between bear and bull markets in US MSCI stock market returns?
By: Maikel Went 1 University of Groningen Faculty of Economics and Business
MSc Finance MSc Finance Thesis
Supervisor: C.G.F. Van der Kwaak, MSc Date: 08-06-2017
Abstract
In this paper, I follow Rapach et al (2005) closely and examine the predictive power of stock returns using nine macroeconomic variables for the US stock market index MSCI. I consider an in-sample and of-sample period to test the predictive power of the macroeconomic variables. For the out-of-sample forecasting performance testing I will use the MSE-F statistic generated by McCracken (2004). I find that inflation and relative government bond yield are statistically significant to have predictive power in 2002, afterwards only inflation is statistically significant from 2003 to 2007. After 2007 all macroeconomic variables are highly insignificant, which can be interpreted as the result of the financial crisis. Therefore, to account for this, I distinguish between bear and bull markets by incorporating dummy variables. I find that this is a stronger predictor of stock returns than macroeconomic variables.
Key words: Return predictability; Macroeconomic variables; Out-of-sample forecasts
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Contents
I. Introduction ...3
II. Literature review ...6
III. Methodology...10
Data replication Rapach et al (2005) ...10
Time period ...11
Sample construction ...12
Descriptive statistics...13
Model ...16
Bootstrap method ...19
Robust standard errors...20
IV. Results ...20
In-sample estimation ...21
Out of sample performance testing ...23
Differentiating between bear and bull markets ...26
In-sample estimation during bear and bull markets ...26
Out of sample performance testing ...27
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I. Introduction
4 compare the new unrestricted model with the original restricted model, a model of forecast return that only depends on a lagged return. I recalculate all the macroeconomic variables and their statistics on their significance level identical to method mentioned before. First I calculate the statistics by using an out-of-sample period of January 1991 to June 2002, afterwards, I extend the out-of-sample period by a year and recalculate the statistics. The recalculation is until December 2010. I find that after distinguishing between bear and bull markets, all macroeconomic variables are highly significant on a 1% level. This finding indicates that it is possible that distinguis hing between bear and bull markets results in better estimates than the restricted model. To formally test this, I exclude the macroeconomic variables from the unrestricted model. The new unrestricted model depends on a lagged return and a dummy variable that distinguishes between bear and bull markets. I recalculate the statistics as mentioned before and find that all MSE-F statistics are highly significant on a 1% level. As a result of this finding I can say that distinguishing between bear and bull markets is a stronger predictor of stock market returns than macroeconomic variables. This paper differs from Rapach et al(2005) by a) a longer out-of-sample period, b) finding that an extension of the out-of-sample period results in insignificant results after 2007. This finding indicates that the financial crisis of 2007 to 2009 has impact on the significance of the statistics. Therefore, c) I will distinguish between bear and bull markets by using dummy variables to better estimate the impact of the financial crisis.
The main purpose to investigate the predictive power of macroeconomic variables is that they are leading indicators of the economy, and are reported frequently, Gupta & Modise (2013). They can possibly be used in arbitrage opportunities or perhaps for controlling of financial markets. According to Rashid (2008) controlling of financial markets is possible when the macroeconomic variables have predictive power. For example, the government could use the money supply or the interest rate in good and bad times to control financial markets. Arbitrage opportunities exist when investors are able to use the macroeconomic variables to predict stock market returns. They can invest accordingly to the reported macroeconomic variables.
5 incorporated in the stock prices. This is under the assumption of rational expectations, Hillier et al (2012), every investor will invest rationally. In theory, an investor is not able to gain from arbitrage opportunities because of this assumption. Macroeconomic variables are freely available information to all investors, presenting the current state of the economy, and should therefore not have predictive power of stock market returns. However, in practice a lot of research shows that there are some macroeconomic variables that tend to have predictive power. For instance, Chen (2009) finds that inflation tends to have predictive power. Furthermore, Rapach et al (2005), and Gupta & Modise (2013) find that interest rate also tends to have predictive power.
Research on the impact of macroeconomic variables on the stock market returns started 40 years ago in which it examined the relationship between the two. Liu & Shrestha (2008), and Perego & Vermeulen (2016) find that there is indeed a relationship between macroeconomic variables and stock returns. Therefore the research on predictive power of macroeconomic variables is extended the past 15 to 20 years. Since then researchers are able to use methodology to predict stock market returns. An example is given by Chen (2009), he uses a Markov-switching model using an in-sample, and out-of-sample period to predict bear markets. He finds that yield curve spreads and inflation tend to have predictive power in the US stock market using a sample from 1957 to 2007. The predictive power of macroeconomic variables is supported by many researchers among which Rapach et al (2005), Bessler & Wolff (2016), and Wu & Lee (2005).
6 The remainder of this paper is as follows. Section two provides a literature overview, section three provides a description of the dataset, the methodology and the hypotheses. Section four presents the results and the analysis of the out-of-sample performance of the macroeconomic variables and the market returns. Furthermore, this section also includes tests for robustness. The discussion of the results is mentioned in section five, and the conclusions are summarized in section six. The appendices are given in section seven.
II. Literature review
In this section I will present the literature review for the predictive power of macroeconomic variables of stock returns. I will present prior research results, and analyze the results to use for my research. Furthermore I will also describe what is new in my research according to prior literature. First I will present the importance of the macroeconomic variables, then I present the relations hip between stock returns and macroeconomic variables. Followed by investigating the prior literature, their findings and methodology they use to test predictive power of macroeconomic variables. I will analyze the different types of models used and their macroeconomic variables.
7 incurred by financial or governmental institutions. Correspondingly this will have impact on the investment strategies of the investors. Consequently, this will also have impact on the stock market returns. This is supported by Liu & Shrestha (2008) and Perego & Vermeulen (2016), they find that macroeconomic variables is positively related to stock markets using GARCH models.
I will distinguish between the various types of models used in prior literature and present their findings accordingly. First of all, prior literature on macroeconomic variables and their predictive power is extensive (Rapach et al, 2005; Flannery & Protopapadakis, 2002; Chen,2009). They use different types of models and methods to estimate the predictive power of macroeconomic variables. Several papers have examined the predictive power by using the GARCH model (Flannery & Protopapadakis, 2002; Conrad & Loch, 2015). They find that housing starts and unemployment rate are statistically significant to have predictive power. Flannery & Protopapadakis (2002) also find that inflation, balance of trade and monetary aggregate are relevant macroeconomic variables. Moreover, Conrad & Loch (2015) also find that term spread, and corporate profits are both relevant. In addition, both papers investigated industrial production index, however neither of the two papers find that this is a relevant macroeconomic variable. The method used by Flannery & Protopapadakis (2002) differs from the other paper along dimens io n, a) the sample period is shorter, January 1980 to December 1996, compared to January 1969 to December 2011. And b) they use a value weighted market index of NSYE, NASDAQ , and AMEX instead of S&P500. In essence, the papers both use GARCH models and find that the matching macroeconomic variables are relevant (housing starts and unemployment rate) and irreleva nt (industrial production).
8 testing compared to using the Capital asset pricing model(CAPM) and the Arbitrage pricing theory (APT).
More recent papers use in-sample and out-of-sample forecasting performance, however they do not use stock market returns, in fact they use industry returns (Rapach et al,2015; Bessler & Wolff, 2016). Bessler & Wolff (2016) find that Chicago Fed National Activity Index (CFNAI), unemployment rate, and trade weighted dollar index have predictive power in industry returns using multivariate predictive regression models.
9 Prior literature as mentioned above use different types of methods, models, and markets. In this paper I will follow Rapach et al (2005), therefore it gets a special place in the literature review. The reason to choose for Rapach et al (2005) is because of a) they find macroeconomic variables that do have predictive power and therefore I can build on their research, b) they use an out-of-sample period, that can be extended to take the financial crisis into account, c) they use a model that is easily extended to investigate different types of markets.
10 tend to have predictive power according to the literature mentioned above. In the methodology section I will motivate the examined macroeconomic variables in this study. I will first use the same in-sample period and out-of-sample period as Rapach et al (2005). Afterwards I will extend the out-of-sample period each time by a year until 2010. The literature mentioned above use different types of models to investigate bear and bull markets. However, this type of market is not investigated in combination with the predictive regression model. Therefore, I will also extend the research by distinguishing between bear and bull markets and use the calculated dates of Nyberg (2013).
III.
Methodology
In this section I will present the methodology that I will use to analyze the predictive power of US macroeconomic variables. I will present the data replication of Rapach et al (2005), the time period, the sample, and the model that I will use to determine the predictive power. In this study I will follow Rapach et al (2005) largely in the following ways, a) I will use their statistically significa nt macroeconomic variables, b) I will use the same methodology to calculate the predictive power of macroeconomic variables, c) I will use the same in-sample period for the estimation of the coefficients, and d) I will first test the macroeconomic variables using the same out-of-sample period. Afterwards I distinguish between Rapach et al (2005) by a) extending the out-of-sample period year by year until December 2010, b) extend the sample of statistically significa nt macroeconomic variables with statistically significant macroeconomic variables according to prior literature. And c) find that all macroeconomic variables are highly insignificant after 2007, and distinguish between bear and bull markets to take the financial crisis of 2007 to 2009 into account.
Data replication Rapach et al (2005)
11 appendix. However I was not able to replicate the exact data for a couple of variables. I compared my transformed data to that of Rapach et al (2005). I even made graphs of the data series, the movements are exactly the same, however the data does not match. I have tried to contact Rapach a couple of times without any success. This inability of perfectly replicating the transformed data and p-values of Rapach et al (2005) is somewhat problematic. However I use the exact same methodology and use the macroeconomic variables that tend to be statistically significant in the in-sample period and the out-of-in-sample period. I find that the same macroeconomic variables are statistically significant on the same significance level. Therefore I am confident to use my code, my data and the methodology of Rapach et al (2005) The code is written in MATLAB and is as well as my data available up on request.
Time period
12 power in this volatile period as well. Therefore I have extended the out-of-sample period to December 2010, it will take the financial crisis into account, but also the subsequent bull market.
Sample construction
In this section I will present the macroeconomic variables and the stock market index that I will use in this study. I will use monthly data and I will focus on the US stock market, and therefore I will use US macroeconomic variables. Due to feasibility and availability of information I will only use data of US markets. Because I follow the methodology of Rapach et al (2005) largely, and I want to investigate whether the macroeconomic variables still have predictive power. I will use the same US stock market index, namely the Morgan Stanley Capital International stock price index (MSCI). In this research I will investigate nine macroeconomic variables, Inflation (INFL), Relative 3-month Treasury bill rate (RTB), Relative long-term Government Bond yield (RGB), Term Spread (TS), Money supply (MS), Chicago Fed National Activity Index (CFNAI), Unemployment rate (UR), Balance of Trade (BOT), and Housing starts (HS).
13 and balance of trade into this research. They are often studied, for instance housing starts by Bessler & Wolff (2016), and all three by Flannery & Protopapadakis (2002). The last one find that these macroeconomic variables tend to have predictive power. All in all, I will use nine macroeconomic variables that tend to have predictive power in prior literature. The macroeconomic variables that I will use and the MSCI market index will be extracted from DATASTREAM, and the Federal Reserve Bank of St. Louis. Appendix A shows a comprehensive version of the extracted data. The macroeconomic variables and the market index are listed with their identical series codes.
Descriptive statistics
In this section I will present the descriptive statistics of this research. Table 1 reports the descriptive statistics of the original data of macroeconomic variables and the stock market index mentioned in ‘Sample construction’. Column 1 presents the macroeconomic variables and the MSCI, column 2 and 3 reports the mean and the standard deviation of the data respectively. Lastly, column 4 presents the units of the variables.
16 because these are already the stock returns. For the US MSCI however I will use real returns, therefore an adjustment is necessary because the original data are stock prices. I will follow Rapach et al (2005) and make the same adjustment, first the stock prices are deflated by the CPI. Afterwards I will take the first difference in the log-levels of these adjusted stock prices. Following Peters (1992), logarithmic returns are a better option to use than normal returns. Logarithmic returns sum to their equivalents and also have the same properties as normal returns. I will use equation 1 to calculate logarithmic returns.
(1) yt = ln ( Pt
Pt−1)
Where yt is the logarithmic return of the MSCI index on day t, Pt is the market index’s closing price on day t and Pt−1 is the stock index’s closing price on the previous day. The adjustments to the macroeconomic variables and the US MSCI as mentioned above result in stationary data and their corresponding descriptive statistics are presented in table 3. Column 1 describes the macroeconomic variables and the US MSCI. Column 2 and 3 reports the mean, and the standard deviation respectively. Lastly, column 4 presents the units of the variables.
Model
17 variables. I will follow Baker and Wurgler (2000) and use the calculated standard errors in table 3 to divide the macroeconomic variables. This will have no effect on my sample inferences, but it makes it easier to compare the estimated beta coefficients in the in-sample period. A one-standard deviation change in the macroeconomic variables can be seen as a change in the expected returns. After this adjustment I will use the predictive regression model, this is a regression that depends on a one period lagged macroeconomic variable, and a lagged return to forecast one period forecast returns. The unrestricted model is given by equation 2.
(2) ŷ1,R+1 = α̂1,R+ 𝛽̂1,𝑅 . zt+ γ̂1,R . yR+ û1,R+1
Where ŷ1,R+1 is the forecast stock market return of MSCI, yt is the lagged stock market return of MSCI, and zt is the macroeconomic variable. I will use these variables to estimate the coefficie nts α
̂, β̂, γ̂, these are the alpha, beta, and the gamma coefficients respectively. I will use two versions of equation 2, the unrestricted model in which the macroeconomic variable zt is included, and a restricted model in which the macroeconomic variable zt is excluded. First I use the restricted and
unrestricted model in the in-sample period of February 1970 to December 1990. I estimate the coefficients alpha, beta, and gamma in the in-sample period. In the unrestricted model I will test the following hypotheses, the null hypothesis H0: β = 0, the alternative hypothesis H1: β ≠ 0. If the null hypothesis is rejected, then the macroeconomic variable has predictive power for future returns, meaning that the macroeconomic variable is statistically significant different from zero. In the in-sample period I will estimate the t-statistic of the β̂, the OLS estimate of β̂, and the goodness of fit measure adjusted r-squared. The r-squared statistic is used to compare the explanatory power of different types of models. I will use the estimated in-sample coefficients to test the forecasting performance of the out-of-sample period. The total sample has T observations, I will split this in in-sample period R observations, and out-of-sample period P observations. Therefore R+P = T observations. I will use equation 3 to estimate the in-sample restricted model coefficients, where the macroeconomic variable is excluded.
(3) ŷ0,R+1 = α̂0,R+ γ̂0,R . yR+ û0,R+1
Where ŷ0,R+1is the forecast of one period stock return, α̂0,R is the alpha or intercept for the restricted model. γ̂0,R is the gamma coefficient calculated by the regression with a lagged return given by yR.
18 unrestricted model the forecast errors are calculated by equation 4.
(4) ûR+1 = yR+1− ŷR+1
Where ûR+1 is the forecast error, yR+1 is the realized return, and ŷR+1 is the forecasted return. When the forecast error is zero, then the estimated return perfectly reflects the realized return. For the restricted model as well as the unrestricted model forecast errors will be generated, and will be compared. In essence, when the forecast errors of the restricted model are less than the unrestricted model, then the restricted model better forecasts the stock returns. To further compare the forecast returns I will use the yR+1 and zR +1 to forecast the restricted and the unrestricted model respectively ŷR+2. Afterwards the forecast errors are calculated by using equation 4 resulting in û1,R+2 and û0,R+2. This process is repeated till the end of the sample leading to two sets of T-R-1+1, one of each for the restricted and the unrestricted models. The set of forecast errors of the restricted model is given by { û0,t+1} T − 1
t = R ,and unrestricted model { û1,t+1} T − 1 t = R
I will use the calculated forecast errors of the unrestricted models and the restricted models to compare the forecast performance of the models. To formally test the forecasting performance I will follow Rapach et al (2005), and use the MSE-F statistic first used by McCracken (2004). This statistic compares the two models and tests the following hypotheses. The null hypotheses tests whether there is no difference between the restricted Mean Squared Errors (MSE) and the unrestricted MSE. The alternative hypothesis is, the one-sided (upper tail) alternative unrestricted MSE < restricted MSE. This means that the unrestricted Mean Squared Errors are smaller than the errors of the restricted model, i.e. the model forecasts the returns of the market index better. The MSE-F statistic used to compare the restricted and unrestric ted MSE’s is given by equation 5
(5) MSE − F =(T − 1 − R + 1) . d̅ MŜE1
The MSE-F statistic is based on loss differential:
19 The MSE-F statistic is just a statistic that compares the unrestricted and restricted forecast errors. However, to test for the significance of the MSE-F statistic I will use the bootstrap method, in which I generate a pseudo-sample of 1000 MSE-F statistics. The distribution of the pseudo-sample will be used to test the significance level of the calculated MSE-F statistic. The 900th, 950th, and
990th values of the MSE-F statistics will be the 10%, 5%, and 1% significance level respectively.
A significant positive MSE-F statistic indicates that the unrestricted model forecasts are superior to those of the restricted model, in that case the macroeconomic variables have some predictive power.
Bootstrap method
I will use the bootstrap method to test the significance of the calculated MSE-F statistic and draw inferences of the results. I will use the same methodology of the bootstrap method described by Rapach et al (2005). To use the bootstrap method I will use equations 6 and 7 under the null hypothesis of no predictability:
(6) yt= a0+ a1 . yt−1+ ε1,t
Where yt is the stock return, yt−1 is a lagged stock return that are used to estimate the coefficie nts
a0, and a1.
(7) zt= b0+ b1 . zt−1+ ⋯ + bp . zt−p+ ε2,t
Where zt is the macroeconomic variable, zt−1 is a lagged macroeconomic variable. The estimates of equation 6 and 7 will be done via OLS with a lag order (p) in equation 7. This p lag order is selected using the AIC in the Adjusted Dickey Fuller test. These number of lags are selected to make sure that the macroeconomic variables are stationary. According to Brooks (2014) includ ing too few or too many lags will bias the results. The selected number of lags for each variable are reported in Table 2 Column 9 considering a maximum lag order of 12. The selected number of lags per macroeconomic variable will be used in equation 7. Equation 6 and 7 result in a disturbance vector εt = (ε1,t , ε2,t ) and is assumed to be distributed independent and identical with the same covariance matrix. The disturbance terms results in a disturbance vector εt equal to T-p observations. Afterwards I will randomly draw T+100 disturbance terms, leading to ε t∗ T+100
20 for yt and zt, and to randomize the initial observations of the lagged return and the lagged macroeconomic variables, I will drop 100 observations resulting in a pseudo-sample of T observation. The pseudo-sample will be used to estimate the t-statistic of the in-sample beta and the out-of-sample period MSE-F statistic. I will repeat this process 1000 times which will generate a distribution of t-statistics of the beta coefficient and a distribution of MSE-F statistics. With this distribution I will be able to test the significance of the estimated beta coefficient and the calculated MSE-F statistic. To check and compare the beta coefficients generated by the bootstrap method I compare the results with the Newey-West HAC errors for robustness.
Robust standard errors
To make sure that the estimated coefficients, t-values, and standard errors in the restricted and unrestricted models are precise, I will have to use robust standard errors. Regularly in financ ia l data there are violations that influence inferences and these violations have to be corrected for. I will use the bootstrap method to calculate the in-sample and out-of-sample statistics. For robustness I will also calculate robust standard errors by using Newey-West Heteroscedastic and autocorrelation consistent standard errors (HAC). According to Brooks (2014) Newey-West HAC standard errors correct for two violations of the OLS assumptions. The first possible assumptio n that is corrected using Newey-West HAC errors is that the error variance is constant over time (independent of time) and finite. The second possible assumption that possibly is violated is, the errors are uncorrelated with each other over time. When one or both of these assumptions is violated, we will lose efficiency, the calculated standard errors for the parameter are wrong and consequently the t-values and F-values are wrongly calculated. For this reason I will use the bootstrap method for calculating in-sample and out-of-sample statistics. I will check the in-sample statistics by using the Newey-West HAC errors.
IV.
Results
21
In-sample estimation
In the in-sample period from February 1970 to December 1990, I will use equation 2 and 3 to estimate the in-sample coefficients of the restricted and unrestricted model. Table 4 reports the statistics of the restricted model in which the macroeconomic variable is excluded. As a result of this, all the in-sample statistics of the restricted model are the same because the regression only depends on a lagged return. The first column of table 4 describes the estimated coefficients, t-statistics, p-values, significance levels, and the adjusted r-squares. Column 2 reports the statistics that are examined individually using equation 3.
23 codes. However the reported beta coefficients do not coincide with my estimated coefficients. This is because Rapach et al (2005) reports the beta coefficients of the whole sample in contrast to the in-sample coefficients that I use. Nevertheless, the estimated beta coefficients are also significa nt on a 1% significance level. Therefore I am confident to use the estimated in-sample coefficie nts for testing the out-of-sample forecasting performance.
Out of sample performance testing
The estimated and reported in-sample coefficients in table 4 and 5 are used for testing the out-of-sample forecasting performance. I will perform the methods described in the Methodology section. I will calculate the out-of-sample forecasting performance for different out-of-sample periods. The results of testing the out-of-sample forecasting performance are reported in table 6. Column 1 reports the examined macroeconomic variables, column 2 describes the reported statistics MSE-F statistic, p-value and their significance level. Column 3 to 11 reports the statistics for the differe nt years.
First I analyze the calculated statistics in column 3, which reports the statistics of the out-of-sample period identical to Rapach et al (2005) i.e. January 1991 to June 2002. It becomes obvious that when I use my data only two of nine macroeconomic variables are statistically significant on a 10% significance level. I find that inflation and relative government bond yield have predictive power, which are exactly the same two variables that Rapach et al (2005) find to have predictive power. In addition to this, we both find that RTB and TS were statistically significant in the in-sample period and are insignificant in the out-of-sample period. Furthermore, I also find that none of the insignificant in-sample macroeconomic variables have predictive power in the out-of-sample period. Therefore I can say that the added macroeconomic variables in the in-sample period present a good indication on the out-of-sample forecasting performance.
24 logarithmic returns will result in somewhat different results according to Peters (1992). Another macroeconomic variable, CFNAI tend to have predictive power according to Bessler & Wolff (2016). Their significant findings does not coincide with my results. The time period is almost identical, however I use the real stock returns of the stock market index MSCI instead of industry indices used by Bessler & Wolff (2016).
26
Differentiating between bear and bull markets
Analyzing the out-of-sample forecast performance results in observing a) Inflation suddenly becomes more significant after 2004, and b) all the macroeconomic variables are no longer significant after 2007. The analyses leads to the extension of my research by distinguis hing between bear and bull markets using data calculated by Nyberg (2013). I will use dummy variables that will take on value one during bear markets and take on value zero during bull markets. I will use the dummy variables for bear and bull markets in the in-sample period as well as the out-of-sample period. The new regression model that I will use to compare with the restricted model is given by equation 8. Equation 8 shows the unrestricted model during bear and bull markets.
(8) ŷ1,R+1= α̂1,R+ δ̂1,RDbear +β̂1,R . zR + φ̂1,RDbear . zR + γ̂1,R . yR + λ̂1,RDbear . yR+ û1,R+1
Where, ŷ1,R+1 is the estimated forecast return for the unrestricted model, α̂1,R is the estimated alpha coefficient, δ̂1,R estimates the extra impact on the alpha coefficient during bear markets. Dbear represents the dummy variable that distinguish between bear and bull markets. β̂1,R represents the
estimated beta coefficient, and the extra impact on the beta coefficient will be measured by φ̂1,R during bear markets. zR represents the macroeconomic variable, and yR represents the return of the stock market. γ̂1,R is the gamma coefficient estimated and the extra impact on the
gamma will be measured by λ̂1,R during a bear market. I will use the same methods as described in section ‘Model’ in the Methodology to estimate the forecast errors and MSE-F statistics.
In-sample estimation during bear and bull markets
27 in table 7, and in table 5. All the adjusted r-squares reported in table 7 are higher than the adjusted r-squares in table 5. This indicates that this model is better explained than the model without dummy variables for bear and bull markets.
Out of sample performance testing
28 different out-of-sample periods. Table 8 reports the out-of-sample forecasting performance when I distinguish between bear and bull markets. Column 1 presents the different types of macroeconomic variables, column 2 describes the MSE-F statistics, p-values, and their significa nce levels. Column 3 to 11 reports the calculated statistics of the out-of-sample period during bear and bull markets.
The results in table 8 show that after I distinguish between bear and bull markets, all the calculated MSE-F statistics for the different types of out-of-sample periods are highly significant. Only one MSE-F statistics is not statistically significant on a 1% significance level, however it is still on a 5% significance level. As a result of the calculated statistics in table 8, all the macroeconomic variables tend to have predictive power when I distinguish between bear and bull markets. When I compare these results to the results in table 6 I observe that all the macroeconomic variables are statistically significant compared to only two in the original model. Therefore it is interesting to compare the different types of unrestricted models. When I use the unrestricted model of equation 2 the forecast returns depend on a lagged macroeconomic variable and a lagged return. The unrestricted model in equation 8 depend on a lagged macroeconomic variable, a lagged return, and a dummy variables that distinguish between bear and bull markets. The only difference between the two unrestricted models is therefore the dummy variable. It is possible that the dummy variable is the key driver of the highly statistically significant results in table 8. To analyze this I will generate a new unrestricted model in which the forecast return only depends on a dummy variable for distinguishing between bear and bull markets, and a lagged return. The new unrestricted model is given by equation 9.
(9) ŷ1,R+1 = α̂1,R+ δ̂1,RDbear + γ̂1,R . yR+ λ̂1,RDbear . yR+ û1,R+1
30 all calculated MSE-F statistics are highly significant on a 1% significance level. This finding indicates that the unrestricted model used in equation 9 better forecasts the forecast errors than the restricted model given by equation 3. Therefore, distinguishing between bear and bull markets using dummy variables lead to statistically significant results to have predictive power.
31 and these can be used in the forecasts. For now, the results show that for the explanation of the predictive power of stock returns, dummy variables that distinguish between bear and bull markets are better than macroeconomic variables.
V. Discussion
32 must be mentioned that this finding is only explanatory, practitioners must be warned to use these findings to forecast stock returns.
VI.
Conclusion
In this research I examine the predictive power of nine US macroeconomic variables of stock returns. I analyze each macroeconomic variable in turn. I have followed Rapach et al (2005) closely by using an in-sample period where I estimate the in-sample coefficients that will be used in testing the forecasting performance of the out-of-sample period. I extended their research by calculat ing multiple out-of-sample periods varying from the original out-of-sample period of January 1991 to June 2002, to January 1991 to December 2010. I extend the out-of-sample period each time by a year and calculate, and check the forecasting performance for each period. To test the predictive power of macroeconomic variable I have used the predictive regression model. To judge whether the macroeconomic variable has predictive power I will use the MSE-F statistic first introduced by McCracken (2004).
First I use the same time period as Rapach et al (2005), the in-sample period of February 1970 to December 1990, and the out-of-sample period of January 1991 to June 2002. I find the same four macroeconomic variables are statistically significant on a 1% level in the in-sample period. In the out-of-sample testing performance I find that inflation and relative long-term government bond yield (RGB) are statistically significant on a 10% level. The in-sample and out-of-sample findings are in line with the findings of Rapach et al (2005).
33 variables into the unrestricted models. I use the same methodology as mentioned before and recalculate all the macroeconomic variables and their significance levels. I find that after distinguishing between bear and bull markets, all the macroeconomic variables are highly significant on a 1% level. To draw inferences I also created a new unrestricted model in which I exclude the macroeconomic variable. I find that all the MSE-F statistics are statistically significa nt on a 1% level. This finding indicates that distinguishing between bear and bull markets by using a dummy variable is a better predictor of stock market returns than macroeconomic variables. The findings of bear and bull markets being a better predictor than macroeconomic variables leads to further research topics. For practical use, a limitation of this study is the look ahead bias for predicting bear and bull markets. Investors only know whether they are in a bear or bull after a couple of months, according to Nyberg (2013) this is however predictable with some delay. Therefore future studies should extend the forecast horizon to at least 12 months. The analysis of this extended forecast horizon will indicate whether the algorithm of Nyberg (2013) can be used to predict stock market returns in practice
VII.
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VIII.
Appendices
Appendix A
In this appendix I will present the data codes used to extract the data from DATASTREAM or the Federal reserve bank of St. Louis.
Inflation (INFL): USI66..IG Consumer Price Index: Total All Items for the United States,
growth rate previous period, Monthly DATASTREAM
Relative 3-month Treasury bill rate (RTB): USI60C in percentages, DATASTREAM Relative long-term Government Bond yield (RGB): USI61 in percentages,
DATASTREAM
Term spread (TS): difference between Relative long-term government bond yield (RGB)
code: USI61 and the 3-month treasury bill rate (RTB) code: USI60C, DATASTREAM
Money supply (MS): M2SL M2 money stock, billions of dollars, monthly, seasonally
adjusted, Federal reserve bank of St. Louis
Unemployment rate (UR): USOCSUN%E Unemployment rate: all persons for the united
states. Percent, monthly, seasonally adjusted. DATASTREAM
Housing starts (HS): HOUST Housing starts, total new privately owned housing units
started, thousands of units, monthly, seasonally adjusted, Federal reserve bank of St. Louis.
Balance of Trade (BOT): M318501Q027NBEA, Balance of trade, billions of dollars,
monthly, not seasonally adjusted. Federal reserve bank of St. Louis.
Chicago Fed National Activity Index (CFNAI): CFNAI, monthly stock returns, Federal
reserve bank of St. Louis.
36
Appendix B.
