stock prices, asset portfolios and macroeconomic variables in ten european countries

Journal of Banking and Finance 13 (1989) 589-612. North-Holland

STOCK PRICES, ASSET PORTFOLIOS AND MACROECONOMIC VARIABLES IN TEN EUROPEAN COUNTRIES

Mads ASPREM*

CSFB, 2a Great Titchjeld Street, London WIP, UK

Received September 1987, final version received November 1988

This paper Investigates the relationship between stock indices, asset portfolios and macroeconomic variables in ten European countries It is shown that employment, imports, mflatlon and interest rates are inversely related to stock prices. Expectations about future real activity, measures for money and the U.S. yield curve are positively related to stock prices. A portfolio of European stock indices was constructed and it is shown that this portfolio is the variable that most strongly explains the variation in the stock prices. The associations between stock prices and macroeconomic variables are shown to be strongest in Germany, the Netherlands, Switzerland and the United Kingdom. There 1s a high degree of similarity between the effects in the first three of these countries. In several instances the stock prices are related to historic value of economic variables indicating that predictive models can be constructed.

1. Introduction

Participants in the financial markets are eager observers of numerous economic figures and, according to market commentators, asset prices regularly react to fluctuations in macroeconomic variables. However, there are no generally accepted asset pricing models that explicitly take economic variables into account. Returns on common stocks have a complicated relationship to macroeconomic variables and portfolios of other assets. For the U.S., some of these relationships were studied by Fama (19X1), Chen, Roll and Ross (1986) and Keim and Stambaugh (1986). Chen, Roll and Ross identified the spread between long and short term interest rates, the expected and unexpected inflation, industrial production, and the spread between high and low grade bonds as systematically affecting stock returns. Fama looked at the correlation between stock returns, real activity, inflation and money. Keim and Stambaugh studied the relations between stock returns and the yield differential between low grade bonds and Treasury bills, the ratio of the Standard and Poors composite index to its previous long run level, and the level of small firms prices.

*This research was conducted at the University of Chicago. I am grateful for the comments of Professor Robert Z. Aliber, Professor George M. Constantinides, Professor Eugene F. Fama, Professor Victor Zarnowitz, Joe Kairys and a referee.

03784266/89/$3.50 0 1989, Elsevier Science Publishers B.V. (North-Holland)

590 M. Asprem, Stock prices, asset portfolios and macroeconomic variables

This paper investigates the relations between a major stock index and macroeconomic variables in ten European countries. It was found that changes in stock prices are positively correlated to some measures of real economic activity, in particular with future industrial production and with exports. Positive correlations are also shown between changes in the stock indices and the yield curve in the U.S., as well as the MI and lagged values of the stock prices themselves. Changes in stock prices are negatively correlated to employment, the exchange rate, imports, inflation and interest rates. These economic variables may be representatives of state variables in the intertemporal capital asset models (I-CAPM). Imports may be perceived as a measure for consumption and the negative correlation between imports and stock prices is evidence in support of the consumption CAPM. U.S. stock prices (S&P 400) and a constructed portfolio of European indices show strong positive correlation with the individual countries stock indices. These two stock portfolios may, together with the macroeconomic variables, be perceived as factors in a factor model.

The evidence is not equally strong in all countries and individual countries may show results contrary to what is expected. In general, the strongest relationships between the stock market and macroeconomic variables are found in France, Germany, the Netherlands, Switzerland and the U.K. The Dutch, German and Swiss markets react to a large extent similarly to the various economic factors.

The remainder of the paper is organized in 9 sections. Section 2 presents the data and discusses the statistical methodology. Section 3 looks at the stock indices in relation to their historic values and to portfolios of other stocks. Section 4 discusses the relationship between movements in stock prices and measures for real economic activity and section 5 studies the relationship between stock prices and consumption. Section 6 looks at exchange rates, section 7 at interest rates and section 8 at inflation and money supply. In section 9 factor models are constructed and in section 10 the results are discussed and the conclusions are drawn.

2. The data

The study uses quarterly data from 1968 to 1984 retrieved from the International Financial Statistics Data File of May 1986. Some parts of the study only cover France, Germany, Italy, Switzerland and the U.K. because a broad range of national account data only exists for these countries. Appendix 1 defines the macroeconomic variables and shows which time series are used. In some cases the time series start later than 1968. Appendix 2 shows the stock indices that are used in the study and table 1 shows summary statistics for the different indices.

M. Asprem, Stock prices, asset portfolios and macroeconomic variables 591

All time series excluding the interest rate series are transformed into rates of change by the formula In (XtjXt - 2) and measured from period to period in order to avoid overlapping time periods which often produce serially correlated error terms.

The regressions are performed by the ordinary least squares method and adjusted for heteroskedasticity using the formula suggested by White (1980). Other procedures were employed to reduce the autocorrelation of the error term, but produced similar results. A statistical significance at the 95% confidence level is referred to as significant later in the paper.

Interest rates and most of the stock indices are period averages. It is plausible to use period averages because most of the markets covered are illiquid and implementation of changes in asset allocation will take time. However, there are limitations in average price data when predictive models are constructed. Period averages also create a higher degree of autocorrelation in the time series [see Working (1960)].

Many of the subsequent regressions have low Durbin-Watson statistics, in particular when stock returns are regressed on only one variable. However, the error terms are expected to be autocorrelated because this single variable is unlikely to explain all of the changes in the dependent variable and because of the high autocorrelation of the stock indices themselves.

In order to reduce the autocorrelated error terms, the Cochrane-Orcutt, the maximum likelihood and the Hildreth-Lu procedures were used in some examples. The Durbin-Watson statistics increased as expected and approached two while the F-statistic and the r-squared were both reduced. The sign and significance of the individual coefficients, however, showed only minor changes.

The stability of the coefficients was checked over different time intervals for most of the key relationships presented. In general, the outcome was the same as for the entire period 1968 to 1984 with no systematic changes in the size or significance of the coefficients.

The stock indices are not adjusted for dividend payments. In percentage terms, the average yield for the ten indices varied from 3.5% in the bull market of 1972 to 6.7% in the 1981 recession according to Morgan Stanley International Capital Perspective. Dividends, however, show a high level of stability over time in absolute terms, and it is the share price appreciation and depreciation which constitute the volatile component of the stock return. Thus, the omission of the dividend payments is not a serious problem when the objective is to explain fluctuations in returns.

3. Portfolios of assets

Table 1 indicates that the stock indices are highly autocorrelated. Regress- ing stock returns on those for the four previous periods gave significant


Table 1 Summary statistics for stock prices.

INT is the quarterly interest rate on long term bonds, RETis quarterly changes in the stock prices, var is the variance of the return on the stock indices and al, a2 and a3 are the

autocorrelation coefficients for lags of one, two and three quarters, respectively.

Den

68-84 58-67 68-75 76-84 INT RET var al a2 a3 RET var RET var RET var

3.2 2.9 9.2 0.57 0.30 0.09 0.9 4.8 2.2 9.3 3.5 9.3 Fin n.a. 3.5 7.8 0.31 0.29 0.27 0.2 4.3 4.4 8.4 2.7 Fra 2.4 1.5 8.6 0.23 0.0 0.12 0.1 6.8 0.8 8.8 2.0 Ger 1.9 0.7 6.0 0.28 -0.10 0.0 3.2 10.7 0.3 6.8 1.1 Ita 3.0 0.3 9.8 0.28 0.10 0.0 1.2 8.5 - 1.7 8.2 2.1 Net 2.1 1.1 7.3 0.19 -0.16 0.15 1.7 6.7 0.2 8.2 1.9 Nor 2.0 1.9 10.7 0.25 0.12 0.12 -0.4 3.9 1.0 11.0 2.7 Swe 2.3 2.8 8.4 0.36 0.13 0.04 1.6 5.0 1.7 6.9 3.7 SW1 1.2 0.6 6.4 0.20 0.05 0.18 1.0 8.2 -0.2 7.7 1.3 U.K. 2.8 2.3 10.6 0.29 -0.07 0.10 2.2 6.2 0.6 13.4 3.7

7.2 8.6 5.1

10.8 6.4

11.5 9.5 4.8 7.1

coefficients for all countries, except Switzerland. For example in Denmark and the U.K., the r-squared figures are 0.37 and 0.16 respectively. This may indicate that technical analysis has validity in making portfolio decisions. However, low liquidity in many of the markets covered by the study is a possible explanation for these results. This is particularly the case for small countries like Denmark. In addition, these results should be interpreted with caution since we are testing period averages.

Do U.S. stock prices have any influence on prices in the local European markets? Regressing the national stock indices on current and past periods returns of the S&P 400 (Standard and Poors industrial index) strongly supports the view that the American market or conditions influencing the American market are correlated with the local European markets. There is a significant positive relationship between the S&P 400 and all of the markets covered with the exception of Finland. In Denmark, Norway and Sweden the results indicate that the stock prices may be predicted based on the last periods prices in the U.S. market. (The results are not shown here.)

An equally weighted portfolio (or a basket) of three European indices: Germany, Sweden and the U.K. was regressed against each individual index. When the basket was regressed against the index of one of the countries making up the basket itself, the index of that country was omitted from the basket. Table 2 shows that the basket exhibits stronger correlation with changes in stock prices in the individual countries than with the S&P 400. This is surprising considering the preoccupation with the U.S. stock market among many European investors. Only in Sweden and the U.K. do the U.S. share prices have the same significance as the other European share prices represented through the basket. In these two countries, however, the basket is made up of only two indices.


Table 2

U.S. and European stock prices.

Changes in individual stock indices (RET) regressed on S&P 400 @US) and a basket of European stock indices (D&W). The absolute t-values are

shown in parentheses below each coefficient.

RET CONS DUS DESH r-sq F-st DW

Den

Fin

Fra

Ger

Ita

Nor

Net

Swe

Swi

U.K.

0.016 (1.59)

0.030 (3.34)

0.003 (0.39)

-0.007 (1.13)

-0.005 (0.44)

0.012 (0.90)

-0.007 (1.37)

0.023 (2.47)

-0.008 (1.41)

0.010 (0.99)

0.08 (0.47)

-0.11 (0.76)

0.34 (1.87)

0.17 (1.89)

0.35 (1.29)

0.20 (0.82)

0.16 (1.80)

0.34 (1.73)

0.26 (2.72)

0.87

(4.40)

0.78 0.30 15.1 1.10 (3.99)

0.41 0.04 2.5 1.42 (2.42)

0.41 0.22 10.4 1.53 (2.01)

0.42 0.38 21.6 1.63 (5.49)

0.26 0.10 4.7 1.41 (1.02)

0.24 0.03 1.9 1.50 (0.99)

0.84 0.62 55.4 1.68 (8.97)

0.30 0.18 8.2 1.56 (1.84)

0.55 0.51 35.6 1.50 (5.88) * 0.19 0.35 18.6 1.57 (1.13)

The basket of the three European indices shows the strongest correlation to the stock prices of all the variables investigated in the study. S&P 400 and the basket of European indices may be thought of as asset portfolios in the sense that is discussed in Appendix 3.

4. Measures of real activity

The present value of the future net income is the central factor in evaluating the value of a firm. In the fundamental valuation eq. (1) in Appendix 3, the future net income is represented by the sum of the future dividend payments, assuming that a liquidation dividend is paid. Assuming rational markets, the asset prices should reflect expectations of these future earnings which again are likely to be influenced by measures for real activity in the national and international economies. In the intertemporal CAPM, macroeconomic variables may represent state variables that change the


investors preferences over time and consequently influence the expected rate of return. In the APT model, the factors determining the asset prices may be represented by macroeconomic variables.

Five measures for the economic activity were looked at. They are changes in industrial production (DIND), real gross national product @GNP), gross capital formation (DCAPI;), employment (DEMP) and exports (DEXP).

Assuming efficient markets, it is expectations about future values of these variables that will influence asset prices. It is difficult to obtain hard figures for the aggregated expectations of future values of economic variables. However, since investors form their expectation based on all currently available information, it is reasonable to assume that the realized economic values are unbiased estimates of the ex ante expectations. Thus, actual future values for the periods t+ 1, t+2, etc. were used as estimates for the expected values for future real activity at time t in order to examine how stock prices were influenced by the expected value of real factors. Lagged values of the variables gain importance if the investors are unable to predict future trends, if there are disagreements of how the asset returns are impacted by the variables or if information disseminates slowly. Under any of these circum- stances, lagged variables can form a basis for predictive models.

Future industrial production was the most promising of the five variables tested. Table 3 presents the results of a simple regression of changes in the stock prices in period t on the growth in industrial production during period t+n where IZ is 0, 1, 2, and 4. All countries, but Sweden, show at least one significantly positive coefficient, but only the Netherlands and Switzerland have an adjusted r-squared above 0.10. Only Germany has a significant contemporaneous effect when the expected future growth rate, represented by the ex post data, is taken into consideration. The data indicate that the Dutch and the British markets are the most forward looking. The French market also seems to discount future real activity to a large degree. An explanation for the lack of a relationship in the Swedish data may be the heavy export orientation of the major industrial firms in the country that make up a large proportion of the Swedish stock market.

Past values of the growth rate in industrial production do, in general, give negative but insignificant coefficients when regressed against the stock market. Thus, the stock market does not react positively to information about past growth in industrial production. This is in accordance with the theory that the stock market reflects expectations of future events in current prices. In Germany, the lagged growth rate is significantly inversely correlated with stock returns.

Regressing the stock returns on the change in capital expenditures does not give strong results. The stock market was regressed against current and two future periods of capital expenditures. All countries, but Italy, had contemporary negative coefficients, while the future periods tended to show


Table 3 Industrial production and stock prices.

Changes in the stock prices (RET) in period t regressed on changes in the industrial production (DIND) in period t+n. The absolute t-values are shown in parentheses below the coefficients.

RET DIND

CONS t DIND t+1

DIND t+2

DIND t+4 r-sq F-st DW

Fin

Fra

Ger

Ita

Net

Nor

Swe

Swi

U.K.

0.025 (1.96)

0.001 (0.10)

0.002 (0.33)

0.001 (0.06)

0.004 (0.41)

0.003 (0.20)

0.023 (2.31)

0.000 (0.00)

0.016 (1.14)

0.24 (0.90)

0.25 (0.73)

0.58 (1.79)

0.19 (0.67)

0.00 (0.00) 0.89

(1.57)

0.12 (0.38)

-0.12 (0.40)

0.18 (0.33)

0.18 (0.72)

0.33 (1.11)

-0.27 (1.06)

0.65 (2.32)

0.71 (1.68)

0.72 (1.77)

0.26 (0.70)

0.54 (1.92)

-0.37 (0.57)

0.21 (0.92)

0.28 (0.78)

0.59 (1.96)

-0.02 (0.09)

0.27 (0.84)

0.01 (0.02)

0.31 (0.91)

0.75 (4.23)

0.27 (0.53)

0.32 (1.29)

1.15 (2.23)

0.61 (1.27)

- 0.28 (1.00) 0.96 (2.47)

-0.33 (0.85)

0.49 (1.34)

0.14 (0.50)

1.50 (3.21)

0.00 0.62 1.57

0.04 1.72 1.65

0.07 2.31 1.58

0.03 1.42 1.36

0.10 2.92 1.74

0.02 1.35 1.60

0.00 0.66 1.37

0.17 4.29 2.00

0.07 2.27 1.64

positive results. This is in accordance with the capital formation theory [Fama (1981)] and with an environment where firms d&invest from the stock market when actual investments take place. However, only England and Italy show significant coefficients in this regression.

Changes in the stock indices were regressed on changes in exports in five countries. When regressing the current and two lagged periods of the export against the stock prices, four out of the five countries showed significant coefficients on the first or second lag. The correlations were in general strongest on the second lag indicating a predictive power of exports. (These results are not shown here.)

One would expect employment to be positively related to real activity and that we would consequently see a positive correlation between the stock return and employment. In table 4, however, we see that this is not the case. On the contrary, there is a strong negative relationship between the stock returns and lagged values of employment. The reason may be that employment is expected to increase only in the later stages of a boom period at a point when declining earnings are expected for most firms.


Table 4

Employment and stock prices.

Changes m stock prices (RET) regressed on changes in employment (DEMP). The absolute t-values are shown in parentheses below each coefficient.

RET DEMP DEMP DEMP

CONS t t-1 t-2 r-sq F-st DW

Den 0.026 (2.91)

Fin 0.035

(3 57)

Fra 0.008 (0.75)

Ger 0.000 (0.01)

Ita 0.002 (0.19)

Net -0.013 (1.07)

SW1 0.003 (0.41)

-0.40 (0.51)

0.67 (0.85)

- 1.88 (124)

-0.59 (0.68)

- 1.27 (1.45)

-3.65 (3.84)

1.31 (1.13)

- 2.70 (2.95)

-0.46 (2.10)

- 1.59 ( 1.06)

- 2.44 (2.35)

-0.24 (0.26)

- 1.20 (1.31)

- 2.48 (2.33)

0.50 0.10 3.33 1.22 (0.63)

0.39 0.04 1.94 0.45 (0.44)

-0.58 0.00 1.10 1.59 (0.33)

0.65 0.14 4.48 1.41 (0.81)

- 1.15 0.00 0.96 1.41 (1.46)

0.60 0.15 4.82 1.57 (0.64)

- OJ2 0.10 3.44 1.70 (0.79)

Data for Nor, Swe and U.K. are not available, for the whole period.

5. Exchange rates

Depreciation of a currency improves the competitive position of domestic industries. Both the prices and volume of their production can result in higher profitability. Earnings brought home from foreign subsidiaries appreciate in value are accounted for in the local currency. Thus, reported earnings for an international or export orientated firm will increase when the currency depreciates.

However, exchange rates do not change in a vacuum. The underlying economic factors causing exchange rate changes may also effect the stock prices. If the exchange rate changes are caused by a deteriorating domestic economy, they should have an adverse effect on the local stock market. If the changes on the other hand are caused by currency overshooting, the first mentioned effect is likely to dominate and the local stock market will benefit from the situation. In some countries, currency depreciation is often followed by raising interest rates. It is later shown that interest rate changes are negatively correlated to stock returns which would imply the same relationship between exchange rates and stock returns.

The evidence about the relationship between the changing currency values and the stock market give some support to the initial hypothesis. Using the effective trade-weighted exchange rate, Denmark, the Netherlands, Norway


Table 5 Exchange rates and stock prices

Changes in the stock prices (RET) regressed on changes on effective trade-weighted local/USD exchange rate (1974-1984). The absolute t-values are in parentheses below

each coefficient.

DEFFX DEFFX DEFFX RET CONS t t-l

Den 0.023 -0.96 -0.14 (1.69) (1.58) (0.27)

Fin 0.016 0.48 -0.41 (1.53) (1.62) (0.77)

Fra 0.034 0.78 0.66 (1.98) (1.14) (1.03)

Ger 0.014 -0.01 -0.25 (1.74) (0.02) (0.85)

Ita 0.021 0.55 -0.43 (0.93) (0.95) (0.64)

Net 0.013 - 1.24 -0.02 (1.26) (3.22) (0.07)

Nor 0.002 - 0.29 -0.23 (0.11) (0.44) (0.30)

Swe 0.025 -0.69 -0.78 (2.30) (1.50) (1.26)

SW1 0.007 -0.37 0.17 (0.74) (1.44) (0.82)

U.K. 0.027 0.35 -0.52 (1.59) (1.10) (1.31)

t-2

-0.58 (1.16)

-0.51 (0.87)

0.78 (1.20)

-0.38 (1.60)

0.71 (1.17)

0.31 (0.65)

-2.14 (2.41)

-0.15 (0.43)

-0.12 (0.43)

0.10 (0.29)

r-q F-st DW

0.08 1.11 0.82

0.00

0.10 2.58 1.57

0.07 2.06 1.73

0.10 2.57 1.51

0.13 3.17 1.25

0.00 0.65 1.60

0.00

0.91 0.93

0.70 1.27

0.53 1.38

0.45 1.40

and Sweden exhibit a negative relation as shown in table 5. The t-statistics, however, are not very strong.

6. Consumption

The U.K. is the only country that showed a significant negative relation between stock prices and consumption. This is not encouraging for the consumption CAPM which tell us that asset return is negatively correlated to the marginal propensity to consume according to eq. (3) in Appendix 3. However, it may be some comfort that what is perceived as the most efficient stock market in Europe displays the expected relation.

A major problem with consumption as an explanatory factor for the changes in the stock prices is the relative stability of consumption over time, Thus, it is unlikely that consumption could be the only state variable in an empirically tested intertemporal CAPM.


Table 6 Imports and stock prices.

Changes in stock prices (RET) regressed on changes in imports (DIMP). The absolute t-values are in parentheses.

RET

Fra

Ger

Ita

Swi

U.K.

CONS

0.03 (2.28)

0.02 (2.18)

0.03 (0.20)

0.07 (0.81)

0.04 (2.74)

DIMP DIMP DlMP t t-1 t-2 r-q F-st DW

-0.32 - 0.40 -0.18 0.09 3.14 1.69 (1.61) (2.20) (0.77)

-0.25 -0.51 -0.16 0.07 2.55 1.48 (1.33) (2.41) (0.93)

0.38 -0.16 -0.36 0.03 1.56 1.46 (2.16) (0.79) (1.08)

0.32 -0.16 -0.36 0.04 1.92 1.72 (1.34) (0.89) (1.60)

- 0.49 -0.41 - 0.47 0.16 5.20 1.64 (2.09) (1.87) (2.02)

Looking at imports may provide an alternative avenue for studying the consumption CAPM. Changes in imports are mainly caused by changes in consumption and investments. As international trade grows, domestic private consumption has become a driving force behind imports in most countries, in particular in the smaller ones where imports make up a large proportion of GNP. Consumer durables constitute a relatively large part of the imports in these countries, thus imports can be expected to be more volatile over time than consumption. Changes in imports may consequently be a good estimator for changes in real consumption and indicate changes in the preference for savings over time. Table 6 shows that there is a significant negative relationship between imports and the stock market in France, Germany, and the U.K. This supports the relationship that was found between stock prices and consumption. Only the U.K., however, shows an r-squared of any substantial size.

7. Interest rate The interest rate is the denominator in the fundamental valuation eq. (1)

in Appendix 3. Thus, we expect a negative relationship between the interest rate and the price changes in the stock market. The opportunity cost for investors in the equity markets is represented by the short term interest rate. In most European countries, however, good measures for the short term rate can only be found for the last ten years. Thus we have chosen to look at the relationship between the long term interest rate and changes in the stock prices even though this is likely to give weaker results because of the lower


Table 7 Interest rates and stock prices.

Changes in stock prices (RET) regressed on interest rates on long term bonds (BOND). The absolute t-values are in parentheses below each coefficient.

RET BOND

CONS t BOND t-1

BOND t-2 r-sq F-st DW

Den -0.015 (0.40)

Fin 0.024 (2.30)

Fra 0.033 (0.98)

Ger 0.062 (1.79)

Ita 0.013 (0.44)

Net 0.078 (1.58)

Nor -0.025 (0.63)

Swe 0.072 (1.74)

Swi 0.100 (2.42)

U.K. 0.048 (0.92)

-0.019 - 0.002 (2.21) (0.14)

0.002 0.002 (1.04) (1.16)

-0.017 - 0.023 (0.61) (0.60)

- 0.027 -0.006 (1.71) (0.26)

- 0.007 - 0.023 (0.33) (0.65)

-0.030 -0.033 (1.62) (1.10)

- 0.003 0.001 (0.43) (0.31)

-0.053b 0.121 (1.45) (2.18)

- 0.038 - 0.035 (1.56) (0.91)

- 0.084 0.070 (5.08) (2.70)

0.024 (2.01)

0.002 (0.90)

0.039 (1.99)

0.026 (1.79)

0.033 (1.45)

0.055 (3.09) 0.006 (1.87)

-0.057 (1.84)

0.054 (2.58)

0.012 (0.78)

0.10 3.42 1.07

0.04 1.97 1.50

0.05 2.15 1.68

0.12 4.04 1.53

0.04 1.80 1.48

0.21 6.95 1.82

0.00 0.50 1.50

0.10 3.43 1.45

0.22 7.01 1.94

0.40 15.72 1.68

Indicates that the coefftcient is significantly negative if the bond yield at time t only is regressed against the stock return.

Indicates that the coefftcient in the regression without any lag is significantly positive.

volatility of the long term rate. This is partly caused by the fact that we only have yield figures instead of holding period returns.

Table 7 strongly supports the hypothesis that changes in stock prices and interest rates are inversely correlated. Again, the results are strong for Germany, the Netherlands, Switzerland and the U.K. There is a lower, but still significant negative relationship in Sweden. The result for Denmark is hard to interpret because of the very low Durbin-Watson statistic.

The results for Finland, France and Norway are peculiar. However, these have been small illiquid financial markets and the credit flows have been highly regulated for most of the period covered by the study. In an attempt to assess how well the long term interest rates reflected the short term rate, we regressed the short term interest rate on the long term rate. There was a lack of correlation between the two rates in Denmark, Finland, France,


Table 8 Term structure and stock prices.

The changes in the national stock prices (RET) on the U.S. yield curve (YC). The absolute t-values are shown in parentheses

below each coetXcient.

RET

Den

Fm

Fra

Ger

Ita

Net

Nor

Swe

Swi

U.K.

YC CONS t

0.017 0.011 (1.09) (1.27)

0.038 - 0.002 (3.43) (0.40)

0.005 0.008 (0.42) (1.19)

- 0.009 0.013 (1.07) (2.93)

0.018 -0.011 (1.05) (1.43)

-0.007 0.016 (0.75) (2.85)

0.027 - 0.007 (1.75) (0.85)

0.023 0.004 (1.94) (0.52)

-0.010 0.014 (1.03) (2.85)

- 0.005 0.24 (0.35) (3.20)

r-sq F-st DW

0.01 1.90 0.82

0.00 0.00 1.36

0.00 1.28 1.56

0.09 7.17 1.51

0.02 2.34 1.53

0.08 6.82 1.73

0.00 0.54 1.51

0.00 0.30 1.26

0.08 6.92 1.65

0.10 8.06 1.56

Norway and Sweden. This is partly caused by poor data and probably also by the highly regulated credit markets in these countries during most of the period investigated.

Strong evidence from the U.S. suggests that the yield curve shifts according to the business cycle. During economic expansions, the difference between the yield on a long term government bond and a short term Treasury bill is large and the yield curve is positively sloped. When the economy is sluggish, the difference has historically been smaller and even produced a downward sloping yield curve. We would consequently expect a positive relationship between the slope of the yield curve and stock market. Keim and Stambaugh show that this holds for the U.S.

The relation between the U.S. yield curve and the European stock indices was looked at because of the lack of good European time series for short term interest rates. The U.S. yield curve is likely to impact European asset returns because of the influence of the U.S. economy on the European economy. The results are shown in table 8. There is a positive correlation


between the U.S. term structure and the stock market in several countries. Again we see that the results are similarly strong in Germany, the Netherlands and Switzerland. These three countries and the U.K. have adjusted r-squares close to 0.10.

8. Inflation and money supply

According to the Fisher equation, there should be a one-to-one relation between the changes in nominal return and the expected rate of inflation, Furthermore, shares are claims on underlying real assets and should therefore provide a hedge against inflation.

Fama and Schwert (1977) showed that stock prices respond negatively to current and lagged values of inflation in the U.S. Since then a number of papers have presented evidence for an inverse relationship between inflation and the stock return both in the U.S. and other stock markets.

Fama (1981) looks at the underlying economics in order to explain the spurious relationship between inflation and stock return. The basis for his test is a rational expectations combination of the money demand function and the quantity theory of money which predicts that higher expected growth in real activity has a negative relation to current inflation. Under the assumption of a stable monetary policy, expectations about future growth in the economy will increase the money demand and induce a reduction in the inflation rate.

Geske and Roll (1983) present a fiscal policy argument instead of a stagflation scenario and argue that stock returns and expected inflation are negatively associated because of a chain of events. Gultekin (1983) and Solnik (1983) conclude that there is a consistent lack of positive association between stock returns and inflation covering several countries. Wahlroos and Berglund (1986) find support for Famas theory in the Finnish stock market.

Several measures for inflation have been used in testing the relation between inflation and stock returns. Fama and Gibbons (1982) constructed measures for expected and unexpected inflation from the short term interest rate. Fama also used the money demand inflation models and several researchers have used ARIMA models. Last, but not least, the relation can be studied just using past and contemporary inflation. Here, the time series of inflation is used as measures for expected and unexpected inflation.

The inflation is highly autocorrelated over time. Thus, the rate of inflation at time t- 1 is a good predictor for the expected rate of inflation at time t. The ex post values of inflation at time t will contain both the unexpected change in inflation and the expected change not explained in the inflation rate at time t - 1. Past values of inflation are therefore viewed as a measure


Table 9 Past inflation and stock prices.

Changes in stock prices (RET) regressed on changes in the price level (DINF). The absolute t-values are in parentheses below each coefficient.

RET DINF

CONS t DINF t-l

DINF t-2 r-sq F-st DW

Den 0.010 (3.55)

Fin 0.097 (5.51)

Fra 0.063 (2.12)

Ger 0.031 (1.83)

Ita 0.00

Nor 0.070 (2.38)

Net 0.060 (2.51)

Swe 0.008 (0.34)

Swi 0.003 (2.42)

U.K. 0.005 (0.18)

-1.50 -0.87 -0.90 (1.88) (1.13) (1.29)

- 0.48 -0.18 - 1.97 (0.49) (0.15) (2.48)

0.63 -0.44 - 2.41 (0.3 1) (0.19) (1.39)

0.01 0.09 -2.24 (0.01) (0.06) (1.99)

- 1.08 2.25 - 1.10 (1.08) (2.06) (1.03)

-0.061 -1.86 -0.13 (0.68) (2.18) (0.13) 0.15 0.09 - 3.52 (0.17) (0.08) (3.80) 0.80 0.56 -0.34 (0.91) (0.69) (0.43)

- 1.51 -0.30 -0.71 (1.52) (0.28) (0.66) 1.08 0.16 -0.60

(0.83) (0.14) (0.55)

0.04 1.94 0.82

0.10 3.45 1.59

0.05 1.11 1.51

0.02 1.44 1.46

0.01 1.24 1.33

0.00 0.98 1.52

0.11 3.70 1.61

0.00 0.40 1.24

0.03 1.70 1.78

0.03 0.60 1.36

The 4th lag becomes positive when the stock return is regressed on the first four lags of the inflation.

for expected rate of inflation. The rate of inflation at time t represent both expected and unexpected rate of inflation.

In table 9 the change in stock prices is regressed on the change in the current and two lagged values of the price level. Denmark, Finland, Germany, the Netherlands, and Norway all show one or more coefficient that indicates a significantly negative relationship, while the results for France and Switzerland are close to being significant. The second lag of inflation is generally most often significant. This indicates that changes in the expected rate of inflation are more important than changes in unexpected inflation in explaining the spurious relation between inflation and stock prices. Only Finland and the Netherlands, however, exhibit adjusted r- squared above 0.10. Thus, on a stand alone basis, inflation does not have much potential explanatory power for the changes in stock prices.

Because of the stability of inflation over time, it is reasonable to assume that a large part of the changes in future inflation are expected changes. Thus it is interesting to investigate the relationship between future values of


Table 10 Inflation and stock prices.

Changes in stock prices (RET) regressed on changes in inflation (DINF). Absolute t-values are in parentheses below each coefficient.

RET CONS DINF t+1

DINF t-l-2 r-sq F-st DW

Den 0.045 -0.67 0.54 (1.87) (0.75) (0.06)

Fin 0.087 -1.77 -0.50 (3.96) (1.66) (0.36)

Fra 0.071 - 1.34 - 1.24 (2.59) (0.71) (0.64)

Ger 0.045 -0.60 -2.98 (3.15) (0.54) (2.70)

Ita -0.001 0.23 -0.09 (0.07) (0.2 1) (0.09)

Net 0.051 -0.44 - 2.28 (2.32) (0.35) (1.85)

Nor 0.089 -2.25 - 1.27 (2.74) (2.04) (1.16)

Swe 0.077 - 1.46 -0.87 (3.60) (1.72) (1.02)

Swi 0.044 - 2.02 -1.48 (3.81) (2.79) (2.18)

U.K. 0.062 1.51 -3.11 (2.30) (1.01) (2.31)

0.00

0.10

0.02

0.10

0.00

0.05

0.05

0.03

0.14

0.15

0.22 0.86

3.91 1.53

1.60 1.53

4.50 1.51

2.73

2.61

1.90

6.41

6.97

1.44

1.63

1.52

1.26

1.83

1.59

inflation and changes in the stock indices. If investors successfully fo&ast inflation, we expect a negative relationship between stock returns and future inflation. Table 10 shows that there is actually a stronger correlation between stock returns and future inflation, than between stock returns and values for current and past inflation. The largest changes in the explanatory power of inflation when it leads rather than lags stock prices, occurs in Germany, the Netherlands and United Kingdom. The signs of the coeffC cients are more consistently negative when inflation leads the stock prices than when it lags. Generally, however, the signs are the same in both regressions.

Firth (1979) showed that there is a significant positive connection between inflation and stock returns in the U.K. The evidence shown in table 9 does not contradict his result. This is peculiar since the U.K. has the largest and probably the most efficient equity market in Europe. The results in table 10, however, where the inflation half a year into the future is negatively correlated with the current period stock prices, indicates that the British might not be so peculiar anyway. They may just possess superior predictive abilities.


Table 11 Money supply and stock return.

Changes in the stock prices (RET) regressed on measures for money supply (DMO, DMl, DM2). The values shown are the sum of the three coefficients of the regression t, t- 1, and t-2.

RET

Fra Ger Ita Net

DMO r-sq F-st DW DMl r-sq F-st DW DM2 r-sq F-st DW

-0.66 0.00 1.10 1.54 -0.30 0.00 0.61 1.47 -0.85 0.00 0.86b 1.49 -0.45 0.01 1.27 1.39 1.08 0.12 4.04b 1.54 1.13 0.10 3.54b 1.32 -0.82 0.01 0.75 1.49 0.56 0.00 1.06 1.41 0.31 0.00 0.85 1.40

1.07 0.17 5.60b 1.72 0.38 0.19 6.0gb 1.56 -1.89 0.25 8.31b 1.60 Swi 0.24 0.03 1.75 1.57 0.86 0.13 4.30b 1.71 0.79 0.00 1.17 1.69 U.K. -0.70 0.05 2.26 1.38 1.58 0.07 2.62b 1.49 -1.22 0.03 1.62b 1.34

Indicates that all three coefficients have the same sign. bIndicates that at least one of the three coefficients is significant at the 95% level. The figures for the Scandinavian countries are not recorded because of highly autocorrelated

error terms. To the degree that the coefftcients showed any sign of significance, they generally showed the same pattern as above.

Inflation and money supply are related according to most economic theory and we would consequently expect some relationship between money supply and stock returns. The quantity theory of money indicates that increased money supply results in increased inflation, holding real activity and velocity of money constant. Thus, higher money supply should create expectations about higher inflation.

Table 11 shows the relationship between different measures for money supply and the stock prices. The monetary base, MO, is generally shown to have a negative relationship to the stock prices. The evidence however, is only significant in the U.K. For the Netherlands, there is actually a strong positive effect.

The broader measures for the money supply show a stronger relationship with the stock prices than the monetary base. The results are significant for Germany, the Netherlands, Switzerland, and the U.K. The positive coefli- cients indicate that there is a liquidity effect at work where the overriding effect of changing monetary supply is to increase the liquidity in the financial markets. The increased liquidity is transferred into demand for financial assets which results in higher return on stocks. Higher demand for bonds decreases the interest rate. The interest rate was earlier shown to have a negative relation to the stock prices which supports the liquidity argument.

Fama and Schwert showed that expectations about inflation works through the Fisherian equation to increase the nominal return on government bonds. A higher interest rate increases the discount factor in the fundamental valuation eq. (1) in Appendix 3. Consequently, this argument should counteract the liquidity effect outlined above. The evidence, however, suggests that the liquidity effect is strongest.

Friedman and Schwartz (1963) showed that the money supply leads business cycles. We have shown that stock prices and real economic activity


Table 12 Inflation, interest rate, money supply and stock prices.

Changes in stock prices (RET) regressed on changes in the price level INF( -2), changes in the money supply @Ml), and the interest rate (BOND). The absolute t-values are in

parentheses below the coefficients.

RET CONS DMl(-1) BOND INF( -2) r-sq F-st DW

Den - 0.024 (0.61)

Fin 0.075 (5.43)

Fra 0.043 (1.32)

Ger 0.069 (1.94)

Ita - 0.027 (0.72)

Net 0.145 (3.32)

Nor - 0.002 (0.05)

Swi 0.124 (2.82)

U.K. 0.085 (1.25)

0.925 0.004 (1.54) (1.43)

0.216 0.006 (1.94) (3.03)

0.225 0.003 (0.71) (0.76)

0.189 0.006 (1.16) (1.17)

0.280 0.002 (1.34) (0.53)

0.087 -0.010 (0.65) (2.03)

0.336 0.005 (2.15) (1.30)

0.372 - 0.027 (2.55) (2.72)

0.516 -0.008 (1.29) (1.15)

- 1.079 (1.26)

-2.52 (4.28)

-3.19 (1.90)

- 1.67 (1.35)

- 3.364 (0.30)

-3.19 (3.26)

- 1.706 (1.77)

0.905 (0.93)

0.578 (0.71)

0.048 2.12 0.96

0.216 7.06 1.64

0.027 1.61 1.49

0.063 2.48 1.46

0.00 0.74 1.43

0.15 4.91 1.64

0.054 2.26 1.46

0.196 6.37 1.82

0.00 0.86 1.50

are positively correlated. Thus, this is poten&illy another explanation for the positive relation between money supply and stock price.

We have seen that stock prices have mgative correlation with both inflation and interest rates and that there is a;positive relation between stock prices and a broad measure of money. In-table 12, the changes in stock prices are regressed on these three monetary variables. It is interesting to note that the evidence is similar for the; three countries making up the European hard currency area: Germany, the Netherlands and Switzerland. However, the significance of the results decreases for Germany when changes in the stock index is regressed on the three variables simultaneously. We also see that the monetary variables have a strong explanatory power for the changes in stock prices in Finland.

The evidence shown in table 12 indicates that inflation is negatively correlated with the stock prices in several countries even after the money supply is added to the equation. The U.S. data presented by Fama shows that the explanatory power of the expected inflation disappears when the stock return is regressed both on the money base and expected inflation.

9. Factor models

Table 13 shows the changes in the stock prices regressed on all the

J B F.-E


Table 13

Stock prices, asset portfolios and macroeconomic variables.

Changes in stock prices (RET) regressed on different asset portfolios and macroeconomic variables. Absolute t-values are in parentheses.

RET Independent variables r-sq DW

Den

Fin

Fra

Ger

Ita

Net

Nor

Swe

Swi

U.K.

0.002+0.49RET( - 1) +0.70DESH (0.28) (5.78) (5.53) 0.54 2.12

0.030-2.33 DINF( -2)+0.38DESH( -2)+ (1.50) (3.77) (2.98)

1.11 DM2(-2)+0.54DXRA( -2)+0.24RET(-1) (3.60) (3.29) (2.38) 0.43 2.29

0.007+0.64DESH-0.57DXRA (0.72) (4.24) (2.72) 0.27 1.65

0.073+0.34DESH -2.08 DEMP( - l)-0.011 BOND+0.41 DM2( - 1) (2.06) (3.77) (3.14) (2.61) (2.25) 0.47 1.87

0.016+0.61DUS-0.48 YC+O.O33 YC(-1) (1.15) (3.55) (3.65) (2.49) 0.24 1.94

0.016+0.80DESH-2.13DINF(-2)+0.34DM1+0.19DM1(-1) (1.43) (9.43) (3.51) (3.59) (2.10) 0.71 1.97

0.042- 1.34DM2 +0.42 RET( - 1) +0.45 DESH (2.73) (4.12) (3.90) (2.43) 0.30 2.05

0.020+0.41DUS+0.63DXRA-0.33DM1+0.21DM1(-2) (2.48) (3.45) (3.30) (3.61) (2.33) 0.35 1.65

0.025 + 0.61 DESH - 0.024 BOND - 0.04 DEXP( - 1) - 1.32 DEMP( - 1) (4.34) (6.73) (4.45) (3.00) (2.37) 0.62 2.14

0.012+0.83DUS-0.49DMO-0.45DIMP(-1)+0.016YC-0.80DIND(+1) (1.00) (5.46) (3.24) (2.47) (2.34) (2.01) 0.49 1.76

variables discussed previously in the paper. The explanatory variables in table 13 are chosen by a stepwise procedure that adds variables to the equation depending on their F-statistics. The equations do not necessarily represent the combinations of independent variables that best explains the variability in stock. The independent variables are included in the equations if their t-values are above two.

The equations in table 13 may be thought of as a factor model according to the discussion in Appendix 3. The portfolio consisting of the British, the German and the Swedish stock indices (DESH) shows up as an explanatory variable in seven countries. Different measures for money supply (DM) are important in six countries. These two factors are by far the most significant in a cross country comparison. Last periods changes in stock prices (RET(- l)), the change in U.S. stock prices @Us) and changes in the exchange rate (DXRA), each are important in three countries. Inflation (DCPI), the U.S. term structure (YC), interest rate (BOND) and employment (DEMP) are of consequence in two countries each.


10. Conclusion

The evidence presented in this paper show that employment, imports, inflation and interest rates are negatively correlated to stock prices. Changes in imports may be viewed as an indicator for changes in consumption. Thus, the relation between imports and stock prices is evidence in support of the consumption capital asset pricing model. The negative correlation between inflation and stock prices can be explained through a combination of the money demand theory and the Fisherian quantity theory of money.

The stock indices in most of the ten countries covered in this study show a high positive correlation between the S&P 400 (S&Ps industrial index) and the stock indices. However, the correlation to a basket of European indices was even stronger.

A positive relation between the yield curve in the U.S. and the local stock prices is discovered as well as between the broader measures for money supply and the stock prices and in some countries between the exchange rates and the stock prices. The positive correlation with money supply implies that monetary liquidity is important for stock pricing. The evidence also shows that movements in stock prices lead measures for real activity, indicating that stock markets make rational expectations about future activity.

In addition to the country-specific variables, inflation, industrial production and money supply for the industrial countries as were tested against stock indices in the individual countries. In general, the significance and the explanatory power of these aggregated variables did not attain the level of their local counterparts.

It is unreasonable to believe that only one economic factor will exhaust possible explanations for movements in stock prices. Most intertemporal asset pricing models suggest that more parameters are important in asset pricing. In table 13, changes in the national indices are regressed on the different economic variables investigated in this study. We observe that the explanatory power of the equations increases substantially compared to when the stock prices were regressed on the individual variables. Not surprisingly, the autocorrelation in the error terms also disappears.

Different capital asset pricing models are derived and discussed in Appendix 3. The covariance term in eq. (4) may represent covariance between the return on an individual asset and the return of asset portfolios. It may also represent covariance between the return on an asset and different macroeconomic variables.

If the return on an individual asset only is correlated with the market as a whole, the covariance term in eq. (4) has a similar interpretation as the beta in the S-L CAP&f. However, other portfolios may be constructed from subsets of the market portfolio and these may show different relationships to


the return on individual assets. The S&P 400 and the constructed European basket presented in this paper, are other such subsets of the market. They may be viewed as two of two or more portfolios to which the Merton intertemporal CAPM relates return on an individual asset.

The different relationships detected between changes in the national stock indices and macroeconomic variables are examples of the covariance term in (4). From the perspective of the intertemporal CAPM, changes in macroeconomic variables are important because they alter the preference for consumption over time.

Several relationships detected indicate that there is a link between past values of macroeconomic variables and changes in stock prices. The factor models in table 13 show many significant coefficients for lagged values of economic variables. A regression of the stock indices on past values of the variables yielded r-squared values between 0.2 and 0.4 for all countries with the exception of Italy and France. These preliminary results indicate that it takes time before the stock market fully reacts to news about changes in economic variables. Further exploration of these relationships may discover opportunities for building predictive models that yield returns above that of the market.

This study has tested the relationships between a large number of variables and the stock indices by using quarterly data. For individual variables it is possible to obtain time series with more frequent data points which probably would produce stronger results when regressed against stock prices than those discovered here.


Appendix 1: List of variables

Variable IMF line Comments

BILL 6Oc

BOND DCAPF DCONS DEFFX

61 93e 96f EUllX

DEMP 67 DESH 62

DEXP DGNP

9oc 99a

DIMP DIND DINF DMO DMl DM2 DVS INT RET YC

98c 66c 64 14 34 34 & 35 62 61 62 6Oc & 61

s-t interest rate; starting end of 70s for most countries

yield on long term government bond private gross fixed capital formation private consumption

trade-weighted exchange rate, MERM, quoted foreign/domestic

employment, seasonally adjusted equally weighted portfolio of the German,

Swedish and U.K. stock indices. exports real gross national expenditures; line 99b,

GDP, is used for Fra, Ita and Swi imports industrial production consumer price index reserve money money money and quasi-money U.S. share prices; S&P 400 long term interest rate change in stock prices difference between U.S. bond and T-bill rate

Variables starting with a D and RET are continuously compounded quarterly changes.

Appendix 2: Stock indices used in the study

Denmark:

Finland: France: Germany:

Italy:

Netherlands: Norway: Sweden: Switzerland:

United Kingdom:

end-of-month quotations of a sample of industrial shares on Copenhagen SE

daily average buying quotations on Helsinki SE end-of-week quotations of 180 shares on Paris SE daily averages covering 95% of quoted industrial

companies daily averages of closing prices of 40 major companies

on Milan SE daily average of 55 general shares on Amsterdam SE mid-month prices of Oslo SE General Index end-of-month prices of all shares on Stockholm SE Friday quotations of 49 industrial shares in

Zurich, Geneva and Base1 daily average of 500 industrial ordinary shares

Appendix 3: Capital asset pricing models

In the traditional Sharpe-Lintner capital asset pricing model (S-L CAPM), asset returns are determined by mean-variance mathematics. The rate of return on an asset is determined by the risk-free rate, rf (or, in the Black-


model, the rate of return on the minimum-variance zero-beta portfolio that is uncorrelated with the market), the market return, rm and the covariance between the returns on the individual asset and those on the market divided by the variance of the market returns. This is a one-period equilibrium model. In a multi-period setting, we would have to assume that the risk-free rate and the market return are constant (or at least non-stochastic) in order to use the S-L CAPM. Empirically, however, it is clear that neither rf nor rm are constant over time.

A realistic multi-period model has to take into account the changes in the state of the economy over time. Merton (1973) derived an inter-temporal asset pricing model (I-CAPM) where the asset returns depend on the covariances between the individual asset and a set of state variables in addition to the covariances between the returns on the asset and those on the market portfolio. In this model, investors choose portfolios to hedge against changes in the state variables. The state variables may be thought of as macroeconomic factors. The investors are, for example, assumed to be interested in hedging against inflation in their portfolio decisions.

In the following, three capital asset pricing models, consumption CAPM (C-CAPM), S-L CAPM and I-CAPM, are derived using the techniques of Constantinides (1986). These derivations show the basic differences between the models in a simple way.

Constantinides derives the C-CAPM by starting with the fundamental valuation equation where the price of an asset is determined by the marginal propensity to consume and the cash flow generated by the firm:

Pit=E[;iTl (z)DiT:It].

Pit is the price of the ith asset at time t, u is a von Neumann-Morgenstern utility function, the subscript c indicated the first derivative and Di is the dividend of the ith form. I denotes the information and : It indicates that the expression is conditioned on the information set at time t. The expression in the inner parentheses is the discount factor. Defining the rate of return as Rit = (Pit + Dit)/Pit - 1 we have

Dividing both sides by Pit - 1, using the definition of Rit and defining the excess rate of return as ri = Ri- Rf where Rf is the risk free rate,


Constantinides gets the expression

E[(uct/uct-l)*rit:It-l]=O.

The inner brackets reduces to uct. Using Steins lemma, which states that cov(x,g(y)) = E[g(y)] * cov(x, y) assuming that x and y are normally distri- buted, the valuation equation becomes:

E[rit] = ( - E[ucct]/E[uct]} * cov(rit, Ct), (2)

where everything is conditioned on It - 1 and Ct is consumption in t. The ratio in the curly brackets on the right-hand side of the equation is a measure of risk aversion. The larger the risk aversion, the lower the expected returns on all assets. In a one-period context, consumption equals aggregated wealth, C= q because the investors consume all of their wealth in period t = 1. In this case eq. (2) collapses to the traditional one-period S-L CAPM:

E[rit] = { - E[uwwt]/E[uwt]} * cov(rit, wt). (3)

The ratio in the brackets becomes a non-asset-specific constant. The covariance term can be written as

cov(w1, ril) = [{cov((wl - wO)/wO, ri))/(var ((wl - wO)/wO)}l

* var((w1 - wO)/wO).

The variance term is a constant and the expression in the large parentheses represents the beta in the S-LCAPM. Thus, we see that the return as defined in (3) is proportional to beta. The risk aversion term in (3) is not readily observable, but multiplied by the constant in the covariance term it may be thought of as the difference between the market premium and the risk free rate in a one period setting.

In an inter-temporal setting the model assumes that the risk aversion term is determined by the information in the consumption time series. However, not all relevant information needed for determining the state of the economy may be reflected in the changes in consumption itself. This happens if ct(lt - 1, st) is different from ct(Zt), where st is a vector of state variables. If that is the case, we need to include more state variables in our information set. In doing so we get the following general valuation equation

E[rit]={ -E[ucct] *cj/E[uct]) *cov(sjt,ct), (4)

where j is an index representing different factors. This is the Merton


I-CAPM where the asset return is dependent on changes in at least one state variable in addition to (or instead of) consumption. The consumption CAPM initially presented by Breeden (1979) may be thought of as Mertons intertemporal model where the information in all the different state variables collapses into the time series behavior of consumption.

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stock prices, asset portfolios and macroeconomic variables in ten european countries

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