Portfolio Theory and the Capital Asset Pricing Model

Ample work has been done on pricing asset due to its vital importance in finance literature. Several researches have been conducted in the area of pricing stock prices Harry Markowitz (1952) gave portfolio theory in his research “portfolio selection”, Sharpe (1964) and Lintner (1965) introduced capital asset pricing model, Sharpe was awarded with noble prize for his work on capital asset pricing model, Stephen A. Ross (1976) came up with arbitrage pricing theory which is much flexible in comparison to portfolio theory and capital asset pricing model because it can incorporate many factors for the purpose of asset pricing . In this chapter of study some theories related to asset pricing and researches conducted based on those theories have been discussed.

PORTFOLIO THEORY

Harry Markowitz (1952, 1959 portfolio selection) introduced the model for portfolio. Markowitz stated two stages of portfolio selection he said that first stage initiates from examination and practice and finishes with views about the potential performance of available securities. The second stage initiates from the relevant views about the potential performance of securities and finishes at the selection of portfolio. Focus of markowitz study was the second stage of portfolio selection. Model developed by markowitz works on the mechanism of expected rate of return and expected risk of portfolio. Markowitz Proved that variance of the rate of return is sensible measure of risk. Markowitz also proposed the formula for the purpose of calculating risk. Markowitz demonstrated that how to diversify efficiently to minimize the total risk of portfolio in order to maximize returns.

Ray ball and Philip brown (1969) conducted study on “portfolio theory and accounting”. The purpose of this study was to prove that portfolio theory can be implemented on several areas of accounting such as capital budgeting, divisional planning and reporting and external reporting. According to author, the application of portfolio theory on capital budgeting has vital role because the rate of return is dependant on the risk associated with the project so the same rate of return on every projects can not be applied. Author beliefs that portfolio theory has several applications on divisional planning and reporting because different rates of return are required for the different divisions so the portfolio theory applies that rate of return in analyzing divisional performance should be according to the extent of volatility against the different economic effects. As far as question of external reporting is concerned it is also connected to portfolio theory because the prediction about the risk and future performance of firm is conducted through the current and past information.

Lindon J. Robinson and John R. Brake (1979) investigated the implementation of portfolio theory on farmer and lender behavior. This study evaluate the formation of portfolio theory and its later application as a farm-planning model under uncertainty. As a monetary model, the assumptions and limitations seem satisfactory: production is linear, asset selections are commonly dividable, and the inconsistency is on the price side. But as a farm-planning instrument, portfolio models appear to be less applicable because production is not linear, asset selections are rarely totally dividable, and inconsistency on the output side is at least as significant as inconsistency on the price side. Yet, as an experimental instrument, it seems better compared to earlier well-liked linear programming models.

This study also evaluated concisely more than a few uses of portfolio theory in agricultural economics. They attended to explain portfolio selections along expected value frontiers and permitted costless changeover from one portfolio to another and from one asset to another. Author disputed on this generalization which pays no attention to a necessary consideration of the investment (chq). The two ideas are same and when their effects are included in a portfolio model, they considerably decrease the economic inducement for portfolio review. Other addition to portfolio theory which author suggested was:

1. Incorporating the value of non deterministic returns in meeting non deterministic cash needs (liquidity risk considerations)
2. Value of firm wealth in generating credit should be accounted and incorporating as a cost.

Finally, authors noticed that unused credit was valuable to a firm, but they found no simple approach to find out its value or best favorable use.

Paul L. McEntire (1984) the theory of independent asset. The notion of the generalized harmonic mean was brought in and was revealed to be the analogue to the risk free rate of return for issues without a risk-free asset. After that, a new ordering theorem was confirmed for portfolio issues with independent assets showing that the mean value of any asset incorporated in an most favorable portfolio is more than or equal to the mean value of any asset which is not incorporated. This theorem is an expansion of Samuelson’s findings, which shows that the asset with the highest mean value is always incorporated.

The other major findings involve the no dependency from unrelated alternatives property.

A utility function satisfies this property if, for any three independent assets A, B and C:

Harry markowitz (1991) discussed the foundation of portfolio theory. He wrote that he got the concept of portfolio theory while he was studying the theory of investment value by Williams. According to Williams theory price of stocks can be calculated by getting the present value of future inflows of dividends. Since the dividends are not certain so markowitz considered the value of stock calculated by future inflows of dividends as an expected value. He added that if investors are looking for the expected value of stocks so they must be also looking for the expected value of portfolio as well in order to maximize their return and minimize risk. Markowitz said that it was clear that investors were interested in risk and return. He selected variance of the portfolio as a measure of risk.

Being an economic student he thought that investor would select the portfolio where he could earn maximum/optimal return at a particular variance from different portfolios.

With the passage of time he kept on adding some details into this idea of portfolio selection. He acknowledges the efforts of sharpe, blume, kings and Rosenberg in clarifying the problem of covariance calculation.

Then markowitz raised the question that if mean and variances were the sufficient criteria for the purpose of portfolio selection?

In order to answer this question he took the support from the theory of rational choice under uncertainty and concluded that investor should be concerned about maximizing returns. In addition in order to answer the raised question he quoted the results of various researches conducted and concluded that the theory of rational choice under uncertainty can be still helpful to give more approaches. It can give additional satisfactoriness of mean and variance or any other useful measures as criteria.

On the basis of Harry Markovitz (1959) portfolio theory the well known asset pricing model called CAPM was built. The portfolio model gives a numerical state, if asset’s mean-variance are given then the portfolio having minimum risk and maximum return is called efficient portfolio. The CAPM makes this numerical statement a testable calculation about the association between risk and expected return by recognizing a portfolio that must be efficient if asset prices are to clear the market of all assets.

CAPITAL ASSET PRICING MODEL

William sharpe (1964) and john lintner (1965) gave very first theory of asset pricing known as CAPM (Capital Asset Pricing Theory).CAPM is the expansion of portfolio theory which allows the pricing of all risky assets. Sharpe (1964) and Lintner (1965) put two more assumptions in portfolio theory in order to recognize mean-variance efficient portfolio First assumption is “Investor agrees on joint distribution of asset returns from t-1 to t. and The second assumption is that there is borrowing and lending at a riskfree rate, which is the same for all investors and does not depend on the amount borrowed or lent.

According to this theory, beta employed to calculate stock market volatility should indicate the investors’ calculation of stock’s future in relation to market risk. For the purpose of estimating betas historical data is used. If there is a consistency in historical betas then investor can use historical betas for estimating future volatility.

Long time has not been passed that two problems were noticed.

1. Estimates of beta individual securities/asset are not consistent which result in measurement error problem when used to describe average returns.
2. The regression residuals have common sources of variation, such as industry effects in average returns. Positive correlation in the residuals produces downward bias in the usual ordinary least squares estimates of the standard errors of the cross-section regression slopes.

As far as the question of beta steadiness is concerned. Robert levy, Marshall blume(1970), Black, Jensen, and Scholes (1972), and many others have conducted studies on this question. Robert levy estimated betas for both individual securities and portfolios and found no consistency in betas of individual stock on the other hand betas of portfolios were found consistent. The study of blume and others also supports these findings.

Fama and MacBeth (1973) came up with the solution for the problem of correlation of the residuals in cross-section regression. They suggested that rather than estimating a single cross section regression of average monthly returns of betas, month by month cross-section regressions of monthly returns should be estimated.

Basu (1977) in his study “Investment Performance of Common Stocks in Relation to Their Price Earnings Ratios: A Test of the Efficient Market Hypothesis.” Confirmed that when common stocks are arranged in the basis of price earning ratios. Returns on stocks having high price earning ratios are greater then the returns estimated by CAPM.

Banz (1981) investigated “The Relationship between Return and Market Value of Common Stocks.” Banz (1981) incorporated firm size effect in his study and confirmed that when stocks are arranged on the basis of market capitalization. Average returns on stocks having little market capitalization is greater than the returns estimated by the CAPM.

Bhandari (1988) conducted study on “Debt/Equity Ratio and Expected Common Stock Returns: Empirical Evidence.” Purpose of study was to incorporate debt/equity ratio for the calculation of common stock returns and confirmed that there is the relation between debt to equity ratio and expected common stock returns. Study verified that common stocks having high debt to equity ratios have very high returns in comparison to market betas.

Statsman (1980) worked on “Book Values and Stock Returns.” Purpose of statsman (1980) study was to incorporate book values of firms in order to estimate returns. Statsman (1980) found the relationship between book values and stock returns. Study confirmed positive relation between book value and stock returns which means that firms having high book value were found having high means of returns that are not described by the market beta.

Rosenberg, Reid, and Lanstein (1985) conducted study on “Persuasive Evidence of Market Inefficiency.” Purpose of study was to incorporate book values of firms in order to estimate returns. Rosenberg, Reid, and Lanstein (1985) found the relationship between book values and stock returns. Study confirmed positive relation between book value and stock returns which means that firms having high book value were found having high means of returns that are not described by the market beta. Results of Rosenberg, Reid, and Lanstein (1985) confirm the Statmans (1980) findings.

Fama and French (1992) in their study on “The cross-section of expected stock returns” Bring up to date and create the proof on the empirical break down of CAPM. Fama and French (1992) proved that market beta alone cannot predict the returns there are some other variables as well such as book to market, debt-equity, earning price ratios and size which add explanatory power in predicting returns when cross-section regression is used. Findings of Fama and French (1992) established the evidence supporting Reinganum, 1981, Stambaugh, 1982; Lakonishok and Shapiro, 1986 that the researches conducted after 1980s on empirical success of CAPM have not shown significant association between average returns and common stocks betas.

Kothari, Shanken, and Sloan (1995) attempted to defend the Sharpe – Lintner CAPM by showing their disagreement on non significant relation between average return. According to Kothari, Shanken, and Sloan (1995) this non significant explanatory power of beta in explaining stock returns is the matter of chance. On the other hand various studies conducted by incorporating various variables proving significant explanatory power of those variables such as market to book, price earning ratio etc give birth to doubts in the study of Kothari, Shanken, and Sloan (1995).

Eugene F. Fama and Kenneth R. French (2004) argued on empirical success of CAPM. They concluded that edition of CAPM introduced by Sharpe (1964) and lintner (1965) has never proved its success empirically. Though, in early studies it has shown some success where but in later on in 1970s, it was revealed by researchers that other variables such as size, several price ratios etc add explanatory power to average return given by beta. Author of this study suggested that CAPM can be helpful to build up the fundamental concepts of portfolio theory and asset pricing but at the same time they warn that even though it’s simple, but the empirical problems associated with this model makes its application invalid.

CAPM is limited to single factor only, which means that CAPM only takes market beta coefficient into account for the purpose of calculating returns. In fact stock return is a function of more than one factor. In order to overcome the limitation of CAPM, Stephen A. Ross (1976) came up with the approach called Arbitrage Pricing Theory (APT).

ARBRITRAGE PRICING THEORY (APT)

A. Ross (1976) came up with the approach called Arbitrage Pricing Theory (APT). APT can employee any figure of factor, which makes the return the function of more than one factor.

The benefit of APT is that it allows more than a few economic factors to predict stock returns on the other hand CAPM considers only one factor which is instability of stock against market portfolio.

At the same time APT has some disadvantages as well such as it does not give clear direction regarding the number and kind of factors influence stock returns. It has not been known yet about the exact factors which predict the stock return.

Many studies have been conducted on the basis of APT by using various macroeconomic factors {John Kraft and Arthur Kraft (1976-1977), Chen, Roll, and. Ross (1986), Pearce and Roley (1985), Prem C. Jain (Apr, 1988), Jorion (Sep, 1991), Bae and Duvall (1996), Poitras (Jan, 2004), Kandir (2008)} in order to find relationship between stock prices or returns and macro economic factors.

John Kraft and Arthur Kraft (1976-1977) conducted a study on determinants of stock prices they tested causal relationship between some determinants of stock prices and stock prices. They used money supply, rate of change in money supply, corporate interest rate and measure of risk as determinants of stock prices they used regression analysis to analyze data and found that there are empirical relations between stock prices and these variables further the test for the presence of causality was conducted and it was found that future prices of stock are not significant in explaining these determinants.

Very popular study conducted on economic forces and stock market was conducted by Nai-Fu Chen, Richard Roll, and Stephen A. Ross (1986) in order to determine the influence of economic variables on stock prices. Influence of Inflation, T-Bill rates, Industrial production, long term government bond return , baa low grade bond return, consumption growth rate and oil prices was tested on stock prices. And it was found that several of these variables had significant influence on expected stock returns. Especially when the variables such as industrial production, change in risk premium, and change in yield curve and inflation were highly volatile.

Douglas K. Pearce and V. Vance Roley (1985) examined the response of daily stock prices against the announcement of money supply, inflation real economic activity and discount rate. Their assumption was that the only surprises and unexpected announcements moves the stock prices. They used regression analysis to analyze the data and they found the significant relation between surprises related to monetary policy and stock prices , limited evidence was found about the relationship between stock prices and no evidence were found supporting relationship between real activity surprises and stock prices.

Prem C. Jain (Apr, 1988) investigated the hourly response of stock prices and hourly trading volume against the various factors such as money supply, consumer price index (CPI), producer price index, industrial production and unemployment rate.

In this study response of trading volume has also been examined against these variables which is something not done in prior studies. it was revealed by the study that CPI and money supply have significant negative relation with stock prices. Findings of the study also reveled that the impact of the announcement of these variables was for the period of one hour or so and it was found that trading volume has no relation with the variables used in the study which opposes the belief of different analytical articles that economic variables have impact on trading volume.

Philip Jorion (Sep, 1991) analyzed the pricing of exchange rate risk in the stock market. In this study two models have been have been deliberated.

Two Factor models that takes market and exchange rate into account, which can be translated as an examination of CAPM in against the substitute that exchange rate factor is not diversifiable.

Another model is the extension of Chen, Roll, and Ross (1986) approach with six factors by adding exchange rate as an additional factor.

Data from January 1971 because it is the year from which exchange rates started floating, till December 1987.

Market returns, industrial production, expected inflation, unexpected inflation, risk premium series, and exchange rate series are the variables included in the study.

Data has been analyzed in two steps.

Ordinary least square

Maximum likelihood procedure.

Findings of the study indicate that there was very minor evidence (around 0.2 percent) that investor needs to compensate for exchange rate risk.

Sung C. Bae and Gregory J. Duvall (1996) attempted to develop multi-index model for US firms operating in the military aerospace industry. They included six variables, including both market and industry, in their study in order to see the affect of these variables on stock returns of selected industry for the ten year from January 1982 to December 1991. Economic/market factors included in study were S&P-500, inflation, risk free rate of return and industrial production index. Two variables related to selected industry (aerospace) were national logarithm of monthly aircraft shipment and natural logarithm of purchases of aircraft. They used multivariate regression to analyze the data. It was found that two variables i.e. S&P-500 index and department of defense expenditures are positively related to stock returns. But the other variables i.e. inflation risk free rate of return, industrial production and natural log of aircraft shipments were found to have insignificant effect on stock returns. Additional regression analysis was also conducted in order to confirm the findings.

Charles M. Jones and Gautam Kaul (1996) examined the response of stock market oil shocks. Purpose of this study was to find if current and future changes in real cash flows and/or changes in expected return play any role in explaining the reaction of international stock market to oil surprises. Study found that reaction of stock prices to oil surprises in era prior to war can be explained completely by real cash flows.

Abhay Pethe and Ajit Karnik (2000) conducted research in Indian stock market. Purpose of study was to examine the impact of macro economic variables on stock prices variables used to predict stock prices were industrial production index, broad money supply, narrow money supply, prime money supply and exchange rate against the dollar. According to the findings of this study there is no long run relation ship between macro economic variables and stock prices. Authors commented that stock markets are demand driven.

Liam A. Gallagher and Mark P. Taylor (2002) attempted to find the temporary and permanent component of stock prices. Purpose of this study was to investigate the contact between macroeconomic surprises and response of stock price movements. Findings of this study suggest that aggregate demand surprises do not have long lasting effect on stock prices on the other hand supply surprises have permanent effect on stock prices in addition; this study revealed that stock prices are not random walks; temporarily impact on stock prices is due to aggregate demand surprises.

Mansor H. Ibrahim and Hassanuddeen Aziz (2003) examined the impact of macroeconomic variables on the equity market of Malaysia. This study investigates underlying relations and active connections between the Malaysian equity market and macroeconomic variables. Macroeconomic variables employed this study were exchange rate against dollar, price level, money supply and industrial. Co integration and VARs was used to discover the long-run relationship and short-run connections among the variables. Data used in the study was the period of 22 years. Findings of this study revealed that two variables i.e. price level and industrial production. Exchange rate was found negatively related to stock prices. As far as money supply is concerned it was found that money supply was positively relates to stock prices in short run but negatively related in long run.

Marc Poitras (Jan, 2004) conducted study on impact of The Impact of Macroeconomic Announcements on Stock Prices by using the consumer price index, the producer price index, the unemployment rate, total no farm employment, the index of industrial production, the U.S. trade balance on goods and services, the Ml money stock, and the Federal Reserve’s discount rate as the predictors.. This study basically is a re-examination of McQueen and Roley (1993) study by updating data by ten years. This study finds that the relationship which exists among macro economic variables and stock prices is so weak that it cannot be proved statistically significant. Only 2% variation was found in stock prices against the macro economic variables used in study. The finding of this study is supporting the findings of earlier studies.

Andreas G. Merikas (2006) conducted study on stock prices response to real economic variables in Germany. This research was conducted with the objective to re-examine the hypothesis of Fama that the relation between stock prices and inflation is negative and this negative relation represents the positive effect of variables on stock. It deals with two Problems first, is to find out if there is any association existing between real and financial segment, secondly if there is any relation than what kind of relation it is . Analysis was done by using data up to 40 years of German market. The findings shows that employment growth is inversely related to stocks in Germany which means that employment growth has negative impact on stocks and effects positively inflation. The fact behind this finding is that employment growth predicts inflation which is likely to wear away firm’s earnings. While discussing the limitations of research author identified that Germany’s economy is largest among all other countries in European Union; the results propose that under the period of investigation, the economy was operating near to its potential point of production and this has inference for policy making. It would be interesting if the data was used on quarterly basis because by doing so it would be possible to test the unification.

Serkan Yilmaz Kandir (2008) conducted a study to examine the effect of macroeconomic variables on stock returns of Turkey. Growth rate of industrial production index, change in consumer price index, growth rate of narrowly defined money supply, and change in change in exchange rate, interest rate, growth rate of crude oil price and return on the MSCI world equity index were the variables used in this study. Only non-financial companies were included in this study and this study was based on portfolios of stocks rather than single stock. For the purpose of making portfolio companies which fulfill the following criteria were included in study:

• market equity
• book to market equity
• earning to price equity
• leverage ratio

Multiple regression analysis was used to analyze the relation between macro economic variables and portfolio stock returns. It was found that exchange rate, interest rate and world market returns are significant in all portfolios returns, inflation effects only three

Portfolios out of twelve portfolios and industrial production, money supply, oil prices do not show any significant effect on stock returns.

Ming-Hua Liu (2008) analyzed the long run relation between macro economic variables and Chinese stock market by using hetroscedastic co integration. Macroeconomic variables used in this study were interest rate, exchange rate, inflation, industrial production and money supply. Purpose of this study was to find this relation by considering the problem of hetroscedasticity. Findings of this study show the existence of relationship between macro economic variables and stock prices in extremely speculative market of china. Moreover, thorough analysis suggests that performance of Chinese stock market shows positive relation to these macroeconomic variables in long run. While discussing the implication of this study authors identified that Chinese economy is likely to perform strongly in future so this study can be beneficial for the investors for the purpose of earning better returns and diversify portfolio. Authors added that this study has contributed in two forms. (1) It has been done for the first time in Chinese market to investigate the long run relation between macro economic variables and stock prices. (2) Problem of hetroscedasticity has been taken under consideration while finding the relationship so this study also addresses the time varying uncertainity.

Recent study has been conducted by M. Shabri Abd. Majid and Rosylin Mohd Yusof (2009) on the long run relationships between islamic stock prices and macro economic variables. Objective of this study was to find the degree to which Islamic stock prices of Malaysia is affected from macro economic variables. Variables incorporated in this study are exchange rate, money supply, Treasury bill and federal fund rate. Findings of the study suggest that these variables are appropriate targets for government for the purpose of Stabilizing Islamic stock markets. Moreover, findings suggest that when interest rate is increased weather it is Treasury bill rate or federal fund rate, encourages Muslim investors to buy shariah based stocks which result in appreciation in the prices of Islamic stocks. It is also found by the authors that changes in both of the policies i.e. local monetary and US monetary policy have significant direct relationship with Islamic stock prices.

Charles K.D. Adjasi (2009) worked in the same area i.e. macroeconomic variables and stock. Their purpose was to analyze the response of African stock market, such as Ghana, to macroeconomic uncertainty. Analysis was conducted in two steps (1) univariate models for each macroeconomic variables i.e. cocoa price, gold price, oil price, interest rate, money supply, exchange rate and inflation, was estimated on the basis of EGARCH.

(2) Instability impact of macroeconomic variables on stock prices was estimated in second step. Findings discovered that the high uncertainty in interest rates and cocoa rate results in increasing uncertainty in stock prices, while high uncertainty in money supply, oil price and gold price result in decreasing uncertainty in stock prices.

Husam Rjoub, Turgut Tugarsoy and Nil Gunsel (2009) investigated the effects of macroeconomic factors on stock returns: Istanbul Stock Market. The objective of this study was to scrutinize the performance of the arbitrage pricing theory (APT) in the Istanbul Stock Exchange (ISE). Data used in study was from January 2001 to September 2005 on a monthly basis. Variables investigated in this study were unanticipated inflation, and unemployment rate. OLS technique was used for the purpose of data analysis. Findings of the study suggest that there is presence of differences between market portfolios. Serial correlation through Durban Watson has been discussed by authors no serial correlation was found in ten from thirteen. This study revealed that there is a large dissimilarity between market portfolios in response to macroeconomic variables because of the variation in R2. No evidence for effect of these variables on stock returns of remaining portfolios was found. Unanticipated inflation was found significant in seven portfolios, risk premium in three portfolio term structure in one and money supply in two, and exchange rate and unemployment rate was not found significant in any of the portfolios.

Khaled Hussainey and Le Khanh Ngoc (2009) examined the impact of macroeconomic variables on Vietnamese stock price. Variables used in this study were interest rate and industrial production. Paper investigated the effect of US macroeconomic variables on Vietnamese stock prices. Monthly time series data of eight years period was used in the analysis. Findings of this study explored that there was a significant relation between macro economic variables (interest rate and industrial production) and stock prices. It is claimed in this study that it is the first evidence ever in Vietnam to have association among three sectors i.e. money market, domestic production and stock market. Moreover, it was also revealed that U.S macroeconomic indicators are significantly related to stock prices of Vietnam. While discussing the contribution of this study in literature authors believe that it is the first of its kind study conducted in Vietnam. Previous studies have focused on developed countries but it is for the first time that impact of macroeconomic variables on stock prices tested in Vietnam.

This study is being conducted to examine the daily response of stock prices of sugar and allied industries of Pakistan against various market factors. The study consists of four market variables which are likely to affect the stock prices. Study variable is stock price which is represented by (p) and predictors are Inflation which is represented by CPI, Risk free rate which is represented by RFR, Karachi stock exchange 100-index which is represented by KSE-100, and exchange rates which is represented by ER.