RISK Management - CAPM and APT

Capital Asset Pricing Model and Arbitrage Pricing Theory

The contemporaneous business community is extremely competitive, meaning as such that the organizational leaders strive harder than ever to overcome the competitive forces. Virtually, they have to hire and retain the best skilled staff members; they have to develop and offer the best quality products and services and they must be able to raise the interest of a vast and large customer base. All these constitute competitive advantages.

Yet, another element which has to be granted the adequate attention is that of the management of assets. The specialized literature offers a multitude of definitions of the concept of asset, yet the underlying idea is basically the same. Stickey, Weil and Schipper (2009) for instance argue that an asset is "a probable future economic benefit that a firm controls because of a past event or transaction" (p.108). The Longman Dictionary of Contemporary English (2009) provides the reader with a more generic definition of an asset, which is described as a thing that is owned by the organization and which can be sold in order to allow the company to pay its debts. Investopedia (2009) combines the two definitions to offer one that is both formal, as well as easy to understand. In their view, an asset is a "resource with economic value that an individual, corporation or country owns or controls with the expectation that it will provide future benefit."

The assets are the core of any business operation; they represent the ability of the company to pay its debts to suppliers, to fund its marketing strategies or to secure the payment of the personnel salaries, but also to generate additional profits and as such support the production process. Given the crucial role of assets, it becomes obvious that their management is a pivotal concern of the modern day manager. Two specific models which address issues related to organizational assets are the Capital Asset Pricing Model (CAPM) and the Arbitrage Pricing Theory (APT).

2. Brief History of the Models

The Capital Asset Pricing Model was first introduced in the 1950s, by Harry Morcowitz, who was at that time working on his PhD. What the model virtually did was to allow prospective investors to measure the maximum efficiency of a portfolio, given existent levels of risk. This would be achieved as the calculi would help the investor identify the most adequate weight of the given stocks within the overall portfolio. The computations were based on the return expected to be generated by the stock, the risk it incurred and the correlation between the two. The result was a portfolio that revealed lower levels of risk and maximized returns.

The theorem was welcomed by both academicians as well as practitioners. The academicians began to work on improving the CAPM formula and theory. Throughout the same decade, Modigliani and Miller believed it would be efficient to include the notions of capital structure irrelevance and the dividend within the theory. They also assumed that markets in which portfolios were traded were efficient; at that time however, the academic field had yet to develop the theory of the efficient market. Their ultimate belief was that investors were indifferent to the decision of organizations to distribute profits in the form of dividends or to retain them within the entity.

In the 1960s, two more movements were made in terms of CAPM. The first belonged to Sharpe, Litner and Treynor and stated that beta was the single force which generated differences between stocks. The second belongs to Eugene Fama; it in fact represents the summation of all the ideas issued, and it represents the theory of the efficient market (Montier, 2007).

The history of asset pricing is generally recognized to have commenced over three centuries before, but modern asset pricing models were only issued after 1950. The basis of modern asset pricing was set by Arrow in 1953, who promoted financial securities as "a series of commodities in various future states with different values" (Cheng and Tong, 2008, p.1). By 1958, Tobin had introduced the ideas of a riskless asset, which led to the emergence of the efficient portfolio as a combination of risky and riskless stocks. The APT was forwarded in 1976 by Ross and...

The Models' Theories and Underlying Ideas

The theory of the Capital Asset Pricing Model is that there exists a close relationship between the risk of an asset and its expected return, and that this relationship should be used to determine the price of risky stocks. The formula of the CAPM is:

(Investopedia)

The basic idea behind the CAPM is that of a necessity for the investors to be rewarded in terms of the time value of money as well as the degree of risk to which they expose themselves. The time value of money is given by the risk free rate and the reward for taking on the risk is computed based on the measure of risk (beta) and the rate of the investment, as difference between the rate of return on the market and the market premium (Investopedia). The relationship between CAPM and beta sees that the investor's knowledge of the beta and its value will help him calculate the price of the security.

The application of the CAPM is best understood by taking a real life example, such as the situation of an investor looking to buy stocks from Associated British Food. Considering a market return of 6%, a risk free rate of 4.7% and a beta of 0.42 (Digital Look, 2009), the return of the Associated British Food stock is computed as follows:

4.7 + 0.42 x (6 -- 4.7) = 4.7 + 0.42 x 1.3 = 5.246

This return is inferior to the return expected on the market, meaning as such that the prospective investor should not purchase the Associated British Food shares.

There are several assumptions which sit at the basis of the CAPM. A first one revolves around the idea that the markets onto which the securities are being traded are perfect. This virtually implies that the actions of investors do not have any impact on the prices of commodities; that the transactions are not subjected to any taxes or any additional costs and that the lending and borrowing operations are unlimited and measured at risk free rates. Secondly, it is presumed that the investors manifest homogenous expectations and that the investors only care about mean and variance (Lundquist College of Business). Other assumptions refer to the beliefs that investors will only accept higher return for higher risk, but never lower return for higher risk (Spiritus Temporis, 2005).

The Arbitrage Pricing Theory states that an investor has the ability to predict the final returns of his portfolio, by identifying the individual return of the stocks, based on a linear function of several macro-economic variables. The formula for the APT is revealed below:

r = rf + ?1f1 + ?2f2 + ?3f3 + ?, with r being the expected return of the stock, f being the separate factor, rf being the risk free rate and ? being the factor of measurement of the relationship between the factor and the price of the assessed security (Money Terms).

The basic idea is that the factors of risk can be used to estimate the ultimate return of the portfolio (Investopedia). Similar to the CAPM, in order for the APT to be applicable, it is necessary for several assumptions to come true. In this line of thoughts, the first assumption at the basis of the APT is that the investors have homogenous expectations in terms of market behavior and expected returns. Secondly, the APT states that the returns on stocks are generated by a factor model. Based on this assumption, it continues to state that the return of an asset is given by the linear function of its sensitivities (U-M Personal World Wide Web Server). The following assumption is given by the existence of a well diversified portfolio in terms of mean and variance. This leads to the construction of two additional assumptions: the first sees that "all the factors can be represented as limits of traded assets" and the second sees that "the variances of incomes on any sequence of portfolios that are well diversified in the limit and that are uncorrelated with the factors converge to zero" (Huberman and Wang, 2005).

5. Benefits and Limitations of the Models

Over the years, the Capital Asset Pricing Model has been accused of several weaknesses. For instance, it is argued that the model does not take into consideration the modern day research relative to management and investment, but that it is constructed on unrealistic assumptions (Rosenberg, 1981). This virtually translates into a reduced applicability of the model in today's context. Then, the inclusion of beta makes the computation difficult to be completed, for the simple reason that not all companies calculate…

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Cheng, B., Tong, H., 2008, Asset Pricing: A Structural Theory and Its Applications, World Scientific, ISBN 9812704558

Fabozzi, F.J., Markowitz, H., 2002, The Theory and Practice of Investment Management, John Wiley and Sons, ISBN 0471228990

Fabozzi, F.J., Focardi, S., Kolm, P.N., 2006, Financial Modelling of the Equity Market: From CAPM to Cointegration, John Wiley and Sons, ISBN 0471699004

This in turn gives the financial professional better idea of the stock's risk behavior. The equation used in this security market line relationship is as follows: Mathis, CAPM, par. 3) The measure of systematic risk is considered Beta or bi while E[Ri] is equal to the expected return on asset I and Rf is the risk-free rate. E[Rm] is the expected return on the market portfolio and E[Rm] - Rf is the

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