Stock returns and volatility in two regime markets: International evidence

Stock Returns and Volatility in Two Regime Markets: International

Evidence

KRISHNA PAUDYAL AND LIESL SALDANHA

This paper examines

the intertemporal

relationship

between stock returns and volatility within a two regime

framework in five countries namely the UK, USA, Germany, Japan and Italy. We extend previous research by examining the relationship between these two variables in regimes that are dependent on factors both exogenous and endogenous to the model. The exogenous separator is the sign of the observed risk premium while the endogenous separator is the sign of the risk premium predicted by different macroeconomic variables. In a regime characterized by positive risk premium, excess returns and expected volatility are positively associated while there exists a negative relation between unexpected volatility and excess returns. This, in itself, is proof of an ex ante positive relationship between risk and return. In the endogenous model, we find that regardless of the regime, there is a positive relation between expected volatility and expected return and a negative relationship between unexpected volatility and excess return. These results are consistent with the behavior of rational investors implying that while modelling this relationship the effect of the economic environment under which rational investors make investment decisions must be taken into account. The results are qualitatively

similar for all countries in the sample.

I.

INTRODUCTION

The estimation of the required rates of return on investments and the pricing of assets are some of the major problems encountered by investors, fund managers and financial managers. They make use of several asset-pricing models to help them with investment and pricing decisions. The dynamic Capital Asset Pricing Model proposed by Merton (1980) is one of the most widely used models in finance. Merton argues that the expected excess return on the market can be approximated by the product of the ‘market price of risk’ and a measure of ‘market risk.” A rational economic agent’s utility function graphed in a risk-return space is concave, displaying risk aversion. Since investment in the stock market is not without risk, such investment must offer a positive risk premium to motivate the risk averse investor to bear more risk. Thus, in an equilibrium market, return on an asset should be an increasing function of the risk borne. In general, within a given time frame, investors expect a higher rate of return from a security that is riskier. However, the empirical evidence available does not provide conclusive evidence on this relationship over time. Whether or not, investors demand a higher risk premium as a reward for investing in a security that is more risky over several investments periods still remains an open question. Krishna Paudyal and Lies1 Saldanha Department of Finance and Accounting, Glasgow G4 OBA. Lies1 Saldanha, Fax: (0141) 331 3171; E-mail: [email protected]. l

Glasgow

International Review of Financial Analysis, Vol. 6, No. 3,1997, pp. 209-228 Copyright Q 1997 by JAI PRESS Inc., All rights of reproduction in any form reserved.

Caledonian

University,

ISSN: 10574’219

210

INTERNATIONAL REVIEW OF FINANCIAL ANALYSIS I Vol. 6(3)

Rational risk averse investors normally require a relatively larger risk premium during times when the payoff from the investment is more risky. However, this may not always be the case as investors may not demand a higher risk premium in time periods that are classified as risky, as these periods may coincide with those time periods when investors are better able to bear particular types of risk. Secondly, a large premium may not be demanded as investors may opt to save relatively more during periods when the future is more risky. Glosten, Jagannathan and Runkle (1993) argue that a positive as well as a negative sign for the covariance between conditional mean and variance is consistent with financial theory. For instance, when all the productive assets that are available for future investment bear some form of risk and no riskless investment is available, then the price of the risky investment is pushed upw~ds and the risk premium will fall. In spite of the theoretical proposition that stock market risk and return is positively related, the empirical evidence available is mixed. For instance, Pindyck (1984) indicates that there is a strong positive relationship between risk and excess return while Shiller (1981), Porteba and Summers (1986). Baillie and DeGennaro (1990). and Theodossiou and Lee (1995) report on the presence of a very weak or nonexistent relationship between these two variables. On the other hand, French, Schwert and Stambaugh (1987) and Shawky and Marathe (1995) suggest that a negative relationship between unexpected volatility and excess return exists. French et al. (1987) argue that the observed negative relationship provides indirect evidence of a positive relationship between expected risk premium and ex ante volatility, Campbell and Hentschel (1992) also propose a positive relationship between risk and return. Fama and Schwert (1977), Campbell (19X7), Pagan and Hong (1989) and Nelson (1991) find a negative relationship. Chan, Karolyi and Stulz (1992) report no significant relationship. Harvey (1989) suggests that the relationship between risk and return may be time varying. These conflicting results documented in the literature warrant further examination of the robustness of these findings using different and probably more approp~ate econometric techniques. The motivation for this study stems from the fact that an analysis of market returns and risk without distinguishing the different financial regimes, as most studies do, may not reflect the true relationship between these variables. 2 An analysis of the risk-return relation in different financial regimes may throw new light on the relation. Although there are some studies based on this approach on the US market (e.g., Turner, Startz & Nelson, 1989; Shawky & Marathe, 1995) there is an absence of a comprehensive intemational study of this nature. Differences in the general macroeconomic conditions, the market microstructure and the distribution of share ownership in different countries, may result in differences in the risk-return relationship in these countries. Aiming to bridge the gap, we examine the intertemporal relationship between risk and return in a two regime market framework using data from five countries namely the UK, USA, Germany, Japan and Italy. Moreover, unlike in previous studies our regimes are based on movements in variables both endogenous and exogenous to the model. The rest of this paper is organized as follows. A brief survey of the previous research on the risk and return relation is provided in section two. Section three covers a discussion of the ~lationship between risk and equity return in a two regime framework. In addition, the econometric methods used are discussed in this section. We describe the data in section four. In section five we report the results and discuss the findings. Section six concludes the paper with a brief summary of the findings.

Stock Returns and Volatility in Two Regime Markets

II.

PRIOR STUDIES ON THE RISK-RETURN

211

RELATIONSHIP

In the recent past, a number of studies have examined the intertemporal relationship between stock return and risk (see, French et al., 1987; Chou, 1988; Campbell, 1987; Nelson 1991; Glosten et al., 1993; Theodossiou & Lee, 1995). However, the empirical evidence on whether risk (volatility) and returns are positively related is mixed. For instance, Pindyck (1984) argues for a strong positive relationship between volatility (risk) and expected return and suggests that much of the decline in stock prices during the 1970s is due to increased volatility. On the other hand, Porteba and Summers (1986) report that the shocks to the volatility process die out far too rapidly to significantly affect stock returns in the long run. However, they concede that it may be possible that these volatility shocks can have a small impact on stock market prices in the short run. Similarly, Shiller (1981) argues that the level of stock market volatility is too high to be explained by the changes in dividend implying little or no relationship between stock market return and volatility. French et al. (1987) report a strong negative relationship between the risk premium and the unpredictable component of volatility and argue that this negative relationship is induced by a positive relationship between expected risk premium and ex ante volatility. Therefore, when the expected and unexpected components of volatility are combined together (measured from ex post returns) the ex ante relationship is obscured. Consistent with the findings of French et al. (1987), Poon and Taylor (1992) report a negative and significant relationship between unexpected volatility and returns in the UK. On the other hand, Theodossiou and Lee (1995) find no relationship between conditional volatility and expected returns in any of the 10 industrialized nations examined. Paudyal and Saldanha (1996) report a significant positive relationship between excess returns and expected volatility for the USA, Japan and Germany but a significant negative relationship for Italy. For the USA and Germany they find a significant negative relationship between unexpected volatility and excess returns. Harvey (199 1) examines the conditional mean and variance of the NYSE market return using nine different conditional variance specifications. He reports a positive relationship between conditional mean and variance and argues that such a relationship depends on the specification of the conditional variance. While most studies focus on the contemporaneous correlation between conditional mean and conditional variance Whitelaw (1994) examines the contemporaneous and non-contemporaneous relationship between these two variables. His findings provide evidence of stock market volatility leading excess stock market returns over the business cycle. However, he concedes that the contemporaneous relation between mean and variance is negative, which is consistent with the results reported by earlier studies. In general, the evidence seems to be mixed, but one common thread running through the results is the negative relation between unexpected volatility and excess return. Further, most of the literature on the subject examines the risk-return relationship over a fairly long period of time, and chances are that this relationship changes in response to changes in market conditions under which investors have to make their decisions. One way to overcome this problem is to study this relationship in different regimes. Using a switching regression model,3 Turner et al. (1989) examine the risk-return relationship in a two regime framework, the regimes being a high variance regime and a low-variance regime. They suggest that the agents are consistently surprised by high variance periods resulting in a negative correlation between movements in volatility and excess returns.

212

INTERNATIONAL

REVIEW

OF FINANCIAL

ANALYSIS

/ Vol. 6(3)

In a recent study Shawky and Marathe (1995) report evidence of an absence of any significant relationship between market volatility and excess returns in a rising market. However, in a regime of falling stock prices they find a significant negative relationship between market volatility and excess returns. When they decompose the volatility into its predictable and unpredictable components, they find a positive and significant relationship between excess returns and predicted volatility during a regime of rising market prices. Whitelaw (1997) investigates the relation between volatility and expected return in an equilibrium exchange economy. Using aggregate consumption data, he attempts to duplicate the salient features of the risk-return relationship. He finds a negative unconditional correlation between risk and return. Key features of his study include a two regime framework with different consumption growth processes and time varying transition probabilities between regimes. This structure generates time varying correlation between stock returns and marginal rate of substitution, thus inducing variability in the short run relationship between expected return and volatility and a weakening of the long run relationship.

III.

RISK AND RETURN

IN A TWO-REGIME

MARKET

A.

Risk and Return: A theoretical perspective Modem finance theory rests on the assumption that the investors are rational utility maximizers. As stated earlier, a rational investor’s utility function in a risk-return space is concave, displaying risk aversion. Since stock markets are risky they must offer a positive risk premium to motivate a risk-averse investor to bear more risk. Thus, in an equilibrium market, return must be an increasing function of the risk borne. If the standard deviation (Q) of the market return (R,) is a sufficient measure of risk, then a general specification of the equilibrium expected excess return can be written as:4

(1)

E(R,- Rft) = Y&o)

Where RB is the risk free rate, g is an increasing function of CJ, and Y is the ‘reward-to-risk ratio.’ Assuming g, cs and state variable (s) are observable, the expected excess return can be written as: E[R, - Rfi I S, 01 = E[Yg(o) 1&o] Since Y is not observable

a following

further condition

is imposed

E[YlS] = E[YiS,o] This implies that given S, the conditional Thus, equation 2 can be written as:

expectation

of Y remains independent

of current (3.

E[R, - Rft I S,o ] = E[YlS]g(o) Under certain conditions Merton (1980)s argues that in the context of an intertemporal librium model, the expected excess return on the market can be approximated by:

(4) equi-

213

Stock Returns and Volatility in Two Regime Markets

(5) Where h is the market price of risk. Assuming that the market is efficient, use the best conditional forecasts of (3 and excess return, the relationship return can be estimated using the following equation:

and that investors between risk and

Merton (1980) points out that in periods of unexpectedly high volatility realized stock returns are usually lower than average. This implies that the expost model (equation 6) may not provide a very close estimate of ex ante model (equation 5). Merton argues that if a representative agent has logarithmic utility or if consumption growth follow an iid process then the coefficient of proportionality between the conditional mean and the conditional variance can be interpreted as relative risk aversion. Under more general assumptions Backus and Gregory (1989) and Campbell (1990) show that this coefficient does not necessarily represent relative risk aversion and, in principal, can be positive or negative. Two tests are commonly employed to examine the relationship between risk and return. The first test examines the hypothesis that the mean is proportional to the variance while the second test is on the hypothesis of the mean being linear in the variance. Proportionality, tests using a linear model for conditional variance is presented in Campbell (1987) and Harvey (1989) for U.S. stock returns. These tests strongly reject proportionality. French et al. (1987) and Chou (1988) find a positive linear relationship between mean and variance while Glosten, Jagannathan and Runkle (1989), Pagan and Hong (1989) and Nelson (1991) find a negative relationship. Most empirical results documented in the literature support the proposition that in periods of unexpected high volatility realised return is lower than average (see for example, French et al., 1987; Turner et al., 1989; Shawky & Marathe, 1995). Estimation of equation 6 using the conventional OLS procedure assumes that 0 is constant over time implying that the risk premium is stable (constant). However, the empirical literature available (e.g., Bollerslev et al., 1988) suggests that stock market volatility and risk premium are not stable but are time dependent. Similarly, Schwert (1989), Breen, Glosten and Jagganathan (1989) and Fama and French (1989) demonstrate that the stock market volatility is affected by the macroeconomic conditions. This, therefore implies that it would be appropriate to allow the coefficient p of equation 6 to vary in response to the current macroeconomic conditions that prevail. In such a situation, the risk-return relationship would depend on the nature of the regime under which the investor has to make his decision. In general: R, = xt(a + @)

+ E,

where pt = 1

or pt = 0

(7)

Where R, is the dependant variable, xt is a vector of the explanatory variable, p, is dependent on an exogenous or endogenous variable. If l3, = 1, then t E I, and if p, = 0, then t E I, and It and I, are the two regimes under scrutiny. This model is normally known as a switching regression model.6 To examine the intertemporal relationship between risk premium and risk we apply a switching regression model where the market is assumed to switch from one regime to another. In general, the regimes are characterized by periods of ‘positive’ and ‘negative’ risk premiums (various approaches adopted in determining the regimes are discussed below).

214

INTERNATIONAL

REVIEW

OF FINANCIAL

ANALYSIS

/ Vol. 6(3)

Having divided the sample into two regimes we describe the market as one which switches between these two states (regimes), as equation 8 illustrates: (Rjr - Rjft) = aj + PjOj, +

Ejf where j = 1 or 2

The market switches between the two states viz. regime 1 and regime 2 represented by j in the equation above. In this separation model we assume that at any point of time only one regime is observed, so each observation of (R, - Rfr) will be associated with the value of ‘T,for that regime. We estimate this relationship using maximum likelihood estimators.7 To examine the relationship between total stock returns and volatility, (Rjt - Rjft ) in equation 8 is replaced by (Rjr).

B.

Identification of Regime Estimation of equation 7 requires an identifier for each regime in the sample. We derived this identifier on the basis of (a) the sign of the observed risk premium for the month, and (b) the sign of the predicted risk premium for the month, where the predictions are made using various macroeconomic variables.8 Glosten et al. (1993) state that any model estimating risk and return must take account of the variables that make up the instrument vector, and they focus their attention on the volatility information contained in variables like the nominal interest rate. The use of the nominal interest rate has some intuitive appeal. Short term interest rates embody expectations about inflation, and to this extent they could be very good predictors of future volatility in excess returns. Using the information contained in nominal interest rates, Fama and Schwert (1977), Campbell (1987), Breen et al. (1989) have demonstrated that it is possible to forecast time periods when the excess returns on stock is relatively large and significantly less volatile. In our endogenous switching regression models (approach b) the sign of the predicted value of risk premium (R, - Rft) assigns the observation to a particular state. The predictions are made using equation 9:

CR,-R$=a+

PXt

Where (R, - Rft>is the risk premium and X, is a vector of macroeconomic variables. If the estimated value of (R, - RfJ > 0, t E regime 1, else it belongs to regime 2.9 We examine the sensitivity of the results using a large number of macroeconomic variables. The results reported in this paper are based on (a) the market rate of interest and (b) a combination of the market rate of interest, inflation and production. to These variables are expected to represent a reasonably good picture of the macroeconomic situation under which investors make their investment decisions. If the relationship between risk premium (or total return) and risk remains independent of the economic conditions that prevail then one would expect the coefficient pj to be similar under both regimes. On the other hand, differences in these coefficients would support the proposition that the risk-return relationship is affected by the state of the economy.

C.

Expected and Unexpected Risk As stated by French et al. (1987) when two components of volatility (measured ex post) are combined together, the ex ante relationship between risk and return is obscured. However, by decomposing the volatility into its expected and unexpected components, we anticipate to

Stock Returns

and Volatility

Table 1 Descriptive Series _ UK R RF RP 0 lse INF PPO RMGB USA R RF RP (J CC INF PPO RMGB Germany R RF RP (5 (se INF PPO RMGB

in Two Regime

215

Markets

Statistics of the Variables

used in this study

N

Mean

0

Skewness

KURTOSIS

AR (1)

227 227 227 227 227 227 221 227

0.958** 0.782** 0.196** 3.684** 3.504** 0.572** 0.145 0.988**

0.054 0.002 0.054 0.015 0.005 0.005 0.017 0.028

-1.107** -0.273 -1.121** 4.363”* 1.141** 1.389** -0.156 0.325

5.179** -0.583 5.107** 34.217*’ 4.011** 4.147** 4.906** 1.231**

0.062 0.962** 0.062 0.397** 0.784** 0.45 I** -0.322** 0.128

299 299 299 299 299 299 299 299

0.564 0.563** 0.001 3.810’* 3.600** 0.460** 0.675** 0.677**

0.044 0.002 0.142 0.020 0.008 0.003 0.001 0.002

-0.586** 0.95 I** -0.602** 6.133** 1.476** 0.731** 0.769** 0.997**

3.451** 0.897** 3.368** 66.625** 4.133** 0.728** -0.252 0.443

0.024 0.974** 0.032 0.389** 0.842** 0.596** 0.987** 0.9s3**

225 225 225 225 225 225 225 225

0.452 0.394** 0.057 1.263** 3.683** 2.617** 0.129 0.607**

0.052 0.001 0.052 0.023 0.012 0.002 0.018 0.00 1

-0.829 0.330 -0.808** 2.693** 0.9a5** 1.716** 0.148 0.456

3.797 -1.309** 3.743** 10.279** 0.466 6.006** s.374** -0.393

0.088 0.986** 0.089 0.469** 0.926** 0.295** -0.414** 0.980**

299 299 299 299 299 299 299 299

0.732 0.268** 0.443 3.469** 3.157** 0.385** 0.26 I 0.554**

0.052 0.000 0.05 1 0.022 0.011 0.007 0.014 0.001

-0.572** 0.035 -0.564** 2.367** 1.166** 1.217** -0.160 -0.209

2.371** -0.542 2.363** 8.45 1** 1.176** 3.275** 0.115 -0.866**

0.048 0.974** 0.049 0.496** 0.848** 0.293** -0.224** 0.976**

275 275 275 275 275 275 275 275

0.670 0.950** -0.280 5.410** 5.060** 0.867 0.181 1.005**

0.072 0.002 0.072 0.027 0.013 0.006 0.028 0.002

0.059 -0.345 0.042 2.373** 1.394** 1.163”* 0.042 0.337

0.850** -0.397 0.816 8.515** 3.440** 1.588** 3.656** 0.001

0.119 0.979** 0.1 16 0.538** 0.741** 0.595** -0.363** 0.986**

Japan R RF RP (3 cfINF PPO RMGB Italy R RF RP (3 CTe INF PPO RMGB Notes:

All variables are measured on monthly basis: R Stock returns (in percent) RF Risk Free rate RP Risk Premium CJ Standard Deviation & Expected Standard Deviation INF rate of Inflation PPO Industrial Production Index RMGB Return on Medium Term Government ‘**‘Indicates significance at the 1% level

Bonds

216

INTERNATIONAL

REVIEW

OF ~ANCIAL

ANALYSIS

I Vol. 6(3)

observe a more realistic relationship between these two variables. More specifically, we expect a positive relationship between the expected volatility and excess return. On the other hand, any unexpected increase in volatility should cause a drop in price resulting in a decline in the observed return to the current holder. Thus, we expect an inverse relationship between unexpected volatility and excess return. In order to decompose the volatility into its expected and unexpected components we use a univariate autoregressive moving average (ARIMA) model where we find an ARIMA( 1,l) to best fit the data for all countries in the sample. The predicted values from fitting an ARIMA( 1,l) to the data is treated as the expected component (cF) of risk while the forecast error is treated as unexpected risk (w). Next, we estimate the following switching regression using the maximum likelihood method in order to examine the relationship between the risk premium (return) and the expected and unexpected components of volatility.’ 1 (Rjt - Rfi) = aj + pjOej, +pjCVjt

+cjt

where j

= 1 or 2

(10)

Where (R, - R& ) is the risk premium and the regimes (i.e., value of indicator j) are determined as explained before. This equation tests the relationship between the risk premium and the expected and unexpected components of the standard deviation of the returns.12 To examine the relationship between total returns and the two components of volatility, (Rjr R& in equation 10 is replaced by (Rjt)-

IV.

THE SAMPLE AND DATA

The data analyzed in this study are daily and monthly aggregates of the changes in the market price indices of the market portfolios in the UK, USA, Germany, Japan and Italy for the period ranging from January 1969 to December 1994. These dates differ for each country and are solely dependent on the availability of the data. The number of observations ranges from 227 to 299. The data set was obtained from Datastream and the LBS database. The data for each country comprises a relevant market index as detailed in the Appendix. Proxies used for the risk free rates are also detailed in the appendix. The data series is purged for weekends and stock exchange holidays. Daily and monthly returns (RJ are the first difference of the logarithm of the price index. The risk free rate (R$ is measured by the rate of return on the relevant country’s treasury bill discount rate in most cases. The risk premium (or excess return) is defined as the excess of the stock returns over the risk free rate i.e., (R, - Rf). The monthly variance (of ) is calculated from the daily data as in equation 11: N

2 of

=

c. (f&-W d= 1

-

2 (11)

Rd,r is daily return during month t, R, is the average daily return in month t and N is the number of daily observations in month c. As discussed in section three, the prevailing macroecono~c conditions are likely to affect the movements of stock market prices and alter the investors’ choice of securities. The macroeconomic variables used in predicting the excess (and total) returns are (a) the market rate of interest, (b) the rate of inflation and (c) the aggregate production growth (see appendix-A for a detailed description of the variables used).

217

Stock Returns and Volatility in Two Regime Markets

Table 2 R,-Rfr= N

constant(a)

a+ PO+ &r

S&v CD)

R,-Rft=a+~,Oe+~o-“+~t Constant (a)

E. Sdev (PI)

LIE. Sdev (&)

PanelA:

Relationship between risk premium and volatility in a two regime market where regime 1 comprises positive risk premiums and regime 2 comprises negative risk premiums. UK Full Sample 227 0.041* -1.089* -0.014 0.535 - 1.373** Regime 1 130 0.106** -1.541** 0.016 1.031 -1.921** Regime 2 91 0.014 0.633** 0.016 0.579** 0.655” USA Full Sample 299 0.023** -0.629** -0.006 0.221 -0.840** Regime 1 153 0.062** -0.833** 0.015 0.479 -1.119** Regime 2 146 0.016** 0.460** 0.01 I 0.606** 0.361* GERMANY Full Sample 225 0.028** -0.714** -0.006 0.282 -1.091** Regime 1 122 0.084** -1.089** 0.038 0.125 -1.502** Regime 2 103 0.021** 0.416** -0.009 1.245** -1.103 JAPAN Full Sample 299 0.025** -0.593** 0.010 -0.122 -0.755** Regime 1 171 0.094** -1.221** 0.072** -0.498 -1.451’” Regime 2 128 0.009* 0.917** 0.006 1.022** 0.864** ITALY Full Sample 275 0.02 1 -0.446* 0.006 -0.152 -0.552 Regime 1 131 0.073** -0.600* 0.042 0.006 -0.813** Regime 2 144 0.036’* 0.413** 0.036* 0.413 0.413**

R,=a+@+q

R,=a+&d+&@+&

Panel B: Relationship between stock return and volatility in a IWO regime market where regime I represents rising markets and regime 2 represents falling markets. UK Full Sample 227 0.049** -1.078* -0.007 0.567 -1.366** Regime 1 142 0.137** -1.727** 0.044 0.813 -2.096** Regime 2 85 0.016* 0.719** 0.014 0.757* 0.705** USA Full Sample 299 0.028** -0.611* -0.002 0.277 -0.832** Regime 1 167 0.077** -0.893** 0.033 0.328 -1.151** Regime 2 132 0.016** 0.533** 0.006 0.808** 0.341 GERMANY Full Sample 225 0.033** -0.72 1** -0.002 0.258 -1.091** Regime 1 128 0.094** -1.139** 0.049* 0.085 -1.545** Regime 2 97 0.023** 0.413** -0.004 1.155** -0.08 1 JAPAN Full Sample 299 0.028** -0.601** 0.014 -0.138 -0.761** Regime 1 182 0.113** -1.401** 0.087** -0.001 -1.652** Regime 2 117 0.009* 0.949** 0.008 0.987** 0.929** ITALY Full Sample 275 0.034** -0.439* 0.015 -0.134 -0.549* Regime 1 146 0.102** -0.743* 0.081* -0.319 -0.888** Regime 2 129 0.036** 0.475** 0.027 0.655* 0.403** Notes:

Sdev ((5) Standard deviation of the market return E.Sdev (Oe) Expected Standard deviation of the market return UE.Sdev (IS”) Unexpected Standard deviation of market returns The expected and unexpected components of volatility are estimated model. ‘**’ indicates significance at the 1% level. ‘*’ indicates significance at the 5% level.

using an ARMA(1 ,l)

218

INTERNATIONAL

REVIEW

OF FINANCIAL

ANALYSIS

/ Vol. 6(3)

Table 1 documents the descriptive statistics of the major variables used in this study. They include the mean, the standard deviation, skewness, kurtosis and the AR(l) coefficient. The sample mean of the monthly stock returns are not statistically different from zero for the USA, Germany, Japan and Italy. For the UK, the mean of the stock return is significantly greater than zero (0.958% per month). The stock return series of the UK, USA and Japan are significantly negatively skewed. Significant Kurtosis is observed in the stock returns series of the UK, USA and Japan. The three macroeconomic variables included in this study are a proxy for inflation, domestic growth and the return on medium term government bonds. Monthly inflation is positive and statistically significant in the UK, USA, Germany and Japan. Monthly industrial growth rate is significant only in the case of the USA. The average rate of return on government bonds is significantly greater than zero for all the countries in the sample.

V.

EMPIRICAL

RESULTS

As discussed in an earlier section, we examine the relationship between risk and excess return in three different ways. First, we regress the risk premium on a measure of total risk (standard deviation). Second, we regress the risk premium on the expected and unexpected components of total risk. Finally, we estimate the relationship under a two regime framework using the switching regression technique. This empirical analysis section is divided into two sub-sections and in each sub-section we discuss the results based on all three models. The first subsection deals with a model with ‘exogenous switching’ where the separation indicator is the sign of the excess stock market return. The second sub-section reports the results of ‘endogenous switching’ where the regime indicator is the sign of the predicted value of excess return. In order to examine the robustness of the results, we estimate all the models using both the risk premium and the total return as the dependant variable of the regression. Panel A of Tables 2 to 4 display the results of the ‘risk premium’ based model while panel B of each table reports the results for the ‘total return’ based model. Primarily, we discuss the results of ‘risk premium’ based model and compare these with the results of the ‘total return’ based model.

A.

Exogenous Separation Model The results documented in Panel A of Table 2 indicate that during the sample period stock markets observed more instances (months) with positive risk premium than negative risk premium in all countries in the sample, except Italy. We also find that the periods of negative risk premium have relatively higher volatility, as compared to the periods of positive risk premiums. The results reveal a significant negative relationship between the contemporaneous risk premium and the volatility of return for the entire sample period for all five countries. This result contradicts the established theory of a positive relation between stock market risk and return. However, when the volatility is decomposed into its expected and unexpected components, a positive (though statistically insignificant) relationship between expected risk and excess return is observed for the UK, Germany and USA and a negative relationship for Japan and Italy. Consistent with the findings of French et al. (1987) for the United States the relationship between excess return and unexpected risk is negative and significant for the UK, USA, Germany and Japan. In the UK and in Germany this coefficient is greater than 1. The observed inverse relationship between unexpected risk and excess return is evidence of a pos-

Stock Returns and Volatility in Two Regime Markets

219

itive relationship between the expected excess return and risk. Therefore, the hypothesis of a positive relationship between expected excess return and risk cannot be rejected. It is therefore evident that when both components of volatility are combined together the ex ante relationship gets distorted. This point is emphasized by French et al. (1987) as well. 1.

Total risk and risk premium in a two regime market In order to overcome the potential problem induced by changes in the economic regime, we use a switching regression model with two regimes to represent two main phases of market movements - rising and falling markets. We define a rising market as a period when the observed risk premium is positive. Conversely, a falling market is a period when the risk premium is negative. Estimates show that the volatility (standard deviation) of stock market return is generally higher during a period of falling market prices. Empirical results presented in Table 2 provide a slightly different picture. In regime 1 we have evidence of a significant inverse relationship between risk and return in all the five countries. This implies that in periods where the holding period excess return is positive, the risk premium is not an increasing function of the risk. This is consistent with the results reported by Glosten et al. (1989) Pagan and Hong (1989), Nelson (1991). In regime 2 the relationship between risk and return is positive and significant, giving further credence to the notion that this relationship is regime specific. The results are similar for all five countries in the sample. Our results contradict the results of Shawky and Marathe (1995) who report no significant relationship between market volatility and excess returns in a regime described by rising market prices in the United States. However, for a regime characterised by falling market prices, they find a highly significant negative relationship between market volatility and excess returns. 2.

Expected and unexpected risk and risk premium in a two regime market In an efficient market, asset price is expected to represent the risk profile of the asset. However Merton (1980) emphasizes that the observed volatility of stock return is larger than the expected volatility of stock return. Therefore, decomposition of total observed volatility into its expected and unexpected components will probably throw more light on the relationship between excess return and volatility. This is also evident from the results for the full sample discussed above. Therefore, we re-estimate the switching regression of excess return on expected and unexpected risk. The results of this estimation (documented in Panel A of Table 2) are more interesting. Consistent with the proposition of modem finance theory, in regime 1 we find a positive (though insignificant) relationship between risk premium and expected volatility in the UK, USA, Germany and Italy. Poon and Taylor (1992) report a similar relationship for the UK, while Shawky and Marathe (1995) report a positive and statistically significant relationship only for a regime of rising prices in the USA. 13 In regime 2 (a period of negative risk premium) this relationship is positive and significant for the UK, USA, Germany and Japan. The finding of a positive relationship between expected risk and return is consistent with the theory of risk and return. This is consistent with the empirical findings reported by French et al. (19X7), Chou (1988) and Harvey (199 1) for the USA, Poon and Taylor (1992) for the UK, Paudyal and Saldanha (1996) for the USA, Germany and Japan. Similarly, Turner et al. (1989) and Shawky and Marathe (1995) report a positive relationship between expected risk and return in the regimes of high variance and rising prices respectively. French et al. (1987) examine the relationship between unexpected volatility and realized risk premium and state that this relationship provides indirect evidence of the effect of expected volatility on the expected risk premium. They find unexpected volatility to be negative and significantly related to risk premium and explain that when the actual standard devi-

220

INTERNATIONAL REVIEW OF FINANCIAL ANALYSIS I Vol. 6(3)

ation is greater than the predicted, future predicted volatility has to be corrected upwards, causing an increase in discount rates. This being the case, in the face of constant cash flows, the present value of all future cash flows is reduced and this exerts a downward pressure on current prices. Hence, they conclude that a positive relationship between predicted components of volatility and the expected risk premium induces a negative relationship between the risk premium and unexpected volatility. Similarly, Whitelaw (1994) reports that the contemporaneous correlation of residuals from the first and second moment equations is negative. This negative relation between unanticipated returns and unanticipated volatility is consistent with a positive relation between expected returns and expected volatility, although the former does not imply the latter as pointed out in Glosten et al. (1988). This may be because an unanticipated increase in volatility may cause an increase in the required rates of return, and in time this increase in the expected returns causes a drop in the current price and an unanticipated negative return to the current holder. Although our finding of positive relationship between the excess returns and the predicted component of volatility is consistent with the expectation of modem finance theory, a positive relationship between the risk premium and the unexpected component of volatility that we find in regime 2 in four countries in the sample (except Germany), remains a puzzle and warrants further analysis. 3.

Total returns and measures of risk Panel B of Table 2 documents the relationship between total stock market return and volatility where the regime indicator is the sign of total monthly returns. Consistent with the results discussed above, a negative and significant relationship between total return and risk is observed for the full sample and for all countries in the sample. However a positive relationship between total return and expected risk is observed for three of five countries - the UK, USA and Germany. The relationship between total return and unexpected risk is negative and significant for the UK, USA, Germany, Japan and Italy. As with the risk premium, the relationship between total return and risk is negative and significant in regime 1 for all five countries. In regime 2 consistent with the risk-return theory, this relationship is significant and positive for each of the five countries in the sample. Examining the relationship between total return and expected volatility under both regimes we find a positive relationship in three countries namely the UK, USA and Germany. Shawky and Marathe (1995) find that there is a positive relationship between excess returns and the predictable component of volatility in rising markets and an absence of any relationship in falling markets in two of the three USA indices examined. Whitelaw (1994) also finds evidence of a positive relationship between these variables during periods of expansion. However our results suggest that during the periods of rising market prices the unexpected components of volatility has a significant inverse relationship with total returns for the UK, USA, Germany, Japan and Italy. During regime 2 (periods of negative returns) the relationship is positive and significant in all cases except Germany. These findings indicate that the relationship between these two variables is time dependent. For the U.S. market, Shawky and Marathe (1995) report a significant and negative relationship between unexpected volatility and excess returns in both regimes only for the S & P 500. In the case of the CRSP portfolios they report a significant negative relationship only for falling markets. Broadly, the results discussed above are consistent with the theory of risk and return and indicate that the expected component of volatility is positively related to the expected stock return while the unexpected component has an inverse impact on the asset price. However, the nature of this relationship is regime dependent.

221

Stock Returns and Volatility in Two Regime Markets

Table 3 R,-Rr= N

a+ PO+ &I

R,-Rft=“+~,@+~@+&,

Constant (a) E. Sdev (PI) UE. Sdev (&) Sdev !P) risk premium and volatility where the regime is dependent on the esti-

Constant (Lx)

Panel A: Relationship between mate of the risk premium Yt UK Full Sample 227 Regime 1 118 Regime 2 109 USA Full Sample 299 Regime 1 189 Regime 2 110 GERMANY Full Sample 225 Regime 1 122 Regime 2 103 JAPAN Full Sample 299 Regime 1 226 Regime 2 73 ITALY Full Sample 275 Regime 1 25 Regime 2 250

0.041* 0.057** 0.076**

- 1.089* -0.5 16 -1.068**

-0.014 0.033

0.535 1.122 0.143

-1.373** -1.002* -1.272**

0.024** 0.070** 0.024**

-0.629** -0.818** -0.142

-0.006 0.046* 0.002

0.221 -0.015 0.495

-o.s40** -0.953** -0.516*

0.028** 0.041** 0.066**

-0.714** -0.568** -0.893**

-0.006 -0.003** 0.035**

0.281 1.187* -0.073

-1.091 -0.677* -1.176**

0.025** 0.038** 0.047**

-0.593** 1.206** -0.826**

0.011 -0.030 0.046**

-0.122 3.524* -0.804**

-0.755** 0.715 -0.833**

0.021** 0.024* 0.205**

-0.446 -0.405** -0.237

0.006 0.007 0.201**

-0.152 -0.039 -0.167

-0.552* -0.533 -0.263

R,=ol+@+&,

0.0004

Rt=a+~,b+~b+&

Panel B: Relationship between stock return and volatiliry where the regime is dependent on the estimate of the returns Yt UK Full Sample 227 0.049** -1.078* -0.007 0.567 -1.366** Regime 1 151 0.126** - 1.396** 0.065 0.297 -1.784** Regime 2 76 0.062** -0.809** 0.013 0.577 -1.058** USA Full Sample 299 0.028** -0.61 l* -0.002 0.227 -0.832** Regime 1 291 0.317 -0.964 0.226 1.230 - 1.424 Regime 2 8 0.029** -0.597** -0.001 0.277 -0.815** GERMANY Full Sample 255 0.033** -0.721** -0.002 0.257 -1.091 Regime 1 185 0.138** -0.760 0.096** 0.318 -1.195* Regime 2 40 0.039** -0.636** 0.001 0.400 -1.018** JAPAN Full Sample 299 0.028** -0.060** 0.014 -0.138 -0.761** Regime 1 292 0.294** -0.476 0.239 1.023 -0.972 Regime 2 7 0.028** -0.584** 0.015 -0.148 -0.736** ITALY Full Sample 275 0.030** -0.439* 0.015 -0.134 -0.549 Regime 1 275@ 0.030** -0.439* 0.015 -0.134 -0.549 Regime 2 Notes:

Y, = p (return on medium term government bonds) + q If ?t > 0, the observation is observed in Regime 1, else in Regime 2. Sdev (0) Standard deviation of the market return E.Sdev (Oe) Expected Standard deviation of the market return UE.Sdev ((3”) Unexpected Standard deviation of market returns The expected and unexpected components of volatility are estimated using an ARMA( 1,l) model. ‘**’ indicates significance at the 1% level. ‘*’ indicates significance at the 5% level. @OLS estimates

222

INTERNATIONAL

REVIEW

OF FINANCIAL

ANALYSIS

/ Vol. 6(3)

B.

Endogenous Separation Models With endogenous switching regression models, the relevant regimes are determined within the model itself. In our analysis the regimes are determined on the basis of the sign of the predicted value of the risk premium where the predictor is a vector of selected macroeconomic variables. Whitelaw (1994) suggests that variables such as yields, yield spreads in the corporate and treasury bonds, and dividend yields have predictive power for returns. Breen et al. (1989), Fama and French (1989), Kandel and Stambaugh (1989, 1990), and Kiem and Stambaugh (1986) use economic variables to study the time variation in the volatility of returns. Since the predicted direction of excess return is the regime indicator variable, these models are expected to capture the behavioral relationship between stock returns and risk in ex ante terms. As stated earlier, the macroeconomic variables we use to predict the risk premium are (a) the market rate of interest and (b) a combination of the market rate of interest, the rate of inflation, and the aggregate production. These variables are used as proxies for the state of the economy. We discuss the results of these two models in turn. 1.

Market Rate of Interest and the equity risk-return relationship Finance literature documents a close link between the market rate of interest and stock returns (see, for instance, Cornell, 1983). Paudyal and Saldanha (1997), report that the market for fixed income securities (government bond markets) in the UK leads the equity market to a large extent. l4 In terms of the length of investment, medium term bonds are more comparable to equity investments and can be viewed as a close substitute for equity investments. When loanable funds switch from one market to another, the additional volatility generated by this movement alters the risk-return profile of financial assets. Moreover, a change in the market rate of interest represents changes in investment opportunities in the economy. Thus, the return on medium term bonds is used in predicting the market risk premium, which in turn is used as a regime indicator variable in this switching regression model. The results reported in Table 3 suggest a significant and inverse relationship between the risk premium and the total risk for the full sample in the cases of the UK, USA, Germany and Japan. When volatility is decomposed into its expected and unexpected components we find a positive (though insignificant) relationship between expected risk and the risk premium for UK, USA and Germany while this is negative in the cases of Japan and Italy. The results also suggest a negative and significant relationship between unexpected volatility and risk premium in all five countries during the full sample period. This is similar to the finding of French et al. (1987) for the US market where they explained that this negative relationship between unexpected volatility and excess returns is in itself indirect evidence of a positive relationship between excess returns and ex ante volatility. When the risk premium is regressed against total risk under a two regime framework, the results reveal a negative relationship between these two variables in both regimes for the UK, USA, Germany and Italy. In most cases the coefficients are significant. In the case of Japan, however, we find a positive and significant coefficient in regime 1 (periods of positive predicted risk premium). On the examination of the relationship between risk premium and the expected risk component of volatility in a two regime market we find it positive and significant in the cases of Germany and Japan in regime 1. On the other hand the observed relationship between unexpected standard deviation and risk premium is negative and significant in both regimes for the UK, USA and Germany. For Japan we find this significant negative relationship only in regime 2. Once again, consistent with the results discussed above, the results documented in Panel A of Table 3 reveal a positive (though insignificant) relationship between risk premium and expected risk, while the relationship between unexpected volatility

Stock Returns and Volatility in Two Regime Markets

223

Table 4 R,-Rfl= N

a+po+&,

Panel A: Relationship between dependent on the estimate of the UK Full Sample 227 Regime 1 119 Regime 2 108 USA Full Sample 299 Regime 1 164 Regime 2 135 GERMANY Full Sample 225 Regime 1 127 Regime 2 98 JAPAN Full Sample 299 Regime 1 231 Regime 2 68 ITALY Full Sample 275 Regime 1 57 Regime 2 218

R,-Rfr=a+~lb+~@+&, Constant (a)

E. Sdev (PI) UE. Sdev (p2) sdev (P) risk premium and volatility in a two regime market where the regime is risk premium Y, :

Constant (a)

0.041* o.o59’* 0.075**

1.089* -0.546 -1.057

-0.014 0.010 0.026

0.535 0.855 0.334

-1.313** -0.957* -1.294**

0.023** 0.059** 0.046**

-0.629** -0.641** -0.539**

-0.006 0.029 0.010

0.22 1 0.177 0.454

-0.840L* -0.820** -0.768**

0.028** 0.042** 0.066**

-0.714** 0.766 -0.949**

-0.06 -0.016 0.041””

0.281 1.610** -0.259

-1.091** -0.648* -1.194**

0.025** 0.061** 0.042**

-0.593** 0.714 -0.723**

0.011 -0.001 0.038**

-0.122 2.774** -0.617*

-0.755** -0.202 -0.758**

0.021 0.041** 0.115**

-0.446* -0.505** 0.167

0.006 0.015 0.141**

-0.152 0.006 -0.328

-0.552 -0.689** 0.369

R,=a+@+&, Panel B: Relationship between dependent on the estimate of the UK Full Sample 227 Regime 1 153 Regime 2 79 USA Full Sample 299 Regime 1 224 Regime 2 75 GERMANY Full Sample 225 Regime 1 174 Regime 2 51 JAPAN Full Sample 299 Regime 1 277 Regime 2 22 ITALY Full Sample 215 Regime 1 259 Regime 2 16 Notes:

Rt=a+&b+&d+s

stock returns and volatility in a two regime market where the regime is stock market return Y, : 0.049** 0.128** 0.061**

-1.078* -1.417** -0.805**

-0.007 0.063 0.014

0.567 0.426 0.538

-1.366** -1.832** -1.047**

0.028** 0.105** 0.037**

-0.611* -0.748** -0.488**

-0.002

0.277 0.214 0.472*

-0.832** -1.055* -0.721**

0.033** 0.084** 0.047**

-0.72 I** 0.198 -0.77 1**

-0.002 0.020 0.017

0.257 1.900* 0.073

-1.091** -0.737 -1.074**

0.028** 0.194** 0.031**

-0.601** -0.354 -0.567**

0.014 0.082 0.021*

-0.138 3.023* -0.275

-0.761** 1.446* -0.670**

0.030** 0.326** 0.031**

-0.439* -0.822 -0.373**

0.015 0.313** 0.014

-0.134 -0.557 -0.486

-0.549 -0.917 -0.488**

0.070* 0.002

Y, = PI (return on medium term government bonds) + p2 (rate of inflation) + & (production growth) + at If ?r > 0 , the observation is observed in Regime 1,else in Regime 2. Sdev ((3) Standard deviation of the market return E.Sdev (@) Expected Standard deviation of the market return UE.Sdev (0”) Unexpected Standard deviation of market returns The expected and unexpected components of volatility are estimated using an ARMA( 1,l) model. ‘**’ indicates significance at the 1% level. ; ‘*’ indicates significance at the 5% level.

224

INTERNATIONAL REVIEW OF FINANCIAL ANALYSIS I Vol. 6(3)

(b”) and risk premium is significant and negative in most cases. Broadly, these findings are consistent with our expectation and the results reported by French et al. (1987) for their full sample and Shawky and Marathe (1995) for the S & P 500 index. Panel B of Table 3 documents the results of the estimation of the total return model. Consistent with the results discussed above, a significant and negative relationship between total risk and return is found for the full sample period for all countries. The results further reveal that the expected volatility and total returns are positively related, although the coefficients remain statistically insignificant. However, a significant and negative impact of unexpected volatility on total return is observed for the full sample as well as under both regimes for the UK, USA, Germany and Japan. Thus, the market rate of the interest based endogenous switching regression model seems to provide evidence of a more meaningful relationship between risk and excess returns than the exogenous model. 2.

Macroeconomic variables and equity risk-return relationship Changes in expected rate of inflation affects the market rate of interest through the Fisher effect, which in turn affects the stock market returns. Porteba and Summers (1986) document evidence of falling stock prices during the period of high inflation. Similarly, Amihud (1996) reports that unexpected inflation has a significant negative effect on stock prices. Hence the rate of inflation may provide some indication of future movement in stock prices. In addition to the effect of market rate of interest and inflation, the general economic situation may also have some implications on the stock market which in turn would have some effects on the riskreturn relationship. In order to examine whether the incorporation of more macroeconomic variables in predicting the risk premium provides a better (clearer) picture on the relationship between excess return and risk, we incorporate the rate of interest, inflation and the growth rate of production into the model. As earlier, the sign of the predicted risk premium from this model is used as the regime indicator. The results of this model are presented in Table 4. Similar results to those reported in Tables 2 and 3 are evident again. We find a significant negative relationship between total volatility and the risk premiums for the full period for each of the countries in the sample. Examining closely the relationship between unexpected volatility and the risk premium we find a significant negative relationship for the UK, USA, Germany and Japan. When the full sample is split into two regimes based on the predicted values of the risk premium from equation 9, we find a significant negative relationship between the risk premium and total volatility in the case of the USA and Italy in regime 1. A similar relationship is observed in the case of the USA, Germany and Japan in regime 2. Examination of the relationship between unexpected volatility and the risk premium suggest a negative and significant relationship in both regimes in the cases of the UK, USA and Germany. The observed relationship between total returns and volatility for the full sample and the two regimes is very similar to the relationship between the risk premium and the volatility detailed above. A comparative analysis of the results reveal that the extensions of the interest rate based endogenous model to incorporate the effect of more macroeconomic variables add very little to the analysis. Interest rate alone seems to capture most of the impact of the state of the economy on stock price behavior. VI.

CONCLUSIONS

This paper examines the relationship between the risk premium (returns) and the volatility of stock market return in the context of a two-regime market. We use switching regression models with both exogenous and endogenous separators to divide the sample observations into

Stock Returns and Volatility in Two Regime Markets

225

regimes. The exogenous separator used in this study is the sign of the observed risk premium. On the other hand, the endogenous separator is the predicted risk premium. Predictions are dependent on the effect of various macroeconomic variables on the risk premium. The macroeconomic variables used for this purpose are (a) the market rate of interest (b) inflation and (c) aggregate production. For the full sample period a significant and negative relationship between excess returns and total risk for all five countries in the sample is observed. A different picture emerges when this relationship is examined in a two regime framework and even more so when total volatility is decomposed into expected and unexpected components. The exogenous separator model based results suggest a mixed relationship between risk and return. Under regime 1, as anticipated, a positive relationship between risk premium and expected volatility is observed in the UK, USA, Germany and Italy, while the relationship is negative and significant with unexpected volatility in the UK, USA, Germany and Japan. On the other hand, under regime 2 both components of risk have a significant and positive impact on risk premium for the UK, USA and Japan. Though the positive impact of expected volatility is consistent with the proposition of modern finance theory, the positive impact of unexpected volatility remains a puzzle. When the effects of macroeconomic variables are built into the model and the sign of the predicted risk premium is used as an indicator variable in the switching regression, a very plausible and significant pattern evolves. Whenever the risk premium predicted by the model is positive (regime 1) the relationship between risk premium and unexpected volatility is negative (significant in most cases) for all the countries, while the effect of expected volatility remains positive. Moreover, the results based on the interest rate model suggest that the expected component of risk has a positive impact on equity risk premium, while the unexpected component has a significant and negative impact. Since the expected standard deviation is a measure of ex ante volatility, one would anticipate the expected risk premium to be positive. On the other hand the unexpected increase in volatility causes the current price of the security to drop. As a result, the observed negative relationship between the risk premium and unexpected volatility provides indirect evidence of a positive relationship between excess return and ex ante volatility. Therefore, these findings are consistent with the behavior of rational investors. In spite of the differences in the market microstructure of different countries, the UK, USA and Germany displayed a similar market reaction to expected and unexpected volatility. Japan and Italy differ slightly in the response to expected and unexpected components of volatility. In conclusion, the relationship between risk-return is not fixed across regimes. It varies in response to the environment under which the investors have to make decisions and while modelling this relationship the effect of macroeconomic variables should be taken into account. ACKNOWLEDGMENTS We gratefully acknowledge Henry and other participants

the comments from Ephraim Clark, Campbell Harvey, of the French Finance Association meeting, 1997.

Olan

NOTES

1.

Derivation and testable proposition Return in a Two Regime Market.’

of this model is discussed in section III, ‘Risk and

226 2. 3. 4. 5. 6. 7. 8. 9. 10.

11. 12.

13.

14.

INTERNATIONAL REVIEW OF FINANCIAL ANALYSIS I Vol. 6(3)

~eoretical discussion of this proposition is given in section 111. For a detailed explanation of these regression models see Goldfeld and Quandt (1973). This part draws heavily on Merton (1980). See footnote 12 of Merton (1980). See Quandt (1958), or Goldfeld and Quandt (1972, 1973) for a description of the model. Shawky and Marathe (1995) use the two Stage Least Squares method. See Schwert (1989) and the references cited therein for a discussion on the implication of macroeconomic variables on stock returns. If the relationship between total returns and the standard deviation of returns is being examined, (R, - Rp) in the equation is replaced by R, _ Other variables we considered in&de money supply, long term government bond returns, and various combinations of these variables. The results based on these variables are qualitatively similar to the results reported in this paper. We thank William Green for his comments on the algorithim used. We use both the expected and unexpected components of volatility in the same equation as they are essentially uncorrelated and therefore p~ and pz will not be affected by the presence or absence of the other. We also separated these components and estimated two distinct equations, as anticipated there was no qualitative difference in the results. Shawky and Marathe’s (1995) results are sensitive to the choice of the return index examined. For the S & P 500 index they find that in both rising and falling markets there is an inverse relationship between excess returns and unexpected volatility. But, for the broader CRSP portfolios this relationship is inverse and significant only during periods of falling market periods. However, they emphasis that the findings are not inconsistent with the Market Efficiency Hypothesis as the lead is short lived, followed by feedback, and the size of the coefficient is too small to exploit profitably after making allowances for transaction costs.

REFERENCES

Amihud, Y. (1996). Unexpected inflation and stock returns revisited - evidence from Israel. Journal of~5~~~,Credit, and tanking, 28,22-33. Baillie, R.T. & DeGennaro, R.P. (1990). Stock returns and volatility. Joz~rnal of ~i?z~~c~u~ and Quantitative Economics, 25,204-2 15. Backus, D.K. & Gregory, A.W. (1989). Theoretical relations between risk premiums and conditional variances. Working paper, Federal Reserve Bank Of Minneapolis: December. Breen, W., Glosten, L.R. & Jagganathan, R. (1989). Economic significance of predicted variations in stock index returns. Journal of Finance, 44, 1117-l 189. Campbell, J.Y. (1987). Stock returns and term structure. Journal Qf Financial Economics 18, 373-400. Campbell, J.Y. (1990). Intertemporal Asset Pricing Without Consumption. Working paper, Woodrow Wilson School, Princeton University. Campbetl, J.Y. & Hentschel, L. (1992). No news is good news: An asymmet~c model of changing volatility of stock returns. Jo~~rna~ofFi~zancia~ Economics, 31, 281-3 18.

Stock Returns and Volatility in Two Regime Markets

227

Chan, KC., Karolyi, G.A. & Stulz, R.M. (1991). Global financial markets and the risk premium on US equity. Jour~~ Of Financial E~onomi&s, 32,3,137-167. Cornell, B. 1983. Money supply announcement puzzle: review and interpretation. 7%e American Economic Review, September, 644-657. Fama, E.F. & Schwert, G.W. (1977). Asset returns and inflation. Journal of Financial Economics, 5, 115-146. French, K.R., Schwert, G.W. & Stambaugh, R.F. (1987). Expected stock returns and volatility. Journal of Financial Economics, 19,3-30. Glosten, L.R., Jagannathan, R. & Runkle, D. (1989). Relationship between the expected value and the volatility of the nominal excess return on stocks. Working paper, Northwestern University. Glosten, L.R., Jag~na~an, R. & Runkle, D. (1993). On the relation between value and volatility of nominal excess returns on stock. JuurnaZ ofF~nff~ce, 48, 1179-l 801. Goldfeld, SM. & Quandt, R.E. (1972). Non-linear methods in econometrics. North-Holland, Amsterdam. Goldfeld, S.M. & Quandt, R.E. (I 973). A Markov model for switching regressions. Journal of Econometrics, 1, 3-16. Harvey, C.R. (1989). Time-varying conditional covariances in tests of asset pricing models. Journal of Financial Economics, 24, 289-3 17. Harvey, C.R. (1991). The specification of conditional expectations. Working paper. Duke University. Kandel, S. & Stambaugh, R.F. (1990). Expectations and volatility of consumption and asset returns. Review of Financial Studies, 3, 207-232. Kiem, D.B. & Stambaugh, R.F. (1986). Predicting returns in the bond and stock market. Journat Of Financial Economics, 17, 357-390. Merton, R.C. (1980). On estimating the expected return on the market an exploratory investigation. Journal of Financial Economics, 8, 323-361. Nelson, D.B. (1991). Conditional heteroscedasticity in asset returns: A new approach. Econometrica, 59, 347-370. Pagan, A. & Hong, Y. (1989). Nonparametric estimation and the risk premium. In Bamet, W. A., J.A. Powell & G.E. Tauchen, (Eds.) Nonparametric And Semi-Nonparametric Models In Econometrics And Statistics: The Fifh International Symposium In Economic Theory And Econometrics. Cambridge: Cambridge University Press. Paudyal, K. & Saldanha, L. (1996). Stock returns and volatility: Inte~ational evidence. Conference paper, 3rd. Multinational Finance Society Conference, Washington DC. Paudyal, K. & Saldanha, L. (1997). Direction of causality across the financial markets. Manuscript, Glasgow Caledonian University. Pindyck, R.S. (1984). Risk inflation and the stock market. American Economic Review, 74, 335-351. Poon. S.-H. & Taylor, S. (1992). Stock returns and volatility: An empirical study of the UK stock market. Journal of Banking and Finance, 16, 37-59. Porteba, J.M. 8r Summers, L.H. (1986). The persistence of volatility and stock market returns. American Economic Review, 76, 1142-l 15 1. Quandt, R.E. (1958). The estimation of the parameters of a linear regression system obeying two separate regimes. Journal of Americun Statistical Association, 53, x73-880. Schwert, W.G. (1989). Why does stock market volatility change over time? ~~~~~~ of Finance, 44, 1115-i 153.

INTERNATIONAL REVIEW OF FINANCIAL ANALYSIS I Vol. 6(3)

228

Shawky, H.A. & Marathe, A. (1995). Expected stock returns and volatility in a two-regime market. Journal qf Economics and Business, 47,409-421. Shiller, R.J. (1981). Do stock prices move too much to be justified by subsequent changes in dividends? American Economic Review, 71,421-436. Theodossiou, P. & Lee, U. (1995). Relationship between volatility and expected returns across intemationa1 stock markets. Jou~~zal of Business Finance and Accu~nting, 22,2, 289-300. Turner, C., Star&, R. & Nelson, C.R. (1989). A Markov model of heteroscedasticity risk and learning in the stock market. Journal of Financial Economics, 25,3-22. Whitelaw, R.F. (1994). Time variation and covariations in the expectations and volatility of stock market returns. Jaarnal Of Finance, 49,515-541. ~itelaw, R.F. (1997). Stock market risk and return: An equilibrium approach. Working Paper, New York University.

APPENDIX

List of the Sample Countries and Respective Indices Country

Index FT-ALL share Index

91 day treasury bill

United States

s & P compasite

Japan

Tokyo NSE index

3-month treasury auction discount rate 3-month time deposit

Germany

Frankfurter

Italy

Milan Banca

General

Period

Risk Free Series

United Kingdom

3 month inter-bank offered rate Discount rate

Macr~conomic Variables Used in the Study UK 1. British government 5 to 15 years total return 2. Consumer price index 3. UK Industrial production: Total Volatility USA 1. Yield on treasury constant matu~ty .5-year (monthly) average 2. Consumer price index - all urban consumers NADJ (P) 3. US Industrial production. Germany 1. Cost of living index for all households. 2. Industrial production including constant maturity 3. Yield on 2nd. h’farket public bonds ( 7 to 15 years) end Period.

Japan 1.Consumer price index- national measure 2. Indus~al production - mining and rn~ufa~tu~ng 3. Yield on government benchmark bonds (8 to 10 ) years end period. Italy 1. Yield on treasury bonds - secondary markets 2. Consumer Price index for families of workers and office employees 3, Indus~~ pr~~ction volume.

Jan. ‘94 Jan. ‘94 Jan ‘94 Jan. ‘94 Jan.

Observations

‘76Dec.

221

‘70-Dec.

299

‘70-Dec.

299

‘76-Dec.

225

‘72Dec.

275