Global coskewness and the pricing of Finnish stocks: empirical tests

Journal of International Financial Markets, Institutions and Money 7 (1997) 137-155

ELSEVIER

INTERNATIONAL FINANCIAL MARKETS, INSTITUTIONS & MONN

Global coskewness and the pricing of Finnish stocks: empirical tests Kim Nummelin

*

Swedish School of Economics and Business Administration, Department of Finance, PO Box 479, FIN-00101 Helsinki, Finland

Abstract This paper

examines

the empirical

performance

of a global

conditional

three-moment

CAPM. We employ monthly Finnish stock market data for 1987-1995. To explore the robustness of the three-moment model, we also examine whether local equity market returns, exchange rate fluctuations and movements in overall stock market turnover come into play after accounting for global market portfolio risk exposures. Our findings indicate that these additional factors are not generally able to detect deviations from the three-moment CAPM and time-varying global coskewness affects the cross-section of expected returns on local size portfolios even after accounting for other factors. 0 1997 Elsevier Science B.V. Keywords:

Conditional

asset pricing; Skewness

1. Introduction Kraus and Litzenberger (1976) derive a static three-moment capital asset pricing model (three-moment CAPM) in which the coskewness of an asset’s return with the return on the market portfolio affects the risk premium of an asset. Positive nondiversifiable skewness (coskewness) in asset returns implies a higher probability of realizing large positive portfolio returns than implied by usual symmetric elliptical distributions (for example, see Owen and Rabinovitch, 1983). Previous empirical studies have examined whether the cross-sectional variation in average asset returns is influenced by the magnitude of average systematic skewness. Kraus and Litzenberger (1976) and Lim (1989) found support for the unconditional threemoment model and its prediction of a preference for positive marginal skewness with respect to local benchmarks. However, some major theoretical and empirical findings in international asset pricing and conditional analysis have emerged in recent years with important implications for asset pricing and tests of pricing models.

* Corresponding author. 1042-4431/97/%17.000 1997 Elsevier Science B.V. All rights reserved. wr cin47-443i~w~nnnlk4

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First, recent empirical findings suggest that exposures to global economic risk factors are important in determining expected returns on local assets (for example, see Harvey, 1991; Ferson and Harvey, 1993). While the pricing of global risk factors is closely linked to the degree of local financial market integration to world capital markets, international asset pricing theories suggest that global systematic risk exposures are important also in markets that are not fully integrated (for example, see Errunza and Losq, 1985). Bekaert and Harvey (1995) fmd that emerging stock markets exhibit time-varying integration to world markets, which is more or less consistent with mild or partial segmentation. However, full integration seems to provide a reasonable working approximation for more developed markets with a large trade sector like Germany (Bekaert and Harvey, 1995). Overall, these findings suggest that local assets’ exposures to global sources of risk should be accounted for. Second, mounting empirical evidence indicates that movements in expected returns, risks and risk premiums can be tracked with a number of predetermined forecasting variables (for example, see Ferson and Harvey, 1993). Moreover, Singleton and Wingender (1986) report that skewness in portfolio returns does not persist across time, while Alles and Kling (1994) document that systematic skewness fluctuates with the stage of the business cycle. Alles and Kling find that portfolio skewness tends to be more negative during economic upturns and even positive during downturns. Hence, average asset returns and risk exposures are not likely to be best estimates of conditional return moments at all times. This paper investigates the empirical performance of a global three-moment CAPM with time-varying risk exposures and rewards to risk. We examine whether and how systematic global skewness in Finnish equity returns is rewarded. Hence, we are testing if a model, which imposes the (unrealistic) assumption of full integration to world capital markets on all local assets, is able to explain the cross-sectional dispersion in expected equity returns. If the Finnish equity market is not well integrated to global capital markets, marginal contributions to the variance and skewness in the global market portfolio returns should not be able to explain the cross-section of conditionally expected returns on local assets. The Finnish market is an exciting and challenging laboratory for the investigation of the implications of an asset pricing model which assumes full integration of world financial markets. We employ data for the 1987-1995 period, which should also be interesting from a conditional point of view since the domestic real economy and asset prices experienced wild swings. A priori, it is not obvious that a global asset pricing model should be able to explain the cross-section of Finnish equity returns. While Finland’s degree of economic integration is traditionally very high, the restrictions on foreign capital flows into Finnish equities were altogether removed only at the beginning of 1993. Moreover, Finland moved from a tight target zone exchange rate regime to a managed float in September 1992, which could affect the way exchange rate risks are cross-sectionally rewarded. In exploring alternative asset pricing stories, we use the information in institutional and regime changes as a part of the conditioning information available to investors. The plan for the rest of the paper is as follows. Section 2 discusses the pricing

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model and testable hypotheses. The data is described in Section 3, whereas Section 4 presents empirical results. Some concluding remarks are offered in Section 5.

2. Test methodology 2.1. The asset pricing model The original static three-moment CAPM of Kraus and Litzenberger (1976) extends to a global conditional setting under similar conditions as the global two-moment CAPM considered in, for example, Harvey ( 1991) and Dumas and Solnik ( 1995). However, asset returns need not be multivariate elliptically distributed or investors’ utility defined solely over the first two moments in this setting. However, two central assumptions here are: (1) capital markets are perfectly integrated; and (2) purchasing power parity (PPP) holds and all investors lack motives to hedge against shifts in the investment opportunity set (e.g. due to logarithmic utility). The assumption of full market integration rules out local factors from the model, while PPP and no hedging desires ensure that exposures to exchange rate fluctuations or movements in the investment opportunity set do not enter the model (for example, see Adler and Dumas, 1983; Errunza and Losq, 1985; Dumas and Solnik, 1995). A conditional version of the global three-moment CAPM places the following restriction on local expected excess returns from time t- 1 to t denominated in a common currency:

~~~,l~~-~I=~~~~~,~~,,l~,-~l+~,~~~,~~,,l~~-~1~

(1)

where at_, is the H x 1 information vector at time t - 1 that investors use to set prices, r, is an N x 1 vector of asset returns in excess of the known local riskless return, rWt is the excess return on the ‘world market portfolio’ measured in local currency, a[ *] is an N x 1 vector of conditional asset covariances with the world return, and 6[ *I= E[(u, &),>Ia;- I1is an N x 1 vector of conditional asset coskewnesses with the world return. Theoretically, A,, is the global market’s marginal rate of substitution of variance for mean (‘reward to variance’) and I,, is global market’s marginal rate of substitution of skewness for mean (‘reward to skewness’). In a static setting with consistency of return moment tastes (for example, see Scott and Horvath, 1980), the three-moment CAPM suggests that investors prefer high asset payoffs when their wealth is low (‘risk aversion’) and when uncertainty in their wealth is high (‘decreasing absolute risk aversion’), which implies A,, >O and 1,, < 0. However, for investors with nondecreasing absolute risk aversion (e.g. cubic utility), we could also have A,, > 0 and i,, > 0 in equilibrium. 2.2. Modeling of conditional asset return moments If investors have rational expectations, the deviations of realized return moments from their conditional forecasts should be uncorrelated with the conditioning infor-

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mation. However, since we do not know the true information set a,_ 1, we condition all asset return moment forecasts on a subset of information, F,_l. Omission of relevant conditioning information can potentially induce ‘missing variables biases’ and a rejection of the three-moment CAPM with ‘too little conditioning information’ does not imply a rejection of the true three-moment model (for example, see Hansen and Richard, 1987). To empirically test the models, we have to parametrize the movements in conditional rewards to variance and skewness, respectively, over time. In addition, we need to specify the dynamics for conditional expected returns and variances, respectively, on the ‘world market portfolio’. The full set F,_, contains both global and local conditioning variables. Since we assume complete market integration, it is reasonable to model the across-all-assets common rewards to variance and skewness, respectively, and the conditional moments on the world market portfolio as functions of global information only or e, (for example, see Ferson and Harvey, 1993). However, we allow conditional covariances and coskewnesses to depend on both global and local conditioning information or F,_ 1. Following previous work (for example, see Ferson and Harvey, 1993; Dumas and Solnik, 1995), we assume linear expectations. We model conditional expected excess returns for the world market portfolio as a linear function of the world forecasting variables or E[r,,lF,_ I1= q,F 1 (‘the statistical model for the conditional benchmark means’). Moreover, we assume that the conditional variance of the excess return on the world market is linear in the global instrumental variables or E[(r,, - qw)‘lF,_ II= rc,~ 1 (‘the statistical model for the conditional benchmark variances’). Finally, we model the reward to variance and skewness, respectively, as a linear function of the global forecasting variables or &=&q 1 and I,, = &v__ 1. However, we do not have to specify the statistical models for conditionally expected returns, second and third co-moments, respectively, on the individual assets. Alternatively, we could, for example, employ a combination of instrumental variables and multivariate GARCH models for capturing the predictable movements in factor risk premiums and risk measures, respectively (e.g. Evans, 1994). While this approach would allow us to recover the model’s fitted values, odds for misspecification of the model’s functional form would increase from the additional structure imposed, and thus decrease the statistical robustness of the empirical model. Hence, our asset pricing model specification allows equilibrium expected asset returns to fluctuate over time as a function of changing asset-speci& covariances and coskewnesses, respectively, and time-varying rewards to variance and skewness, respectively. While the rewards to risk and skewness, respectively, are essentially ‘latent’ parameters in our model specification (we have not imposed any risk-return relationship on the benchmark portfolio), we are identifying a benchmark portfolio with respect to which marginal risks are measured. One alternative framework for studying the existence of predictable joint movements in asset returns employs latentvariable models (e.g. Ferson et al., 1993). However, in our case, a pure latent variable method is unsuitable for identifying whether a global benchmark is efficient. Because we only employ domestic test assets, the method would be unable to discriminate between the efficiency of latent ‘local’ and ‘global’ portfolios. We

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explictly examine whether our proxy for the ‘world market portfolio’ is conditionally mean-variance-skewness efficient. Besides studying the performance of the threemoment CAPM, it is also interesting to examine whether world skewness is rewarded in the model and if the rewards to variance and skewness, respectively, change predictably over time (for example, see Dumas and Solnik, 1995). The three-moment model outlined above is a very simple description of asset pricing. Hence, it is also worthwhile to track potential sources of rejection to alternative asset pricing models. First, if the Finnish market is not fully integrated to world markets, the local market may come into play in determining expected returns on local assets (for example, see Errunza and Losq, 1985). Second, even if financial markets are fully integrated, exposure to exchange rate fluctuations could well affect the cross-section of expected local returns if PPP does not hold (e.g. Adler and Dumas, 1983). Third, exposures to changes in overall trading volumes could be rewarded especially on more thinly traded markets. To explore all considered asset pricing alternatives, a general expanded threemoment asset pricing model implies the following Nx 1 vector of ex post ‘pricing errors’:’

where X, is the out-of-model variable under consideration. The vector ht contains the forecasting errors from the linear projection of the pricing benchmark excess returns on VI. The forecasting errors from the linear regression of the benchmark return variances on the predetermined global conditioning instruments are given by v . The empirical three-moment model in Eq. (2) implies the null hypothesis Hi: E[u,&~-~] =E[v,,@~-,] =E[ej,@F,_J =0 for all j assets from 1,. . .,N. Equivalently, I?[&(@)]= 0. Hence, if the model specification in Eq. (2) does a good job in explaining expected returns over time and across assets, then the model residuals e, should be random white noise. The original three-moment model CAPM null is a= 0.Thus, if the nested threemoment model is valid, out-of-model asset specific constants or risk exposures to nonmodel factors should not be different from zero across all assets, implying that the variable will not be priced after controlling for the sources of risk in the threemoment model. Moreover, we will estimate and test the constrained (a=O)baseline model null E[h,(@)*] = 0. Hence, when testing and examining the baseline model, we estimate the model in Eq. (2) without a&, which corresponds to our empirical counterpart of Eq. (1). Taking conditional expectations of Eq. (2) with a=0 with

’We have employed the moment simplification trick of, for example, Harvey (1991) for covariances in Eq. (2). However, we cannot directly employ a similar simplification for coskewnesses. The reason is that - for asset j - we have S[rj,, r,,] = I~[(z+I&)]=E[(rj&,)] --E[rjJq&] = E[(rj&)] - E[rj,]az[r,]. Hence, the latter term does not - strictly speaking - cancel out since the variance in market portfolio returns is not generally zero. However, when examining the robustness of the empirical model, we also perform tests of the model where the coskewness for asset j is approximated simply by E[(rj&,)].

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respect to F,_, defines the restrictions placed by our version of the asset pricing model in Eq. ( 1).2 The factor model specification a& corresponds to an asset pricing model with time-invariant latent risk exposures a and a predetermined benchmark X, with timevarying expected returns (for example, see Harvey, 1991). To account for the impact of ‘regime shifts’, we will also consider intercepts with multiplicative dummy variables of the form ax =aDX,, where D is the dummy variable for the regime known at the beginning of each period. In these tests, we include D in the conditioning information set as a local variable, i.e. we allow investors to have different expectations of risk exposures in different regimes. Overall, this extended model specification seems reasonable since the contribution of time-variation in risk exposures to overall return swings is often empirically negligible (for example, see Ferson and Harvey, 1991, 1993). Because the latent risks in a are not restricted to be second comoments or ‘betas’, a is also consistent with constant total risk exposures to X, in a threemoment CAPM (for example, see Lim, 1989). 2.3. Test method To test the model in Eq. (2), we use the stacked the [(N+ 2) x 1] vector of model error terms. With h conditioning variables in F,_l (including the unit vector) and h-l instruments in F,, there are (h- 1) x 2 + h x N moment conditions. When testing H,,, @ contains 4 x (h - 1) +N parameter estimates. H, is a joint hypothesis about conditional benchmark portfolio efficiency, linear expectations for world returns and constant parameters. Since the three-moment CAPM null, H,: B[h,(@)]= 0, forms a system of moment conditions, it can conveniently be estimated with the generalized methods of moments (GMM).3 The validity of Ho is tested for with an asymptotically X2-distributed goodnessof-fit statistic developed in Hansen (1982). The degrees of freedom for the test equal the number of free moment conditions, i.e. total moment conditions less the number of estimated parameters. We use the iterated version of the GMM to improve small sample properties (see Ferson and Foerster, 1994). Using likelihood ratio tests (see Newey and West, 1987a), we perform a host of diagnostic tests to learn more about the properties of the model and to see which out-of-model factors capture deviations from the model. Although GMM tests tend to produce biased parameter estimates and overstate parameter significance in small samples, the goodness-of-fit test statistic generally performs well. The goodness-of-fit test statistic from an iterated GMM estimation with 120 time series observations, 10 assets and three instruments (close to our case) tends to only weakly overreject the restrictions of a single-factor model (see Ferson and Foerster, 1994). Even though our asset pricing model is more complicated that 2This follows, since ~~~~l~,-ll=~~~tl~~-~l-~~~~~~~l~,-~l-~~~~~~~~~~-~~~~-~l~~-~l= E[r,lF,_ J - A,.K &, r,lF,_ iI --A= &r,, rJF,_ J =0 from the co-moment definitions. 3 One major advantage of a GMM test in the present context is that the method does not impose strong distributional conditions on the disturbance terms such as normality.

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the models examined by Ferson and Foerster (1994), their simulation results suggest that the iterated GMM estimator should fare reasonably well also when testing our model. However, because parameter estimates are likely to be biased, we will concentrate on tests of the functional form of the model. For a complicated nonlinear option pricing model, simulation results by Rindell (1995) suggest that the GMM likelihood ratio test statistic (Newey and West, 1987a) is able to correctly detect deviations from a restricted model even in small samples.

3. The data The estimation period covers 108 months of data from January 1987 to December 1995. Competitively determined domestic short-term interest rates have existed during the whole time period. Hence, excess returns can be calculated with greater precision. We employ continuously compounded asset returns throughout the paper since they describe more accurately price changes during a volatile time period. The considered test period is not entirely homogenous. First, deregulation of capital flows from and to Finland proceeded step-wise up to January 1993. Prior to 1993, most Finnish companies had restricted and unrestricted share classes and foreigners could only hold the latter class of shares. The decision to lift the ownership restrictions was widely known in the autumn of 1992. Foreign ownership in Finnish companies soared following the abandoning of ownership restrictions. In the 1987-1991 period, aggregate foreign ownership in Finnish companies listed at the Helsinki Stock Exchange (HSE) hovered in range 6-10% of total market capitalization and it was some 8% at year-end 1992. However, foreign equity holdings surged to some 20% of total market capitalization by the end of 1993, and they subsequently increased to roughly one-third at year-end 1995. Hence, the data may look different from 1993 onwards and local sources of risk could potentially be more important prior to 1993. Second, the FIM moved into a managed float regime in September 1992 from a tight target zone regime which did affect the exchange rate adjustment process and potentially also the rewards to exchange rate risk. Large discrete jumps in the exchange rate or target zone realignments occurred prior to October 1992, and expected equity returns could have been affected by ‘peso problems’. Third, at the market liquidity trough in 1991, aggregate share turnover at HSE was merely 10% of total market capitalization. In contrast, the corresponding figure was some 33% in 1987 and almost 50% in 1995. Overall, liquidity risks could have been clearly higher in the sleepy 1990-1992 period than at other times. We will address all of these issues in the asset pricing tests by examining whether Finnish asset excess returns are affected by each of these out-of-model factors after controlling for global market portfolio risks. 3.1. The asset return data To represent global market portfolio risks, we employ the Morgan Stanley Capital International world equity index (MSCI). The index is value-weighted and it includes

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gross dividends. The original MSCI returns are denominated in USD and we have converted them into FIM with the end-month FIM/USD exchange rates. As a proxy for the local riskfree return measured in FIM for month t, we use the 1 month holding period return on a 1 month inter bank money market note - calculated from the Helsinki Interbank Offered Rate (Helibor) - on the last trading day of month t-l. The stock return data employed in this paper consist of monthly returns on stocks listed on the Helsinki Stock Exchange some time during December 1986-December 1995. The stock returns series are adjusted for stock splits and share issues and dividends are accounted for by assuming that dividends received on a stock are reinvested in the same stock. Seven total market-capitalization sorted, value-weighted stock portfolios serve as test assets. Size portfolios are frequently used in empirical tests (for example, see Harvey, 1989). Overall, the data has been very loosely screened and survivorship biases are likely to be insignificant since the use of past or future information for selecting which companies to include in the sample is generally negligible. First, we have tracked listings and de-listings on a monthly basis, and our portfolios are rebalanced each month t based on market values available at the end of month t - 1. Hence, a given company’s shares only have to be listed for two consecutive months to qualify for our sample. Second, for each firm only one series - the most actively traded - was chosen. Our liquidity screen uses future information, but only for choosing which of the usually multiple stock series to employ for each company. Hence, companies are not included or excluded depending on overall share liquidity relative to other companies. Third, the seven size portfolios contain both restricted and unrestricted shares depending on the outcome of the liquidity screen.4 All size portfolios have roughly the same number of stocks at each month t. Since large blue chip companies are generally more actively traded than shares of smaller companies, and we use the most actively traded share series for each fhm, thin trading problems should not be too severe in monthly returns from value-weighted portfolios. As seen in Table 1, the mean excess returns of all seven size portfolios are weakly negative for the 1987-1995 period. The monthly mean excess return on a valueweighted local share price index including dividends is also negative for this period (-0.244%). Moreover, the mean FIM return on the world equity index in excess of the local riskless return is in the red. On an annualized basis for 1987-1995, the local riskless return averaged 10.2%, while the FIM appreciated on average by 1.1% 4 Theoretical models of partial segmentation (e.g. Hietala, 1989; Bergstrom et al., 1993) suggest that assetspecitic global risk exposures could differ across otherwise similar restricted and unrestricted shares. However, if the in- and outflow constraints on capital are not strictly binding (more or less our case), the existence of foreign ownership restrictions does not necessarily imply segmentation and there could be sufficient ‘pricing externalities’ from unrestricted shares to restricted shares. Anyway, we cannot focus solely on either restricted or unrestricted shares due to data considerations. On one hand, the ownership restrictions were lifted in 1993 while our sample ends in 1995. On the other, we would get a less representative sample if we would only employ unrestricted shares. Overall, the use of both restricted and unrestricted shares should make it more likely to detect deviations from a global pricing model.

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Table 1 Descriptive statistics for the monthly excess asset returns Variable

Mean

SD

Skewness

p-value

Autocorrelation Pl

Value-weighted size portfolios ranked from largest 1987:01-1995:12 Size 1 -0.2018 7.4088 0.152 size2 -0.5515 7.6200 -0.151 Size 3 -0.6729 7.1937 0.278 Size 4 -0.6821 7.9676 -0.176 Size 5 - 1.5346 7.4459 0.097 Size 6 - 1.5510 8.2725 - 0.400 Size I - 1.4707 9.7240 0.903 World (FIM )

-0.0762

4.8190

- 1.018

Pz

PlZ

PlS

-0.015 - 0.078 0.082 -0.018 - 0.048 -0.091 - 0.076

to smallest firms 0.350 0.665 0.225 0.487 0.816 0.432 0.275

0.198* 0.298** 0.309** 0.132 0.162 0.194* 0.091

0.066 -0.002 0.110 -0.087 -0.001 -0.167 0.060

0.101 0.243* 0.043 0.126 -0.002 -0.188 0.064

0.064

0.280**

-0.017

-0.110

0.009

Note: the unconditional skewness measure is standardized by dividing the third central moment by the cube of the unconditional standard deviation. The significance of skewness is tested in a GMM system of the three first return moments using a Wald test with one degree of freedom (Bekaert and Harvey, unpublished data). The p-values are heteroskedasticity and first-order auto correlation consistent (see Newey and West, 1987b). The asymptotic standard errors for autocorrelation coefficients are given by m, where r is the number of observations. *,**Denote significance at the 5 and 1% levels, respectively. The monthly returns are multiplied by 100.

the USD. However, changes in the trade-weighted index of the FIM indicate that the markka depreciated by on average 0.77% annually against a basket of all major currencies during 1987-1995. There is significant first-order autocorrelation in excess returns from four of the seven size portfolios, and in the excess return from the world index measured in FIM. However, there is no evidence of autocorrelation in USD denominated returns on the MSCI (the first-order autocorrelation coefficient is 0.02). This suggests that the serial correlation in FIM excess returns is driven by the other return components. For size portfolios 2 and 3, the first-order autocorrelation coefficients are around 0.3 which means that some 9% of the return variation can be explained by oncelagged own returns. In returns from size portfolio 7 - the smallest firms - there is no significant serial correlation. Hence, if anything there seems to be autocorrelation in the monthly returns from large firms which suggests that the serial dependence is not induced by thin trading. To further explore data properties, we use a Wald test to see if the asset returns contain unconditional excess skewness or deviations from unconditional normality. We employ a set of moment conditions similar to those in Bekaert and Harvey (unpublished data), but we only consider here the three first moments of the return distributions. We estimate a set of moment conditions corresponding to the moment definitions for three first moments for each asset separately. Hence, we obtain asset specific estimates of sample mean return, variance and a standardized measure of total (systematic and unsystematic) skewness. As seen in Table 1, the GMM results against

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suggest that the hypothesis of no excess skewness on average can be rejected at the 10% level only for the world market. However, this first look does not tell us much about the existence of time-varying systematic skewness, which is the focus of this paper. In Section 4.1, we examine the existence of predictable time-variation in coskewnesses between the assets and the world market portfolio. 3.2. The forecasting instruments We employ a set of global and local predetermined forecasting variables for tracking predictable time-variation in returns, risk exposures and rewards to risk exposures. The global information variables, v 1, are: ( 1) a constant; (2) the lagged return on the MSCI world index measured in own currencies; and (3) the lagged return on the Salomon Brothers World Government Bond Index measured in FIM. The information set F,_l also contains (4) the lagged return on the Finnish stock market to represent local information. Overall, all used instrumental variables are readily available and we have chosen this set of instruments on the basis of parsimony, previous empirical procedures (e.g. Ferson and Harvey, 1993) and theoretical content (e.g. Merton, 1973; Adler and Dumas, 1983). Past world equity returns are not directly affected by exchange rate swings, but lagged world bond returns contain information about shifts in the global investment opportunity set seen from a Finnish perspective. This design should reduce any collinearity among the two global variables. On integrated world asset markets, global bond returns measured in FIM should be in parity to local bond returns adjusted for some risk premium. Hence, the bond variable should contain information about changes in the global investment opportunity set and exchange rate movements that may influence future equity returns. As seen in Table 2, the employed instrumental variables appear to have stationary and ergodic (unconditional) distributions - precisely as one would expect from asset returns. The pairwise correlations are also fairly low. The only nontrivial correlation, 0.455, is between the lagged world returns and past local market returns.

4. Empirical results 4.1. Descriptive tests

Before proceeding with the empirical tests, it is useful to examine the predictive power of the forecasting variables. Recall that our empirical three-moment CAPM assumes that expected returns are determined by expected rewards to variance and skewness, which are global measures, and by asset-specific risk exposures, which are influenced by both global and local information. Expected return moments on the world market portfolio are determined only by global conditioning information. Hence, while local asset returns are likely to be predictable with both global and local information, the local information should enter through the risk exposures in the full integration asset pricing model. Our model in Eq. (2) assumes a linear hlter

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K Nummelin /ht. Fin. Markets, Inst. and Money 7 (1997) 137-155 Table 2 Summary statistics for the monthly instrumental variables data Variable

1987:01-199512 r(MSCI),_, r(SWB),-I r(HSE),-,

Mean

SD

Autocorrelation Pl

P2

PlZ

P18

4.2023 2.9266 7.0760

0.112 0.184 0.244*

- 0.026 0.091 -0.053

-0.019 -0.046 0.113

- 0.022 0.017 0.012

r(MSCI),_,

r(SWB),- I

WSW-I

1.000 -0.023 0.455

1.000 0.118

1.000

0.6804 0.7084 0.7649

Pairwise correlations 1987:01-199512

r(MSCI),_r r(SWB),-r r(HSE),-I

Note: r( MSCI),_ i is the return on the Morgan Stanley Capital International world index in own currencies, r(SWB),_, is the return on the Salomon Brothers World Government Bond Index in FIM terms and r(HSE),_i is the return on a value-weighted share price index for the Helsinki Stock Exchange. The asymptotic standard errors for the auto-correlation coefficients are given by m, where r is the number of observations. *,**Denote significance at the 5 and 1% levels, respectively. Monthly returns are multiplied 100.

for world market means and variances to the global information variables. However, the model does not require that individual asset returns or the asset-specific risk measures are linear in the conditioning information. Table 3 shows that excess returns on the seven size portfolios and the world equity market can be predicted by the employed instruments in a standard linear regression model. The adjusted proportion of the variation in size portfolio returns explained by global and local instrumental variables range from 12.5 to 21.5%. Not surprisingly, F-tests strongly reject constant conditional means for all seven portfolios. Global conditioning information is generally important, but lagged local market returns seem to provide incremental explanatory power mainly for returns from smaller firms. According to an F-test, local information adds explanatory power at the 1% level in the returns from four of the seven size portfolios. From a global asset pricing perspective, this suggests that exposures to global factors should be predictable with local information or it could be a sign of a lower degree of integration of small firms to world markets. Finally, global market excess returns measured in FIM seem to be predictable with our global conditioning information. The adjusted R* is 9.2%, and an F-test again rejects the hypothesis that conditionally expected world market excess returns are constant. To obtain an idea of whether global risk measures are predictable with our instrumental variables (especially lagged local market returns), we perform an exactly identified GMM estimation with four equations. For each asset separately, we model the predictability in asset and world market return means, covariances and

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Table 3 Predictability in excess returns All information R2

F( 3,104)

Global information p-value

adjusted 1987:01-1995:12 Size1 0.125 Size 2 0.215 Size 3 0.197 size4 0.130 size5 0.136 Size 6 0.134 Size 7 0.185 World (FIM)

R2

F(2,105)

Exclude local information p-value

F(lJO4)

p-value

adjusted

6.08 10.75 9.72 6.31 6.60 6.50 9.07


0.118 0.208 0.108 0.127 0.076 0.062 0.089 6.45

8.18 15.06 7.48 8.77 5.39 4.54 6.23


0.188 0.174
0.002

Note: OLS regressions of excess returns on the forecasting variables and a constant. The global instrument set consists of lagged world equity returns in own currency and world bond returns in FIM terms. The full information set also contains lagged local stock market returns. A heteroskedasticity and first-order autocorrelation consistent F-test is used to examine if the forecasting variables are able to jointly explain movements in asset excess returns. The degrees of freedom are reported in parenthesis after the test statistics.

coskewnesses. For the means, we use linear titers onto the appropriate information sets. For global risk exposures, we consider a regression model with both linear and quadratic forecasting variables.5 Overall, there is some evidence of predictably changing global risk measures. As seen in Table 4, variables based on lagged local market returns seem to be able to track time-variation in coskewness at the 10% level for five of the seven size portfolios. Moreover, there is some evidence that all the included forecasting variables are able to jointly capture movements in global coskewnesses: using an F-test in OLS framework, we reject the null hypothesis of constant coskewness at the 5% sigiri6cance level for four of the seven size portfolios (not reported). Covariances do not ,generally appear to be predictable with local information. However, with 90% cotidence, the empirical evidence suggests that covariances for three of the seven size portfolios can be forecasted with all the considered instrumental variables (not reported). Interestingly, the covariances and coskewnesses for the largest and smallest size portfolio, respectively, appear to contain significant predictable elements. To sum up, our model specification in which local information enters through predictable movements in risk exposures appears to be underpinned by the data. 5Following the suggestion of an anonymous referee, we also tried an OLS regression of risk exposures on plain, squared, cubic and cross products of all the instruments. While theoretically more correct, adding cross and cubic products of the instrumental variables did not generally improve the model fit. The standard errors for the coefficient estimates for the plain and squared instruments also generally became a good deal larger, which suggests that the extended regression model is not empirically well specified.

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Table 4 Predictability in co-moments with plain and squared instruments Wald tests of jointly zero coefficients

Exclude local information Coskewness

Covariance

1987:01--1995:12 Size 1 Size 2 Size 3 size4 Size 5 Size 6 Size 7

X1

p-value

X2

p-value

4.07 0.99 2.43 6.32 0.62 0.84 2.85

0.131 0.609 0.300 0.042 0.733 0.657 0.241

6.90 7.77 0.42 8.79 8.03 0.22 4.92

0.032 0.021 0.811 0.012 0.018 0.894 0.085

Note: regressions of co-moments on plain and squared forecasting variables in GMM. For each asset, a system consisting of: (1) a linear regression of world excess returns on the global instruments; (2) a linear regression of asset excess returns on all instruments; (3) a regression of covariance on all plain and squared instruments; and (4) a regression of coskewness on all plain and squared instruments is estimated. The estimation is exactly identitied. The global instrument set consists of a constant, lagged world equity returns in own currency and world bond returns in FIM terms. The full information set also contains lagged local stock market returns. A heteroskedasticity and hrst-order autocorrelation consistent Wald test is used to examine whether the forecasting variables are able to jointly predict movements in co-moments. All Wald tests have two degrees of freedom.

For conditional market return variances, our empirical model assumes a linear filter to the global conditioning information. The data is not at odds with our specification: a Wald test in GMM rejects constant market return variances at the 1% level. 4.2. The pricing of systematic skewness In this section, we document results from tests of the general null hypothesis of the baseline (i.e. constrained) three-moment CAPM, &h,(Q)*] =O. We also conduct tests of time-variation in implied rewards to variance and skewness and examine whether marginal global skewness affects the cross-section of expected size portfolio returns, ASK i = 0, after accounting for the reward to global market variances. Overall, the results in Table 5 indicate that the three-moment CAPM with timevarying rewards to co-moments performs reasonably well for the stormy 1987-1995 period. For the baseline model, we are unable to reject the orthogonality restrictions which is not very surprising since the estimated moment conditions are likely to be rather volatile. However, we overwhelmingly reject the hypothesis of constant rewards to variance and skewness jointly and individually for each of the two rewards to risk. Moreover, we find strong evidence suggesting that the implied rewards to global market variance and skewness, respectively, are different from zero. This suggests that global covariance and coskewness risks influence the crosssection of the expected size portfolio returns.

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Table 5 Generalized methods of moments tests of the three-moment CAPM Model specifications Baseline model

Seven value-weighted size portfolios as test assets 1987:01-1995:12 Goodness-of-fit Reward to global variance=0 at all times Reward to global skewness=0 at all times Both rewards to global risks are constant Constant reward to global variance Constant reward to global skewness

Model 2

x2

p-value

x2

22.77 13.08 19.22 18.85 10.99 13.09

0.415 0.004
21.80 5.41 22.61 17.90 4.79 15.35

Model 3 p-value

0.472 0.144
x2

23.43 28.46 160.71 46.30 27.15 16.68

p-value

0.378
Note: the baseline model is given by e, = rt - &K 1(rtu~) - A,= i (r& - rzq&“_J, model 2 is given by e,=r,-~_,(r,~)-~~~i(r,~,) while model 3 is given by e,=r,-~,(r,~)-~~~,(r,l~(). The global instrument set consists of a constant, lagged world equity returns in own currency and world bond returns in FIM terms. The full information set Ft _ i also contains lagged local stock market returns. The iterated, unrestricted GMM estimation is conducted with the heteroskedasticity and autocorrelation consistent weighting matrix of Newey and West (1987b) with one moving-average term. The p-value is the probability under the null hypothesis of realizing a higher x2 value than the observed sample value. All goodness-of-fit tests have 22 degress of freedom, tests of a zero reward to each global risk have 3 degrees of freedom, the test of constant rewards to both global risks has 4 degrees of freedom and tests of a constant reward to each global risk have 2 degrees of freedom.

If we change the definition of coskewness from E[r&,-~,K&‘L i]Ft-J to E[r,& ]Ft_r], the estimated model - model 2 in Table 5 - is statistically more robust for specification of the dynamics in conditional market portfolio return variances. However, the model’s goodness-of-fit is essentially unchanged. Again, the results strongly support the hypotheses that global skewness affects the cross-section of returns, and that the rewards to global variance and skewess change predictably through time. However, the reward for global covariance risk seems to be indistinguishable from zero in this model variant. Since we employ data from a time period with huge price swings, the good performance of three-moment model could be driven by ‘outliers’. Skewness is potentially sensitive to extreme price swings since it depends on the third power of the return forecast errors. To examine this possibility, we report results for a model variant with coskewness defined as E[ju,,Jr,lF,_ J, which is model 3 in Table 5. Hence, we replace the squared market return innovation with the absolute value of the innovation. While not strictly speaking consistent with original three-moment CAPM, this specification should clearly play down the sensitivity of coskewness to extreme observations. Our results suggest that model fit deteriorates weakly. However, global ‘co-skewness’ seems to affect the cross-section of expected size portfolio returns with very high statistical confidence. Moreover, there seems to be significant predictable time-variation in the rewards to global risks. Thus, the cross-

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Table 6 Tests of nested restrictions on expanded three-moment CAPMs Tested restrictions on the general model Nested model null

Seven value-weighted sire portfolios as test assets 1987:01-1995:12 Baseline three-moment CAPM augmented with: Asset-speci6c constants 1987-1995 Asset-specific exposures to local stock market 1987-1995 Asset-specific exposures to local stock market 1987-1992 Asset-specific exposures to local stock market 1993-1995 Asset-specific exposures to squared local market returns 1987-1995 Asset-specific exposures to squared local market returns 1987-1992 Asset-specific exposures to squared local market returns 1993-1995 Asset-specific exposures to changes in FIM 1987-1995 Asset-specific exposures to changes in FIM 1987-1992:09 Asset-specific exposures to changes in FIM 1992:10-1995 Asset-specific exposures to changes in market liquidity 1987-1995 Asset-specific exposures to changes in market liquidity 1990-1992

Reward to global skewness = 0

p-value

~2

p-value

14.08 10.88 9.76 2.00 16.59

0.050 0.144 0.203 0.960 0.020

8.17 9.46 12.42 25.47 15.21

0.043 0.024 0.006
21.35

0.003

35.63


11.17

0.131

20.98

< 0.001

8.09 14.52 9.72 8.38

0.325 0.043 0.205 0.300

5.31 9.46 11.71 9.12

0.150 0.024 0.008 0.028

8.46

0.294

18.64


Note: the augmented baseline model is e, =rl - ax, - m- l(rtuw)- l,r_ ,(r&, -r,k&Y_1)for each definition of X,. The three-moment model null is a=O. The subperiod analyses are conducted by using multiplicative dummy variables of the form OX, and D is also included as a local variable in the conditioning information set. The global instrument set r- 1 consists of a constant, lagged world equity returns in own currency and world bond rertums in FIM terms. The full information set F,_, also contains lagged local stock market returns and a regime dummy where appropriate. The iterated, unrestricted GMM estimation is conducted with the heteroskedasticity and autocorrelation consistent weighting matrix of Newey and West (1987b) with one moving-average term. The p-value is the probability under the null hypothesis of realizing a higher x2 value than the observed sample value. AU tests of the nested threemoment model null have seven degress of freedom, while tests of a zero reward to global skewness have 3 degrees of freedom.

sectional pricing of coskewness does not seem to be driven by outliers in the data.6 However, as seen in Table 6, if we inject asset-specific constants into the threemoment CAPM in Eq. (2), we reject the conditional mean-variance-skewness effi’Table 3 does not contain results for the model variant, where coskewness is given by E[~,~uJ -r,lc, c iIF,_ i]. These results are almost identical with those for model 3, which are reproduced in parenthesis. The ,$ statistics for goodness-of-fit and a zero reward to global skewness are 23.11 (23.43) and 146.27 (160.71), respectively, and degrees of freedom are the same as for model 3. While the zero reward to skewness restriction is very strongly rejected, the parameters in the unrestricted model are also estimated with very high precision. Overall, we are confident that all restricted estimations are at global minimums.

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ciency of the world market portfolio the model is now weakly rejected, returns still seems to come into play specmc intercepts. The p-value for a extended three-moment CAPM.

at the 5% significance level. However, while coskewness with the world market portfolio after controlling for covariance risk and assetzero reward to global skewness is 4.3% in this

4.3. Diagnostics: local market excess returns To see on which accounts the model fails, we report results from the diagnostic tests of the three-moment CAPM against a ‘partially segmented’ three-moment CAPM, in which the conditionally expected risk premium on the local market also enters as a factor. However, since all restrictions on foreign ownership were removed at the beginning of 1993, the pricing may look different in the earlier part of the data. Hence, using a dummy variable, we split the data into two parts: 1987-1992 and 1993-1995, respectively. In the empirical model, we allow conditional marginal risks to change as a function of this regime shift. Hence, we will examine whether the local market enters the pricing equation in: (1) the whole time period; (2) 1987-1992; and (3) 1993-1995. Moreover, to account for the potential pricing of higher moments in local market returns, we perform the same set of regressions by replacing local market returns by squared local returns. The results appear in Table 6. We do not find reliable evidence suggesting that local market returns are important in determining the cross-section of expected returns on Finnish size portfolios for any time period. For 1993-1995, we find no evidence of the local market’s influence which is consistent with full integration after the deregulation. Admittedly, the power of test could be weaker for the 1993-1995 period than for longer time periods. However, the evidence of local pricing is weak also for the overall period and - very surprisingly - for the 1987-1992 period. This finding is at odds with partial segmentation models (e.g. Hietala, 1989) but it is consistent with results of Bekaert and Harvey (1995) for developed countries. However, squared local market returns seem to enter the pricing equation for the whole period and the 1987-1992 period, but this domestic factor fails to detect any deviations from the global three-moment CAPM for the deregulated 1993-1995 period. Again, the conditional reward to global skewness is reliably nonzero across all test designs. To summarize, there seems to be scope for the local market to enter through higher moment effects, but local influences are not able to deteriorate the significance of global coskewness. 4.4. Diagnostics: currencyfluctuations

As noted earlier, our three-moment model does not take exchange rate risk into account. To gage on the ability of currency fluctuations to explain deviations from the three-moment CAPM, we insert asset-specific risk exposures to movements in the external value of the FIM to the model in Eq. (2). If the baseline three-moment CAPM is appropriate, currency movements should not affect expected returns after controlling for global market portfolio risks. We use monthly changes in the Bank of Finland’s trade-weighted currency index as a proxy for the foreign exchange

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factor in the model. Dumas and Sol& (1995) use multiple foreign exchange factors, while Ferson and Harvey (1993) also consider one aggregate exchange rate factor. For subperiods, we allow conditional global market risk exposures to change with shifts in the exchange rate regime. The results show that exchange rate movements are able to capture deviations from the global three-moment CAPM, but only for the period from January 1987 to September 1992. Hence, since the exchange rate adjustment process became smoother following the floatation of the FIM, monthly currency fluctuations do not seem to be able to explain the cross-section of expected returns after controlling for global market factors. These results do not agree well with previous empirical evidence (e.g. Dumas and Solnik, 1995). However, a significant currency factor for the pre-floatation period suggests that large discrete policy shifts or ‘peso problems’ may affect expected returns. In any case, global skewness still seems to significantly affect the cross-section of size portfolio returns, especially if we allow market risks to differ in the semi-fixed and managed float exchange rate regimes. Using currency regime dummies as additional local conditioning variables for risks, we reject a zero reward to skewness at the 1% level. 4.5. Diagnostics:

changing market liquidity

Finally, we will examine whether low market liquidity affects expected returns after controlling for global market portfolio risks. If liquidity risks are important, it should be difficult to explain expected size portfolio returns only by looking at the conditional exposures to the global market portfolio. To obtain a measure of market liquidity in volume terms, we take the accumulated monthly market-wide share turnover in FIM and deflate it with the overall share price index to remove ‘price effects’ from the series. We then use monthly changes in real market volumes to capture liquidity risks. If overall market liquidity falls, the transaction volumes in thinly traded firms - usually small caps - are likely to be most adversely affected. Hence, beyond global market portfolio risks, investors may have to be compensated for poor trading opportunities in the Finnish market. Using a dummy variable, we will also examine whether liquidity risks come into play during 1990-1992 when share turnover to total market capitalization was exceptionally low. Our results indicate that changes in market liquidity do not seem to affect the cross-section of expected size portfolio returns after controlling for market risks. This is true both for the overall time period and the period of unusually slow trading in 1990-1992. Moreover, inclusion of a market liquidity factor does not seem to destroy the significance of the coskewness factor. In fact, if we allow market risks to shift in the 1990-1992 period, we reject the hypothesis of a zero reward to global skewness with very high confidence.

5. Conclusions In this paper, we have examined the empirical role of conditional global coskewness in the pricing of Finnish equities. We report that the conditional version of the

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global three-moment CAPM performs well when confronted with the data and global coskewness seems to affect the cross-section of expected returns across all test designs. To gage on the ability of a global three-moment CAPM to explain expected equity returns, we inject a number of additional factors into the model. We consider local market returns (e.g. Errunza and Losq, 1985), exchange rate fluctuations (e.g. Adler and Dumas, 1983) and movements in stock market trading volumes. Our general finding is that the three-moment model survives surprisingly well the attacks of these additional factors. We find that none of the our-of-model factor returns are able to incrementally explain asset returns after accounting for the expected returns suggested by the global three-moment CAPM. However, we report some evidence suggesting that higher moments in local stock market returns and large discrete exchange rate movements or realignment risks prior to the floatation of the FIM in September 1992 did affect the dispersion in expected size portfolio returns even after controlling for global market risks. Our tests could underestimate the role of outof-model factors since we assume constant risk exposures to them. However, none of the additional factor specifications is able to crowd out the global skewness factor in explaining the cross-section of expected returns. Based on our results, one potentially fruitful avenue of future research would be to specify an extended three-moment asset pricing model, which incorporates large discrete regime shifts, to approximate expected returns. By accounting for, for example, exchange rate regime uncertainty or changing conditional capital market integration in an extended three-moment model, we should obtain a richer picture of asset pricing especially on smaller markets in transition (e.g. compare with Bekaert and Harvey, 1995).

Acknowledgements I gratefully acknowledge the many useful comments and suggestions by Campbell Harvey, anonymous reviewers and Anders Loflund. All errors are mine.

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