Josine Romme
Studentnumber 10991123 University of Amsterdam
Economics & Business – Finance and Organization Supervisor: Sjoerd van den Hauwe
Date: 15-07-2020
CONSUMPTION BASED ASSET
PRICING MODELS
Abstract
Consumption-based asset pricing models are built on strong economic intuition, however have proven to hold weak forecasting power over the risk premium especially over the length
of one business cycle. Consumption-aggregate wealth ratio has predictive power over risk premia through investors’ expectations. The relationship is assumed to be nonlinear as it is influenced by the state of the economy. A consumption-based model including a recession state component is proposed to forecast excess returns within the business cycle. To estimate
the effect of the market state on the predictability of excess returns by macroeconomic factors, a quantitative research on historical data from the S&P500 is executed. Quarterly forecasts are estimated and the effect of the recession state variable is taken into account. Results show that the state of the economy affects the relationship between
consumption-aggregate wealth ratio and risk premium. This is attributed to investors’ increased risk aversion caused by recessions. In future research the risk aversion and variation over the
business cycle could be further explored.
1. Introduction
A fundamental topic in finance is the equity premium puzzle (Jacobs, Pallage, & Robe, 2013). The inability of economic models to explain average returns on the market portfolio over riskless assets, constitutes one of the central research questions in financial economics (Cochrane, 2005). This risk premium is determined by both the riskiness of an asset and the attitude of investors towards risk (Yoon, 2017). To estimate the risk premium, most applied work in finance use portfolio-based models where covariance with market risk is a forecaster for excess returns (Berk & DeMarzo, 2017). Breeden et al. (1979) found that the excess return on any security is proportional to its covariance with respect to aggregate consumption. However, consumption-based models have been rejected broadly on historical data (Campbell & Cochrane, 2000).
Traditional models like the Capital Asset Pricing Model, have been found to have only weak forecasting power for excess returns over the length of one business cycle and fail to explain cross-sectional returns on assets (Berk & DeMarzo, 2017). With the introduction of factor models by Fama and French (1993) cross-section of returns improved, but these
models lack economic intuition. Consumption-based models have, despite their shortcomings, a well-preserved theoretical framework with an unmatched level of purity (Lettau &
Ludvigson, 2001b).
As excess returns vary with the business cycle, Lettau and Ludvigson (2001b) found that macroeconomic variables that share a common trend, hold forecasting power over equity premia at cyclical frequencies. These results provide evidence for the time-variation in the relationship between macroeconomic and an explanation for its fluctuation with the business cycle.
The idea that the risk premium is based on expectations of forward-looking investors and that investor behavior has predictive power over excess returns is explored by Lettau and Ludvigson (2001a). In an attempt to resurrect the previously rejected Consumption-CAPM (Breeden et al., 1979), the consumption-based model was expanded by a conditional scaling term. This improved the model and their findings suggest that an asset’s risk is determined not by its unconditional correlation with the consumption term, but rather by its correlation conditional on the state of the economy.
The state of the economy could improve predictability of asset pricing models. On one hand, the performance of the consumption-based models can be improved by including this. On the other hand it can provide an economic explanation for risk premium, something that
portfolio-based models lack. An insightful link between financial markets and the real economy can be provided. By estimating the variation in the relationship between consumption and risk premia over time and how it is affected by the business cycle,
forecasting power within the business cycle is aimed to be improved. Furthermore, analyzing the relationship between risk factors and excess returns and how it is affected by the business cycle, could contribute to literature on economic intuition behind asset pricing models.
In this paper, the relationship between consumption and the return premium is further explored to provide an economic explanation for risk premium. Weak predictability of excess returns over the length of one business cycle is suspected to be attributable to time-variation in risk premia, which is caused by investors’ time-varying attitudes towards risk (Yoon, 2017). Therefore, the focus will be on the time-variation in the relationship between
consumption and the risk premium. The current part of the business cycle could influence this relationship, as it is found by Guiso et al. (2018) that individual investors’ risk aversion largely increase following a recession.
This thesis builds on the framework by Lettau and Ludvigson (2001b) and expands the proposed asset pricing model by taking the state of the market into account. Including a recession state variable could capture the time-variation in risk aversion.
The question of interest is: Does the state of the economy have a significant effect on the relationship between excess returns and consumption risk? To answer the research question, the assumed relationship between the consumption-aggregate wealth factor and excess returns is estimated first. Expected is that in line with Breeden et al. (1979), Lettau & Ludvigson (2001) and Bianchi et al. (2017), the consumption-aggregate wealth ratio holds forecasting power over excess returns. The model is then expanded with a recession state variable. Expected is that the state of the economy influences the assumed relationship, as Lettau and Ludvigson (2001b) found risk to be correlated to consumption conditional to the state of the economy.
Expected is that the state of the market influences investors’ attitude towards risk, which is related to demanded risk premia on assets (Yoon, 2017).
The thesis consists of six chapters, including the introduction. Chapter two provides an overview of the theory behind consumption-based models and forecasting power of the consumption-aggregate wealth ratio. The hypothesis are described in chapter two as well. In chapter three the data is described. Chapter four describes the methodology and analysis. The results are presented in chapter five. The thesis is concluded in chapter six, where the
2. Literature
This study focuses on the forecasting power of consumption-based asset pricing models within one business cycle. Relevant literature on consumption-based asset pricing models and motivation behind a recession state variable is discussed first, before moving on to the theory behind time-variation in the risk premium and time variation in risk aversion. Finally, their hypothesized links to expected returns are discussed.
2.1 Consumption-aggregate wealth ratio and returns
Links between asset markets and macroeconomics can be suspected according to Campbell & Cochrane (1999) by just observing data characteristics, with the most important being that equity premia seem to rise at business cycle troughs. Campbell & Cochrane (1999) explain this, using the fact that consumption declines towards its trend in a business cycle trough and the curvature of the utility function rises, which means investors’ come to dislike risk more. As a consequence, prices of risky assets fall and expected returns rise. In their model, consumption growth and consumption claim returns are perfectly correlated.
Consumption risk is described as a form of undiversifiable risk by Semenov (2017). Stated is that investors maximize their expected present value of lifetime utility of realized consumption. Investors face capital market risk and an additive background risk, that can’t be diversified. It is stated that in the presence of this risk, investors are unable to fully insure their future consumption which makes consumption uncertain. Semenov (2017) finds that a substantial part of the historical average equity premium can be attributed to this background risk in investors’ consumption. The intuition behind the predictive power of consumption growth, is that investors want to maintain a flat consumption path over time. When higher returns are expected, investors will react by increasing consumption out of asset wealth and labor income, and consumption will rise above its trend (Lettau & Ludvigson, 2001). Bansal & Yaron (2004) state that in response to higher expected returns, investors increase their asset holdings which increases the wealth-consumption ratio. In their model, a decreased
consumption-aggregate wealth ratio is thus associated with a positive risk premium. In line with this theory, consumption risk is associated with a risk premium, and it is expected that deviations from the consumption trend hold forecasting power over excess returns. This is in line with the findings by Lettau and Ludvigson (2001a), and leads to the following hypothesis:
H1: consumption-aggregate wealth ratio has a negative relationship with excess returns.
This relationship forms the theoretical starting point for consumption-based asset pricing models.
2.1.1 Consumption based asset pricing models
The traditional CAPM model is adjusted to form a consumption-CAPM model that uses covariance with marginal utility of consumption as forecaster of excess returns (Breeden et al., 1979). This model was later expanded by Lettau and Ludvigson (2001b) to form a conditional CCAPM, with the consumption-aggregate wealth as a forecaster for excess returns. It was based on the idea that the log of consumption-aggregate wealth ratio predicts asset returns because it is a function of expected future returns on the market portfolio (Campbell & Mankiw, 1989).
As the aggregate wealth ratio is unobservable, Lettau and Ludvigson (2001a) argue that the important predictive components can be expressed in observable components. A cointegrated variable was constructed, combining consumption, asset holdings and current labor income. 𝑐𝑎𝑦! is a cointegrated variable, containing logarithm of consumption 𝑐!, asset
wealth 𝑎!and labor income 𝑦! (Lettau & Ludvigson, 2001a). The trend deviation is defined by 𝑐!− 𝛽𝑎!− (1 − 𝛽)𝑦!, (1)
as it is stated that each period’s consumption consists of investors’ income on assets and labor income. From this definition the expectations of the consumption-aggregate wealth ratio can be derived. Lettau and Ludvigson (2001a) define asset wealth and labor income together as the aggregate wealth. As seen in equation 1, when investor’s aim to keep consumption constant over time, an increase in asset wealth decreases labor income and the consumption-aggregate wealth ratio.
The idea is that these variables share a common trend and deviations from this trend hold predictive power over asset returns. This follows from the fact that the consumption-aggregate wealth ratio summarizes agents’ expectations of future returns on the market portfolio (Lettau and Ludvigson, 2001a).
In an attempt to resurrect the earlier rejected consumption-based CAPM model, Lettau and Ludvigson (2001b) express the model using 𝑐𝑎𝑦!as a proxy for systematic risk. A conditional version is used as they assume risk premia are not constant over time. They find an implied average risk premium for consumption-growth risk. This CCAPM model uses the
covariance of asset returns with the marginal utility of consumption to measure fundamental risk of assets, instead of the covariance of asset returns with returns of the market index like the traditional CAPM. In line with earlier research, it is expected that the trend deviation has predictive power over excess stock returns.
Investors are assumed to be forward-looking and risk attitudes are influenced by future expected income and returns (Guiso et al., 2018).
According to Lettau and Ludvigson (2001b), previous studies and consumption-based models have been rejected as they made inadequate allowance for time variation in the conditional moments of returns, which explains the poor empirical performance. They find that an asset’s risk is determined not by its correlation with the model’s underlying factor, but rather by the correlation conditional on the state on the economy. This supports the idea that the state of the economy impacts the relationship between the consumption-aggregate wealth ratio and excess returns. In this paper, an excess return forecast will be expressed by similar methodology.
2.1.2 Transitory movements
Furthermore, Cochrane and Campbell (2000) find that dips in consumption will predict high expected returns for those periods, but when consumption declines for several years in a row, stock prices fall as well. The movements in the relationship might be transitory. The idea of time-variation in the relationship between consumption-aggregate wealth ratio and stock market movements was confirmed by Chang et al. (2019). This implies not only 𝑐𝑎𝑦!"# is
related to excess returns, but its lag 𝑐𝑎𝑦!$%"#as well. Lettau and Ludvigson (2001a) support this
idea and find that 𝑐𝑎𝑦!$%"#has predictive power over excess returns. Their findings suggest that
deviations from the shared trend in consumption, labor income, and assets are better described as transitory movements in asset wealth than as transitory movements in consumption or labor income.
2.1.3 Monetary policy and reaching for yield
In more recent literature, Bianchi et al. (2017) state that the relationship between consumption and asset returns is non-linear, and infrequent shifts attributable to monetary policy have been found. The CCAPM is expanded, by taking the monetary policy into account. It was found that equity premia are strongly correlated with the real interest rate that is attributable to changes in the monetary policy. Including a factor on monetary policy improved the
forecasting power of the model. In this paper the model by Lettau and Ludvigson (2001b) will be used and expanded by the monetary policy variable and a recession state variable.
The rationale behind this is the idea that investors “reach for yield”. This implies that, as investors attempt to shift portfolio allocations toward higher-return assets in low interest rate environments, return premia adjust (Bianchi et al, 2017). Therefore, a change in monetary policy in combination with reaching for yield will have pricing effects that differ across assets, depending on the riskiness of the assets.
In line with this theory, the variable 𝑐𝑎𝑦! was adjusted to contain an intercept term that has a time-varying mean depending on the existence of a state variable that can take on one of two values, corresponding with the monetary regimes. This variable is denoted by 𝑐𝑎𝑦"# and
will be the variable of interest in the rest of the paper. The full methodology is described by Bianchi et al. (2017). They find that return premia on the market are strongly positively correlated with the interest rate changes attributed to changes in the conduct of monetary policy, and the variable has greater forecasting power than the original 𝑐𝑎𝑦!. The improved predictability of this variable implies that correlation with consumption risk is variable with respect to the monetary regime and supports the idea of a time-varying relationship between the trend deviation term and asset returns. This variable is used as it has improved
forecasting, but the effect of monetary policy on risk premium is beyond the realm of this thesis, as the focus is on the effect of the state of the economy.
2.2 The role of recession state
As stated earlier, forecasting power of several asset pricing models is weak over the length of one business cycle, and performs better in the long term. Cochrane and Campbell (1999) introduce a consumption-based model that explains the procyclical variation of stock prices within the business cycle. They state that equity premia seem to be higher at business cycle troughs than they are at peaks, and investors risk aversion rises as well. Therefore, risky asset prices fall and expected returns rise. This results in a time-varying and countercyclical risk premium. They find that as consumption declines towards the trend, expected returns rise dramatically over the constant risk free rate.
Cochrane and Campbell (1999) base their findings on the idea that consumers don’t fear stocks because of the risk to wealth or consumption, but because stocks are likely to perform worse in times of recession. It is stated that variation across assets in expected returns is driven by variation in covariances with recession more than their variation in covariances
with consumption growth. Therefore, the state of the market could impact the forecasting power of the consumption-aggregate wealth ratio on excess returns. It is implied a recession state variable might improve the model, as risk aversion might be time-varying and therefore the demanded risk premia is not constant. In the model presented in this paper, a variable is included that takes the effect of the state of the market into account. Expected is that
including this variable in the model will improve forecasting power, because the relationship between the consumption-aggregate wealth ratio and excess returns depends on the state of the market. This can be concluded from previous research by Yoon (2017) on time-variation in risk aversion, as elaborated in the next paragraph.
Recessions are defined by the National Bureau of Economic research, as the period between a business cycle peak and trough. Starting from the peak, the economy contracts until a trough is reached. From the trough it expands to a new peak. This distinction between a recession and economic expansion is used in this paper to estimate the effect of a recession state.
2.2.1 Time-varying risk aversion
The risk premium for each asset is determined by both the riskiness of an asset and the attitude of investors towards risk. In an attempt to estimate time-variation in the attitude of investors towards risk, it is approximated by Yoon (2017) as the risk aversion. If the risk premium is time-varying, either the asset’s riskiness, risk attitudes or both of them should be time-varying. If predictability of returns is attributed to the time-varying risk premium, one or both could predict future returns. It was found by Yoon (2017) that risk premium is
sufficiently time varying and its movement can be captured by the movement of investors’ risk aversion.
Guiso et al. (2018) research the idea that risk aversion exhibits large increases following a financial crisis. Risk aversion would be higher after a recession, which would increase risk premia in the period following a recession as investors demand higher returns for the risk. Guiso et al. (2018) suggest that this contributable to expected future income, in particularly labor income. It is suggested that investors become more risk averse as expected future labor income decreases. Therefore, it is expected that the occurrence of a recession affects the relationship between the consumption-aggregate wealth ratio and excess returns. As risk aversion rises after a recession and higher risk premia are demanded, the relationship between a recession state variable and excess returns is expected to be positive.
Suspected is that the state of the economy influences the risk premium through investors’ attitudes towards risk. Risk premium is determined by both the riskiness of an asset and investors’ risk attitudes (Yoon, 2017). If risk premium is time-varying, one or both of these should be time-varying. Yoon (2017) and Guiso et al. (2018) found that time-variation in risk aversion provides an important implication for time-varying risk premium. This leads to the following hypothesis:
H2a: Recession state affects the relationship between the consumption-aggregate wealth ratio and the risk premium.
H2b: Recession state increases risk premium.
3. Data
The financial data consisted of quarterly returns on the S&P500 index from 1951Q1 until 2013Q2, because data on the independent variable is available for this time period and intervals, and contains enough periods of both market states. Excess returns over a riskless asset are taken to define the risk premium. To construct excess returns over the risk free rate, the returns on the 1-month US Treasury bill were used and the log is denoted by 𝑟’. The log of returns on the S&P500 index are denoted by 𝑟#&'((.
Table 1
Summary of descriptive statistics
Obs Mean Std. Dev Min Max
𝑟#&'(( 247 .0173971 .0692389 -.2687005 .2220785 𝑟) 247 .0111765 .0072829 0 .0373663
𝑐𝑎𝑦"# 247 -.001971 .0117675 -.0377882 .0281993
The trend deviation variable, was retrieved from professor Ludvigson’s website (Ludvigson, 2020). The data is quarterly and it is constructed by combining the log of consumption, log of labor income, total household wealth and a term for monetary policy in the United States over a time period of 62 years. The individual variables for consumption, asset wealth and labor income that form the trend deviation term are in per-capita terms, measured in 1992 US dollars. The constructed variable is denoted by 𝑐𝑎𝑦!"#and referred to as
the consumption aggregate wealth ratio. The total data consists of 247 data points and a summary of descriptive statistics is provided in Table 1.
Figure 1 plots the data on consumption-aggregate wealth ratio and returns over time. To compare, the data is expressed in standardized units by dividing with their standard
deviations. As seen in the figure, periods of low returns are often preceded by a dip in the consumption-aggregate wealth ratio, as seen in 1997 and 2006 for example. Both variables seem to show a cyclical movement at a similar frequency.
Figure 1. Returns and consumption-aggregate wealth ratio over time
4. Methodology
4.1 Measurements and procedure
A linear regression was used to estimate quarterly returns on the S&P500. The log of excess returns was the dependent variable. The independent variables were 𝑐𝑎𝑦!"# , its first lag
𝑐𝑎𝑦!$%"# and the dummy variables for the state of the market.
Table 2
Distribution of dummy variable
Recession Expansion Total
Frequency 46 201 247
Percentage 19.62 81.38 100
To estimate the effect of the business cycle by the current state of the economy, a recession state was included. The market is assumed to be in either one of two states, being a recession or expansion. The definition is described by the National Bureau of Economic Research, and data on time intervals of the economic cycles is retrieved from the website (NBER, 2020). The time period from the peak to the trough is defined as a contraction or recession. The time period between the trough going to the peak is defined as an expansion. The expansion state is assumed the base, as the state of interest is the recession state.
An intercept dummy was included as well as a slope dummy, to estimate the interaction between the consumption-aggregate wealth ratio and excess returns in times of an economic recession. The dummies take value 0 in times of an expansion and value 1 in times of a recession. By the NBER definition, 46 quarters are marked periods of economic recession. The distribution of recession and expansion is summarized in Table 2.
4.2 Analyses
Table 3 presents correlations of the variables and autocorrelation in the first lag for all variables. Correlation between the independent variables showed to be small. A negative correlation between consumption-aggregate wealth and excess returns was found. The correlation between consumption-aggregate wealth ratio and a recession state, was found positive.
Table 3
Correlation and autocorrelation
𝑟#&'((− 𝑟) 𝑐𝑎𝑦"# 𝑟𝑒𝑐𝑒𝑠𝑠𝑖𝑜𝑛 𝑟#&'((− 𝑟) 1.00 𝑐𝑎𝑦"# -.158 1.00 𝑟𝑒𝑐𝑒𝑠𝑠𝑖𝑜𝑛 .160 .2052 1.00 𝑎𝑢𝑡𝑜𝑐𝑜𝑟𝑟𝑒𝑙𝑎𝑡𝑖𝑜𝑛 .127 .810 .733
Autocorrelation in the first lag of returns is small as well. The trend deviation term shows a positive autocorrelation of 81% in the first lag. Because other OLS assumptions were not violated, the model is estimated by an OLS regression, with Newey-west corrected standard errors. This is because the structure is assumed to be heteroscedastic and autocorrelated up to
some lag. This is also in line with the method by Lettau and Ludvigson (2001b), where 𝑐𝑎𝑦!is used to forecast excess returns.
To test the hypotheses in order to draw a conclusion about the effect of the consumption aggregate wealth ratio on the risk premium (H1) and the role of the recession state (H2a and H2b), several OLS regression will be executed.
First, a simple regression for the effect of 𝑐𝑎𝑦!"#on excess returns will be conducted.
Next, the first lag of 𝑐𝑎𝑦! will be added, denoted 𝑐𝑎𝑦!$%"#. A regression with a dummy for the
recession state will be executed, to estimate the effect of the dummy on excess returns. The interaction term will be added, to estimate the effect of the state variable on the slope of the regression. To test for the significance of the difference between the market states, an F-test will be conducted. Expected is that there is significant difference between the market states.
5. Results
To test the hypotheses 1, 2a and 2b, four OLS regressions were conducted with excess returns as the dependent variable. A model to forecast excess returns over the S&P500 is estimated, using the consumption-aggregate wealth ratio and a recession state component. In table 4, the results of the empirical analysis are provided. The table reports the coefficients of the one-quarter ahead forecast model of excess returns on the S&P500 over the risk-free rate as defined above. The coefficients and their heteroskedasticity and autocorrelation corrected t-values are provided.
As summarized in table 4, the first regression using only the first lag of consumption-aggregate wealth as an independent variable, does not hold any forecasting power (𝑅*=.000).
In regression II, current period consumption-aggregate wealth ratio does have a significant strong negative effect on excess returns (𝛽 = −.945). In the third regression, both current period and the first lag of consumption-aggregate wealth ratio are included and both have a significant effect on excess return of about the same size, with a different sign (𝛽% =
2.141, 𝛽* = −2.665). In other words, as hypothesized in H1, a negative effect of
consumption-aggregate wealth ratio on next period excess returns was. The effect of current period’s consumption aggregate wealth ratio was found positive.
To test H2a and H2b, the state variables were added in regression IV and V. Including the interaction term with current consumption-aggregate wealth in regression IV, increases 𝑅* to over ten percent. However the interaction term is not significant. Including the
significant coefficient for the effect of a recession on the current consumption-aggregate wealth ratio. The interaction term with lagged consumption-aggregate wealth ratio itself is however not significant. From regression IV, both H2a and H2b were rejected and no significant effect of the recession state on the relationship between consumption-aggregate wealth ratio and excess returns was found. In recession V, the hypotheses are not directly rejected as a significant effect was found (p=.043).
To evaluate the joint significance of the coefficients, an F-test was conducted. Table 5 shows the respective F-values for the regressions with multiple variables. In both regressions that include the recession state, the null hypothesis of the same variance can be rejected at the 1 percent significance level. The results of the joint significance test indicate that the model is significant at the one percent level. The model including the variable performs better than the intercept term alone. This implies that the effect of the combination of variables is significant, even though not all individual independent variables have a significant effect.
Table 4
Forecasting quarterly excess returns
𝐶𝑜𝑛𝑠𝑡𝑎𝑛𝑡 (t-stat) 𝑐𝑎𝑦!$%"# (t-stat) 𝑐𝑎𝑦!"# (t-stat) 𝑟𝑒𝑐𝑒𝑠𝑠𝑖𝑜𝑛 (t-stat) 𝑐𝑎𝑦!"# ∗ 𝑟𝑒𝑐𝑒𝑠𝑠𝑖𝑜𝑛 (t-stat) 𝑐𝑎𝑦!$%"# ∗ 𝑟𝑒𝑐𝑒𝑠𝑠𝑖𝑜𝑛 (t-stat) 𝑅* I .006 (1.19) -.026 (-.06) .000 II .004 (.87) -.945** (-2.11) .025 III .005 (1.04) 2.141*** (3.87) -2.665*** (-4.11) .069 IV .012*** (2.69) 2.034*** (3.66) -2.115*** (-3.27) -.0270* (-1.70) -1.513 (-1.04) .105 V .012*** (2.64) 1.476*** (2.62) -1.656** (-2.53) -.0258* (-1.68) -3.190** (-2.03) 2.176 (1.52) .113
Table 5
F-test for joint significance results
IV V
𝑑𝑓 (4, 241) (5, 240)
𝐹 5.96 5.26
𝑝𝑟𝑜𝑏 > 𝐹 .000 .000
6. Conclusion & Discussion
In this research, excess returns on the S&P500 were forecast in a linear regression, using the consumption-aggregate wealth ratio as a predictive variable and a recession state to estimate the effect of the business cycle component. The goal of this study was to find a variation in the relationship between excess returns and de consumption-aggregate wealth ratio with respect to the state of the economy. The research question, if the state of the economy impacts the relationship between consumption-aggregate wealth ratio and excess returns can be
answered affirmative.
Current time-period consumption-aggregate wealth and excess returns seem to be negatively correlated in all regressions. The first lag however, appears to be positively correlated. This could be attributable to the implied transitory movements. This could be attributable to transitory movements in consumption-aggregate wealth. Investors were assumed to be forward looking. Their consumption behavior today, is adjusted to future expected returns and income according to previously mentioned theory. This could provide an explanation for the difference in effect of consumption-aggregate wealth ratio on next
quarter’s excess returns and the returns thereafter. An interesting topic for further research, would be the time frame of this transitory movements. Several lags of consumption-aggregate wealth could be included to estimate their forecasting power over excess returns.
Another explanation could be the delay between macroeconomic factors and stock price returns. Financial markets might be able to react quickly to shocks in the real economy, where real economy variables could take longer to adjust. Again, this would be interesting for further research.
From previous literature, it was expected that the recession state affects the effect of the consumption-aggregate wealth ratio on the risk premium, and including this will improve forecasting power of the model. This hypothesis is partly rejected, because the interaction
term with current consumption-aggregate wealth ratio was not significant. This might be attributable to the size of the sample, as barely 20 percent of the quarters were qualified as a recession state. The interaction term with the first lag of consumption-aggregate wealth ratio was found not significant, but including this improved the interaction term with current period consumption-aggregate wealth ratio.
It was expected that the occurrence of a recession would increase investors’ risk aversion, which would make them demand a higher risk premium. The intercept dummy for recession state was however negative. During a recession, excess returns over riskless assets is implied to decrease. The findings in this study are therefore not in line with previous literature and theory on asset pricing models. Risk premia are expected to be low in times of an economic expansion, as less risk is assumed. Again this could be attributable to the sample size. Another explanation could be that a lagged recession term should be included, as
investor behavior was suspected to change after a recession instead of during (Yoon, 2017). The results of the empirical analysis showed that including the interaction term taking the effect of the state of the market into account, improved the fitness of the model by about three percent. However, these conclusions should be taken with caution, as results are not convincingly significant.
Limitation of the research arise from the classifications of the business cycle moments that were distinguished. The NBER provided the starting dates of economic cycles (NBER, 2020). The NBER defines a recession as the period in the business cycle between the peak and the through, and an expansion as the period from the trough to the peak. According to this distinction however, a market can only be contracting or expanding. There would be no “steady state” to compare effects of the more volatile markets to. The dummy variable and its classification strongly influences the outcome of the research, as it defines the current point in the business cycle that a datapoint is assigned to. A biased classification biases the
coefficients and their significance. The periods declared as an economic contraction by the NBER could be considered to classify economic recessions (NBER, 2020).
The influence of the recession state on the behavior of excess returns, provides
insights in the movement of the risk premium with business cycle movements. These findings can be used in explaining the linkage between financial markets and the real economy. The state of the real economy could influence investor behavior and risk attitudes, which increases the excess returns demanded for holding risky assets. The findings of this study contribute to the existing literature on economic intuition behind risk premium and asset pricing models.
Further research could be aimed at explaining the cross-section of asset returns with macroeconomic variables. The factor model by Fama and French (1993) could be expanded with a recession state, to estimate the influence of the business cycle on different portfolios. Furthermore, the time-variation in risk aversion is an interesting field for extended research on the intuition behind movements in the demanded risk premium.
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