Forecasting Stock Market Returns With Financial Ratios Finance Essay

Forecasting Stock Market Returns With Financial Ratios Finance Essay

Predicting stock market returns is important in the fiscal markets since it consequences have considerable influence on investing determination, hazard direction and market ordinance. Therefore, many faculty members and practicians have strived for happening the right reply for the inquiry how to calculate stock returns most exactly. Many variables and methodological analysiss have been employed to prosecute that purposes, nevertheless, no peculiar consensus has been reached during the last two decennaries. The chief intent of this survey is to analyze the predictability of stock market returns onto dividend output and earning-price ratio. By measuring the three stock indices including the Standard & A ; Poor 500 ( S & A ; P500 ) , the FTSEA ActuariesA All Share Index ( FTSE All-Share ) and the Hang Seng index ( HSI ) , we conduct in-sample and out-of-sample trials in order to non merely make up one’s mind whether dividend output and earning-price ratio have explanatory powers but besides explore whether the variable theoretical accounts could surpass the simple historical mean return theoretical account. The in-sample trial reveals that both the two forecasters are powerful across all stock markets, except for the earning-price ratio when foretelling FTSE All-Share returns. Besides, the out-of-sample trials which conclude statistical and the Goyal-Welch ( 2003 ) graphical attacks exhibit that the dividend output seems to be more outstanding campaigners to calculate stock returns. Overall, we conclude that stock market returns are predictable by dividend output and earning-price ratio at some certain grade.

List of Tables

Table 3.1

Descriptive Statisticss before Winsorising


Table 3.2

Descriptive Statisticss after Winsorising


Table 5.1

In-sample univariate arrested development


Table 5.2

Out-of-sample public presentation: Forecast Error


Table 5.3

Diebold and Mariano ( 1995 ) trial


Chapter 1: Introduction

1.1 Background and Aims

The issues of stock return predictability have been progressively of a immense involvement to both practicians and faculty members during the last two decennaries. However, the inquiry about whether stock return is predictable and if there is a dependable variable to calculate future returns, is still improbable to make a common consensus. A figure of variables have been employed in an effort to foretell stock returns runing from fiscal ratios such as dividend output ( Ball, 1978, Rozeff, 1984, Shiller, 1984, Fama and French, 1988 ) and the book-to-market ratios ( Kothari and Shanken, 1997 ; Pontiff and Schall, 1998 ) to economic factors such as the rising prices rate ( Lintner, 1975 ; Fama and Schwert, 1977, Fama, 1981 ) . Among these parametric quantities, dividend output and earning-price ratio ( or gaining output ) are deemed to be the most outstanding campaigners since they both demonstrate dealingss to stock market return at some certain grade.

The contention environing the return predictability continues challenge the economic experts since an agreeable methodological analysis could non be made. The typical traditional method often used is an ordinary least squares ( OLS ) arrested development of stock returns into the slowdown of the fiscal variable. However, there is deep concern over the traditional prediction appraisal – the in-sample arrested development theoretical accounts that they gave serious colored appraisals which result in widespread “ semblance ” about the explanatory ability of independent variables. Some new methodological analysiss including Monte-Carlo simulation and bootstrapping were introduced to cover with these prejudices and their consequences implied rejections of the prognostic power ( Nelson and Kim, 1993 and Goeztmann and Jorion, 1993 ) . In add-on, a category of economic experts expressed considerable uncertainty about the statistic significance of in-sample trials that it does non vouch a good out-of-sample prognosis which is described to better capture the information available to the predictor in the “ existent clip ” ( Diebold & A ; Rudebusch, 1991 ) .

The chief intent of this thesis is to look into whether dividend output and gaining output are good forecasters to calculate stock market returns. In this survey, both in-sample trials and out-of-sample trials are employed to foretell future stock returns in three stock markets i.e. United State, United Kingdom and Hong Kong. The in-sample statistic significance will be comprehensively assessed by traditional OLS t-statistic, the Newey-West ( 1987 ) statistic and the bootstrap statistics. Meanwhile, the out-of-sample prediction public presentation will be critically evaluated through two attacks. The first 1 is the statistical attack chiefly based on Mean Absolute mistake ( MAE ) and Root mean square mistake ( RMSE ) in concurrence with the Diebold and Mariano ( 1995 ) trial which checked equal prognosis truth. Second, the graphical method followed Goyal and Welch ( 2003 ) which visually inspects the net cumulative sum-squared mistake to make up one’s mind which theoretical account outperforms. This current survey purposes to carry through the undermentioned aims:

To analyze the ability of prognosis stock market returns i.e. to indentify whether stock returns follow a random walk procedure.

To place whether dividend output and gaining output pose statistic significances over the in-sample periods in the three stock markets.

To robustly look into whether the additive arrested development prognosiss give important prejudices as reported in old literatures.

To research whether conditional theoretical accounts on dividend output and gaining output outperform the unconditioned moving mean return theoretical account via both statistical and graphical attacks.

To analyze which variable ( dividend output or gaining output ) gives a better prognosis if the variable theoretical accounts outperform the predominating average theoretical account.

This thesis strives for adding an extension and a addendum to the bing literatures in three facets. First, we capture the most up-to-date informations sets embracing from 01 July 1982 to 01 July 2012. Second, we extend to analyze three stock markets i.e. US, UK and HK in which the last two have attracted minor attending in old surveies. Third, we alleviate the consequence of specious outliers in the information series utilizing the winsorising method proposed by Hasings et Al ( 1947 ) . To our best cognition, such method to cut down the specious outliers in the information series has non been focused in old literatures published.

1.2. Structure of thesis

The current survey is divided into six Chapters:

Chapter 1 – Introduction gives general background about return predictability and point out the primary aims of this survey. Besides, this portion besides mentions the part of this thesis to the bing literature.

Chapter 2 – Literature Reviews summarizes the theoretical backgrounds used in this thesis every bit good as reappraisals the empirical consequences on the stock return predictability based on dividend output and earning-price ratio.

Chapter 3 – Data presents the informations employed in this survey, the intervention with natural informations in order to give better prognosiss.

Chapter 4 – Methodology provides the inside informations of methodological analysiss utilizing throughout the current thesis including in-sample predictability and out-of sample prediction public presentation.

Chapter 5 – Empirical Results delivers the consequences derived from the methods as described in the methodological analysis portion. A comparing and contrast between findings from this current thesis with old surveies is besides made in this portion.

Chapter 6 – Decision sums up the most of import findings made in this thesis and discusses some restrictions of this survey every bit good as proposes some suggestions for farther surveies in the hereafter.

Chapter 2: Literature Reappraisal

The purpose of this chapter is to reexamine the literatures on predictability of stock returns, which has been intensively researched given its important function in finance, through both theoretical and empirical facets. In peculiar, the construction of this chapter is as follow

Section 2.1 proposes the theoretical background by first indicating out why this thesis chooses dividend output and earning-price ratio as outstanding fiscal ratios to calculate stock returns. After that, some cardinal cognition backgrounds used in this thesis are discussed.

Section 2.2 continues by reexamining empirical consequences on the stock return calculating based on dividend output and earning-price ratio. Since so the determination of this survey demonstrated in the following chapters will compare with in order to present a comprehensive position of stock return predictability.

After all, Section 2.3 points out some reasoning recognitions.

2.1. Theoretical Backgrounds

2.1.1. Reason for taking Dividend Yield and Earning-Price ratio as an outstanding forecaster of stock returns

Among assorted fiscal ratios used to calculate stock returns, this survey recruit dividend output and earning-price ratio as prognostic variables as they portion some common characteristics and relate to stock returns in some grade.

First, as stated in Lewellen ( 2004 ) , these ratios should hold positive relation with expected returns since they both have monetary value in the dominator. Harmonizing to the mispricing position in inefficient market, the ratios reflect the degree of stock monetary value at a given point of clip, such as low ratios indicates that stock are overpriced and high ratios implies stock monetary value are undervalued. An alternate position is the rational-pricing position in efficient market where the ratios track time-variation in price reduction rate. In peculiar, keeping expected cashflows comparatively unchage, an addition in price reduction rate would cut down market value and raise both fiscal ratios and expected returns. In understanding with this point of position are Keim and Stambaugh ( 1986 ) and Fama and French ( 1988 ) .

Another explaination for the relation between stock returns and the two ratios is suggested by Lamont ( 1998 ) . Lamont claimed that dividend output hold the information about future returns under as they help gauge future dividends, whereas gaining output contain information since they are in relation with concern conditions. These variables hence should be utile forecasters for future returns.

2.1.2. Hypothesis Testing

As remarked by Gujarati and Porter ( 2009 ) , a hypothesis testing is developing regulations or processs by which the determination of rejecting a void hypothesis denoted by or non could be made. In this survey, the void hypothesis is stated that there is no relation between stock returns and explainatory variables, i.e. dividend output and gaining yield.Hypothesis can be tested utilizing two reciprocally complementary attacks, viz. , assurance interval and trial of significance or t-test. Our survey will utilize the latter one. Assurance Time interval

The assurance interval gives a scope of possible value for the parametric quantity. If a value of parametric quantity under bull hypothesis does non fall in that scope, the void hypothesis should be rejected and frailty versa.

Null hypothesis

Alternate hypothesis

The assurance interval based on estimated parametric quantity ( denoted by is

Then is rejected if

In words, if the estimation is excessively far from, where standard mistake is unit to mensurate the distance, the void hypothesis is rejected. Statistical Significance Test

The key thought behind this sort of hypothesis testing is to analyze the t-statistic generated by trying distribution under the void hypothesis in order to make up one’s mind whether or non to reject the void hypothesis. The OLS t-statistic, which developed by R.A. Fisher and jointly by Neyman and Pearson, is deemed to be the standard statistic of significance trial. This OLS t-ratio has long tradition applied to prove the predictability of returns on independent variables in old literatures such as Rozeff ( 1984 ) and Fama and French ( 1988 ) .

However, the traditional t-statistic is criticized non to capture autocorrelation and heteroscedasticity in mistake footings, which may do colored appraisal. Newey-West ( 1987 ) hence proposed a new method to obtain standard mistakes of OLS calculators that are adjusted for the problems.The standard mistakes in this new method are known as HAC ( stands for heteroscedasticity- and autocorrelation-consistent ) criterions mistakes or merely Newey-West standard mistakes. Unlike its predecessor, the White ( 1980 ) criterion mistakes which was designed entirely for heteroscedasticity, the Newey-West standard mistakes can foster handle autocorrelation. As accounting for both autocorrelation and heteroscedasticity in mistake footings, the HAC standard mistakes are larger than the OLS standard mistakes and therefore the HAC T ratios are smaller than the traditional t-statistic. The Newey-West statistic is applied in many researches including Goyal and Welch ( 2003 ) and Ang and Bekaert ( 2007 ) .

2.1.3. Forecasting Performance Evaluations

Harmonizing to Brooks ( 2008 ) , it is typical to measure the prediction public presentation of the theoretical accounts by spliting the information set into in-sample period and out-of-sample period.In this survey, we use full sample period as in-sample period to gauge the theoretical account parametric quantities which are used to bring forth predicted variables in the out-of-sample set. Then a comparing between the fittingness of conditional theoretical account appraisals and the unconditioned return appraisals ( which bases simly on historical mean ) is made to find whether the usage of preditive variable will give superior prognosiss.

A good prognostic theoretical account would be the theoretical account which minimise the prognosis mistakes ( Marcucci, 2005 ) . As suggested by Makridakis et Al. ( 1998 ) , the prognosis mistake for observation at the clip T can be defined as the difference between the existent value and the prognosis value at the clip T, formulated as follow:

Where, is the existent and forecast value at the clip period severally.

To avoid the beginning between positive and negative value of mistakes, forecast mistakes are usually considered under the absolute value or square signifiers ( Brooks, 2008 ) . As reported by Bluhm and Yu ( 2001 ) , the most common mistake steps used in old literature are RMSE, MAE and intend absolute per centum mistake ( MAPE ) . Theil-U statistics and the LINEX loss map are besides employed but less popular. Apart from mentioned symmetric appraisals, Brailsford and Faff ( 1996 ) recruited asymmetric appraisals such as the mean assorted mistake under and the mean assorted mistake over to mensurate mistakes.

There appears to be the inquiry of taking the best mistake step. However, each step has a comparative truth that we can non place the better 1, as remarked by Lopez ( 2001 ) . Therefore, assorted statistic steps will be used in this survey which helps giving comprehensive ratings of the forecasting public presentation among viing theoretical accounts. In line with many old literature such as Diebold & A ; Rudebusch ( 1991 ) , Stock & A ; Watson ( 2002 ) and Goyal and Welch ( 2003, 2008 ) , the survey employs two popular statistics RMSE and MAE. For more convenient comparing, the survey will utilize Goyal and Welch ( 2008 ) attack, which assess the difference between MAE ( denoted by MAE ) and the difference between RMSE ( denoted by RMSE ) of the out-of-sample benchmark prognosis and the out-of-sample conditional prognosis utilizing dividend output and gaining output.

It is noted that there is a instance that the viing theoretical accounts give equal prognostic ability. There are three popular trials that compare the out-of-sample prognostic truth of viing theoretical accounts which have equal mean squared mistake ( MSE ) or equal root mean squared mistake ( RMSE ) . They are a regression-based trial introduced by Granger and Newbold ( 1977 ) , a t-type trial attributed by either Diebold and Mariano ( 1995 ) or West ( 1996 ) , and F-type trial which has the same spirit to Theil ‘s U and possibly similar to likelihood ratio trial proposed by McCranken ( 2007 ) . Similar with some researches such as Goyal and Welch ( 2008 ) and Kellard, Nankervis and Papadimitriou ( 2010 ) , this survey uses Diebold and Mariano ( 1995 ) which will be farther discussed in the chapter of methodological analysis.

2.2. Empirical Reappraisal

Since the current survey focal point on the prognostic powers of dividend output and gaining output in calculating stock return based on both in-sample and out-of-sample trial, this subdivision starts by giving the general thoughts about stock return predictability, following by empirical literatures on dividend output and gaining output as a forecaster. Following, the arguement around in-sample trial methodological analysiss and a treatment about out-of-sample trial are presented. Meanwhile, the readings of this survey ‘s findings are interspersed.

2.2.1. General positions of stock returns predictability

During last two decennaries, many empirical literatures have been sought for reply of the predictability of stock returns. Kendall ( 1953 ) observed that stock returns seem to follow a random walk procedure, which would oppugn the value of much of attempts devoted to foretell the stock returns whether utilizing past returns or any prognostic variables. Poterba and Summers ( 1987 ) examined returns during the sample periods from 1871 to 1985 but they could non reject the void hypothesis that stock return wander indiscriminately. Nevertheless, the position of random walk procedure has been refused by the construct time-varying in expected stock return, as confirmed in Rozeff ( 1984 ) , Keim and Stambaugh ( 1986 ) , Fama & A ; French ( 1988 ) and many empirical literatures. Agree with the modern position, this survey confirms that stock returns are extremely predictable. However, the inquiry of how to calculate stock returns is in het argument.

A big figure of variables hence are employed in effort to calculate stock returns. They include economic indexs such as industrial production assessed in Balvers, Cosimano and McDonald ( 1990 ) and Schewrt ( 1990 ) ; the rising prices rate: , Lintner ( 1975 ) , Fama and Schwert ( 1977 ) , Fama ( 1981 ) ; and assorted fiscal variables such as dividend output: Ball ( 1978 ) , Rozeff ( 1984 ) , Shiller ( 1984 ) , Fama and French ( 1988 ) , Hodrick ( 1992 ) , Park and Jinlee ( 2003 ) , Menzly, Santos, and Veronesi ( 2004 ) ; the earnings-to-price ratios: Shiller ( 1984 ) , Campbell and Shiller ( 1988 ) , Lamont ( 1998 ) ; the book-to-market ratios: Kothari and Shanken, ( 1997 ) , Pontiff and Schall ( 1998 ) , short-run involvement rates: Campbell ( 1987 ) , Hodrick ( 1992 ) ; Ang and Bekaert ( 2007 ) ; yield spreads: Keim and Stambaugh ( 1986 ) , Campbell ( 1987 ) , Fama and French ( 1989 ) .

2.2.2. Empirical on dividend output as a forecaster

Among these prognostic campaigners, dividend output has been believed as one of the most powerful forecasters. The belief comes from the fact that the stock monetary value is determined by dismissing the future dividends to present value, and following the establishment of “ efficient market ” introduced by Dow ( 1920 ) every bit good as the “ mispricing position ” as mentioned above. Harmonizing to Cochcrane ( 1997 ) , dividend output “ must calculate either future stock returns or the dividend growing rate. ”

Therefore, dividend output has gained a batch of economic experts ‘ attending and has been examined in assortment of markets, sample periods and methodological analysiss. Rozeff ( 1984 ) sampled the S & A ; P500 stock returns from 1962 to 1982 to compare the anticipation between dividend output method and realized return method, he found that dividend output significantly better reflect expected stock returns. Similar determination is proposed in Fama and French ( 1988 ) when calculating the NYSE index stock return with the sample from 1927 to 1986, including 720 observations for intervals between one month and four old ages, utilizing simple arrested development theoretical accounts.

Another survey has shown favors to dividend output is Hodrick ( 1992 ) . Using the same information with Fama and French ( 1988 ) , he explored three alternate techniques to analyze the prognostic power of dividend output toward expected returns. The first methodological analysis was a combination of Fama and French ( 1988 ) arrested development and an alternate calculator of the standard mistakes built on Richardson and Smith ( 1991 ) . The 2nd attack followed Jegadeesh ( 1990 ) which reformulated the Fama and French ( 1988 ) arrested development by altering the clip of both regressor and regressand. The purpose of this 2nd method was to measure the statistical significance of the arrested development prognosis. The 3rd methodological analysis, in line with Kandel and Stambaugh ( 1988 ) , Campbell and Shiller ( 1988a ) , and Campbell ( 1991 ) , used the parametric quantity of Vector Autoregression ( VAR ) to measure the incremental power of dividend output with lagged returns. After treating different trials, Hodrick concluded that these methodological analysiss give similar consequences which support for the prediction ability of the dividend output.

However, there appears to be an opposite position that rejects the statistical significance of dividend output in calculating stock returns. Measuring the intrinsic value of 30 stocks in the vitamin E Dow Jones Industrial Average from 1963 to 1996, Lee et Al. ( 1999 ) used the bottom-up attack based on price-to-book ratio, price-to-earning ratio, dividend output and value-to-price ratio, and but merely the last 1 has dependable prognostic power, as he stated. Sharing a similar position is Ang and Bekaert ( 2007 ) who derived a structural theoretical account of return based on dividend output, and found that dividend output have good prognostic power for future hard currency flows growing rates, but non for future extra returns. In other words, they indicated that one variable as a entirely forecaster of additive theoretical account is non able to catch all the predictable constituents in stock returns.

It is noted that most of the above literatures examined the statistic significance of dividend output on the US stock markets. This thesis surveies two more stock markets, apart from US, which are UK and HK and comes up with farther grounds of the prognostic power of dividend output. The consequences presented subsequently on are in line with Fama and French ( 1988 ) and Hodrick ( 1992 ) , clearly contradicted with findings found in Lee et Al. ( 1999 ) and Ang and Bekaert ( 2007 ) .

2.2.3. Empirical on gaining output as a forecaster

As mentioned in the old subdivisions, earning-price ratio is believed to hold dealingss with stock returns under both mispricing position and rational-pricing position. It has been long tradition consideration that earning-price ratio is a return forecaster alongside dividend output. Shiller ( 1984 ) and Fama and French ( 1988 ) acknowledge the prognostic power of both dividend output and gaining output when gauging US stock returns in the sample period of 1926-1984 and 1927-1986 severally. After researching one-year, quarterly, and monthly US informations, Campbell and Motohiro ( 1996 ) found sustainable grounds that earnings-price ratio reliably predicts returns at all frequences in the sample period 1926-2002.

However, many surveies have pointed out that gaining output seems has less dependable explanatory power compared with dividend output. Fama and French ( 1988 ) pointed out that “ Net incomes are more variable than dividendsaˆ¦ If this higher variableness is unrelated to the fluctuation in expected returns, E/P is a noisy step of expected returns than D/P ” . In understanding with Fama and French ( 1988 ) , Lamont ( 1998 ) , who examined the same stock market with the two old literatures but sample period covered from 1947 to 1994, admitted the superior anticipation of dividend output. Nevertheless, in contrast to Fama and French ‘s ( 1988 ) account, he denied that higher variableness of net incomes is noise and it is related to expected returns alternatively. He claimed that less prognostic power of gaining output is due to its enlightening feature in which net incomes contain information correlated with concern conditions.

InA consonanceA with the old researches, this survey notices the explanatory ability of earning-price ratio although that ability is recorded non every bit strong as of dividend output in all three stock markets.

2.2.4. Argument around In-sample trial method

In order to calculate stock return, a huge assortment of methodological analysiss have been proposed which led to different decisions. It can be seen that many typical research workers have recruited the Ordinary Least Square ( OLS ) arrested development method to measure the statistical significance of return predictability. Although this method might look to be straightforward, Elliott and Stock, ( 1994 ) ; Mankiw and Shapiro ( 1986 ) and Stambaugh ( 1986 ) observed that the OLS method rejects the void hypothesis of non-predictability excessively frequently and doubt if type I error happens, where the true hypothesis of no predictability is falsely rejected. They judged the traditional method on giving biased appraisal which is arisen from the correlativity between the arrested development perturbations and the hereafter values of prognostic variables.Boudoukh, Richardson, and Whitelaw ( 2008 ) pointed out that the prejudices in many literatures comes from high continuity of the forecasters. This current survey perceives the prejudices in OLS appraisal, nevertheless, we observes that the prejudices are non singular plenty to dramatic turn the decisions.

Since the statistic significance of OLS method is in statement, a new attack which is so called simulation methods appears to measure the statistic significance of the arrested development grounds. Nelson and Kim ( 1993 ) replicated the Fama and French ( 1988 ) trials, used vector autoregressions ( VARs ) attack to explicate stock returns and dividend output on lagged returns and output and so generated unreal informations by randomising the sample remainders. Examing the stock US market for the period 1872 to 1986, they claimed that the upward prejudice in coefficient happens in all skyline and that is why the t-statistic and of prognostic arrested developments are seen to be big. Since the prejudice are important, their survey rejected the explanatory power of dividend output towards stock returns. Similar consequences are reported by Goeztmann and Jorion ( 1993 ) .

Kothari and Shanken ( 1997 ) executed both traditional bootstrap method to prove the hypothesis of no predictability, and the Bayesian-bootstrap simulation to gauge the likeliness of different arrested development incline values. Their survey analysed the same stock martket with Nelson and Kim ( 1993 ) but for the period 1926 to 1991. However, after seting possible prejudices, they confirmed the dependable relation between dividends output and stock returns, which contradicts to the determination of Nelson and Kim ( 1993 ) . In line with Kothari and Shaken ( 1997 ) , this survey recruits the bootstrap statistic utilizing vector autoregressions to corroborate the explanatory powers of dividend output and gaining output after bias-adjustment.

2.2.5. Out-of-sample trial

While in-sample trial methods are in cardinal of statement, out-of-sample trials examine the truth of in-sample predictability on merely mensurating how “ tantrum ” it is towards the subsequent sample period. It is said that out-of-sample prognosiss is by and large performed more trust worthy than in-sample trials which are critised to be sensitive to data excavation and outlier. In add-on, Diebold & A ; Rudebusch ( 1991 ) noticed that out-of-sample prognosiss better capture the information available to the predictor in “ existent clip ” .

Ang and Bekaert ( 2007 ) employed the present value theoretical account and showed that over long skylines, the predictability is non statistically important, non robust across states, and different sample periods. They found that both Hansen and Hodrick ( 1980 ) or Newey and West ( 1987 ) criterion mistakes lead to severe over rejections of the void hypothesis of no predictability at long skylines.

Another out-of-sample method is found in Goyal and Welch ( 2003 ) who used graphical attack for out-of-sample predictability which is based on the net amount squared mistakes between the predominating average theoretical account and viing theoretical accounts. The cardinal advantage of this attack is that it is rather simple to visually make up one’s mind which theoretical account ( predominating average theoretical account or conditional theoretical account ) outperforms in each specific period of clip. By diagrammatically analysing the US stock markets during the out-of-sample period 1946-2002, Goyal and Welch ( 2003 ) concluded that the strong in-sample prognostic power of dividend output is merely an semblance as it does non vouch for out-of-sample prediction truth. In fact, any explanatory ability of dividend output prior to the 1990s was dominated by merely two old ages 1973 and 1974. Goyal and Welch besides argued that over the periods of 5 old ages, the dividend output fundamentally predicts dividend growing rate instead than future returns.

In order to beef up their consequences in wider graduated tables, Goyal and Welch ( 2008 ) conducted an scrutiny of the return predictability which is “ may be simple, even fiddling, but its deductions are non ” . This clip, they remain analyzing US stock market but at longer periods covered from 1871 to 2003 and different prediction periods which begin at either 1902 or 1964. More specially, the variables employed are besides spread outing to ten ratios including both dividend output and earning-price ratios. As a consequence, the calculating power of each entirely variable is denied and real-world investors are suggested better use the prevalent historical mean theoretical account alternatively.

Sharing the same out-of-sample graphical method but Kellard, Nankervis and Papadimitriou ( 2010 ) delivered different position point of return predictability by analyzing the US and UK stock markets from 1975 to 2009. After confirm the in-sample predictability of both US and UK returns, they set uping two out-of-sample trials including statistic method utilizing the mean, standard divergence, RMSE, MAE and Diebold and Mariano ( 1995 ) statistics, every bit good as the graphical rating method of Goyal and Welch ( 2003 ) . They agreed that the dividend output theoretical account fails to surpass the historical moving mean theoretical account in the US stock market but in UK the theoretical account poses prognostic power at some grade.

Chapter 3: Datas

This chapter will foremost explicate how the informations are collected, processed and so uniting visually review and descriptive statistics to measuring the clip series informations.

3.1. Introduction

Three of the major universe ‘s stock market indices are employed to analyze the prognostic power of fiscal ratios such as Dividend output and Earning-Price ratio on stock market returns: Standard & A ; Poor 500 ( S & A ; P500 ) , FTSE All-Share index and Hang Seng Index ( HSI ) . Harmonizing to the Financial Development Report 2011 by the World Economic Forum WEF, Hong Kong, United States and United Kingdom are top three of the universe ‘s most developed fiscal markets. The survey expects these major stock indices could be the best simulation of alleged “ efficient market ” in order to analyze more exactly the prognostic power of the fiscal ratios so compare their prediction ability together.

The first index is considered to be the best representation of the United State market. It is the value-weighted stock market of 500 taking publically traded American companies, capturing 75 % of the entire market capital[ 1 ]. FTSE All-Share index comprise about 1000 of more than 2000 companies listed on the London Stock Exchange. Hang Seng Index records day-to-day alterations of the largest publically traded Hong Kong companies, stand foring about 67 % of capitalisation of the Hong Kong Stock Exchange[ 2 ].

In footings of information frequence, this survey employs monthly informations, which is in line with many empirical researches such as Fama and French ( 1988 ) , Hodrick ( 1992 ) , and Nelson and Kim ( 1993 ) . As suggested in Kellard, Nankervis and Papadimitriou ( 2010 ) , the advantage of monthly informations is to let the scrutiny of intra-annual prediction.

For calculating skyline, Cochrane ‘s ( 1997 ) accounting individuality implied that skylines longer than about 5-10 old ages give better return predictability for the ground that the self-predictive belongingss of regressors ( e.g. Dividend Yield or Earning Yield ) could be dominated under such long skylines. Therefore, this survey employs 30 twelvemonth informations set, which is covered from 01 July 1982 to 01 July 2012, with the sum of 361 observations. Datas are acquired from Datastream and processed in Eviews, Stata and Excel.

3.2. Treatment of natural informations

The monthly returns on the index are calculated as:

Where denotes the monthly returns of the market stock index ; denotes the stock index degree, measured in local currency and is the paid dividends. This expression of logarithm returns is in common with old literature, such as Goyal and Welch ( 2003 ) . Logarithm returns are used alternatively of natural returns because the skew of log signifier is negative ( as we will see in the descriptive statistics analyzed below ) compared with the positive skew in the natural signifier.

Dividend Yield ratio ( ) as suggested in Lewellen ( 2002 ) , is used under the signifier of logarithm of the aggregative dividends divided by the aggregative stock market value ( ) .

And the Earning Yield ratio, denoted by is calculated as:

Where is the aggregative one-year net incomes per portion.

It is noted that if the distribution of independent and dependent variables are significantly non-normal, the mistake distribution might non-normal, which violates the normalcy premise of OLS and hence lead to terrible prejudice in appraisal. By visually inspecting the clip series informations of log return, log dividend output and log gaining output in Figure 3.1 every bit good as analysing the descriptive statistics given in Table 3.1, this survey observes many outliers in all informations series. As stressed in Campbell and Motohiro ( 2006 ) : “ A arrested development of stock returns onto a lagged i¬?nancial variable has low power because stock returns are highly noisy. If we can extinguish some of this noise, we can increase the power of the trial. ” Hence, in order to heighten the OLS public presentation, this survey will further transform the informations utilizing winsorising method proposed by Hasings et Al ( 1947 ) . The thought behind this technique is truly simple: restricting the utmost values in the information series to decrease the consequence of specious outliers. By specifying the recognized percentiles ( i.e 5-percentile and 95-percentile in this survey ) , utmost observations below the 5-percentile and 95-percentile will be replaced by the several percentile. The information after the transmutation are diagrammatically displayed in Figure 3.2 and statistically analyzed in Table 3.2.

It is noted that the current survey has already run the in-sample trial and out-of-sample trial ( which will be described in the undermentioned chapters ) with the informations set before and after winsorising method. The consequences are surprisingly non important but the informations with winsorising method exhibited better prognosiss in both in-sample and out-of-sample predictability.

Since so, this subdivision will diagrammatically research the clip series informations in footings of the stock returns, the dividend output and the earning output in three stock markets including US, UK and HK, as displayed in Figure 3.2.

Interestingly, all these market ‘s monthly returns portion the same form. In peculiar, downward tendencies are records across all those markets in late 1980s, which may due to the fiscal crisis of many Latin-American- state debt defaults in 1980s. A crisp diminution in the late ninetiess and early 2000s is passively caused by 1997 planetary fiscal crisis. In footings of dividend output, all markets experience a downward tendency until 2001 and so witness an addition thenceforth. There are no common forms for gaining output, nevertheless, the graph shows a heavy autumn in 2010 across all markets.

It can be visually inspected that all stock return series exhibit autocorrelation, which is understood as little motion is followed by little motion and likewise, big motions consequence in similar graduated table supplanting. It implies the presence of heteroskedasticity ( discrepancy is non changeless over clip ) and hence heteroskedasticity should be taken into consideration.

Figure 3.1: Time Series Data before Winsorising

S & A ; P500

FTSE All-Share


Figure 3.2: Time Series Data after Winsorising

S & A ; P500

FTSE All-Share


After visually researching the information series, this subdivision continues to analyse informations through some statistics ( mean, average, skewness and kurtosis ) which is expressed in Table 3.2. As remarked by Angabini and Wasiuzzaman ( 2011 ) , the mean of a return series is expected to be positive and close-to-zero. That statement is confirmed in this survey as all the agencies and medians of monthly returns for each market are positive and non significantly different from nothing, which signals for a inclination to increase somewhat over clip of stock monetary value. After detecting mean and median of dividend output and gaining output series, we observe that dividend output, in general, is about four-time larger than gaining output in all markets.

In order to measure the distribution in the clip series informations, this survey employs skewness, kurtosis and the Jarque-Bera ( Jarque and Bera 1980 ) trial. While skewness reflects how asymmetric a information set is ( negative versus positive ) , kurtosis measures how “ peakedness ” of the chance distribution is ( Brooks, 2008 ) . For a normal distribution, these two parametric quantities receive the values of 0 and 3 severally. The Jarque-Bera trial is jointly built on lopsidedness and kurtosis.The void hypothesis is that the distribution of a sample is normal i.e. lopsidedness being 0 and kurtosis being 3. A drumhead note for the distribution of the informations sets is as follows:

Return Series: All returns exhibit negatives kewness which indicates that most markets have non-symmetric returns with the tail widening more towards negative values. In other words, most return series have asymmetric distributions skewed to the left. With their kurtosis statistics below the value of 3, all series exhibit platykurtic feature. The highest kurtosis of returns belongs to S & A ; P500 ( 2.786093 ) while the lowest kurtosis estimation is for HSI ( 2.451302 ) . These kurtosis statistics suggest that all indices returns display the thin-tailed distributions.

Dividend Yield Series: The dividend output informations series in S & A ; P500 and HSI portion the same forms. Positive value of skweness in the two markets indicates left-tail distribution and below 3 value of kurtosis implies platykurtic which express thin-tail distributions. On the contrary, a right-thin-tail distribution is recorded for FTSE dividend output due to negative sknewness ( -0.314960 ) and lower value of 3 kurtosis ( 2.128316 ) .

Gaining Yield Series: All gaining series exhibits thin-tail distribution with the value of kurtosis is smaller than 3 ( 2.285953, 2.843593 and 2.369347 for S & A ; P, FTSE and HSI severally ) . Except for S & A ; P500 with left-skew distribution, the staying earning output distributions are all skewed to the right with sknewness value is 0.653323 for FTSE and 0.372383 for HSI.

3.3. Decision

This chapter has shown how informations is collected and transformed, every bit good as provided analytical sum-ups of those informations via both graphical and statistical attack. It is noticed that all return series experience autocorrelation which should be considered when proving the statistic significance of prognostic variables in the undermentioned chapters.

Table 3.1: Descriptive Statisticss before Winsorising


S & A ; P500

FTSE All-share














































Std. Dev.













































Table 3.2: Descriptive Statistic after Winsorising


S & A ; P500

FTSE All-share














































Std. Dev.













































Chapter 4: Methodology

The old chapter has shown the chosen informations set chose and intervention of the information. This chapter will explicate the methodological analysiss every bit good as theoretical accounts employed in this survey. The cardinal thought of the current research is to analyze whether the variable arrested development tantrum in the in-sample period and so measure the theoretical accounts ‘ public presentation during out-of-sample period. Hence, the construction of this chapter is as follows: Section 4.1 nowadayss in-sample predictability method which specifically is Ordinary Least Square every bit good as the Newey-West t-statistic adjusted for heteroskedasticity and bootstrap statistic. Section 4.2 continues with the rating method of the out-of-sample prediction public presentation of viing theoretical accounts. Finally, some chief points of this chapter will be summarized in subdivision 4.3.

4.1. In-sample predictability

In order to prove the relation between prognostic variables and stock returns, we will analyze the prognostic arrested development theoretical account as follow:

Where the regressands can be either lagged dividend output ( or earning-price ratio ( .

If stock returns follow a random walk procedure i.e. there is no relation between stock returns and prognostic variables, the incline coefficient would be nothing. In this instance, the theoretical account becomes the benchmark in measuring return predictability. In contrast, stock returns could be reflected by prognostic variables if is statistically different from nothing.

In peculiar, we will prove the hypothesis to see whether we can reject or accept the void hypothesis by the criterion and Newey-West ( 1987 ) T statistic corrected for autocorrelation and heteroskedasticity in the remainders of the arrested development and exert the bootstrap attack to capture the little sample prejudices.

4.1.1. Standard t-test

The hypothesis under the trials would be made as follow:

Null hypothesis

Alternate hypothesis

The t-statistic is so calculated under the normalcy premise of the variables as follow:

Since this statistic follows the t distribution with n-2 df, the assurance interval so can be given as:


Where is the estimated value of the arrested development incline coefficient ; and are the values of the critical T value for ( ) degree of significance. If the t-statistic is greater than 2.58, 1.96 or 1.64, we can reject the void hypothesis with 99 % , 95 % , 90 % degree of assurance, severally.

4.1.2. Newey-West t-statistic

However, in instance autocorrelation and heteroskedasticity exist in the remainders from these arrested developments, it is criticized that the estimated OLS-t values by and large will be larger than the existent value it should be. As a consequence, that upward bias might take to type I error where the true hypothesis of no predictability is falsely rejected. In order to account for the autocorrelation and heteroskedasticity, we adjust the mistakes with the Newey-West ( 1987 ) criterion mistake, or called the heteroskedasticity- and autocorrelation- consistent ( HAC ) criterion mistake.

Harmonizing to Stock and Watson ( 2003 ) , the HAC criterion mistake is calculated as the square root of the HAC calculator of the discrepancy of, which is:

Where is the calculator of least square discrepancy of without the being of consecutive correlativity, and be given by:


Where, m is the maximal slowdown which is called the shortness parametric quantity. Different from the White ( 1980 ) criterion mistakes, which require no judgement, the HAC standard mistakes depend on the pick of maximal slowdown m. Stock and Watson ( 2003 ) besides suggests a guideline for taking m as: m=0.75 with T is the sample size. It is noted that this current survey employs 361 monthly observations which lead to the value of m should be 5. Therefore, the HAC standard mistakes in this survey will be computed with the slowdown shortness m=5.

4.1.3. Bootstrap Algorithm

To bring forth the bootstrap critical value ( or bootstrap p value ) for the in-sample trial statistics under the void hypothesis of no return predictability, allow ‘s denotes the trial statistic of involvement or specifically is in this survey. We start by define the informations bring forthing procedure, or bootstrap DGP as used in Stambaugh ( 1986,1999 ) , Mankiw and Shapiro ( 1986 ) and Nelson and Kim ( 1993 ) :

Where the first equation is the prognostic arrested development and the 2nd specifies a first-order autoregressive ( AR1 ) procedure. As the incline is correlated with the independent variable ‘s autocorrelation, any information conveyed by the autocorrelation enhances the power of predictability.

Next we estimate this theoretical account is subjected to the limitation that in the first equation is zero. Then we can bring forth the unreal observations given the entire observations known is T which, in peculiar, is 361 monthly observations in this survey:

The bootstrap re-sample process will randomly pull the pseudo invention term based on the set of ascertained remainders. The initial observation is indiscriminately drawn from the existent information. The inquiry is how many times the resample process should be taken. Efront and Tibshirani ( 1986 ) and Mooney and Duval ( 1993 ) suggested that in most instances, it is adequate to reiterate more than 1000 ( B & gt ; 1000 ) . This survey will make 5000 reproductions of bootstrapping.

For each bootstrap reproduction, we construct the bootstrap trial statistic of involvement. Since so we compute both bootstrap critical value and bootstrap p-value as.

Assuming is an whole number, bootstrap critical value at degree is calculated as:

And the bootstrap one-side p-value of is:

Based on the two bootstrap statistics, we can analyze the statistic significance of the arrested development, which already account for little sample prejudice. That is, if the bootstrap one-side p-value is smaller than 0.01, 0.05 and 0.10, we can reject the void hypothesis of no predictability at 99 % , 95 % and 90 % degree of assurance severally.

4.2. Out-of-sample predictability

As in Goyal and Welch ( 2003, 2008 ) , under premise that there is non any ex-post information available such as the entire-sample arrested development coefficients or constructed variables, real-world investors would hold had to foretell future returns based on merely available informations. Hence, it is of import to show a good out-of-sample prediction public presentation instead than a merely fitted in-sample arrested development. This subdivision will demo the out-of-sample rating methods in order to find which prognostic variables could be used by comparing the public presentation of the conditional arrested development anticipations against the simple unconditioned historical – the predominating moving mean anticipations.

4.2.1. Statistic rating method

In order to do a comparing, the nested theoretical accounts i.e. the prevalent historical norm prognosis and the competing theoretical accounts are defined as follow. To be noticed that the anterior 1 is used as a benchmark theoretical account.

Benchmark theoretical account:

Competing theoretical accounts:

The estimated prognosis mistakes so are calculated by:

Benchmark theoretical account:

Competing theoretical accounts:

Where, , are estimated coefficients with in-sample informations. From the clip series and rating statistics can be generated to compare one-step-ahead prognosis from the viing theoretical accounts against the prognosis from the benchmark theoretical account.

As mentioned in chapter 2, in line with old literatures such as as Diebold & A ; Rudebusch ( 1991 ) and Stock & A ; Watson ( 2002 ) , the statistics used are MAE and RMSE to mensurate the fittingness of arrested development theoretical account towards the existent in-sample information set. MAE is defined as the norm of the absolute values of forecast mistakes while RMSE is based on squared mistake ( Makridakis et al. , 1998 ) . As noted by Brook ( 2008 ) , RMSE would be more sensitive to outliers than MAE due to its association with quadratic signifiers and this might diminish its rating truth. This survey will utilize Goyal and Welch ( 2008 ) attack which examines the difference between MAE ( denoted by MAE ) and the difference between RMSE ( denoted by RMSE ) of the out-of-sample benchmark prognosis andthe out-of-sample conditional prognosis utilizing the variables, i.e. dividend output and gaining output.

Given entire observations known is T: , see out-of-sample period usage P observations. This survey uses T = 361 monthly observations and P= 121 observations ( since out-of-sample period covers from July 2002 to July 2012 ) . Let ‘s and denote the one-step aheadunconditional and conditional prognosis severally. Then MAE and RMSE are given by:

For both statistics, a positive value implies that the variable theoretical account outperforms the historical moving mean theoretical account ; a negative value implies that the historical moving norm behaves better than the variable. Since we use different statistics to measure the prediction public presentation of the theoretical accounts, we expect some dissensions among these loss maps.

Next the survey will mensurate the Diebold and Mariano ( 1995 ) statistic to look into equal prognosis truth from nested theoretical accounts. The expression for DM statistic for h-step in front prognosis is computed as:


The Diebold Mariano statistic for 1-step in front prognosis therefore would be

The void hypothesis for Diebold Mariano ( DM ) statistic is that the RMSEs for the benchmark and variable theoretical account are equal while the alternate hypothesis is that the variable theoretical account has lower RMSE. If the DM trial consequences can non reject the void hypothesis of equal prediction public presentation, the conditional theoretical account fails to surpass the naA?ve prevailing average theoretical account. In other words, a real-world investor could calculate stock return merely based on historical informations instead than use independent variables to calculate.

4.2.2. Graphic rating method

Apart from statistic rating method described above, this survey recruits a graphical method following Goyal and Welch ( 2003 ) to measure out-of-sample public presentation in order to present farther inside informations about the dynamic nature of stock predictability. This attack can besides be found in Goyal and Welch ( 2008 ) and Kellard, Nankervis and Papadimitriou ( 2010 ) . The thought behind this method is to visually inspect the net cumulative sum-squared mistake ( ) which is the cumulative sum-squared mistake of the historical moving mean theoretical account minus the cumulative sum-squared mistake of the conditional theoretical accounts. More specifically, the difference is calculated by:

Where is the squared mistake of out-of-sample anticipation in twelvemonth t. The unconditioned SE is acquired when the predominating up-to-date return norm is employed to calculate the following month ‘s return. The conditional SEs are obtained from recursive arrested developments with the regressands either lagged dividend output ( or lagged gaining output ( to foretell the following month ‘s return. If the value of is positive, the variable theoretical account had lower prediction mistake in a given month and hence outperformed the unconditioned theoretical account at that period of clip which stress the prognostic power of variables i.e. dividend output and gaining output. Vice versa, if the value is negative, the anterior theoretical account failed to surpass the latter one.

4.3. Drumhead

This chapter explains the methodological analysiss used in this thesis in order to analyze the return predictability of variables i.e. dividend output and earning-price ratio. The empirical survey will first prove the statistic significance of in-sample predictability and so measure the prediction public presentation of prognostic variables by both statistic and graphical rating method. The consequences from these empirical trials for three stock markets including UK, US and HK will be presented in the following chapter.

Chapter 5: Empirical Consequences

The old chapters have proposed theoretical background every bit good as empirical grounds, the informations description and the methodogies exploited in this survey. The methodological analysiss will be applied to see the empirical consequences for the prediction public presentation of stock returns on dividend output and gaining output. More specifically, the construction is as follow:

Section 5.1 presents the in-sample predictability in which the prediction abilities of dividend output and gaining output are evaluated.

Section 5.2 studies the out-of-sample prediction public presentation of conditional theoretical accounts when compared against the prevalent return mean by both statistic and graphical appraisals.

Section 5.3 compares the findings of current survey with old researches.

Section 5.4 provides a general sum-up of this chapter.

5.1. In-sample tantrum

Table 5.1 shows the consequences of the univariate arrested development in which stock market returns are explained by the lagged dividend output and or the lagged earning output are showed in the in-sample period, which is the whole sample from July 1982 to July 2012 in this survey. Besides the standard t-statistics, the in-sample trial besides produce the Newey-West t-statistics ( denoted by NW ) , and bootstrap statistic which adjust for the heteroskedasticity and autocorrelation.The superiors * , ** , *** indicate statistical significance at 90 % , 95 % and 99 % degree of assurance, severally. The p-values are reported in parentheses.

It can be seen from the tabular array that the incline coefficient is positive every instances, which is in line with the theoretical background discussed in Chapter 2, expected return is little when dividend output ( or gaining output ) is low and frailty versa. Furthermore, we can detect the upward prejudice of OLS t-statistic in whole in-sample period, as suggested in Stambaugh ( 1986 ) , Mankiw and Shapiro ( 1986 ) and Nelson and Kim ( 1993 ) , i.e. the t-statistic for both dividend output and gaining output across 3 stock markets are all larger than the Newey-West and bootstrap statistics. For case, the OLS t-statistic, NW and bootstrap statistic for dividend output in Hang Seng stock market are 5.62, 4.84 and 4.25 severally. However, on occasion, the recorded OLS t-values are surprisingly smaller than NW and bootstrap statistics adjusted for autocorrelation and heteroskedasticity as in sub-sample 1982-2002. Contradict with the research of Nelson and Kim ( 1993 ) , this survey happen that the prejudices ( if any ) are non singular plenty to extenuate the return predictability. In peculiar, the prejudice is merely about 2 % to 5 % and the p-value of all the statistics delivers the same consequences of accepting or rejecting the void hypothesis of no predictability. The analyses of each stock market are as follows:

S & A ; P500: There is grounds that the dividend output is statistically important for the whole period.The absolute value of t-statistics is 6.88 with the p-value is 0.0000. Such consequences can reject the void hypothesis at 99.99 % degree of confidence.NW t-and bootstrap statistics besides support for the observation with its absolute value are 4.18 and 6.76 severally, both p-values are 0.0000.

However, the dividend output fails to calculate US stock return in the period 1982-1997 ( table 5.1 panel B ) , which might due to the terrible planetary economic recession in 1980s. When widening the sub sample period until 2002 ( Table 5.1 panel C ) , this variable additions statistical significance with 99 % degree of assurance ( p-values are all 0.000 )

With regard to earning-price ratio, the survey finds strong calculating power in all sample periods including full sample and both sub-sample. In item, the t-statistic scopes from 2.63 to 4.98 which p-value supported to reject the void hypothesis at 99 % degree of assurance. That degree of assurance besides can be found in NW and Bootstrap statistics for all sample periods.

FTSE All Share: In the whole in-sample period, dividend output shows robust calculating ability in UK market with the t-statistic, NW and bootstrap statistics are correspondingly 4.06, 2.61 and 3.51 which can all reject the nothing at 99 % degree of assurance.

Similar in US market, as affected by 1980s planetary economic crisis, dividend output can non reject the nothing in sub-sample 1982-1997 but turns to be statistically important at 99 % assurance degree in the larger sub-sample from 1982 to 2002 with all the statistics including criterion and NW t-values, bootstrap statistic value of 2.97, 2.29 and 2.03 severally.

Gaining output as a forecaster seems non work in UK market in the in-sample period since we can non reject the void hypothesis of no prognostic power in all full and sub-samples. Specifically, the criterion and NW t-statistics every bit good as the bootstrap are rather low ( scopes from 0.12 to 1.13 ) that can non accept the alternate hypothesis at any degree of assurance.

Hang Seng: In HK stock market, all OLS T value, NW and bootstrap statistics shows favour for strong prognostic ability of dividend output in the whole period 1982-2012 at 99 % degree of assurance ( with the value of 5.62, 4.14 and 4.25 correspondingly and p-values are all 0.0000 ) . In the two sub-sample periods, on the contrary, these statistics portion the same consequences that can non reject the nothing of no predictability.

A duplicated signifier is observed in earning-price ratio as this forecaster shows good statistic significance in the whole in-sample period but fail to calculate returns in two sub-periods. That hapless public presentation might due to 1980s planetary economic crisis every bit good as the 1997-1998 currency crises took topographic point in Asia.

After analysing ‘vertically ‘ , we continue to construe the consequences from horizontal position utilizing the goodness of fit ratio As analyzed above, dividend output and gaining output are both statistically important in all markets for the whole in-sample period, excepting the power of gaining output in the UK market. The dividend output theoretical account is best fitted in US and the fittingness decreases to UK and HK, which can be visually inspected in Graph 3. In peculiar, highest value of is recorded for S & A ; P500 ( 10.20 % ) and lowest value is recorded for Hang Seng index ( 8.10 % ) . In footings of earning-price ratio, the survey finds comparative good prognostic power on market stock return in US and HK but really hapless in UK. In UK, is highly little ( 0.007 % ) whereas US and HK markets retain higher value of ( 4.39 % and 2.90 % severally ) .

Table5.1: In-sample univariate arrested development

Panel A: Full moon sample 1982:07 – 2012:07



S.E. %



S.E. %

S & A ; P500













( 0.0000 )


( 0.0000 )



( 0.6656 )


( 0.0001 )

NW t-stat


( 0.0010 )


( 0.0000 )

NW t-stat


( 0.5252 )


( 0.0001 )

Bootstrap t-stat


( 0.0000 )


( 0.0000 )

Bootstrap t-stat


( 0.718 )


( 0.0000 )














( 0.0000 )


( 0.0000 )



( 0.0337 )


( 0.8743 )

NW t-stat


( 0.0810 )


( 0.0174 )

NW t-stat


( 0.0004 )


( 0.0898 )

Bootstrap t-stat


( 0.00