To be able to show the problems, I make use of the study done by Lehman and Modest (1985), which come up into three conclusions. The analysis of Lehman and Modest was able to show that one of the problems in determining the factor for asset pricing is the proper or the correct use of procedure. Lehman and Modest opposed Fama-Macbeth in using the maximum likelihood analysis in determining the factors. Another study included in this paper is the one done by Enrico Altay (2003) using the Germany and Turkish stock exchange. In his study he uses the Fama-Macbeth maximum likelihood analysis. This causes the difference in the result.
Therefore, in analysing the stock exchange one should be aware of the models and theory being used. The arbitrage pricing theory may encounter several problems especially in analyzing the factors. The macroeconomic factors may affect the outcome in pricing the asset. The analysis in which the best portfolio perform best remains. The arguments are presented in the later part of the paper.
Arbitrage Pricing Theory (APT), is a general theory of asset pricing. It holds the expected return of a financial asset that can be modelled as a linear function of various macro-economic factors or theoretical market indices, where sensitivity to changes in each factor is represented by a factor specific beta coefficient. This theory was initiated by the economist Stephen Ross in 1976.
The Arbitrage Pricing Theory establishes an equilibrium pricing relation between each asset's expected return and all others. In analyzing the theory, we must first discuss the covariance matrix and the portfolio risk. There are several method in estimating covariance matrix one can be by using the simple volatility estimator (Garman-Klass, 1980) or with GARCH estimators (Engle,1982; Bollerslev, 1986). Another method is that, assuming the drivers of volatility is known the historical data can be estimated if the variables are picking and the relation between each driver and each stock are identified.
Portfolio return is the weighted average of the individual asset returns, using the portfolio holdings as weighs. The portfolio risk is the weighted sum of the individual asset variances and covariances with all other assets, using as weights the squared portfolio weights. Portfolio risk is its weights the squared portfolio weights. The original return units can be used to compute variance. The portfolio risk is usually reported as the square root of the variance, the volatility of portfolio returns.
To compute for the portfolio risk we must collect the return variances and covariances in a table - the "covariance matrix". We must identify the portfolio holdings weights and apply the portfolio risk formula - a function dubbed a quadratic form by mathematics. The portfolio analysis is important in correlating with the common factors in showing the validity of the APT.
The APT based on Ross (1976) takes the view that there is no single way to measure systematic risk. The risks arise from the unanticipated changes in the following fundamental economic variables:
1. Investor confidence
2. Interest rate
4. Real Business Activity
5. A market index
Each stock and portfolio has exposures or betas with respect to each of these systematic
risks. Risk Exposure Profile is the pattern of economic betas for a stock or portfolio. The profile indicated how a stock or portfo