An Empirical Investigation of Arbitrage Pricing Theory: A case Zimbabwe
University of Zimbabwe
This study investigates the Arbitrage Pricing Theory for the case of Zimbabwe using time series data from 1980 to 2005 within a vector autoregressive (VAR) framework. The Granger causality tests are conducted to establish the existence of causality among the variables like inflation, exchange rate and Gross Domestic Product. The VAR estimates as shown by the impulse response and variance decomposition together with the Granger causality test show that there is unidirectional causality from Consumer Price Index to Stock Prices. Although the Granger causality test has indicated that there is no causality between RGDP and Stock Prices, the variance decomposition has shown that the real GDP explains deviations in the Stock Prices in the long run. Granger causality tests found no meaningful relationships between Stock Prices and Exchange Rate but considering impulse response functions the effect is significant as early as the first period.
Keywords: Arbitrage, Capital Asset Pricing Model (CAPM), Efficient Market Hypothesis, Vector Auto Regression Model (VAR), Impulse Response, Variance Decomposition.
The Capital Asset Pricing Model (CAPM) and the Arbitrage Pricing Theory (APT) have emerged as two models that have tried to scientifically measure the potential for assets to generate a return or a loss. Both of them are based on the efficient market hypothesis, and are part of the modern portfolio theory. The Efficient Market Hypothesis (EMH) (Fama, 1965), states that at any given time, security prices fully reflect all available information. If the asset is overpriced, then arbitrageurs will short the asset, until reduced demand for purchasing it caused the price to fall. The opposite is true for underpriced securities. The CAPM is based on several simplifying assumptions and because most of these assumptions appear to be unrealistic in the real world, it has been argued that they are the cause of flaws in the CAPM (Watson and Head 1998; Harrington 1987). Several of the CAPM assumptions have been criticized. For instance, the assumptions that there are no taxes and no transaction costs do not conform to reality. In addition, the assumption of homogeneous expectations is also open to doubt, because investors usually have divergent expectations, apply various investment holding periods, differ in respect of their decision-making processes and so on. (Levy and Solomon 2000). Some researchers have also suggested that the CAPM is incorrect in respect of its description of expected returns and that a multi-factor model offers a better explanation. The Capital Asset Pricing Model (CAPM) has run into several roadblocks such as Roll's (1977) suggestion that it is not a testable scientific theory and a plethora of empirical anomalies which provide empirical evidence that the usual market proxies are not mean-variance efficient. In 1976 Ross introduced the Arbitrage Pricing Theory (APT) as an alternative to the CAPM. The APT has the potential to overcome CAPM’s weaknesses. It requires less and more realistic assumptions to be generated by a simple arbitrage argument and its explanatory power is potentially better since it is a multifactor model. The APT relates the expected rate of return on a sequence of primitive securities to their factor sensitivities, suggesting that factor risk is of critical importance in asset pricing (Gilles and Leroy, 1990). It tries to capture some of the non- market influences that cause securities to move together. The APT rests on the hypothesis that the equity price is influenced by limited and non- correlated common factors and by a specific factor totally independent from the other factors. The main empirical strength of the APT is that it permits the researcher to select whatever factors provide the best explanation for the particular sample at hand...
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