Common Macro Factors and Their Effects on U.S Stock Returns

Transcription

1 2011 Common Macro Factors and Their Effects on U.S Stock Returns IBRAHIM CAN HALLAC 6/22/2011

2 Title: Common Macro Factors and Their Effects on U.S Stock Returns Name : Ibrahim Can Hallac ANR: Date of Graduation: August, 2011 Graduation Department: MSc Finance Supervisor Name: Lieven Baele Faculty Name: Faculty of Economics and Business Administration Abstract This paper studies explanatory power of macro variables on the variation of stock returns for U.S economy. 131 Macroeconomic variables : are used to analyze cross section of returns. I used dynamic factor analysis to extract 8 latent factors to summarize the information in 131 monthly series. A two step test procedure of Fama-Macbeth is implemented to measure the empirical performance of factor model. I found macro factors have significant effect on explaining the common variation in U.S stock returns as well as the variables used in the literature like market risk factor, size factor, value factor and momentum factors. In addition to Fama French 100 portfolios formed on size and book, the tests are done using Fama French 49 industry portfolios as independent variable. Moreover, the factor model is constructed for expansion and contraction periods. Unlike expansion periods, in recession periods the relationship between latent factors and stock returns turns out to be insignificant. 2

3 Contents 1-Introduction Literature Review CAPM and APT Models Principal Component Analysis Methodology Factor Model Extracting Latent Factors Fama-MacBeth Two Pass Regressions Estimation of Factor Betas Estimation of Factor Risk Premiums Data and Factors Stock Returns & Fama French Factors Macroeconomic Series & Latent Factors Results Conclusion References Appendix

4 1-Introduction This paper investigates the explanatory power of macroeconomic variables on cross section of US stock returns. Standard economic theory would suggest that there is a link between financial markets and macro economy. I don t take a stand for particular theory, but there are various studies which relates asset prices and returns to macro variables like production, consumption, inflation In practice it is hard to determine which macro variables should be linked to which asset prices. There are various measures of production, consumption and price level. This analysis gives an empirical support for this link. Traditionally, papers used few variables to analyze the cross section of stock returns. I consider large data set. 131 Macroeconomic variables of U.S economy are employed to dynamic factor analysis to extract common macro factors which are considered to have significant power on explaining the common movements in asset returns. This brings challenges and opportunities for us. Large number of factors will mean that possible measurement errors in individual series will not be significant when compared to few number of factors since they will get diversified with aggregation. Also one macro series may not be a priced factor but when we combine tens of them they may become a priced factor together. In this paper I found latent macro factors are significant priced risk factors when they are regressed on Fama French 100 portfolios formed on size and book. Also some of those latent macro factors have explanatory power beyond the benchmark model CAPM, Fama French 3 factor model and Fama French 3 factor model plus momentum factor. Furthermore, to check robustness, the research is done with different portfolio structures, for instance 49 industry portfolios. I found that the latent factors are insignificant in explaining the common movement of industry portfolios. Lastly, the tests are done for boom and recession periods separately. For recession periods, extracted factors fail to be priced risk factors while in boom periods, some of latent factors remains to be significant. Next section is about review of literature. Section 3 explains the methodology of this paper. Section 4 presents the data and factors used in the research. Section 5 demonstrates and discuss the empirical results. Section 6 concludes. 4

5 2-Literature Review 2.1. CAPM and APT Models Factor models provide us a framework to consider risk and return relationship, besides they claim systematic risk or diversifiable risk is wholly captured by the corresponding factors. Factors of a factor model explain us why certain group of stocks returns tend to move together and they help us to understand common elements of the fluctuations of stock returns. Capital Asset Pricing Model(CAPM) and Arbitrage Pricing Theory (APT), which are two most widely used and popular theories in asset pricing literature, are special cases of factor models in which some model parameters or the number of factors are restricted based on equilibrium or arbitrage considerations. CAPM is a model that suggests the only explanation for the differences in stock returns is the beta (systematic risk) of the corresponding asset. The larger the beta, the larger the expected return should be. On top of this statement, CAPM mentions that that the relation between expected return and beta is linear. The model is built and introduced by Jack Treynor (1961), William Sharpe (1964), John Lintner (1965), Jan Mossin (1966) independently and it relies on the earlier work of Harry Markowitz Modern Portfolio Theory (MPT) which is developed in 1950 s. CAPM is valid with certain assumptions. Those assumptions are as following: -Investors agree on the distribution of asset returns. -Investors have same fixed investment horizon. -Investor hold efficient frontier portfolios. This assumption links CAPM with MPT. -Investors can borrow and lend at risk free rate. -Demand of assets equal to the supply in equilibrium. -Investors are risk averse and rational with assuming all information is available at the same time to all investors. Empirical studies of Gibbons (1982), MacKinlay (1987), Reinganum (1981), Lakonishok and Shapiro (1986) and Coggin and Hunter (1985) all show that CAPM does not hold for many cases. 5

6 Then, people start to ask such questions like Are there any other explanatory variables besides beta? Is it possible to construct a more general model to explain the cross sectional differences of expected return with less demanding assumptions than CAPM? Arbitrage Pricing Theory is developed by Ross (1976) as an answer to those questions. APT predicts a relationship between an asset return and various factors risk premiums. This theory differs from CAPM in the sense that APT does not use an equilibrium argument as CAPM so it does not identify the factors. Also APT has less stringent assumptions. The assumptions of APT are as following: -All common variation between returns can be described by a factor model. -There are no arbitrage opportunities. -Idiosyncratic risk can be diversified through portfolio formation. -There is perfect competition in the market. There is no assumption about utility functions and mean variance analysis in APT different than CAPM. CAPM can be considered a special case of APT. To implement APT, we need factors. As theory does not specify them, we need certain strategies to derive factors. Three strategies in the literature are set to find factors: using macroeconomic variables, using statistical analysis and data mining. Macroeconomic models compare a stock s return with such factors as inflation, GDP, Treasury bill rates. Chen, Roll and Ross (1986) used some macroeconomic variables as factors to explain variation in stock returns. The factors are the spread between long and short term interest rates, expected and unexpected inflation, industrial production, and the spread between high- and low-grade bonds. Statistical models are used to derive factors through statistical methods such as factor analysis and principal component analysis. Through statistical methods, Roll and Ross (1980) found at least 3 probably 4 factors are significant in explaining asset returns using the data of individual equities between 1962 and 1972 period. Data mining allows us to find portfolios whose returns can be used as factors. Using data mining methods, Eugene Fama and Kenneth French found that two factors, in addition to market risk (beta), namely value and size, have great descriptive and predictive power for the returns of listed stocks. Actually those factors are proxies for macroeconomic sources of risks which are unknown to 6

7 us. Those two factors are called SMB and HML. SMB is the abbreviation of Small minus Big and it refers to additional returns generating from investing in stocks with relatively small market capitalization. HML, which stands for High minus Low, suggests extra returns provided to investors for investing in companies with high book to market ratios. Those premiums are called as size and value premiums respectively. Fama French Three Factor Model is improved by Carhart. Carhart(1997) extended Fama French Model by adding a momentum factor (MOM). This factor represents the persistency of stock returns over short periods. In this paper, I would like to use macroeconomic models to explain the variation in stock returns for U.S economy. Also for the first time in literature, 131 Macroeconomic variables of U.S economy are employed to dynamic factor analysis to extract common macro factors which are considered to have significant power on explaining the common movements in asset returns and certain linear factor models such as CAPM and Fama French Three Factor Model will be used as benchmarks in assessing the success of the model Principal Component Analysis Principal Component Analysis is a common technique for finding the patterns in data of high dimension where graphically representing the data is infeasible and explaining the data in such a way as to highlight their similarities and differences. In order to find the patterns, PCA exploits the correlation structure of the data. The major aim of the PCA is to use only a reduced set of principal components to represent the original variables. This technique is developed by Pearson (1901) and Hotelling (1933). I used principal component analysis to overcome the problems related with measurement error in individual series. It anticipates that few latent common factors can explain large number of macro series. Stock and Watson (2002) showed that those factors can be derived by principal component analysis and Bai and Ng (2002) developed criteria to determine number of those latent factors. Stock and Watson (2006) used dynamic factor analysis in various forecasting techniques. They discuss various opportunities and challenges of factor analysis. They compare the performance of forecasting methods for U.S. industrial production using 130 predictors. In their word, dynamic factor analysis allows us to turn dimensionality from a curse into a blessing. Ludvigson and Ng (2007) also used dynamic factor models to extract latent factors from quarterly 209 macro series and 172 financial series. Using those factors they model conditional mean and volatility of excess stock market return. 7

8 They found positive relation between conditional risk return relations. They found 2 factors from financial variables which help to predict excess stock market return. Lastly, Ludvigson and Ng (2009) use macro series to extract factors using monthly data from 1964 to They found these factors have predictive power for excess bond returns beyond the Cochrane Piazzesi factor. As you can observe the principal component analysis are widely used for predictability analysis before. In this paper, I will employ this technique to extract latent factors and test if those factors explain cross section of stock returns and whether they are priced or not. 3-Methodology In this section I explain asset pricing methods of the research. Asset pricing process includes extracting latent factors through principal component analysis, and two pass Fama-Macbeth regressions of portfolios on those latent factors. 3.1 Factor Model I would like to price r it,return at time t, using large number of explanatory variables. I propose the following statistical model. r it = a i + b ij *I j + e it ; E(e it ) = 0 ; cov(e it I j ) = 0 where, r it is the actual return on portfolio i a i is the unique part on the expected return on portfolio i b ij is the beta coefficients I jt is the factor j realizations e it is the stochastic part of the actual return on portfolio i The model above becomes a factor model if we add the assumption that cov(eit,ejt) = 0 (the residuals are uncorrelated with each other). This means that all common variation between asset returns is explained by the factors and the covariances among the factors. The residual component of 8

9 an asset's return is assumed to be unrelated to that of any other asset, and hence totally specific to that asset. In the above model it is also assumed that the error terms are uncorrelated with the factors. As we can observe on the factor model above, the factors are not indicated so first of all factors should be derived of the model. The literature suggests three strategies to specify the factors. The first one is to use the macroeconomic variables such as changes in GDP, inflation, interest rates etc.. Second way is to use a statistical model to select factors by exploiting the correlation structure of the data, as in Principal Components Analysis. Finally, one can take advantage of data mining to decide on the factors. Fama-French three-factor model was developed with the help of this technique in such a way that they came up with proxies for the true sources of risk which are unknown. 3.2 Extracting Latent Factors I would like to use macroeconomic variables to explain the variation in stock returns for U.S economy. Hence, I jt represents the 131 macroeconomic time series variable in this setting. Running the factor model utilizing so huge data may result with possible measurement errors in individual series. To overcome the dimensionality problems, I propose a factor structure on I jt. Denote I t = ( I 1t, I 2t, I nt ) and ᴧ= (λ 1, λ 2, λ n ) I jt =λ i f t +e it where f t is an r x 1 latent common macro factors λ i is an r x 1 factor loadings e it is errors t is estimated by principal component analysis. Sum of squared residuals (I t - ᴧ f t ) is minimized this way. 9

10 3.3 Fama-MacBeth Two Pass Regressions After the construction of macro model, the model should be tested to measure its empirical performance. A two step APT test procedure of Fama-Macbeth can be implemented in this aspect. Fama-Macbeth(1973) is a method that we use to estimate APT parameters. Those parameters are estimated in two steps: First, time regression is conducted. Each asset is regressed against its risk factors and corresponding betas for each factor are estimated. Second, all asset returns for a certain time period are regressed against estimated betas from first pass regressions to find out the risk premium for each factor Estimation of Factor Betas r it = i + b 1 f 1t + b 2 f 2t + b 3 f 3t + b 4 f 4t + b 5 f 5t + b 6 f 6t + b 7 f 7t + b 8 f 8t + e it r it - i = b 1 f 1t + b 2 f 2t + b 3 f 3t + b 4 f 4t + b 5 f 5t + b 6 f 6t + b 7 f 7t + b 8 f 8t + e it i =(1,.N) where r it is the time series of portfolio i returns b k is the factor beta coefficients f kt is the factor k realizations e it is the stochastic part of the actual return on portfolio i Each portfolio is regressed against latent common macro factors that are extracted through principal component analysis and corresponding betas for each factor are estimated. In the above equation, only latent macro factors are considered as risk factors of the model. The regressions are also done with the addition of market risk factor-beta-, size, value and momentum factors. The first pass regression equation with latent factors and market risk factor beta- : 10

11 r it = i + b 1 f 1t +..+ b 8 f 8t + β i (r mt r ft )+ e it r it - i = b 1 f 1t +..+ b 8 f 8t + β i (r mt r ft )+ e it i =(1,.N) The first pass regression equation with latent factors, market risk factor beta-, size and value factors of Fama French 3 factor model: r it = i + b 1 f 1t +..+ b 8 f 8t + β i (r mt r ft )+ s i SMB t + h i HML t + e it r it - i = b 1 f 1t +..+ b 8 f 8t + β i (r mt r ft )+ s i SMB t + h i HML t + e it i =(1,.N) The first pass regression equation with latent factors, market risk factor beta-, size, value and momentum factors r it = i + b 1 f 1t +..+ b 8 f 8t + β i (r mt r ft )+ s i SMB t + h i HML t + m iwml t + e it r it - i = b 1 f 1t b 8 f 8t + β i (r mt r ft )+ s i SMB t + h i HML t + m iwml t + e it i =(1,.N) where r it is the time series of portfolio i returns b k is the factor beta coefficients f kt is the factor k realizations e it is the stochastic part of the actual return on portfolio i β i is the market risk factor beta r m is the market return and r f is the risk free rate s i is the level of exposure to the size risk h i is the level of exposure to the value risk m i is the level of exposure to the momentum risk 11

12 SMB is the size risk premium HML is the value risk premium WML is the momentum risk premium Estimation of Factor Risk Premiums r i = λ 0 + i1λ 1 + i2λ 2 + i3λ 3 + i4λ 4 + i5λ 5 + i6λ 6 + i7λ 7 + i8λ 8 + e i i= (1,.N) for each t = (1,..T) where r i is the portfolio i returns ik is the estimated factor beta coefficients of portfolio i to factor k λ k is the factor risk premium e i is error term All portfolio returns for each time period is regressed against estimated betas that are derived from first pass regressions to find out the risk premium for each factor. The above equation is related with second pass regressions done with only latent macro factors. Those regressions are done also with additional factors: market risk factor-beta-, size, value and momentum factors. The equations are as following: Latent factors and market risk factor beta: r i = λ 0 + i1λ 1 + i2λ 2 + i8λ 8 + iλ capm +e i i= (1,.N) for each t = (1,..T) Latent factors, market risk factor beta, size and value factors of Fama French 3 Factor Model: r i = λ 0 + i1λ 1 + i2λ 2 + i8λ 8 + iλ CAPM + iλ SMB + iλ HML +e i 12

13 i= (1,.N) for each t = (1,..T) Latent factors, market risk factor beta, size, value and momentum factors r i = λ 0 + i1λ 1 + i2λ 2 + i8λ 8 + iλ CAPM + iλ SMB + iλ HML + iλ WML +e i i= (1,.N) for each t = (1,..T) where r i is the portfolio i returns ik is the estimated factor beta coefficients of portfolio i to factor k λ k is the factor risk premium e i is error term i is the estimated market risk factor beta coefficient I is the estimated size risk coefficient I is the estimated value risk coefficient I is the estimated momentum risk factor coefficient Second pass cross sectional regression generates time series of lambdas (λ ). Finally, I conduct t tests on the average of lambdas (λ ). The hypothesis here says that those average lambdas for each factors are significantly different from 0. 4-Data and Factors 4.1. Stock Returns & Fama French Factors Stock returns and fama french factors with additional momentum factors are obtained from Fama French Data Library which is available in Kenneth R. French s website. 13

14 For the stock returns two separate data sets are used: 100 portfolios formed on size and book and 49 industry portfolios. Using portfolios instead of individual stocks help on testing my factor model. The betas obtained by using portfolios is less noisy than individual stocks so that our Fama-Macbeth regressions to test the model will be more healthy. Both data sets are monthly, value weighted and restricted to the timeline between 1964:1-2007:12. Please see appendix table A.1 and table A.2 for summary statistics of those portfolios. Also the map that demonstrates which industry portfolio number refers to which industry could be seen on appendix table A.4. As mentioned the factor model is constructed also for expansion and contraction dates. Those dates are obtained from national bureau of economic research website. Boom and recession times throughout history can be observed from the table in appendix table A.5. When portfolio statistics of expansion and contraction dates are compared, not surprisingly, we can see that expansion periods have higher average returns. Another important point that we can infer from the comparison is that the returns have higher standard deviation in contraction dates. This proves the asymmetric volatility fact which states bad news tend to increase conditional volatility more than good news. Please refer to appendix table A.3 to see the comparison table of expansion and recession periods Macroeconomic Series & Latent Factors 131 monthly macroeconomic series from 1964:1-2007:12 are obtained from Ludvingson s website. This data set is also used in Ludvingson and Ng (2009b). They used this data set to analyze the predictive power of macroeconomic factors for excess bond returns. Also Stock and Watson (2005) and Ludvingson and Ng (2009a) used similar macroeconomic series. Stock and Watson (2005) data sets cover 132 macroeconomic time series from 1959:1-2003:12. Ludvingson and Ng (2009a) utilized just same series with Stock and Watson (2005) but their series start in 1964:1 to match with bond yield data. Ludvingson and Ng (2009b) spanned the data to 2007:12 from 1964:1 and took one series out since it is not available after The main source of the data sets mentioned are Global Insights Basic Economics Database and The Conference Boards Indicators Database. Various normalization techniques applied to each series to induce stationary ( first difference, logarithm, first and second difference of the logarithm). Also I standardize these series by subtracting the mean from the observations and dividing it by the standard deviation before applying principle component analysis to extract series. 14

15 Macro series consists of 8 groups: Group 1: Output and Income 1-20 Group 2: Labor Market and Group 3: Housing Group 4: Consumption, Orders and Inventories 3-5, Group 5: Money and Credit Group 6: Bond and Exchange rates Group 7: Prices Group 8: Stock Market Please refer to appendix 1 table A.6 for more detail about those macro series. From the macro series, I estimate 8 latent monthly factors 1964:1-2007:12 using principal component analysis. To determine number of factors, I use criteria developed in Bai and Ng (2002). According to criteria they develop, the correlation structure of 131 macro series is well explained by 8 factors. Table 4.2 Summary Statistics for it i AR1 R AR1 is the first order autocorrelation coefficient for it, R 2 is total variance explained in the data by factors 1 to i 1 Appendix is cited from Ludvingson and Ng (2009b) appendix. 15

16 Table 1 summarizes how factors are related to macro data. Second column shows the persistence of the factors, they are not very persistent variables, highest is 0.77, minimum is Third column shows the variance in the 131 series explained by the factors, 8 factors explain 49% of the variation in the data. Estimated factors are orthogonal to each other by construction. The first factor reveals the most important pattern, the second one reveals the pattern that has a lesser importance, and the third one explains the pattern that has a much lesser importance and so on. It is hard to name factors in an economically meaningful way, since they are loaded from various macro series. In the following figures I report the marginal R-squares for all eighth factors. Marginal R-squares is estimated by regressing each macro series on the estimated factor. It can be interpreted as factor loadings; it shows how estimated factor is related to the series. As it is apparent from the figure, first factor is loaded on most of the series and especially on output, income, labor market and housing variables. We can call it real factor since it is connected to the real economy. Second factor is loaded heavily on the series from 80 to 100 which consists of group 8 Stock Market and group 6 Bond and Exchange rates , we can call it financial factor. The third and fourth factors attach on inflation and price macro series. Factor 4 is also related with the nominal interest rates level. Nominal interest rates by nature can disclose information about inflationary expectations. Therefore, factor 3 and factor 4 can be called inflation factors. Factors 5 and 6 loaded on everywhere, it is not possible to make certain economic interpretation on them. Factor 7 sticks mostly on money and credit data series. Factor 8 loaded mainly on stock market series ( like S&P return, price dividend ratio, price earning ratio ). 16

17 ** Series are regressed onto factor 1 and corresponding R-squares are reported on chart. ** Series are regressed onto factor 2 and corresponding R-squares are reported on chart. 17

18 ** Series are regressed onto factor 3 and corresponding R-squares are reported on chart. ** Series are regressed onto factor 4 and corresponding R-squares are reported on chart. 18

19 ** Series are regressed onto factor 5 and corresponding R-squares are reported on chart. ** Series are regressed onto factor 6 and corresponding R-squares are reported on chart. 19

20 ** Series are regressed onto factor 7 and corresponding R-squares are reported on chart. ** Series are regressed onto factor 8 and corresponding R-squares are reported on chart. 20

21 5-Results Model specification is the main challenge in the empirical strategy used in this paper. I need to determine which factors should be used for factor model in addition to 8 latent factors. As additional factors; market risk factor-beta-, size factor, value factor and momentum factors are utilized. Four different factor models are constructed using different combination of latent factors and additional factors. Those are as following: - 8 latent factors are the factors of the model. The research question here is that Do latent factors extracted through large macro series have an effect on explaining the common variation in U.S stock returns? - 8 latent factors plus market risk factor-beta- are the factors of the model. The research question here is that Are latent factors significant priced risk factors in addition to market risk factor- beta-? - 8 latent factors plus fama french 3 factors namely market risk factor beta, size and value factors are the factors of the model. The research question here is that Are latent factors significant priced risk factors in addition to market risk, size and value factors of FF3? - 8 latent factors plus fama french 3 factors and momentum factor are the factors of the model. The research question here is that Are latent factors significant priced risk factors in addition Fama French 3 factors plus momentum factor? After constructing the factor models, I need to measure the empirical performance of each. Fama Macbeth two pass regression methodology arises in this point. To check robustness while conducting Fama Macbeth regressions, I also used four different data sets as independent factors: -Fama French 100 portfolios formed on size and book. -Fama French 49 Industry portfolios. -Fama French 100 portfolios formed on size and book at expansion periods only. -Fama French 100 portfolios formed on size and book at contraction periods only. In performing Fama Macbeth tests, firstly, estimation of betas by regressing each portfolio with the predetermined risk factors are realized. 21

22 Table 5.1 Time Series Regression Results of Fama French 100 Portfolios Formed on Size and Book factor1 factor2 factor3 factor4 factor5 factor6 factor7 factor8 F Test Average R squared Percentage of 1% 42% 100% 0% 42% 83% 50% 2% 100% 100% Latent Factors Significant Latent Factor Beta 5% 68% 100% 1% 67% 96% 76% 13% 100% 100% Coefficients 10% 80% 100% 3% 75% 100% 80% 17% 100% 100% Percentage of Latent factors & Significant Latent Market Risk Factor Factor Beta Beta Coefficients Latent factors & Market Risk, Size and Value Factors of FF3 Latent factors & Market Risk, Size Value and Momentum Factors of FF4 Percentage of Significant Latent Factor Beta Coefficients Percentage of Significant Latent Factor Beta Coefficients 1% 2% 29% 1% 4% 13% 10% 2% 53% 100% 5% 17% 44% 5% 13% 32% 33% 7% 66% 100% 10% 35% 57% 12% 21% 40% 48% 19% 68% 100% 1% 4% 13% 6% 0% 3% 1% 4% 6% 100% 5% 20% 22% 16% 6% 12% 6% 16% 14% 100% 10% 31% 27% 24% 12% 28% 11% 23% 19% 100% 1% 4% 14% 5% 0% 3% 0% 4% 6% 100% 5% 21% 23% 17% 7% 14% 6% 14% 14% 100% 10% 34% 27% 28% 13% 28% 14% 25% 19% 100% Fama French 100 Portfolios Formed on Size and Book is regressed on latent factors and other additional factors. Percentage of significant factor beta coefficients, F test results and average R-square are reported. Table 5.1 shows the beta coefficient estimates of risk factors in Fama French 100 portfolios formed on size and book. The rate of portfolios with significant beta estimates are demonstrated. F test is also stated for the significance of the regression formula overall. Lastly, we can observe average level of the coefficient of the determination from the table. When F significance levels are investigated, it is observed that in all four different structured factor models, 100% of time series regressions have significant F test figures at 1%, 5% and 10% levels. Secondly, we can infer from the table that adding the market risk factor beta to the factor model with only latent factors has increased the average coefficient of determination significantly from to Inserting Size (SMB) and Value Factors (HML) to the model has also a positive effect 22

23 on the average coefficient of determination. It rose up to from Momentum Factor (WML) which is an additional factor to the Fama French Three Factor Model has slightly increased the r squared balance from to Thirdly, we can see that when only latent factors are set as factors, high number of portfolios have significant factor beta estimates other than the betas corresponding to factor 3 and factor 7. As mentioned before factor 3 attaches to inflation and price macro series and factor 7 is related with money and credit variables. This means, inflation factor and money credit factor do not have a significant effect on 100 portfolios formed on size and book. Factor 2 and Factor 8 which are related with stock markets and bond returns have the highest percentage of significance. Lastly, when factor 3 and factor 7 are put aside, individual significance of the factors tend to decrease with the inclusion of the market risk factor-beta, size, value and momentum factors into the factor model structure. We can observe that the most effected factor with addition of other factors is the factor 2. Factor 2 is related with stock market and bond returns so that it is called as financial factor as stated before. Since market risk factor-beta, size, value and momentum factors are also financial factors, the significance level of factor 2 decreases sharply. 23

24 Table 5.2 Time Series Regression Results of 49 Industry Portfolios factor1 factor2 factor3 factor4 factor5 factor6 factor7 factor8 F Test Average R squared Percentage of 1% 33% 100% 4% 35% 59% 20% 10% 100% 100% Latent Factors Significant Latent Factor Beta 5% 57% 100% 6% 61% 80% 37% 27% 100% 100% Coefficients 10% 69% 100% 6% 71% 88% 57% 35% 100% 100% Latent factors & Market Risk Factor Beta Latent factors & Market Risk, Size and Value Factors of FF3 Latent factors & Market Risk, Size Value and Momentum Factors of FF4 Percentage of Significant Latent Factor Beta Coefficients Percentage of Significant Latent Factor Beta Coefficients Percentage of Significant Latent Factor Beta Coefficients 1% 14% 14% 8% 10% 2% 4% 10% 29% 100% 5% 35% 27% 14% 14% 12% 10% 27% 39% 100% 10% 39% 35% 24% 20% 14% 22% 29% 47% 100% 1% 14% 6% 8% 8% 4% 2% 14% 4% 100% 5% 33% 18% 18% 18% 8% 10% 27% 18% 100% 10% 41% 27% 27% 24% 14% 18% 37% 27% 100% 1% 16% 6% 8% 6% 4% 0% 14% 4% 100% 5% 33% 18% 18% 18% 8% 12% 29% 18% 100% 10% 39% 27% 27% 24% 14% 16% 35% 27% 100% Industry Portfolios is regressed on latent factors and other additional factors. Percentage of significant factor beta coefficients, F test results and average R-square are reported. Table 5.2 shows the beta coefficient estimates of risk factors in Fama French 49 Industry Portfolios. F tests for Industry portfolios states that 100% of regressions have significant f significance level. Also average coefficient of determination figures have increased with the addition of market risk factor beta, size, value and momentum factors. When factor models with 100 portfolios and 49 industry portfolios are compared, we observe factor models with 49 Industry portfolios have smaller average r squared values. Factor 3 and factor 7 again has statistically insignificant effect on 49 industry portfolios but the percentage of significant beta coefficients for those risk factors are higher than that of 100 industry portfolios. The significance level of beta coefficients for the other factors are decreasing with addition of beta, size, value and momentum factors. 24

25 Table 5.3 Time Series Regression Results of Fama French 100 Portfolios Formed on Size and Book (Expansion Periods) factor1 factor2 factor3 factor4 factor5 factor6 factor7 factor8 F Test Average R squared Percentage of 1% 13% 100% 0% 9% 50% 46% 0% 100% 100% Latent Factors Significant Latent Factor Beta 5% 35% 100% 0% 30% 73% 72% 3% 100% 100% Coefficients 10% 57% 100% 1% 46% 88% 83% 14% 100% 100% Percentage of Latent factors & Significant Latent Market Risk Factor Factor Beta Beta Coefficients Latent factors & Market Risk, Size and Value Factors of FF3 Latent factors & Market Risk, Size Value and Momentum Factors of FF4 Percentage of Significant Latent Factor Beta Coefficients Percentage of Significant Latent Factor Beta Coefficients 1% 1% 27% 0% 3% 4% 4% 1% 50% 100% 5% 9% 45% 5% 16% 16% 13% 6% 61% 100% 10% 16% 54% 9% 21% 31% 25% 15% 67% 100% 1% 4% 10% 5% 1% 1% 3% 1% 7% 100% 5% 16% 22% 14% 9% 6% 10% 8% 15% 100% 10% 21% 27% 22% 16% 12% 15% 14% 22% 100% 1% 4% 9% 6% 1% 2% 3% 1% 6% 100% 5% 19% 21% 18% 9% 7% 11% 9% 15% 100% 10% 27% 29% 27% 16% 15% 18% 19% 20% 100% Fama French 100 Portfolios Formed on Size and Book for expansion periods is regressed on latent factors and other additional factors. Percentage of significant factor beta coefficients, F test results and average R-square are reported. Table 5.4 Time Series Regression Results of Fama French 100 Portfolios Formed on Size and Book (Recession Periods) factor1 factor2 factor3 factor4 factor5 factor6 factor7 factor8 F Test Average R squared Percentage of 1% 0% 91% 0% 0% 6% 0% 0% 91% 98% Latent Factors Significant Latent Factor Beta 5% 0% 96% 0% 1% 47% 0% 0% 96% 99% Coefficients 10% 1% 100% 0% 6% 76% 0% 0% 96% 99% Percentage of Latent factors & Significant Latent Market Risk Factor Factor Beta Beta Coefficients Latent factors & Market Risk, Size and Value Factors of FF3 Latent factors & Market Risk, Size Value and Momentum Factors of FF4 Percentage of Significant Latent Factor Beta Coefficients Percentage of Significant Latent Factor Beta Coefficients 1% 0% 0% 0% 1% 0% 0% 0% 0% 100% 5% 3% 0% 0% 2% 2% 4% 1% 8% 100% 10% 10% 6% 0% 4% 4% 12% 3% 22% 100% 1% 1% 2% 0% 1% 1% 1% 2% 0% 100% 5% 6% 9% 3% 5% 4% 6% 11% 0% 100% 10% 16% 14% 6% 9% 8% 14% 13% 7% 100% 1% 2% 1% 0% 2% 0% 1% 1% 0% 100% 5% 6% 12% 2% 6% 3% 6% 6% 0% 100% 10% 16% 20% 8% 10% 6% 13% 10% 8% 100% Fama French 100 Portfolios Formed on Size and Book for recession periods is regressed on latent factors and other additional factors. Percentage of significant factor beta coefficients, F test results and average R-square are reported. Considering the different behavior of stock returns in expansion and contraction periods, I propose two factor models for those periods. Time series regression results of expansion periods and contraction periods of Fama French 100 portfolios formed on size and book are reported in table

26 and table 5.4 respectively. It is observed that by contrast to expansion periods most of the factors are not significant on portfolio returns. Furthermore, the percentage of significant beta coefficients has a tendency to drop in values with the insertion of beta, size, value and momentum factors for both expansion and contraction periods. Another thing that we can derive from the tables is that average coefficient of determination is higher for the recession periods. This means the proportion of the sample variance of recession periods portfolio returns explained by the model are higher than that of the boom periods. Overall significance level of models which is stated by F tests are substantially high for both sub periods. After estimation of beta coefficients, the next step is to run cross sectional regressions to estimate the lambdas using the beta coefficients obtained from the first pass regressions as regressors. Cross sectional regressions are conducted for each month and lambdas are estimated. After then, I average the lambdas and t test is performed on the average of the series. 26

27 Table 5.5 Cross Sectional Estimation Results of 100 Portfolios Formed on Size and Book Latent factors Latent factors & Market Risk Factor Beta Latent factors & Market Risk, Size and Value Factors of FF3 Latent factors & Market Risk, Size, Value and MomentumFactors of FF4 λ1 Average Std. Dev t-stat ** λ2 Average Std. Dev t-stat 3.927*** 1.834* λ3 Average Std. Dev t-stat 2.736*** λ4 Average Std. Dev t-stat 1.790* 2.636*** 3.167*** 2.365** λ5 Average Std. Dev t-stat 2.798*** λ6 Average Std. Dev t-stat * * λ7 Average Std. Dev t-stat * * λ8 Average Std. Dev t-stat 1.738* * λcapm Average Std. Dev t-stat * λsmb Average Std. Dev t-stat λhml Average Std. Dev t-stat 2.170** λwml Average Std. Dev t-stat 2.989*** This table shows the cross-sectional regression estimation results using the Fama French 100 portfolios formed on size and book to market portfolios. * Significant at 10% ** Significant at 5% *** Significant at 1% 27

28 Table 5.5 presents the average, standard deviation and t-stat results of risk premiums (lambdas) of corresponding latent factors of Fama French 100 portfolios formed on size and book. When only latent factors are determined as the factors of the model, all lambdas are statistically significant at 10%. Moreover, lambda 1 is significant at 5% and lambda 2,3 and 5 are significant at 1%. Those results implies that the latent macro factors are statistically significant priced risk factors. When market risk factor-beta- is included in the factor model, we observe that the significance of t stats are decreasing. Only risk premias of factor 2, factor 4 and factor 7 and factor 8 are significant. This leads to the fact that when market risk factor beta is penetrated to the model; stock market and bond return series (factor 2), macro series related with nominal interest rate level (factor 4), money and credit data series (factor 7) and stock market series (factor 8) have a significant effect on Fama French 100 portfolios which represents U.S stock returns. Size, value and momentum factors also have a negative effect on the significance of latent macro factors on explaining the common variation in Fama French 100 portfolios as could be observed on the table. 28

29 Table 5.6 Cross Sectional Estimation Results of 49 Industry Portfolios Latent factors Latent factors & Market Risk Factor Beta Latent factors & Market Risk, Size and Value Factors of FF3 Latent factors & Market Risk, Size and Value Factors of FF4 λ1 Average Std. Dev t-stat * 2.061** λ2 Average Std. Dev t-stat λ3 Average Std. Dev t-stat λ4 Average Std. Dev t-stat λ5 Average Std. Dev t-stat λ6 Average Std. Dev t-stat λ7 Average Std. Dev t-stat λ8 Average Std. Dev t-stat * λcapm Average Std. Dev t-stat λsmb Average Std. Dev t-stat λhml Average Std. Dev t-stat λwml Average Std. Dev t-stat 1.881* This table shows the cross-sectional regression estimation results using the Fama French 49 industry portfolios. * Significant at 10% ** Significant at 5% *** Significant at 1% Table 5.6 summarizes the cross sectional regression results of Fama French 49 Industry Portfolios. Different than 100 portfolios, lambdas are insignificant which refers to latent factors have no relationship with the 49 industry portfolios returns. Only factor 1 and factor 8 seems to have a 29

30 significant effect on returns when fama french 3 factors are included with latent factors. By adding momentum factor to those factors we observe that only factor 1 which is qualified as real factor remains as significant. Table 5.7 Cross Sectional Estimation Results of 100 Portfolios Formed on Size and Book (Expansion Periods) Latent factors Latent factors & Market Risk Factor Beta Latent factors & Market Risk, Size and Value Factors of FF3 Latent factors & Market Risk, Size and Value Factors of FF4 λ1 Average Std. Dev t-stat λ2 Average Std. Dev t-stat 3.405*** 1.941* λ3 Average Std. Dev t-stat 1.784* λ4 Average Std. Dev t-stat *** λ5 Average Std. Dev t-stat λ6 Average Std. Dev t-stat *** ** *** ** λ7 Average Std. Dev t-stat ** λ8 Average Std. Dev t-stat ** λcapm Average Std. Dev t-stat ** λsmb Average Std. Dev t-stat 1.722* λhml Average Std. Dev t-stat 1.801* λwml Average Std. Dev t-stat 3.334*** This table shows the cross-sectional regression estimation results using the Fama French 100 portfolios formed on size and book to market portfolios * Significant at 10% ** Significant at 5% *** Significant at 1% 30

31 Table 5.8 Cross Sectional Estimation Results of 100 Portfolios Formed on Size and Book (Recession Periods) Latent factors Latent factors & Market Risk Factor Beta Latent factors & Market Risk, Size and Value Factors of FF3 Latent factors & Market Risk, Size and Value Factors of FF4 λ1 Average Std. Dev t-stat λ2 Average Std. Dev t-stat λ3 Average Std. Dev t-stat λ4 Average Std. Dev t-stat λ5 Average Std. Dev t-stat λ6 Average Std. Dev t-stat λ7 Average Std. Dev t-stat λ8 Average Std. Dev t-stat 1.932* λcapm Average Std. Dev t-stat λsmb Average Std. Dev t-stat λhml Average Std. Dev t-stat 1.709* 1.710* λwml Average Std. Dev t-stat This table shows the cross-sectional regression estimation results using the Fama French 100 portfolios formed on size and book to market portfolios for recession periods. * Significant at 10% ** Significant at 5% *** Significant at 1% 31

32 Table 5.7 and table 5.8 shows the different results of cross sectional regressions for expansion and contraction periods of Fama French 100 portfolios. In recession periods, latent macro factors fail in explaining the variation in returns. Only factor 8 which is loaded on stock market series has a significant effect when only latent factors are considered as the factors of the model. On the other side, the results of expansion periods show that there is evidence of significant relationship between some of the latent factors and portfolio returns. Table 5.9 Average Coefficient of Determination for Cross Sectional Regressions Independent Variable Latent factors Latent factors & Market Risk Factor Beta Latent factors & Market Risk, Size and Value Factors of FF3 Latent factors & Market Risk, Size and Value Factors of FF4 100 Portfolios Formed on Size and Book 100 Portfolios Formed on Size and Book ** Expansion Periods 100 Portfolios Formed on Size and Book ** Contraction Periods 49 Industry Portfolios Average R Adjusted Average R Average R Adjusted Average R Average R Adjusted Average R Average R Adjusted Average R The R squared figures is within the range of and meaning that 25% to 54% of the cross sectional variation in portfolio returns are explained by the model. Adding market risk factor- beta, size, value and momentum factors increases the average coefficient of determination. When r squared balances are adjusted, the coefficient of determination also increase with addition of risk factors but this time in a smaller magnitude. Another point that we can derive from the table is that explained variation for recession periods is higher than the explained variation for expansion periods. Lastly, we can observe that the proportion of variance explained by the factor model that uses 49 Industry Portfolios as independent variables is higher than the proportion of variance explained by the factor model that uses 100 portfolios. 32

33 6-Conclusion The results show that extracted latent factors through large macroeconomic series have an effect on explaining the common variation in U.S stock returns. This support the link between macro economy and stock returns. Latent macro factors are found to be priced risk factors when portfolio returns are regressed only on the latent factors. When market risk factor-beta, size, value and momentum factors are employed in 3 different factor structure, some of the latent factors remains to be significant and some others turns out to be insignificant risk factors. This shows us that market risk factor-beta-, size, value and momentum factors captures some of the explanatory power of the extracted latent factors. When different portfolios are used rather than Fama French 100 portfolios formed on size and book, the results dramatically change. The latent factors are not priced risk factors anymore when specific type of portfolios such as Fama 49 Industry portfolios are considered. Lastly, I found that latent factors do not behave same on explaining the cross sectional variation for expansion and contraction periods. For contraction periods, nearly none of latent factors have an explanatory power. The reason may be the shortness of the recession periods and abnormal high fluctuations on the asset returns. On the other hand, for the expansion periods, some of latent factors stay to be significant priced risk factors. For future work, this paper can be extended in various ways. We can extend the analysis in other assets, commodities, currencies and corporate bonds for asset pricing and predictability. Results may get more robust, if we can find explanatory power of latent macro series on the common variation of stock returns for other economies. It will also be interesting to find different methodologies to extract factors from macro series. Lastly, model specification can be improved by adding different factors and their functional forms to the factor model. 33

34 References Bai, J., and S. Ng Determining the Number of Factors in the Approximate Factor Models, Econometrica 70: Connor, G., and R. Korajczyk Performance Measurement with the Arbitrage Pricing Theory: A New Framework for Analysis. Journal of Financial Economics 15: Connor, G., and R. Korajczyk Risk and Return in an Equilibrium APT: Application of a New Test Methodology. Journal of Financial Economics 21: Ludvigson, S. C., and S. Ng The Empirical Risk-Return Relation: A Factor Analysis Approach. Journal of Financial Economics 83: Ludvigson, S. C., and S. Ng. 2009a. Macro Factors in Bond Risk Premia. The Review of Financial Studies 22: Ludvigson, S. C., and S. Ng. 2009b. A Factor Analysis of Bond Risk Premia. Handbook of Applied Econometrics forthcoming Stock, J. H., and M. W. Watson Macroeconomic Forecasting Using Diffusion Indexes. Journal of Business and Economic Statistics 20: Erdinç Altay The Effect of Macroeconomic Factors on Asset Returns: A Comparative Analysis of the German and the Turkish Stock Markets in an APT Framework Fama, Eugene F.; French, Kenneth R. (1993). Common Risk Factors in the Returns on Stocks and Bonds. Fama, Eugene F.; French, Kenneth R. (1992). The Cross-Section of Expected Stock Returns. Carhart four-factor model (1997) - extension of the Fama-French model Eugene F. Fama; James D. MacBeth (1973) Risk, Return, and Equilibrium: Empirical Tests. Nil Gunsel; Sadik Cukur (2007)The Effects of Macroeconomic Factors on the London Stock Returns: A Sectoral Approach Ross, S. (1976) The Arbitrage Pricing Theory of Capital Asset Pricing. Sharpe, W. F. (1964) Capital Asset Prices: A Theory of market Equilibrium under Condition of Risk. 34