The Total Wealth model and the cross-section of stock returns

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Master thesis

The Total Wealth model and the cross-section of stock returns

Karina van Kuijk 11853581

MSc Finance: Asset Management July 2018

Thesis supervisor: mw. dr. E. Eiling

Abstract

The static CAPM has been rejected by academic researches for its empirical failings. The equity market beta fails to explain the cross-section of stock returns. This paper aims to improve the linear asset pricing model by capturing returns of the total wealth portfolio rather than just the equity market returns. A new model is proposed, which is called the Total Wealth model. The proposed model includes four factors, which are the equity market factor, the human capital factor, the real estate factor, and the private business factor. Results of Fama-MacBeth regressions of different stock portfolios on multiple asset pricing models show that the Total Wealth model definitely improves the CAPM. In all tests, the Total Wealth model is the second best performing model to explain the cross-section of excess stock returns. It can be stated that the components of the wealth portfolio are important for asset pricing and perform the best when combining them into one model.

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Statement of originality

This document is written by Student Karina van Kuijk who declares to take full responsibility for the contents of this document.

I declare that the text and the work presented in this document are original and that no sources other than those mentioned in the text and its references have been used in creating it.

The Faculty of Economics and Business is responsible solely for the supervision of completion of the work, not for the contents.

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1. Introduction

The Capital Asset Pricing Model (CAPM) is the standard model used for a long time in asset pricing. William Sharpe won the Nobel Prize for his contribution to the CAPM in 1990. Nowadays, the model is still used by academics and investors in asset pricing and portfolio management. The static CAPM uses the equity market beta to explain the excess returns of the market portfolio. The equity market beta is the equity market risk premium, which is the difference between the expected market return and the risk-free rate. The CAPM states that the expected returns on securities are positive linear to their market beta. (Fama & French, 1992).

However, a number of studies reject the classical model for multiple reasons. The rejection of the CAPM is caused by both theoretical and empirical failings. One main reason is the inability of the CAPM to explain the cross-section of stock returns. The lack of empirical support for the CAPM makes the subject interesting to investigate. For years, it is under discussion whether academics and investors can rely on asset pricing models in real life situations.

Multiple researchers aim to improve the CAPM in order to explain returns of the market portfolio. This is where factor based models are constructed. Factor based models include economic variables which are added to the model as factors to explain stock returns. In this way, the CAPM model is extended with more variables rather than just the equity market risk. One famous factor based model is the three factor model of Fama and French (1993). This model expands the CAPM with a size and book-to-market equity factor. More recently, Fama and French (2015) upgraded the model to a five factor model by adding a profitability and investment factor. Jagannathan and Wang (1996) propose the conditional version of the CAPM, which assumes that the betas and market risk premium vary over time.

This thesis builds further on the existing literature on factor based models. The market portfolio consists of more components rather than just traded financial assets. This makes it interesting to investigate whether components of the aggregate wealth portfolio of the investor are important for asset pricing. This thesis focusses on variables from the total wealth portfolio and the cross-section of excess stock returns.

Human capital, real estate, and private businesses form a substantial part of the aggregate wealth portfolio of households. Human capital is one of the biggest sources of personal income

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of the investor. Besides the income from wages and salaries, the income from the investor could be generated from private businesses. This makes entrepreneurial income also a part of the total wealth portfolio. Real estate is both held as a residence and as an investment in the portfolio. It is interesting to research the relation between these wealth factors and stock returns because they can be important for asset pricing.

Earlier researchers have examined the components of the wealth portfolio in asset pricing. Human capital returns (Jagannathan & Wang, 1996; Eiling (2013), Real estate returns (Kullman, 2002) and proprietary income returns (Heaton and Lucas, 2000) are proven to help explain the cross-section of stock returns. However, in the existing literature, each factor is tested separately in order to explain the cross-section of stock returns. This paper proposes a new variant of the linear asset pricing model, the Total Wealth model. This new model combines the components of the wealth portfolio in one multifactor model. The Total Wealth model includes a constant and four factors in total. In this research, these four factors are called the wealth factors. The factors examined are the equity market risk factor, the human capital factor, the real estate factor, and the private business factor. The constant refers to the pricing error. The model is used to explain the cross-section of excess stock returns. The Total Wealth model is a contribution to the existing literature because it combines factors of the total wealth portfolio in one model, instead of testing them separately. Using this model, there could be directly tested which components of the overall wealth portfolio are important for asset pricing.

The main research question of this thesis is whether human capital returns, real estate returns and private business returns could explain the cross-sectional variation in excess stock returns. The excess stock returns are defined as the risk premium. This is the expected stock return in excess of the risk-free rate. Following the existing literature, the expectation is that the wealth factors should have a positive effect on the stock risk premium. This indicates that investors need to be compensated with a risk premium on stocks for the systematic risk which is associated with human capital, real estate, and proprietary income.

Asset pricing models are important to investigate both from an academic and investor point of view. From an academic view, it is important to understand which economic factors could influence the asset’s risk and return. This research is important from an investor view in terms of better portfolio decision making. The thesis relates to the extensive literature on asset pricing and factor based models. This thesis contributes to the existing literature on asset pricing models

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with the proposition of the new factor based model, the Total Wealth model. The main purpose of this study is to improve the asset pricing model adding factors to the static CAPM and point out which elements are important for asset pricing.

The research of this thesis is conducted as follows. Factor based models are tested on pre-sorted stock portfolios in order to explain the risk premium. The models which are tested are the static CAPM, the five factor model of Fama and French (2015), the conditional CAPM of Jagannathan and Wang (1996), a human capital model, a real estate model, a private business model, and the Total Wealth model. Equivalent to the existing researches on the subject, the main test assets used are the 25 Fama and French (1992) sorted Size and Book to Market portfolios. The 25 Size and BM portfolios are the main tests assets used in this research. In addition to these test assets, new portfolios are created. Three new sets of 25 portfolios are created which are sorted by size and human capital sensitivity, real estate sensitivity or private business sensitivity. The models are tested on the test assets using Fama-MacBeth regressions. This procedure is the most common methodology in the existing literature to test the cross-sectional variation in stock returns.

The main finding of the research is that the Total Wealth model definitely improves the CAPM. The model is able to explain more of the cross-sectional variation of the excess stock portfolio returns than the other tested asset pricing models. This is with the exception of the five factor model of Fama and French (2015), which is the best performing model in all tests to explain the excess stock portfolio returns. According to the adjusted R-squared, the Total Wealth model is able to explain up to 56% of the cross-sectional variation in the excess stock portfolio returns. From the tests results, it can be stated that the wealth factors are important for asset pricing and that they perform the best when combining them into one model. When comparing the performance of the wealth factors, the private business factor shows the best results. It has a significant positive effect on the excess stock returns of the 25 Size and BM portfolios. This means that investors need to be compensated with a positive risk premium for the risk which is associated with proprietary income. The human capital factor and real estate factor also show that they have a positive effect on the risk premium. However, these results are not significant. Furthermore, the results for the 25 Size and Factor sensitivity portfolios are rather dispersed. The results are surprising because significant negative estimates are found. This would indicate a negative effect of the wealth factors on the risk premium, which is not in line with the

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performed using Fama and French (2015) pre-sorted 25 Operating Profitability and Investment portfolios. In addition to this, a different proxy for the real estate factor is used. However, neither of the robustness checks improves the performance of the Total Wealth model, nor the separate human capital and real estate factors.

The outline of the thesis is as follows. First, an extensive literature review is discussed about asset pricing models and the proposed factors. Second, the methodology and data in the study are discussed. Thereafter, the results of the regressions are showed and analysed. In addition to this, robustness checks are performed and discussed. The last part of the thesis consists of a discussion of the main research findings and a conclusion. All tables are shown in the appendix.

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2. Literature review

In this section, the existing literature of the subject will be analysed. At first, basic linear asset pricing models are discussed. Thereafter, factors from the wealth portfolio are extensively described.

2.1 The Capital Asset Pricing Model

The asset pricing theory begins with the Capital Asset Pricing Model (CAPM) of William Sharpe (1964) and John Lintner (1965). William Sharpe won the Nobel Prize in 1990 with his contribution to the CAPM. The CAPM is still widely used by financial managers in assessing the performance of managed portfolios. The static CAPM consists of a constant and an equity market factor. This factor also called the equity market beta. The CAPM measures the expected excess stock returns by the equity market beta times the excess market return. The constant refers to the pricing error. In an efficient market, the pricing error should be zero. The CAPM is seen as the classic asset pricing model. However, there is a lot of criticism against the CAPM. Academic researchers mention multiple reasons why static CAPM fails. The CAPM is proven to work as a theoretical model. However, there is not much empirical evidence which supports the model.

The basic CAPM is proven to explain the expected stock returns in time-series regression tests. However, it fails to explain the cross-sectional variation of expected stock returns. (Fama & French, 2004). In theory, the equity market beta should fully explain the expected excess stock returns and the pricing error should be zero. Fama and French (1992) found a positive, but flat relation between the equity market beta and expected stock returns in cross-sectional tests. Fama and French (2004) mention early empirical tests where the model fails to explain the cross-sectional variation of stock returns. Two main problems are mentioned in the empirical tests. The beta estimates are too imprecise and measurement errors exist in the explanation of average stock returns. The regression residuals have common sources of variation, such as industry effects in average returns (Fama & French, 2004). Furthermore, the pricing errors are not equal to zero in empirical tests. This is because, in the real world, the market is never efficient. A positive pricing error means that an investor outperforms the market. He is more rewarded with a risk premium on returns than is expected from the systematic risk.

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As a reaction to the flaws of the static CAPM, researchers tend to improve the asset pricing model in several ways. Research shows that the use of diversified sorted portfolios instead of individual stock returns gives a more precise estimation of betas. Fama and French (2004) mention that the use of portfolios as test assets instead of individual stocks reduces the errors in the cross-section of average returns.

2.2 Factor based models

Factor based models are asset pricing models which measure whether asset prices are influenced by economic variables. Factor based models are used in order to improve the asset pricing model. Factor based models are used for the concept of factor based investing. This is different from the traditional way of investing. In a factor based investment strategy, investors select stocks based on factors which are proven to be correlated with stock returns. Nowadays, this strategy is widely used by portfolio managers.

A lot of literature exists on factor based models. Fama and French (1993) propose the well-known three-factor model. In this model, the CAPM average return anomalies are captured by the sensitivity of its return to the following three factors. The equity market beta, the difference between the return on a portfolio with small and large stocks (SMB factor) and the difference between the return of a portfolio of high and low book-to-market stocks (HML factor). (Fama & French, 1993). The three factor model has a higher explanatory power for both the time-series variation and cross-section variation of stock returns in comparison to the static CAPM. (Fama and French, 1996). In further research, this factor model is extended with more proposed factors. In the five factor model, Fama and French (2015) add two more factors to the model. The factors are the profitability factor (RMW) and the investment factor (CMA). These factors also seem to have explanatory power. The five factor model has even more explanatory power of stock returns than the basic three factor model of Fama and French (1993). Higher expected profitability would cause higher expected returns, and higher expected rates of investment would cause lower expected returns. (Fama & French, 2006). This implies that the profitability factor causes a positive risk premium and the investment factor a negative risk premium on stock returns.

More researchers investigate economic variables as factors in order to improve the asset pricing model. New risk factors are suggested to help explain expected returns. Examples of

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macroeconomic factors are consumption growth (Breeden, 1979), investment returns (Cochrane, 1991) and industrial production and inflation (Chen, Ross & Roll, 1986), but also human capital (Jagannathan & Wang, 1996). The latter factor is extensively investigated in this thesis.

Roll and Ross (1994) did further research on the true beta and cross-sectional returns. They criticize the performance of the existing factor based models. They argue that in an efficient market, the equity market beta should be able to explain the cross-section of expected returns. However, in an inefficient market, any variable as a proxy for the market index could have explanatory power and have a positive slope. On top of this, there is more critique on the standard approach for testing asset pricing models. Lewellen, Nagel & Shanken (2010) argue that asset pricing tests are often misleading and they offer suggestions for improving the existing empirical evidence on factor based models.

Multiple variations of proposed factor based models seem to have a good explanatory power in size and book-to-market portfolios. However, Lewellen, Nagel & Shanken (2010) argue that these results are not surprising. This is because according to them, almost any proposed factor is likely to explain the expected returns in size and book-to-market portfolios. Most of the academic researchers show a high R-squared and small pricing errors in the cross-sectional tests. This indicates that pre-sorted size and book-to-market portfolios seem to have a strong factor structure. A strong factor structure means that a random economic factor is likely to be correlated with the size and book-to-market equity factor. This would result in a higher explanatory power of the economic factor. The results are misleading because it suggests biased results and weak support for factor based models which are tested on portfolios with a high factor structure. Lewellen, Nagel, & Shanken (2010) offer suggestions for improving the empirical tests and evidence. They suggest expanding the set of test assets with the inclusion of different sorted portfolios, like industry portfolios. They suggest reporting the GLS R-squared instead of the OLS R-R-squared. This is because the problems are less severe for GLS regressions. They also suggest reporting confidence intervals and more test statistics than only the R squared.

The proposed factor based models are tested on sorted stock portfolios in order to explain the cross-section of stock returns. Blume (1973) originally proposed the use of sorted portfolios as

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1973; Fama & French, 1992) in the cross-sectional regression tests of factor models. According to Blume (1973), the use of sorted portfolios in cross-sectional tests would reduce the errors-in-variables problem. The use of factor portfolios reduces the idiosyncratic risk and therefore the standard errors of the factors. Fama and French (1992) formed stock portfolios which are sorted on size and book-to-market equity. These stock portfolios are used as test assets for their three factor model. The use of these stock portfolios has become the standard in research to test asset pricing models. In addition to this, Fama and French (2015) formed stock portfolios based on operating profitability and investment factors. These portfolios are more recently used in asset pricing tests.

2.3 The conditional CAPM

Jagannathan and Wang (1996) improve the linear asset pricing model by proposing the conditional version of the CAPM. The conditional CAPM addresses two main problems which arise with the use of the classic CAPM. The classic CAPM assumes a static world with no time-varying variables. The CAPM assumes a one single period economy. However, it could be criticized that the world is dynamic and economic variables vary over time. The conditional CAPM implies that betas and market risk premium vary overtime in a multi-period framework. Another problem of the CAPM is that it is not able to observe the return on the aggregate wealth portfolio of the investor. The conditional CAPM observes returns of the aggregate wealth portfolio by including human capital as a factor. Results show that the conditional CAPM performs better than the static version.

Furthermore, an unconditional version could be derived from the conditional model. The unconditional model is implied by the conditional model. The unconditional model is also assumed to have time-varying betas and market risk premium. The model is constructed by including two factors in the linear asset pricing model. The factors are the equity market beta and a premium beta. Jagannathan and Wang (1996) measure the premium beta as the corporate bond yield spread. The premium beta measures the beta-instability risk. Heaton and Lucas (2000) did further research on the conditional model. They add proprietary income as a risk factor to the conditional model rather than only labor income. Their results show evidence that this would improve the conditional CAPM. Human capital and proprietary income form together with real estate the core of the research of this paper.

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2.4 The total wealth portfolio

The total wealth portfolio of the investor consists of different components. Heaton and Lucas (2000) specify the composition of the total wealth of the investor by liquid assets, financial assets and other sources of income. The liquid net worth of an investor is calculated by the sum of cash, bonds, bills, and stocks minus debt. The financial net worth is calculated by the liquid net worth plus the value of real estate, private businesses, pensions, and trusts. The total net worth of the investor consists of the financial net worth plus the income from labor and social security (Heaton and Lucas, 2000).

Stocks are a part of the liquid net worth of the investor and form only a small part of the aggregate wealth portfolio (Jagannathan and Wang, 1996). The income which is generated from stocks is the total capital gains, which is the stock return and dividend. The total capital gains only form a small part of the total income of the investor, which makes it useful to investigate more variables of the aggregate wealth portfolio.

This thesis proposes the Total Wealth model. The Total Wealth model extends the CAPM by adding three extra components of the investor’s total wealth portfolio. The model consists in total of a constant and four wealth factors. The factors examined are equity market, human capital, real estate and private business. The combination of those factors into one model is important in particular. This is because previous researches have examined the four wealth factor separately. This research contributes to the existing literature by combining the factors into one linear asset pricing model. This is important to investigate because, in this manner, there could directly be determined which components of the overall wealth portfolio are important for asset pricing. The components of the total wealth portfolio are further discussed in the following subsections.

2.4.1 Human capital

Human capital is examined as a factor because it forms a big part of the overall wealth of the investor. The income from salaries and wages forms the biggest part of the total personal income of households in comparison to other sources. Other sources of personal income are supplements to wages and salaries, proprietary income, rental income, receipts on assets and social benefits.1_{Human capital is one of the most important sources of income for the}

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investor. This means that human capital should be included in measuring wealth and therefore might be important for asset pricing.

Human capital returns are already investigated as a factor in an asset pricing model by different researchers. Jagannathan and Wang (1996) include human capital as a factor in the conditional CAPM in order to explain the cross-section of returns. Results show that human capital is able to explain stock returns in the conditional model. Human capital is found to have a bigger explanatory power in the cross-section of stock returns than the size and book-to-market variables of the basic three factor model. (Jagannathan and Wang, 1996) However, human capital is a non-tradable asset and therefore should be treated differently than other assets. Human capital is investor-specific which depends on elements like education, age, and industry. These elements make human capital heterogeneous among investors. Eiling (2013) did further research on industry-specific human capital. This model contains multiple human capital factors from different industries. The research shows that human capital heterogeneity affects the cross-section of average stock returns. However, the research of this thesis focusses solely on aggregate human capital returns.

2.4.2 Real estate

Like human capital, real estate is also a substantial part of the total wealth of the investor. Unlike human capital, real estate is a tradeable asset. Real estate is the most widely held asset in the United States (Kullman, 2002). Real estate is a widely held asset for both households and investors. It is held as a primary residence as well as stocks in the portfolio from investors. Moreover, housing is the most important collateral asset for households. (Lustig & van Nieuwerburgh, 2005) This makes it likely that real estate is a substantial part of the aggregate wealth portfolio and therefore could be important for asset pricing. Lustig & van Nieuwerburgh (2005) focusses on housing as a collateral asset and asset pricing. They show that housing as a collateral asset affects asset returns through the collateral ratio. The collateral ratio is the ratio of housing wealth to human wealth. The housing wealth includes the value of the real estate in possession of the investor which can be collateralized. The ratio is interesting to investigate because it changes the distribution of consumption growth across households (Lustig & van Nieuwerburgh, 2005). Results of their study show that aggregate stock returns could be predicted by the collateral ratio. The collateral factor model performs better than the standard

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conditional model. Different from the standard conditional model, the collateral model assumes that risk-sharing is imperfect.

Kullman (2002) investigates real estate returns as a factor in the asset pricing model to explain the cross-section of stock returns. Results show strong evidence that real estate returns help to explain the cross-sectional variation in stock returns. Kullman (2002) investigates both commercial and residential real estate returns as proxies for the real estate factor. The research of this thesis solely investigates the residential real estate returns. The results of Lustig & van Nieuwerburgh (2005) and Kullman (2002) suggest that real estate is important for asset pricing.

2.4.3 Private business

The income from private businesses is, next to labor income, a part of the total wealth of the investor. The income of private businesses refers to proprietary income, which is the income derived from entrepreneurial ventures. Entrepreneurial risk is shown to be more highly correlated to stock returns than the risk from labor income. (Heaton and Lucas, 2000) Heaton and Lucas (2000) include the income generated from private businesses as a risk factor in the conditional asset pricing model of Jagannathan and Wang (1996). They showed evidence that entrepreneurial income risk has a significant effect on asset prices. The linear asset pricing model including both human capital and private businesses factor performs better than a similar model including only a human capital factor. (Heaton and Lucas, 2000). Their research determines that both human capital and private business returns are important for asset pricing.

Heaton and Lucas (2000) point out that, in the total wealth portfolio of the investor, the level of proprietary income has an effect on portfolio choice. The share of stockholdings has a negative relationship with the variability of the growth rate of proprietary income. Households with a relatively higher income from private businesses hold less wealth in stocks. (Heaton and Lucas, 2000). These households carry a larger risk exposure to entrepreneurial risk than similarly wealthy households. The investors need to be compensated by the risk which they carry from the proprietary income.

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2.5 Expectations

The Total Wealth model is tested using time-series and cross-sectional regressions. Further explanation of this could be found in the methodology section. The expectation of the performance of the factors investigated could be derived from the results of the existing literature. The beta estimates, which result from time-series regressions, measure the factor exposure. Lambda estimates are derived from the cross-sectional regressions. The lambda estimates measure the price of risk. Ultimately, the factor risk premium is determined by the factor exposure times the price of risk. The factor risk premium indicates the effect of the relevant factor on excess stock returns. A positive beta estimate indicates a positive factor exposure of the stock returns and a positive lambda estimate indicates a positive effect of the factor on excess stock returns. Positive lambda estimates would suggest that the investor is compensated with a risk premium on stock returns for the risk which is associated with the relevant factor.

Following the existing literature, the sign for the estimates should be positive. Jagannathan and Wang (1996) show significant positive estimates for the human capital factor in cross-sectional tests of size and book-to-market equity portfolio returns. Kullman (2002) shows evidence for a strong significantly positive risk premium for real estate. The lambda estimates for real estate returns show a significant positive sign. Kullman (2002) also showed a little evidence for a positive risk premium for human capital. The lambda estimates of the cross-sectional regression results show insignificant positive signs or significant negative signs. The previous research on the human capital factor has shown that the positive estimates are not always significant. However, a recent study by Eiling (2013) shows that tests for human capital on an industry-level give better results rather than aggregate income labor risk. According to Heaton and Lucas (2000), both the human capital and private business factor are important for asset pricing. Both the human capital and private business factor have a positive significant effect on the asset risk premium.

The equity market factor is proven to fail in explaining the cross-sectional variation of stock returns. Adding human capital, real estate, and private business should improve the asset pricing model. The overall expectation is that the Total Wealth model improves the CAPM and that all wealth factors are important for asset pricing. According to the results in the existing literature, the expectation of this research is that all four factors of the Total Wealth model show a positive factor exposure and a positive market price of risk. The positive risk premium

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indicates that investors have to be compensated for the systematic risk which is associated with market equity and their labor income, real estate assets and entrepreneurial income. It is assumed that the market is not fully efficient. This implies that the average pricing error should not be equal to zero.

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3. Methodology

In this section, the methodology of the research will be discussed. In the first part of the methodology, the Fama-MacBeth regression procedure is explained and the construction of the Total Wealth model. Thereafter, the formation procedure of the portfolios as test assets is explained.

3.1 Fama-MacBeth regressions

Fama and MacBeth (1973) introduced a regression method which addresses measurement errors in cross-section regressions. This is a two-stage regression method where month-by-month section regressions are conducted of month-by-monthly returns instead of a single cross-section regression. In the first stage, the betas for the tested factors are estimated for each asset return in a time series regression. These beta estimates represent the factor exposures. In the second stage, the asset returns are regressed against the estimated betas for each point in time in a cross-sectional regression. The cross-sectional regression results in lambda estimates of the factors. The lambda estimates represent the market price of risk. The factor exposure and market price of risk determine together the relevant factor risk premium. The Fama-MacBeth regression procedure is used to test linear asset pricing models. This is because it ensures that the effects of residual correlation in the regression coefficients are captured by repeated sampling. (Fama & French, 2004). The Fama-MacBeth approach and the use of diversified portfolios in testing have become the standard approach to test asset pricing models. The main research of this thesis will be conducted using the Fama-MacBeth regression method.

The methodology of this research is mainly based on the previously discussed literature, but with a few alterations. In this research, multiple models are tested on stock portfolios using the Fama-MacBeth procedure. To conduct the regressions for the research, panel data is needed on stock returns. This is multi-dimensional data of multiple observations at different points in time. Time-series data is needed for the variables which are tested as factors in the model.

The main factor model which is tested is called the Total Wealth model. The two-step regression procedure for the Total Wealth model will be conducted as follows. In the first step, the betas from the proposed factors are estimated in a time-series regression on the whole sample. In this way, the exposures from the factors on the portfolio return are determined. The main time-series regression model is stated according to formula (1).

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𝐸[𝑅_%− 𝑅_']₎ = 𝛼_%+ 𝛽_./),%𝑅_./),)+ 𝛽_12,%𝑅_12,)+ 𝛽_34,%𝑅_34,)+ 𝛽_56,%𝑅_56,)+ 𝜀₎%₍₁₎

The dependent variable is the excess return on test asset i, which in the model is the excess monthly portfolio return. This is calculated from the monthly value-weighted returns minus the risk-free rate. The excess portfolio returns are regressed on a constant and the equity market factor, the human capital factor, the real estate factor and the private business factor. The equity market factor RMkt is the equity market risk, which is calculated by the value-weighted CRSP

index minus the risk-free rate. The human capital factor RHc, Real estate factor RRe, and private

business factor RPb are measured using proxies for their returns. The constant denotes the

pricing error. is the regression error term.

In the second step of the procedure, the estimated factor betas from the first step are used in a second regression. In this step, the estimated factor betas are regressed on the cross-section of the monthly excess returns for each point in time. This step is needed to determine how much the factor explains the cross-section of the test asset returns. The cross-sectional regression model is stated according to formula (2).

𝐸[𝑅%− 𝑅𝑓]) = 𝜆0+ 𝜆𝑀𝑘𝑡𝛽_{𝑀𝑘𝑡,𝑖}+ 𝜆𝐻𝑐𝛽_{𝐻𝑐,𝑖}+ 𝜆𝑅𝑒𝛽_{𝑅𝑒,𝑖}+ 𝜆𝑃𝑏𝛽_{𝑃𝑏,𝑖}+ 𝑎𝑡𝑖 (2)

In this model, the dependent variable is still the monthly excess portfolio return. The lambdas refer to the cross-sectional regression estimates of the independent variables. The monthly excess portfolio returns are regressed n a constant and the factor beta estimates resulting from the first pass regression. These are the beta estimates of equity market risk, human capital, real estate, and private business. The lambda estimates represent the market price of risk of the wealth factors. This lambda estimate determines the factor risk premium on stock returns. The dependent variable in the Fama-MacBeth regressions is the monthly excess portfolio return. The proposed model is tested on different stock portfolios. The basis test assets used are the 25 Size and BM portfolios which are pre-sorted by Fama and French (1992). This is because the pre-sorted portfolios have become the standard for test assets in the existing literature. This makes it easy to compare the research results with the existing academic researches. In addition to this, new portfolios are used as test assets which are based on size and factor sensitivity.

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Alternative model testing

In addition to the Total Wealth model, more tests are performed on the test portfolios to show an alternative view. Variables from existing factor models are also tested on the excess portfolio returns. The additional models of analyses are the CAPM model, the five factor model of Fama and French (2015), and the conditional model of Jagannathan and Wang (1996). In this study, the unconditional model is expressed as a conditional model by adding a premium beta to the model. The premium beta is measured with respect to yield spread. The one-month lagged yield spread is used and it is calculated by the difference between the Moody's Aaa corporate bond yield and the Baa Corporate bond yield. The human capital factor, real estate factor, and private business factor are also tested in a separate asset pricing model. This model includes a constant, the equity market factor, and a relevant other wealth factor.

3.2 Reported variables

The reported variables of interest are the averages of the estimates from the second regression. Reported are the factor mean lambda estimate constants, the mean lambda estimates for each factor, the t-statistics of the estimates, the R-squared, and adjusted R-squared. The mean constant refers to the mean pricing error. The mean lambda estimates could be calculated using formula (3). The t-statistics are calculated using a Student’s t-test of the estimators. T-statistics determine whether the lambda estimates are significantly different from zero.

𝜆E = F

G ∑ 𝜆E)

G

)IF (3)

Common problems in time-series regressions are autocorrelation and heteroscedasticity of the error terms. The standard errors need to be adjusted to avoid these problems. Therefore, the t-statistics of the reported variables are calculated using Newey-West (1987) standard errors. There are four lags used in the t-test because this is the most common in the existing literature on asset pricing models.

The two-pass regression method faces the problem of errors in the variables. The residuals need to be corrected for the factor that the betas are estimated in the time-series regressions. Shanken (1992) suggests to correct the standard errors and subsequently correct the t-statistics for the lambdas. This results in two t-statistics reported for each lambda. A t-statistic which is corrected using Newey-West and the Shanken adjusted t-statistic. Following Shanken (1992) suggestion

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for standard error correction, the adjusted standard errors are calculated according to formula (4) and t-statistics are calculated according to formula (5). t refers to the unadjusted t-statistic.

𝑐 = J KL MN(KL)Q R (4) 𝑡ST ₌ ) √FV2 (5)

The R-squared shows the explanatory power of the relevant asset pricing model of the excess portfolio returns. However, the interpretation R-squared can be misleading, since it automatically increases when more factors are added to the model. The adjusted R-squared copes with this problem by computing the explanatory power for independent variables that actually affect the dependent variable. This makes the interpretation of the adjusted R-squared more reliable.

3.3 Portfolio formation procedure

In addition to the existing portfolios, three new sets of portfolios are created which are sorted by size and factor sensitivity. 25 portfolios are created which are sorted by size and human capital sensitivity, 25 portfolios are created which are sorted on size and real estate sensitivity, and 25 portfolios are created which are sorted on size and private business sensitivity. The new portfolios are used to test whether the wealth model could explain the cross-sections of portfolios with different exposures to the risk factors. The new portfolios are created followed by the two-way sort procedure of Fama and French (1992). The two-way sort procedure refers to portfolio formation based on two different factors.

For the portfolio construction, a sample of all CRSP firms is used with monthly return data within the period of January 1975 until December 2017. More details of the sample are further explained in the Data and descriptive statistics section. The portfolio formation procedure is as follows. At first, the market capitalization is calculated for each firm at the end of each month. The market capitalization is calculated by multiplying the firm’s closing price by its common shares outstanding for each month. Only non-financial firms are included in the analysis. This is because financial firms have the property of a high leverage, which is not the same for non-financial firms. To be included in the size portfolio, the firm should have a closing price or

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bid-ask price each month in order to calculate the market capitalization. In addition to this, the condition is that the firm should exist for a minimum of 60 months. All firms of the sample are sorted into five quantiles by their market capitalization. The portfolio sorting process is repeated for each month. The smallest firms are sorted into the first quintile and the biggest firms in the last quintile. The size breakpoints are determined by NYSE stocks as a quintile criterion. This is to prevent a bias of breakpoints determined by an overrepresentation of small stocks which are listed in the other listed exchanges. After the size sorting process, the pre-formation betas are calculated. The pre-formation betas are calculated in order to sort the sample firms by their factor sensitivity. The betas refer to the factor sensitivity for human capital, real estate, and private business. The betas are estimated using regressions with a rolling estimation window of the past 24-60 months.2 The rolling regressions are performed per company. The resulting pre-formation betas are used in the portfolio constructions. All sample firms are sorted into five quintiles by their factor sensitivity within each size quintile. This portfolio sorting by factor sensitivity is also repeated for each month. The first quintile contains the firms with the lowest factor sensitivity and the fifth quintile contains the firm with the highest factor sensitivity. This creates in total 25 portfolios based on size and factor sensitivity. The portfolio returns are calculated as the value-weighted average returns. The value-weighted averages are computed by the firm’s market capitalization for each portfolio for each month. This portfolio formation procedure results in a time-series of monthly returns for the 25 portfolios from January 1977 until December 2017. The sample includes 492 months.

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4. Data and descriptive statistics

In this section, the data used in the analysis is thoroughly discussed. This section includes the descriptive statistics of the variables.

4.1 Stock portfolio returns

To perform the analysis, panel data is needed on monthly stock returns.

The models will be tested on different stock portfolios. As discussed earlier, the test assets used for the analysis are the 25 Size and BM portfolios and three new sets of 25 Size and Factor sensitivity portfolios. The 25 Size and BM stock portfolios are pre-sorted by Fama and French and could be retrieved from the data library on the Kenneth R. French website. The monthly value-weighted portfolio returns are used for the analysis. The sample consists of monthly data which goes from January 1975 until December 2017. The stock returns are based on the value-weighted returns from all CRSP firms incorporated in the US and which are listed on the NYSE, NYMEX, and NASDAQ.

For the three sets of 25 Size and Factor sensitivity portfolios, also stock return data is needed for each firm. For each firm over the sample period of January 1975 until December 2017, the holding period of the firm’s stock is used. The holding period return includes the dividends. The firm's size is measured by their market capitalization for each month. The market capitalization is calculated for each firm by the price times the common shares outstanding in each month. The share price used is the monthly closing price. If the monthly closing price is not available, the bid/ask average is used at the end of the month. Data of the holding period return, price and common shares outstanding could be retrieved from the CRSP database. For estimating the pre-formation betas of factor sensitivity, the variables of the proposed factors from the human capital factor, real estate factor, and the private business factor.

4.2 The wealth factors

The first wealth factor is the equity market factor. This factor is calculated by the monthly return on the CRSP value-weighted index minus the risk-free rate. The risk-free rate is based on the 30-day T-bill rate. The equity market factor could be easily retrieved from the data library on the Kenneth R. French website. The other wealth factor is measured with proxies for human capital returns, real estate returns and private business returns.

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A more in-depth explanation of how these proxies are measured as described in the following subsections.

4.2.1 The Human capital factor

Jagannathan & Wang (1996) assume that the return on human capital is a linear function of the growth rate in per capita labor income. Wealth due to human capital can be expressed as the labor income divided by the discount factor minus the growth rate.

Jagannathan and Wang (1996) use the aggregate labor income with one month lag. The one month lag is motivated by minimizing the measurement errors due to the reporting delay of the labor income data. Jagannathan and Wang measure the labor income including wages, proprietary income, and net interest payments. However, there are critics of this approach for measuring human capital returns. According to Heaton and Lucas (2000), one month lag in the growth rate is not accurate enough. They argue that investors could observe their own income and stock returns at the same time. It could also be the case that announcement effects of labor income data bias the effect of labor income on stock returns. (Eiling, 2013). Heaton and Lucas (2000) measure the labor income as wages and proprietary income separately. They use the contemporaneous growth rate for their analyses. Eiling (2013) also measures human capital returns as the contemporaneous growth rate in labor income. In this thesis, the methodology of measuring human capital returns is based on the research of Heaton and Lucas (2000). This means that the human capital returns are measured using the contemporaneous growth rate. The human capital factor is calculated using formula (6).

𝑅₎T2 ₌ WX6YZ %[2Y\4]

WX6YZ %[2Y\4]^_ -1 (6)

The labor income refers to the total of wages and salaries from all private industries and the government. The labor income data can be downloaded from the US Bureau of Economic Analysis (BEA). The monthly data is retrieved from the National Income and Product Account (NIPA) Table 2.6. The sample period goes from January 1975 until December 2017. This includes a testing period of 516 months.

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4.2.2 The Real estate factor

Kullman (2002) examines the real estate factor in the asset pricing model. In her research, a differentiation is made between commercial and residential real estate.

Commercial real estate refers to real estate which is used for commercial purposes as a business objective. Residential real estate refers to the real estate properties of households which are used as a resident. Kullman (2002) uses proxies for both residential and commercial real estate returns. Kullman (2002) uses equity Real Estate Investment Trust (REIT) from the National Association of Real Estate Investment Trusts returns as a proxy for the commercial real estate. The REIT equity return data is not available prior to 1972. Kullman (2002) uses the percentage change in the median price of existing homes sold from the National Association of Realtors as a proxy for the residential real estate. The latterly mentioned data is not publicly available. This thesis uses the growth rate of a national house price index of the United States as a proxy for real estate returns. The Freddie Mac US house price index is used. This particular index is used because it provides a measure of typical house price inflation in the United States. Also, this index is not seasonally adjusted and is reported since 1975. The growth rate of the Freddie Mac index solely represents the residential real estate returns. The index is publicly available and could be retrieved from the Freddie Mac website. The percentage change of this index will represent the monthly growth rate of this index and will be used for the analysis. Monthly data of the index is retrieved from January 1975 until December 2017. The real estate factor is calculated using formula (7).

𝑅)3` = _{1YaM4 bZ%24 %[N4c}1YaM4 bZ%24 %[N4c]

]^_ -1 (7)

4.2.3 The Private business factor

Jagannathan and Wang (1996) measure human capital as the one month lagged labor income growth. Heaton and Lucas (2000) separate the human capital returns into two components. They separate between the wages and proprietary income. In their research, human capital is separated in wage income growth and non-farm proprietary income growth. The wage income growth and non-farm proprietary growth are both measured as the contemporaneous growth rate.

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The research of this thesis follows the methodology of Heaton and Lucas (2000) to measure the private business factor as the non-farm proprietary growth. The private business factor is calculated using formula (8).

𝑅₎5d ₌ 5ZYbZ%4)XZe %[2Y\4]

5ZYbZ%4)XZe %[2Y\4]^_ -1 (8)

The monthly data of the non-farm proprietary income is retrieved from the NIPA table 2.6 with monthly data. The monthly data is retrieved from January 1975 until December 2017.

Additional factors

As discussed earlier, more models are tested on the portfolio returns to show an alternative view. The other factors examined are SMB, HML, RMW, CMA, and the return premium. The data for the factors of the five factor model of Fama and French (2015) could be retrieved from the Kenneth French data library. For the conditional model of Jagannathan and Wang (1996), the lagged yield difference between Moody’s Baa and Aaa corporate bond yield is calculated. This is denoted as the return premium RPrem. The corporate bond spreads are retrieved from the

Federal Reserve Bank website

4.3 Descriptive statistics

The summary statistics and the correlation matrix are calculated over the value-weighted equity return and the factors that will be tested. The value-weighted equity return is the monthly return on the CRSP value-weighted index. The sample for all factors contains monthly data from January 1975 until December 2017. This gives a number of 516 observations. The summary statistics of all variables used are shown in Table 1. This table could be found in the appendix. Panel A shows the descriptive statistics and Panel B shows the correlation matrix of the monthly returns. The correlation matrix shows the pairwise correlations. The significance of the variables in a Pearson correlation test is indicated at a 1%, 5%, and 10% confidence level, respectively. The correlation matrix shows that human capital, real estate, and private businesses are positively correlated with the CRSP stock returns. The positive correlation for the private business factor with the stock returns is significant at a 1% confidence level. The positive correlations are in line with the expectations. Human capital, real estate, and private businesses returns correlate all positively with the risk-free rate. There is also a positive

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correlation between the variables of the wealth model. Human capital, real estate, and private business return all positively correlated with the risk-free rate. The risk-free rate is the expected return on an investment without any risk. The economic intuition behind the positive correlation between the risk-free rate and the wealth factors is that an increase in the risk-free rate and the wealth factors both indicate an increase in the overall risk of holding an asset. Investors must receive higher returns on their investment as a compensation for the increased risk.

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5. Results

In this section, the results of the analysis are showed and thoroughly discussed. First, the results of the time series and cross-sectional regressions are discussed of the basic test assets, the excess returns of the 25 Size and BM portfolios. Second, the results are discussed of the newly created portfolios based on size and factor sensitivity. Finally, the main findings of the analyses are summarized in the last section. All the tables of the results are shown in the appendix.

5.1 The 25 Size and Book to Market portfolios

The 25 Size and BM portfolios are used as the basic test assets in the analysis. This is because the use of these test assets is very common in the existing literature. This makes it easier to compare the regression results. The human capital factor, real estate factor, and private business factor are tested in two different ways. The factors are tested in a separate model together with the equity market factor and they are tested in one combined model. The main focus of the results discussion is to understand to what extent the factors of the wealth portfolio cause a risk premium in the portfolio returns. The risk premium is the portfolio return in excess of the risk-free rate, which is a compensation for the risk when holding the stock. In order to determine the factor risk premium of the portfolio returns from the wealth factors, the factor exposure and market price of risk is analysed. In addition to the model of focus, the cross-sectional results of the alternative asset pricing models are analysed.

In the first set of tests, the time-series regressions are performed of the excess portfolio returns on the CAPM, the five factor model of Fama and French (2015) (FF5), the conditional model of Jagannathan and Wang (1996) (CCAPM), a human capital model, a real estate model, a private business model, and the Total Wealth model. The beta estimates of the factors from the Total wealth model for the 25 Size and BM portfolios are reported in Table 2. These beta estimates represent the wealth factor exposures of the excess portfolio returns. The unadjusted t-statistics are reported in parentheses under the beta estimate. The beta estimates are sorted according to their size and book-to-market equity portfolio from low to high. The significance of each estimate is indicated with stars at a 0.1%, 1%, or 5% confidence level. The significance refers to the likelihood that the effect of the dependent variable is attributable to the independent variable.

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The equity market beta estimate shows the highest t-statistics in the time-series regressions. This is expected since the equity market factor is proven to explain time-series excess stock returns. (Fama & French, 2004). The time-series results for the wealth factors are rather dispersed. The human capital shows solely insignificant negative beta estimates. This indicates negative factor exposures. This result is not in line with the expectations. According to the existing literature, the human capital factor should have a positive exposure to the excess portfolio returns (Jagannathan and Wang, 1996; Heaton and Lucas, 2000). Jagannathan and Wang (1996) show significant positive estimates for the aggregate human capital growth when they are tested on the excess portfolio returns of 25 Size and BM portfolios and 100 Size and market beta sorted portfolios. The negative pattern in the beta estimates could be caused by the measurement of the human capital growth rate. Jagannathan and Wang (1996) calculate the human capital factor as the lagged growth rate of the labor income, which includes proprietary income. The use of this measurement for the human capital factor gives positive significant estimates for the Size and BM portfolio returns. In this analysis, the human capital factor is calculated solely by the contemporaneous growth rate of wages and salaries in the corresponding month. This human capital factor excludes the proprietary income. Furthermore, equal to the analyses of Jagannathan and Wang (1996), the human capital factor is determined as the aggregate labor income risk. In contrast to the previous analyses in the existing literature, Eiling (2013) measures the human capital factor on an industry-level rather than aggregate labor income risk. The use of the heterogeneity of human capital gives better results than the aggregate human capital factor.

The real estate beta shows some positive significant beta estimates in the larger book to market equity portfolios. This indicates that value firms tend to be more sensitive to real estate returns. The private business factor shows two positive significant beta estimates at a 5% confidence level. These patterns in the betas are in line with the expectations of the existing literature. According to the research of Kullman (2003), the residential real estate should have a positive factor exposure on the excess portfolio returns. According to the results Heaton and Lucas (2000), proprietary income should also have positive factor exposures on the excess portfolio returns.

In the second set of tests, cross-sectional regressions are performed with the factor exposures of the tested models. Table 3 shows the results for the cross-sectional regressions for the 25

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errors, the average lambda estimates, the R-squared, the adjusted R-squared, and the t-statistics. The adjusted R-squared is different from the normal R-squared. The t-statistics are used as a measure to indicate whether the estimator is significant. Low t-statistics indicate that the beta is not significantly different from zero. There are two t-statistics reported for each lambda estimate. The first statistics are adjusted using Newey-West with four lags. The second t-statistics are adjusted using Shanken error correction.

The results for the cross-sectional regressions differ from the first stage regressions. The estimates from the cross-sectional regressions are the average lambdas. The average lambdas represent the market price of risk. The market price of risk is used to determine the factor risk premium.

Comparing the R-squared and adjusted R-squared of all models, it is notable that the five factor model of Fama and French (2015) has the highest explanatory power of the cross-sectional variation of the excess portfolio returns. After this, the Total Wealth model has the highest explanatory power. This result indicates that the combination of the wealth factors into one model is more able to explain the cross-section of stock returns rather than testing the wealth factors separately. This is evidence that the combined model performs better than the separate wealth factors. The adjusted R-squared for the five factor model is 0.49 and it is 0.45 for the Total Wealth model. This means that the Total Wealth model explains 45% of the cross-sectional variation in the excess portfolio returns. The results are in line with the expectation that the adding more wealth factors to the CAPM definitely improves the linear asset pricing model.

The explanatory power of the five factor model is not surprising since the model is proven to improve the CAPM. (Fama & French, 2015). Fama and French (2015) show evidence that the five factor model is able to explain up to 94% of the cross-sectional variance of the tested pre-sorted portfolio returns. Fama and French (2015) also use portfolios which are pre-sorted based on size and book-to-market equity and portfolios which are sorted based on operating profitability and investment. As expected, the profitability factor (RMW) causes a positive risk premium on the portfolio returns, and the investment factor (CMA) causes a negative risk premium on the portfolio returns. The factors of human capital, real estate, and private business are smoother compared to the five factors of Fama and French (2015). This is common for macroeconomic factors. It means that stock returns react slower to changes in macroeconomic variables. This

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could explain the higher explanatory power of the five factor model compared to the Total Wealth model. It is also notable that the conditional version of the CAPM performs better than the standard CAPM. According to the adjusted R-squared, the CAPM solely explains solely 19% of the cross-sectional variation in the excess portfolio returns and the CCAPM explains 28%. The results of these tests support the empirical evidence of the conditional CAPM of Jagannathan and Wang (1996).

The average lambda estimates of the wealth factors could be compared to each other. As discussed earlier, the lambda estimates indicate the effect of the factor on the stock risk premium. As expected, the pricing errors are never zero. They have a positive value, which means that investors are more rewarded for the overall risk that is expected from the systematic risk. From the wealth factors, the private business has the only significant positive lambda estimate at 1% confidence level. This counts both for the separate tests and combined model. However, the result for the private business factor is not surprising, since the inclusion of proprietary income in the human capital factor improves its performance. The private business factor has also the highest influence on the portfolio risk premium. The results show that a 1% increase in entrepreneurial risk increases the portfolio risk premium by 1.86%. From the wealth factors, the private business factor explains the most of the cross-sectional variation of the excess portfolio returns. These results support the empirical evidence of Heaton and Lucas (2000), which proves that entrepreneurial risk is more correlated with stock returns than human capital risk. The human capital and real estate factors show also a positive lambda estimate for the separate tests and combination model. This positive estimate is in line with the results in the existing literature, which is discussed earlier. The positive lambda estimates indicate that the investor needs to be compensated with a risk premium for the risk which is associated with the wealth model components. It is notable that the negative time-series beta estimates of the human capital result in an overall positive average lambda estimate in the cross-sectional tests. This result indicates that it is more reliable to test the cross-sectional variation in the excess portfolio returns rather than the only test for the factor exposures.

In contrast to the other wealth factors, the equity market risk factor shows an insignificant negative lambda estimate. This result supports the empirical evidence of Fama and French (1992), which shows that the equity market beta fails to explain the cross-section of stock returns. they show a flat relation between the equity market beta and the expected stock

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insignificant negative lambda in the static CAPM and all tested wealth models. The equity market risk factor is significant in the CCAPM and the five factor model. However, the lambda sign is negative. The results also indicate that the performance of the CAPM factor is not improved by adding the wealth factors to the asset pricing model.

The positive lambdas for the wealth factors are in line with the overall expectations of the Total Wealth model. However, the positive lambda estimates for the human capital and real estate factor are insignificant. The t-statistics for human capital are small or close to zero. The Shanken t-statistic does not give any different results in all tests. This is because the Shanken t-statistic is close to the unadjusted t-statistic. For the wealth factors, the Shanken t-statistic is even lower.

As discussed earlier, Kullman (2002) shows that the real estate factor explains the cross-sectional variation of the 25 Size and BM portfolios. These results suggest a positive significant lambda estimate for the real estate factor of this analyses. However, Kullman (2002) investigates both commercial and residential real estate returns. The real estate factor of this analyses solely captures the residential real estate returns. Also, a different proxy is used to measure the residential real estate growth rate. The alternative proxy for the real estate growth rate could explain the insignificance of the real estate factor in the cross-sectional tests. A new analysis for the real estate factor will be performed in the robustness check section. The real estate growth factor will be measured by a different house price index. As a robustness check, a different measure is used for the real estate factor in order to improve the results. A further explanation of this could be found in the robustness check section.

Overall, from the test results of the 25 Size and BM portfolios, it can be concluded that the Total Wealth model definitely improves the CAPM. The combination of the wealth factors into one model improves the linear asset pricing model rather than just testing the separate wealth factors. The private business factor is the best performing factor. This emphasizes the importance of entrepreneurial risk in asset pricing.

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5.2 Portfolios sorted by size and factor sensitivity

As discussed earlier, the stock portfolios are sorted using the two-way sorting procedure of Fama and French (1992), with a few alternations. Fama and French (1992) have sorted the stock portfolios based on the size and book to market equity of the sample firms. The portfolios of this analyses are sorted based on the size and factor sensitivity of the sample firms. This results in three new sets of 25 stock portfolios which are sorted based on size and the sensitivity to human capital, real estate, and private business of the sample firms. The portfolio returns are calculated as the value-weighted equity returns. The lowest decile contains from the smallest firms with the lowest sensitivity to the factor. The highest decile contains the returns from biggest firms with the highest factor sensitivities. The time-series averages of the monthly portfolio returns are shown in Table 4. The average returns get smaller as firm size increases. This phenomenon is called the size effect. It implies that small firms have higher returns in comparison to big firms. This effect is supported by Fama and French (1992) who also found the highest portfolio returns for the smallest firms. The value-weighted average equity returns could also be analysed with respect to the factor sensitivity. With the exception of the first group, the average returns generally increase as the factor sensitivity increases. This result could be expected because the sample firms in the higher groups contain higher overall risk exposures. The higher risk exposure needs to be compensated with higher returns for holding the stocks of the concerned firms. However, the expectation is that the average returns increases by increasing the factor sensitivity does not count for all groups and factors. It is notable that in the extreme groups of the lowest and highest factor sensitivities have the highest returns in comparison to the other groups. The extreme return values can be due to measurements problems. Measurement errors in the estimation of the pre-formation betas could lead to inconsistent results. The extreme sensitivity groups contain the most outliers which can influence the sorting process.

Tables 5 and 6 show the two-stage regressions results for the 25 Size and Human capital sensitivity portfolios. Equal to the Size and BM portfolios, the results of the time-series regressions are solely showed for the factors of the Total Wealth model. The results of the cross-sectional regressions are shown for the CAPM, CCAPM, five factor model, the separate wealth factor models, and the Total Wealth model. The beta estimates of the time-series regressions which are displayed in Table 5, refer to the factor exposures of the portfolio returns to the relevant wealth factors. The factor exposures are rather small. This is why the beta estimates

The Total Wealth model and the cross-section of stock returns

Master thesis