An Analysis of the Arbitrage Pricing Theory

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 Literature Review

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.

OTHER EMPIRICAL STUDIES

Indeed, over past years the link between macroeconomic variables and stock market returns has been well documented in the finance literature. Several studies depicted that macroeconomic variables influence stock market to a great extent. Numerous interesting results have also been found, but both the academics and the practitioners have not arrived at a consensus on the direction of the causality among these variables, which have at times led to ambiguity in the studies. The vector autoregressive VAR, by Sims (1980), was used to find short run causality between macro economic variables and stock prices. As a result, it was found that macro economic variables do affect stock returns greatly. Darrat and Mukherjee (1987) used a vector autoregressive model on the Indian data over 1948-1984 and showed that a causal relationship do exist between stock returns and macro economic variables. Granger (1986) and Engle and Granger (1987) concluded that the soundness of long term equilibria between variables can be studied using cointegration methods. In fact, they have been applied to the long run relationship between stock prices and macroeconomic variables in numerous studies. The Johansen (1988), method of testing for the existing of cointegration relationships has become the standard in the econometrics literature. His multivariate cointegration test favored long run equilibrium relationship between financial and real sector. The following papers Fama and French (1989), Schwert (1990) and MacDonald (1997), a significant relationship was gained between stock market returns and changes in macroeconomic variables like the inflation, risk premium, yield curve, interest rates and industrial production. Brown and Otuski (1990) found that crude oil prices, exchange rate, call money rate, residual market error, production index and money supply affect the Japanese stock market and is linked with risk premia. Hamao and Campbell (1992) concluded a smaller positive coefficients for the dividend price ratio and the long short interest rate spread on stock markets returns in Japan relative to the US in a studying a sample casing monthly data from 1971 to 1990. Mukherjee and Naka (1995) test the dynamic relationship between six macroeconomic variables and the Japanese Stock market by using a vector error correction model of seven equations. They found that a long term equilibrium link between the Japanese stock market and macroeconomic variables like the exchange rate, money supply, inflation, industrial production, long term government bond rate and call money rate. Kwon, Shin and Bacon (1997), assessed the stock market behavior and various multiple macroeconomic variables namely, production index, inflation, expected inflation, risk premium, term structure, dividend yield, trade balance, foreign exchange rate, oil price and money supply. They were time series data regressed on monthly returns of the value weighted Korean composite stock price index. As a consequence, they concluded that Korean stock market was more sensitive to real economic and international trading activities, - like the trade balance, exchange rate, money supply and production index - than that of US and Japanese stock indices. Nasseh and Strauss (2000), found a significant link between stock prices and domestic and foreign activity in France, Germany, Italy Netherlands Switzerland and UK. Positive coefficients for industrial production, consumer price index, short term interest rates and business surveys of manufacturing. However, negative coefficients were obtained for long term interest rates. Furthermore, the European stock market was found to be integrated with that of Germany. Rapach (2001) analyzed the impacts of supply shock factors on real U.S stock prices in a structural VAR model and found that real stock returns were negatively correlated with inflation. Maysami, Howe and Hamzah (2004), investigated the link between macroeconomic variables and the stock market returns in the Singapore stock market. The macroeconomic variables are interest rates, inflation, exchange rates, industrial production and money supply. Singaporean stock market index All-S equities property index proved to share significant relationship with all variables. However, the All-S equities finance index and All-S equities hotel index form significant relationship with only selected variables. Basher and Sadorsky (2006) scrutinized the effect of oil price changes on the stock market returns of 21 emerging economies. Evidence found were positive and significant at 10% level to stock market returns for most if not all countries. A.Humpe and P.Macmillan (2007), made an attempt to examine the long term stock market movements caused by macroeconomic variables. They in fact, made a comparison between the US and Japan. For the US and the Japan macroeconomic variables were, industrial production, consumer price index, money supply, rate of interest which were taken into consideration. Monthly data over the last 40 years were used. As a result, in US, variables like the industrial production positively affect stock prices while negatively affected by inflation and rate of interest. Money supply had an insignificant influence over stock prices. In Japan, two cointegrating vectors were found. Stock prices were positively affected by industrial production and negatively to money supply. The second cointegrating vector depicts that industrial production is negatively related to interest rate and consumer price index. A.Anokye and T. George (2008) examine the influence of a number of macroeconomic variables on stock prices in Ghana. Variables are inflation, interest rate, exchange rate, oil prices, inward FDI. Ghana stock market formed significant relationship with the macroeconomic variables selected. In fact, the presence, of a cointegrating relationship between the variables and stock prices is a signal that stock market efficiency is in doubt. In the short run, establishing lead and lag through error correction model shows that investors can cause past values to reap abnormal profits. Kandir (2008) in his investigation, examined the Turkish stock market and how do the growth rate of industrial production index, change in consumer price index, growth rate of narrowly defined money supply, change in exchange rate, interest rate, growth rate of international crude oil price affect the return on the MSCI World Equity Index. A macroeconomic factor model is employed for the period that spans from July 1997 to June 2005. N. Sohail and Z.Hussain (2009) explored the relationship between Lahore stock market and macroeconomic variables. Monthly time series were used and variables were, consumer price index, real effective exchange rate, 3-month treasury bill, industrial production and M2(money supply). Data from 2002-2008 were taken into consideration. As a matter of fact, two long run relationships were found. In the long run, inflation negatively affected stock prices whilst, industrial production, exchange rate and money supply positively affected them. On the other hand, treasury bills had an insignificant effect on stock prices. The results of the Variance Decomposition showed that inflation explained the maximum variance. K.Jiranyakul (2009) used a set of four macroeconomic variables, namely; the real GDP, money supply, nominal effective exchange rate and Thai stock market index. A positive relationship was found between them using data from (1993-2007). The Engle granger test does not show cointegration, however the Johansen cointegration test exhibits cointegration. There are two cointegrating equations; industrial production had a positive relationship on stock prices whilst inflation had a negative one. Nominal exchange rate adversely affected stock prices. The fundamental crisis imposes no impact on long run relationship. Moreover, there exist bidirectional causality between stock market and economic growth. MW Mahmod and NM Dinniah (2009) carried out a study of how macroeconomic variables, inflation, output and exchange rate of six Asian Pacific regions affect stock prices. Monthly data for Malaysia, Thailand, Korea and Japan and quarterly data for Hong Kong and Australia were used. According to the Granger test and Johansen and Juselius maximum likehood procedure, there is sufficient evidence showing that there is long run relationship between the selected variables in all three countries. Furthermore, the error correction model depicts a short run link only between foreign exchange rate with stock price of Hong Kong and real output and stock price of Thailand. E. Cagli, U Halac and D.Taskin (2010), studied the relationship of the Turkish stock prices with macroeconomic variables, like the exchange rate, GDP, industrial production, inflation, money supply, interest rates and oil prices and monthly data from Jan 1998-Dec 2008 were used. The cointegration test suggests that GDP, oil price, industrial production are cointegrated. Inflation is not cointegrated. According to the unit root test with structural breaks exchange rate, rate of interest are dropped out for the reason they are found to be integrated of order (0) they are hence stationary. D.Plinkus (2010) carried an analysis of how macroeconomic variables affect stock market of main Baltic. Monthly data from Jan 2000 - Dec 2008 were used. Indeed, results obtained present granger causality between selected variables and the stock market indices. Nearly all the variables, Gross Domestic Product, unemployment, foreign direct investment, state debt, money supply, export, import, trade balance, shorter interest rates and harmonized consumer price index were found to be causing movements in stock returns. Moreover, the relation between macroeconomic variables and stock returns in Baltic were found to be more reliable in the long run. J.Garcia and M.Juarez (2010) investigated the influence of Chinese and American macroeconomic variables in the stock market indices of Brazil, Chile and Mexico. Monthly data for industrial production and interest rates for the period of Jan 200 - Dec 2009 were used. As a result, a cointegrating relationship between the USA with the Brazil, Mexico and Chile were obtained whereas at least two cointegrating relationship between China Mexico and Brazil were gained and one with Chile. Implying that Chinese, macroeconomic variables appear to be more cointegrated with Latin American stock. The granger causality tests show that US macroeconomic variables granger cause stock market performance in Mexico and Chile. As a matter of fact, Mexico is found to be the only country which exhibits causality between China and USA.

How do the selected macroeconomic factors affect stock returns?

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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