Comparing the Arbitrage Pricing Theory and the Capital Asset Pricing Model:There are inherent risks in holding any asset, and the capital asset pricing model (CAPM) and the arbitrage pricing model (APM) are both ways of calculating the cost of an asset and the rate of return which can be expected based on the risk level inherent in the asset.

The Capital Asset Pricing Model (CAPM) is a special case of the Arbitrage Pricing Model (APT) in that CAPM uses a single factor (beta as sensitivity to market price changes) whereas the APT has multiple factors which may not include the CAPM beta.

CAPM is considered 'demand side' in that it is based on the market's aggregation of individual investors' utility maximization curves. APT is 'supply side' in that it usually includes macroeconomic factors.

Capital Asset Pricing Model

The CAPM formula is:

ra = rrf + Ba (rm – rrt)

where ra is the rate of return for a risk-free security

rm is the broad market expectation on the rate of return

B is the beta of the asset

The figures used for rrf, rm and Ba are decided on by the analyst, although most investors use a Beta figure which has been calculated by a third party. The most common use for the CAPM is calculating the fair price of an asset.

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Arbitrage involves making two simultaneous transactions in two markets, taking advantage of the differences in price between the two markets. Technically arbitrage is considered to be risk-free, but fluctuations in market conditions may reduce expected profit in normal times, and can be severely affected by events such as devaluations.

Issues with the CAPM:

The CAPM makes several assumptions: There are no transaction costs (e.g. taxes)

Assets are dividable

There are no restrictions to investment in assets

Investors will maximize their expected utility

Prices cannot be influenced by investors

There is a homogeneity of beliefs

All assets are marketable

The calculations are on a single time period

There are issues over the linearity of the equation used to calculate the CAPM, but perhaps the most critical issue is that recent calculations have shown that the CAPM calculations do not match empirical results.

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Arbitrage Pricing Theory:

The Arbitrage Pricing Theory (APT) was developed by Ross (1976) as a substitute for the CAPM. The basic principle of the APT is that the payoff from each asset can be described as a weighted average of all assets in a portfolio.

The APT formula is:

E(rj) = rf + bj1RP1 +bj2 RP2 +......bjnRPn

Where E(rj) is the expected rate of return on the asset

Rf is the risk-free rate

Bj is the sensitivity of the asset’s return in this particular case

RP is the risk premium in this particular case

The thinking behind the APT is that there are two main issues which can influence the rate of return on an asset: the macroeconomic environment in general and how likely it is that the environment might influence the movement of the asset. Influences in the macroeconomic environment include inflation, levels of confidence of investors, changes in interest rates, and so on.

The assumptions made by the APT are:

It is assumed that returns will follow the above equation

Investors tend towards risk aversion There are no transaction costs There are no restrictions on the availability of assets Short sales are not restricted

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No arbitrage possibilities exist (in equilibrium) All investors think alike. Issues with the APT

The major issue with the APT is attempting to accurately define the level of risk which applies to any given asset. It may be possible to find a ‘factor portfolio’ where the risks are very similar, but generally the level of risk is determined by macroeconomic factors.

Comparison between the CAPM and the APT:

APT may be informative over the medium to long term, but are not considered to be accurate in the short term. The CAPM, on the other hand, is a snapshot, and appears to be more accurate in the short term than it is in the long term.

The APT focuses on risk factors rather than assets, so it has an advantage over the CAPM in that it does not have to create an equivalent portfolio to assess risk.

The CAPM assumes that there is a linear relationship between the assets, whereas the APT assumes that there is a linear relationship between risk factors. This means that where there no linear relationship exists, the models are unable to adequately predict outcomes.

However, both the CAPM and the APT make relatively unrealistic assumptions in that assets are freely available and desirable, there are no costs incurred in the acquisition of assets and that all investors tend to think alike and come to the same conclusions. This seems intuitively contradictory, as the most successful investors are likely to be those who are able to spot potential which has remained unnoticed by the market as a whole. Indeed, when all investors do think alike, a ‘bubble’ can be created which inflates the asset price and downplays the risks inherent in the asset. In this circumstance, assessing the risk of an asset based on

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the mood of the market is likely to be far more risky than can be predicted by either the CAPM or the APT. Theoretically, therefore, it could be argued that using a CAPM or APT analysis is likely to increase the propensity for ‘bubbles’ to emerge, as they are using static predictions of behavior by investors.

This is compounded by the subjective decisions made by analysts creating risk projections: although it may be professionally desirable for analysts to consider levels of risk in a rational and objective fashion, it is unlikely that they have no preferences or particular areas of expertise – or areas where they lack knowledge – and this will impact on the validity of the results of mathematical projections. That is, the calculation is only as good as the analyst who is choosing the factors to be included in it.

Therefore, although the CAPM and APT are useful as rule-of-thumb heuristics of the market as it currently operates, they are both static models which use a limited number of factors (Krause, 2001) to predict risk in a highly complex market. Although they are based on mathematical principles, they are subjective in that the analyst performing the calculation has the freedom to decide which factors are relevant in each particular case.

One of the great advantages of the CAPM is its simplicity. But to test the CAPM two problems arise. Firstly, the CAPM is concerned with expected returns and secondly, the market portfolio should include all risky investment, whereas most of the market indexes contain only a sample of common stocks.

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