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# An Analysis of the Arbitrage Pricing Theory

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The Arbitrage Pricing Theory (APT) was developed primarily by Ross (1976a, 1976b). Indeed, it is a one-period model in which every investor believes that the stochastic properties of returns of capital assets are consistent with a factor structure. The basis of arbitrage pricing theory is the idea that the price of a security is driven by a number of factors. These can be divided into two groups: macro factors, and company specific factors. The name of the theory comes from the fact that this division. Each F is a separate factor and each ? is a measure of the relationship between the security price and that factor.

## The APT: Assumptions

The APT relies on the following assumptions:
• Returns are generated according to a linear factor model
• The number of assets is close to infinite
• Investors have homogenous expectations
• Capital markets are perfect (i.e. perfect competition, no transactions costs

## The APT: Factors

Even if, the arbitrage pricing theory does not explicitly state the relevant macro economic factors, they can be empirically constructed. As a matter of fact, it has been observed that the following factors tend to influence the price of the security under consideration:
• Change in industrial production or GDP.
• Unanticipated inflation or deflation.
• Shifts in the Yield Curve
• Investor confidence measured by surprises in default risk premiums for bonds
• Changes in oil prices (proxy for price level)

## The Capital Asset Pricing Model

In finance literature, the capital asset pricing model (CAPM) is used to determine a theoretically appropriate required rate of return of an asset, if that asset is to be added to an already well-diversified portfolio, given that asset's non-diversifiable risk. The model takes into account the asset's sensitivity to non-diversifiable risk (also known as systematic risk or market risk), often represented by the quantity beta (?) in the financial industry, as well as the expected return of the market and the expected return of a theoretical risk-free asset. The CAPM, is a model, for pricing an individual security or a portfolio. For the individual securities on the other hand the security market line (SML), The general idea behind CAPM is that investors need to be compensated in two ways: time value of money and risk Based on the Markowitz's mean-variance model, the CAPM inherits all the shortcomings of the latter in addition to its own assumptions such as: 1. Investors are rational and risk averse. They pursue the only interest of maximizing the expected utility of their end of period wealth. Implication: The model includes the single time horizon for all investors. 2. The markets are perfect, thus taxes, inflation, transaction costs, and short selling restrictions are not taken into account. 3. Investors can borrow and lend unlimited amounts at the risk-free rate 4. All assets are infinitely divisible and perfectly liquid. 5. Investors have homogenous expectations about asset returns. In other words, all investors agree about mean and variance as the only system of market assessment, thus everyone perceives identical opportunity. The information is costless, and all investors receive the same information simultaneously. 6. Asset returns conform to the normal distribution. 7. The markets are in equilibrium, and no individual can affect the price of a security. 8. The total number of assets on the market and their quantities are fixed within the defined time frame.

## The Implications

The investors will choose to hold a portfolio of risky assets in proportions of the market portfolio. Market portfolio will be on the efficient frontier and will be the tangency portfolio to the optimal capital line. Hence, the capital market line will be the line from the risk free rate through the market portfolio, M, which is also the best attainable capital allocation line. The risk premium on the market portfolio will be proportional to its risk and the degree of risk aversion of the investor. The risk premium on individual assets will be proportional to the risk premium on the market portfolio, M, and the beta coefficient of the security relative to its market portfolio. The CAPM formula: Ri = Rf + ?i (rm-rf) Whereby Ri is the expected return by CAPM, rf is the risk free rate, rm is the market return and ?i is the risk factor.

## The security market line

Expected return sml Rm Rf beta The SML essentially graphs the results from the capital asset pricing model (CAPM) formula. The x-axis represents the risk (beta), and the y-axis represents the expected return. The market risk premium is determined from the slope of the SML. The security market line is a useful tool in determining whether an asset being considered for a portfolio offers a reasonable expected return for risk. Individual securities are plotted on the SML graph. If the security's risk versus expected return is plotted above the SML, it is undervalued because the investor can expect a greater return for the inherent risk. A security plotted below the SML is overvalued because the investor would be accepting less return for the amount of risk assumed. Capital asset pricing model has the following limitations: It is based on unrealistic assumptions. It is difficult to test the validity of Capital asset pricing model. Betas do not remain stable over time.

## Empirical tests of APT and CAPM

Empirical tests of the APT have been questionable because no two researchers could agree on the value of the coefficients of any of the exogenous variables (Chen 1983, Chen, Roll and Ross 1983, Roll and Ross 1980, Kryzanowski et al 1994). Kryzanowski et al (1994) showed that the explanatory variables are correlated. Hard work to generate orthogonal factors results in one principal factor and APT models that retain multiple explanatory variables are unstable. A closer look at Chen (1983) reveals these aspects of APT research. Chen, a great fan of the APT, reports that he was unable to find any evidence that the APT is not valid. In each case, his null hypothesis was that the APT is valid; and in each case, he was unable to reject this hypothesis. N.Soufian (2001) examined the validity of the CAPM and APT across time during three sub samples for periods (1980-1989 and 1990-1997). This study demonstrated how risk premium, term structure, changes in industrial production affect average returns. The assumption of a constant beta is the major difficulty in the empirical support of static CAPM and its factor models when applied across time. It is however clear that the APT is much better behaved than the CAPM. In J Shanken's study (1982), the CAPM model, was not found to be testable in a strict sense. Much of this acceptance can be attributed to the persuasive analysis of Roll, who argues that the CAPM, is not testable unless the market portfolio of all assets is used in the studies. The APT of Ross, is viewed as a testable substitute to the CAPM.

## Gross Domestic Product (GDP)

The relationship between economic activity (proxy by GDP) and stock market has been an issue of great interest to many researchers. Mostly, studies have been carried out to find out whether stock prices are influenced by economic changes or determined by speculative bubbles. In the light of mixed empirical evidences, it is found that during recession, stock market returns are low whereas during economic boom and in presence of future expectations about increase in level of economic activity, returns soar. Oskoe (2010) studied stock market performance of Iran with respect to changes in economic growth. As a result a causal relationship between GDP and stock market were found. The Johansen cointegration test showed that stock prices are moved by level of economic activity.

## Inflation and rate of interest

Inflation is defined as a period where there is persistent rise in general price level of goods and services. It affects the stock market in sense that it increases the rates of interest. If the inflation rate is high, the interest rate is also high thus, the creditor will have a tendency to compensate for the rise in interest rates and the debtor has to avail of a loan at a higher rate. This prohibits funds from being invested in stock markets. In addition when the government has enough funds to circulate in the market, the cost of goods, services usually rise. This leads, to the decrease in the purchasing power of individuals and in the value of money. Concisely, for the economy to flourish, inflation and stock market ought to be more conforming and predictable. Feldstein (1980a) stated that inflation decreases share prices because of the link between inflation and the tax system.

## Money supply

Intuitively an increase in the rate of growth of money supply strengthens the rate of increase in stock prices. Conversely, a fall in the rate of growth of money supply should slow down the growth momentum of stock prices.

## Oil prices

Indeed oil prices are very volatile by nature and any fluctuation in such prices affect the economy as a whole. In most if not all economies, all industries, they rely on fuel to run properly. In their study, N.Mujahid, R.Ahmed and K.Mustafa (2006) used data from March 1998 to Dec 2005 and found that there is actually no relationship between oil prices and stock market of Pakistan. The reason behind this is because due to an increased use of gas and liquidity. In fact stock a positive relationship between gas prices and stock market was found.

## Exchange rates

A depreciating currency may depress stock market and hence stock returns. This happens due to expectations of inflation (Ajayi and Mougoue 1996). In this connection, foreign investors are less willing to hold assets in currency that depreciates as this will erode their return on investment. However an appreciating currency will boost the economy as well as the stock market and finally stock returns. Hence exchange rates do affect stock market returns to high extent. Moreover, M.Rahman (2009), studied how stock prices in three merging countries like the Bangladesh, India and Pakistan, interact with respect to fluctuations in exchange rates. Using data from Jan 03 - June 2008, result showed that there is no cointegrating relationship between stock prices and exchange rates. The Granger causality test likewise the Johansen test, depicted no causal relationship between stock prices and exchange rates. Result showed there is no way causal relationship between stock prices and exchange rates in the countries.
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An Analysis of The Arbitrage Pricing Theory. (2017, Jun 26). Retrieved July 23, 2024 , from
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