The Capital Asset Pricing Model and someMultifactor Models: Comparative Test Evidences in Nigeria.Arewa Ajibola* Tobira L L***Lagos State University, Faculty of ManagementSciences, Department of Banking and Finance. E-mail:ajibolaarewa@yahoo.com. Tel: 08060962048.

** University of Port Harcourt, Faculty of ManagementSciences, Department of Finance and Banking

AbstractIn this study, the researcher investigated the superiority of the CAPMC orFF3FM to the CAPM using residual, post error odds ratio, Mackinnon andDavidson techniques over the period Jan, 2002 to December 2011 inNigerian stock market. The residual based test revealed that the CAPMcould not provide explanation for the information missed by either theCAPMC or FF3FM. In the same token, the CAPMC or FF3FM could notexplain the information missed by the CAPM. The test on the Mackinnonand Davidson yielded inconclusive results but, however, the post error oddsratio overwhelming supported the CAPM among the three models. Thus, weconcluded that the CAPM is still an adequate discounting technique whenthere is absence of conditional information.

Keywords: CAPM, CAPMC, FF3FM1 Introduction

The CAPM has lived approximately 50 years with verystern criticisms. One of such criticisms is that itsuffers from dimensional inadequacy. However, itsseductive simplicity coupled with mean variance

1

sufficiency pushes the model to the frontier of Finance(Roll, 1977). Beta the fulcrum of the CAPM has notsufficiently explained the variations in mean return;purporting that the CAPM is death in its application.Therefore, the need to expand the dimension of the CAPMbecame inevitable. This led to the development of theskewness preference model (Kraus & Litzenberger, 1976),the higher order CAPM comoment (Fang & Lai, 1997) andthe three factor model (Fama & French, 1992). What isreally appealing here is have these subsequent versionsimproved upon the descriptive ability of the CAPM? Thisissue has been investigated in all of the advanced andsome emerging markets; while the African marketsincluding that of Nigeria have not been examinedempirically for the deficiencies of the CAPM and how itcan be improved. The quest to fill this research gap isthe driving force behind this study.

The CAPM has made a fundamental contribution to theunderstanding of how risk factor can be determined in aportfolio (Perold, 2004); but unfortunately, theempirical results of the model are so poor that itspractical applications can be invalidated (Fama&French, 2004). This was the reason, Anton, Adli andMd. Azizul (2013) augmented the CAPM with higherorder co-moments and documented that the CAPM’sexplanatory power was improved so long the model isextended to include systematic skewness and kurtosis

2

factors. Arewa, Onafalujo and Nwakanma (2015) suggestedthat the conditional information provided empiricaldistinction between the CAPM and the CAPM with higherorder co-moments; thereby confirming the claims ofAttiya and Eatzaz (2008). Tamara and Evgeniya (2011)emphasized that the higher order CAPM was a bettermodel that explained variations in return than thetraditional CAPM.

Cao, Leggio and Schniederjans (2005)compared theexplanatoriness of the CAPM and the three factor modelwith the artificial neural network model and linearmodels and confirmed that the composed linearmodels produced much more significant results than theartificial neural networks. Iqbal and Brooks (2007)applied GARCH and EGARCH technique to compare theCAPM and Fama-French three factor. They vindicated thethree factor model the more superior to the CAPM. Thisposition was overwhelmingly supported by O’Brien,Brailsford and Gaunt (2008). In their study it wasascertained that the premium factors in the threefactor model captured about 70 percent changes in meanreturn. Unlu (2013) provided evidence in favor ofmultifactor model as an attractive alternative to theCAPM.

The peculiarity of these studies is that they allextended the dimension of the CAPM; and tested whetherthe premium factors in the extended versions are priced

3

conditionally or in some cases unconditionally.Therefore, our study intends to add to the existingliterature by comparing the CAPM with its subsequentmultifactor relations using Residual, Davison/Mackinnonand Post Odd Error Ratio Techniques in a distinctfashion. To the best of our knowledge, the Nigeriancapital market appears to be the first place in WestAfrica, where these techniques have been applied incomparing the superiority of the higher order CAPM orFama-French three factor model to the CAPM. The restsof the paper are organized as: literature,methodology/data, result, conclusion andrecommendation.

2 Literatures

Over the years till now, frantic efforts have beenexerted to correct the deficiencies of the CAPM. Theearliest ones are credited to Kraus and Litzenberger(1976), Fang and Lai (1997); even Fama and French(1992) made important contributions. The views of thesescholars are still reverberating in Finance literature.In recent decade, Griffin (2003) documented that thepower of the three factor model has significantlyimproved for explaining stock return in Japanese,England and Canadian markets. Cao, Leggio andSchniederjans (2005) compared the CAPM and the threefactor model with the artificial neural network modeland linear models in Shanghai Stock Exchange (SHSE)

4

for the period December 1999 to December 2002.Their results were in favor of the composed linearmodels in comparison to the artificial neural networks.Iqbal and Brooks (2007) applied GARCH and EGARCHtechniques to compare the CAPM and the Fama-Frenchthree factor model in Karachi Stock Exchange (KSE).They used 89 stocks of daily, weekly and monthly dataover the period of March 1999 to March 2005. Theirfindings suggested that the risk factors in the threefactor model were more significant than the CAPM.O’Brien, Brailsford and Gaunt (2008) compared the CAPMwith the three factor model in Australian market over asample period 1982 to 2006 and it was concluded thatthe three factor model was more successful than theCAPM.

Unlu (2013) conducted a test to compare the singlefactor CAPM, the power of three factor, four factorand five factor models in explaining stockreturns for the Istanbul Stock Exchange (ISE).Data were selected for the period covering July 1992 toJune 2011. The author reported that in addition tothe market risk, size, book to market ratio,momentum and liquidity factors commanded riskpremium in the market. Anton, Adli and Md. Azizul(2013) analyzed the higher moment capital asset pricingmodel for Dhaka Stock Exchange (DSE) market over theperiod January 2005 to December 2009. They confirmedthat the co-skewness risk is compensated in the DSE

5

market for the sampling period; therefore, it must berewarded by the market. They concluded that indescribing risk-return relationship in emerging marketslike Bangladesh stock market, the higher moment CAPMperforms comparatively well.

Arewa, Onafalujo and Nwakanma (2015) employed theconditional and unconditional information in NigerianStock Exchange (NSE) over the period January 2003 toDecember 2011 to discuss the empirical proof of theCAPM with higher order and documented that the modelwas a good explanation of risk-return relationshipbased on conditional information. Tepmony (2010)performed empirical experiment to examine the effect ofincluding or excluding co-skewness and co-kurtosis riskfactors in the classical CAPM. The results of theexperiment revealed that when excluding the skewnessand kurtosis effects in the model, the adjusted Rsquares were about 31% and 32% respectively on theaverage. On the contrary the adjusted R square increasedsignificantly to 38.39% when these two factors wereincluded in the model. This suggests that thesystematic skewness and the systematic kurtosis improvethe CAPM descriptive ability.

3.1 Methodology

The theoretical assumptions on which CAPM is standinggive rise to a specification of a pricing equation that

6

shows the intricate relationship between return and ameasure of systematic risk called market beta. This wasan intuitive simplicity once preached by Sharpe (1965),Litner (1966) and Mossin (1969) respectively. In linewith this reasoning, Fama and Macbeth (1973),Pettengil, Sunderam and Mathur (1995) among others madea useful contribution towards the development of asingle factor pricing equation otherwise known as theCAPM. In this study, a little modification is made tothese authors’ a priori pricing specifications with theaim of justifying, revalidating and improving on theempirical stance of the CAPM in Nigerian capitalmarket.3.1.1 Two Moments CAPM Specification: rt- rft = ai + bi(Rmt – Rft) + µt …………………………………(3.1) Where: rt is the return on security say (i) at time(t).

rft is the risk free rate at time (t) ai is the constant return earned in each periodfrom security (i). Rmt is the return on market portfolio at time(t). bi is the estimate of beta for security (i)representing the

systematic risk. µt is the residual term.

The estimated beta (i.e. βi) is then used as theindependent variable in the following equation:

7

ri = λ0 + λ1β^i + εi ……………………………………….(3.2)

Where: ri is the average returns of ith securities. λ0 is the intercept term

λ1 is the regression parameterβ^

i is the estimated beta for ith securities.µi is the random variable.

3.1.2 The Three Moments CAPM Pricing Equation:r~

i= α0 + α1β^i + α2(sk^)i + µi …………………..(3.3)

Where: r~i is the average return on ith securities

β^i is the estimated beta for ith

securities (sk^) is the estimated skewness for ithsecurities α0 ………α3 are the regression parameters µi is the residual error term.The systematic risk proxy can be derived from the timeseries regression below: rt-rft = a0+ β(rmt – rft) + sk (rmt – rft)2 + εt ………….. (3.4) Where: β and sk are the estimated risk proxies for β^

and sk^ respectively in equation 3.3; other variables had beendefined in equation 3.1. Note that equation 3.4 is referred to pricing kernelsor quadratic market equation.3.1.3. The Four Moments CAPM Fundamental Equation:Fang and Lai (1997) interdependently developed anextension of the Krans and Litzenberger two-factorCAPM, popularly referred to as the four moment CAPM

8

pricing error relation. Their specification is statedthus unconditional format as: ri= µ0 + λ1βi + λ2ski + λ3kti + vi…………………………… (3.5)Where: kti is defined as systematic co-kurtosis Deriving a proxy for kti involves stating the cubicmarket equation as follows: rt-rf t= b0+ β(rmt – rft) + sk (rmt – rft)2 + kt(rmt – rft)3 + wt

……….. (3.6)Therefore, estimating the following equations givesloadings for sk and kt respectively. The β loadingshad been discussed in equation 3.1.rt-rf t= b0+ sk (rmt – rft)2 + µt……………………….………..(3.7)rt-rft = a0+ kt (rmt – rft)3 + et ……………………….….……..(3.8)3.1.4. The Fama-French Three Factor Model (FF3FM)rt – rft = α0 + βt(rm – rft)t + st(SMB)t + ht(HML)t + zt…………(3.9)Where: (rt – rft) is the excess return on security i attime (t)

(rm – rft)t is the market risk premium at time (t) (SMB)t is the size factor at time (t) (HML)t is the value factor at time (t) α0 is the intercept βt,St and ht are the regression parameters. Note that:

SMB = (S/L + S/M +S/H) – (B/L + B/M + B/H)……………. (3.10) 3 3

Where: SMB is small minus big, which means thedifference between the returns

9

on a portfolio of small stock and aportfolio of big stocks

S/L means portfolio of small size and low valuecompanies S/M means portfolio of small size and mediumvalue companies S/H means portfolio of small size and highvalue companies

HML = (S/H + B/H) – (S/L + B/L)………………………….. (3.11) 2 2Where: HML is high minus low that is the differencebetween the return on a portfolio of high BE/ME stocks and thereturn on a portfolio of low BE/ME

B/L means portfolio of big size and low valuecompanies B/M means portfolio of big size and medium valuecompanies B/H means portfolio of big size and high valuecompanies BE means book equity

ME means market equity SMB and HML portfolios are constructed to beneutral of value and size respectively.

10

To derive proxies for the size and value risk factors;the following analogous equations can be regressed.rt – rft = b0 + s(SMB)t + µt…………………………….(3.12)Where: the estimated value of s is the factor loadingfor size factor other variables had been previouslydefined. rt – rft = a0 + h(HML)t + et……………………………. (3.13)Where: the estimated value of h is the factor loadingfor value factor other variables had been previouslydefined. Therefore, the sensitivity of excess returnwith the return of SMB gives loadings for size factorwhile that of HML portfolio gives loadings for valuefactor. To achieve the main object of this study, The authorsdeveloped expressions to compare the CAPM with the CAPMwith higher order Comoment (CAPMC) and the Fama-FrenchThree Factor Model (FF3FM) using the Residual, Post-Error Odds Ratio, Mackinnon and Davison Techniques.Thus:3.1.5 The Comparison between the CAPM and CAPMC usingResidual Method Obtained the residuals in equation (3.2) regress themagainst the factors in equation (3.5) and then runalternative regression by obtaining the residuals inequation (3.5) against the factor in equation (3.2).That is:εi = y0 + y1β^

1 + y2(δ^k)i + y3k^t + vi …………………… (3.14)µi = a0 + a2β^

1 + wi …………………………………………. (3.15)

11

On the a-priori, equation 3.14 will display largervalue of Adjusted R-squared than equation 3.15 for theCAPMC to be more superior to the CAPM. 3.1.6. The Comparison between the CAPM and CAPMC usingDavidson and Mackinnon ri = λrCAPM + (1-λ)rCAPMC + vi…………………………….. (3.16)Where: λ is the measure of effectiveness between theCAPM and the CAPMC, for the CAPM to be more effectivethan the CAPMC, λ must be close to one (1). 3.1.7. The Comparison between the CAPMC and the CAPMusing Posterror Odds Ratio. In terms of the CAPMC and the CAPM, the ratio can beexpressed as:R = ESSCAPMC n/2

ESSCAPM X n(kCAPMC - kCAPM

) /2

.........................................(3.17)

On the a-priori, the ratio is stated in favor of theCAPMC and it is expected that R will be less than one(1) for CAPMC to be more effective and applicable thanthe CAPM.3.1.8. Comparison between FF3FM and CAPM based onResidual MethodTo compare the FF3FM and CAPM, the residuals inequation (3.2) are regressed against the factors inequation (3.9) and then run analogous regression byobtaining the residuals in equation (3.9) against thefactor in equation (3.2). Thus:εi = b1 + β^ +b2s^ +b3h^ + µi ……………………..………(3.18)

12

µi = c0 + c1β^i + ei……………………………………… (3.19)

On the a-priori equation (3.18) is expected to have astronger explanatory power than 3.19. 3.1.9. Comparison between the FF3FM and the CAPM basedon Davidson and Mackinnon Method ri = br(CAPM) + (1-b)rFF3FM + µi………………………(3.20)Where: the value of b must be close to one (1) for theCAPM to be more effective than the FF3FM3.1.9. Posterror Odds Ratio on the Comparison betweenthe FF3FM and CAPMR = ESSFF3FM n/2 ESSCAPM X n(kFF3FM

- kCAPM) /2

.........................................(3.21)

On the a-priori: R is expected to be less than one forthe FF3FM to be more effective than the CAPM.

3.2 Data SourceThe raw prices of selected quoted companies in NigerianStock Exchange (NSE) are employed in this study.Therefore, our data are raw prices which do not includedividends but they are adjusted accurately in order forthem to be standardized. The time series of excessreturn on the market and individual securities aretaken over the three months Government Treasury BillRate; which is assumed to be the short-term interestrate or risk free rate. Data on individual securitiesprices and market share index are sourced from NSEWebsite (www.cscsnigerialtd.org) and Daily Official

13

List respectively. The monthly returns are calculatedusing the logarithmic approximation formular (Rj(t) =log(pj(t)/pj(t-1)). In the same vein, the monthly marketreturns are calculated using Rm = log(closingindex/opening index). Rjt is the return on security say(j) at time (t), pjt is the current price of securitysay (j), pj(t-1) is the previous price of security say (j)and Rm is the return on market portfolio. However, thedata set covers a period of 96 months ranging fromJanuary 2003 to December 2011. 4.1 ResultThe test results on the superiority of the CAPMC to theCAPM using Residual Based, Posterror Odds Ratio,Davidson and Mackinnon Techniques are extracted fromequations 3.14, 3.15, 3.16 and 3.17. These results aresummarized jointly in table 4.1.Table 4.1: Comparing the superiority of the CAPMC tothe CAPM based on Residual, Posterror Odds Ratio, Davidsonand Mackinnon Techniques. Residual Based Davidson and Mackinnon

posterior Odds

Method Method

Ratio

Model AR2 F-stat

α 1 – α value14

CAPM -0.019 1.14E-10(1.000) 0.066[0.228]

0.934(0.08)

CAPMC -0.041 0.312(0.816)

31.953Note: The values in parenthesis and bracket are the probability and t-values respectively. * denotes significant at 99%confidence level. The posterior odds ratio 31.953 is by far larger than one.

Source: Authors’ ComputationThe residual based method shows that the CAPMC fails tocapture the variance which the CAPM does not explainneither does the CAPM explain the variance of theCAPMC. This reveals that there are some latent marketfactors or non-markets factors which are incorporatedin the APT or other similar model that could explainthe variances in these models. Therefore, beta factor,systematic co skewness and co kurtosis are notsufficient in explaining average monthly return inNigerian capital market. The Davidson and Mackinnonmethod shows that the CAPMC has a coefficient 1- αclose to one but it is not significant. Thus, there islack of inconclusive evidence to support the CAPMCsuperiority to the CAPM using this method. Also theresult of the posterior odds ratio (31.953) is largelyin favor of the CAPM. Since the posterior odds ratio isconsidered to be theoretically sounder than theDavidson and Mackinnon method, we can infer that theCAPM performs better than the CAPMC on portfolio basisusing unconditional test but the CAPMC has improved the

15

descriptive ability of the CAPM on the basis ofindividual securities (see, appendix)

In comparing the FF3FM and the CAPM, equations 3.18,3.19, 3.20 and 3.21 are estimated to test whether FF3FMperforms better than the CAPM. The results are reportedin table 4.2.Table 4.2: Results of the Test conducted on theComparison between FF3FM and CAPM using ResidualBased, Davidson & Mackinnon and Posterror Odds RatioTechniques. Residual Base Method Davidson and Mackinnon Method

Post-error Odds Ratio

Model AR2 F-stat b 1– b valueCAPM -0.013 0.778(0.512) 0.089[1.591]FF3FM -0.019 0.024(0.876)0.911[0.028] 15.151 Note: The figures in parenthesis and brackets are the probabilities and t-values respectively. The value of thePosterror Odds Ratio is found to be 15.151

Source: Author’s ComputationThe Residual Based Method shows very weak and negativeAR2 in respect of the CAPM and the FF3FM. This means theFF3FM risk factors fail to explain the variation in theCAPM residuals, also the CAPM factor does not explainthe variations of the FF3FM residuals. Therefore, basedon this test the FF3FM cannot be said to be moreeffective or applicable than the CAPM. Furthermore,

16

Davidson and Mackinnon method also shows that thecoefficient 1-b is not significant which means thereis no sufficient evidence in support of the FF3FMsuperiority to the CAPM. However, the Posterror OddsRatio is quiet larger than one, suggesting that theCAPM could perform better than the FF3FM. Hence, wehave discovered that the CAPM is more applicablethan the CAPM and FF3FM on portfolio basis usingunconditional approach but on individual stock basisthe FF3FM performs better (see appendix two)

5. Conclusion and Recommendation

The study presents an empirical investigation on thesuperiority of either the FF3FM or CAPMC to the CAPM.The researchers adopt the residual, post-error oddsratio, Mackinnon and Davidson techniques in theirinvestigation. The residual based method reveals thatnone of the three models represents a good pricingidentification when conditional information is missed.Thus, this evidence confirms the study of Arewa et al(2015). However, the test conducted on the basis ofMackinnon and Davidson provides inconclusive results;while the post error odds ratio yields overwhelmingevidences in supporting the superiority of the CAPM toCAPMC and FF3FM. Therefore, the need to test thesemodels using conditional information is strongly

17

recommended in this study. Also, we recommend that theCAPM should be applied when conditional in informationis lacking as an appropriate discounting technique.

ReferenceArewa, A., Onafalujo, A. K., & Nwakanma, P. C.(2015). Empirical proof of the CAPM with higher order co-moments inNigerian stock market: the conditional and unconditional basedtests. Journal of Applied Finance & Banking, 5(1), 151-162Anton , A. K., Adli, M., & Md. Azizul, B. (2013). Anempirical analysis of higher moment capital asset pricing model forBangladesh stock market. Modern Applied Science, 7(5), 11-12.Attiya , Y. J., & Eatzaz, A. (2008). Test of multi-moment capital asset pricing model: evidence from Karachi stockexchange. Pakistan Institute of Development Economics Islamabad WorkingPapers (49). Cao, Q., Leggio, K.B., & Schniederjans, M.J.(2005). A comparison between Fama and French’s model andartificial neural networks in predicting the Chinese Stock Market. Computers &Operations Research, 32, 2499-2512.http://dx.doi.org/10.1016/j.cor.2004.03.015Fama, E.F., & Macbeth, J.D. (1973). Risk, return andequilibrium: Empirical tests.

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Journal of Political Economics, 81(3), 607-636.Fama, E.F., & French, K.R. (1992). The cross-section ofexpected stock returns. Journal of Finance, 47(2), 427-465.Fang, H., & Lai T.Y. (1997). Co-kurtosis and capitalasset pricing. The Financial Review, 32, 293-307.

Fama, E.F., & French, K.R. (2004).The capital assetpricing model: theory and evidence. Journal of Economic Perspectives, 18(3),25–46.Griffin J., Ji, X., & Martin, S. (2003). Momentuminvesting and business cycle risk: evidence from pole to pole. The Journalof Finance, 57(6), 2515-2547. http://dx.doi.org/10.1046/j.1540-6261.2003.00614.xIqbal, J., & Brooks, R. (2007). Alternative betarisk estimators and asset pricing tests in emerging markets: the case ofPakistan. Journal of Multinational Financial Management, 17, 75-93Kraus, A., & Litzenberger, (1976). Skewness preferenceand valuation of risk assets. Journal of Finance, 31, 1085-1100.Lintner, J. (1965). The valuation of risk assets andselection of risky investments in stock portfolios and capital budgets.Review of Economics and Statistics, 47, 13-37.

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Mossin, J. (1966). Equilibrium in a capital assetmarket, Econometrica,34, 764-783.O’Brien, M., Brailsford, T.J., & Gaunt, C.(2008). Size and book-to-market factors in Australia, 21st Australasianfinance and banking conference paper. Working Paper Series.Perold, A.F. (2004).The capital asset pricing model.Journal of Economic Perspectives, 18(3), 3–24.Pettengill, G.N., Sunderan, S., & Mathur I. (1995). Theconditional relation between beta and returns, Journal of Financial andQuantitative Analysis, 30, 101-116Roll, R. (1977). A critique of the asset pricingtheory’s tests; part I: On past and potential testability of the theory.Journal of Financial Economics, 4(2) 129-176. Sharpe, W.F. (1964). Capital asset prices: A theory ofmarket equilibrium under conditions of risk. Journal of Finance, 19, 425-442. Tamara, T., & Evgeniya, S. (2011). A higher momentdownside framework for conditional and unconditionalCAPM in the Russian stock market. Eurasian Economic Review, 1(2), 157-178Tepmony, S. (2010). Detecting premium portfolios inhigher-order moments

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CAPM. Unpublished M.Sc Theses. FoscariUniversity of Venice, Unlu, U. (2013). Evidence to support multifactor assetpricing models: the case of the Istanbul stock exchange. Asian Journal ofFinance & Accounting, 5, (1), 197-208

APPENDIX ONE : TIME SERIES ORONE PASS REGRESSION RESULTS ON CAPM & CAPMC

S/N COMPANY r Β^ AR2F-STAT S^K AR2

F-Stat K^t AR2

F-Stat

1 AG Leventis x1 0.0000190.384 0.2

27.859

-0.53

90.2

128.78

2 0.3 0.0385.198

2 Alico x2 0.00730.462

0.239

34.669

-0.50

10.1

418.77

40.3

6 0.0445.9

6

3 Ashaka cement x3-

0.0086050.458

0.272

41.067

-0.59

60.2

4 34.570.3

5 0.0516.804

4 Academy x4 0.0018350.438

0.365

62.588

-0.49

10.2

434.02

20.4

6 0.14318.79

5 Avoncrown x5 0.0100580.482

0.297

46.119

-0.46

70.1

4 18.730.4

6 0.09111.71

6 Beta Gas x6 0.0039890.477

0.357

60.528

-0.43

80.1

520.08

70.4

9 0.13117.15

7 Bocgas x7 0.0018370.4

40.268

40.141

-0.52

8 0.227.53

4 0.4 0.0759.724

8 Cadbury x8-

0.0016490.458

0.359

61.013

-0.47

4 0.227.13

10.4

9 0.14719.44

9 Champion brew x9 0.10380.456

0.234

33.724

-0.49

10.1

418.05

70.4

8 0.0911.57

10 CAP x10 0.00550.457

0.336

55.221

-0.45

10.1

722.22

90.4

6 0.11614.98

11 CCNN X11 0.0000330.476

0.246

35.816

-0.56

80.1

824.35

7 0.4 0.0567.326

21

12 D N meyer x12 0.00580.4

40.247

36.15

-0.46

90.1

418.75

90.4

9 0.10813.66

13 Dunlop x13 0.00850.5

10.25

36.706

-0.46

7 0.113.38

10.5

1 0.08410.86

14 Ekocorp x14 0.003910.4

90.343

56.884

-0.44

3 0.118.50

70.4

9 0.1215.66

15 First bank x15 -0.006880.458

0.338

55.635

-0.53

70.2

434.67

40.3

6 0.079.062

16 First bank x16 -0.00580.517

0.381

66.978

-0.40

60.1

215.04

40.5

9 0.17623.81

17 Flour mills x17 0.006050.491

0.303

47.548

-0.50

50.1

621.77

60.4

6 0.0911.62

18 Glaxosmith x18 0.005880.4

70.417

77.437

-0.53

20.2

841.55

20.4

7 0.14519.

1

19 Guaranty x19 0.003360.481

0.377

65.736

-0.55

0.25

37.338

0.42 0.097

12.58

20 Guiness x20 0.002460.502

0.457

91.094

-0.47 0.2

28.346

0.52 0.173

23.45

21 John Holt x21 0.0060110.502

0.322

51.854

-0.48

10.1

519.76

30.4

8 0.10213.02

22 Jullius begger x22 0.0017060.426

0.272

41.018

-0.52

40.2

1 29.840.3

2 0.0496.502

23 Mobil x23 0.0155280.406

0.146

19.234

-0.43

0.08

10.455

0.48 0.071

9.165

24 Mrs x24 0.0022220.455

0.442

85.798

-0.48

10.2

537.27

50.4

9 0.18525.26

25 May &baker x25-

0.0004370.526

0.376

65.468

-0.43

80.1

316.97

50.4

7 0.10113.02

26 Nigeria ropes x26 0.0283670.576

0.091

11.76

-0.52

80.0

4 4.8390.4

8 0.0162.742

27 Nigerins x27 -0.003240.513

0.372

64.496 -0.5

0.18

24.365

0.54 0.147

19.41

28 Niwicable x28 -0.001790.476

0.226

32.272

-0.58

0.17

23.221

0.43 0.061

7.942

29 NNFN x29 0.006030.479

0.336

55.204

-0.45

90.1

620.74

5 0.5 0.12716.

5

30 Okomu x30 0.00909 0.40.337

55.506

-0.39

70.1

722.61

6 0.4 0.11715.24

31 Oando oil x31 -0.002990.103

0.008 1.85

-0.00

5 -0 0.0020.0

1-

0.0090.007

32 Pz x32 0.00806 0.491

0.417

77.616

-0.46

0.19

26.325

0.51

0.159 21.29

22

7

33 Presco x33 0.003020.546

0.373

64.552

-0.47

50.1

4 18.490.5

7 0.14218.78

34 Prestige x34 -0.003260.514

0.436

83.847

-0.36

50.1

113.90

20.5

6 0.18425.14

35 RT Briscoe x35 0.003780.463

0.365

62.481

-0.48 0.2

27.829

0.49 0.143

18.83

36 Royalex x36-

0.0028760.448

0.266

36.699

-0.46

80.1

519.37

30.4

5 0.01211.81

37 Total x37-

0.0044890.486

0.45

88.69

-0.45

4 0.227.74

80.5

3 0.18825.

8

38 Trippleg x38 0.0091790.481

0.205

28.53

-0.53

80.1

316.98

50.4

5 0.0587.644

39 UBA X39-

0.0010760.541

0.255

37.562

-0.43

50.0

8 9.8590.5

5 0.08611.

1

40 Unilever plc x40 0.00529 0.50.393

70.224

-0.52

0.22

30.551

0.43 0.101

13.06

41 Union bank x41-

0.0134370.547

0.308

48.51

-0.60

10.1

9 26.050.4

2 0.067.836

42 UAC X42-

0.0003950.4

90.429

81.554

-0.45

50.1

925.64

40.5

8 0.21229.85

43 UACN X43 0.0007450.457

0.446

87.135

-0.45

40.2

221.13

90.4

7 0.16522.16

44 UNIC X44-

0.0010770.486

0.298

46.456

-0.45

80.1

317.37

80.4

1 0.0698.872

45 UTC X45 0.0062560.509

0.259

38.365

-0.61

30.1

926.53

70.4

5 0.0668.581

46 UPL X46 0.0045980.489

0.291

46.761

-0.46

40.1

417.70

80.4

7 0.09311.93

47 UNTL X47 -0.00420.434

0.224

31.923

-0.44

10.1

215.02

40.4

3 0.0739.393

48 Vital foam x48 -0.003320.442

0.309

48.85

-0.51

90.2

231.03

80.3

9 0.08210.52

49 Vono x49 0.001240.1

70.241

36.646

-0.46

0.16

20.578

0.39 0.071

9.238

50 Wapco x50 0.002680.522

0.425

80.055

-0.51

20.2

129.04

60.4

8 0.12416.

1

51 Wapic x51 0.003890.5

20.366

62.824

-0.49

80.1

722.84

70.5

4 0.13918.21

52 Wema Bank x52 -0.0216 0.562

0.206

28.692

-0.16

0 1.059 0.68

0.105 13.59

23

8

537 up bottling company x53 -0.0105

0.368

0.159

21.261

-0.58

20.2

129.52

10.3

3 0.0395.309

APPENDIX TWO: UNCONDITIONAL TEST OF THE FF3FM

sn β AR2 S^ AR2 H^ AR2FF3FM AR2

X10.384 0.201

2.199

0.553

24.76 0.553 0.544

-27.83

5

-133.

1 -133.1 -43.532

X20.462 0.24

2.053

0.391

23.13 0.39 0.406

-34.7

-69.5

5 -69.53 -43.532

X30.459 0.273

1.615

0.276

18.18 0.275 0.33

-41.09

7

-41.6

8 -41.68 -18.602

X40.438 0.365

1.973

0.611

22.21 0.611 0.039

-62.55

7 -169 -168.9 -64.099

X50.482 0.297

2.336

0.577

26.31 0.577 0.581

-46.12

6 -147 -147 -50.469

X60.477 0.358

2.005

0.518

22.58 0.518 0.556

-60.56

6

-116.

1 -116.1 -45.587

X70.4

4 0.2682.312

0.615

26.04 0.615 0.614

-40.20

-171.

-171.7 -57.678

24

1 8

X80.458 0.359

1.908

0.512

21.49 0.512 0.552

-61.03

4

-113.

4 -113.4 -44.866

X90.456 0.234

2.011

0.377

22.65 0.377 0.391

-33.74

6

-65.8

5 -65.84 -23.89X10

0.457 0.336

2.108

0.589

23.74 0.589 0.609

-55.26

3

-154.

4 -154.4 -56.505X11

0.476 0.245

2.287 0.47

25.75 0.47 0.474

-35.78

7

-95.8

8 -95.87 -33.088X12

0.44 0.247

2.137

0.484

24.07 0.484 0.484

-36.13

1

-101.

2 -101.2 -34.448X13

0.511 0.25

2.571

0.526

28.95 0.526 0.524

-36.37

-118.

7 -118.7 -39.859X14

0.49 0.343

2.37

0.663

26.69 0.663 0.671

-56.90

1

-211.

6 -211.6 -73.777X15

0.458 0.338

2.002

0.533

22.55 0.533 0.556

-55.64

2 -123 -122.1 -45.694

25

X16

0.517 0.382

2.242 0.59

25.25 0.59 0.633

-67.00

9

-514.

9 -154.8 -62.643X17

0.491 0.203

1.908

0.375

21.49 0.375 0.417

-47.54

-65.2

4 -65.25 -26.484X18

0.47 0.417

2.109 0.69

23.74 0.69 0.726

-77.45

9

-239.

1 -239 -95.645X19

0.481 0.377

2.051

0.563

23.09 0.563 0.597

-65.76

5

-138.

8 -138.8 -53.834x20

0.502 0.457

1.869

0.598

21.05 0.518 0.603

-91.18

3

-115.

1 -115.9 -55.23X21

0.502 0.322

2.419

0.619

27.24 0.619 0.629

-51.85

9

-174.

6 -174.6 -61.475X22

0.426 0.273

1.694

0.353

19.07 0.353 0.39

-41.03

9

-59.3

4 -59.33 -23.815X23

0.406 0.146

1.448

0.152

16.31 0.152 0.197

-19.23

3

-20.1

2 -20.11 -9.729X2 0.4 0.447 1.9 0.65 21. 0.659 0.703

26

4 55 39 9 83-

85.785

-207.

8 -207.8 -85.57X25

0.526 0.376

2.07

0.477

23.31 0.477 0.53

-65.51

4

-98.7

8 -98.78 -41.192X26

0.576 0.091

3.741

0.337

42.13 0.337 0.327

-11.76

3-

55.3 -55.31 -18.322X27

0.513 0.372

2.338

0.636

26.32 0.636 0.673

-64.51

-188.

1 -187.9 -74.377X28

0.477 0.226

2.405 0.48

27.09 0.48 0.477

-32.28

5

-99.6

5 -99.63 -33.568X29

0.479 0.337

2.16

0.565

24.33 0.565 0.584

-55.27

7

-139.

7 -139.7 -50.994X30 0.4 0.338

1.908

0.633

21.48 0.633 0.648

-55.51

7

-185.

5 -185.4 -66.673

X31

0.103 0.008

0.061

-0.00

90.683 -0.009 0.004

-1.857

-0.05

2 -0.052 -1.14X3 0.4 0.017 2.0 0.60 23. 0.601 0.667

27

2 91 7 1 31-

77.615

-168.

2 -168.1 -72.388X33

0.546 0.373

2.016

0.414

22.7 0.414 0.486

-64.57

5

-76.6

1 -76.64 -34.741X34

0.514 0.436

1.964

0.522

22.12 0.522 0.596

-83.81

3

-117.

7 -117.7 -53.549X35

0.463 0.365

2.107

0.623

23.73 0.623 0.642

-62.45

5 -178 -178 -65.002X36

0.448 0.266

2.155

0.508

24.26 0.508 0.513

-39.70

7

-111.

5 -111.5 -38.564X37

0.486 0.45

1.988

0.619

22.39 0.619 0.674

-88.66

1

-174.

6 -174.6 -74.834x38

0.481 0.285

2.743

0.559

30.82 0.559 0.553

-28.53

2

-136.

5 -136.5 -45.084X39

0.549 0.255

2.488

0.432

28.02 0.432 0.441

-37.55

5

-82.2

6 -82.3 -30.151X40 0.5 0.393

1.956

0.491

23.03 0.491 0.549

28

-70.21

5

-104.

4 -104.3 -44.41X41

0.547 0.308

2.427

0.499

27.34 0.499 0.917

-48.52

8

-107.

7 -107.7 -39.077X42

0.49 0.429

2.191

0.705

24.67 0.705 0.738

-81.50

8

-256.

6 -256.6 -101.261X43

0.457 0.446

1.916

0.642

21.57 0.642 0.69

-87.16

5

-193.

1 -193.1 -80.511X44

0.486 0.298

2.059

0.431

23.11 0.431 0.461

-46.47

1

-84.9

7 -84.94 -32.605X45

0.501 0.259

2.773

0.638

31.22 0.637 0.634

-38.35

8

-189.

2 -189.1 -62.891X46

0.489 0.291

2.917

0.499

24.74 0.499 0.517

-46.83

-107.

7 -107.7 -39.182X47

0.434 0.224

2.094

0.433

23.58 0.433 0.432

-31.90

7

-82.7

4 -82.74 -28.139X48

0.442 0.309

1.874

0.457

21.1 0.457 0.486

- - -91.03 -34.736

29

48.873

91.05

X49

0.417 0.241

2.115

0.534

23.82 0.534 0.535

-36.61

4

-123.

6 -123.6 -42.01X50

0.522 0.425

1.954

0.486

22.01 0.496 0.562

-80.10

4

-102.

6(102.283 -46.796

X51

0.52 0.366

2.352

0.616

26.48 0.616 0.638

-62.78

1

-172.

4 -172.4 -63.93X52

0.562 2.206

2.335

0.293

26.3 0.293 0.306

-28.69

8

-45.3

3 -45.32 -16.739X53

0.368 0.159

1.572

0.241

17.7 0.241 0.276

-21.28

6

-35.0

5 -35.02 -14.581

30