Excerpt

## Table of Content

List of Tables

Abstract

1 Introduction

2 Applied Macroeconomic Time Series Data Source

2.1 Standard & Poor’s 500 Index

2.2 Stock Prices and Industrial Production Index

2.3 Stock Return and M1 Money Stock

2.4 Stock Return and Total Consumer Credit Outstanding

2.5 Stock Return and Term Structure of Interest Rates

2.6 Stock Return and Consumer Price Index

3 The Expected Outcome of Regressors

4 Analysis of Test Results

4.1 Stationarity and Weak Dependence

4.2 Testing for Time Trend and I(1) process

4.3 Lagged Variables

4.4 Multicollinearity

4.5 Model Re-Specification

4.6 Regression Results

4.6.1 CPI

4.6.2 IPT

4.6.3 Money Stock M

4.6.4 TCC

4.6.5 Term

5 F-Test

6 Serial Correlation

7 Testing for Heteroskedasticity

8 Model Re-Specification

8.1 Using Robust-Standard Errors

8.2 Omitting all Insignificant Variables

9 Conclusion

Bibliography

Appendix

## List of Tables

Table 1 Depiction of the variables including informative details and measurement

Table 2: Testing for time trend

Table 3: Testing for I(0) process

Table 4: Proof of multicollinearity

Table 5: OLS Regression that regresses ld_SP500 on all independent variables

Table 6: Obtaining ût_1 using the OLS regression (6)

Table 7: ût2 regressed on the time series data set to obtain R2û2

Table 8: OLS Regression applying robust standard errors to explain ld_SP500

Table 9: OLS Regression omitting all insignificant variables to explain ld_SP500 using

## Abstract

The objective of this paper is to examine whether the unanticipated change of specific macroeconomic variables influences the US stock market represented by the S&P 500 using monthly data from 1986 to 2007. Thereby, the performance of the arbitrage pricing theory of Ross (cp. Ross, S., 1976) shall be studied. To explain the behavior of the US stock market return the paper contains the five predefined variables consumer price index (CPI), industrial production index (IPT), money stock M1 (M1), total consumer credit outstanding (TCC) and the term structure of interest rates (Term) which are approximately similar to those variables used by Ross (cp. Chen N. F. et al., 1986, pp. 383-403). Applying the OLS method, it was found that CPI, IPT and Term are negatively related to the US stock return. It was also detected that M1 affects the stock market lagging 8 months and 12 months. However, the test statistics showed that TCC has rather no impact on the US stock market return. To ensure that the ultimate results are not spurious, care will be taken in regards to autocorrelation, multicollinearity, serial correlation as well as heteroskedasticity.

## 1 Introduction

No satisfying theory would bring forward the debate that the relationship between the financial market and the macroeconomy can be channeled in purely one sole direction. Nevertheless, stock prices are generally considered as reacting to external factors although they may give feedback to the other factors, too. From a neutral prospect, it is obvious that every economic factor is endogenous to some final extent and thus only natural factors such as earthquakes and climate can be considered exogenous, influencing the world economy. But to establish an asset pricing model that considers those systematic physical factors is beyond the current scope (cp. Chen N. F. et al., 1986, p. 384). Therefore, the aim of this paper is to ‘merely’ form a model that explains US stock market returns as a function of macroeconomic variables. Herein, the basis shall be the arbitrage pricing theory (APT) that was primarily developed by Ross (cp. Ross, S., 1976, pp. 341-360). The APT model especially posits that stock returns are influenced by unanticipated changes in macroeconomic variables. This change can be explained by the difference between the expected change and the actual realized change. Certainly, an important question is how investors have formed their expectations. Among different approaches, the simplest one is to assume naive static expectations. Under those expectations investors will assume that the value in the next period equals the current value. Therefore, the unanticipated change, however, will then be expressed as the non-zero difference between the current value and actual realized value (cp. Brooks, C., 2008, p. 100). Therefore, one can generate the following model:

Abbildung in dieser Leseprobe nicht enthalten

where:

• The stock return Ri linearly depends on the unanticipated changes in k factors (Fi1,Fi2,…,Fik) and an unobservable risk εk. The degree to which the return on the asset reacts, eventually relies on the coefficients given by the factor loadings bi1,bi2,…,bik (cp. Renström, T., 2002, p. 4).

## 2 Applied Macroeconomic Time Series Data Source

To price an asset the most common theory involves the discounting of future cash flows. Thus variables that influence future cash flows or the risk adjusted discount rate of a company have to be incorporated into a linear model as suggested by the APT of Ross (cp. Günsel, N./Cukur, S. , 2007, p. 143). Since the theory itself does not clarify the influencing factors, the multiple factors model can be build relying on the data set that was provided by the lecturer. Therefore, this empirical study employs the five macroeconomic variables consumer price index (CPI), industrial production index (IPT), M1 money stock (M1), total consumer credit outstanding (TCC) and the term structure of interest rates (Term) to test whether macroeconomic variables have an impact on stock market returns represented by the S&P 500.

Herein, the time series data consists of 254 monthly observations available from the fourth quarter of 1986 to the fourth quarter of 2007 with no missing observations. The data collection, provided by the St. Louis Fed is seasonally adjusted for the CPI and IPT measured in index points; and seasonally adjusted for the TCC and M1 expressed in billion US$. The time series data set of the S&P 500 at its closed price has been retrieved from Yahoo Finance. The author intends to estimate a constant elasticity model under the OLS technique. Thus, the dependent variable as well as the independent variables will be defined in log terms, so that the data applied forms a log-log model (cp. Wooldridge, J. M., 2002, p. 44). Furthermore, since the APT presumes that only unexpected changes influence the stock market return the differences of the variables have to be determined. Given the transformed time series data, the model in a functional form can therefore be written as follows:

Abbildung in dieser Leseprobe nicht enthalten

Table 1 Depiction of the variables including informative details and measurement

### 2.1 Standard & Poor’s 500 Index

As mentioned earlier, the stock market is to be assumed endogenous. As the given data set contains only US data, the S&P 500, an index that contains the 500 largest publicly listed US firms, is chosen as a dependent proxy variable for the aggregated US stock market and the respective stock market return.

### 2.2 Stock Prices and Industrial Production Index

The IPT measures the increase in production in the real sector. It is a good proxy for reflecting overall economic activity within the economy and has a strong effect on stock prices since it influences future cash flows of firms. This reveals a positive relationship between the changes in industrial production and stock market returns, as an increase in future cash flows causes higher dividend payments and ultimately higher share prices (cp. Mohammad, S. D./Hussain, A./Ali, A., 2009, p. 99). However, the effect on stock prices could be also adverse if industrial production is approaching potential output causing unanticipated inflationary expectations by investors for any unexpected positive change.

### 2.3 Stock Return and M1 Money Stock

An unanticipated money stock increase causes a portfolio rebalancing with respect to other real assets. This reallocation process induces an upward pressure on share prices (cp. Günsel, N./Cukur, S., 2007, p. 145). Moreover, a growing money stock leads to a reduction in real interest rates and thus bringing a stimulus to overall economic activity. The resulting consequence is that firms will make adjustments to their investments to generate higher sales and profits causing greater future cash flows and subsequently higher share prices (cp. Günsel, N./Cukur, S., 2007, p. 145). Nevertheless, an increase in the money stock may also relate to unanticipated inflation and thus to uncertainty in future inflation adversely affecting share prices (cp. Humpe, A./Macmillan, P., 2007, p. 6). This economic explanation between money supply and stock returns makes it sufficient to incorporate the money supply as a significant macroeconomic variable in the regression model.

### 2.4 Stock Return and Total Consumer Credit Outstanding

The total consumer credit outstanding reflects the spending behavior of consumers which accounts for 70 % of the gross domestic product in the US (cp. Federal Reserve Bank of San Francisco, 2008). Thus, an increase in total consumer credit outstanding has a direct affect on US economic activity and thus influences the industry’s and firms’ sales revenue leading to an increase in share prices due to additional profit gains. But, a higher amount of total consumer credit outstanding can also induce a wealth effect causing a decrease in future consumption. Hence, the ultimate consequence may lead to falling share prices.

### 2.5 Stock Return and Term Structure of Interest Rates

The stock price is directly determined by the discount rate as mentioned earlier. It is generally agreed that the discount rate as an independent risk factor on stock returns must be contained in an asset pricing model. However, since discount rates can be strongly correlated to many other macroeconomic variables, the 3 month US Treasury yield and the 10 year US Treasury yield can alternatively be replaced by the term structure of interest rates to avoid such problem (cp. Günsel, N./Cukur, S., 2007, p. 143). The term structure of interest rates is measured by the difference of long term and short term US government bond yields. That is in detail, the difference of 10 years US treasury bonds and 3 month US treasury bills.1 If the spread of the term structure increases investors prefer to hold liquidity in form of short term investments rather than long term investments such as stocks. Hence, while the discount rate for short term investment decreases it increases for long term investment. Assuming all else equal in the discounted cash flow model, expected future cash flows will then consequently be discounted with a higher rate causing stock prices to fall.

### 2.6 Stock Return and Consumer Price Index

An increase in the CPI affects the sales revenue, the borrowing behavior of firms due to changes in nominal cash flows and the interest rate. Since an expected shift in the CPI is already included in the interest rate and in sales prices only the unexpected change should have a negative impact on the share price (cp. Günsel, N./Cukur, S., 2007, p. 144). Furthermore, it is also argued that an unexpected increase in the CPI has an initial negative effect on the income of firms because of a sudden rise in overall costs and the slow adjustment of output prices causing profits to decrease and therefore share prices to fall (cp. Humpe, A./Macmillan, P., 2007, p. 6).

## 3 The Expected Outcome of Regressors

As the effect of these selected macroeconomic variables on the US stock market return has been previously explained, the author is able to give a qualified opinion about the expected sign of each variable in the regression equation.

1 Since the time series data for the Term variable is already provided in percentage, only the first difference will be taken.

- As an unexpected increase in the CPI is negatively correlated with stock returns b1 is expected to show a negative sign.

- An unanticipated increase in industrial production can be both beneficial and harmful for the stock price so that b2 is expected to show a positive or negative sign.

- It was shown that an unexpected increase in money supply ambivalently affects the stock market return. Therefore, the expected sign of b3 can either be negative or positive.

- US activity is significantly determined by the domestic consumption rate. Therefore, an unanticipated expansion in consumer credit shall positively affect stock market returns. However, due to the arising wealth effect consumers may reduce their future consumption. Thus, the coefficient b4 is expected to reveal either a positive or negative sign.

- An unexpected widening of the term structure gap points out that short term yields are sharply rising implying that inflationary pressure is expected to continue. As this rise in yields causes future cash flows to be discounted with a higher interest rate the eventual impact will be adverse to stock prices. That is why a negative sign of Term is expected.

## 4 Analysis of Test Results

### 4.1 Stationarity and Weak Dependence

To provide sound conditions for an econometric model with respect to the given assumptions, the conditions of stationarity and weak dependence must be met.

To comprehend the relationship between two or more variables using regression analysis, some form of stability is needed. Otherwise, if the relationship of the variables e.g. (yt and xt) changes arbitrarily in each period of time, the obtained result will be spurious. Therefore, in a regression model for times series data a certain form of stationarity has to be established so that the joint distribution of the time series remains unchanged over time. In detail, taking a set of random samples in order and shifting it h time periods ahead, the joint probability distribution should not alter.

Interdependent to stationarity but very different is the concept of weak dependence which substitutes the assumption of random sampling. It provides that the correlation between xt and xt+h approaches zero ‘sufficiently quickly’ as h goes to infinity (cp. Wooldridge, J. M., 2009, p. 379). The prime assumption for a weak dependent series is the stability condition ρ < 1 where ρ = corr(yt,yt-1) in an autoregressive process of order one [AR(1)]. If the time series data shows ρ < 1 in the AR(1) model the series is said to be integrated of order zero and nothing needs to be done to the data before employing them in the regression equation. However, if ρ = 1 in the AR(1) model, the time series data would show a random walk which depicts a special case of a unit root process.2 In this case the series would be highly persistent in the sense that today’s value of y is essential to determine the value of y in the very remote future. High persistence in a regression model can lead to spurious results so that it will be required to transfer the time series data into weak dependence (cp. Wooldridge, J. M.,2009, pp. 377-395). As the APT model already requires differenced data to obtain the unanticipated change of the employed variables and is therefore transferred beforehand, it is expected that the data generated will be weak dependent.

### 4.2 Testing for Time Trend and I(1) process

Before obtaining the first order autocorrelation all variables should be detrended, otherwise the correlation tends to be overestimated which results in a bias finding a unit root process. As the time series has been differenced the proof of a time trending series, that is yt = α0 +α1t + εt, may already be statistically insignificant as visual inspection suggests in figure 1 (see appendix).3

Abbildung in dieser Leseprobe nicht enthalten

Table 2: Testing for time trend

As seen above, the null hypothesis H0: α = 0 against the alternative H1: α ≠ 0 cannot be rejected for every variable. Although the time trend variable in SP500, IPT, TCC and Term can be proven to be insignificant at any conventional level, the time trend in CPI and M1, although small, is significant at any conventional significance level. Therefore, the time series data will be controlled for the time trend except for those who have been proven not time trending, to examine whether the time series data is highly persistent. This gives reason to estimate ρ within the AR(1) model for any detrended macroeconomic variable. As a rule of thumb |ρ1| > 0.8 implies a process integrated of order one I(1) whereas |ρ1| < 0.8 would imply a process integrated of order zero I(0) (cp. Wooldridge, J. M., 2009, p. 394).

Abbildung in dieser Leseprobe nicht enthalten

Table 3: Testing for I(0) process

Since |ρ1|< 0.8, it follows that none of the time series data can be proven highly persistent, so that the stability condition in an AR(1) process is fulfilled. The autocorrelation function (ACF) 2 The correlaVon coefficient denoted as ρ1 is employed to determine whether Vme series property of each variable is I(1) or I(0). As ρ1 is only an estimate, its process applied is only a rule of thumb estimation to decide whether ρ < 1. 3 The following estimations and scatter plots throughout the empirical study are established by using the GRETL econometric analysis software.

**[...]**

- Quote paper
- Dennis Sauert (Author), 2010, Do Macroeconomic Variables have an Effect on the US Stock Market?, Munich, GRIN Verlag, https://www.grin.com/document/158131

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