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... E (Ri) in excess returns form; E (Ri) - RF = &# 955; 1 bi 1 ++ &# 955; kit, this is the APT equation. E (Ri) - RF is excess return on risk free asset. &# 955; k = risk premium; price of risk in equilibrium for the kth factor. &# 955; k = &# 948; k-Rf, &# 948; k; is expected returns on a portfolio with the unit sensitivity to the kth factor and zero sensitivity to all other factors. And so risk premium, &# 955; k, is equal to the difference between the expectation of a portfolio that has unit response to the kth factor and zero response to the other factors and Rf. We can now rewrite APT equation in the following form; E (Ri) - RF = [ &# 948; 1 -Rf ] bi 1 +[&# 948; 2 -Rf] bi 2 +... +[ &# 948; k-Rf] bik If this equation is interpreted as a linear equation, then the coefficients bik, are defined in the same way as beta in the CAPM model; bik = Cov (Ri, &# 948; k) /Var (&# 948; k). Beta here will give relation of i to various factors.
The APT seems to be stronger than the CAPM; APT makes no assumptions about the distribution of asset returns. CAPM assumes that the probability distributions for portfolio returns are normally distributed. The APT does not make any strong assumptions about utility function (only risk averse). According to the CAPM investors are all risk averse individuals who maximise their expected utility of their end of period wealth.
The APT allows the equilibrium returns of assets to be dependent on many factors not just one. The APT produces a statement about the relative pricing of any subset of assets; we do not need to measure the entire universe of assets in order to test the theory. There is no special role for the market portfolio in the APT, whereas the CAPM requires that the market portfolio be efficient. Before we go into detailed discussion of the two models, we should quickly mention some empirical tests about APT itself and its comparison with CAPM.
Factor analysis is used in first empirical tests of APT. One problem with any approach to testing the APT is that the theory itself is completely silent with respect to the identity of the factor structure that is priced. Chen, Roll, Ross (1983) found that a collection of four macroeconomic variables that explained security returns fairly well. But Dhrymes, Friend, Gultekin (1984) point out that the more stocks you look at, the more factors you need to take into account. Chen (1983) compared CAPM and APT.
First APT model was fitted to the data as in the following equation; R&# 61486; i = &# 955; ^ 0 +&# 955; ^ 1 bi 1 ++ &# 955; ^kit+&# 949; &# 61486; i (APT) The CAPM was fitted to the same data; R&# 61486; i = &# 955; ^ 0 + &# 955; ^ 1 &# 946; i+&# 951; &# 61486; i (CAPM) Next the CAPM residuals &# 951; i were regressed on the arbitrage factor loadings, &# 955; ^k, and APT residuals, &# 949; i were regressed on the CAPM coefficients. The results showed that the APT could explain a statistically significant portion of the CAPM residual variance, but the CAPM could not explain the APT residuals. This shows that the APT is more reasonable model for explaining the cross sectional variation in asset returns. Fama, French (1992) found that Beta did a relatively poor job at explaining differences in the actual returns of portfolios of US stocks.
Instead Fama and French noted that there were other variables beside beta with respect to market that explained returns. These findings were interpreted as strong indications that CAPM does not work. Haugen (1999) tests with predictive power of APT with different factors. According to his findings APT appear to have predictive power.
However, its power falls short of adhoc expected return factor models. We so far tried to give some theoretical understanding of these two models. Lets go further to examine the two models; APT has a number of benefits; it is not as restrictive as the CAPM in its requirements about individual portfolio. It allows multiple sources of risk, indeed these provide an explanation of what moves stock returns. The APT demands that investors perceive the risk sources and that they can reasonably estimate factor sensitivities. In fact even professionals and academics can not agree on the identity of the risk factors, and the more betas you have to estimate the more noise you must live with.
The CAPM is theoretically pleasing, however its biggest criticism is that it is not testable. The APT came out as a testable alternative, but its testability is an open question as well. Some would argue that models should not be judged on the basis of the accuracy of their assumptions, but rather on the basis of their predictive power. The CAPM makes a single prediction, the efficiency of the market portfolio, which has been argued to be untestable. The power of the APT in predicting future stock returns falls short of adhoc expected return factor models. The problem may well be that the arbitrage process presumed in the APT is difficult; If not impossible to implement on a practical basis.
The APT calls for arbitraging away nonlinearity in the relationship between expected returns and the factor betas. We arbitrage by creating restless stock portfolios with differential expected returns. However, you will find that it is impossible to create restless portfolios comprised exclusively of risky securities such as common stocks. In one important respect, both models exhibit a similar vulnerability. In the case of both models, we are looking for a benchmark for purposes of comparing the export performance of portfolio managers, and the exact returns on real and financial investments.
In the case of the CAPM, we can never determine the extent to which deviations from the security market line benchmark are due to something real or are due to obvious inadequacies in our proxies for the market portfolio. In the case of the APT, since theory gives us no direction as to the choice of factors, we can not determine whether deviations from an APT benchmark are due to something real or merely due to inadequacies in our choice of factors. As we know that the APT really makes no predictions about what the factors are. Given the freedom to select factors without restriction, it can be argued that you can literally make the performance of a portfolio anything you want it to be. In the case of the CAPM, you can never know whether portfolio performance is due to management skill or to the fact that you have an inaccurate index of the true market portfolio. Another problem with CAPM that hedging motive does not enter in it, and therefore people hold the same portfolio of risky assets.
In reality people might have different tastes and, it may make sense for them to hold different portfolios. The CAPM says that investors will price securities according to the contribution each makes to the risk of their overall portfolios. This is intuitively appealing. CAPM is an accepted model in the securities industry. It is used by firms to make capital budgeting and other decisions.
It is used by some regulatory authorities to regulate utility rates (e. g. electric utilities). It is used by rating agencies to measure the performance of investment managers. The APT can also be applied to cost of capital and capital budgeting problems, but APT seems to be practically difficult for capital budgeting. There is a practical problem of the estimating the state-contingent prices of the comparison stock and the risk free asset.
If we summarize what we said so far; APT and CAPM generally address the same basic issues: how should we measure the risk of a risky asset? how should we compute required return? CAPM takes an oversimplified view of economy-wide news; consider a stock, according to the CAPM, every time economy-wide news makes the market go up by 1 %, we expect this stock to go up by 1 % times beta of this stock. What type of economy-wide news made the market go up does not matter. The stock reacts the same way to all types of economy-wide news. But According to the APT, what type of economy-wide news it is should matter.
For example; BP would be more sensitive to an oil factor than Coca-Cola. CAPM assumes that a given stock is equally sensitive to different type of economy-wide news. APT assumes that a given stock has a different sensitivity to different types of economy-wide news. In the CAPM all economy-wide news is lumped together into one single equation, and stocks beta is the sensitivity to all types of economy-wide news. The APT assumes that random returns are given by the kth factor model instead of the market model. The single term representing economy-wide news in CAPM has been broken in to k separate terms.
So there are k different types of economy wide-news. bi 1 is the stock is sensitivity to type 1 news, bi 2 is stock is sensitivity to type 2 news. Each of these Betas are different. CAPM lumps all systematic risk together into one term; so there is a single risk premium. APT says there are k types of systematic risk, so there are k risk premiums, one for each type of systematic risk. &# 955; i 1 bi 1 is the risk premium for type 1 risk. &# 955; i 2 bi 2 is the risk premium for type 2 risk.
Just like CAPM, bi 1 is the amount of type 1 risk this stock has, and &# 955; 1 is the market price for type 1 risk. The risk of a stock is measured jointly by its k betas, and then the required return is determined by the equation. It is clear from all of our discussion that conceptually APT is an improved version of the CAPM, but why do we still use CAPM as well? Because, in practise, APT does not work better than CAPM. That happens because of estimation error. APT does not tell us how many factors we should use and it does not tell us what the factors are.
The CAPM is more simple-minded model but we can estimate &# 946; i and RM a lot more precisely, so the required return is reasonably accurate. The APT may be more advanced conceptually, but this is cancelled out by the greater estimation error. In practise, the required return we come up with is not more accurate than the CAPM. The CAPM is simpler to understand, easier to use. The APT is more difficult to understand much harder to use. APT is rarely used for computing required return, but it has useful applications in investment management.
After seeing both models, we can say that if we choose one against the other, then in each one unfortunately you win some and you lose some. Neither can the two models outperform each other completely. Rather than trying to persuade each other, one is better than the other. We should thoroughly understand their weakness as well as their strengths, so that we will know when and how, which model we can rely on in making financial decision. References: Bower, D.
H; Bower R. S; Logue, D. E, 1984. Arbitrage Pricing Theory and Utility Stock Returns. The Journal of Finance. Bradley, R. /Myers, S. 1991.
Principle of Corporate Finance, McGraw-Hill. Chen, N. F. 1983, Some Empirical Tests of theory of Arbitrage Pricing, Journal of Finance. Chen N, Roll R, and Ross SA, (1986). Economic Forces and the Stock Market, Journal of Business. Copeland/Weston, 1988, Financial Theory and Corporate Policy, Addison Wesley/Longman.
Costas Lapavitsas, 2003, Lecture Notes on Capital Markets, Derivatives and Corporate Finance, SOAS, University of London. Dhrymes, P. , Friend, I. , and Gultekin, N. 1984. A Critical Reexamination of the Empirical Evidence on the Arbitrage Pricing Theory, . Journal of Finance. Elton/Gruber, 1995, Modern Portfolio Theory and Investment Analysis, John Wiley&Sons, Inc. Fama, E.
F, and K. R. French, 1992, Cross-Section of Expected Stock Returns, Journal of Finance. Haugen, R, 2001, Modern Investment Theory, Prentice Hall. Jagannath an, Ravi. , Meier, Iwan. Do we need CAPM for capital budgeting? , Financial Management.
Koppenhaver, G. D Lecture Notes on Capital Market Theory, Iowa State University. Seth, S. Lecture notes on Financial Markets College of Business, University of Illinois.
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