Capital asset pricing model

CHAPTER ONE: Introduction


The Capital Asset pricing model, almost always known as CAPM. It is a set of prediction of the risk and return in modern financial economic. It is an economic model for valuing stocks, securities, derivatives and/assets with their respective risk and return.CAPM is based on idea that investors demand additional expected return (called the risk premium) if they are asked to accept additional risk. The model gives us clear-cut prediction of the relationship between the risk and the expected return of an asset. This relationship serves two vital functions. First, it set a benchmark rate of return for a investment and Second, model helps the investor to make an educated prediction about the expected return on asset.

CAMP starts with a requirement of investor point of view, investor likes the overall portfolio reward (expected return) and dislike overall portfolio risk (standard deviation of return). So as a result investors will invest in those stocks that have low risk and high rate of expected return. Although, those stocks which have lower risk will ask for a higher price.

Capital Asset Pricing Model (CAPM) is based on two factor portfolio analysis developed by Markowitz (1952). It is the typical risk and return model used by most annalists for their decision making. The fundamental concept of CAPM is that, investors are compensated for only that portion of risk which is not diversifiable. This non-diversifiable potion is called beta, to which expected returns are linked.1

The Sharp-Lintner-Black CAPM states that the expected return on an asset is proportional to its systematic risk measured by the beta. By Appling some assumptions, the CAPM is a linear function of a risk free rate, beta and the expected risk premium.

This is required for public and private funds evaluation and their decisions. The CAPM has been widely used for knowing the performance of managed funds and calculating the cost of capital. Implementation of the CAPM on emerging markets seems problematical. This is due to immaturity in these markets this included insider trading, prohibiting foreign capital, and high transaction costs, as well as data problems such as irregular trading. These assumptions are not as hard as they seem. The model has been tested in many emerging markets in the world including those in Asia, Latin America South East, Europe, and also the developed markets of the US, the UK and Australia. 1

There is small empirical support on the risk and return relationship and asset pricing tests in Pakistan. From the last five years the trading activity in the Karachi stock market had a mix trend. There was an increasing trend from 2004 to April,2008 and than market started declining its index point till December,2008 and after that the increasing trend till now October 2009.But an average its much batter than some other markets. Remittance of Pakistani workers' in the banking sectors, global ban on unofficial banking channels. This extra liquidity in the banks was spread as portfolio investment in stock market and the fall in interest rates are also made equity investment good looking. Increased in foreign exchange also added in this regard. 1

Overview of Karachi Stock Exchange

The Karachi Stock Exchange came into existence on 18th September 1947. It was later transformed and listed as a company limited by guarantee on 10th March 1949. At beginning 90 members were registered. However, six of them were acting as brokers and only five companies were listed with a Rs. 37 million paid up capital. The KSE is the main center of activity where 75-80% of current trading takes place.

KSE 100 index was started in November 1991 with a base of 1000 points.

In 2002, when the Karachi stock market was doing best in the world, the US Dow Jones and the European markets' indexes were at their lowest level in seven years. This was relatively more diversified market and opened for international investors in 1991, therefore this appeared to provide great potential for international diversification. The low correlation provides a hedge against the shock transfers from the developed markets and other emerging markets. The Karachi Stock Exchange's unique international portfolio implications and attractive capital gains make the study of risk return relationship an interesting task. It will be important for international investors to know the nature of risk return relationship and other factors explaining these high rates of returns in this growing market.

Near past years the Karachi stock market trading activity has increased significantly. The market was acknowledged the best performing stock market in the year 2002 in terms of the percentage raise in the market index.100 index of Karachi Stock Exchange has increased by 112.2 % during 2002. It was rose from 1145 on 1 September 1992 to 11342 on 28 April; it was an increase of approximately 990 %, which amounts to an annual gain of approximately 64%.

But from 2008 it start declining dramatically and it has lost the index from 15,274 to 5,865 indexes. But again in 2009 it showed a increasing trend and till 29 october it has gain KSE 100 index 9,169.00 points.

Over the past few years Securities and Exchange Commission of Pakistan has been taking measures to restore confidence of the investor - both foreign and domestic in the capital market of Pakistan. The SECP ensures that the market functions in a smooth and transparent manner and is also vigilantly observing the market. Its regulatory mechanisms aims to minimize elements of systematic risk and other possible defaults on the one hand and promotes institutional strengthening building of various segments of the capital market on the other. The SECP has been actively pursuing a reform agenda since 2001 for the capital market.

Choice of Subject

As I mentioned above, CAPM is truly a popular in the western financial world, so I believe there is a need to test the validity of CAPM under Pakistani Economic condition, since KSE is the key player in the Pakistani economy. By investigating the validity of the CAPM, I think the results are of interest for financial manager in Pakistan who is thinking about using (or already used) the CAPM partly in their decision.

Purpose of Study

This study is regarding the price of financial asset and would evaluate the Predictive applicability & efficiency of CAPM model with reference to Karachi Stock Exchange.

The main objectives are:

  • Whether the higher/lower risk will yield higher/lower expected rate of return.
  • Whether the expected rate of return is linearly related with the stock beta, i.e. its systematic risk.
  • Whether the non-systematic risk affect the portfolios' return,(CAPM predicts that only the systematic risk has the explanation power on the rate of return)

Scope of the study

This study emphasis on detail discussion on CAPM model and will use returns data Of 21 companies for period of 5 years From (Oct 2004 to Oct 2009) predictive Power of Capital Asset Pricing Model (CAPM).

Scheme of Study

CHAPTER ONE: Introduction

  • Short Introduction of CAPM
  • Short Introduction of KSE
  • Choice of Subject
  • Purpose of Study
  • Scope of the study
  • Scheme of report

CHAPTER TWO: Literature review

CHAPTER THREE: Methodology and Simple Selection

  • Sample selection
  • Data selection
  • Empirical method of CAPM testing

CHAPTER FOUR: Regression analysis and result

CHAPTER FIVE: Conclusion and Recommendation

CHAPTER SIX: References

CHAPTER TWO: Literature review


Theoretical discussion on CAPM:

The Capital Asset Pricing Model (CAPM) has a long history of theoretical and Empirical analysis. Several authors contributed toward the development of a model describing the pricing of Capital asset under condition of market equilibrium including William Sharp (1964), Micheal jenson(1972), Fisher Black(1972), Chen, Roll (1985), jack Treynor, Ferson, Kandel and Stambaugh (1987), Bollerslev, Engle and Woodridge (1988), Harvey (1989), Ng(1991), and Fama and French (1996).

From the past three decades mean variance efficient Capital Asset Pricing Models of Sharp Liner and Balck Have served as the corner stone of financial theory. Another important theory is the arbitrage pricing theory (APT) of Ross (1976) and The Fame French (1997), which is also based on similar institution as CAPM, but is much more general.

Portfolio theory

Portfolio theory was presented by Harry Mark Ovitz (Noble prize winner) in 1960s. While before this investors knew without any justification that it is smart to diversify (that is "don't putt all your eggs in one basket").

Mark Ovitz was the first among them who justify this concept that diversification in your investment will reduce the risk. he proved that the return on your portfolio is the weighted average return of the assets but the risk attach with a portfolio is not the weighted average risk of individual assets,it will be the less if there is no perfect positive correlation between the assets.

He was also the first, who introduced the concept of an "efficient portfolio". An efficient portfolio is that one which has the smallest risk for a given level of expected return. Or at a given level of risk it has Largest expected return.

The process for finding an optimal correlation coefficient portfolio commonly uses historical measure for

  1. Returns
  2. Risk
  3. Correlation coefficients.

For each asset which is included in the portfolio or series of portfolios generally have unique level of risk and return. They also act differently, at the same time value of some assets increasing and the value of another may be decreasing or not decreasing as much as the other increased and vise versa.

The method which use for this incident is called the correlation coefficient.

CAPM; Sharp Linter Version

The sharp linter model extension of one period mean variance portfolio model of mark Ovitz (1959) and Tobin (1958)which in turn are built on the expected utility model of Von Neumann and Morgenstem (1953) The Mark- Ovitz's mean -variance analysis are considered with how the investor should allocate their wealth among the variance assets available in the market.

Capital Asset Pricing Model (CAPM) is based on two factor portfolio analysis developed by William Sharpe (1964). It is the typical risk and return model used by most annalists for their decision making. The fundamental concept of CAPM is that, investors are compensated for only that portion of risk which is not diversifiable. This non-diversifiable potion is called beta to which expected returns are linked. 3

This model was developed by William Sharpe (1964), John Linter (1965) and Jan Mossin (1966) In the equation form model can be expressed as follows:

E (R i) =Rf+ i [E (R M) -R f]............................................. (1)

Where, E (R i) = expected rate of return on ith asset

R f = risk free rate of return

E (R M) = expected rate of return on market portfolio

i = estimate of beta for the ith stock, i.e. the non diversifiable risk for ith asset.

Equation (1) describes the relation between expected rate of return on market portfolio & expected rate of return on asset i, its also known as Security Market Line (SML). If CAPM is valid than all stocks will lie in a straight line in the E (R i), i space, called SML. The SML implies that the return is a linearly increasing function of risk. However, the market risk is only factor which affects the return. The risk which is non diversifiable also known as the market risk and also referred as "systematic risk". The beta of a stock shows that how much market risk attaches with a particular stock, i.e. the sensitivity of an asset with respect to market portfolio. Stability of is very significant, because almost all investment decisions s play an important role in risk measurement & risk management. Now if s are not stable over time then it loses its significances. If a stock has zero betas the expected return of that stock should be equal to risk free asset (Rf).

Equation (1) can be written as

E (R i) - R f = i [E (R M) -R f].................. (2)

E (R i) = i [E (R M)........................... (3)

Where (Ri) is excess return on assets i and the Rm is the excess return on market portfolio over the risk free. Equation (2) show the expected risk premium is equal to its beta multiplied by the expected risk premium.

CAPM is a relationship between expected return on an individual stock and the market portfolio. There are basically two equilibrium relationships has been explained by the theory.

Capital Market Line (CML)

Capital market line explains the relation between expected risk and return for efficient portfolios. It's mean that E(R) =Risk free rate + risk premium

T bill rate is used as a risk free rate, while risk premium is determined by the;

  1. portfolio risk (s)
  2. current market risk premium per unit of market risk

The expected return for the efficient portfolio would be:

E (Rp) = sp (E (Rm) - Rf/ sm


E(Rp) is expected return of market

Rf is risk free rate

Rm is market portfolio return

sp is the standard deviation of the portfolio return

sm is standard deviation of the market portfolio

Only efficient portfolio having of risk-free asset and market portfolio lies on Capital market Line.

Always Capital market line will be upward slope because the risk must always be positive and risk averse investors will only assume risk if they are dually compensated.

Security Market Line (SML)

Security market line shows a picture of the relationship between risk and expected rate of return. Beta is plots on X-axis and expected return is plotted on Y-axis.

If a security gives a higher actual return than the required rate of return always will be above the SML and this security will consider under value.

Investor can expect the return in terms of a risk free rate plus relative risk of a security or portfolio.

The SML with respect to security, it can be written as;

E (R i) =Rf+ i [E (R M) -R f] ................... (5)


i = Cov (Ri, Rm) / Var(Rm)

Where Cov (Ri, Rm) is the correlation between security return and market portfolio return.

The beta can be interpreted as, the amount of non-diversifiable risk, inherent in the security, relative to the risk of the market portfolio.

Equation (5) is the version of CAPM.

Some assumptions are employed to develop CAPM can be summarized as follows:

  • Investors are risk averse and they have a like expected return but dislike risk.
  • Investors' investment decision is based on expected rate of return & the variation of the asset return. i.e. assumptions of two-parameter utility function.
  • Investors want to keep themselves a portfolio that lies along the efficient frontier. (That is also known as diversification frontier)
  • There are risk free asset & investors can lend or borrow at that risk free rate.
  • Investors are price takers and have the same expectation about the asset return, i.e., they cannot influence prices.
  • Aim to maximize economic utility.
  • Trading of stocks without transaction or taxation costs. Its means, there are no costs involved in diversification & there is no differential tax treatment of capital gain & ordinary income.
  • Assume all information is at the same time available to all investors.
  • Perfect Competitive Markets, all security prices are fully reflect all the changes in future expected inflation.

Even though, some of the assumptions are not practical, that's why analysts are saying that CAPM is a one of the most challenging topics in financial economics.


The standard methodology in estimating the CAPM is the two-pass regression method. Some may criticize this method but it is fact that it is used as the standard in the current Financial economy. This empirical method was developed by Black, Jenson and Scholes (1972) and refined by Fama and Macbeth (1973). The fama-macbeth approach properly adapted in the choice of empirical asset pricing method. It must be understood that the based on the Ross Critique (1977), a reliable test of CAPM is not a possibility. Netherless; the empirical approach draw here to prove a numerical evaluation of the usefulness of a particular CAPM formulation. For now we must keep in mind that the empirical content of the Sharpe-Liner Version of the CAPM is the following;

Rit - Rft = s + itx +eit, Where s =0, x=Rm - Rf ...... (1a)

As roll (1976) has shown in equation (1a) will hold empirically, if and only if the proxy selected to represent the market portfolio is on the portfolio frontier. Where the proxy is on the frontier is evaluated ex post, meaning that a frontier is built from the actual observation treated in the testing the model and that the location of the realized mean standard deviation of the proxy return relative to the frontier is considered. Obviously, if the proxy is not close to being efficient equation (1a) will not hold approximately.

The two-pas regression methodology concentrate on the "testable" implications in equation (1a).In the first "pass" time series estimates individual asset betas. In the second "pass" these beta estimates are employed in a cross sectional regression to obtain parameter x, which are averaged over time. These parameter averages are finally compared statistically to their predicted value of Rm-Rf respectively. This method in its simplest version is employed in Markowitz and Shapiro (1986) and a series of empirical issues that is carry out more appropriately by Fama and Macbeth (1973).

I next outline step by step the gist of Fama and Macbeth's (1973) approach and indicate where it significant from the Black, Jensen and Scholes (1972) version.

As regard the test of CAPM on portfolio, Fama and Macbeth have performed the classical test. The study estimated beta from time series regression over the monthly data for the period 1935-1968 and then performed a cross sectional regression for each month to compute the risk premium. Fama and Macbeth have formed twenty portfolios of assets. Their results show that the coefficient of the beta is statistically significant and its value has remained small for many sub-periods. Fama and Macbeth have validated the CAPM on all stocks listed on NYSE during 1935 to 1968, while Tinic and west (1984) who had used same NYSE data for the period 1935 to 1982 have founded contrary evidence.

Sauer and Murphy (1992) have conformed that CAPM is the best model for describing the German Stock Market data. In a more detailed study Hawawini (1993) could not conformed the validity of CAPM in the equity market in Belgium, Canada, France, Japan, UK and USA. The other studies which have been tested CAPM for different countries include Lau et al (1975) for Tokyo Stock exchange, Sareewiwathana and Malone (1985) for Thailand Stock exchange and Bark (1991) for Korean Stock Market.

In an early work on conditional CAPM fame and Macbeth (1974) expended CAPM to multi-period analysis but empirical test indicate poor performance of the model.

Harvey (1989) conduct test of conditional CAPM that allow for both time varying expected returns and conditional co-variances and they use generalized method of moments (GMM) as estimation technique.

Person and Harvey (1991, 1993 and 1999) in their studies of US stocks and bond returns, show that the premium in the time variation for beta risk is more important than the changes in the betas themselves. This is because equity risk premiums are found to vary with market conditions and business cycles.

Sehwert (1989) attributes differential risk premium between up and down market due to varying systematic risk over the business cycle. Jagannathan and Wang (1996) have shown that above 50 percent cross sectional variation in average return is expected by conditional CAPM. The study by Jagannathan and Wang also find empirical support for conditional CAPM when betas and expected return are allowed to vary over time assuming that CAPM hold period by period.

Some recent studies about the empirical evidence of CAPM.

Grigoris Michailidis, Stavros Tsopoglou, Demetrios Papanastasiou (2006) tested the Capital Asset Pricing Model (CAPM) for the Greek stock market. The findings of this article were not supportive of the theory's basic statement that higher risk (beta) is associated with higher levels of return. The tests were carrying out to explore the relationship between return and betas support the hypothesis that the expected return-beta relationship is not non-linear. Additionally, this paper explore whether the CAPM effectively covers all-important facts of returns or not. For that reason the study includes the variance of stocks as an descriptive variable. The results showed that risk has no effect on the expected returns of portfolios.

Attiya Y. Javid & Eatzaz Ahmad (2008) did an effort to empirically investigate the risk and return relationship of individual stocks traded at KSE (Karachi Stock Exchange) the main equity market in Pakistan. The empirical findings of this study did not support the standard CAPM model in Pakistani equity market. The key term of CAPM, i.e. there is a positive trade-off between risk and returnis rejected and residual risk plays some part in pricing risky assets.

In September 2008 Jonali Sarma & Pranita Sarmah did an empirically study the stability of stock s using chow test on Bombay stock exchange and the result investigates that betas are unstable over time.

In 2007Sromon Das tested the constancy of betas for individual stocks using two econometric tests on NSE Nifty over a period of time from (February 1999 to September 2007), and took 3 sub-periods as sample period, two bullish and one bearish. by using the regression Under one method (time as a variable) the researcher came to know that 85% of the stocks had a constant beta, while applying the second regression method (using dummy variables) 65% of the stocks had constant betas.5

CHAPTER THREE: Methodology and Simple Selection


The econometric analysis to be performed in the study is based on the data of 10 selected firms listed on the Karachi stock exchange, one of the important stock exchanges of Pakistan & 10 important industry indices published by BSE for the period from November 2004 to October 2009. This particular time period has chosen because it is characterized by historically high & low values of the weighted proxy market indices. These 10 companies are selected out of 30 companies represented in the SENSEX according to the BSE listing at April 10, 2000. In selecting the firms two criteria were used:

Companies had represented in SENSEX at the day April 10, 2000.

Almost all the important sectors are covered in data, namely information technology, FMCG, oil & gas, finance & Healthcare.

Sample selection

The study covers the period from November 1, 2004 to October 31, 2009. The selection of stock was made from the KSE 100 listed companies which were presented at October 28, 2009. I selected those companies for my research which have more then 1 % weight in KSE 100 index. I found only 21 companies which have more than 1% weight in KSE 100 index.

The study used daily share prices data for the sample of KSE 100 index from November 1, 2004 to October 31, 2009.

  1. Share prices of selected companies stocks (November 1, 2004 to October 31, 2009).
  2. KSE 100 index (November 1, 2004 to October 31, 2009).
  3. A risk free rate

In order to obtain better estimates of the value of beta, I used the daily stock return. The reason for choosing the daily returns is that return calculated using a long time period (i.e. the monthly or weekly) might changes of beta. This would create biases in beta estimation over the examined period.

T bill rate has taken as a rate of risk free rate. That is the average annual T-bill rates are taken and then divided by 12 to get the monthly T-bill rates.

Empirical testing of Capital Asset Pricing Model

The regression analysis used on monthly average Stock prices and KSE 100 index for the period November 1, 2004 to October 31, 2009.

The following steps involved for estimation;

  1. The average monthly stock prices and market indexes are averagely summarized together to find out the return (Capital gain) and market condition.
  2. Regression analysis is used to check the predictive power of CAPM on the Ri and Rm values for all firms separately and than on the average value of all firms.

Hypothesis and variables

Null Hypothesis

Return on market portfolio is not a significant determinant for predicting individual; stock return.

Alternate Hypothesis

Return on market portfolio is a significant determinant for predicting individual; stock return.

Independent Variable

Value on market return is taken as Independent Variable is (x)

Dependent Variable

Value of individual stocks returns are considered to be dependent variable. That is (Y).

Analysis Technique

Our analytical tool is regression analysis, using time series data of average monthly stock returns and KSE 100 index returns for five years.

Calculation of (Ri-Rf)

Ri-Rf indicates return for individual asset.

For this purpose, I Calculated the average actual monthly returns for each stock from the daily closing share prices and then subtracted the corresponding monthly Risk free rate(T bill rate) from the corresponding average actual monthly return of the securities for the whole Five years.

Calculation of (Rm-Rf)

I calculated the return on market portfolio by taking the average monthly return of market index then I deducted risk free rate from their respected each Rm monthly value.

Calculation of Beta

Beta is calculated for from the average monthly return for 21 companies individually and as a whole for 21 companies in one row through using Ms Excel.

Though I got 22 betas for five year interval.

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