on a number of underlying assumptions. To measure the performance contribution from actively managing an investment portfolio, an equilibrium model can be used, that takes into account the systematic risk and its reward by the market. Commonly used equilibrium models are the one-factor capital asset pricing model (CAPM) or the multifactor arbitrage pricing theory (APT). Both the CAPM and the APT assume a linear relation between systematic risks and expected return. These theories give the risk-return menu, which each fund manager can achieve through a passive portfolio strategy. 1.1Problem Statement and Purpose of Study The CAPM extends portfolio theory, in which prices are exogenously specified, to a market equilibrium setting by making assumptions about the market in which securities are traded and about market participants. The APT arises out of limitations of CAPM laying less restriction on Investors’ preference and permits existence of one or multiple factors for determining asset prices. Against this background, this paper aims at contributing to the ongoing debate of the CAPM and the APT as investment mechanism for investment fund managers. In particular, the paper intends to compare the CAPM and the APT in relation to how the two can assist a UK based fund managers in their activities. Thus the main research question in this paper is how can the CAPM be compared to the APT in relation to the UK fund manger? This will be possible through a critical review of relevant literature drawn from business source premier and science direct. This paper therefore critically compares the arbitrage pricing theory (APT) with the capital asset pricing model (CAPM), for use by a fund manager in the U.K. 1.2 Structure of work The introductory part of this paper sets the principal arguments underlying this study. The most important themes needed to be discussed have also been introduced. The remaining part of the paper will be structured as follows. Section two of the paper discusses the theoretical framework while reviewing relevant literature in line with the research question. Section three now presents the uses and importance of CAPM and APT to a UK fund manager. The last part of the paper presents a conclusion and recommendation. 2.0Review of Related Literature In Risk Management and investment theory, fund manager skills relate to the ability to actively outperform a given benchmark strategy. Selectivity and market timing are important factors related to manager skills. To measure the performance contribution from actively managing an investment portfolio, an equilibrium model can be used, that takes into account the systematic risk and its reward by the market. Commonly used equilibrium models are the one-factor capital asset pricing model (CAPM) or the multifactor arbitrage pricing theory (APT). Both the CAPM and the APT assume a linear relation between systematic risks and expected return. These theories give the risk-return menu, which each fund manager can achieve through a passive portfolio strategy. Hence, the CAPM and the APT provide an adequate benchmark for active portfolio management. With the ex-post version of the CAPM or APT, an excess performance achieved by the funds manager, can be measured (Gregoriou, 2008). 2.1 The Capital Assets Pricing Model In the 1960s, the capital asset pricing model (CAPM) was developed by William Sharpe and his team consisting of Lintner and Mossin. The key elements of the CAPM is that markets compensate investors for accepting systematic or market risk, but do not discount for idiosyncratic risk, which is specific to an individual asset and can be eliminated through diversification. The relevance of this theory is that it affects decisions about hedging, and about whether or not to reduce specific risks. The company cost of capital is defined as the expected return on a portfolio of all the company’s securities. The cost of capital is the discount rate that is used in discounting he cash flows on projects that have similar risk to that of the firm as a whole. Companies often undertake a series of projects with different risks. Consequently, the cost of capital for the company can only be used to discount cash flows if the projects in question have similar risks to that of the firm as a whole. (Myers and Brealey, 2002). Estimating the cost of capital is often a daunting task to most companies. Companies generally start estimating the cost of capital by estimating the return that investors require from the company’s common stock. This is often done using the capital asset pricing model. (Myers and Brealey, 2002). Understanding how to price risky assets or otherwise determining the cost of capital for risky investments has been a prominent problem in finance. (Furman and Zitikis, 2008). This has led to the development of a number of capital asset pricing models. (CAPMs) (Furman and Zitikis, 2008). The most frequently used of these CAPMs is that of Sharpe (1964), Lintner (1965) and Black (1972). The CAPM relates the expected return on an asset to the expected return on the market portfolio of all assets in the market. The CAPM states that “the expected excess return of any asset is linear in its covariance with the expected return on the market portfolio”. (Hogson et al., 2001: p. 2). If we assume that Ri and Rm are random variables that represent the return on security i and the return on the market portfolio m, respectively, then under specific assumptions such as 1. the investor’s utility functions are either quadratic or logarithmic, or 2. the pair (Ri, Rm) posseses the bivariate normal or elliptical distributions, then the CAPM implies that the expected return on the risky asset is the risk-free rate of return rf plus a risk premium that is proportional to the difference between the expected return on the market portfolio and rf., that is, we have the equation (Hodgson et al., 2001; Furman and Zitikis, 2008; Ross et al., 2008): : (1) Where (2) The equilibrium return on risky assets can be determined using the capital asset pricing model. If we consider capital markets to be continuously in equilibrium, with price changes over time reflecting the instantaneous adjustment to new equilibrium, and focus on the market portfolio, that is the portfolio of all existing assets traded in the markets, then in equilibrium, all investors should individually hold different portfolios of risky assets such that a combination of all the individual portfolios should sum up to the market portfolio. (Bodie et al., 2005; Ross et al., 2008). In other words if we assume that all investors have the same estimate of systematic and unsystematic risk, then each investor will find it optimal to hold the market portfolio. Assume also that all investors are risk adverse but with slight variations. All investors will investors will consider the market portfolio to be the optimal portfolio. All investors will therefore hold a combination of risk-free assets Rf and the market portfolio of risky assets. The proportion that each investor chooses to invest in each of the portfolios will depend on the risk aversion of the individual investor. Those with relatively low degrees of risk aversion will borrow (that is, hold a negative quantity of the risk-free asset) and invest everything in the risky portfolio. Such an investor will invest a negative proportion in the risk-free asset and a greater than one proportion in the risky asset. Such an investor will invest in security A as shown in the security market line (SML) in figure 1 below. Figure 1. The Security Market Line Source: (Ross et al., 2008) As can be seen, the less risk adverse investor bears more systematic, which is measured by the standard deviation (WM Stdev (RM)) of the portfolio. As we can see, this security has a higher return (RA). The variance of this portfolio is calculated by squaring the standard deviation, that is, WM2Var(RM) which is higher than the variance on the market portfolio. (Var2(RM)) since WM2 is greater than one. The expected return on portfolio A is greater than the expected return on portfolio M because the systematic risk component in portfolio A is higher than that for portfolio M. As earlier mentioned, this risk component is measured by beta and is calculated as shown in equation (2) above. Beta in equation 2 above measures the systematic risk of asset i relative to the overall risk in the market, given by the variance of the market portfolio. An asset that approximates the market portfolio is therefore going to have a beta of 1 since the covariance of an asset with itself is equal to its variance. (Ross et al., 2008). The equilibrium relationship between a security and the expected return can be stated as shown in equation 1. Equation (1) is otherwise referred to as the security market line. (Ross et al., 2008). The security market line indicates that the higher the beta, the higher will be the return that the asset must pay, thus reflecting investor’s reward for systematic risk. (Ross et al., 2008). A beta of 1 results in an expected return equal to the return on the market portfolio. When beta is smaller than 1, the expected return is lower than the return on the market portfolio and if beta is greater than 1, the expected return is greater than the return on the market portfolio. (Ross et al., 2008). From figure 1 above, we can confirm that the beta of security A is greater than 1 since the proportion invested in the security is greater than one. Consequently, the expected return on the security is higher than the expected return on the market portfolio. In effect, we can see that the SML is actually the CAPM relationship. For example, the return on security A can be stated in terms of the risk-free rate and the market return as follows: (3). Where (4) The CAPM can be used to estimate the cost of capital for risky investments. The decision rule for evaluating risky investments is often based on an estimation of the NPV of the project. Since there are always uncertainties, it is difficult to be a hundred percent sure that the estimated cash flows that are being discounted to present value to arrive at the NPV will actually be realized. The CAPM enables companies to compute the NPV using an appropriate measure of the cost of capital of the project. (Ross et al., 2008). If the firm is an all-equity financed firm, the cost of equity capital can be estimated from the security market line. If the firm is financed by both debt and equity, the discount rate is the overall cost of capital often referred to as the weighted average cost of capital. (Ross et al., 2008). 2.2 The Arbitrage Pricing Theory On the other hand, the arbitrage pricing theory (APT) developed by Stephen Ross in 1976 was built on the foundation that the price of a security is driven by a number of factors, which are either macroeconomic or market indices. The relevance of this model is that it permits segmentation of CAPM systematic risk into factors or components. “If prices diverge from expected returns, investors can use arbitrage to bring them back into line” (Buehler et al, 2008: 95). Company shares have a value that reflects the views of investors about the likely future dividend payments and capital growth of the company; this value is quantified by the price at which they are bought and sold on stock exchanges. In the collection or markets assets of various kinds are bought and sold. As markets have become more sophisticated, more complex contracts such as “financial derivatives, derivative securities, derivative products, or contingent claims give investors an extensive range of opportunities to tailor their dealings to their investment needs” (Wilmott et al, 1995: 4). The APT unlike the CAPM imposes more structure upon returns by postulating that they must satisfy a linear factor model. This model and structure imposed by APT enable a fund manager make a risk return tradeoff. The CAPM characterizes prices resulting from a competitive equilibrium, whereas the classical APT characterizes prices resulting from only the absence of arbitrage opportunities. However, this distinction separates the original 1976 APT model of Ross from its more recent equilibrium versions (Jarrow, 1988). The APT is not inconsistent with the CAPM. Here the model assumes that, the security returns are generated by single or multiple factors. In the APT framework, the relationship between security returns and factors (i.e., factor betas and factor prices) is linear and there are no restrictions on short selling. With the CAPM, only the beta factor is relevant in determining the fund manager risk return trade-off. Here, according to the APT model, factor price depends upon the risk-aversion of investors and how important the factor is as a source of stock variability. 3.0 Findings and Conclusion 3.1 Uses of CAPM and AP to the UK fund Manager Another assumption of the CAPM is that investors possess a quadratic utility function as well as that asset returns are normally distributed. However, Hodgson et al. (2001) notes that the CAPM holds under normality for a much broader class of utility functions since quadratic utility functions have the unappealing property that they are decreasing at high consumption levels, thereby making the CAPM to be comforting to its proponents. Hodgson et al. (2001) further states that the assumption of normality is not appropriate for asset returns. Therefore it may be difficult for the CAPM to hold unless the assumption of normality in asset returns is true. If it is true that the asset returns are non-normal, then this may have serious implications for the econometric implications of the CAPM. (Hodgson et al., 2001). Hodgson et al. (2001) also notes that the standard estimator of the CAPM is ordinary least squares (OLS) regression, which is only fully efficient under nomarlity but is likely to fail should normality fail. For example, Hodgson et al. (2001) cites Zhou (1993) who considers implementation of OLS under possible non-normality deriving a procedure to correct the size problems that may occur in CAPM tests if returns are elliptical and rather than normally distributed. Based on the assumption that returns have an elliptical symmetry rather than normally distributed as assumed in earlier tests of the CAPM, Hodgson et al. (2001) developed a test of the CAPM. The elliptical symmetry assumption allowed them to avoid the curse of dimensionality problem that typically arises in multivariate semi-parametric estimation procedures. The results retain betas that are lower than the OLS estimates and parameter estimates that are less consistent with the CAPM restrictions than corresponding OLS estimates. The CAPM derived in section two implies that fund managers will only be rewarded for the systematic risk that they incur. As has been demonstrated the, extension APT of the basic CAPM framework retain this property. Underlying the systematic risk/ return relationship is the plausible implication that fund managers can diversify away non-systematic risk by holding portfolios of securities; since this latter dimension of risk is avoidable, there is no reward available from the market, at equilibrium. 3.2 Conclusion and recommendation The purpose of this paper was to critically compare the CAPM to the APT in relation to their uses and support to a UK fund manager. From existing research and the work of leading professionals in the field the paper make three important findings. The CAPM and the APT provided a framework for evaluating the performance of investment managers and funds. In this direction, performance of the UK fund managers may be evaluated in terms of two dimensions. That is risk and return. The CAPM and the APT provide the means of evaluating both the fund and fund manager performance in terms of returns relative to the degree of risk borne. In finance for example, it is assume that, return increases with risk. This is the assumption behind investors when they choose to invest in risky asset as opposed to risk free assets. According to Roll (1977), the main conclusion to be drawn from a study such as this is somewhat ambiguous. Here, using different proxies gives rise to different market rankings. The CAPM and APT provide positive implications regarding the structure of equilibrium returns for risky assets. The underlying theory still retains implications of importance to portfolio managers. It follows that the beta (systematic risk) factor is a variable of considerable importance to portfolio management, since UK fund managers are rewarded for this dimension of risk only. From the foregoing, we see that the normality assumption as well as the quadratic utility function assumption leads the beta coefficient of the security market line to be overstated. This in turn overstates the risk of the investment or security and therefore the cost of equity capital. The implication of this is that UK fund managers tend to reject projects that would have otherwise been accepted if these problems were not inherent in the asset pricing model which is often used to estimate the discount rate used in evaluating these investments. Consequently, it is essential for the CAPM assumptions to be refined so that a more robust CAPM can be developed that provides accurate measures of risk and thus the discount rate. The APT model, overcome these assumptions by providing fund managers with a multivariate model. References Bodie Z., Kane A., Marcus A. J. (2005). Investments. Sixth Edition. McGraw-Hill. Buehler, K., Freeman, A. & Hulme, R. (2008). The new arsenal of risk management. Harvard Business Review, September 2008: 93-101. Cochrane, J.H. (2001). Asset pricing. New Jersey: Princeton University Press. Coggin, T.D. & Fabozzi, F.J. (1998). Applied equity valuation. The United States of America: John Wiley & Sons, Inc. Donovan, E. (2007). Capital asset pricing model vs Arbitrage pricing theory. Touro University International. Retrieved on 27th April, 2009 from: http://www.eddiedonovan.com/publications/FIN501MOD3CASE.pdf Gregoriou, G.N. (2008). Encyclopedia of alternative investments. London: CRC Press. Jarrow, R.A. (Summer, 1988). Preferences, continuity and the Arbitrage Pricing Theory. The Review of Financial Studies, 1 (2): 159-172. Jarrow, R. & Rudd, A. (1983). A comparison of the APT and CAPM. Journal of Banking and Finance, 7: 295-303. Koller, T., Goedhart, M. & Wessels, D. (2005). Valuation: measuring and managing the value of companies. Edition 4. New Jersey: John Wiley & Sons, Inc. Pratt, S.P. & Grabowski, R.J. (2008). Cost of capital: applications and examples. Edition 3. New Jersey: John Wiley & Sons, Inc. Wilmott, P., Howison, S. & Dewynne, J. (1995). The mathematics of financial derivatives: a student introduction. Cambridge: Cambridge University Press. Furman, Edward and Zitikis, Ricardas (2008). "General Stein-Type Decompositions of Covariances: Revisiting the Capital Asset Pricing Model". Available at SSRN: http://ssrn.com/abstract=1103333 Hodgson, Douglas J., Linton, Oliver B. and Vorkink, Keith (2001). "Testing the Capital Asset Pricing Model Efficiently Under Elliptical Symmetry: A Semiparametric Approach". Available at SSRN: http://ssrn.com/abstract=283364 or DOI: 10.2139/ssrn.283364 Myers S. C. Brealey R. (2002). Principles of Corporate Finance. Seventh Edition. McGraw-Hill Irwin. Ross, Westerfield, Jaffe & Jordan. (2008). Modern Financial Management", (authors), McGraw-Hill International Edition, 8th Edition,   ISBN: 978-0-07-128652-7 Roll, R., "A critique of the asset pricing theory's tests: Part I: On past and potential testability of the theory", Journal of Financial Economics Vol. 4, 1977. Read More