Asset Pricing Model

A Test of Asset Pricing Model: Developing

Country (Bangladesh) perspective

Submitted To:

Mr. Mohammed Sawkat Hossain

Assistant Professor & Course teacher

FNB 501: QTF

Submitted by:

Name of the members Student ID.

Lamia Nuzhat Shashi 422

Touhida Tahamin Shampa 430

Rajesh Paul 438

Mohsi Nihad Mosabbir Ornab 439

Md. Shariar-Al-Arman

440

M.A. Naim

444

Md. Rafiur Rahman 446

S. M. Kaiser Ahmed 456

Md. Shuaib Shahriar Rusho 457

MBA Program

Batch: 02

September 14,

2015 Department of Finance & Banking

Jahangirnagar University, Savar, Dhaka

Abstract:

With the advancement of technology the world is changing every day and to cope up with the

changing environment we have to change our thinking, life style, behavioural pattern etc. and in case

of financial modelling the same thing also applicable new models are developed to eliminate the

limitations of old one. Over the last decades spontaneous and development which come under the

label of Arbitrage Pricing Model (APT), following the development of Capital Asset Pricing Model

(CAPM) model (Sharpe, 1964 Lintner, 1965) is to develop an accurate estimation model for

expected return. The asset pricing theory is spontaneously developing over several decades. We can

show a developing trend starting from Efficient Frontier and end with FF3 & other multifactor

model.

Efficient Frontier CML SML CAPM APT FF3 & Others

The main purpose of our academic coursework is to test the CAPM model and APT model on given

secondary data and experience with hypothesis testing which makes selected models whether fits or

not for asset pricing. Using samples of monthly data (January 2008- December 2014), regression

model has developed to review the CAPM and APT model. The findings show that there are slight

differences between CAPM and APT. Two basic assumptions of APT are efficient markets

information and diversified investment. When portfolios investments are diversified this means

Market Risk Exposure includes most of micro-macroeconomics factors’ effects. But using APT have

better explanatory power (R2 and Adjusted R2) than CAPM which makes APT model more attractive

to the scholars to suggest use of APT in estimation of expected return. And if we incorporate more

and more independent variable the value of R2 and Adjusted R2 will change and the APT model will

get better explanatory power than before. And FTSE Market Excess Return makes the most

important factors apart from other small affecting factors in most researches. But scholars find that

accepting APT is better than CAPM but it is not error-free to estimate expected return in all

condition. As assumptions makes it difficult to predict actually in the markets. However, FF3 Model

(Fama and French, 1992) has developed further supportive model but in the end like all of the

scholars, it is expected that missing information (Aggelidis and Mandotinos, 2007) will further

improve through development and modification of arbitrage pricing model for the demand of the

time.

Introduction:

As the course work is based on CAPM and APT model testing so we should have a better

understanding of these models. The Capital Asset Pricing Model (CAPM) is widely accepted as an

appropriate technique for evaluating financial assets. It is used to construct portfolios, measure the

performance of investment managers, develop project screening rates for capital budgeting, and

value companies. In case of CAPM the market is considered as a single risk factor and CAPM

doesn’t consider other macro economics factor which is the major limitations of CAPM and to

eliminate this limitation the APT model arrives which incorporates many other factors. The

Arbitrage Pricing Theory (APT)(S. A. Ross, 1976) which offers an alternative explanation of the

relationship between risk and return including Macro and Micro-economic factors, while CAPM has

the limitation especially in the emerging markets where the perfect market assumption do not apply,

are only superficially mentioned.

CAPM, APT and FF3 (modified theory of CAPM by using additional two Fama and French

Factors) models are applied for constructing portfolios, measuring the performance of

investment managers, developing project screening rates for capital budgeting, valuation of

companies, determining cost of capital and so forth. Therefore, asset pricing model has

definitely got a wide range of significant and practical implications as a research based

current issue especially in the domain of finance and investment. As APT model adjusted risk

factors and other micro and macro economics variables so we can say that this will provide a

better result than CAPM.

Objectives:

The main objective of this course work is to test the CAPM & APT model to calculate the

risk return relationship of TESCO share price

How we can use the CAPM and APT model in asset pricing and investment decision

Use of CAPM and APT model to estimate expected returns which depends on various

dependent factors including Market Index, Inflation and Retail Sales

Different statistical measurement and their interpretation also done in the course work.

Comparison between CAPM and APT Model is also included in the objective to realize how

these two models differ to give most predictable solution of return.

Literatures Review:

As we consider CAPM and APT model for our test there are thousands of literature are available on

this regard. After development of CAPM as a model of predicting asset’s return from the market by

Sharpe (1964) and Lintner (1965), in the introductory period this model was best in the world to

predict returns on investment. But for the time-being differences limitations occurred for which new

Asset Pricing Theory, which is developed by Ross (1976) is known as APT Model (or Arbitrage

Pricing Theory). And also CAPM model is expanded by FF3 model by Fama and French (1992,

1993, and 1996) by adding two new factors with the existing market index for more fitted model in

predicting the returns.

CAPM theoretically suggests that a security could be added to a portfolio, based only on its

systematic risk or beta. Fact is that the beta is only priced by the market because all non-systematic

risk is eliminated by diversification. CAPM basic equation is:

𝐸(𝑟𝑖) = 𝑟𝑓 + 𝛽𝑖[𝐸(𝑟𝑚) − 𝑟𝑓]

Where subscript i refers to individual price; E(ri) is expected return on ith security; (rf) is the return on

risk-free asset; E(Rm) is expected return on market portfolio and βi is the measure of risk or

definition of market sensitivity.

An application of Arbitrage Pricing Theory on KSE-100 Index; A study from Pakistan (2000-2005)

by Anam Gul and Naeemullah Khan published in IOSR Journal of Business and Management

(IOSR-JBM) e-ISSN: 2278-487X. Volume 7, Issue 6 (Jan. - Feb. 2013), PP 78-84.In their research

paper they state that- “Arbitrage Pricing Theory takes into account more influencing factors other than

the simple systematic risk, as defined in CAPM. In this study, we aim to evaluate stock returns using

Arbitrage Pricing Model considering four macroeconomic factors i.e. Money supply, Interest Rate,

Industrial Production and Foreign Exchange Rate. The prediction of stock returns is done by taking

values of stocks of 37 companies from KSE 100 index on monthly intervals for the period 2000-

2005. The results that came out for this study proved that APT does not prove to be effective in

predicting stock prices in Pakistan.”

(M.H.Ebrahimi Sarvolia , A.saleh Ardestani , J.Hajibozorgi , H.Ahmadinia, 2010) did research on

portfolio management in an Investment Company in Tehran stock exchange (TSE) using CAPM,

APT, Systematic and Unsystematic Risk indicators. They examined 12 firms since 21 March 2005 to

20 March 2009, selected from Tehran stock exchange and the results suggested that systematic &

unsystematic risk, CAPM & APT should be observed all together in performing evaluation

procedure of investment company’s performances.

Another study was conducted in Australia (Gaoxiang Wang, 2008) in which he studied that whether

the macroeconomic variables defined through Arbitrage Pricing Theory (APT) can explain the

returns on the stock indexes in Australia. This research was based on the returns of stocks listed on

the Australian Stock Exchange (ASX) during the period from 31 March 2000 to 31 December 2007.

The research concluded that industry indices' returns can only be explained by three to five of the

thirteen macroeconomic variables selected in the research. Empirical results suggest that

macroeconomic variables, used in an APT framework, can explain consumer discretionary, energy,

financial, IT, and materials, price index returns, but cannot explain other index returns. Generally,

APT is a desirable model in examining the ASX200, as it explains half of the industry indices'

returns.

Another important study was conducted in Indonesia (Erie Febrian, Aldrin Herwany, January 2010)

in which the researchers wanted to investigate the ability of CAPM and APT in explaining the

additional returns of portfolio of stocks traded in Jakarta Stock Exchange (JKSE). They used data

from three important economic eras i.e. pre-crisis period (1992-1997), crisis period (1997-2001), and

post-crisis period (2001-2007). The results came out in the favour of APT as it proved that Beta is

not the only factor that can explain the portfolio’s additional returns. APT has proven to be right in

explaining the portfolio excess returns in the periods in which they observed i.e. they found out that

excess return averages are found to be consistently negative. They also found out that risk-premiums

vary over the observation periods in which the study was conducted.

Models like APT for more factors which affect returns. But in 2007, Aggelidis and Manditinos found

that APT is better than CAPM in Athens Stock Exchange but APT does not explain the overall

variance properly, maybe there is some missing information and that is why APT fails to explain

fully the returns covariance and means returns. There can be several possible explanations (Cheng,

1995). First, risk and expected return may not be stationary as it is assumed not to change during the

period; secondly, APT pricing relationship could hold only in some months of the year, and there is

evidence of a “January effect” on the capability of the APT to explain the return-risk-relationship

(Gultekin and Gultekin, 1987); and thirdly, there is a possibility of non-linear pricing relationships.

In the end, it is recommended that higher-order factor models would provide more accurate

predictions.

Similar problems arise in (Huberman and Wang, 2005; Aggelidis and Manditinos, 2007) in

Burmeister and McElory (1988) article where January effects also found, rejection of CAPM in favor

of the APT; however, it cannot reject the APT restrictions on the linear factor model.

Methodology and Data Analysis:

The main purpose of this report is to assess the role and practical implementation of CAPM and APT

model as the mechanism for investment strategy. To serve the purpose the work has mainly

emphasised on quantitative analysis. In testing the models, the time series (historical) data have been

considered where the values of one or more variables are observed at different points in time. Data

has already been given and the process used in the research is the linear regression line.

The Capital Asset Pricing Model (CAPM):

The Asset Pricing Model is based on CAPM (Sharpe 1964, Linter 1965). CAPM states that it is only

degree of systematic risk as expressed by beta (𝛽𝑝) that will determine the degree of returns for

diversified portfolio. When we should no longer rely on /SD at portfolio (as per Marketing 1954,

Tofin 1959), CAPM does not consider Macro/Micro Factor, CAPM consider the market index is the

only risk as single risk factor. Basic CAPM equation as follows:

𝑬(𝑹𝒑) = 𝑹𝒇 + (𝑹𝒎 − 𝑹𝒇) × 𝜷𝒑

In the basic model of CAPM 𝛽𝑝 can be measured by the formula:

𝛽𝑝 =𝜎𝑥×𝑟(𝑥,𝑦)

𝜎𝑦

Also it can be measured by the regression line and here we calculate the Beta by regression line

between Given TESCO share Excess Return and FTSE Market Index.

Analysis and interpretations:

Annual Return & Excess Return Data:

Calculated Annual Return and Excess Return for TESCO share and FTSE market index table is

given below based on these two formulas:

Annual Rate of Return = (Pt – Pt – 1) / Pt – 1 *100

Where,

Pt = Current Price

Pt – 1 = Beginning Price

Excess Rate of Return = Annual Return (%) – Risk-free Return (%)

= Rp - Rf (Treasury Bills Rate)

Regression model (Excel):

As in the early we stated that basic model of CAPM: 𝑬(𝑹𝒑) = 𝑹𝒇 + (𝑹𝒎 − 𝑹𝒇) × 𝜷𝒑 where the βp

can be measured by Regression model between TESCO Share Excess Return and FTSE Market

Index Excess Return (Data from Annual & Excess Return Table – 01). Regression Model will be:

𝑦𝑖 = 𝛼 + 𝛽1𝑥1 + 𝜇

[Where, = alpha or intercept between two data set, β1 is the coefficient between TESCO Excess

Return and FTSE Market Index Excess Return; and error terms]

As per Regression model for CAPM, it has been estimated from the Excel Output:

TESCO excess return = -1.202 + 1.386*FTSE excess return +.

o R = .943a;

o R Square (R2) = .890;

o Adjusted R Square (R2) = .888

Sample Interpretations:

From output on dependent variable TESCO excess return, we can interpret the result as:

If FTSE excess return goes up by $1 TESCO share will also go up by $1.386.

Alpha TESCO:

From SPSS output we have got = - 1.202 which is the constant or intercept value between TESCO

Share Excess Return and FTSE Market Index Excess Return. But this is inclusive because of P-value

and t-value of the result, because:

As P-value of Alpha is .230 which is higher than 0.05 (at 95% interval) which mean it is

insignificant.

t-value of Alpha is -1.210 which is lower than 2. As t < 2 then it is inclusive with TESCO

Share Excess Return.

B TESCO (Beta):

There is only one beta result as CAPM model only consider the market index as market risk, no other

Macro or Micro factors. Beta represent degree of systematic risk. Beta for TESCO share is:

β = 1.386

P-value of β is 0.00 which lower than .05 so value is significant.

t-value of β is 23.778 which higher than 2 (t > 2) which indicates there is relation between

TESCO Excess return and FTSE Market Index Excess return.

R Squared:

R Squared (R2) is an measure of –

Overall goodness of fit of the model.

Explanatory power of the model indicating how closely the TESCO excess return is

associated with Market, Inflation and Retail Sales.

It represents whether the model fits the real data set

R2 = 1 represents linearly fits the data set

Here, R square (R2) =.890 which indicates that 89% of the variability in TESCO returns is

explained by explanatory variable Market Index (FTSE). R2 shows very good explanatory

power and linearly fits data set.

Correlation coefficient:

Correlation coefficient or Multiple Regression which is denoted by R refers to the degree of

relationship whose value range is 0 to +1. Near to 1 means there is a high degree of relationship

between variables. From the SPSS output, we get

R = 0. 943a

This result shows high degree of relationship between FTSE market Index and TESCO Share excess

return variables.

The Arbitrage Pricing Theory (APT):

Arbitrage Pricing theory is proposed alternative in predicting require rate of return in spite of CAPM

in stock market. It is also the expansion of CAPM beta where CAPM consider only one beta (Stock

to Market Index), however APT consider multi-factor beta to determine the required rate of return

such as Market Index, Inflation, Retail Sales, Central Bank Rate etc. APT or Arbitrage Pricing theory

works through regression line where dependent variable expressed as of independent variables beta.

The regression equation of APT by most scholars is:

𝑌 = 𝛼 + 𝛽1𝑥1 + 𝛽2𝑥2 + 𝛽3𝑥3 +⋯+ 𝛽𝑛𝑥𝑛 + 𝜇

Where,

Y = required rate of return for individual stock.

= incept between dependent and independent variables

β1, β2, β2 … βn are the beta for different factors regarding returns

X1, X2 … Xn is the individual stock which affect by beta from independent variables.

is the independent error terms.

SPSS Output:

As per multi-factor asset pricing model using Arbitrage Pricing Theory (APT), it has been estimated

from the SPSS Output:

TESCO excess return = - 4.512 + 1.343*FTSE excess return - .070*Inflation Rate + 1.026

*Retails Sales Rate +.

R =.946a;

R Square (R2) = .895;

Adjusted R Square (R2) = .891

Sample Interpretations:

From the SPSS output on dependent variable TESCO excess return, we can interpret the result as:

If FTSE excess return goes up by $1 TESCO share will also go up by $1.343 by holding

Inflation Rate and Retails Sales Rate constant.

Holding FTSE excess return and Retails Sales Rate constant, if Inflation rate goes up by $1

TESCO share will go down by 7 pence.

Holding FTSE excess return and Inflation rate unchanged, if retail sales rate goes by $1

TESCO share price will all go up by $1.026

Hypothesis Testing:

Hypothesis Testing is important for the reasons below:

Significance testing for accepting a result of a model based on a sample.

To infer the result of an operation based on sample.

Procedure used to accept/reject the null hypothesis or alternative hypothesis

Whether the variable support the model scientifically or not.

In the model γi = + β1x1 + β2x2 + β3x2 + - the collective name for , β1, β2, β3 are the

Coefficients (or parameters). Testing of the results from these parameters is included in Hypothesis

testing. In every test, we have two hypothesis

H0 = null Hypothesis and H1 = alternative hypothesis

Where it is expected to have the null hypothesis rejected and alternative hypothesis is accepted

through different hypothesis testing.

t-statistic (or t-ratio):

In order to carry out the hypothesis test we need to consider the estimated coefficient in relation to

the size of its associated standard error.

In t-statistic (or t-ration) hypothesis ratio if the result is t 2 (equal or higher than 2) than it is

assumed that there is a relation but on the contrary there is no relation between dependent and

independent variables.

Hypothesis: H0: = 0 (or t < 2, then there is no relation)

H1: 0 (or t 2, then there is relation between variables)

Parameters Alpha FTSE Excess

Return

Inflation Rate Retail Sales Rate

Hypothesis H0: true = 0

H1: 0

H0: true β1 = 0

H1: β1 0

H0: true β2 = 0

H1: β2 0

H0: true β3 = 0

H1: β2 0

SPSS Result -1.947< 2 21.633> 2 -.122< 2 1.823 < 2

Accept & Reject H1 rejected &

H0 accepted

H0 rejected & H1

accepted

H1 rejected & H0

accepted

H1 rejected & H0

accepted

Interpretation As intercept or

(alpha) is not

significant from

0, so it is not

meaningful

As FTSE Excess

Return is

significant from

0, so market

index has

relation with

TESCO

As Inflation (%)

is not significant

from 0, so

Inflation has no

relation with

TESCO

As Retail Sales

(%) is not

significant from 0,

so it has no

relation with

TESCO

P-value:

For 95% interval if P > .05 then reject null hypothesis (H0) and P < .05 then accept the alternative

hypothesis (H1). So, hypothesis are:

H0: a = 0 (P > .05; no relation and reject)

H1: a 0 (P < .05; there is relation and accept)

Parameters Alpha FTSE Excess

Return

Inflation Rate Retail Sales Rate

Hypothesis H0: true = 0

H1: 0

H0: true β1 = 0

H1: β1 0

H0: true β2 = 0

H1: β2 0

H0: true β3 = 0

H1: β2 0

SPSS Result .056 > .05

.000 < .05 .903 > .05 .073 > .05

Accept &

Reject

H1 rejected &

H0 accepted

H0 rejected & H1

accepted

H1 rejected & H0

accepted

H1 rejected & H0

accepted

Interpretation Intercept or

alpha value is

not meaningful

FTSE Excess

Return has relation

with TESCO share

excess return

Inflation (%) has

no relation with

TESCO

Retail Sales (%) has

no relation with

TESCO

Testing R-square (R2) & Adjusted R-square (R2):

In the model summary of SPSS output, the R2 variable gives the proportion of variance that can be

predicted by the regression model using the data provided (Rahman, 2006). So, R2 is an measure of –

Overall goodness of fit of the model.

Explanatory power of the model indicating how closely the TESCO excess return is

associated with Market, Inflation and Retail Sales.

It represents whether the model fits the real data set

R2 = 1 represents linearly fits the data set

On the other hand Adjusted R2 is the modified R2 that adjusts the degree of explanatory variables.

The relation between R2 and adjusted R2 is that if R2 increase, Adjusted R2 should be increased but

never exceeds R2.

Here, R square (R2) = .895 which indicates that 89.5% of the variability in TESCO returns is

explained by variations in explanatory variables like Market Index (FTSE), Inflation and

Retail Sales. R2 result shows very good explanatory power and linearly fits data set.

The F-test:

F-test is used to test the R2 which justify the reliability of overall model (but t-value is for individual

variable). The hypothesis for F-test are:

H0: the true R2 = 0 (no relationship)

H1: the true R2 0 (there is a relationship)

Here, significance F less than < .05 or Sig. F Change .00<.05 which means alternative hypothesis H1

is accepted and there is much evidence of overall relationship in the model.

Durbin-Watson d Test:

Auto-correlation is a concept if the variables have the tendency to follow negative or positive.

Normally error terms mean = 0 and no auto-correlation is good subject to biased negative or positive

tendency.

Auto-correlation complicates statistical analysis by altering the variance of variables, changing the

probabilities that statisticians commonly attach to making incorrect statistical decisions (Griffith

1987). The mechanism which has used for testing auto-correlation is DW d test which is calculated

from the residuals. So, Durbin-Watson (D.W) d test is:

To test the auto-correlation we have to test D.W d test

Auto-correlation complicates the statistical decisions by changing the values of variances.

Successive errors terms have the same sign error.

The Hypothesis for D.W d test are

H0: = 0 (means there is no auto-correlation)

H1: > 0 (means there is positive auto-correlation)

H1: < 0 (means there is negative auto-correlation)

Also it is important to see the result from Durbin-Watson table from which we can formulate, if

du > DW value, then H0: accepted.

dL < DW value, then H1: accepted.

dL > DW value, the test is inclusive.

In the model summary, the Durbin-Watson value is 1.046 which is higher than 0, so we could

have positive auto-correlation indicating that successive error terms have the same sign. Here,

the DW value = 1.05 less than dL = 1.525 (using DW table). Therefore, we would reject the null

hypothesis and conclude that there is positive auto-correlation.

Testing value of tolerance (multicollinearity):

The value of tolerance close to 0 indicates that a variable is almost a liner combination of the

other independent variables and such data are called multi-collinear (Norusis, 2005).

If the tolerance statistic is below .2, multicollinearity can be biasing the results (Menard,

1995). Also there is no-correlation between variables.

Strong relationship between two, then if one increases then other will increase but dependent

may not increase. So it may be biased.

For testing value of tolerance (multicollinearity) the hypothesis are:

H0: a = 0 (or H0 < .02 multicollinearity can bias the result)

H1: a 0 (or H1 > .02 multicollinearity cannot bias the result)

Since tolerance value of X variables (.863, .908, .789) all are close to 1, so H1 Hypothesis is

accepted which indicates X variables are independent and there is no room for

multicollinearity.

Conclusion:

The findings shows that there are some differences between CAPM and APT. As the assumptions of

arbitrage pricing model holds two basic assumptions of APT – efficient markets information and

diversified investment. When portfolios investment are diversified this means Market Risk Exposure

includes most of micro-macroeconomics factors’ effects. But using APT and Extension of APT have

better explanatory power (R2 and Adjusted R2) then CAPM which makes APT model more attractive

to the scholars to suggest use of APT in estimation of expected return. But scholars find that

accepting APT is better than CAPM but it is not error-free to estimate expected return in all

condition. As assumptions makes it difficult to predict actually in the markets.

References:

Turgut Türsoy, Nil Günsel & Husam Rjoub, 2008. “Macroeconomic Factors, the APT and the

Istanbul Stock Market”, International Research Journal of Finance and Economics, Issue 22, pp. 50-

56.

M.H.Ebrahimi Sarvolia , A.saleh Ardestani , J.Hajibozorgi , H.Ahmadinia, 2010. “ A Study of

Portfolio Management in Accepted Investment Company in Tehran stock exchange using of CAPM,

APT, Systematic and Unsystematic Risk Indicators", Working Paper Series

Erie Febrian, Aldrin Herwany, January 2010. “CAPM and APT Validation Test Before, During, and

After Financial Crisis in Emerging Market: Evidence from Indonesia”, The International Journal of

Business & Finance Research, Vol.10, No. 1.

[9] Gaoxiang Wang, 2008.“Test of Macroeconomic Variables Through Arbitrage Pricing Theory in

Different Industry Indices in the

Australian Stock Market”, Working Paper Series

Aggelidis, T. N. V. and Maditinos. D. (2007). Testing the relation between risk and returns using

CAPM and APT: The Case of Athens Stock Exchange (ASE).

Appendix

rate of return(%)

mkt return (%)

Excess Return (Rp)

Mkt acess return (Rm)

32.2219 34.8164312 28.3919 30.99

42.9810 27.75101362 39.0810 23.85

44.7131 26.57398659 40.7331 22.59

25.2287 18.28390167 21.1287 14.18

19.6625 11.83342391 15.4725 7.64

35.2375 13.05814555 30.8975 8.72

8.5283 7.156054785 3.9483 2.58

5.8824 7.238199483 1.2424 2.60

17.2381 12.03075375 12.5181 7.31

12.7188 8.106353247 8.0288 3.42

25.1611 9.246198852 20.4811 4.57

28.0985 9.213184862 23.4385 4.55

23.9028 11.61903891 19.2228 6.94

14.8935 11.23512867 10.2335 6.58

23.1477 11.86907422 18.4577 7.18

9.4569 7.13838755 4.6869 2.37

18.4530 12.78675272 13.7530 8.09

11.9330 14.8743421 7.2730 10.21

19.5834 20.642545 14.9634 16.02

19.9627 20.0985462 15.5027 15.64

18.2454 20.87098918 13.8354 16.46

27.2817 15.96145644 22.8817 11.56

23.2031 16.87865905 18.8031 12.48

16.7503 18.09685782 12.3303 13.68

18.0036 19.96296934 13.5736 15.53

26.6303 18.45992322 22.2403 14.07

30.6633 24.01524984 26.2833 19.64

41.1331 28.25180952 36.7331 23.85

25.0076 17.45625868 20.5876 13.04

27.7223 15.91339638 23.2223 11.41

13.9357 13.59410152 9.3957 9.05

24.9561 13.09787493 20.4261 8.57

30.4471 11.09516751 25.6971 6.35

20.4998 17.86781264 15.6598 13.03

18.9647 13.81952172 14.0247 8.88

20.9191 13.15059255 15.9091 8.14

18.1726 9.673013358 13.0926 4.59

7.5177 8.191819006 2.2177 2.89

-2.5475 7.718277143 -7.8875 2.38

2.7285 9.151470598 -2.6015 3.82

11.9481 17.89087543 6.5181 12.46

1.1003 14.71097662 -4.4497 9.16

0.1770 9.48114024 -5.4930 3.81

-1.5413 8.411277103 -7.3113 2.64

-1.8684 8.734805471 -7.6584 2.94

1.7723 9.98735858 -3.9177 4.30

-9.5870 5.161145568 -15.1970 -0.45

-14.5253 2.025504281 -20.0253 -3.47

-20.5887 -6.592482814 -25.8887 -11.89

-21.9558 -5.792488463 -27.0758 -10.91

-13.1370 -10.84792018 -18.1570 -15.87

-16.1539 -7.61890571 -21.0339 -12.50

-16.8092 -10.36554512 -21.6392 -15.20

-29.0510 -16.11126452 -34.0010 -21.06

-23.1270 -16.41502894 -28.2370 -21.53

-23.5400 -12.01632888 -28.6200 -17.10

-32.5430 -25.12051952 -37.4930 -30.07

-49.6175 -36.78013503 -54.3575 -41.52

-39.2977 -34.95658164 -42.9777 -38.64

-40.0608 -32.7802913 -42.0508 -34.77

-48.3239 -30.7049765 -49.6139 -31.99

-51.1159 -35.95296414 -52.0059 -36.84

-62.1582 -32.2126373 -62.8782 -32.93

-45.8430 -29.89993355 -46.4430 -30.50

-42.6720 -26.91596426 -43.3020 -27.55

-26.3433 -23.93852274 -26.8733 -24.47

-24.8736 -14.39468065 -25.3736 -14.89

-14.6876 -12.13201845 -15.1276 -12.57

3.0778 6.084544243 2.6878 5.69

2.9914 7.774913106 2.4914 7.27

9.6665 18.11957882 9.2265 17.68

26.8650 19.25958113 26.4750 18.87

SPSS Output CAPM

Descriptive Statistics

Mean Std. Deviation N

TESCO EXCESS RETURN -.7489 25.21511 72

FTSE EXCESS RETURN .3271 17.16710 72

Correlations

TESCO EXCESS

RETURN

FTSE EXCESS

RETURN

Pearson Correlation TESCO EXCESS RETURN 1.000 .943

FTSE EXCESS RETURN .943 1.000

Sig. (1-tailed) TESCO EXCESS RETURN . .000

FTSE EXCESS RETURN .000 .

N TESCO EXCESS RETURN 72 72

FTSE EXCESS RETURN 72 72

Variables Entered/Removedb

Model Variables Entered

Variables

Removed Method

1 FTSE EXCESS

RETURNa . Enter

a. All requested variables entered.

b. Dependent Variable: TESCO EXCESS RETURN

Model Summaryb

Mode

l R

R

Square

Adjusted R

Square

Std. Error of

the Estimate

Change Statistics

Durbin-Wats

on

R Square

Change

F

Change df1 df2

Sig. F

Change

1 .943a .890 .888 8.42871 .890 565.416 1 70 .000 .999

a. Predictors: (Constant), FTSE EXCESS RETURN


ANOVAb

Model Sum of Squares df Mean Square F Sig.

1 Regression 40168.918 1 40168.918 565.416 .000a

Residual 4973.017 70 71.043

Total 45141.935 71

a. Predictors: (Constant), FTSE EXCESS RETURN


Coefficientsa

Model

Unstandardized

Coefficients

Standardiz

ed

Coefficients

t Sig.

95% Confidence

Interval for B Correlations

B Std. Error Beta

Lower

Bound

Upper

Bound

Zero-ord

er Partial Part

1 (Constant) -1.202 .994 -1.210 .230 -3.184 .779

FTSE EXCESS

RETURN 1.386 .058 .943 23.778 .000 1.269 1.502 .943 .943 .943

a. Dependent Variable: TESCO EXCESS

RETURN

Coefficient Correlationsa

Model

FTSE EXCESS

RETURN

1 Correlations FTSE EXCESS RETURN 1.000

Covariances FTSE EXCESS RETURN .003

a. Dependent Variable: TESCO EXCESS RETURN

Residuals Statisticsa

Minimum Maximum Mean Std. Deviation N

Predicted Value -58.7297 41.7358 -.7489 23.78570 72

Residual -1.60502E1 20.01771 .00000 8.36914 72

Std. Predicted Value -2.438 1.786 .000 1.000 72

Std. Residual -1.904 2.375 .000 .993 72

a. Dependent Variable: TESCO EXCESS RETURN

SPSS Output APT

Correlations

AEXCRT FTSEXCRT INFR RETSAL

Pearson Correlation AEXCRT 1.000 .943 .076 .415

FTSEXCRT .943 1.000 .062 .367

INFR .076 .062 1.000 .299

RETSAL .415 .367 .299 1.000

Sig. (1-tailed) AEXCRT . .000 .263 .000

FTSEXCRT .000 . .302 .001

INFR .263 .302 . .005

RETSAL .000 .001 .005 .

N AEXCRT 72 72 72 72

FTSEXCRT 72 72 72 72

INFR 72 72 72 72

RETSAL 72 72 72 72

Variables Entered/Removedb

Model Variables Entered

Variables

Removed Method

1 RETSAL, INFR,

FTSEXCRTa . Enter

a. All requested variables entered.

b. Dependent Variable: AEXCRT

Model Summaryb

Model R R Square

Adjusted R

Square

Std. Error of

the Estimate

Change Statistics

Durbin-Wats

on

R Square

Change

F

Change df1 df2

Sig. F

Change

1 .946a .895 .891 8.33874 .895 193.734 3 68 .000 1.046

a. Predictors: (Constant), RETSAL, INFR,

FTSEXCRT


Descriptive Statistics

Mean Std. Deviation N

AEXCRT -.7489 25.21511 72

FTSEXCRT .3271 17.16710 72

INFR 2.7624 1.80250 72

RETSAL 3.4290 1.98014 72

ANOVAb

Model Sum of Squares df Mean Square F Sig.

1 Regression 40413.580 3 13471.193 193.734 .000a

Residual 4728.355 68 69.535

Total 45141.935 71

a. Predictors: (Constant), RETSAL, INFR, FTSEXCRT


Coefficientsa

Model

Unstandardized

Coefficients

Standardiz

ed

Coefficient

s

t Sig.

95% Confidence

Interval for B Correlations

Collinearity

Statistics

B Std. Error Beta

Lower

Bound

Upper

Bound

Zero-ord

er Partial Part

Toleran

ce VIF

1 (Constan

t) -4.512 2.317

-1.947 .056 -9.136 .112

FTSEXC

RT 1.343 .062 .914 21.633 .000 1.219 1.466 .943 .934 .849 .863 1.159

INFR -.070 .576 -.005 -.122 .903 -1.220 1.079 .076 -.015 -.005 .908 1.101

RETSAL 1.026 .563 .081 1.823 .073 -.097 2.149 .415 .216 .072 .789 1.268

a. Dependent Variable: AEXCRT

Collinearity Diagnosticsa

Model

Dimensi

on Eigenvalue Condition Index

Variance Proportions

(Constant) FTSEXCRT INFR RETSAL

1 1 2.692 1.000 .02 .00 .03 .02

2 1.007 1.635 .00 .83 .00 .00

3 .189 3.776 .09 .03 .93 .25

4 .112 4.896 .88 .14 .04 .72


Residuals Statisticsa

Minimum Maximum Mean Std. Deviation N

Predicted Value -59.4785 40.6214 -.7489 23.85803 72

Residual -1.59243E1 17.71840 .00000 8.16067 72

Std. Predicted Value -2.462 1.734 .000 1.000 72

Std. Residual -1.910 2.125 .000 .979 72


Asset Pricing Model

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