Factors Affecting the Arbitrage Pricing Theory Finance Essay

Capital Markets play a vital role in the financial sector of each economy. The primary role of the capital market is to raise long-term funds for governments, banks, and corporations while providing a platform for the trading of securities. An efficient capital market can promote economic growth by attracting domestic and foreign capital.

1.1.2 Karachi Stock Exchange and its profile

The Karachi Stock Exchange is an example of a capital market which is the biggest and most liquid exchange in Pakistan. It was declared the 'Best Performing Stock Market of the World for the year 2002.' A total of 650 companies were listed on the Karachi Stock Exchange (KSE) as of end March 2010, with paid up capital of Rs. 894.2 billion. Aggregate market capitalization as at end March, stood at Rs. 2,890 billion (US$ 35 billion). (Source: Economic Survey of Pakistan)

1.1.3 KSE- 100 INDEX

The primary objective of the KSE100 index is to have a benchmark by which the stock price performance can be compared to over a period of time. In particular, the KSE 100 is designed to provide investors with a sense of how the Pakistan equity market is performing. The KSE-100 Index was introduced in November 1999 with base value of 1,000 points. The Index comprises of 100 companies selected on the basis of sector representation and highest market capitalization, which captures over 80% of the total market capitalization of the companies listed on the Exchange. Out 35 Sectors, 34 companies are selected i.e. one company from each sector (excluding Open-End Mutual Fund Sector) on the basis of the largest market capitalization and the remaining 66 companies are selected on the basis of largest market capitalization in descending order. This is a total return index i.e. dividend, bonus and rights are adjusted.

The formula for calculating the KSE- 100 Index is:

[(Sum of Shares Outstanding x Current Price) / Base Period Value] x 1000 Or (Market Capitalization / Base Divisor) x 1000

1.1.4 Top 30 KSE 100 Index Companies

The following is a list of 30 companies with the highest market capitalization volume and their respective weightages in the index and account for over 80% of the KSE index as of February 20, 2008: Number Company Name Weightage (%) Market Capitalization (PKR) 1 OGDCL 14.14 550,948,930,000 2 MCB 7.17 279,583,150,000 3 National Bank of Pakistan 5.43 211,726,900,000 4 Pakistan Petroleum 5.06 197,201,080,000 5 Standard Chartered Bank 4.41 171,704,800,000 6 PTCL 4.28 166,810,800,000 7 United Bank Limited 4.13 161,025,160,000 8 Jahangir Siddiqui & Company 2.66 103,600,000,000 9 Pakistan State Oil 2.08 81,034,440,000 10 Allied Bank Limited 2.01 78,371,670,000 11 Nestl© Pakistan 1.93 75,280,250,000 12 Pakistan Oilfields 1.71 66,824,220,000 13 Fauji Fertilizer Company 1.68 65,607,390,000 14 ABN AMRO 1.63 63,666,370,000. 15 Engro Chemical 1.45 56,492,990,000 16 Arif Habib Securities 1.40 54,660,000,000 17 NIB Bank 1.27 49,320,250,000 18 Kot Addu Power Company 1.19 46,565,400,000 19 EFU General Insurance 1.16 45,300,000,000 20 Bank of Punjab 1.13 43,869,030,000 21 Fauji Fertilizer Bin Qasim 1.06 41,474,480,000 22 Bank Alfalah 1.03 39,975,000,000 23 Adamjee Insurance 1.01 39,258,300,000 24 Pakistan Tobacco Company 0.99 38,707,280,000 25 Sui Northern Gas Pipelines 0.98 38,300,100,000 26 Hub Power Company 0.98 38,128,240,000 27 Dawood Hercules Chemicals 0.91 35,549,620,000 28 Habib Metropolitan Bank 0.91 35,354,280,000 29 EFU Life Assurance 0.89 34,750,000,000 30 Lucky Cement 0.86 33,593,480,000

Relevance of the Topic and Research Title

This research aims to identify what extra market factors should be considered as likely candidates when investigating stock market volatility and in that lies this research titles relevance. The APT model is dependent on many variable factors and there are various adverse factors in Pakistan which affects stocks returns in the KSE like political tensions, law and order situation, water shortage, floods, earthquakes and flood and energy crisis. So this thesis paper will help to identify the factors which have a positive, negative or no correlation with stock returns.

Impact of 2008 Economic/ Political Crisis on KSE 100 - Index

The KSE 100 Index had many swings during the fiscal year 2008 and the key factors affecting it were as follows: May 23: High inflation in the month of May, 2008 resulted in the unexpected increase in the interest rates by State Bank of Pakistan which eventually resulted in sharp fall in Karachi Stock Exchange and its indexes. July 16: KSE-100 Index dropped one-third from an all-time high hit in April, 2008 as rising pressure on Pakistan's government to tackle Taliban militants worsens concern about the country's economic woes. July 17: Angry investors attacked the Karachi Stock Exchange in protest at plunging Pakistani share prices which further led to a decrease in share prices. August 18: KSE 100 Index rose more than 4% after the announcement of the resignation of President Pervez Musharraf. So the chain of events/ facts shows how different incidents/ factors can affect the share prices in Pakistan and that is what this research paper will aim at.

Background information and Evolution

Capital Asset Pricing Model (CAPM)

The capital asset pricing model states that the price of a stock is related to two variables; the time value of money and the risk of the stock.A  The time value here is represented by the risk free rate of interest. The CAPM model keeps into account the overall stock market risk and that is the only factor which it incorporates, something which became dubious when this asset pricing model was used in earlier times. Later, researchers figured out that there were other factors as well which would affect stock returns so a new model for pricing was needed.

Arbitrage Pricing Theory (APT)

The APT states that each stock's return to the investor is influenced by several independent factors. It is given by the following formulae: Expected Return = RF + B1 x (factor 1) + B2 x (factor 2) + ... + Bn x (factor n) Where: RF = the risk free interest rate is the interest rate the investor would expect to receive from a risk free investment.A b = the sensitivity of the stock to each factor. Factor = the risk premium associated with each factor. There are no specific factors for this model as theory doesn't suggest any, because the stock returns could vary as one stock might be more sensitive to one factor than another. For example the price of crude oil might be sensitive to the share of OGDCL but not to the share of MCB. There are other various macroeconomic variables which affect the arbitrage pricing model which includes Inflation, GNP, Shifts in Yield Curve and Investor Confidence.

Characteristics of the Arbitrage Pricing Model

Arbitrage Pricing Model considers the following risk factors: Company specific risk. Interest rate (time horizon risk). Inflation risk. Confidence risk. A multi factor or multi variable model best describes the arbitrage pricing model. It does not specify its risk factors. Timely and accurate information of the variables is required. The relationship should be theoretically justifiable on economic grounds. It works better for individual stocks rather than for a group of stocks. It is used less than the Build-up model, CAPM model or the Discounted Cash Flow model.

1.3.4 Difference between CAPM and APT model

The difference between CAPM and arbitrage pricing theory is that CAPM has a single non-company factor and a single beta, whereas arbitrage pricing theory separates out non-company factors into as many as proves necessary to be included. Each of these requires a separate beta. The beta of each factor is the sensitivity of the price of the security to that factor.

1.3.5 Advantages and limitations of the APT model

Following are the advantages of the APT model: It is not as restrictive as the CAPM in its requirement about individual portfolios and with respect to the information structure it allows. It allows multiple sources of risk which provides an explanation of what moves stock returns. Limitation of the APT model: APT expects investors to assume or perceive the risk sources.

1.3.6 Assumptions of the Arbitrage Pricing Theory

Capital Markets are perfectly competitive. Investors always prefer more wealth to less wealth. Perfect competition prevails and there is no transaction cost in the market: frictionless market.

Managerial Concerns pertaining to Research

Decisions are made by managers every day. And in order to make fruitful decisions one needs to have firm knowledge over the issue or need to research and know about it to master at whatever they want to do. So the more important the decisions and their impact, the more important the research becomes. If decisions are made randomly then their consequences would be resulting in considerable harm to a large number of people related to it. Hence the research should be refined so that managers can use them to apply the theory and findings to their daily life. From this research, managers can get to know which factors affect their company's stock prices so they would devise policies with regard to that in the favor of their companies to avoid losses.

Academic Concerns pertaining to Research

Students and researchers might find it important to consult the research paper in order to understand the underlying concept of the topic researched on. It could be of vital importance if they want to derive on to something related to the topic. Also the research can be used to see how analysis is carried out in the case of stock returns and its factors and which factors affect the stock returns.

Keywords and Definitions

Arbitrage:

It is the process of earning profits by taking advantage of differential pricing for the same asset.

Arbitrage Pricing Theory:

The theory focuses to calculate the returns in absence of arbitrage-condition of artificially overpricing or underpricing a product. It applies to economies that are regulated by the Law of One Price which states that two identical goods can't be sold at the same price.

Arbitrage Pricing Model:

An asset pricing model which predicts a relationship between the returns of aA portfolio and the returns of a single asset through a linear combination of many independent macro-economic variables.

Stock Market:

It is the market in whichA shares are issued and traded either through exchanges orA over-the-counter markets. Also known as the equity market, it is one of the most vital areas of a market economy as it provides companies with access to capital and investors with a slice of ownership in the company andA the potential of gains based onA the company'sA future performance.

Multifactor Model:

A multifactor model is an alternative to a single risk based model. It can either be from an Arbitrage pricing theory or from a multi-beta CAPM perspective incorporating multiple factors which are responsible for the asset returns.

Study Objectives

To find out which factors have a linkage with stock prices in general and with respect to Karachi Stock Exchange. To find out which factors have a positive, negative or no correlation with stock prices in the stock market.

Chapter 2: Literature Review

Various literatures were consulted for this research paper and it was found that the level of return achieved or expected from an investment is dependent on a variety of factors. The single index model or the CAPM was developed by Sharpe (1963) which was unsuccessful as its main shortcoming was that it used only the market return as a single factor to determine security return. This led way to the multifactor model or APT model developed by Ross (1976) which incorporated other variables affecting stock returns.

2.1 Evidence from Stock Markets

2.1.1 Evidence from the Japanese Stock Market

A.A Azeez and Yasuhiro investigated the evidence of pricing of macroeconomic factors in the Japanese stock market during the bubble period using the Arbitrage Pricing Theory model. They also examined the pre and post bubble periods in order to compare the robustness of prices factors over the bubble period. The main objective of their study is to analyze empirically the asset pricing mechanism of Japanese stock market during the bubble economy by the use of macroeconomic based APT. The data is divided into the three bubble categories in order to analyze the results and in each period there are four factors which carry risk premiums in the Japanese stock market; money supply, inflation, exchange rate and industrial production. In choosing the variables special consideration is given to any economic announcements which will affect stock price movements if the new information revealed by announcements affects either expectations of future dividends or discount rates or both. [1]

2.1.2 Evidence from Turkish Stock Exchange

Ahmet gave evidence of effects from Turkish Stock Exchange stating seven macroeconomic variables (consumer price index, money market interest rate, gold price, industrial production growth index, oil price, foreign exchange rate and money supply) affecting the Istanbul stock Exchange Index- 100. He designed a multiple regression model and concluded saying that interest rate, industrial production index, oil price and foreign exchange rate have negative effect on ISE-100 index while money supply has a positive one. On the contrary inflation rate and gold price does not have any significant effect on the dependent variable.

2.1.3 Evidence from Indian Stock Exchange

Aman from India has carried out a research based on literature review and has concluded the relevance of macroeconomic factor for stock markets. According to his findings stock markets are affected by macroeconomic factors which may be local or international. Key variables mentioned by him affecting in the longer run are industrial production, inflation, foreign exchange rate, interest rate and money supply.

2.1.4 Evidence from Italian Stock Market

Arduino Cagnetti did an empirical study in the Italian Stock Market by comparing the APT and CAPM models and found that APT performs better than the CAPM in all aspects. Many of the factors that he found significant were inflation, interest rates, money variables, market indices, production indices and international trade variables.

2.1.5 Evidence from Karachi Stock Market

Babar, Kashif, Aslam and Nadeem documented the results by examining the stock returns variations to specific economic variables by applying a multi factor model in context of Karachi Stock Exchange. The 32 firms for which data was taken were related from the two most important industries of Pakistan: Banking and Textile Industry which were the top performers at KSE-100 index. They incorporated variables like market index, consumer price index, risk free rate of return, exchange rate, industrial production growth rate, money supply and individual industrial production to run analysis using the GARCH model. Javed Iqbal and Aziz Haider provide evidence from the Karachi Stock Exchange by carrying out the exploratory factor analysis by breaking the sample for stability testing. They chose sixteen macroeconomic variables out of which some were interest rate, money market rate, long term interest rate yield and regional market.

2.2 Joint estimation of factor sensitivities and risk premia for the APT

In this study Edwin and Marjorie maintained a linear factor model and used both measured and unmeasured factors to estimate a LFM, the APT, and a CAPM. They found that the January effect is an important determinant of expected returns. The existence of a January effect that is not explained by this set of factors is evident, but, it would be trivial to add a portfolio that exhibits a strong January effect and hence represents a "January factor."

2.3 The Conditional relation between Beta and Returns

In this paper, Glenn, Sridhar and Ike find a consistent and highly significant relationship between beta and cross-sectional portfolio returns. The key distinction between the tests is the recognition that the positive relationship between returns and beta predicted by the Sharpe-Lintner-Black model which is based on expected rather than realized returns. In periods where excess market returns are negative, an inverse relationship between beta and portfolio returns should exist.

2.4 Explaining the cross section of returns via a multi factor APT model

This paper by Jianping uses an autoregressive approach to test a multi-factor model with time-varying risk premiums. A quasi-differencing approach is used to eliminate the unobservable factors in the model. It is found that the model is capable of capturing the "size effect" and the "dividend yield effect," but is incapable of explaining the "book-to-market effect" and the "earnings-price ratio effect." Thus, it is concluded that a constant-beta multi-factor model will not be able to explain the cross-sectional variation in expected returns.

2.5 Economic Forces and the Stock Market

This paper tests whether innovations in macroeconomic variables are risks that are rewarded in the stock market. Financial theory suggests that the following macroeconomic variables should systematically affect stock market returns: the spread between long and short interest rates, expected and unexpected inflation, industrial production, and the spread between high and low grade bonds. It is found that these sources of risk are significantly priced. Furthermore, neither the market portfolio nor aggregate consumption is priced separately. Also the oil price risk is not separately rewarded in the stock market.

2.6 Macroeconomic factors do influence aggregate stock returns

This paper helps to find that the stock market returns are significantly correlated with inflation and money growth. The impact of real macroeconomic variables on aggregate equity returns has been difficult to establish, perhaps because their effects are neither linear nor time invariant. GARCH model of daily equity returns is used for estimation, where realized returns and their conditional volatility depend on 17 macro series announcements. Six factors are used: three nominal (CPI, PPI, and a Monetary Aggregate) and three real (Balance of Trade, Employment Report, and Housing Starts). Popular measures of overall economic activity, such as Industrial Production or GNP are not used.

Chapter 3: Methodology and Analytical Choices

3.1 Framework of Analysis

Dependent Variable: KSE 100 index Independent Variables (Factors): Consumer Price Index (measure of inflation) Money supply Interest Rates Exchange Rates Gross Domestic Product (measure of output) Potential Factors which haven't been incorporated: Business cycle/ Time Horizon Regional Market Return Political Events (corruption, Assassinations, law and order situation) Natural Disasters/ Calamities Gold Price Industrial Production Growth Rate Oil Price Shifts in yield curves Default risk premiums for bonds(measures investor confidence) Private placements January effect Bank mergers Announcement effects (mergers, monetary policy)

3.2 Statement of Research Hypothesis

Hypothesis 1:

Ho: Consumer Price Index has a significant impact on KSE 100 index. H1: Consumer Price Index does not have a significant impact on KSE 100 index.

Hypothesis 2:

Ho: Money supply has a significant impact on KSE 100 index. H1: Money supply does not have a significant impact on KSE 100 index.

Hypothesis 3:

Ho: Interest Rates have a significant impact on KSE 100 index. H1: Interest Rates do not have a significant impact on KSE 100 index.

Hypothesis 4:

Ho: Exchange rates have a significant impact on KSE 100 index. H1: Exchange rates do not have a significant impact on KSE 100 index.

Hypothesis 5:

Ho: GDP have a significant impact on KSE 100 index. H1: GDP do not have a significant impact on KSE 100 index.

3.3 Elements of Research Design

Type of Research: Exploratory research as the problem has not been clearly defined and the problem has multiple sensitivities attached to it. Study Setting: Natural as the data will be derived without any intervention from the natural environment. Nature of Data: Time Series Data.

Data Collection Preferences

Data is to be calculated for a period of 10 years so that there is no potential bias due to time horizon. Variable Definition Sources KSE 100 index It is a stock index acting as a benchmark to compare prices on the Karachi Stock Exchange (KSE) over a period of time State Bank of Pakistan Consumer Price Index It measures changes through time in the price level of consumer goods and services purchased by households Federal Bureau of Statistics Gross Domestic Product It is the market value of all final goods and services made within the borders of a country in a year CIA World Fact book Money Supply Money and quasi money comprise the sum of currency outside banks, demand deposits other than those of the central government, and the time, savings, and foreign currency deposits of resident sectors other than the central government. This definition is frequently called M2 International Financial Statistics Interest Rate It is the money market interest rate. State Bank of Pakistan Exchange Rate This entry provides the official value of a country's monetary unit at a given date or over a given period of time, as expressed in units of local currency per US dollar CIA World Fact book

3.5 Data Collection and Related Procedures

Exploratory research often relies on secondary sources such as reviewing available literature or data so secondary sources will be used to collect data. That includes research papers and literature reviews taken online from various electronic journals and databases and course books for theory purposes.

3.6 Statement of Analytical Approach and Methodology

Descriptive Statistics will be used initially and then covariance of dependent and independent variables will be seen to check for variables. When variables will be finalized, autocorrelation will be done to check for stationarity and then econometric modeling will be done by using multi regression model using the OLS to find out the hypothesis results.

3.7 Limitations

With Arbitrage Pricing Model it is difficult to identify the appropriate relevant factors as theory does not suggest any specific ones. Monthly data was not available for all variables so yearly had to be taken into account which might affect the analysis results.

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