stock returns and macro risks: evidence from finland

Research in International Business and Finance 26 (2012) 47– 66

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Research in International Businessand Finance

journal homepage: www.elsevier.com/locate/r ibaf

Stock returns and macro risks: Evidence from Finland

Nader Shahzad Virk ∗

Hanken School of Economics, Finance and Statistics, Harustie 8 A 8, 00980 Helsinki, Finland

a r t i c l e i n f o

Article history:Received 30 September 2010Received in revised form 2 May 2011Accepted 16 June 2011

Available online 23 June 2011

JEL classification:G12E44

Keywords:CAPMMacro risksCross-sectional variationsHansen and Jagannathan (1997)specification measure

a b s t r a c t

Deviations from the CAPM have generally been observed for thestock markets. One of many alternative approaches is using macrovariables as systematic risks. We tested with a number of macrorisks for the explanation of Finnish industry returns for a periodfrom 1993:03 until 2008:07. The evidence suggests macro risksexplain larger cross-sectional variations in average industry returnsthan the market factor alone and same is reported with the Hansenand Jagannathan (1997) specification measure. The changes inexpected returns with a positive shock in the exchange rate risk andunanticipated inflation remain economically persistent for the posteuro period, arguably a sign for the regulatory impact of the coor-dinated policies from European central bank (ECB). The robustnesschecks show the prevalence of macro risks, and market risk cannotbe ignored altogether.

© 2011 Elsevier B.V. All rights reserved.

1. Introduction

Post Fama and French (1992), unconditional tests of the capital asset pricing model (CAPM) areregarded insufficient to explain cross-sectional variations in stock returns. Their results confirmedthe limitation of CAPM to explain the average spread on size and book to market ratio (BM) sortedportfolios. The use of uncorrelated risk factors as allowed with the arbitrage pricing theory (APT)of Ross (1976) prompted multifactor modelling for the explanation of average returns. It leads tothe development of new risk factors for the explanation of variations in the average returns, such asfactors based upon market size and BM characteristics (Fama and French, 1993), the momentum factor(Jegadeesh and Titman, 1993), and the liquidity risk factor (Pastor and Stambaugh, 2003) and report

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48 N.S. Virk / Research in International Business and Finance 26 (2012) 47– 66

0

50

100

150

200

250

300

1990 1995 2000 2005

Market Ca pitalisa�on of list ed Compn aies as %age of GDP

FIN

US

GER

SWE

Fig. 1. The percentage stock market capitalization to gross domestic product (GDP) ratio is graphed for Finnish stock marketalong with US, German and Swedish stock markets from 1990 to 2008.Source: World Development Indicators, World Bank.

substantial empirical evidence for asset pricing anomalies. These studies demonstrate the success ofmultifactor models than theoretically more upright models such as CAPM and consumption basedequilibrium counterparts. Promising avenues of research that retain a single factor structure havebeen conditional variants of the CAPM (Ferson and Harvey, 1991; Jagannathan and Wang, 1996; Angand Chen, 2007) to name a few among many.

Another import strand of research is the macroeconomic explanation of asset returns. The changesin economic variables have an exogenous impact on stock prices and shift the demand curve forstocks and assets.1 Chen et al. (1986) used theoretical explanations for the identification of economicstate variables as systematic influences to model variations in the stock returns, rather than bearingdiversifiable risk. It proposes if the economic variables capture the changes in aggregate marginalutilities than the relationship is consistent to account for investors intertemporal hedging needs andfound a number of economic risks priced cross-sectionally. A number of studies have reported positiverelation between stock returns and real economic activity (Fama, 1981; Kaneko and Lee, 1995; Lee,1992) for US market. Moreover, Apergis et al. (2011) in contemporary work showed the presence offoreign exchange risk for cross-section of German stock portfolios in the post euro period.

1.1. Case Finland

Finland stock market has conventionally been regarded a small yet developed2 market with primaryreliance on foreign trade. The enhanced industry specialization and liberalized economy makes it openfor international investment. The resilience of Finnish economy during the current global recessionmakes it even more important to satisfy diversification needs of global investors than many emergingor frontier markets. Since late 1990s Finnish stock market has shown a much higher market capitaliza-tion to GDP ratio than other European economies as shown in Fig. 1. The ratio in the pre-liberalizationperiod was marginally smaller but geared in the later part of the decade and accounted more than50%. The liberalization3 in 1993 provided the impetus for international investment in a stock marketwith substantial expected growth. The years 1998 and 1999 observed an unprecedented growth in themarket capitalization ratio to previous years, larger than other developed economies. The enormous

1 Theory suggests that information regarding the expansion (continuation or discontinuation) of an economy will shift thedemand curve for investments for example stocks (right or left). Similarly, there are also certain movements of the demandcurve for changes in investment decisions for different assets in aggregate for other macro and business cycle variables.

2 It has been part of MSCI world index since 1997 though its capitalization makes only 1% of the total index.3 The market liberalization process could be tracked back to early 1980s (Berglund and Knif, 1999) which culminated to its

fullest with no restrictions of the ownership of Finnish shares in 1993.

N.S. Virk / Research in International Business and Finance 26 (2012) 47– 66 49

growth in Nokia4 and other high-tech companies was the main reason for inflating Finnish marketcapitalization and the GDP ratio during the period. The subsequent periods though have flattened theratio, but it still remains at a reasonable level to regard Finland a capitalized economy.

There is a wide body of literature on asset pricing for the Finnish stock market. Numerous studiestested CAPM for Finland such as Berglund (1986), Berglund and Knif (1999) and Malkamäki (1993) andthe consensus has been the market risk is time varying. Vaihekoski (2000) performed unconditionaltests of single and multifactor models in international settings using characteristics portfolios whereasVaihekoski (2009) reported significant liquidity premia in the Finnish market. Antell and Vaihekoski(2007) and Nummelin and Vaihekoski (2002) noted that local risks are significantly priced besidesthe significance of global and currency risks for Finnish stocks. These studies also tested with macrofactors such as inflation and currency risks, but used more as control variables than as drivers, toexplain the differences in average asset returns. Junttila et al. (1997) reported that studies in generalemployed latent pricing variables, from a number of macro variables, using factor analysis and testedfor their exposures for aggregate market return. This approach has potentially two drawbacks; firstly, itundermines the exposure of different asset classes such as industries and trade orientation to prevalentrisks for using market index. Secondly, using latent factors leave the identification of economic risksunresolved as the determinant of variability in stock returns.

This study attempts to abridge this gap for cross-sectional predictability of Finnish stock returnswhile accounting for a number of macro risks in line with Chen et al. (1986). Moreover, the study isalso important to report the impact of coordinating monetary and fiscal policies by European Union(EU) and its respective mandated agencies onto the performance of stock return from a representativeeuro zone country. It will substantiate implications for euro zone countries regarding different macrovariables as potential risks since the adoption of a single currency unit. The price of risk estimationsis done with Fama and MacBeth (1973, FM from here on) method for 25 industry portfolios from1993:03 to 2008:07. All the estimations are repeated with samples before and after the introductionof euro as tangible currency in Finland. The results are compared against the benchmark CAPM withthe specification measure given by Hansen and Jagannathan (1997) and referred as HJ distance. The2nd stage FM cross-sectional regressions for each model are tested twice using first stage rolling betasprojected with least square method (OLS) and generalised method of moments (GMM). This exercise5

is extended to see when the first stage GMM are conditioned upon some additional information vari-ables, along with exact identification moments, does it improve the model performance in the 2ndstage FM regressions than the OLS rolling betas.

The sample selection makes the study important on two fronts. Firstly, the sample covers the fullyliberated times for Finnish stocks market and include key events such as joining EU and Europeanmonetary union (EMU) in 1995 and 1999 respectively. Secondly, the post euro period makes theanalysis convenient to compare the performance of Finnish stocks against pre euro sample. Thesetests are important to see the impact, if any, has been generated while using a single currency andother coordinated policies for its member states. Besides, EU integration makes growth opportunitiesin Finnish stocks relevant to larger representative investor base, with euro as their denominationcurrency. Nevertheless, with sufficient potential to fulfil diversification needs for an internationalinvestor. Smimou (2011) noted among a sample of euro-zone stock markets the cross correlation hasrisen during the post euro period, but it does not preclude diversification gains. Moreover, the growthin Finnish stocks is not sample specific as Nyberg and Vaihekoski (2010) showed that growth in Finlandstock market is a long run pattern for approximately last 100 years.

The peculiar institutional features, market characterisation, coverage of key events during the sam-ple period and implications for a large geographical block make it an interesting asset pricing test to

4 It grew from a 3 billion euro business in the year 1994–250 billion euro enterprise in the year 2000 and was approximately80% of the total market capitalization. But this particular effect has been rounded to a large extent that for the year 2008 theNokia capitalization accounted for 37% of the total market value.

5 The study only reports the factor betas and does not take into account the time varying components of conditional beta forthe factors in the model. An unconditional test of a conditional model require the estimation of additional scaled factors thatcome into equation as product of conditioned variable (zt) and the factors (ft+1) in the model (see Jagannathan and Wang, 1996or Cochrane, 2005 for text book references).


identify types of significant systematic risks for Finnish stocks. The results for average industry returnsare expected to approximate the significance of macro risks same as for German stocks than US market.The results for German market have shown successful size and value risk factors from Fama and French(1993) could only explain as much as a macro-conditioned CAPM (Schrimpf et al., 2007). However,these results are not in accordance with the evidence reported for US in Fama and French (1993). Ina similar manner, Jagannathan and Wang (1996) also reject the Chen et al. (1986) macro explanationto be cross-sectionally priced when taken along a scaled factor specification of CAPM.

The exploration for Finnish industry returns shows CAPM is unable to relate its theoretical predic-tions both with the time series and cross-sectional specifications for the explanation of average stockreturns. The tests with macro risks explain larger cross-sectional variability in industry returns thanCAPM. The risk premium for changes in variables such as interest rates, exchange rate and inflationare robust among other macro risks. There is no particular discernability among unconditional mod-els in terms of HJ distance measure except for pre euro period when the HJ pricing errors with macrorisks and market factor model are at the least distance from the set of true pricing kernels among thecompeting models. The results suggest the unit shocks in the mentioned variables are economicallyof large quantity across all testing periods. The post euro results show exchange rate risk induces sub-stantial changes in industry returns, and unanticipated inflation remains persistent. The scaled factortesting with SDF-GMM methodology for selected macro factors produce even smaller pricing errorsthan unconditional models. The performances could further be bettered if the conditional settingsare augmented with market factor. The robustness tests show that the parameters from stochasticdiscount factor (SDF)-GMM estimations with market factor and exchange rate changes explain largertime series variability in industry returns.

The remainder of the paper is organized as follows. Section 2 details the methods used and Section3 describes the data and notations used in the study. The results from the estimations in the paper arediscussed in Section 4 and Section 5 concludes the article.

2. Data

The monthly end-of-period total returns for sector indices were retrieved from Datastream forthe period from 1993:03 to 2008:07. The previous five year data has been used for first stage rollingbeta estimates as the Datastream indices for Finnish industries go back until 1988. All the selectedprice series and subsequent returns are in the euro denominations to maintain European investorperspective, in general. The data length is reasonable for asset pricing analysis and comprises 185monthly observations. The Datastream total returns indices are adjusted for dividends, splits and otherforms of cash payouts. The model estimations in the study are done using continuously compoundedexcess returns6. The annualized mean and standard deviations for the excess returns are presented inTable 1 along with risk free rate and all share market index excess return7. The sample statistics forfull sample, sample before and after the introduction of euro are under panels A, B and C respectivelyand this notation is maintained through the course of this study. All industries with an exception ofpaper and general industrials have positive annualized average returns.

The percentage Sharpe ratios for the industry portfolios during the pre euro sample are on averagelarger than the post euro sample. The Sharpe ratio improves in sample C for sectors, i.e., industrialengineering, industrials, industrial goods and services and industrial machinery than their pre eurosample. It is one indication of the booming state of Finnish economy in the later years of 1990s, whenthe additional unit of risk was compensated with larger proportional increase in mean returns thanthe post euro sample, assuming normality. In the pre euro sample six industries offered the one-on-one reward to risk ratio and in the cases of high tech sectors was even better. Moreover, in the fullsample it shows on average the industries which offer higher expected returns are also with a higher

6 The SDF-GMM (cross-sectional) estimations use gross returns for the calculation of HJ-distance for ranking the performanceof tested models.

7 The one month European interbank offer rate is used as a proxy for the risk-free rate, for the period before 1999:01 theseries is completed with HELIBOR.

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26 (2012) 47– 6651

Table 1Summary statistics for market and sector indices.

Rf rm Banks Financials Insurance Nonfinancial

Food and drugretailers

Broadlineretailers

Consumerstaples

Forestryand paper

Paper HHG&HC W&Dservices

Healthcare

A: 1993:03–2008:07� 3.80 14.10 15.40 14.80 17.30 14.20 7.00 8.00 7.10 3.60 −2.20 12.50 13.00 9.40� 0.40 29.70 31.50 27.60 31.00 30.40 25.70 25.20 26.40 29.10 32.40 28.80 26.80 22.20S.R. 47.47 48.89 53.62 55.81 46.71 27.24 31.75 26.89 12.37 −6.79 43.40 48.51 42.34B: 1993:03–1998:12� 4.62 31.41 25.11 25.22 28.04 31.99 9.84 17.32 16.11 12.50 6.64 30.74 20.11 12.33� 0.44 25.76 42.98 35.54 37.73 25.72 25.27 24.72 26.78 28.94 32.74 29.81 28.47 25.37S.R. 121.93 58.42 70.96 74.32 124.38 38.94 70.06 60.16 43.19 20.28 103.12 70.64 48.60C: 1999:01–2008:07� 3.28 3.60 9.47 8.43 10.79 3.42 5.31 2.38 1.66 −1.78 −7.61 1.37 8.64 7.54� 0.27 31.56 21.83 21.32 26.07 32.57 26.12 25.43 26.18 29.27 32.17 27.88 25.78 20.21S.R. 11.41 43.38 39.54 41.39 10.50 20.33 9.36 6.34 −6.08 −23.66 4.91 33.51 37.31

G.R. Media Consumerservices

Basicmaterials

Generalindustrials

Industrialengineering

Industrials IndustrialG&S

Industrialmachinery

IndustriesM&M

TechnologyH&E

S&Cservices

Tech.

A: 1993:03–2008:07� 8.03 10.90 6.90 6.40 −3.00 10.20 9.80 9.00 13.70 10.00 24.50 13.20 24.20� 25.20 29.80 20.10 26.90 27.50 25.80 24.60 22.20 25.00 30.50 44.80 43.50 44.20S.R. 31.87 36.58 34.33 23.79 −10.91 39.53 39.84 40.54 54.80 32.79 54.69 30.34 54.75B: 1993:03–1998:12� 17.30 26.70 20.20 11.60 −1.50 8.50 10.30 9.40 4.00 1.20 62.00 60.90 62.00� 24.70 31.40 21.10 26.70 34.00 28.30 27.90 25.20 26.90 31.10 43.10 36.70 42.40S.R. 70.04 85.03 95.73 43.45 −4.41 30.04 36.92 37.30 14.87 3.86 143.85 165.94 146.23C: 1999:01–2008:07� 2.40 1.20 −1.10 3.30 −3.90 11.20 9.50 8.70 19.60 15.40 1.60 −15.70 1.20� 25.40 28.60 19.30 27.10 22.80 24.30 22.50 20.30 23.70 30.10 44.70 45.30 44.20S.R. 9.45 4.20 −5.70 12.18 −17.11 46.09 42.22 42.86 82.70 51.16 3.58 −34.66 2.71

The sectors household goods and home constructions, waste and disposable services, general retailers, industrial goods and services, industries metals and mines, technology hardwareand equipment, software and computer service, technology are abbreviated with HHG&HC, W&D Services, G.R., Industrial G&S, Industries M&M, Technology H&E, S&C Services and Tech.respectively. The continuously compounded returns for the risk free rate, market factor and industry portfolios are reported for the sample periods denoted as A, B and C for full sample,before the introduction of euro and after the introduction of euro respectively. The reported percentage sample averages and standard deviations for all the variables are annualized suchthat sample monthly means are multiplied by 12 and (12)1/2 respectively. The reported Sharpe ratio (S.R.) is computed by dividing the annualized excess mean with the respective sectordeviation and is reported in percentage points.


Table 2Explanatory variable, symbols and definitions.

Symbol Variable Definition/source

Basic variablesRf Risk free rate Percentage monthly return on one month

Interbank offered rate/Bank of Finland (BOF)LGB Long term govt. bond Percentage monthly return on Finnish ten years

Govt. bonds/BOFEXR [D/$] Exchange rate Euro per US dollars exchange rate/BOFUE Unemployment rate Percentage monthly rate/Statistics FinlandCPI Consumer price index The price development of goods and services

(Base year 1981)/Statistics FinlandCCI Consumer confidence index Consumers’ monthly views and expectations on individual

and national development/BOF and Statistic FinlandDerived variablesIRt+1 Inflation rate Percentage log relative of consumer price index

ln[CPI(t + 1)/CPI(t)]RHOt+1 Real interest rate (ex post) Rf(t + 1) − IR(t)EIRt+1 Expected inflation rate Time series methoda

Rf(t) = E[RHO(t + 1)/I(t)] + E[IR(t + 1)/I(t)]Unanticipated inflation IR(t + 1) − EIR[(t + 1)/I(t))]

DXRt+1 Exchange rate changes Percentage log relative of exchange rateln[EXR(t + 1)/EXR(t)]

TSt+1 Term structure LGB(t + 1) − one month interbank rate (t)

The explanatory variables are listed, along with the symbols and respective definitions in the paper. The macro informationvariables are detailed as basic and derived variables. The consumer confidence index is obtained from Bank of Finland till2007:04 and later period data is completed from Statistics Finland database.

a Irving Fisher (1930) noted that nominal interest rates can be expressed as the sum of an expected real rate and an expectedinflation rate as modelled in Fama and Schwert (1977).

proportional increase in means than the industries which have lower average returns. There are onlyfour sectors in the full sample which offers 25% premium per unit of risk or less, emphasizing thehigher average growth in Finnish stocks for bearing a unit risk.

Table 2 lists the macro variables and derived variables. Chen et al. (1986) argued that “no satisfactorytheory would argue that the relationship between financial markets and the macro economy is entirelyin one direction”. The general equilibrium theory describes the adjustment of financial market demandcurves (left or right) with the arrival of new information such as future profits, economic expansionand interest rates. The selection of feasible macro variables as systematic influences on investmentrisk is critical and for a detailed discussion on it we refer to Chen et al. (1986). In this study, we useeconomic variables such as term structure spread of interest rates, exchange rate fluctuations, returnon long return bond, expected and unanticipated components of inflation and consumer confidenceindex. The interest rates variables and currency rates are provided by Bank of Finland, whereas allother are downloaded from Statistics Finland database. We also retrieved monthly unemploymentrate, industrial output, foreign direct investment and industrial confidence index but their inclusioncould not improve on the cross-sectional explanation for variations in stock returns. Therefore, weresubsequently dropped from the main analysis though unemployment rate is used as an instrumentvariable for projecting GMM based first stage rolling betas.

All the economic variables are endogenous and using these variables together as exogenous vari-ables is questionable. In order to deal with endogneity of macro variables, we employ orthogonaldecomposition of macro variables and return on the market index as is done in Campbell (1996).It gives us a non-overlapping linear ability of the market factor and macro factors to explain con-temporaneous variations in the asset returns. The orthogonal decomposition induces some spuriouscorrelation among few of macro factors. However, to maintain the robustness of statistical estimations,we used innovations to the factors in the model same as in Chen et al. (1986).

It is intuitive and suits well with the purpose of the study to look for economic state variablesthat could potentially explain the contemporaneous movements in the asset returns. Moreover, stockprices are dynamic and are updated frequently with the changing states of economy whereas macro


Table 3Correlations between factor risks and instruments.

rm �TS �DXR �CCI �LGB �EIR UI rm,t−1 TSt−1 UEt−1

rm 1�TS 0.02 1�EXR −0.01 0.05 1�CCI 0.05 0.12 0.07 1�LGB −0.15 0.27 −0.07 0.01 1�EIR 0.14 0.01 0.03 −0.06 −0.01 1UI 0.1 −0.04 0.12 −0.07 0.1 0.04 1rm,t−1 0.24 0.04 0.01 0.21 −0.1 −0.05 0 1TSt−1 0.18 0.23 0.07 0.15 −0.01 −0.03 0.11 0.20 1UEt−1 0.19 0.06 0.01 0.16 −0.16 −0.02 −0.12 0.24 0.18 1

The table reports the correlations between the factors used in different models, that is, return on market index and macro shocks.In addition to factors cross correlations among factors and first lag of market index [rm(−1)], term structure and unemploymentare also reported. These variables are used as conditional variables for the estimation of first stage GMM betas along with themoments of just identified case. The cross correlations between the factors and the instruments are presented in bold.

information is prior period aggregated information. There is considerable chance that some of collectedinformation is already incorporated in stock prices before their formal release. Therefore, shocks mayprove better candidates than the level of macro variables to capture the underlying stochastic shiftsin the investment set to explain the variations in asset returns. The shocks to macro variables arecalculated as unexplained part of the macro variables from an AR (1) process.

Table 3 reports cross correlation among the market factor, shocks to orthogonal macro variablesand instrument variables used in GMM estimations only. The cross correlations among the factor aremarginal to have any estimation problems for the robustness of the results. The correlation amongmacro shocks decreases to range between −0.15 and 0.27 from −0.81 to 0.57 among the levels of macrovariables (not reported). The lags for the term structure spread, unemployment rate and market factorshow a reasonable positive correlation with aggregate return index and changes in the consumerconfidence index. The selection of instruments could be one short coming since they are supposedto be strongly correlated with factors in the model. However, the identification of instruments isconstrained to remain in the scope of study. Therefore, we proceed with the estimation of GMM betasto capture additional linear explanation, if any, than the OLS betas.

3. Model

The models in the study are motivated from the linear stochastic discount factor (SDF)representation8 which under law of one price implies

Et(Mt+1Ri,t+1|It) = 1 ∀i (1)

where Ri,t is the gross return to asset i and Mt is the SDF that prices all risky payoffs such that there arenot any arbitrage opportunities, and Et(|It) represents the expectation conditional on the investor’sinformation set (|It) at time t. As Cochrane (2005) noted the absence of arbitrage opportunities leadsto above pricing relation where one may not require assumptions regarding investors’ utility function,aggregation, complete markets, etc. which otherwise are necessary to derive general equilibriumor complete market models. Besides, all, single factor or multi factor asset pricing models can benested as a special case of relation (1) under the model assumptions. Let Ft+1 = [1 ft+1] be a matrix

8 The SDF representation helps to specify the models in expected return-beat specification under the subsequent assumptionson period utility, formation of expectations and etc. Besides, the explanation of Hansen and Jagannathan (1997) specificationmeasure stems from Eq. (1) for comparing and ranking the performance of different models and for that is more convenient tostart and map proceeding model equations and specification measures.


comprising constant and risk factors and B = [b0 bk] be the vector of slope coefficients. Assuming alinear functional form for the SDF,

Mt+1 = B′Ft+1 = b0 + b′kft+1 (2)

where ft+1 is k × N factor matrix and is bk is k × 1 coefficient vector. If we substitute the SDF into Eq.(1) and take unconditional expectations following moment restriction can be obtained:

E[(b0 + b′kft+1)Ri,t+1] = 1 (3)

These moment conditions for cross-section of i assets can be used to estimate the bk column vec-tor of k discount factor sensitivities by GMM which will be used for the calculation on HJ-distanceas explained in Section 3.2. But the focus of this study leads us to expected return-beta represen-tations to see if factor k carries a significant cross-sectional risk premium. Furthermore, with somerearrangements Eq. (3) gives the expected return-beta representation for the k factor model:

E(Ri,t+1) = E(R0,t) + ˇ′�, ∀i and ̌ = Cov(ft+1, ft+1)−1Cov(ft+1, fi,t+1) (4)

where E(R0,t) is the zero beta rate, � = −E(R0,t)Cov(ft+1, ft+1)′bk are the model risk premiums for kfactor risks and ˇs are quantities of risk for respective factors. It is important to note that elements of�, that is, �j can only be regarded as factor price of risk in a cross-sectional setting for non tradablefactor risks. The FM cross-sectional regressions with the scope of this study take care of this fact. Thetestable model implications are derived from Eq. (4) for example, if we tie the SDF to the return on thewealth portfolio instead of k factors such that ft+1 = Rm,t+1 and assume the presence of risk free rate. Itderives single factor CAPM under the assumptions of market completeness. The unconditional testableimplication of the model, when returns on test assets are excess of risk free rate and are continuouslycompounded, is such that

rei,t+1 = ˛i + ˇi,mre

m,t+1 + εi,t+1, εi,t+1∼IID(0, �2)10

(5)

Similarly, if the SDF consists of a number of factors as is the case in this study, the equivalentmulti-factor macro model used for first stage rolling betas is

rei,t+1 = ˛i + ˇi,mre

m,t+1 + ˇi,�TS�TSt+1 + ˇi,�EXR�EXRt+1 + ˇi,�CCIt+1�CCIt+1

+ ˇi,�LGB�LGBt+1 + ˇi,EIREIRt+1 + ˇi,UIUIt+1 + εi,t+1 (6)

The rolling betas from first stage rolling betas are then used in 2nd stage FM (1973) cross-sectionalregressions for the period from 1993:03 till 2008:07.

3.1. Fama and MacBeth (1973) 2nd stage estimations

In the 2nd stage the portfolio excess returns are regressed on estimated betas from Eqs. (5) and (6)in cross-sectional regression. The 2nd stage FM (1973) model equation estimated at each time periodt is:

rei,t = at + ˇ′

t�t + et+1, i = 1, . . . , N, t = 1, . . . , T (7)

where ˇi is a matrix of factor loadings from first stage and �t are slope coefficients interpreted as factorrisk premiums. In the case of market model �t reduces to 1 × 1 vector at each time period otherwiseits dimensions are k × 1. The parameter estimates and sampling errors for parameters a and � arecomputed as in the FM (1973) from the time series collection of intercepts and slope coefficients fromthe T cross-sectional regressions.

3.2. GMM estimations and specification tests

The first stage rolling betas in this study are estimated with OLS and GMM estimation methodsboth. The GMM betas are obtained as a result of over identified moment conditions. The purpose of


this exercise is only to see if the first stage estimates with these two estimation method does have someeffect on the cross-sectional performance of the competing model. In order to explain the estimationof first stage GMM betas, the moments implied by the specified model (that is, Eqs. (5) and (6)) shouldsuppress pricing errors with the estimated parameter vector b = [ ̨ ˇ] such that following identity isas closely matched as possible

gT (b) ≡ ET [εi,t+1], ET [εi,t+1] = 1T

T∑

i=1

re − ˛i − ˇi1T

T∑

i=1

ft+1 (8)

where gT(b) is the vector of pricing errors and is obtained as sample estimate of the from the specifiedmodel moments which if approximate the contemporaneous asset returns exactly should be zero.The estimation of parameters in GMM requires at least as many moment conditions as the numberof parameters, for example, if L represents the number of moment conditions then to get the b esti-mates for k parameters in the model L ≥ k. In order to get additional moments for the estimation ofparameters9 we may introduce some additional instruments correlated with factors in the model. Letzt be the set of instruments which may further suppress the predictability in the model pricing errorssuch that ET[εi,t+1 ⊗ zt] = 0. In this case the population moments of the model are approximated fromits sample counterpart:

gT (b) = ET [εi,t+1 ⊗ zt] = 1T

T∑

i=1

[εi,t+1 ⊗ zt] (9)

The number of conditioning variables in zt for each model Eqs. (5) and (6) and industry i have beensuch that it provides the over identifying moment conditions to get GMM parameter estimates. Theselected instrument vector for first stage GMM betas estimations is such that Hansen’s (1982) overidentification test is not rejected and comprises exact identification factors, lagged level of term struc-ture of interest rates and lagged unemployment rate. The rolling coefficient estimates are calculatedusing the Hansen (1982) two step GMM methods which minimizes the quadratic function of type

jT = argminb

gT (b)′WgT (b) (10)

where W is L × L weighting matrix10. Hansen (1982) shows that W = S−1 is statistically optimal weight-ing matrix and produces estimates with smallest standard errors. It also gives the over identificationtest11 for the model fit and specifies the model moment conditions are true under the null hypothe-sis. But the weighting matrix can otherwise also be specified independent of model, for example 2ndmoment of return matrix of the test assets or identity matrix, etc., as in the calibration of HJ distance.

9 Because, we are only with one moment condition as implied by Eqs. (5) and (6) but the number of parameters to be estimatedare respectively 2 and 7, which requires specification of additional moments.

10 The spectral density matrix S =∞∑

−∞

gT (�)tT−j(�)′ is the Newey and West (1987) HAC (heteroskedasticity and autocorrelation

consistent) estimator. Bartlett kernel is used to downgrade the auto-covariances structure for the positive semi definiteness ofthe S. The bandwidth algorithm is set to be Newey and West (1994) nonparametric method based on a truncated weighted sumof the estimated cross-moments, which controls the number of auto-covariances in the HAC estimator and is very important forconsistent finite sample properties of S. The statistically optimal (most efficient) weighting matrix is obtained as the inverse ofthe covariance matrix of the sample orthogonality conditions that is, W = S−1. It provides the smallest possible standard errorswhereas any sub optimal matrix may produce inconsistent estimates. For a detailed description of these concepts, see Neweyand West (1987).

11 It shows that when optimal weighting matrix is used in the 2nd stage GMM iteration the minimised value of j-statistic timenumber of observations (T), that is, Tj∼�2

L−kasymptotically and L–k are the degree of freedoms equalling number of specified

moments subtracted with number of model parameters. Note that the asymptotic properties of the moment condition are usedin deriving the �2 limit.


Table 4GRS F-test for CAPM.

OLS estimations GMM estimations

Joint test H0: �i = 0A: 1988:4–2008:7F test statistic (p-value) 3.01 (<0.001) F test statistic (p-value) 4.14 (<0.001)�2(25) (p-value) 53.57 (<0.001) �2(25) (p-value) 107.42 (<0.001)B: 1988:12–1998:12F test statistic (p-value) 2.38 (0.007) F test statistic p-value 2.74 (0.002)�2(25) (p-value) 64.47 (<0.001) �2(25) (p-value) 87.1 (<0.001)C: 1999:1–2008:7F test statistic (p-value) 2.26 (0.01) F test statistic (p-value) 3.48 (<0.001)�2(25) (p-value) 72.83 (<0.001) �2(25) (p-value) 91.07 (<0.001)

The table reports small sample GRS F-test with corresponding asymptotic �2 test. The variance covariance matrices are con-structed with the time series residuals, for all industry portfolios, both with OLS and GMM estimations, separately.

The estimation of HJ distance uses the sample analogue of Eq. (1), that is, E[MRi] = 1 ∀ i in orderto rank the performance of tested model SDFs. The resulting measure of model misspecification asdefined in Hansen and Jagannathan (1997) is:

HJ distance = ıHJ = [argminbgT (b)′E[R′R]−1gT (b)]1/2

(11)

The proposed HJ distance12 has very important economic intuition, which could be interpreted aspercentage pricing errors and provides a direct comparison between the competing models. Becauseof the sub optimality13 of the 2nd moment matrix of test assets Hansen’s (1982) over identification testis not applicable to the asymptotic distribution of modified HJ-distance. We report p-values againstthe null that the HJ-distance is zero with Jagannathan and Wang (1996) simulation method as detailedin Appendix C.

4. Estimations and results

4.1. Inference form time series regressions for CAPM

The non tradability of macro factors disables us to compare measures of model misspecificationbased upon time series regressions using multiple assets that is, GRS F statistic of Gibbons et al. (1989).However, we report the GRS F statistic from time series regressions for robustness and inter compara-bility with the evidence from cross-sectional regressions for market model. Table 4 reports, the GRS Fstatistics and its asymptotic counterpart for all the samples. The reported GRS tests for joint insignifi-cance of the ˛’s across all industry portfolios rejects CAPM for all samples at the 1% level. It is importantevidence since for US with GRS F statistic, there is not any significant evidence against CAPM in thelong run (Ang and Chen, 2007). The inference from time series regressions with OLS or GMM methodsdoes not show any discernable pattern besides over rejection of null with GMM estimations.

The non rejection of null characterises large pricing errors and also rejects the efficient markethypothesis (EMH) under which they are expected to be zero. It goes hand in hand with studies whoargue for the impossibility of perfectly efficient markets. It represents a scenario which involves noabnormal gains for agents who collect information, for example, market makers, traders, rating agen-cies, etc. Besides, agents who beat the market often besides pure chance have information not availableto others, a violation of the complete agreement assumption and EMH. For this reason, the focus hereis on additional sources of risk (macro) with respect to the investor information set.

12 The specification measure estimates the minimum distance of model based SDF from the set admissible region discountfactors that prices the assets correctly.

13 In that regard any weighting matrix that is not model dependant is sub optimal and produces model parameters with largersampling uncertainty.

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Table 5Fama–MacBeth regressions with OLS betas.

Sample �0 �rm ��TS ��DXR ��CCI ��LGB ��EIR �UI Avg. R2

A1993–2008 0.3 0.42 – – – – – – 0.19

(0.47) (0.44) – – – – – –1993–1998 0.203 2.08 – – – – – - 0.18

(0.21) (1.85) – – – – – –1999–2008 0.351 −0.587 – – – – – – 0.20

(0.44) (−0.48) – – – – – –B1993–2008 0.91 – −0.36 0.05 0.09 −0.04 −0.11 0.17 0.50

(1.61) – (−1.63) (0.08) (0.23) (−0.79) (−0.98) (2.10)1993–1998 2.03 – −1.02 2.12 0.15 −0.12 0.06 0.29 0.51

(2.78) – (−2.13) (2.94) (0.20) (−0.91) (0.27) (2.54)1999–2008 0.23 – 0.04 −1.2 0.06 0.003 −0.22 0.1 0.50

(0.32) – (0.76) (−1.89) (0.14) (0.14) (−1.9) (0.99)C1993–2008 0.7 0.08 −0.31 0.02 0.08 −0.05 −0.08 0.18 0.61

(1.50) (0.10) (−1.77) (0.04) (0.23) (−1.00) (−0.71) (2.34)1993–1998 1.24 0.954 −0.869 1.842 0.245 −0.111 0.134 0.302 0.59

(1.88) (0.95) (−2.29) (2.57) (0.42) (−0.93) (0.72) (3.39)1999–2008 0.38 −0.45 0.03 −1.08 −0.02 −0.01 −0.21 0.11 0.61

(0.64) (−0.41) (0.75) (−2.04) (−0.06) (−0.43) (−1.84) (1.07)D1993–2008 0.65 0.12 −0.21 0.07 − − −0.02 0.13 0.47

(1.16) (0.13) (−1.98) (0.13) – – (−0.24) (1.67)1993–1998 1.36 0.89 −0.6 1.61 – – 0.15 0.17 0.45

(1.58) (0.80) (−3.41) (2.25) – – (1.00) (1.15)1999–2008 0.22 −0.35 0.03 −0.87 – – −0.13 0.11 0.50

(0.34) (−0.30) (0.77) (−1.80) – – (−1.09) (1.26)

The results from the cross-sectional regressions are presented for full sample, sample before the introduction of euro and after the introduction of euro represented by sample lengths1993–2008, 1993–1998 and 1999–2008 respectively. Each panel reports the results from the tested models across the samples. The t-statistics are reported in () and calculated withNewey and West (1987) standard errors. The significant coefficients and their t-statistics at 10% and below critical values are presented in bold fonts. The reported �j ’s are the reward torisk and column 9 reports the average R2 for the FM cross sectional regressions.


4.2. Cross-sectional regressions

This section provides the comparison between the CAPM and different augmentation of modelswith economic state variables. The results from FM regressions are reported with OLS and GMM betasare reported in Tables 6 and 7 respectively. The reported t-statistics are calculated with Newey andWest (1987) standard errors correcting for autocorrelation and heteroskedasticity in GMM errors toimprove the discriminatory power of the cross-sectional tests.

The results in Table 5 show price of market risk in all samples are estimated lower than the respec-tive sample average and insignificantly except for sample B. This effect is substantial to the extentthat the risk premium is negatively estimated in the sample C. The risk premium in sample B gets itsbest chance to near its sample average of 2.61% per month significantly with GMM betas(reported inTable 6) that is, 2.58% per month, whereas the premium with OLS betas is 2.08% per month, signifi-cant at 10% critical values. The asset prices, for intertemporal hedging needs and in efficient markets,should compensate for the state variables that describe the economy. Therefore, the signs on the macroshocks are not taken presumptuously fixed a priori rather are assumed to explain the expectations onvariations in industry returns. For that, maintaining all other characteristics of the analysis equal, thesign of each macro variable is presumed to explain the prevailing type of risk. In addition, the expla-nations are also rendered for its effect on expectations to assign marginal wealth for stocks, which payoff handsomely in poor times and vice a versa.

The panel B of Table 5 reports the results from the model which only takes into account macroshocks, that is, changes in TS, DXR, CCI, LGB, EIR and UI. The significant negative sign for changes interm structure in full sample and sample before the introduction of euro is same as Chen et al. (1986)and regard stocks which time their returns with long term bond returns, cetris paribus, are consideredmore valuable than stocks that are inversely related with them. The cross-sectional variations in stocksreturn on the same note follow contrarian argument in sample C when the market is arguably moreinternationally integrated and may represent complete signs of liberalization of the economy. Theeffect of exchange rate movements is asymmetric to appreciating–depreciating currency regimes,as reported by Koutmos and Martin (2003). The premium for exchange rate changes is, likewise,positively rewarded a depreciating currency regime in sample B and is negative in sample C duringan appreciating regime for euro against USD. However, in the full period it is substantially lower andinsignificant than its partitioned sub samples. The risk premium with OLS betas is considerably largerthan estimated with GMM betas but signs for full estimations are different. Overall, the variations inexchange rate risk essentially track the appreciating and depreciating currency regime over the periodof tested samples.

The signs for changes in the consumer confidence index for all three samples are plausible. Theexpected returns for industries are substantially lower in sample C than the full sample and pre eurosample but are imprecise. The signs on the changes on long term maturity bonds are consistent withthe results obtained with �TS but are insignificantly estimated in all the cases. In the post euro sample,the changes in LGB have a marginal effect any economic significance for average industry may alsomanifest the larger effects of ECB’s monetary policies that have steadied the markets to assign anypremium to changes in maturity bonds.

The effect of inflationary pressures seemingly has sufficient significance over the samples. The signfor premium on expected changes in inflation is consistent with Chen et al. (1986). The significanceof premiums for expected inflation in sample C and for unanticipated inflation in the sample A and Bshows the stringent inflation targeting14 by ECB, which has smoothed out any unanticipated inflation-ary pressures for Finnish industry returns in the later period. However, the unexpected inflationaryshocks across all the samples require positive compensation, which is not consistent with Chen et al.(1986) and Pearce and Roley (1988). This effect could be explained as stocks may not be consideredas safe hedges by the investors against the substantial discounting of their investments, keeping all

14 The European central bank (ECB) identifies its primary function to keep inflation rates below, but close to, 2% in mediumterm.

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Table 6Fama–MacBeth regressions with GMM betas.

Sample �0 �rm ��TS ��DXR ��CCI ��LGB ��EIR �UI Avg. R2

A1993–2008 0.28 0.64 – – – – – – 0.15

(0.46) (0.83) – – – – – –1993–1998 −0.45 2.58 – – – – – – 0.12

(−0.36) (2.59) – – – – – –1999–2008 0.73 −0.53 – – – – – – 0.16

(1.20) (−0.62) – – – – – –B1993–2008 0.72 – −0.06 −0.04 0.002 0.14 −0.03 0.03 0.51

(14.52) – (−2.88) (−0.42) (0.44) (1.41) (−1.93) (2.06)1993–1998 0.93 – −0.13 0.02 0.03 0.01 −0.07 0.02 0.51

(59.89) – (−3.65) (0.14) (2.79) (0.09) (−5.86) (1.49)1999–2008 0.6 – −0.01 −0.08 −0.01 0.21 0.001 0.03 0.51

(13.37) – (−2.08) (−0.69) (−3.26) (1.56) (0.13) (1.64)C1993–2008 0.39 0.63 −0.04 0.09 0.02 0.13 0.01 0.16 0.62

(0.73) (0.78) (−0.32) (0.21) (0.49) (0.31) (0.13) (1.74)1993–1998 0.62 1.74 −0.19 1.02 0.05 0.54 0.14 0.38 0.59

(0.59) (1.52) (−0.55) (1.12) (0.50) (0.68) (0.73) (3.23)1999–2008 0.25 −0.05 0.05 −0.47 0 −0.13 −0.06 0.03 0.63

(0.43) (−0.05) (1.19) (−1.34) (0.13) (−0.31) (−0.57) (0.27)D1993–2008 0.18 0.71 0.04 −0.21 – – 0.18 0.05 0.46

(0.28) (0.82) (0.35) (−0.42) – – (0.50) (0.43)1993–1998 −0.25 2.35 0.05 0.43 – – 0.69 0.27 0.43

(−0.19) (1.69) (0.17) (0.36) – – (0.92) (1.20)1999–2008 0.43 −0.3 0.03 −0.6 – – −0.13 −0.08 0.48

(0.71) (−0.31) (0.92) (−1.80) – – (−0.38) (−0.65)

The results from the cross-sectional regressions are presented for full sample, sample before the introduction of euro and after the introduction of euro represented by sample lengths1993–2008, 1993–1998 and 1999–2008 respectively. Each panel reports the results from the tested models across the samples. The t-statistics are reported in () and calculated withNewey and West (1987) standard errors. The significant coefficients and their t-statistics at 10% and below critical values are presented in bold fonts. The reported �j ’s are the reward torisk and column 9 reports the average R2 for the FM cross sectional regressions.


Table 7The model pricing errors with Hansen and Jagannathan methodology.

M1 M2 M3 M4

Sample A 0.22 0.19 0.19 0.20[0.02] [0.01] [0.001] [0.00]

Sample B 0.82 0.79 0.69 0.75[0.001] [0.02] [0.01] [0.00]

Sample C 0.34 0.29 0.28 0.29[0.001] [0.03] [0.0] [0.00]

Table reports the pricing errors using the model SDF with the moment conditions as implied by Eq. (3) for the cross-section ofindustry portfolios. M1, M2, M3 and M4 represents CAPM, market factor and macro shocks taken together, model with macroshocks only and market factors and selected state variables as reported in the panels A, B, C and D of Tables 5 and 6 respectively.The HJ distance are reported under the respective column headings and p-values with Jagannathan and Wang (1996) simulationmethod for H0: HJ-distance = 0 are presented in []. The simulated p-values which cannot reject the null are presented in bold.

other facts equal. Therefore, investors for inflationary shocks require larger compensation for bearingit and otherwise may look for larger risk adjusted pay off from fixed income assets than stocks15.

It is generally argued that market factor is sufficient to capture the pricing impact coming from themacro variables. Therefore, it will be an important test to take market factor and macro shocks togetherand to see the impact of both on the pricing of stock returns. The results from these regressions arereported in panel C of Table 5. The signs for premium for market risk and macro shocks are similarto the reported results in panel A and B respectively. The particular departure is the insignificanceof the market factor in sample B which otherwise was significant for market model estimations forthe same period. The results from panels B and C show that shocks from the maturity bonds andconsumer confidence index does not yield any significant premium for the pricing of stock returns.It motivated us to drop them and replace with market factor to see if any particular differences thanresults in panels A, B and C can be observed. The results are reported in panel D and differ only forthe significance of inflationary pressures. The expected inflation is no more significant in sample C,whereas the unanticipated part is only precisely estimated in the full sample. It shows in the contextof the study the marginal effects coming from the changes in the long term bond and consumerconfidence index are submerged into market risk and may not require independent specification. Inthe same line, it also shows the marginal effects from changes in term structure, exchange rate andinflationary risks are separate from the market risk and require separate identification for the Finnishindustry returns.

The time series for model R2 is obtained in a similar manner as of model parameters from the 2ndstage FM regressions. The R2 values are reported to see how good a model fits the data over the periodsof time on average. The models in panels B, C and D explain larger cross-sectional variations in industryreturns than the market model. The CAPM has only 19% explanatory power compared with models inB, C and D explaining 50%, 61% and 47% respectively for the full sample. The hierarchy of explanationfor industry returns between these models is same across the results from the sub samples. However,the average R2 values for model using only macro shocks are proportionally 10% higher than the testswhere the market factor replaces changes in LGB, and CCI. The model intercepts across all estimationsare insignificant but close to zero, which should be a case under the correctly specified model. Themodel mispricing is significant and large in sample B for results in panels B and C.

The results with GMM betas are reported in Table 6 and are with no particular departure from theresults with OLS betas in terms of the model R2 values. The expected inflation is significant only in panelB for samples A and B, whereas unanticipated inflation is significantly priced for factor combinationsreported in panel B for full sample and in panel C for full and pre euro samples both. The market factoris significantly priced, when we replace it with changes in LGB and CCI, in sample B and risk premiumis close to time series average. The significance of changes in CCI is observed in panel B for pre and post

15 The Sharpe ratio for 10 year government bonds over the risk free rate is sufficiently larger than aggregate market index orany other industry in all the samples. The corresponding reward to risk ratio is 139%, 210% and 148% for samples A, B and Crespectively.


euro sample periods. The changes in TS are significant in panel B, whereas, changes in the exchangerate are negatively rewarded in sample C panel D same as OLS betas.

The R2 values for market model with GMM betas are lower than OLS betas. They are, however,marginally higher than the corresponding values with the cross-sectional tests using first stage OLSbetas. Overall, the hierarchy established with OLS betas is maintained with GMM beta 2nd stage cross-sectional tests. The signs for macros shocks are not necessarily same as with estimations in Table 5.However, the importance of macro variables, that is, inflationary pressures, changes in term structureof interest rates and changes in DXR, likewise, to results in Table 5 are evident across the samples inpanels B, C and D. The model intercepts are insignificantly different from zero for all samples in panel.

The factor combinations used in panels A, B, C and D will be referred as M1, M2, M3 and M4 fromhere on for convenience in comparing the performance of tested models. The ranking among themodels with the Hansen and Jagannathan (1997) distance measure16 is reported in Table 7 and is notas clear as with cross-sectional R2 values. The pricing errors with M2 are considerably discernable thanM1, M3 and M4 in pre euro sample. Nevertheless, are too large for all models to favour any model tobe an approximation of the correct model. The pricing errors for full and post euro samples are notsubstantially different among models M2, M3 and M4 but are sufficiently smaller than correspondingvalues for pre euro sample. However, market model remains at loggerheads with the cross-sectionalvariations in average industry returns and produces the largest mispricing among all models. Thedismal performance of CAPM with HJ distance is consistent with the lowest R2 values in cross-sectionalFM tests. Furthermore, simulated p-values reject all the models that the distance between the modelsimplied SDFs to the set of admissible region pricing kernel is equal to zero.

4.3. Economic significance and additional estimations

The estimations in Tables 5 and 6 gave satisfactory evidence of cross-sectional premium for changesin TS, DXR and inflationary pressures. The close analysis for the economic significance17 of thesevariables shows that they induce sufficient changes in expected industry returns. The unit positiveshock in term structure of interest rates, exchange rate changes, expected and unanticipated inflationthe associated contemporaneous movements in average industry returns are −2.5%, 0.84%, −0.24%and 1.6% per annum respectively. The shock to term structure of interest rates has a larger impact onthe changes in average returns in pre euro period than the post euro period. It may show investorshave placed larger beliefs in the liberalization of Finnish economy since the introduction of euro. Theassociated absolute average return changes in the post euro sample are proportionally only 5% of itspre euro level.

Further, the sub sample estimations show the innovations in the exchange rate have an alternatingpremium and induce substantially larger changes in the cross-sectional returns in sub samples than inthe full sample. Similarly, a unit change in the levels of expected inflation requires an annual incrementin industry returns of 1.8% in sample B and −1.54% in the sample C. It could be argued that Finnisheconomy in the aftermath of early 1990s recession was on a lower expectation for growth in stocksin general. The shocks to expected inflation during the period were perceived as bad news for whichaverage returns have to be increased at large to keep investors attracted. It changed sign and possiblyinvestor expectations after the introduction of euro. It shows the tight monetary control of ECB for theeuro region overall and so forth the changes in expected inflation are incorporated as an expectationfor future growth with lower current period average returns. However, the changes in unexpectedinflation throughout are considered to be a signal for bad states of the economy by investors inducingpositive changes in average industry returns across all the samples.

16 The HJ-distances among the tested models were also computed with Identity matrix to weigh the imposed moments fromeach model, but the corresponding errors provide very similar results as we report with the Hansen and Jagannathan (1997)2nd moment matrix. The results for HJ-distance with identity as spectral density matrix could be provided on request.

17 The economic significance of cross-sectional premiums is only discussed here for cross-sectional premiums estimatedwith OLS betas as in panel D for simplicity to generalize. It is also important to note that the cross-sectional premium formacro variables in panel D are lower than their counterpart estimates in the models reported in panels B and C. Therefore allsubsequent estimates for changes in expected industry returns are conservative among others.


The risk premium for these macro variables carries alternating signs in sub sample estimationsexcept for unanticipated inflation. The unit change in unanticipated inflation requires higher averagereturn from cross-section of industry portfolios as risk compensation and shows the persistence ofunanticipated inflation for Finnish stocks over varying business cycle conditions. The appreciatingeuro against USD, lower short rates and controlled changes in expected inflation in the post europeriod than the earlier period show the importance of these variables to proxy changes in investors’marginal utilities and in forming aggregate beliefs for expected return changes in Finnish stocks.The contemporaneous changes induced by shocks to macro variables are of a substantial amounteconomically. The significant premium associated with of changes in term structure and unanticipatedinflation in the full sample and exchange rate in sub samples make it a worthwhile case to see theirimportance in suppressing mispricing independently. It motivated us to do robustness tests on thecross-sectional capabilities of mentioned macro variables. The reporting of all additional tests is limitedto full sample only to simplify generalizations.

The subsequent robustness check takes into account the performance of mentioned macro variablesin conditional18 settings. In order to establish it, we make use of well reported fact that conditionalimplications of a single factor model can be tested unconditionally in a multifactor model as inCochrane (1996) and Jagannathan and Wang (1996), etc. We specify single factor SDFs using levelsof term structure of interest rates, exchange rate fluctuations and expected inflation and conditionedthem with lagged macro shock of same variable, referred as CA. Then we augment the linear SDFswith return on the market factor to see their joint performance in suppressing cross-sectional pricingerrors and refer it with CB.

4.3.1. Pricing errors from conditional settingsThe macro variable as we have them after the triangular decomposition, detailed in Section 2,

are assumed to follow an AR (1) process such that yt+1 = c + yt + et+1. The model SDF regard AR (1)component as the level of the macro variable and the first lag to the remaining unexplained componentis regarded as the conditioning variable. The GMM estimation and testing with scaled factor SDF, inprinciple, is a general test of a conditional factor pricing model (for detailed review see Cochrane, 2005).The results for conditional model pricing errors as measured with HJ-distance are reported in Table 8.The pricing errors implied by the SDFs of conditional models are always better than the unconditionalmarket model SDF (reported in Table 7). The SDF with expected inflation and its unexplained partyields the minimum distance from the set of true pricing kernels and more importantly the simulatedp-values are also not able to reject zero distance. The pricing errors with term structure and exchangerate changes based SDFs are marginally larger than M2, M3 and M4.

However, the pricing errors under the setting CB for above noted macro variables are smaller thanall unconditional models and importantly are improvements on the results with CA. The smallestpricing errors still come from inflationary pressure augmented with the market factor. All modelimplied SDFs in CB reject the null with the simulated p-values. Nevertheless, the conditional tests showthat the industry returns could be explained with lesser factors and more parsimoniously than theunconditional settings. These results, in it, reinforce the significance of term structure of interest rates,exchanges rate changes and inflationary pressures for the explanation of average industry returns.

18 The unconditional estimations reported in Tables 5 and 6 carry minimum five pricing factors besides model intercept andthe calculation of any conditional model would have required the study to estimate the pricing impact of interaction termsbetween the model pricing factors and conditioning variables. If, for example, we would have estimated a conditional modelwith five pricing factors and one conditioning variable, it would have required us to estimate additional six parameters and inthe case of n conditioning variables the number of additional parameters would have been n*(k + 1), where k is the number ofpricing factors in the model and so on. But the manifestation of the study is not to compare the performance of unconditionalmodels with the implications of conditional models therefore; we have not estimated cross-sectional risk premiums for anyfactor in conditional setting. But in order to see the robustness of successful macro variables in this study we only did SDF-GMMestimations for the HJ distance respective to scaled factor model. The estimation of conditional risk premiums would haveshifted the focus from the pricing ability of macro state variables to gauging the comparable performance of unconditional andconditional models which is not in the scope of this study. The well documented non-convergence of estimations and parsimonyof model estimates, in the wake of sufficiently large number of model parameters, would also have been related issues.


Table 8HJ-distances for conditional models.

TS EXR EIR

Model CA

0.21 0.21 0.17[0.01] [0.59] [0.95]Model CB

0.17 0.20 0.16[0.02] [0.01] [0.03]

Table reports the pricing errors for the conditional models CA and CB with the simulated p-values in [] to test H0: HJ-distance = 0for the tested model as given in Jagannathan and Wang (1996). The conditional models assume a linear SDF of the form[(b0 + b′

kft+1) ⊗ zt ]. In the case of CAft+1 is level of the macro factor given by AR (1) process, as in the header of the table columns,

and is conditioned with first lag of macro shock, that is, zt which resultantly implies a SDF of scaled factor model such that[(b0,1 + b0,2zt + b′

k,1ft+1 + b′

k,2ft+1zt )]. Similarly, CB is a conditional setting where ft+1 comprises level of macro variable, as in

the header of the table columns, and market factor such that it is again conditioned with previous period shock to macrovariable. The conditional models imply 4 factor and 6 factor linear SDFs which are then used to calculate HJ-distance across thecross-section of industry portfolios same as in Eq. (3) using GMM.

Moreover, the performance of these variables considerably improves when taken with market factorin conditional settings.

4.3.2. Dynamic model evaluationsThe previous section highlights the importance of conditional tests in suppressing cross-sectional

pricing errors than unconditional tests besides the larger significance of noted macro risks. In thissection, we analyze the robustness of the conditional tests relative to the unconditional tests withFarnsworth et al. (2002) test based upon dynamic performance of SDF models. The idea behind thistest is that if a model is assumed to capture the time variation of test assets, the model’s time seriespricing errors19, that is, ˆ̨ i,t+1 = Mt+1(b̂)Ri,t+1 should not predictable with any information availablein previous periods. They propose to get linear projections of ˆ̨ t+1 across all test assets onto a set ofconditioning variables available in period t. The average standard deviation of the fitted values of ˆ̨ t+1from these predictability regressions serves as a measure to capture the time series variation in testassets among competing model SDFs.

In order to evaluate the performance of all the models, we identify a conditioning vector(TStDXRtIRt) with the macro factors which has shown larger explanation for contemporaneous vari-ations in average industry returns. After computing the model respective pricing errors, we run thepredictability regressions to see if there is any explanation left for asset return variations extractablewith available information in period t. The small volatility of the fitted residuals will indicate the betterperformance of the specific model in capturing the time series predictability of the excess industryreturns. The average standard deviations of the projected alpha values across the industry returns,along with minimum and maximum, are presented in Table 9. The Farnsworth et al. (2002) test showsconditional models have fared better than the unconditional models in capturing the predictable pat-terns for the industry returns. The SDF implied by the exchange rate fluctuations and market factorhas the smallest average standard deviation closely followed by the SDF of the unconditional modelwith only macro risks, i.e., M2 and SDF model with expected inflation and market factor respectively.The lower average standard deviations of the SDF models in CB are also consistent with our earlierobservation that the selected macro factors do better when combined with market factor. Otherwise,when they are tested with the SDFs in the CA, the average standard deviation is with no particulardiscernability.

The important fallout is the performance of SDF implied by inflationary changes with dynamicSDF tests, which produced the smallest HJ distance in CA but was unable to replicate with the timeseries predictability of the industry returns. It produced the largest standard deviation for the most

19 The SDF model pricing errors should be equal to one in case of gross returns and in the case of excess returns should bezero, if the specified model SDF exactly approximates the true model.


Table 9Dynamic SDF models performance.

Mean Minimum Maximum

Panel A: unconditional modelsM1 1.123 1.044 1.238M2 1.021 1.008 1.034M3 1.153 1.055 1.274M4 1.118 1.047 1.222

Panel B: conditional modelCA TSt+1 1.127 1.030 1.243

EXRt+1 1.071 1.032 1.136EIRt+1 1.150 1.007 1.430

CB TSt+1 and Rm,t+1 1.101 1.050 1.215EXRt+1 and Rm,t+1 1.016 1.006 1.033EIRt+1 and Rm,t+1 1.028 1.012 1.062

Table reports the results from the predictability regressions for the pricing errors ˆ̨ i,t+1Mt+1(b̂)Ri,t+1 onto a set of conditioningvector zt = (TStDXRtIRt)) as proposed by Farnsworth et al. (2002). TSt is prevailing difference between long rate series and onemonth EURIBOR series, EXRt is the change in euro against USD at time t and IRt is the inflation rate. The pricing errors arecomputed for 25 industry portfolios using the SDF implied by each tested model. The unknown parameters for model basedSDF are estimated with GMM-HJ estimation. M1, M2, M3 and M4 represents SDFs implied the unconditional models. CA and CB

are the conditional model SDFs. The robustness measures are reported in panel A for listed unconditional model and in panel Bfor conditional models. The 2nd column in panel B lists the number of factors in the SDF implied by the model additionally thesefactors are also scaled by the lagged shock of the macro variables listed in the column only. The table reports the average standarddeviation of fitted values for pricing errors from the predictive regressions from a candidate model along with minimum andmaximum standard deviations across 25 industry portfolios. The lower average shows a particular model performs better incapturing the time series variability of asset returns in comparison to the results reported for other tested models.

mispriced portfolio among all test models. However, its performance gets better to give the thirdsmallest average standard deviation when augmented with market factor. Overall, we summarize thenoted macro risks are important for Finnish stocks and their impact to explain average industry returnsis separate from market risk and so should be accounted in forming expectations and intertemporalhedging needs. The robustness tests reprieved the market factor and showed in conditional settingit along with macro risks improves the model performance and its impact to explain average returnscannot be ignored altogether. The results with dynamic model performance check are consistent withFarnsworth et al. (2002) such that their conditional models, other than the conditional counterpartsof their unconditional models, perform better than the unconditional models.

5. Conclusions

This study attempts to explain the average cross-sectional variations in Finnish industry returnswith macro systematic risks in addition to aggregate market risk. In pursuit, we explored a number ofmacro risks. The analysis further delves and reports the cross-sectional premia for macro risks beforeand after the introduction of euro and the analysis is important to report evidence in the dynamicsof changes in expected returns for a euro zone country. The cross-sectional tests using macro shocksare compared with the benchmark CAPM. The FM regressions are done with OLS and GMM first stagerolling betas. However, it does not impart substantially different explanation for the cross-sectionalvariations in average industry returns in terms of model R2. The evidence suggests different macrofactor combinations with or without the market performs better than CAPM, unconditionally.

The changes in term structure of interest rates, exchange rate and inflationary pressures bothexpected and unanticipated are reported as significant risks across different samples. The significanceof unanticipated inflation is larger during a comparably volatile period than other macro risks. Themarket premium is with a correct sign more often and is approximately corresponding to its time seriesaverage in the post euro sample but overall remains insignificant whether tested alone or with macrorisks. The notable observation from the FM tests is the larger explanation of industry returns comingfrom macro shocks than the market model. It signifies the importance of macro information in generaland shocks to term structure of interest rates, exchange rates and inflationary changes, in particular.


The waning of CAPM to explain the variations in average industry return is further consolidated withthe HJ distance measure which showed smallest pricing error are produced when we only use macroshocks.

The importance of changes in term structure, exchange rate fluctuations and inflationary changesas systematic risk motivated this study to see the performance of SDFs implied by the levels of macrovariables independently in scaled factor settings. The results are significant improvements in terms ofminimum distance from true pricing kernels from the unconditional models. The smallest HJ distanceswere produced by the SDF implied inflationary changes. The distance was even shortened when theconditional macro SDFs were augmented with market factor. The evidence for smaller distances withconditional settings were further encouraged by the dynamic performance of SDF models as proposedby Farnsworth et al. (2002) such that the conditional settings were better in capturing the predictablevariations in the test assets than unconditional models.

The evidence suggests macro risks capture the investor’s investment set better than the marketfactor to explain cross-sectional variations in the average Finnish industry returns. Additionally, theresults show the tight inflation targeted monetary policy from ECB has changed investor expectationsfor a unit increase in expected inflation and term structure of interest rates than pre euro sample.The robustness tests report improved performance of conditional specifications than the uncondi-tional models and also suggest the market risk cannot be ignored. It shows the impact coming fromimportant macro variables is separate and above of market risk, otherwise. The exchange fluctua-tions and unanticipated inflationary pressures seem to be most important macro risks for changesin expected industry returns. Their importance could be rationalized with the larger dependenceof Finnish industries on foreign trade and early 1990s recession, which still cause aversion amonginvestors to inflationary discounting of aggregate wealth. The robustness checks show the impact ofmacro risks is pervasive and therefore, should be accounted separately for Finnish industry returns.Finally, we conclude unconditionally macro risks outperform CAPM but in conditional settings its roleto explain average returns cannot be ignored altogether.

The results from this analysis suggest further deliberations for Finnish stocks taking into accountthe conditional simplifications of the CAPM such as Jagannathan and Wang (1996), Hodrick and Zhang(2001) and Lettau and Ludvigson (2001a,b). The asset pricing anomalies literature such as the Famaand French (1993) three factor model, Jegadeesh and Titman (1993) momentum factor, Pastor andStambaugh (2003) liquidity factor could also be interesting tests while taking into account key charac-teristics of Finnish stock market for out of sample international evidence. Moreover, another directioncould be analysing a sample of euro zone countries to report independent evidence if the impact ofcoordinated polices from EU and ECB cause reversals in macro risks than pre euro period in their stockreturns same as for Finnish stocks.

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