The predictive power of the payout yield in comparison to the short interest index

The Predictive Power of the Payout Yield in

Comparison to the Short Interest Index

From 1973 until 2010

Master of Science Fawad Tajqurishi

10358854 Msc. Finance

Specialization: Asset Management

Supervised by Dr. L. Zou

July 1, 2018

Statement of originality

Hereby, I, Fawad Tajqurishi, declare that this thesis is written solely by myself. I am willing to take full responsibility of the whole content of this thesis. Furthermore, I declare that the text and the work are written by myself and everything is original. Except the sources that are mentioned in the bibliography, no other sources are used to write and complete this thesis. Finally, Faculty of Economics and Business at the University of Amsterdam is solely responsible for the supervision and completion of this thesis. However, the content of this thesis is excluded from the scope of the responsibilities of the above-mentioned faculty.

Abstract

Asset pricing is important to various groups. Mainly, they want to find out a predictor which can efficiently predict excess market returns. Rapach et al. (2016) showed in their research that the short interest index is the best predictor compared to 14 different predictors to forecast excess market returns across four different horizons, namely; monthly, quarterly, semi-annually and annually horizon. Rapach et al. (2016) performed an in-sample and out-of-sample regression to provide evidence that the short interest index outperforms all 14

predictors across all horizons. However, they did not include the payout yield in their study. Furthermore, Boudoukh et al. (2007) mentioned in their study that dividend-to-price ratio has lost its predictive power over time and the payout yield has become a substitute for it. In this thesis, I use ordinary least squared regression, in-sample and out-of-sample regression to investigate the predictive power of the short interest index and the payout yield regarding excess market returns. Moreover, I will investigate whether dividend-to-price ratio has lost its predictive power over time.

My robust out-of-sample results show that the short interest index outperforms the payout yield and other predictors across all horizons. Also, my robust out-of-sample results show that the payout yield outperforms dividend-to-price ratio at the quarterly, semi-annually and annually horizon, suggesting that the payout yield is a better predictor than dividend-to-price ratio. At the monthly horizon, however, both the payout yield and dividend-to-price ratio fail to outperform the historical benchmark.

Contents

1) Introduction ... 5

2) Literature review ... 7

2.1. The payout yield... 7

2.2. Short interest position of the investors ... 8

2.3. Known predictors and the model ... 10

2.3.1. Inflation rate ... 11

2.3.2. Term Spread ... 11

2.3.3. Dividend to Price ratio ... 12

2.3.4 Price to Earnings ratio ... 12

2.3.5. Default Spread ... 13 2.4. Model ... 13 3) Econometric Analysis ... 14 3.1. Source of Data ... 14 3.2. Descriptive Statistics... 17 4) Methodology ... 19 5) Results ... 21 5.1. In-sample Regression ... 22 5.2. Out-of-sample R2 _{... 26} 5.3. Robustness Check ... 28 6) Conclusion ... 30 7) Appendix ... 31 8) Bibliography ... 33

1) Introduction

Many researchers attempted to predict excess market returns, also called the equity premium. This has been a long tradition in the world of finance. There is a lot of literature about this issue and it is hard to absorb all of them. Different researchers used different techniques, time spans and variables to efficiently predict excess market returns. Although their results and techniques differ, they are all convinced that prediction of excess market returns can work. According to the research of Chen and Zhang (2011), the modern asset pricing is able to predict the aggregate excess market returns. With all the new technologies, methods and researches, we can exploit more opportunities to efficiently predict the aggregate excess market returns. It is important to understand what asset pricing actually is and why do people care about asset pricing?

The main idea of asset pricing is to find out the best predictors which are efficiently able to predict excess market returns. First of all, Chen and Zhang (2011) showed in their research that proxies for payroll growth and net job creation are able to predict excess market returns at the business cycle frequencies. According to them, their main dependent variable is the most significant variable amongst all variables used in their research to predict excess market returns. Secondly, Lettau and Ludvigson (2001) performed a different research compared to Chen and Zhang (2011). They showed in their study that consumption to wealth ratio is significantly able to predict excess market returns. They also conclude that their variable of interest is the strongest variable compared to other variables used in their research. Moreover, Campbell and Thompson (2008) used many ratios in their research and their results showed that those predictors are able to beat the historical average and they conclude that we are able to predict excess market returns. They used in their research variables like dividend-to-price ratio, price-to-earnings ratio, book-to-market ratio, return on equity, term spread and default spread. Moreover, Rapach et al. (2016) showed in their research that information on the short interest position of investors is the strongest predictor amongst the variables used in their research to predict excess market returns. In this thesis, I will build on the research of Rapach et al. (2016). Furthermore, Eiling et al. (2016) used cross-sectional return volatility as their main variable to predict excess market returns. They conclude that their main variable is the strongest variable after the short interest index. Finally, Boudoukh et al. (2007) used the payout yield and net payout yield as their main variables of interest and they also conclude that their variable is significantly able to predict excess market returns both in time-series as in cross-section. In this thesis, I will build on this paper as well.

All the above-mentioned researchers used different variables and methods to predict excess market returns and most of them argue that their predictor is one of the strongest. This is contradictory. The core purpose of this thesis is to combine two of those strongest

predictors and perform a quantitative research to identify the more significant predictor. The most recent study is the research of Rapach et al. (2016) about the short interest position of investors. The research of Boudoukh et al. (2007) is built on many other researches about the relationship between dividend yields and excess market returns. In this thesis, I will combine the short interest variable and the payout yield together and study which of these two

variables has a stronger effect to predict excess market returns across different horizons, performing an ordinary least squared (OLS), in-sample and out-of-sample regression. Therefore, the research question of this thesis will be:

‘’Does the short interest index or the payout yield have a stronger predictive power regarding excess market returns across different horizons’’?

Variables which significantly can predict excess market returns are important to various groups. First of all, academics care about asset pricing. The core research question for them is to understand which economic factors and mechanisms drive stocks’ risk and its returns. Moreover, investors care about predicting excess market returns because it allows them to make better decisions regarding their portfolio. Finally, the general public cares about consistently predicting excess market returns. The reason is that all pensions depend on a good investment decision. For all of them, it is important and useful to have a variable that will help them to forecast excess market returns. Due to unexpected market shocks, it is not entirely possible to predict excess market returns very precisely. The academics, investors and general public are aware of this fact. However, finding a good variable which significantly and consistently can forecast excess market returns is highly credible as well for the researchers as for the application in real events.

To be able to answer the research question of this thesis, section 2 will provide a literature review about the research so far about the variables payout yield, short interest index and other variables which are known predictors to forecast excess market returns. Section 3 discusses about the source of the data which is used to perform the quantitative research of this thesis. Section 4 discusses the methodology of this thesis. The results from the regression outputs are discussed in section 5. The final section gives a conclusion.

2) Literature review

In this section, a detailed literature review is provided about the variables which are used for the quantitative research of this thesis.

2.1. The payout yield

In 1988, Fama and French wrote an article about forecasting stock returns with the main explanatory variable dividend-to-price ratio, also called the dividend yield. In their article, they stated that the R-squared (R2_{) measures the forecast power of the dividend yields} and it increases as the horizon increases. The explanation behind this reasoning is that the autocorrelation increases as the horizon increases. They conclude that the dividend yields explain 5% of the variance of short horizon returns, which are monthly or quarterly returns. Moreover, they stated that the dividend yields can explain up to 25% of the variance of long horizon returns, which are two- to four-year returns.

Miller and Modigliani (1961) introduced the irrelevance theorem. According to this theory, we should not doubt that dividends have an important role in determining the equity returns. However, they stated in their research that the theory does not say much about the usefulness of dividends explaining equity returns. Therefore, it should not be surprising that there exist a lot of literature explaining the role of dividends and dividend yields for asset pricing in time series as well as in cross section. Motivation for this reasoning comes from the Gordon Growth model. In this model, dividend yields are written as the return minus the growth in the dividends (Fama and French, 1988). Therefore, according to Lucas (1978) and Shiller (1981), dividends covary with the aggregate consumption. Another reasoning comes from the heterogeneity in taxes and asymmetric information considerations.

Boudoukh et al. (2007) built further on the research of Fama and French (1988). They propose that the above-mentioned reasoning refers to the cash flow which is received by the equity holders. Such outgoing cash flows can be dividends, or it might be something else which can be seen as a substitute for dividends, such as repurchases. To extend the findings of other researchers that dividends are a good variable to emphasize the asset pricing models (Fama and French, 1988), (Cochrane, 1992), (Benartzi et al., 1997), two important questions may arise, which are; are dividends a good proxy for the total payout and are there some mismeasurements? According to Fama and French (2001), Grullon and Michaely (2004) and Brav et al. (2005), repurchases have become a substitute for dividends over the last two

decades. Hence, it can be discussed whether dividends and repurchases are entirely independent. In this thesis, I will mainly follow the structure provided by Boudoukh et al. (2007) to define the payout yield. Boudoukh et al. (2007) performed a quantitative research about predicting excess market returns. The main difference with Fama and French is that Boudoukh et al. (2007) used the payout and net payout yield as their main explanatory

variable instead of dividend yield. According to Boudoukh et al. (2007), dividend yield can be written as return of dividends minus the growth rate, which is also a variation of the Gorden growth model. According to Boudoukh et al. (2007), the dividend yield has lost its

explanatory power over time. In line with the findings of Boudoukh et al. (2007), Lettau and Ludvigson (2001) conclude in their research that the dividend yield is not a good explanatory variable to predict excess market returns. Moreover, Boudoukh et al. (2007) stated in their research that the loss in the predictive power of the dividend yields are explained by the method how the payout yield is defined. They show that the payouts are underestimated if the repurchases are ignored. According to Boudoukh et al. (2007), the payout yield is defined as dividends plus the net purchases and net payout yield is defined as dividend plus repurchases, minus issuances. Boudoukh et al. (2007) found that the payout yield is the best predictor if a time-series analysis is used. The net payout yield is the best predictor if a cross-sectional analysis is performed. Since this thesis is based on a time-series analysis, the payout yield is used as one of the main explanatory variables. The results of Boudoukh et al. (2007) show that once repurchases are taken into account, the ability to predict excess market returns is more significant both in time-series as in cross-section analysis.

2.2. Short interest position of the investors

Nowadays, the risk premium of the equity market has a huge impact to many financial areas. The risk premium affects the portfolio theory to capital budgeting. As mentioned before, there are a lot of researches which describe that excess market returns are predictable. Rapach et al. (2016) argue that the short interest index is the strongest predictor to forecast excess market returns. They compared short interest index with many other variables, which can be used as a predictor for excess market returns. Their results show that the short interest index outperforms all other predictors as well in the in-sample regression as in the out-of-sample regression. Also, they stated that the short interest index generates gains in utility and Sharpe ratio, which exceeds compared to the other variables used in their research. Moreover, Rapach et al. (2016) provide evidence that the predictability of the short interest index to

forecast excess market returns stems mainly from the channel of cash flow. They suggest that short sellers have more information than others. They can easily anticipate to the changes in the cash flow and adjoined changes in market returns in the future. Furthermore, Rapach et al. (2016) stated that if the short interest index contains information about future excess market returns, higher values of the short interest index (SII) are expected in order to predict lower future excess market returns. The time span of their research is from January 1973 until December 2014. For the in-sample regression, their results show that one basis point increase in the SII corresponds to a decrease in excess market returns by six to seven percentage points. The corresponding R2 _{is 1.24% for the monthly horizon and 12.89% for the annually} horizon. They compared the predictive power of the short interest index with 14 different variables, which are derived from the research of Goyal and Welch (2008). They compared the short interest index with the 14 different variables across different horizons. The research of Rapach et al. (2016) show that the short interest index outperforms all 14 variables at the monthly, quarterly, semi-annually and annually horizon. According to Goyal and Welch (2008), even if some variables are able to predict excess market returns based on an in-sample regression, it can fail to significantly predict excess market returns based on an out-of-sample regression. Rapach et al. (2016) performed also an out-of-sample regression. They found a positive R2 _{for the short interest index. The corresponding R}2 _{statistics are; 1.94%, 6.54%,} 11.70% and 13.24% for the monthly, quarterly, semi-annually and annually horizon. Finally, these R2 _{statistics are higher and more significant compared to the 14 variables used in their} research.

The main question which can be asked from the literature above is: how can the short interest index significantly predict the future excess market returns? As already mentioned before, Rapach et al. (2016) suggest that the short interest index primarily operates through a cash flow channel. Campbell and Ammer (1993) mention that variables which are able to predict excess market returns can be divided into three categories, namely; expected return component, discount rate component and lastly, the cash flow news components. Rapach et al. (2016) suggest that the ability of the short interest index to predict excess market returns in the future comes from the component of the cash flow news. They use in their research

popular variables as a proxy for the market information. Their results show that investors who short sell, mainly possess information about acquisitions. This result is consistent with the findings of Akbas et al. (2017) and Boehmer et al. (2008). Rapach et al. (2016) show that investors with a short positions are efficiently able to predict future excess market returns due to their information of the cash flow in the future. Therefore, it should not be doubted that the

information based on short selling is economically highly credible than it was considered before.

Besides Rapach et al. (2016), there are not many other researchers who studied the effect of short interest position of the investors on the aggregate excess market returns. For example, in 1967, Seneca wrote an article about the relationship between the stock market and the short interest index. Seneca found a negative relationship between those two variables. However, the writer did not examine the predictive power of the short interest index to forecast excess market returns. Also, Lamont and Stein (2004) performed a research about short selling. They focused more on how arbitrage opportunities can prevent short sellers from correcting mispricing for firms registered in Nasdaq. Also, they did not perform any research on the predictive power of the short interest index. Next, Eiling et al. (2016)

performed a research about the predictive power of short interest index. However, their main variable of interest is cross-sectional return volatility. They compare their variable of interest with other variables and one of them is the short interest index. This means that their core focus does not rely short interest index.

To differentiate from the study of Rapach et al. (2016), in this thesis, I will combine the short interest index with the payout yield and other known predictors to forecast excess market returns ahead for different horizons. Rapach et al. (2016) used 14 different variables to compare it with the short interest index. However, they did not include the payout yield into the set of 14 different variables. As described above, there is a lot of literature which state that the payout yield is an important determinant to predict excess market returns and some of them argue that the payout yield has become a substitute for dividend-to-price ratio. This reasoning enables this thesis to conduct the following two hypotheses:

Hypothesis 1: Does the short interest index also outperform the payout yield across all

horizons in order to predict excess market returns?

Hypothesis 2: Has dividend-to-price ratio lost its predictive power over time and has the

payout yield become a better predictor?

2.3. Known predictors and the model

Some other predictors are added in the regression to have a better understanding about the predictive power of the short interest index and the payout yield. Most of the variables are derived from the research of Goyal and Welch (2008). Natural logarithm of price-to-earnings

ratio, inflation rate, term spread, natural logarithm of dividend-to-price ratio and default spread are included in the research. Goyal and Welch (2008) mention that these variables are the most popular set of variables to predict excess market returns.

2.3.1. Inflation rate

Gultekin (1983) studied the relationship between the inflation rate and excess market returns. He stated that most investors are poorly hedged against unexpected and expected inflation rate. According to him, the latter statement is against the Fischer hypothesis which says that there is a positive relationship between the expected inflation and the expected nominal return. Gultekin (1983) studied the relationship between excess market returns and inflation rate in many countries. He mentions that in the United States (US) there is a negative relationship between the inflation rate and excess market returns while there is a positive relationship between those two variables in the United Kingdom (UK). To have a better understanding about the relationship between excess market returns and inflation rate, Gultekin (1983) studied the effect between excess market returns and inflation rate in 26 different countries. His results show that there is no positive relationship between excess market returns and inflation rate for those 26 countries using time-series models. His finding is not consistent with the Fisher hypothesis. Therefore, investors should take the inflation rate into account in order to hedge themselves better.

2.3.2. Term Spread

Viceira (2012) mentions that the difference between the yields of long-term bonds and short-term bonds, also called the term spread, are able to predict future excess market returns positively at time-varying horizons. Moreover, he stated that the yields of long-term bonds are a proxy for the business conditions, while the yields of the short-term bonds are a proxy for economic uncertainty. The yields on the long-term bonds are time varying. As result, this time variation is positively correlated with the term spread. Furthermore, Viceira (2012) stated that yields on the short-term bonds are able to positively predict the volatility of the excess market returns and the volatility in the exchange rate. Finally, in the equilibrium, asset pricing models predict that the expected excess market return of an asset is equal to the systematic risk of the given asset times the price of the given asset. According to these models, variation in time in the expected excess market returns are either the result of variation in price of risk or either the quantity of the bond, or in both.

2.3.3. Dividend to Price ratio

Cordis (2014) mentions that stocks with high dividend-to-price ratio have on average higher excess market returns than stocks with lower dividend-to-price ratio (D/P ratio). This reasoning is also true for stock with higher book-to-market ratio. These regularities are viewed as market inefficiency. The intuition behind this reasoning is that stocks with higher book-to-market ratio and dividend-to-price ratio are often undervalued compared to stocks with the opposite characteristics. Moreover, proponents of the market efficiency hypothesis argue that dividend-to-price ratio is a proxy for unobserved risk factors. Study of Fama and French (1988) shows that the predictive power of the D/P ratio increases across the horizon. The motivation behind this reasoning is that stock prices are directly related to the earnings. The out-of-sample results of Cordis (2014) show that the D/P ratio is able to positively predict excess market returns. According to her, investors should take the D/P ratio into account in order to predict excess market returns and to effectively formulate strategies for their portfolios.

2.3.4 Price to Earnings ratio

Lam (2002) argues that price-to-earnings ratio (P/E ratio) and some other ratios are able to positively predict excess market returns. He focusses on the Hong Kong market. He mentions that the P/E ratio has a dominant effect to capture the average returns of an asset. Also, Basu (1983) found that the P/E ratio has an additional predictive power to forecast excess market returns in the US. Moreover, Ball (1978) stated in his research that the P/E ratio can be a proxy for unnamed factors in excess market returns. He reasons that when a stock has a higher risk and higher expected returns, the prices will be lower compared to the earnings and therefore the P/E ratio is likely to be higher.

The results of Lam (2002) show that the P/E ratio is able to capture the cross-sectional variation in average returns over the period. According to the result of Lam (2002), the P/E ratio should be used as a proxy for risk. Finally, he states that the P/E ratio can be used for the portfolio performance by fund managers and investors.

2.3.5. Default Spread

Chen et al. (2017) performed a research on variables of the credit market which are able to predict excess market returns. They performed an in-sample and out-of-sample regression. Amongst the variables they used, the out-of-sample regression show that the default spread has the strongest predictive power. The strongest predictive power is for the quarterly horizon. According to them, this suggests that the content of external finance premium is informative in order to predict excess market returns.

The default spread contains information about the government policy perspective. Therefore, the default spread contains information of the business cycle. Swings in the default spread can efficiently be used to predict excess market returns (Chen et al., 2017). Hence, monetary authorities are responsible for the stability and maintenance of the financial markets. Ex ante, monetary authorities are also able to use information about future market booms and busts when they have to implement a monetary policy.

2.4. Model

In short, to test the predictive power of the short interest index and the payout yield, an in-sample and out-of-sample regression is performed. Equation (1) represents the regression equation which will be used to predict excess market returns for the different horizons for the in-sample regression. Equation (2) is used to perform the out-of-sample regression. The variables which are used to perform the quantitative research are listed in Table 1. Each variable is regressed separately on the excess market returns for the given horizon.

rt: t+h = a +bi * Xi,t + et: t+h (1)

𝑟#t: t+h = a#t + b$tXt (2)

Where:

3) Econometric Analysis

Thus far, in the previous section a detailed literature review is provided about the variables of interest; the payout yield, the short interest position of the investors, inflation rate, price-to-earnings ratio, term spread, dividend-to-price ratio and the default spread.

This section will discuss about the source of the data which is used to perform the quantitative research of this thesis. Furthermore, it will provide the descriptive statistics.

3.1. Source of Data

In this thesis, I will focus on the United States (U.S) excess market returns, specifically on the returns on the S&P 500 index. The time frame of this thesis will be from January 1973 until December 2010. This thesis contains data of 38 years. This gives 456 monthly observations for each variable. This time frame is chosen because some variables have missing values for the following years and the time frame of Rapach et al. (2016) is approximately the same. Therefore, the results obtained can be compared with the results of Rapach et al. (2016). First, the value-weighted monthly excess market returns on the S&P 500 is downloaded from the website of David. E. Rapach. Second, the one-month T-Bill rate is used as a measure for the risk-free rate. The corresponding data is downloaded from the database of Rapach. Third, the excess market return is defined according to the study of Rapach et al. (2016):

Excess Market Return = Ln(1+Rm) – Ln(1+Rf) (3)

Data for the short interest index is also downloaded from the website of David. E. Rapach. From the website of Rapach, we can download the equal-weighted mean of all asset-level short interest data, also called EWSI. In this thesis, I will follow the method of Rapach et al. (2016) to construct the short interest index. First, the natural logarithm of EWSI is

Table 1

R Excess market returns for the given horizon

PO Payout Yield

SII Short Interest Index

Log (PE) Natural Logarithm Price to Earnings Ratio

I Inflation Rate

TS Term Spread

Log (DP) Natural Logarithm Dividend to Price Ratio

computed (as a percentage of shares outstanding). This contains all the information about short selling in the economy. Figure 1 plots the short interest series. It shows that there is an upward trend over the sample time frame of this thesis. This trend can be explained because equity lending has become easier over time and as a consequence, short selling has become easier over time. Furthermore, the number of hedge funds has increased over time and the amount to short arbitrage has also increased over time. The data for the short interest series is detrended to capture the variation in the short interest series (Rapach et al., 2016). The detrended short interest series is standardized in order to create the short interest index (SII). Figure 2 plots the SII. Both figures are the same as in the study of Rapach et al. (2016).

Fourth, the data for the payout yield, which is defined as the paper of Boudoukh et al. (2007), is provided by the database of Michael. R. Robert’s (Eiling et al., 2016). Fifth, natural logarithm of price-to-earnings ratio is defined as the log of the earnings on the S&P 500, minus the log of stock prices (Goyal and Welch, 2008). The corresponding data is

downloaded from the website of Rober Schiller (Eiling et al., 2016). Sixth, natural logarithm of dividend-to-price ratio is defined as the log of dividends paid, minus the log of stock prices on the S&P 500. The corresponding data is downloaded once again from the website of Robert Schiller. Seventh, the term spread is defined as the difference between the long-term yield minus the 3-month treasury bill rate (Eiling et al., 2016). The long-term yields are the 10-year government bonds. Data for the 10-year government bonds and 3-month treasury bill rate are downloaded from Rapach’s database. Eight, the default spread is computed as

proposed by Eiling et al. (2016). They propose that the default spread can be viewed as the difference in the yield between Moody’s Baa and Aaa rate for the corporate bonds. Data for the yields on the Baa and Aaa for the corporate bonds are also downloaded from the website of Rapach. Finally, database of the Federal Reserve Bank of St. Louis is used to obtain data

Figure 3. Excess Market Return

This figure represents the excess market returns of the whole sample period of this thesis. We can observe that there are some peaks mid 1970’s. This is due the oil crisis. Also, there are some peaks in 1990, 2000 and 2008. This due to the second shock in the oil prices, internet bubble and the recent financial crisis.

3.2. Descriptive Statistics

Table 2

This table reports the summary statistics of the dependent variable excess market return and the seven potential predictors. Those predictors are; natural logarithm of the payout yield, short interest index, inflation rate, term spread, default spread, natural logarithm of price-to-earnings ratio and the natural logarithm of dividend-to-price ratio, represented in column 1 to 8. For each variable the mean, median, standard deviation, 5% percentile, 95% percentile and the total observation are respectively reported in this table. Descriptive Statistics Variable Names Excess market return

(1) Log Payout (2) SII (3)

Inflation rate (4) Term Spread (5) Default Spread (6) PE-ratio (7) DP-ratio (8) Mean 0.0032 -2.2395 8.78e-10 0.0036 0.0168 0.0112 2.8454 -3.6202 Median 0.0078 -2.2134 -0.1476 0.0031 0.0181 0.0096 2.8900 -3.5665 Standard Deviation 0.0460 0.2461 1.0000 0.0035 0.0135 0.0048 0.4829 0.4351 5% Percentile -0.0775 -2.7229 -1.5106 -0.0005 -0.0067 0.0061 2.1400 -4.3569 95% Percentile 0.0717 -1.9506 2.0209 0.0102 0.0350 0.0215 3.6600 -3.0107 Observation 456 456 456 456 456 456 456 456

Table 3

This table reports the correlation matrix between the main dependent variable excess market return and the potential predictors. A correlation matrix will give a precise overview if the sample suffers from the multicollinearity problem.

Correlation Matrix

Excess Market

Return Payout Yield SII

Inflation

Rate Term Spread Defaul Spread ratio PE- ratio DP-Excess Market Return 1.000 Payout Yield 0.0204 1.000 SII -0.0911 0.3005 1.000 Inflation Rate -0.1126 0.2695 0.0364 1.000 Term Spread 0.0835 0.1161 -0.0897 -0.4161 1.000 Defaul Spread 0.0203 0.3906 -0.1057 -0.0229 0.1825 1.000 PE-ratio -0.0198 -0.7833 0.0304 -0.4271 -0.0289 -0.5687 1.000 DP-ratio -0.0601 0.8140 0.0351 0.4328 -0.0046 0.4843 -0.9677 1.000 Column 1 of the correlation matrix is the most crucial column. It shows the correlation between the dependent variable excess market return with the potential predictors. We can observe from the table above that the correlation between the payout yield and excess market return is equal to 2.04%. This means that both are linearly correlated, but not perfectly. The correlation between the short interest index and excess market return is -9.11%. Both are negatively correlated. This is corresponding with the study of Rapach et al. (2016).

Finally, the control variables are also correlated with the excess market return. Some are negatively correlated and others positively. However, none of the predictors are perfectly correlated with the dependent variable excess market return.

It is also important to look at the correlation between the predictors in order to avoid the multicollinearity problem. When two independent variables are highly correlated, it will introduce the multicollinearity problem. Grewal et al. (2004) mentioned in their study that many researchers fail to take into consideration the multicollinearity problem due to practical considerations. Biased results are obtained when there are highly correlated variables in the sample. According to Grewal et al. (2004), two variables are highly correlated when the correlation between those two variables is higher than 0.80 or lower than -0.80. If this is the case, type II errors will occur. The consequence of this type of error is that we cannot precisely detect the significance effect of those variables. Therefore, it is better to exclude highly correlated variables. The most important remark is that the two main variables of this thesis, SII and payout yield, are not highly correlated with other predictors. Said in other

words, the SII and the payout yield contain different information compared to other predictors to forecast excess market returns. The concern of the multicollinearity problem is only an issue for the OLS regression. It should not be a problem for the in-sample and out-of-sample regression, since each predictor is regressed separately on the dependent variable excess market return.

Given the results of table 3, we can observe that only price-to-earnings ratio and dividend-to-price ratio are highly correlated. This is understandable, because in both ratios prices are included. Therefore, in this study multicollinearity is not a major concern for the OLS regression.

4) Methodology

The approach of Rapach et al. (2016) is used to perform the quantitative analysis and answer the research question. In this thesis, I will perform three different types of regressions in order to predict excess market returns across different horizons, namely; ordinary least squared regression, in-sample regression and out-of-sample regression. First of all, I will perform the OLS regression. All the predictors are regressed simultaneously on the dependent variable excess market return for the different horizons. The sample of this thesis contains monthly data for 38 years, which is equal to 456 monthly observations. I will predict excess market returns for four different horizons, namely; 1, 3, 6 and 12 months. The total

observations to predict 1, 3, 6 and 12 months ahead excess market returns for the OLS, in-sample and out-of-in-sample regression are respectively 455, 453, 450 and 444. Data of excess market returns is compounded in order to be able to predict excess market return ahead. For one month ahead, the first future value of the excess market return, which is February 1973, is matched with the data of January 1973 of each predictor. Consecutively, data of March 1973 of excess market return is matched with the data of February 1973 of each predictor. For the first observation of 3 months ahead excess market return, the sum of observations of the months February till April of excess market returns is matched with the first observation of each predictor, which is January 1973. Consecutively, for the second observation of 3 months ahead excess market return, the sum of observations of the months March till May is matched with the second observation of each predictor, which is February 1973. This technique is extended in order to match all 3 months ahead excess market returns with the predictors. This technique is also used for the horizon 6 and 12 months in order to match data of excess market returns with the data of each predictor. Therefore, this method gives for the horizons

of 1, 3, 6, 12 months respectively 455, 453, 450 and 444 observations for the data of excess market returns.

Secondly, the in-sample regression is performed. Rapach et al. (2016) mention in their study that the OLS regression will probably give poor results due to overfitting, because all explanatory variables are regressed simultaneously on the dependent variable. Therefore, each predictor should be regressed separately on the dependent variable excess market return. The purpose of the in-sample regression is that it clarifies which variable has a strong predictive power once the total observation of each predictor for each horizon is regressed separately on the dependent variable excess market return. The regression model for the in-sample

regression is provided in equation (1) above and it is used to perform the in-sample regression. The total observations for each predictor for each horizon for the in-sample

regression is the same as for the OLS regression. The only difference with the OLS regression is that each predictor is regressed separately on dependent variable for each horizon.

After the in-sample regression is performed, I will perform the out-of-sample

regression. The regression model used to perform the out-of-sample regression is provided in equation (2) above.

As already mentioned before, in this thesis, I will predict excess market returns for four different horizons, namely; 1 month ahead, 3 months ahead, 6 months ahead and 12 months ahead. The sample of this thesis contains observations of 38 years, which is equal to 456 monthly observations. The total observations for excess market returns for each horizon is the same as the OLS and in-sample regression. The only difference for the out-of-sample regression is that the first 20 years of the data of each predictor is used to predict k-months (1, 3, 6 and 12 month) ahead excess market returns. Thus, 20 years is equal to 240 monthly observations for each predictor. I use these 240 observations to predict the following 215 excess market returns for the monthly horizon (240+215=455). I can predict the following 213 excess market returns for the quarterly horizon (240+213=453), 210 excess market returns for the semi-annually horizon (240+210=450) and 204 excess market returns for the annually horizon (240+204=444). To perform the out-of-sample regression for each horizon, the first 20 years of observations of each predictor is used to forecast the next monthly, quarterly, semi-annually and annually excess market returns. Since the sample contains data from January 1973 until December 2010, the first 20 years is from January 1973 up to December 1992. For example, for the monthly horizon we have 455 observations. Data for the first 20 years is equal to 240 observations. These 240-monthly observations are used to predict the 241th _{monthly observation. Consecutively, observation 2 till observation 241 is}

used to predict the 242th _{observation. A loop in Stata is created to perform the out-of-sample} regression for each horizon. Once the predicted excess market returns are obtained for each predictor and horizon, the out-of-sample R2 _{is computed. The following equation is used in} order to compute the out-of-sample R2_:

𝑅

_{= 1-}

∑340_,5678(+,-.:,-01:+̅,-.:,-0)6

This equation describes exactly how the R2 _{is computed for each horizon. t stands for the first} 20 years of observations for each horizon, which is equal to 240 observations for each

horizon. T stands for the total observations for each horizon (455, 453, 450 and 444). k stands for each horizon (1, 3, 6 and 12).

The numerator of equation (4) is the sum of the squares realized excess market return minus the predicted excess market return. The denominator of equation (4) is the sum of the squares realized excess market return minus the horizon (k=1, k=3, k=6 and k=12), times the average excess market returns up to time t. The advantage of the out-of-sample regression is that we can compare which predictor has the strongest predictive power across different horizons. An important point which should be taken into consideration is that the out-of-sample R2 _{can be negative. This means that the given predictor fails to outperform the} historical mean. In other words, the historical mean is a better predictor than the predictor which is used to forecast excess market returns for the given horizon.

5) Results

Table 4 in the appendix represents the ordinary least squared regression output. The dependent variable is the excess market return. Furthermore, the explanatory variables are regressed on the different horizons of excess market returns. For example, h=1 represents one month ahead excess market returns. Consecutively, h=3 represents three months ahead excess market returns. From table 4 column 2, we can observe that the short interest index is

significant at 5% level and dividend-to-price ratio is significant at 10% level for the monthly horizon. However, the SII has a larger t-statistics compared to the D/P ratio. Also, the D/P ratio is more significant than the payout yield. Another statistic that should be considered is the R2_{. The variation of the dependent variable explained by the independent variables is}

given by the R2_{. Thus, the variation of one month ahead excess market return explained by the} independent variables is 2.9%.

From column 3 we can observe that the SII, D/P ratio and P/E ratio are significant at 1% level. Once again, the SII is more significant than other predictors and the D/P ratio is more significant than the payout yield. The corresponding R2 _{for predicting 3 months ahead} excess market returns is 9%. Moreover, from column 4 we can observe that the payout yield, SII, D/P ratio and P/E ratio are significant at 1% level. The default spread is also significant but at 10% level. Once again, in this regression, the SII is a more significant coefficient than other predictors and the D/P ratio is more significant than the payout yield. The corresponding R2 _{of the regression is 18%. Finally, from column 5 we can observe that all predictors, except} the default spread, are significant at 1% level. The default spread is not significant anymore at any level. SII is still the most significant predictor for the annually horizon and the D/P ratio is more significant than the payout yield. The corresponding R2 _{for predicting 12 months} ahead excess market returns is now 32.8%. Thus, the R2 _{increases as the horizon increases.} This is because the autocorrelation increases as the horizon increases. Furthermore, over longer horizon the uncertainty increases, and the forecast is less reliable.

To conclude, from the OLS-regression outputs we can observe that the SII is more significant than all the other predictors, even the log of payout yield, which is the other main variable of interest. Moreover, dividend-to-price ratio is more significant than the payout yield across all horizons. From the OLS regression we can conclude that dividend-to-price ratio has not lost its predictive power over time.

Although significant results are obtained, and we can conclude that some variables are able to predict excess market returns, Rapach et al. (2010) suggest that we should not include all the variables simultaneously into one regression, also called the kitchen sink regression. The OLS regression results into poor outcomes due to overfitting, especially for the out-of-sample regression. Therefore, the OLS results are not very reliable and it is better to perform an in-sample and out-of-sample regression.

5.1. In-sample Regression

The regression model which is used to predict excess market returns for the in-sample regression is described in equation (1): rt: t+h = a +bi * Xi,t + et: t+h. The dependent variable, rt: t+h, is the excess market returns on the S&P 500 and Xt represents the predictor. As described by Rapach et al. (2016), the main objective is to test the significance of b in equation (1).

Rapach et al. (2016) recommend in their research that we should perform a one-sided test to test the significance of b. Since overlapping will increase as the horizon increases, we use heteroskedasticity and robust t-statistic to test the following null-hypothesis (H0) versus the alternative hypothesis (HA):

H0 : bi = 0 vs HA : bi > 0 (for positive predictors) HA : bi < 0 (for negative predictors)

In this thesis, the sample period is from January 1973 till December 2010. After considering for lags and overlapping, I have 455 observations for the monthly horizon (h=1), 453 observations for the quarterly horizon (h=3), 450 observations for the semi-annually (h=6) horizon and 444 observations for the annually horizon.

Table 5 reports the results of b, t-statistic and the R2 _{for each predictor for the different} horizons. For the monthly horizon, column 2 and 3, we can observe that only SII is significant at 5% and thus only for the SII coefficients we can reject the null-hypothesis. One standard deviation increase in the SII results in 0.00501 basis point decrease in the next month’s excess market return. Furthermore, the corresponding R2 _{of SII index is 1.2%. This result is in line} with the study of Rapach et al. (2016). Thompson and Campbell (2008) argue in their study that a R2 _{larger than 0.5% is sufficient enough to represent that a variable has a meaningful degree} of predicting excess market returns. The coefficient of the log payout and all other predictors are insignificant for the prediction of one month ahead excess market returns. Moreover, all the predictors have the expected signs as described by the literature. As expected, the coefficient of SII and inflation rate should be negative, and all other predictors should be positive. From the results of table 5 we can observe that this is indeed correct.

Colum 4 and 5 reports the results for predicting excess market return for the quarterly horizon (h=3). From column 4 we can observe that three variables have a significant effect in order to predict excess market return for the quarterly horizon; SII, the D/P ratio and the term spread. First, the coefficient of SII is significant at 1% level and has an R2 _{of 4.2%. Second, the} coefficient of dividend-to-price ratio is significant at 10% level and has an R2 _{of 0.8%. Third,} the coefficient of the term spread is significant at 5% level and has an R2 _{of 1.3%. Amongst the} significant coefficients, SII is the strongest predictor with the largest R2_{. The payout yield is} insignificant for the monthly and quarterly horizon. So far, for horizon 1 and 3, dividend-to-price ratio is more significant than the log payout. Moreover, as described before, all these

significant variables have an R2 _{higher than 0.5%. Thus, all these significant predictors can be} used to predict excess market returns for the quarterly horizon.

Column 6 and 7 represents the results for predicting excess market return for the semi-annually horizon (h=6). From column 6 we can observe that all variables have a significant effect in order to predict excess market return for the semi-annually horizon; SII, log payout, log D/P ratio, log P/E ratio, default spread, term spread and the inflation rate. First, the coefficient of SII is significant at 1% level and has an R2 _{of 7.8%. Second, the coefficient of} the payout yield is significant at 10% level and has an R2 _{of 0.8%. Third, the coefficient of} dividend-to-price ratio is significant at 1% level with an R2 _{of 1.7%. Fourth, the coefficient of} price-to-earnings ratio is significant at 5% level with an R2 _{of 1%. Fifth, the default spread is} also significant at 5% level with an R2 _{of 1.8%. Sixth, the terms spread is significant at 1% level} with an R2 _{of 2.1%. Seventh, the inflation rate is significant at 10% level with an R}2 _{of 0.8%.} Once again, all the predictors have an R2 _{higher than 0.5%. Therefore, we can conclude that all} significant predictors can be used to predict excess market returns for the semi-annually horizon.

Furthermore, the SII has the highest R2 _{compared to all predictors and therefore it} explains the highest variation of excess market returns for the semi-annually horizon. For horizon 1 and 3 we observed that the log D/P ratio had a larger estimated 𝛽= compared to the estimated 𝛽= of the payout yield and it was also more significant than the payout yield. For horizon 6 we can observe that the payout yield has a larger estimated 𝛽= compared to the D/P ratio. However, the dividend-to-price ratio is still more significant than the payout yield.

Column 8 and 9 represent results for predicting excess market returns for the annually horizon. We can observe that all coefficients are significant at 1% level. The R2 _{of SII, payout} yield, log D/P ratio, log P/E ratio, default spread, term spread, and inflation are respectively; 11.7%, 3.4%, 3.6%, 2.3%, 2%, 6.5% and 3%. The SII explains the largest variation in predicting excess market returns for the annually horizon compared to the other predictors. Also, in this case the estimated 𝛽= of the payout yield is larger than the estimated 𝛽= of the D/P ratio, but the D/P ratio is more significant. From the results of the in-sample regression we can conclude that the SII coefficient explains most of the variation of excess market returns compared to the other predictors for all horizons.

In short, SII has a lager R2 _{compared to other predictors across all horizons. The} obtained R2 _{for SII are almost the same as the R}2 _{found in the results of Rapach et al. for all} horizons. (2016). Finally, as described above, many researchers argue that dividend-to-price

ratio has lost its predictive power and we should use the payout yield instead. The in-sample results show that dividend-to-price ratio is still useful to predict excess market returns. It has not lost its predictive power over time.

Table 5

Table 5 represents the results of the in-sample regression output, 1973:01-2010:12. This table reports the estimated beta, t-statistics and the R2 _{for the predictive regression model which is; r}

t: t+h = a + bxt +

et: t+h for t = 1, … , T-h. rt is the dependent variable excess market return on the S&P 500 for the given

month t. xt is the predictor which is listed in column 1. The description of the variables in column 1 are

explained above in table 1. For each predictor the 𝛽=, t-statistic and the R2 _{are represented for the}

different horizons. h=1, h=3, h=6 and h=12 represent 1, 3, 6 and 12 months ahead excess market return. Robust t-statistics are represented between the brackets. * denotes significant at 10% level, ** at 5% level and *** at 1% level, respectively.

Dependent Variable (1) (2) (3) (4) (5) (6) (7) (8) (9) h=1 h=3 h=6 h=12 Predictor 𝛽= R2 _{𝛽= R}2 _{𝛽= R}2 _{𝛽= R}2 SII -0.00501** 0.012 -0.0168*** 0.042 -0.0335*** 0.078 -0.0591*** 0.117 (-2.27) (-3.98) (-5.15) (-6.20) Log Payout 0.00526 0.001 0.0149 0.002 0.0429* 0.008 0.128*** 0.034 (0.54) (0.92) (1.87) (4.00) Log D/P-ratio 0.00503 0.002 0.0165* 0.008 0.0361*** 0.017 0.0742*** 0.036 (0.97) (1.94) (2.92) (4.21) Log P/E-ratio 0.00322 0.001 0.0106 0.004 0.0244** 0.010 0.0537*** 0.023 (-0.70) (1.40) (2.19) (3.33) Default Spread 0.362 0.001 1.157 0.005 3.272** 0.018 5.000*** 0.020 (0.67) (1.14) (2.57) (3.03) Term Spread 0.254 0.006 0.687** 0.013 1.283*** 0.021 3.272*** 0.065 (1.57) (2.39) (3.08) (5.35) Inflation Rate -0.706 0.003 -1.121 0.002 -3.003* 0.008 -8.549*** 0.030 (-0.99) (-0.78) (-1.68) (-3.58) N 455 453 450 444

5.2. Out-of-sample R2

Table 6 reports the results of the out-of-sample regressions for the different horizons. Goyal and Welch (2008) suggested that the out-of-sample regression is important, because the results of the in-sample regression about the predictive power of a given variable to forecast excess market returns does generally not hold for the out-of-sample regressions. Therefore, Goyal and Welch mentioned in their study that the out-of-sample regression can be viewed as a robustness check for the in-sample regressions.

As already described, equation (2) is used to perform the out-of-sample regression. The a# and the b$ are the ordinary least squared estimates for the a and the b described in equation (1). The estimated alpha and the estimated beta is based on the data from the beginning of the sample till month t, which are the observations of the first 20 years. For example, I have data which is monthly based for each predictor. I have data for 38 years for each variable, which is equal to 456 monthly observations. To compute the out-of-sample R2 for the monthly horizon for a given variable, I use observations of the first 20 years (240 monthly observations) to predict the 241th _{observation. Thereafter, I use equation (3) to} compute the out-of-sample R2_{. Equation (3) takes the sum of the squares realized excess} market return minus the predicted excess market return divided by the sum of the squares realized excess market return minus the horizon (1, 3, 6, 12), times the average excess market returns up to month t. Moreover, the average excess market returns up to month t also serves as the natural benchmark.

Table 6

Table 6 reports the results of the out-of-sample R2 _{which is calculated with the equation (2) above,}

1993:01-2010:12. This table reports the R2 _{statistic for the predictive regression model which is:}

𝑟#t: t+h = a#t + b$tXt for t = 1, … , T-h. rt is the dependent variable excess market return on the S&P 500

for the given month t. xt is the predictor which is listed in column 1. The description of the variables in

column 1 are also explained in table 1. For each predictor, the R2 _{is represented for the different}

horizons. h=1, h=3, h=6 and h=12 represent 1, 3, 6 and 12 month ahead excess market returns R2

(1) (2) (3) (4) (5) Out-of-sample R2 Predictor h=1 h=3 h=6 h=12 SII -0.00250 0.0750 0.3773 0.8202 Log Payout -0.0156 0.0249 0.3725 0.8248 Log D/P-ratio -0.0169 0.0393 0.3867 0.8283 Log P/E-ratio -0.0119 0.0498 0.3985 0.8357 Default Spread -0.0527 -0.1901 0.2308 0.8167 Term Spread -0.0139 0.0383 0.3996 0.8351 Inflation Rate -0.0139 0.0363 0.4045 0.8390

Column 2 through column 5 reports respectively the out-of-sample R2 _{for the horizon} 1, 3, 6 and 12 months for each predictor. The out-of-sample R2 _{is based on the sample period} 1993:01 till 2010:12. From column 2 we can observe that the known predictors have a negative out-of-sample R2 _{for the monthly horizon. This result is in line with the results of} Goyal and Welch (2008) and Rapach et al. (2016). Also, we can observe from column 2 that the SII and log payout have a negative out-of-sample R2_{. This is not corresponding with the} results of Rapach et al. (2016). They found a positive out-of-sample R2 _{for the SII for the} monthly horizon. A negative out-of-sample R2 _{means that the given predictor fails to} outperform the historical mean benchmark. This is applicable for all predictors for the

monthly horizon. For the quarterly horizon, we can observe that only the default spread has a negative R2_{. All other predictors have a positive R}2_{. The R}2 _{for the SII, payout yield,}

dividend-to-price ratio, price-to-earnings ratio, term spread, and inflation rate are

respectively; 7.5%, 2.49%, 3.93%, 4.98%, 3.83% and 3.63%. Thus, SII has the largest R2_{. SII} outperforms all the other predictors for the quarterly horizon. For the quarterly horizon, the dividend-to-price ratio has also a higher R2 _{than the payout yield.}

For the semi-annually horizon we can observe that all predictors have a positive R2_. However, SII does not have the largest R2 _{anymore. The inflation rate has the highest R}2_. Furthermore, SII has a larger R2 _{than the payout yield. Therefore, we can conclude that SII is} a better predictor than the payout yield for the semi-annually horizon. Also, the

dividend-to-price ratio has a higher R2 _{than the payout yield. Once again, dividend-to-price ratio is a better} predictor than the payout yield for the semi-annually horizon.

For the annually horizon, we can observe that all predictors have a positive R2_{. The} inflation rate has the highest R2_{. For the annually horizon, we can observe that the payout} yield has a larger R2 _{than the SII. So, for the annually horizon, the payout yield is a better} predictor than the SII. Furthermore, dividend-to-price ratio still has a larger R2 _{than the payout} yield for the annually horizon. We can conclude that the dividend-to-price ratio is a better predictor than the payout yield for the annually horizon.

Rapach et al. (2016) showed that the SII outperforms all other predictors across all horizons. In this thesis, the out-of-sample results showed that the SII is the strongest predictor solely for the quarterly horizon. The results of table 6 also showed that the payout yield is able to outperform the SII for the annually horizon. Finally, results of table 6 showed that dividend-to-price ratio has not lost its predictive power. The dividend-to-price ratio is able to outperform the payout yield across all horizons.

5.3. Robustness Check

In order to control whether the results obtained from the out-of-sample regressions are robust, a robustness check is performed. To perform the robustness check, an out-of-sample regression is performed, but this time with a smaller sample. The total sample contains data from January 1983 till December 2010.

As mentioned before, Rapach et al. (2016) suggested in their study that the OLS regression will give poor results due to overfitting and hence, it will result in a kitchen sink regression. Goyal and Welch (2008) mentioned that the out-of-sample regressions are important, because the results obtained from the in-sample regression about the predictive power of a given variable to forecast excess market returns does generally not hold for the out-of-sample regressions.

Table 7 provides the robust results for the out-of-sample regression. To predict one month ahead excess market returns, we can observe that only SII has a positive R2 _{of 6.8%.} All other predictors have a negative R2_{.To predict three months ahead excess market returns,} we can observe that SII again has the highest R2 _{of 23.6%. We can observe from column 3} that the payout yield also has a positive R2 _{of 2.8%. The D/P ratio has a negative R}2 _{for the} quarterly horizon. Thus, the payout yield is a better predictor than the D/P ratio for the quarterly horizon. For the semi-annually horizon, we can observe that SII still has the highest

R2 _{and the payout yield again outperforms the D/P ratio. For the annually horizon, the SII has} still the highest R2 _{and the payout yield outperforms the D/P ratio. The results obtained from} the robustness check are more in line with the results of Rapach et al. (2016). The SII

outperforms all other predictors across all horizons. We can conclude that SII is the strongest predictor in predicting excess market returns for the different horizons.

In line with the theory of Boudoukh et al. (2007), the payout yield outperforms the D/P ratio across all the horizons. Although, Boudoukh et al. (2007) did not perform an out-of-sample regression, they suggested that the D/P ratio has lost its predictive power over time. The robustness check of this thesis showed that this is indeed the case.

Furthermore, the results obtained earlier showed that SII was not the strongest predictor for the different horizons. In contradiction, the robustness check showed that SII is the strongest predictor across the different horizons.

To perform the robustness check, data over the period January 1973 till December 1982 was deleted. This might have resulted that the SII is now able to outperform all other predictors across all horizons. Rapach et al. (2016) suggested that the SII has become more popular over the last two decades. Short-selling was not very easy before that period. Compared to 1973, short-selling is much easier now. Equity lending has become easier over time and as a consequence, short selling has become easier over time. Furthermore, the number of hedge funds has increased over time and the amount of short arbitrage has increased over time.

Finally, the D/P ratio has a positive R2 _{for the annually horizon only. The payout yield} has a positive R2 _{for the quarterly, semi-annually and annually horizon. Thus, the earlier} results were not robust. The D/P ratio has lost its predictive power over time and as

mentioned by Boudoukh et al. (2007), the payout yield should be used as a substitute for the D/P ratio. According to Boudoukh et al. (2007), repurchases have become more important in the last two decades. Therefore, deleting data might give the payout yield a stronger effect.

6) Conclusion

The main question of this thesis was whether the short interest index or the payout yield is a better predictor to forecast excess market returns across different horizons. Rapach et al. (2016) found in their study that the short interest index is the strongest predictor compared to 14 different known predictors. Moreover, Boudoukh et al. (2007) suggested in their research that the dividend-to-price ratio has lost its predictive power over time and the payout yield has become a good substitute for the dividend-to-price ratio. Hence, the two main hypotheses of this thesis were:

Hypothesis 1: Does the short interest index also outperform the payout yield across all

horizons in order to predict excess market returns?

Hypothesis 2: Has dividend-to-price ratio lost its predictive power over time and has the

payout yield become a better predictor?

The first results showed that the short interest index is a better predictor than the payout yield. However, the short interest index was not the strongest predictor once the out-of-sample regression was performed. Moreover, the OLS, in-sample and out-out-of-sample

regression showed that the D/P ratio has not lost its predictive power over time. Moreover, the results from the robustness check were more in correspondence with the results of Rapach et al. (2016) and Boudoukh et al. (2007). In line with the results of Rapach et al. (2016), the robustness check showed that the SII outperforms all other predictors across all horizons, including the payout yield. Furthermore, the same results showed that the payout yield is a better predictor than dividend-to-price ratio. The main reason why it firstly failed, was that short-selling and repurchases have become more important and trending in the last two decades. Those two components were not trending in the 1970’s and 1980’s.

For further research, it would be interesting to include theory from behavioral finance. Odean and barber (2008) found that investors are the net buyers of attention grabbing stocks, e.g., stocks which were recently on the news, stocks with abnormal high trading volume and stocks with extreme returns. They conclude that most investors will buy stocks which have grabbed their attention. In another study of Odean (1999), he writes that investors will overestimate the signal they get. In case of short-sellers, Rapach et al. (2016) suggest that short-sellers have more information than others. If a short-seller overestimates his/her signal or information, it might result that the SII is not the strongest predictor anymore.

7) Appendix

Table 4

This table represents the OLS-regression output. The dependent variable is the excess market return. Column 2 represents the regression of short interest, natural logarithm of payout, natural logarithm dividend-price ratio, natural logarithm of price-earnings ratio, default spread, term spread and inflation rate on the dependent variable excess market return one month (h=1) ahead. Column 3, 4 and 5

represent respectively the regression output for 3 (h=3), 6 (h=6) and 12 (h=12) months ahead. The t-statistics are reported between the parentheses. * denotes significant at 10% level, ** at 5% level and *** at 1% level, respectively. Dependent Variable Predictor (1) h=1 (2) h=3 (3) h=6 (4) h=12 (5) Log Payout 0.00944 0.0318 0.0982*** 0.275*** (0.55) (1.16) (2.71) (5.17) SII -0.00650** -0.0218*** -0.0456*** -0.0862*** (-2.48) (-4.76) (-7.10) (-10.71) Log D/P-ratio 0.0413* 0.134*** 0.258*** 0.361*** (1.87) (3.52) (5.22) (5.45) Log P/E-ratio 0.0363 0.125*** 0.256*** 0.361*** (1.57) (3.51) (5.83) (6.00) Default Spread 0.205 1.063 3.218* 1.487 (0.25) (0.79) (1.90) (0.79) Term Spread 0.151 0.510 0.650 1.507*** (0.89) (1.55) (1.54) (2.70) Inflation rate -0.653 -0.459 -2.088 -8.606*** (-0.80) (-0.24) (-0.91) (-3.29) Constant 0.0683** 0.190*** 0.408*** 0.927*** (2.13) (3.28) (4.97) (9.52) N 455 453 450 444 R2 _{0.029 0.090 0.180 0.328}

Table 7

Table 7 reports the robust results of the out-of-sample regressions which are calculated with equation (2) above, 2003:01-2010:12. This table reports the R2 _{statistic for the predictive regression model}

which is: 𝑟#t: t+h = a#t + b$tXt for t = 1, … , T-h. rt is the dependent variable which is excess market return

on the S&P 500 for the given month t. xt is the predictor which is listed in column 1. The description

of the variables in column 1 are explained in table 1. For each predictor the R2 _{is represented for the}

different horizons. h=1, h=3, h=6 and h=12 represent 1, 3, 6 and 12 months ahead excess market return R2_. (1) (2) (3) (4) (5) Out-of-sample R-squared Predictor h=1 h=3 h=6 h=12 SII 0.0678 0.2361 0.3369 0.5712 Log Payout -0.0222 0.0276 0.1842 0.4824 Log D/P-ratio -0.1840 -0.4198 -0.2408 0.0784 Log P/E-ratio -0.0374 -0.0373 0.1295 0.4548 Default Spread -0.0146 0.0202 0.2037 0.5189 Term Spread -0.0205 0.0083 0.1609 0.5449 Inflation Rate -0.0764 0.1039 0.2269 0.5023

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