Macroeconomic Variables as Predictors of US Equity Returns

PDF: Macroeconomic Variables as Predictors of US Equity Returns Doyon Yulianto


A significant amount of literature investigating the relationship between equity returns and macroeconomic variables has been produced since the 1970โ€™s. While some studies confirmed the relationship between certain variables and equity returns in the U.S. equity market, many others give contradicting results. Disparity in findings also exists regarding the cause and effect relationship between macroeconomic variables and equity returns. The purpose of this study is to conclude whether macroeconomic variables can explain real equity returns in the U.S. equity market. Macroeconomic variables considered in this paper include those studied previously, and also the so-called leading indicators, such as consumer confidence and housing starts. The significance of macroeconomic variables in explaining equity returns is measured using multivariate linear regressions. Contrary to previous researches, this study found a significant relationship between annual real equity returns and the change in consumer confidence and in housing starts. A relationship is also found between real equity returns and the risk premium, as measured by the spread between the yields on BBB corporate bonds and U.S. Treasury bonds. No significant relationship between current real equity returns and future industrial production was found. However, using monthly real equity returns, 1-month lead consumer confidence, 6-month lead change in housing starts and 11-month lag money supply growth are found to be significant. Finally, using those variables and testing both annual and monthly models in out-of-sample data, the result supports the argument that macroeconomic variables do have power in explaining real equity returns.
Keywords: Economic Variables, Stock Return, United States

Chapter I
1.1 Research Background
1.1.1 A Simple Model of Equity Value
In doing valuation of equity securities, the equity value contains expectation regarding future cash flows, the growth rate of those cash flows, and their riskiness. Riskiness of the security is reflected through the discount rate in the Gordon Growth Model and is dependent on the non-diversifiable risk that investors set in market equilibrium.
๐‘ƒ๐‘ก= ฮฃ๐ท๐‘–(1+๐‘)๐‘–โˆž๐‘–=1
In the present value model presented above, Pt represents the stock price at time t, p is a discount rate that includes a risk premium that compensates investors for holding on to the risky asset, and Di is the dividend paid at time i. Hence, the determination of the current price depends solely on the future dividends, the risk-free rate, and the risk premium associated with holding that specific security.
1.1.2 Macroeconomic variables and Equity Value
Macroeconomic variables affect certain drivers of equity value presented above. Two of the most common macroeconomic variables used to proxy for future dividends and the risk premium of equities are industrial production and interest rates, respectively. An increase (decrease) in industrial production is proposed to affect stock price in the same direction, through an increase (decrease) in the expected future dividends. In contrast,
changes in interest rates affect equity prices in the opposite direction, as it increases the denominator value in the Gordon Growth Model.
Changes in interest rates are hypothesized to affect equity prices in two different ways. First, a change in the interest rates affects equity value directly, through the increase in discount rates, and a change in interest rate also indirectly impact the equity value through changes in future production, which then influence future dividends in the numerator of Gordon Growth Model. Higher interest rates decrease investment and future production level, which then translates to lower dividend payment in the long run (Peiro, 2016). Empirically this is proven by study that concludes equity prices in the US are positively impacted by future variation in industrial production and negatively by current changes in interest rates (Peiro, 1996).
Macroeconomic news therefore, can be representative of the risk factors to firmโ€™s cash flows. Economic data partly reflects the prevalent economic environment in which firms operates, which influences the availability of investment opportunities and future cash flows (Chen, Roll, and Ross, 1986; Flannery and Protopapadakis, 2002).
Early studies support the argument that macroeconomic variables influence the risk premium required by investors in determining the discount rate for a security, hence it could be considered as a proxy for pervasive risk factors in the market (Chen, Roll, and Ross, 1986; Priestley, 1996; Kryzanowski et al, 1997). However, later studies show conflicting results that question the evidence of whether equity returns are influenced by macroeconomic developments (Chan, Karcesky, and Lakonishok, 1998; Flannery and Protopapadakis, 2002). There seems to be no existing consensus on whether equity returns can be explained by macroeconomic variables.
1.2 Problem Statements
There is a gap in understanding how various macroeconomic variables affects stock returns, and whether current stock returns also affect economic conditions in the future. Industrial production growth and long-term interest rates have long been documented to significantly affect stock returns, despite the feedback loop relationship may be involved
with these variables and stock returns. Nevertheless, the impacts of macroeconomic developments on stock returns and the direction of the relationship linking them have been unclear and even contradictive across studies. In short, this research seeks to address the following questions:
1. Is there a relationship between change in industrial production, housing starts, or consumer confidence and real equity returns?
2. Is there a relationship between long-term real interest rate, risk premium, or term structure and real equity returns?
3. Is there a relationship between change in money supply (M2) and real equity returns?
4. Is there a relationship between real equity returns in and real economic activity?
1.3 Research Objectives
This research seeks to find evidence and explanation regarding the relationship between various macroeconomic variables and real equity returns in the US stock market. More specifically, this research seeks to find the answer of whether real equity returns predict future industrial production, or industrial production growth can be used to predict real equity returns. The results could offer better clarity on contradictive findings concerning the directions and relationship between macroeconomics variables and equity returns. In addition to that, this research further tests if the relationship that was claimed to hold between certain macroeconomic variables and equity returns in the past still holds when tested using longer sample period (1972-2013). Finally, this paper also seeks to find out whether certain less documented macroeconomic variables, such as the change in housing starts, contributes in explaining variation of real equity returns.
Chapter II
Literature Review
2.1 Macroeconomic Variables and Equity Returns
Since 1960, researches have been done to find macroeconomics variables that could help predict equity returns. The idea was to explain how economic activity or production could be translated into macroeconomic data, and how it could affect prices in the equity market. Money supply is a variable that was commonly used in studies in explaining stock returns, changes in money supply affect the equilibrium position of money in the market, thereby changing the prices of securities and the composition of the investorโ€™s portfolio (Cooper, 1974).
Changes in money supply are also hypothesized to affect real economic variables, such as employment, trade balance, and housing starts, which then have an indirect effect on future equity market returns (Rogalski and Vinso, 1977). These direct and indirect impacts suggest that an increase in money supply has a positive effect on equity market returns. Following this hypothesis, researches have been done to seek the evidence of different macroeconomics variables that influence equity market returns.
Chen, Roll and Ross (1986) are amongst the pioneers who tried to answer whether certain macroeconomic variables could serve as a proxy for risks factors that reward investors in the equity market. They found that macroeconomic variables, such as the term spread between long-term and short-term interest rates, the expected and unexpected inflation, the industrial production, and the spread between high and low-grade bonds, do reward investors in the US equity market.
The use of term spread by Chen, Roll and Ross (1986) had also been found to explain stock and bond returns in a study by Keim and Stambaugh (1986). Furthermore, Fama and French (1989) linked the cyclicality in expected stock returns to the term spread, arguing that a high spread referred to a business cycle through while a low spread referred to a peak in the cycle.

Chen, Roll, and Ross (1986) also included a default spread (the difference between corporate bond yield and government bond yield) in their analysis, to serve as a proxy for business conditions that affect equity returns. They argue that this spread is high during poor economic conditions, as investors shy away from assets of riskier firms and opt for safe-haven securities such as government bond, while the spread is low during good economic condition, when investors are less worried in holding risky assets. On a subsequent study, Chen (1989) proves that the default spread has a negative correlation with past and future output growth, making it a good variable to represent business conditions that affects expected equity returns.
Bilson, Brailsford, and Hooper (2000) conducted a study focusing on emerging markets equities and found that equity returns in their sample were significantly related to the lagged money supply and the exchange rate but are weakly related to goods prices or real activity.
Study done in the US stock market (Humpe and Macmillan, 2009) concludes that equity prices are positively affected by industrial production and negatively by long-term interest rates as well as the consumer price index. More recently, Peiro (2016) uses an updated sample period in the European market, in an effort to find the dependence of equity returns on macroeconomic variables in the French, German, and the British markets. His findings are similar to those of Humpe and Macmilan (2009), in which he found industrial production and long-term interest rates are two variables having an important explanatory power. Together, those two variables account for about one-half of annual variations in equity prices, with industrial production relates to real stock returns in an increasingly important manner over time, as compared to interest rates.
After establishing empirical fact regarding relationship between economic variables and equity returns, researches began questioning whether the sequence of economic data announcement affect the relative impact to equity returns. With this regard, Flannery and Protopapadakis (2002) look at economic variables announcements made at the beginning of the month and compare the impact of those announcements on equity prices with the impact of announcements made later in the month. They conclude that the sequence of announcement of macroeconomic variables is not as important as the macroeconomic variables themselves in affecting equity returns.
2.2 Nominal Economic Variables and Equity Returns
Early papers discussing the relationship between equity returns and macroeconomic variables focuses on the use of variables often labelled nominal economic variables. Those nominal variables include money supply, inflation rate and the level of interest rates, usually proxied by nominal bond yields.
Initial research by Fama and Schwert (1977) found negative relationship between inflation and nominal stock returns. However, that study was not able to conclude on the causality between inflation and return. Further researches on the topic show that inflation and money supply growth are negatively related to stock returns, with the rational that higher money supply will trigger inflation, which then forces central bank to raise interest rates that is detrimental to equity returns (Flannery and Protopapadakis, 2002; Peace and Roley, 1985; Bodie, 1976).
Decades after the initial study on the topic, Chan, Karceski, and Lakonishok (1998) refute the argument that macroeconomics factors affect equity returns, on the basis that any relationship found to be statistically significant in previous studies was simply due to randomly generated series of numbers that were picking up covariation in returns.
The contradictive conclusion reached by authors who worked on the relationship between equity returns and inflation makes it difficult to conclude on whether stocks can effectively protect invested capital from the eroding effect of inflation. Nevertheless, equities are commonly theorized to be an effective hedge against inflation. Thinking of it from a capital structure perspective, equity security is a residual claim on the nominal assets of the firm. Thus, it is a residual claim on the cash and cash equivalent as well as on the real assets of the firm. The inflation hedge property is claimed to exist because in the presence of inflationary pressure, an increase in the value of the real assets of the firm should also translate into a higher value for a claim on the residual asset of that firm. However, it is important to note that this inflation-hedge property gets weaker apart when a firm holds a substantial amount of cash balance, receivables, or fixed income securities.
If we exclude financial and utilities firms, the median cash ratio of US firms was 13.3% in 2006, a significant increase since from 5.5% in 1980. Kahle, and Stulz (2009) found that firms now have less receivables and more cash on hand. In addition to that, they also concluded that the cash flows of the firms were more volatile, and firms were spending more on research and development in 2006 than they were in 1980. Given the higher cash flow volatilities in 2006, one can argue that firms keep more cash on hand to fund their research and development activities, in order to avoid having to cut on research and development during economic downturn. By doing so, they should be even more exposed to inflation, which increase the importance of investigating whether stocks are a good hedge against inflation.
If we assume that investors price financial assets in real terms, i.e., considering the erosive impact of inflation on their future spending abilities, then we could conclude that inflation affects equity market returns. In fact, Chen, Roll and Ross (1986) found that both expected and unexpected inflation can helps explain variations in equity returns.
In the Gordon Growth Model discussed earlier, the discount rate employed to discount dividends has two components, the risk-free rate and the risk premium, which both can be derived from nominal government and corporate bond yields. Apart from the level of interest rate itself, it was found that the slope of the yield curve also matters in pricing equity value. Risk premium in this model refers to the one present in the fixed income market that corresponds to the additional return required to hold a risky corporate debt as opposed to holding a risk-free government debt (Chen, Roll and Ross, 1986).
2.3 Real Economic Variables and Equity Returns
Real economic variables are also frequently used in academic research to explain equity returns. One of the first such real economic variable used to explain equity returns is the industrial production. Fama (1990) shows industrial production could explain more of the equity return variation than other real variables such as the growth rates of the Gross National Product or the Gross Private Investment.
The level of production in the economy is hypothesized to correlate positively with higher cash flows generated by the firm. Indeed, in a booming economy where production is rising, the increase in production is commonly associated with an increase in the profitability of the firm, resulting in higher expected cash flows for investors. Assuming stock prices reflect investorโ€™s expectation of future cash flows in the future, it means that the change in stock prices partially reflects the level of industrial production investors are expecting in the coming months (Chen, Roll, Ross, 1986). Cutler, Poterba and Summers (1989) also found that industrial production growth was significantly and positively correlated with real equity returns. This relationship also holds in the European market, where study done by Canova and De Nicolo (1995) shows that equity returns are found correlate significantly to industrial production level.
However, even though some models of real macroeconomic variables were found to explain some variations in equity returns, the R-squared of those models are commonly very low, implying it could only explain a small fraction of variation in equity market returns. Therefore, one could not rely on such model for predictions (Roll, 1988). McQueen and Roley (1993) argued that this low R-Square comes from the fact that economic data surprises have different implications for equities in different stage of the business cycle. Therefore, they claimed few variables could explain equity returns in a consistent manner across the business cycle. They found that using a model with constant coefficients, only two out of the eight macroeconomics variables considered are significant in explaining returns on the S&P500. One of those two variable is the month-on-month growth in industrial production. When considering a model that varies in different economic regimes, they found that six out of the eight macroeconomic variables considered became significant in explaining market returns.
The argument relating to economic data surprise having different implications in different economic regimes is also supported by Boyd, Jagannathan and Hu (2001). Their research shows surprisingly high unemployment rate have a positive impact on equity returns during economic expansion but a negative one during economic contraction.

Therefore, the nature of relationship between level of employment and equity returns is complex and less agreed upon. On one hand, an increase in employment typically depicts an improving economic environment, which tend to be accompanied by positive equity returns. However, as the employment level increase, it can also be followed a rise the inflation rate, which can trigger monetary policy tightening. As a result, an environment of increasing interest rate translates into lower equity returns (Peiro, 2016).
To investigate whether macroeconomic variables could be implemented to earn excess return in the stock market, Lamont (2000) considered portfolios that tracked real variables such as the growth rate of the industrial production, consumption and labor income. The result of that study is that portfolios could generate abnormal positive returns by using signal from some of these real indicators. However, it was found that portfolios tracking the growth in the Consumer Price Index, i.e, portfolios tracking the inflation rate, could not generate abnormal positive returns.
Another decent variable that helps explain equity returns is consumer confidence, often proxied by the University of Michigan consumer confidence index (CCI). Otoo (1999) found that returns of the Wilshire 5000 Index are related to future rise in consumer confidence. Meanwhile, Fisher and Statman (2002) found a statistically significant relationship between the returns of the S&P500 Index and the change in consumer confidence.
As a forecasting variable, Lemmon and Portniaguina (2006) found that consumer confidence holds forecasting power for the returns of small cap stocks in the US market, but this relationship holds only for the period after 1997. In a subsequent study, Fisher and Statman (2002) found consumer confidence can help predict future economic activity but they found no statistically significant relationship when trying to explain the S&P500 Index returns with past consumer confidence data. However, they also note that consumer confidence tends to move in tandem with equity prices, the relationship between equity returns and concurrent consumer confidence is statistically significant.
The housing starts figure is also often referred to, alongside the consumer confidence, as a leading indicator for equity returns. However, the relationship between that variable and equity returns is not heavily documented. Given it is often paired with consumer confidence, one could theorize it could also have an interesting explanatory power investigates on whether it could be used as a replacement of consumer confidence in some model to explain return variations.
2.4 Cause and Effect Relationship Between Macroeconomic Variables and Equity Returns
The direction of the relationship between macroeconomics variables and equity returns is a source of debate in the literature. There is strong evidence of a very significant positive relationship between industrial production and returns of the U.S. equity market. However, the cause and effect of that relationship is not clear. For instance, some papers found that models with lags of industrial production could explain current equity returns (James, Koreisha, and Partch, 1985). On the other hand, other studies arrive to the opposite conclusion.
Even though the direction of the relationship between the equity market performance and macroeconomic variables is not yet fully understood, most authors, treat stock market returns as an endogenous variable that responds to macroeconomic forces. This is in line with the approach taken by Chen, Roll and Ross (1986) when they first tackled the problem of explaining equity returns with macroeconomic variables.
Fama (1990) argues that macroeconomic variables should not predict equity returns. His argument is that stock prices should reflects expected future cash flows. Therefore, as future cash flow should also relate to production, then stock prices should predict the future macroeconomic environment. Fama showed the existence of a strong relationship between real stock returns and the growth rate in industrial production. Those conclusions also agree with the earlier findings of Fischer and Merton (1984) and recent study by Peiro (2016), who concludes that equity returns do forecast future industrial production. In his study, Peiro (2016) found that equity prices predict movements in production one year ahead and equity prices move concurrently with interest rates. One-half of the variations in equity returns can be explained by changes in industrial production and interest rates.

2.5 Theoretical Framework
Figure 2.5. Real equity returns and macroeconomic explanatory candidates
Chapter III
Research Methodology
3.1 Data and Data Sources
To investigate the relationship between various macroeconomic variables and stock returns, we use data from the 1972 โ€“ 2013 to capture the long-term relationship between the variables outlined in Table 3.1 and real US equity returns. We consider both monthly and annual data for our analysis.
Table 3.1 present the variables used in the analysis, the data used to construct each one of those variable, as well as the sources of those data.
Table 3.1. Data and Variables Summary
VariableData Data SourceReal Stock Return YoY S&P 500 Total Return Index (SPXT)BloombergUS Consumer Price Index, All Items (CPI)US Bureau of Labor StatisticsIP Growth YoYUS Industrial Production Index (IP)Federal Reserve Real Interest RateUS Government Benchmarks, 10 years, USD (USG10)MacrobondUS Consumer Price Index, All Items (CPI)US Bureau of Labor StatisticsM2 Growth YoYMoney Supply, USD, (M2)US Conference BoardHousing Starts Growth YoYUS Residential Construction Starts, New Privately Owned (HS)US Census BureauConsumer Confidence Growth YoYConsumer Confidence Index (CCI)US Bureau of Labor StatisticsRisk PremiumUS Corporate Benchmarks, 10 year, USD, BBB rated (USC10)MacrobondUS Government Benchmarks, 10 years, USD (USG10)MacrobondTerm StructureUS Government Benchmarks, 10 years, USD (USG10)MacrobondUS Government Benchmarks, T-Bills, Secondary Market, 1 Month Yield (USG3m)Federal Reserve
The formulas for constructing each variable is presented below:
1- Inflation rate YoY (๐œ‹๐‘ก):
2- Nominal stock return YoY (๐‘Ÿ๐‘ก):
3- Real equity returns YoY (๐‘…๐‘ก):
๐‘…๐ธ๐‘…๐‘ก=๐‘Ÿ๐‘กโˆ’ ๐œ‹๐‘ก
4- IP Growth YoY (ฮ”๐ผ๐‘ƒ๐‘ก):
5- Real Interest Rate (๐ผ๐‘…๐‘ก):
๐ผ๐‘…๐‘ก= ๐‘ˆ๐‘†๐บ10๐‘กโˆ’๐œ‹๐‘ก
6- M2 Growth YoY (ฮ”๐ผ๐‘ƒ๐‘ก):
7- Housing Starts Growth YoY (ฮ”๐ป๐‘†)
8- Consumer Confidence Growth YoY (๐ท๐ถ๐ถ):
9- Risk Premium (๐‘…๐‘ƒ๐‘ก):
๐‘…๐‘ƒ๐‘ก= ๐‘ˆ๐‘†๐ถ10๐‘กโˆ’๐‘ˆ๐‘†๐บ10๐‘ก
10- Term Structure (๐‘‡๐‘†๐‘ก):
๐‘‡๐‘†๐‘ก= ๐‘ˆ๐‘†๐บ10๐‘กโˆ’๐‘ˆ๐‘†๐บ3๐‘š๐‘ก
3.2 Research Design
3.2.1 Research Framework
This paper attempts to provide empirical evidence on US equity returns and macroeconomic variables with a longer sample period (1972-2013). Most of these variables have previously been studied and documented in different sample period, but most of the researches are limited to a narrow sample period, with the exception of study by Peiro (2016). Our analysis combines variables from some of those studies, but also includes other ones, less documented, but considered as good leading indicators of equity returns by practitioners (see table 3.1).
The approach taken in this research follows Peiro (2016) in using real terms for both macroeconomic variables and equity returns. The motivation to work with real equity returns is further reinforced by the work of Fama (1990), which highlights the inflation hedge property exhibited by equities over the 1953-1997 period. Furthermore, one of our regressor variable is the industrial production, which itself measures production of real goods in the manufacturing sector. Therefore, working in terms of real equity returns provides consistency.
Selection of the time interval is also an important factor in analyzing the ability of macroeconomic variables to explain real equity returns, and this paper use both a monthly and annual time interval. The reason comes from the goal of the study, which is to compare the results obtained from monthly and annual returns models with the findings of previous papers. As an example, when regressing stock returns over macroeconomic variables, Fama and Kaul (1981) found that when they could only explain 6% of the variation in monthly returns. However, using annual returns, they obtained a model with
a much higher R-squared of 43%. Similarly, Peiro (2016) found out that the he could explain up to 44% of the variation in real equity returns when using a model with annual returns while only 14% of the variation in real returns could be explained by using a model with monthly data. Performing the analysis on both annual and monthly returns also allows us to compare and possibly contrast the set of variables which provide significant explanatory power for each model.
3.2.2 Regression Model
To measure how the set of macroeconomics variables presented in table 1 relates to the real equity returns over our sample period, linear regression model is used. Real equity returns are treated as the dependent variable and are regressed against macroeconomic variables, which are used as independent variables in the linear model. Annual and monthly dataset is used to develop the model that best explain the variation in real equity returns. The linear regression model has the following form:
๐‘…๐ธ๐‘…๐‘–ฬ‚= ๐›ผ +๐›ฝ1๐‘‹1,๐‘– + ๐›ฝ2๐‘‹2,๐‘– + …+ ๐›ฝ๐‘›๐‘‹๐‘›,๐‘– +๐œ€๐‘–
๐‘…๐ธ๐‘…๐‘–ฬ‚ = ๐‘๐‘Ÿ๐‘’๐‘‘๐‘–๐‘๐‘ก๐‘’๐‘‘ ๐‘Ÿ๐‘’๐‘Ž๐‘™ ๐‘’๐‘ž๐‘ข๐‘–๐‘ก๐‘ฆ ๐‘Ÿ๐‘’๐‘ก๐‘ข๐‘Ÿ๐‘›๐‘  ๐‘–๐‘› ๐‘๐‘’๐‘Ÿ๐‘–๐‘œ๐‘‘ ๐‘–
๐›ฝ๐‘–= ๐‘Ÿ๐‘’๐‘”๐‘Ÿ๐‘’๐‘ ๐‘ ๐‘–๐‘œ๐‘› ๐‘๐‘œ๐‘’๐‘“๐‘“๐‘–๐‘๐‘–๐‘’๐‘›๐‘ก ๐‘๐‘œ๐‘Ÿ๐‘Ÿ๐‘’๐‘ ๐‘๐‘œ๐‘›๐‘‘๐‘–๐‘›๐‘” ๐‘ก๐‘œ ๐‘Ÿ๐‘’๐‘”๐‘Ÿ๐‘’๐‘ ๐‘ ๐‘œ๐‘Ÿ ๐‘‹๐‘–
๐œ€๐‘–= ๐‘Ÿ๐‘’๐‘ ๐‘–๐‘‘๐‘ข๐‘Ž๐‘™ ๐‘’๐‘Ÿ๐‘Ÿ๐‘œ๐‘Ÿ ๐‘ก๐‘’๐‘Ÿ๐‘š ๐‘๐‘œ๐‘Ÿ๐‘Ÿ๐‘’๐‘ ๐‘๐‘œ๐‘›๐‘‘๐‘–๐‘›๐‘” ๐‘ก๐‘œ ๐‘๐‘Ÿ๐‘’๐‘‘๐‘–๐‘๐‘ก๐‘–๐‘œ๐‘› ๐‘–
3.2.3 Validating for Stationarity using Unit Root Test
To justify the use of a linear regression model, stationarity check of each macroeconomic variables used as regressors must be done. Unit root test was conducted for each of the time series variables presented in table 1 using the Augmented Dickey-Fuller (ADF) method. The null hypothesis Ho states that the time series possesses a unit root, implying
the variable is not stationary. If the null hypothesis is rejected for a variable, then the non-stationarity is rejected, justifying the possible inclusion of that independent variable in the linear model. In the model using annual real equity returns as the dependent variables, the long-term real interest rate was found to be non-stationary. As some of the values for the real long-term interest rate were negative, first differencing long-term real interest rate gives a figure that is economically hard to interpret. For that reason, it was decided to drop the long-term real interest rate altogether from the analysis.
3.2.4 Specifying Regression Model Variables
Once stationarity is validated, the next step is to find the variables that affect real equity returns, keeping in mind that, as found in past academic studies, some macroeconomic variables could affect stock returns in a leading, concurrent or even lagging time period. For that reason, it is important to not only find which variables help explain equity returns, but also, if applicable, determine the lags or leads of those variables. From findings of past studies and economic rationale, it was decided to limit the range of lags and leads from a one-year lag to a one-year lead for each macroeconomic variable for the annual dataset, and for the analysis of monthly returns, the model allowed lags or leads of up to 12 months for each regressor. This is also justified by the design of our data, which corresponds for many variables in a year-on-year growth rate. To determine the variables, lags, or/and leads that are linked to real equity returns, we did Pearson correlation analysis and univariate regression between real equity returns and each macroeconomic variable to look for variables that is significant at the 5% level. The results allow us to determine initial candidate for the independent variables on which to regress the real equity returns.
3.2.5 Best-Subsets Approach
In constructing the multivariate regression model, it is important to keep in mind that each regressor added to the model may helps explain part of the variation in returns but is not justified by the addition of complexity in the model, or possibly without an economic
justification. To remedy this issue and potentially avoid overfitting the model, the adjusted R-squared is considered, which penalizes for the number of regressors used in the model. ๐ด๐‘‘๐‘—๐‘ข๐‘ ๐‘ก๐‘’๐‘‘ ๐‘…2 = 1 โ€“ [(1โˆ’๐‘Ÿ2)๐‘›โˆ’1๐‘›โˆ’๐‘˜โˆ’1]
๐‘Ÿ2=๐‘…๐‘’๐‘”๐‘Ÿ๐‘’๐‘ ๐‘ ๐‘–๐‘œ๐‘›๐‘  ๐‘ ๐‘ข๐‘š ๐‘œ๐‘“ ๐‘ ๐‘ž๐‘ข๐‘Ž๐‘Ÿ๐‘’๐‘ ๐‘‡๐‘œ๐‘ก๐‘Ž๐‘™ ๐‘ ๐‘ข๐‘š ๐‘œ๐‘“ ๐‘ ๐‘ž๐‘ข๐‘Ž๐‘Ÿ๐‘’๐‘ 
n = sample size
k = number of independent variables in the regression equation
To start, regression between real equity returns over the complete set of independent variables is conducted. To narrow the number of independent variables in the regression, variables that are significant at the 5% level in the Pearson correlation table are included.
From the regression result, we then look for the significance of each regressor at the 10% level. If few regressors are found to be not significant, the least significant one, i.e., the one with the largest p-value, is dropped from the model. This process is repeated until we obtain a linear model where all regressors are significant at the 10% level.
As illustrated in figure 2, we use the best-subsets approach to obtain the most efficient model possible. It deals with the potential multicollinearity between independent variables and exclude redundant variables (see section 3.2.6 for more on multicollinearity testing). The efficiency of each linear model is measured by its adjusted R-squared and the presence of low or no multicollinearity. In addition to that, an F-test, as described below, is performed to assess the significance of every coefficients in the model simultaneously.
๐น0 =(๐‘†๐‘†๐‘…๐‘Ÿ โˆ’ ๐‘†๐‘†๐‘†๐‘ข๐‘Ÿ) / ๐‘ž๐‘†๐‘†๐‘…๐‘ข๐‘Ÿ/(๐‘›โˆ’(๐‘˜+1))
SSRr = Sum of Squared Residual of the Restricted Model
SSRur = Sum of Squared Residual of the Unrestricted Model
n = Number of Observation
k = Number of Independent Variables in the Unrestricted Model
General hypothesis for F-test:
โ€ข H0: b0 = b1 = b2 = b3 = bi = 0 (intercept only model is superior)
โ€ข Ha: at least one of biโ‰  0 (model with predictors is superior)
Validating the significance of the model could be done through the p-value of the F-test. If that p-value is greater than the desired level of significance โˆ, then the null hypothesis is accepted. On the other hand, if the p-value is less than โˆ, then we can conclude that the linear model using the set of regressors provides a better fit of the data than the model with intercept only.
Figure 3.2.5. Best-Subsets Approach (Levine et al., 2008)
3.2.6 Assumptions tests
To justify the use of a linear model to make statistical inferences or predict real equity returns, the linear model obtained must respect the 4 following assumptions: no or low multicollinearity, independence and normality of residual terms, and homoscedasticity. Each of these assumptions and the associated test is briefly explained below. Testing for Multicollinearity between Independent Variables
To investigate high correlation between independent variables, a test on multicollinearity has to be done. A common approach is to use the Variance Inflationary Factor (VIF) method to test for multicollinearity: ๐‘‰๐ผ๐น๐‘–=11โˆ’๐‘…๐‘–2
VIFi = Variance Inflationary Factor for the independent variable i
๐‘…๐‘–2 =๐ด๐‘‘๐‘—๐‘ข๐‘ ๐‘ก๐‘’๐‘‘ ๐‘Ÿ2 ๐‘ฃ๐‘Ž๐‘™๐‘ข๐‘’ ๐‘œ๐‘“ ๐‘š๐‘œ๐‘‘๐‘’๐‘™ ๐‘ข๐‘ ๐‘–๐‘›๐‘” ๐‘ฃ๐‘Ž๐‘Ÿ๐‘–๐‘Ž๐‘๐‘™๐‘’ ๐‘– ๐‘Ž๐‘  ๐‘‘๐‘’๐‘๐‘’๐‘›๐‘‘๐‘’๐‘›๐‘ก and other variables (except i) as the independent variables
When a variable has a VIF > 5, it means that the variable has a strong correlation with another independent variable used in the model and must be eliminated (Levine et al., 2008). Independence of Residual Terms
To use a linear regression model, it is necessary that the residuals terms be independent. Given the use of time series data, there must be no autocorrelation between residuals terms. To verify the independence of the prediction error terms, we use the Durbin-Watson test. The test statistic of the Durbin-Watson test is given below:
๐ท= ฮฃ(๐‘’๐‘–โˆ’๐‘’๐‘–โˆ’1)2๐‘›๐‘–=2ฮฃ๐‘’๐‘–2๐‘›๐‘–=1 ๐‘’๐‘–=๐‘Œ๐‘–โˆ’๐‘Œฬ‚๐‘–
Where: ๐‘›=๐‘›๐‘ข๐‘š๐‘๐‘’๐‘Ÿ ๐‘œ๐‘“ ๐‘œ๐‘๐‘’๐‘Ÿ๐‘ฃ๐‘Ž๐‘ก๐‘–๐‘œ๐‘›๐‘ 
๐‘’๐‘–=๐‘Ÿ๐‘’๐‘ ๐‘–๐‘‘๐‘ข๐‘Ž๐‘™ ๐‘ฃ๐‘Ž๐‘™๐‘ข๐‘’
๐‘Œ๐‘–=๐‘Ž๐‘๐‘ก๐‘ข๐‘Ž๐‘™ ๐‘ฃ๐‘Ž๐‘™๐‘ข๐‘’ ๐‘œ๐‘“ ๐‘‘๐‘’๐‘๐‘’๐‘›๐‘‘๐‘’๐‘›๐‘ก ๐‘ฃ๐‘Ž๐‘Ÿ๐‘–๐‘Ž๐‘๐‘™๐‘’ ๐‘Œ
๐‘Œฬ‚๐‘–=๐‘๐‘Ÿ๐‘’๐‘‘๐‘–๐‘๐‘ก๐‘’๐‘‘ ๐‘ฃ๐‘Ž๐‘™๐‘ข๐‘’ ๐‘“๐‘Ÿ๐‘œ๐‘š ๐‘Ÿ๐‘’๐‘”๐‘Ÿ๐‘’๐‘ ๐‘ ๐‘–๐‘œ๐‘› ๐‘š๐‘œ๐‘‘๐‘’๐‘™
The value of the test statistic D is then compared to a value in the Durbin-Watson table corresponding to a significance level โˆ, a sample of size n and the number of independent variables k to conclude if autocorrelation is present or not. That table specifies an upper value dU as well as a lower value dL. If we have D>dU, then no autocorrelation is present between residual terms, while on the other hand, if D<dL, then autocorrelation is present between residual terms. Finally, if dL<D<dU, then it is not possible to conclude whether autocorrelation is present or not and if further testing is required. When the Durbin-Watson statistic is inconclusive, Runs test is conducted to conclude whether autocorrelation of the error terms is present. Normality of Residual Terms
While the distribution of the dependent variables and of the independent variables is not of significant importance to use a linear regression model, the error terms (๐‘’๐‘–) must be normally distributed. There are several options to verify the normality of residuals, one of them is Kolmogorov-Smirnov test, which is used in this study. Derivation of the residualsโ€™ empirical distribution function is formulated below:
๐น๐‘›(๐‘ฅ) = 1๐‘› ฮฃ๐ผ[โˆ’โˆž,๐‘ฅ]๐‘›๐‘–=1(๐‘‹๐‘–)
Fn(x) = empirical distribution function
n = number of sample
๐ผ[โˆ’โˆž,๐‘ฅ] = indicator function, equal to 1 if Xi < x or 0 otherwise
Then, computation of the Kolmogorov Smirnov statistic Dn is as follows: ๐ท๐‘› = ๐‘ ๐‘ข๐‘ ๐‘ฅ| ๐น๐‘›(๐‘ฅ) โˆ’ ๐น(๐‘ฅ) |
Where ๐น(๐‘ฅ) represents the hypothesizes distribution function. Here, given the assumption, that hypothetic distribution of residual terms would be a normal distribution.
Then, hypothesis testing is performed, based on the p-value of the above Kolmogorov Smirnov statistic, where:
โ€ข H0: residual value distribution is normal
โ€ข Ha: residual value distribution is not normal
If the p-value is greater than the desired level of confidence โˆ, then H0 is accepted, implying that the error terms in the linear model satisfy the normality assumption of linear regression models. If the p-value is less than โˆ, then Ho would be rejected, implying a violation of the normality assumption.
22 Homoscedasticity
Homoscedasticity, or constant variance of the error terms, is also a central assumption of linear regression models. When heteroscedasticity is present, on the other hand, it becomes difficult to obtain the error terms for forecast values of the dependent variable, as the standard deviation in confidence intervals will not be constant across forecast values. For some values, it will be higher, while it will be lower for some other ones. Plotting residual terms against predicted values is a graphical way to visualize if heteroscedasticity is present (See figure 3 below).
Figure Heteroscedasticity and Homoscedasticity Illustration
Heteroscedasticity can be tested using the Glejser test, in which the residuals of the initial regression are themselves regressed on each variable suspected to have non-constant variance. More precisely, the absolute value of the residuals is regressed over the independent variable, as well as two transformations of that same variable (see the 3 regression equations below).
|๐œ–๐‘–|=๐›พ๐‘œ+๐›พ1๐‘‹1+๐›ฟ๐‘– |๐œ–๐‘–|=๐›พ๐‘œ+๐›พ1โˆš๐‘‹1+๐›ฟ๐‘– |๐œ–๐‘–|=๐›พ๐‘œ+๐›พ11๐‘‹1+๐›ฟ๐‘–
From the 3 regression models above, one with the highest R-squared is selected and is used to do hypothesis testing, where the null hypothesis is that there is no heteroscedasticity indication. Based on the p-value, null hypothesis is accepted if the p-value is greater than โˆ, and rejected when p-value is below โˆ.
3.2.7 Regression with Heteroscedasticity-Robust Standard Errors
If any of the assumptions regarding independence of errors, normality of error terms, or homoscedasticity is violated, transformation of one or more of the independent variables are needed to meet these assumptions. Various method such as using heteroscedastic-robust standard error and differencing technique (quadratic model and interaction model) could also be used.
If heteroscedasticity happens to be present, an estimate derived from the linear regression model is still an unbiased and consistent estimator, meaning that the estimated coefficient of the regression is not affected. The real issue comes from the fact that heteroscedasticity might results in the normal standard error to be biased. This affects the calculations of the t-statistic and F-statistic that often causes Type I error, which can lead to the rejection of a true null hypothesis H0 (Yamano, 2009).
To correct for heteroscedasticity, several options are available. A popular solution is to use heteroscedasticity-robust standard errors, also known as the White-Huber standard errors. These standard errors are typically more conservative than the homoscedastic standard errors. Even without heteroscedasticity being present, we could use White-Huber standard errors to calculate t-statistic in ordinary least-square regression (Yamano, 2009).
In the application of using heteroscedasticity-robust standard errors, this study was done by regressing each model again using the SPSS macro written by Andrew F. Hayes that accommodates heteroscedastic robust standard errors (Foster, 2011).
3.3 Research Hypotheses
Annual real equity returns model: ๐‘น๐‘ฌ๐‘น๐‘จ=๐œท๐ŸŽ+๐œท๐Ÿ ๐‘ฎ๐‘ฐ๐‘ท+๐œท๐Ÿ ๐‘ด๐Ÿ+๐œท๐Ÿ‘๐‘ผ๐Ÿ‘+๐œท๐Ÿ’ ๐‘ซ๐‘ช๐‘ช+๐œท๐Ÿ“ ๐‘ซ๐‘ฏ๐‘บ+๐œท๐Ÿ” ๐‘น๐‘ท+๐œท๐Ÿ• ๐‘ป๐‘บ
โ€ข H0: YoY growth in industrial production, YoY growth in money supply, unemployment rate, YoY change in consumer confidence, YoY change in housing starts, risk premium, and term structure do not affect YoY change in real equity returns.
โ€ข Ha: YoY growth in industrial production, YoY growth in money supply, unemployment rate, YoY change in consumer confidence, YoY change in housing starts, risk premium, and term structure affect YoY change in real equity returns.
Monthly real equity returns model: ๐‘น๐‘ฌ๐‘น๐‘ด=๐œท๐ŸŽ+๐œท๐Ÿ ๐‘ฎ๐‘ฐ๐‘ท+๐œท๐Ÿ ๐‘ด๐Ÿ+๐œท๐Ÿ‘ ๐‘ผ๐Ÿ‘+๐œท๐Ÿ’ ๐‘ซ๐‘ช๐‘ช+๐œท๐Ÿ“ ๐‘ซ๐‘ฏ๐‘บ+๐œท๐Ÿ” ๐‘น๐‘ท+๐œท๐Ÿ• ๐‘ป๐‘บ
โ€ข H0: YoY growth in industrial production, YoY growth in money supply, unemployment rate, YoY change in consumer confidence, YoY change in housing starts, risk premium, and term structure do not affect MoM change in real equity returns.
โ€ข Ha: YoY growth in industrial production, YoY growth in money supply, unemployment rate, YoY change in consumer confidence, YoY change in housing starts, risk premium, and term structure affect MoM change in real equity returns.
Chapter IV
Results and Discussion
4.1 Results
4.1.1 Correlation
Table 6.1 Variables Correlation with Annual Dataset (1972-2013)
To understand the relationship and direction between real equity return and various economic variables, we conducted Pearson correlation analysis to both annual and monthly dataset for the period 1972-2013. From the annual data correlation results, we could observe that real equity return is significantly correlated with YoY growth in Industrial Production, change in Housing Starts, change in Consumer Confidence, Risk Premium, next 1-year YoY change in Industrial Production, and next 1-year unemployment rate.
The result is in-line with the economic intuition that when the economy is on expansion, equity return is expected to be positive alongside growth in industrial production, housing starts, and consumer confidence. Meanwhile, good economic condition is also negatively correlated with risk premium, where the yield spread between risky corporate bonds and government bonds is expected to be lower.
RERGIPM2U3DHSDCCRPTSLAG_LTRIRLAG_GIPLAG_M2LAG_U3LAG_DHSLAG_DCCLAG_RPLAG_TSLEAD_LTRIRLEAD_GIPLEAD_M2LEAD_U3LEAD_DHSLEAD_DCCLEAD_RPLEAD_TSRER1.500**-.056-.036.585**.639**-.452**.061.200-.105-.*-.009-.359*-.220-.073-.210-.154GIP1-.101-.319*.383*.673**-.755**.050.345*.**.396**-.023.454**-.103.122.000-.531**-.205-.349*-.300-.456**M21.199.042-.038.302-.123-.181.045.557**.**.201-.020-.051.028-.042U31.203.063.473**.435**-.158-.545**.138.761**-.283-.307*.552**.**.398**.488**.023.477**DHS1.558**-.212.214.158-.201-.010.397**-.119-.044.320*.461**.199.442**.098-.263-.119.221-.319*-.005DCC1-.484**.362*.064-.317*.008.472**.243-.070.432**.338*.103.393*.116-.309*-.024-.056-.337*-.165RP1.193-.248-.317*-.021.033-.338*-.344*.251-.168.153-.025.076.560**.313*.428**.254.607**TS1.248-.460**-.057.479**-.018-.180.608**.498**.198.444**-.212.078.472**.342*-.155.510**LAG_LTRIR1.**.441**.105-.289-.279-.061-.130-.178.066LAG_GIP1-.051-.325*.400**.685**-.748**.067-.238-.212-.077-.406**-.180-.229-.102-.504**LAG_M21.170.095-.008.287-.081-.135-.080.281.154-.112-.131-.051-.096LAG_U31.187.057.472**.428**.244.361*.195.382*.276.265-.209.218LAG_DHS1.563**-.208.227-.057.060-.099-.362*-.071-.271-.294-.218LAG_DCC1-.485**.350*-.136-.125.033-.327*-.116-.318*-.095-.372*LAG_RP1.199.090.296-.**LAG_TS1-.100.371*-.334*-.300.035.156-.476**.010LEAD_LTRIR1.**LEAD_GIP1-.190-.294.393*.659**-.749**.070LEAD_M21.263.037-.096.370*-.111LEAD_U31.195.079.459**.424**LEAD_DHS1.571**-.213.220LEAD_DCC1-.468**.382*LEAD_RP1.185LEAD_TS1*. Correlation is significant at the 0.05 level (2-tailed).**. Correlation is significant at the 0.01 level (2-tailed).Correlations
Interestingly, equity return is positively correlated with the next 1-year YoY growth in Industrial Production and negatively correlated with next 1-year unemployment rate. This could potentially mean two things, first is that equity return may have a feedback loop to the economy, where increasing return translates to confidence on future economic condition and spurs company to hire more employees. Or second, equity return itself is a leading indicator of future economic condition, here proxied by industrial production growth and unemployment rate in the future.
Table 6.2 Variables Correlation with Monthly dataset (1972-2013)
From the monthly dataset correlation analysis, the result confirms the direction of the relationship between various economic indicator and real equity return. Next one to twelve months YoY change in Housing Starts is significantly correlated with equity return, which means that equity return this month may be able to predict Housing Starts figure in the upcoming 12 months. Similar result is found with Consumer Confidence and Industrial Production, while the term structure in the past ten to twelve months may be used to predict the equity return this month.
The results make sense economically because as discussed previously, stock return could be used as an indicator of future economic condition, which is also proxied by Housing Starts and Consumer Confidence. Manufacturing activities, as indicated by
growth in Industrial Production, also increase during period of economic expansion, which is usually priced in by the market five to twelve months before.
4.1.2 Regression and Forecasting Result with Annual Dataset
Following the best-subset approach to build our model for annual time-period, we come up with two forecasting model that pass various assumption tests in Ordinary Least Square Regression. These two models are outlined below:
๐‘…๐ธ๐‘…๐ด=0.170+0.225 ๐ท๐ป๐‘†+0.206 ๐ท๐ถ๐ถโˆ’4.55 ๐‘…๐‘ƒ
Adjusted R-Square: 48.1%
๐‘…๐ธ๐‘…๐ด=0.064+0.213 ๐ท๐ป๐‘†+0.275 ๐ท๐ถ๐ถ
Adjusted R-Square: 45.8%
RER: Real Equity Return (% YoY)
DHS: Change in Housing Starts (% YoY)
DCC: Change in Consumer Confidence (% YoY)
RP: Risk Premium or the spread between 10-year BBB US Corporate Bond and Treasury Bond
Our finding shows that for our model, there is no multicollinearity in the model (VIF <5 for all variables), no autocorrelation of errors (Durbin-Watson = 1.601 and Runs Test p-value = 0.639), and the errors are independent (Kolmogorov-Smirnoff p-value = 0.2). However, there is heteroscedasticity for variable DCC (YoY Change in Consumer Confidence) and RP (Risk Premium). To avoid rejecting a true H0, we ran the model regression again using the Heteroscedasticity-Robust Standard Errors (Hayes and Cai, 2007). After correcting for heteroscedasticity, it was found that the model variables are still significant at the 10% level. However, we do not necessarily want to be strict in using a precise alpha (e.g. 5%), as we care more about the prediction ability of the model than mere statistical
significance. Our modelsโ€™ adjusted r-square of 48.1% and 45.8% is slightly higher than those developed by Peiro (2016) and Fama and Kaul (1981), which are at 44% and 43% respectively.
Run MATRIX procedure:
HC Method
Criterion Variable
Model Fit:
R-sq F df1 df2 p
.5192 16.1017 3.0000 38.0000 .0000
Heteroscedasticity-Consistent Regression Results
Coeff SE(HC) t P>|t|
Constant .1695 .0691 2.4552 .0188
DHS .2250 .0702 3.2039 .0027
DCC .2064 .0795 2.5955 .0134
RP -4.5499 2.5970 -1.7519 .0879
From the two different models we developed, we test our modelsโ€™ prediction ability to annual, out-of-sample data in the period 2014-2017, the result is shown below; Our model is based on data from the period 1972-2013. Comparing the Real Equity Return to the Forecasted Real Equity Return by the two models, it was found that our models have a decent predicting power for out-of-sample, annual equity return (R-Square 70.01% and 42.59%), but less so when performed on rolling monthly basis (R-Square 5.42% and 14.99%).
Table Forecasting Results using Annual Model
RER (YoY)RER=0.170+0.225 DHS+0.206 DCC-4.55 RPRER=0.064+0.213 DHS+0.275 DCC201717.61%12.36%10.86%20168.76%11.79%12.07%20150.04%1.75%5.18%201413.02%16.64%18.02%R-Square70.01%42.59%
Table Forecasting Results using Annual Model on Monthly Rolling Time Period
4.1.3 Regression and Forecasting Result with Monthly Dataset
Our investigation of the relationship between various macroeconomic variables on Real Month-on-Month Stock Return also concludes that change in housing starts and consumer confidence significantly affect Real Stock Return. Following the exact same method above on a monthly dataset, we arrived at the equation specified below:
๐‘…๐ธ๐‘…๐‘€=0.014โˆ’0.130 ๐ฟ๐ด๐บ11_๐‘€2+0.028 ๐ฟ๐ธ๐ด๐ท6_๐ท๐ป๐‘†+0.028 ๐ฟ๐ธ๐ด๐ท1_๐ท๐ถ๐ถ
Adjusted R-Square: 6.4%
RER: Real Equity Returns (% YoY)
DateRER (YoY)Model 1*Model 2**DateRER (YoY)Model 1*Model 2**2017-01-0115.75%16.84%14.25%2015-07-0110.40%13.35%9.69%2016-12-019.23%15.36%12.33%2015-06-016.97%16.55%12.11%2016-11-016.07%13.22%10.38%2015-05-0111.12%15.22%12.01%2016-10-012.77%18.92%15.81%2015-04-0112.32%16.70%13.35%2016-09-0112.86%8.05%4.11%2015-03-0111.98%13.49%10.37%2016-08-0110.74%11.48%7.20%2015-02-0114.51%12.90%10.19%2016-07-014.59%12.43%8.03%2015-01-0113.51%19.77%17.04%2016-06-012.88%11.68%7.87%2014-12-0112.16%17.49%15.22%2016-05-010.65%11.38%6.76%2014-11-0114.32%11.84%9.21%2016-04-010.06%9.65%5.10%2014-10-0114.32%19.05%16.51%2016-03-010.89%14.11%9.64%2014-09-0116.34%19.03%16.80%2016-02-01-7.35%16.64%11.52%2014-08-0120.81%14.46%11.21%2016-01-01-2.01%10.18%5.45%2014-07-0113.69%17.34%14.24%2015-12-010.71%10.63%5.86%2014-06-0119.97%14.34%11.21%2015-11-012.27%15.17%10.91%2014-05-0116.47%12.81%9.30%2015-10-014.93%10.23%6.19%2014-04-0116.59%17.40%14.04%2015-09-01-0.63%15.96%11.89%2014-03-0118.19%13.06%10.48%2015-08-010.24%16.68%13.33%2014-02-0121.50%15.96%14.27%R-Square Model 1*R-Square Model 2***Model 1: RER=0.170+0.225 DHS+0.206 DCC-4.55 RP*Model 2: RER=0.064+0.213 DHS+0.275 DCC5.42%14.99%
LAG11_M2: 11 months lag of Money Supply Growth (% YoY)
LEAD6_DHS: 6 months lead of change in Housing Starts (% YoY)
Lead1_DCC: 1 month lead of change in Consumer Confidence (% YoY)
The model specified above has no multicollinearity (VIF<5) and no positive autocorrelation among residual terms (Durbin-Watson Test>Du). However, the assumption on independence of error terms is violated (Kolmogorov-Smirnoff 0.024) and heteroscedasticity is present on LEAD1_DCC variable (p-value= 0.000). To correct for this issue, we ran the regression again using heteroscedasticity-robust standard error and found that all the variables are still significant. Our modelโ€™s adjusted r-square is at 6.4% for monthly real equity return, higher than those developed by Fama and Kaul (1981) that has r-square of 6% but is lower than Peiroโ€™s (1986) model that has 14% of r-square.
Run MATRIX procedure:
HC Method
Criterion Variable
Model Fit:
R-sq F df1 df2 p
.0694 8.6633 3.0000 501.0000 .0000
Heteroscedasticity-Consistent Regression Results
Coeff SE(HC) t P>|t|
Constant .0140 .0039 3.5985 .0004
LAG11_M2 -.1296 .0540 -2.4024 .0167
LEAD6_DH .0276 .0095 2.9167 .0037
LEAD1_DC .0278 .0094 2.9672 .0031
Using 36 out-of-sample dataset from 2014 to 2016, we use our monthly model to forecast Month-on-Month Real Equity Return and found that it explains 3.75% of the variation in Real Equity Return. The forecasting power is not as strong as implementing the model to
forecast annual return due to the noise in Real Equity Return on a Month-to-Month basis that could be impacted by news not directly related to the general economic strength, such as geopolitical tension, industry scandal, and government policy.
Table 4.1.3 Forecasting Results using Monthly Time Period
4.2 Discussion
Our research shows that equity returns do have relationship with macroeconomic developments, especially those that commonly considered as leading indicators themselves such as housing starts and consumer confidence. Contrary to study done by Flannery and Protopapadakis (2002), we found that equity returns are affected by housing starts. The difference in results may be attributed to the use of real equity return in our research instead of nominal equity return and the different time period and interval being used.
DateRER (MoM)ModelDateRER (MoM)Model2017-01-011.37%1.32%2015-07-011.92%1.06%2016-12-011.66%1.27%2015-06-01-2.24%0.94%2016-11-013.47%1.07%2015-05-010.95%1.06%2016-10-01-2.11%1.08%2015-04-010.87%0.88%2016-09-01-0.17%1.32%2015-03-01-1.88%1.53%2016-08-01-0.07%0.90%2015-02-015.40%1.42%2016-07-013.63%0.98%2015-01-01-2.44%1.25%2016-06-01-0.01%1.03%2014-12-010.07%2.06%2016-05-011.53%0.81%2014-11-012.82%1.68%2016-04-010.04%1.26%2014-10-012.41%1.55%2016-03-016.36%0.22%2014-09-01-1.42%1.22%2016-02-010.06%0.72%2014-08-013.94%1.17%2016-01-01-5.16%0.65%2014-07-01-1.51%1.42%2015-12-01-1.50%0.48%2014-06-011.91%1.12%2015-11-010.17%0.62%2014-05-012.15%0.54%2015-10-017.97%0.67%2014-04-010.52%1.13%2015-09-01-2.29%1.16%2014-03-010.65%1.21%2015-08-01-6.22%1.64%2014-02-014.40%1.21%3.75%RER=0.014-0.130 LAG11_M2+0.028 LEAD6_DHS+0.028 LEAD1_DCCR-Squared (3 Year Period)
Industrial production has been used by almost all researcher in this topic as an output variable of the economy. We do find that real equity returns correlates positively with current and future industrial production change, confirming the results done by Cutler, Poterba, and Summers (1989) and Canova and De Nicolo (1995). This is not surprising, as the argument that stock prices reflect investorโ€™s confidence on future economic condition has long been established by Chen, Roll, and Ross (1986).
A more interesting conclusion is the causality effect between industrial production growth and real equity returns. Related to this, we found that real equity returns forecast growth in the future industrial production in the month 5 to 12 and the relationship is significantly positive. This finding also gives a greater support to Fama (1990) that argues macroeconomic variables does not predict stock return, but it is stock return that predicts future macroeconomic development. Fama (1990), Fischer and Merton (1984), and Peiro (2016) all found that real equity returns forecast future production level one year ahead, which is in line with our findings, and contrary to the arguments that past industrial production predicts equity returns (James, Koreisha, and Partch, 1985).
However, the explanatory power of industrial production to real equity returns is low due to the different implication of economic data surprise to returns in different business cycle. McQueen and Roley (1993) have similar findings that out of eight macroeconomic variables being tested, only two becomes significant in its relationship with equity returns, one of them being month-on-month growth in industrial production. Controlling the economic regimes increase the number of significant variables from two to six.
Our findings also confirm that changes in money supply does affect real economic variables, which then affect future stock market returns (Cooper ,1974); Rogalski and Vinso,1977). Bilson, Brailsford and Hooper (2000) does a similar study in the emerging market, finding that equity returns were significantly related to lagged money supply, exchange rate, and weakly related to real activity. However, contrary to few literatures, we found that money supply is negatively correlated with future real equity returns, supporting previous findings by Peace and Roley (1985) and Bodie (1976). More specifically, on our monthly model, lag 11 months of money supply negatively affects real equity return. Our intuition is that increase in money supply creates inflation in the
following periods and force central bank to tighten the monetary policy, which is detrimental to equity returns. This argument is backed by the findings that changes in real economic activity affects money supply growth, which then results in expected inflation and increase in interest rates that is detrimental to equity returns. (Geske and Roll, 1983; James, Koreisha, and Partch, 1985).
Risk premium does significantly and negatively affect real equity returns, where risk premium here is defined as the spread between BBB corporate bond yield minus US Treasury bond yield with 10 years maturity. The result is very intuitive as it is common that investors shy away from risky assets such as equity and corporate debt altogether during period of high volatility or poor economic condition (Chen, Roll, and Ross, 1986).
This argument also backs Chen, Roll, and Ross (1986) statement that macroeconomic variables do serve as a proxy for risk factors in the stock market. On a separate study, Chen (1989) found that risk premium has a negative relationship with past and future output growth, which makes it a good proxy of business conditions that indirectly affect expected equity returns. Although we do not investigate the transmission effect of risk premium to real equity returns, we do find that risk premium is negatively related to both growth in industrial production, real equity returns, consumer confidence, and is positively related to unemployment rate. This result concludes that risk premium tends to be higher during poor economic condition and it could be attributed to deterioration of market confidence in the economy.
Ten months to twelve months lags of term spread are also found to have positive effect on current real equity returns. Although these variables are not significant in our model, they have a statistically significant correlation with real equity returns. A steepening of the yield curve is commonly associated with economic expansion, where the long-end of yield curve increase by more than the short-term end, or the short end of the curve drops by more than the long end. This could be attributed to higher expectation of inflation in the long-run as the economy improves, which increases the long-end of the curve, or due to the policy rate cut that boost the economy through lending activities. Fama and French (1989) argues that high term spread indicates a business cycleโ€™s bottom and low term spread indicates peak of the cycle.
Relating equity returns with the labor market, the causality between unemployment rates and equity returns is less clear. It could be that high equity return embeds expectation of good economic condition ahead, hence lower unemployment rate, or it could be low unemployment rates is a proxy of good economic condition and moves concurrently with higher equity returns.
We found that real equity returns predict future 1-year unemployment rate, and the relationship is negative and significant. The logical explanation is that high equity return today is an expectation by the market of good economic condition in the future, which is reflected by among other variables, lower unemployment rate in the next 1-year period. However, we do not find significant relationship between real equity returns and current unemployment rates. Boyd, Jagannathan, and Hu (2001) argues that high unemployment rate has a positive impact to stock price during economic expansion but decreases stock price during economic contraction. On the other hand, Peiro (2016) states that increase in employment will also be followed by increase in inflation and interest rates, which is detrimental to stock price; our findings do not support this hypothesis.
Causality of high stock return and consumer confidence is not clearly determined. Otoo (1999) argues that high stock returns can lead to increases in consumer confidence through two channels, first one being that high stock return increases investor wealth, therefore increasing the consumer confidence. Second, stock market is leading indicator to the economy; high stock returns are a leading indicator to high income in the future, therefore boosting consumer confidence. In the paper, Otoo (1999) also found that consumer confidence is moving concurrently with Wilshire 5000 Index.
Previous literature suggests that high consumer confidence during one period is generally followed by low equity returns. Fisher and Statman (2002) use consumer confidence figure that is available by the end of each month to predict returns in the following calendar month and found that there is a significant relationship between consumer confidence and subsequent Nasdaq and small cap stock returns, but not to S&P500. They also documented that high stock returns on various equity indices, including S&P500, are concurrently moving with an increase in consumer confidence, this relationship is significant statistically.
Our study confirms the later, that as leading indicators, stock returns and consumer confidence are moving together in the same direction. Change in consumer confidence and housing starts is a good predictor of equity returns in all three models. Our monthly RER model incorporates 1-month leading consumer confidence and 6-months leading change in housing starts as a predictor of current month equity return, which could mean two things. First, stock market incorporates expectation of future economic condition faster than consumer confidence and housing starts figure does. Or second, there is a one month reporting lag for Consumer Confidence figure announcement, from the data collection process up to the publication in the third week of the month by the Conference Board. We found no satisfying explanation for the relationship between current real equity returns and 6-months leading housing starts growth. In fact, it would be interesting to find out whether high stock return leads real estate developer to construct new private houses, as economic condition is expected to improve.
๐‘…๐ธ๐‘…๐ด=0.170+0.225 ๐ท๐ป๐‘†+0.206 ๐ท๐ถ๐ถโˆ’4.55 ๐‘…๐‘ƒ
๐‘…๐ธ๐‘…๐ด=0.064+0.213 ๐ท๐ป๐‘†+0.275 ๐ท๐ถ๐ถ
๐‘…๐ธ๐‘…๐‘€=0.014โˆ’0.130 ๐ฟ๐ด๐บ11_๐‘€2+0.028 ๐ฟ๐ธ๐ด๐ท6_๐ท๐ป๐‘†+0.028 ๐ฟ๐ธ๐ด๐ท1_๐ท๐ถ๐ถ
Chapter IV
Our annual model suggests that Real Equity Returns are best explained by the change in Consumer Confidence, Housing Starts, and Risk Premium during the same period. Real Equity Return, Consumer Confidence, and Housing Starts are all a proxy for future economic condition while Risk Premium affects stock return through the risk aversion prevailing in the market.
As specified by our model, change in Housing Starts and Consumer Confidence have positive relationship with Real Equity Returns while Risk Premium has a negative relationship with Real Equity Returns. Meanwhile, higher Risk Premium, often occurring during economic contraction is associated with lower equity returns, hence the negative sign.
๐‘…๐ธ๐‘…๐ด=0.170+0.225 ๐ท๐ป๐‘†+0.206 ๐ท๐ถ๐ถโˆ’4.55 ๐‘…๐‘ƒ ๐‘…๐ธ๐‘…๐ด=0.064+0.213 ๐ท๐ป๐‘†+0.275 ๐ท๐ถ๐ถ
We also found that Real Equity Returns are highly correlated with change in Industrial Production in the next five to eleven months, although the variable is not significant in our annual and monthly model. This is consistent with previous literatures that conclude equity return as a predictor of the next one-year economic output, as often proxied by industrial production.
๐‘…๐ธ๐‘…๐‘€=0.014โˆ’0.130 ๐ฟ๐ด๐บ11_๐‘€2+0.028 ๐ฟ๐ธ๐ด๐ท6_๐ท๐ป๐‘†+0.028 ๐ฟ๐ธ๐ด๐ท1_๐ท๐ถ๐ถ
However, when we use monthly dataset to analyze the relationship in a more discrete manner, we found that change in consumer confidence moves one month after the change in real equity returns while change in housing starts moves six months after. We also note that change in money supply eleven months ago has a negative impact to current real equity returns, because increase (decrease) in money supply will generally creates inflation (disinflation/deflation) and forces central bank to tighten (ease) the monetary policy, which is detrimental (supportive) to equity returns. This also means that among the group of leading indicators, real equity return is the variable that is most responsive to expectation regarding future economic condition.

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“La Citadelle, Quebec City”


The photograph was taken during my third month studying at McGill University, Canada. Back then, I was exhausted from pulling all nighter almost everyday to keep up with the abundant tasks the program required (it is a Master of Management in Finance). My mind was in chaos, my body exhausted and the lack of sleep really drove my emotional control. Knowing I have to had a break, I decided to go to Quebec City after the final exams are over, before the beginning of another course. It was just me, my camera, and a suitcase.

The weather was cold, and strong wind was blowing my face as I stand on the top of the hill. But the sky was just so gorgeous that I could not leave it before it turned black. The first day’s sunset was not very bright, as the cloud was covering the sky. This photograph was taken on the second day, the sun’s reflection on Chateau Frontenac was just right, the cloud’s orange color was a warmth in the middle of the cold evening.

I spend 3 days in the Old Town area f the city, touring around museum and historic sites in the day, and watching the sunset on the evenings. It was one of the best trip I have taken so far, where I could think about life and reflect on my priorities. I have this picture set as the background of my laptop now, as it makes me more relaxed before working on financial modeling and studying.



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Things You Must Do in Quebec City for Solo Traveler

In the last two months, I have been working and studying excessively at McGill University. I have been in campus past midnight several times in a week and eating a lot of Korean foods located at a building nearby. When Labor Day comes, I planned a trip to Quebec City to treat myself and detached from all the stress coming from university life and finding a job. I am traveling alone, without any expectation of the city, to explore this beautiful place all by myself.

PSX_20170901_143453Chateau Frontenca from the Citadel during the day

Currently, I am writing this post on Dufferin Terrace, sitting in a chair outside the Starbuck cafรฉ in Chateau Frontenac. It is 9.39 in the morning and tourist starts coming to the terrace. There is a lady singing classical music in front of the chateau, I see people taking photographs of each other, Indian and Chinese tourist go on and off their bus.

PSX_20170901_143300Quebec Cityscape taken from Observatoire de la Capitale

From my three days trip, these are the highlight and most enjoyable moment to me:

  1. Hike to Montmorency Falls

I took the fifteen minutes trip from the city by Uber, costing me CAD$20 for a one-way trip. The admission to the waterfall is less than CAD$5, but you might have a difficulty in going back to the city. Luckily, there is an Uber dropping a passenger in the falls, so I could find my way back easily. Once you arrived at the terminal building, there is a bridge to get closer to the waterfall where you could find the stairs to the top of the hill. Mind you that there is a lot of staircase and it is quite challenging to get to the top (but is possible if you take it slowly). There is several โ€œcheckpointโ€ on the way to the top where you could take photograph and rest. After reaching the top of the stairs, I walk further to the suspension bridge above the waterfall to take some pictures.

PSX_20170902_144254Montmorency Falls

PSX_20170902_144339ย Montmorency Falls

Why is it enjoyable? If you are lucky, you will see a rainbow at the foot of the fall. And as you get closer to the waterfall, feel the water splashing your face. The view from the second checkpoint is the best, in my opinion.


  1. Sunrise and Sunset at the Citadelle

I am staying at Hotel Cap Diamant, a nice place in the city and is very close to the Citadelle, so I could wake up at 5.30 in the morning and watch the sunrise by 5.50 am at the top of Citadelle facing Chateau Frontenac. There is an entry gate if you walk across Dufferin Terrace, next to US consulate building, leading to the hill (do not mistaken it with the stairs at the end of Dufferin Terrace, which leads to Abrahamโ€™s plain).

PSX_20170901_235720Sunrise from the Citadel

PSX_20170903_072735Sunrise from the Citadel

PSX_20170903_072931Sunrise from the Citadel

PSX_20170902_000143Quebec City at Night

When I watched the sunrise this morning, only a couple was there beside me, which make the place a great spot for having time alone. I found the sunset to be very gorgeous; the backdrop of the city lights mixed with the orange sky is just perfect. And if you have the time, wait for one more hour after the sunset to see the cityscape at night, which is equally amazing. I like to spend my time listening to classical music while taking the photographs (bring a tripod if you are a professional). The wind is strong up on the hill, so make sure you are appropriately dressed like an astronaut.


  1. Touring Around the City on Foot

The old town area is not very big and it is possible to see 70% of the historical site and museum in one day, which I did on the first day. I visited Rue de Petit Chaplain three times in different time (early morning, noon, evening) despite not buying anything there. Make sure you visit Notre-Dame Basilica de Quebec, which has amazing architecture inside and outside. Also visit Morrin Library, which was a prison and then converted into college. There is a guided tour (CAD$9-15) for 45 minutes every hour, which is worth your time. For the sake of enjoyment alone, I walked on Dufferin Terrace over 10 times in my three days stay, just because it felt amazing to have wind blowing to your face and listen to the street musician.

PSX_20170902_144159Notre-Dame Basilica

PSX_20170902_161131Terrace Dufferin

PSX_20170903_073048ย Rue de Petit Champlain in the morning

  1. Sunset from Levis

One and a half hour before sunset, take a ferry across the Saint Lawrence River (CAD$3.55) and wait for the sunset. The ferry is available every 30 minutes in the evening and took only 15 minutes to get across. In the ferry terminal at Levis, there is a Tim Hortons store, where I pick up a big cup of hot tea to drink while waiting for the sunset. Beside the ferry terminal, there is a small park with very convenient chairs and beach-chairs where you could see the city over the river.

PSX_20170902_191047Sunset from across Saint Lawrence River

PSX_20170902_233944The City at Night

Why is it enjoyable? I spent my time waiting by reading a book and listening to classical music (a recurring theme, isnโ€™t it?) while waiting for the sky to turn orange, then dark blue. I just love the experience of seeing the sky change its color and the city lights turned on one-by-one.


  1. Listening to Street Performers (Especially Claude Berger)

This activity is actually not planned in my trip, but I found it to be the most enjoyable experience during the three days trip, seriously. I was passing the street in front of Chateau Frontenac on Saturday night after having the sunset from Levis, to found a small crowd around a street musician named Claude Berger. He is very good at playing saxophone and singing old-time songs, which made you feel the city is becoming more romantic as time goes by. There is a love in the air. I sat for more than an hour and listen to his performance, as the crowd grew larger and larger.

The next thing you know, people are dancing on the street and the environment gets lively pretty fast. You may want to come early and reserve a seat in front of the Manoir Hotel, where he usually performs. Some of his performances that I love are โ€œMy Wayโ€ (his last song), โ€œWhat a Wonderful Worldโ€, and โ€œStand by Meโ€.


PSX_20170902_000256Terrace Dufferin at Night

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Taipei One Day Trip


We arrived last night in Taipei, on a transit flight to New York. Last night we slept at 1 am, but this morning we managed to woke up at 6 am to have a day trip in the city. We have breakfast at Cuto Hotel, where we stayed at (given by eva air), 40 minutes away from the city by car. Around 8 am we departed from our hotel and rode a taxi to the city. It is rush hour time, so there was quite a traffic on the highway and in the city , but we managed to arrive at Taipei 101 slightly before 9 am.


The observatory on Taipei 101 is open at 9 am, we were the first guest today so we could enjoy all the view without so many crowd. We spent about an hour on the deck, there was a small theatre as well at the 91st floor showing the building process of Taipei 101. The view is great, but the lighting could be better in the evening rather than in the morning.


Afterwards, my mother and sister wanted to go to Line store. Yes, it is the social messaging app that is fanous for it’s iconic characters. It is located nearby, about 10 minutes walk away. The store is located on a luxury brand complex, including several brands such as Hermรฉs and Chanel. While my mother and sister were shopping, I walked around to capture Taipei 101 from the ground. There were also few people doing weddding photoshoot in the complex.

It was 12 am when we were finished, so we rushed back to the shopping mall at Taipei 101. Initially we want to eat at Din Tai Fung, but it was lunch time and the queue was very long, so we decided to take away a burger and eat it at hotel.

We took a taxi from the mall with an old driver who does not speak English at all, mind you that most people in Taipei does not speak english or speak very little of it. Our hotel is quite far from the city and although our driver had a gps, he could not use it very well. We got lost and miss an exit on the highway, before eventually I helped him with the navigation using body languange and very basic Mandarin. When we arrived at our hotel, we have to paid NTD 1700 ($60). He asked us to pay only NTD 1500, but we just could not, we feel sorry for him.

It was 2.15 pm. At the hotel we had our lunch and took a shower before taking a bus to airport at 4 pm. We have to paid an extra of NTD 1500 ($55) for the late check out. I received my Financial Risk Manager Level 2 exam result, which I passed! The shuttle to airport was free, arranged by eva air. Taipei airport is very clean and has many branded goods store, we take a look around but shoppped nothing. Our flight departed at 6.20 pm and we begin our 14 hours flight to New York.

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A Lesson from Seneca on Life

Recently I have been reading the writing’s of Seneca, a popular stoic written during the Roman era. I have read the writings several time before but reading it again and again has always give me new perspective, that is the reason I recommend people to read the same book every two years, because our experience during those period may provide us with different way of thinking.

One message that is clear throughout Seneca’s writing is that most human waste their time on unnecessary preoccupation and activities. It’s not that we are given a short time, but rather we waste those time unwisely. Let’s take a very common example in our daily life, when we are faced with a project that we deemed as difficult and time consuming, it is our nature to delay doing the project. We often make planning on when we will do it, but when the time comes, we defer doing the project to tomorrow. In my own experience recently, I often distract myself with social media and reading email instead of studying for an exam. Such activities are counterproductive and hinder our progress to finish the main task at hand.

Now let’s look at the broader application to life in general. Sometimes I look at people like a drunken sailor, who keeps on rowing their boat (life) without first setting a direction on where they want to go. They may say things like,”wherever I arrive, that’s where I am destined to go”. No wonder that some of us are living a life in the same way we have been living in the past several years. It is important to have a goal to be achieved and a timetable for its completion, without it, our life is like a boat floating on the ocean. Very few times, the wind is favourable and bring us to a beautiful island. Most of the time, however, we are just floating on the water until our time is up.

Seneca also teach about having a balanced life, in social setting and in private life. A man ย busy with daily occupation may be so absorbed to his job, as if it worth his whole life. When retirement comes, he find it meaningless to live since he is not useful to anyone. But it couldn’t be further from the truth, in fact he may find enjoyment in his solitude, a luxury he may not be able to obtained in his work. True, he may not be as functional to public service as he was, but public service is not limited to a formal position. Teaching a children kindness, manner, and other social work also counts as public service.

In short, his writing teaches me to:

  • Have a plan for life, what I want to achieve and when
  • Make a plan for achieving those goals, and do what it takes to achieve them without procrastinating when a task is due
  • Have a balanced life in both social and private setting. We never know when our time is up, so it is best to enjoy every day as if it is our last, while working as if we will live forever.

โ€œIt is not that we have so little time but that we lose so much. … The life we receive is not short but we make it so; we are not ill provided but use what we have wastefully.โ€
โ€•ย Seneca,ย On the Shortness of Life


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