toolreport.Rnw

<< eval = TRUE, echo=FALSE,message=FALSE,fig.pos='h',results='asis' >>=
load("bb_issuersTOOL.Rdata")
run_shiny_tool = 1
if(run_shiny_tool) suppressPackageStartupMessages({
  library(Rcpp)
  library(RcppArmadillo)
  library(stringr)
  library(gtools)
  library(timeDate)
  library(Hmisc)
})

library(knitr)
opts_chunk$set(cache=FALSE)
inline_hook <- function (x) {
  if (is.numeric(x)) {
    # ifelse does a vectorized comparison
    # If integer, print without decimal; otherwise print two places
    res <- ifelse(x == round(x),
                  # use comma for 1000s
                  sprintf("%s", prettyNum(x, big.mark=",")),
                  sprintf("%.2f", x)
    )
    paste(res, collapse = ", ")
  } else {
    x
  }
}
knit_hooks$set(inline = inline_hook)

###

suppressPackageStartupMessages(source("lib_helpers.R", chdir=TRUE))
source("latex_code.R")
source("ff_industries_sic.R")
source("Paper_global_parameters.R")

# All the report parameters
startdate = report.list$startdate
enddate= report.list$enddate
market_cap_min = report.list$market_cap_min
market_cap_max= report.list$market_cap_max
industry  = report.list$industry
characteristic= report.list$characteristic
characteristic_single_analysis= report.list$characteristic_single_analysis
quantile_used = report.list$quantile_used
characteristic_single_analysis_sign= report.list$characteristic_single_analysis_sign 
high_EU_index_thres= report.list$high_EU_index_thres 
low_EU_index_thres= report.list$low_EU_index_thres 
quantile_used_ind= report.list$quantile_used_ind
quantile_used_all= report.list$quantile_used_all
characteristic_irats1= report.list$characteristic_irats1
characteristic_irats2= report.list$characteristic_irats2
characteristic_irats3= report.list$characteristic_irats3
characteristic_irats4= report.list$characteristic_irats4
characteristic_irats5= report.list$characteristic_irats5
characteristic_irats6= report.list$characteristic_irats6
characteristic_irats1_sign= report.list$characteristic_irats1_sign
characteristic_irats2_sign= report.list$characteristic_irats2_sign
characteristic_irats3_sign= report.list$characteristic_irats3_sign 
characteristic_irats4_sign= report.list$characteristic_irats4_sign
characteristic_irats5_sign= report.list$characteristic_irats5_sign
characteristic_irats6_sign = report.list$characteristic_irats6_sign

###
@


<< eval = TRUE, echo=FALSE,message=FALSE,fig.pos='h',results='asis' >>=
# Filter the data now - as in Index.rmd

FirstTrade = startdate
starting = startdate 
ending = enddate   
if (ending - starting < 3*365)
  ending = starting + 3*365

market_cap_min = as.numeric(market_cap_min)
market_cap_max = as.numeric(market_cap_max)
if (market_cap_max < market_cap_min)
  market_cap_max = ceiling(max(BUYBACK_DATA_TOOL$Market.Cap))

useonly_industry = !(BUYBACK_DATA_TOOL$Industry_name %in% industry) 

useonly_report = which(BUYBACK_DATA_TOOL$Event.Date >= starting & BUYBACK_DATA_TOOL$Event.Date <= ending &
                         scrub(BUYBACK_DATA_TOOL$Market.Cap) >= market_cap_min & 
                         scrub(BUYBACK_DATA_TOOL$Market.Cap) <= market_cap_max &
                         useonly_industry) 

value.weights = rep(1, length(BUYBACK_DATA_TOOL$Prior.Returns.Score))
DATASET_NEW = list(
  BUYBACK_DATA_TOOL=BUYBACK_DATA_TOOL[useonly_report,],
  returns_by_event_monthly = returns_by_event_monthly[,useonly_report],
  DatesMonth  = DatesMonth[,useonly_report],
  value.weights = value.weights[useonly_report],
  subset = useonly_report
)

@

<< eval = TRUE, echo=FALSE,message=FALSE,fig.pos='h',results='asis' >>=

firstyear = as.character(format(startdate,"%Y"))
lastyear = as.character(format(enddate,"%Y"))
report_months_cal = c(as.numeric(reported_times[1:(length(reported_times)-1)]),1)
value.weights = rep(1,length(BUYBACK_DATA_TOOL$Prior.Returns.Score))

@

\documentclass{article}
\usepackage{setspace}
\usepackage{hyperref}
\usepackage{float}

\begin{document}


\title{\textbf{Volatility and the Buyback Anomaly: Online Interactive Tool Report}}%\footnotetext{}

\author{\uppercase{ Theodoros Evgeniou$^*$, Enric Junqu\'e de Fortuny$^{**}$,\\
Nick Nassuphis$^{***}$,} and \uppercase{Theo Vermaelen}\thanks{INSEAD, Bd de Constance, 77300 Fontainebleau, France, phone: +33(0)1 6072 4000, $^{**}$Rotterdam School of Management, Burgemeester Oudlaan 50, 3062 PA Rotterdam, The Netherlands, $^{***}$31, St. Martin's Lane WC2N 4ER London, United Kingdom, e-mail:   \href{mailto:theodoros.evgeniou@insead.edu}{theodoros.evgeniou@insead.edu}, \href{mailto:enric.junquedefortuny@insead.edu}{enric.junquedefortuny@rsm.nl},  \href{mailto:nicknassuphis@gmail.com}{nicknassuphis@gmail.com}, and \href{mailto:theo.vermaelen@insead.edu}{theo.vermaelen@insead.edu}. }}


\date{\today}              % No date for final submission

% Create title page with no page number

\renewcommand{\thefootnote}{\fnsymbol{footnote}}

\singlespacing

\maketitle

\vspace{-.2in}
\begin{abstract}
\noindent This is a customized report of the online interactive tool for the paper {\it ``Volatility and the Buyback Anomaly''} by T. Evgeniou, Enric Junqu\'e de Fortuny, Nick Nassuphis, and Theo Vermaelen. 

There is no guarantee that there is no error in all possible customized reports. 


\end{abstract}
%\vspace{2cm}

\medskip
%\noindent \textit{Keywords}: Share Buybacks; Seasoned Equity Offerings; Anomalies; Volatility

\thispagestyle{empty}

\setcounter{page}{1}

\doublespacing


\section{Report Parameters}
\label{sec:parameters}

The time period used in this report is from \Sexpr{startdate} to \Sexpr{enddate}. We only consider firms with a market capitalization the month before the event being between \Sexpr{market_cap_min} and \Sexpr{market_cap_max}. In addition to the financial and utilities sectors, we also remove the following sectors: \Sexpr{ifelse(length(industry) == 0, "None", paste(industry, collapse=", "))}. This leaves a total of \Sexpr{length(DATASET_NEW$value.weights)} buyback events. 


\section{\Sexpr{gsub("\\.", " ", characteristic_single_analysis)} and Excess Returns}

We consider the IRATS Cumulative Abnormal Returns (CAR) and Calendar Time method Abnormal Returns (AR) of the high and low quantiles of events defined using the selected event characteristic, namely \Sexpr{gsub("\\.", " ", characteristic_single_analysis)}. Table \ref{tbl:indcharacteristic} shows the results. Figure \ref{fig:indcharacteristic} shows the excess returns of a strategy  that trades only the high or low percentile stocks for this event characteristic (the strategy is designed as described in the paper). Table \ref{tbl:indcharacteristicpnl} shows the monthly and yearly returns of the high percentile events strategy. 


<<   eval = TRUE, echo=FALSE,message=FALSE,fig.pos='h',results='asis' >>=
# FOllowing Index.Rmd, generate first the tables as needed

thesign = ifelse(characteristic_single_analysis_sign, -1, +1)
thefeature = thesign*DATASET_NEW$BUYBACK_DATA_TOOL[[which(names(DATASET_NEW$BUYBACK_DATA_TOOL) == characteristic_single_analysis)]]
thefeatureQ = thesign*BUYBACK_DATA_TOOL[[which(names(BUYBACK_DATA_TOOL) == characteristic_single_analysis)]]  
quantile_used_ind = as.numeric(quantile_used)

High_feature_events = !is.na(thefeature) & scrub(thefeature) >= quantile(scrub(thefeatureQ[!is.na(thefeatureQ)]),1-quantile_used_ind)
Low_feature_events  = !is.na(thefeature) & scrub(thefeature) <= quantile(scrub(thefeatureQ[!is.na(thefeatureQ)]),quantile_used_ind)

res = round(cbind(
  car_table(DATASET_NEW$returns_by_event_monthly[, Low_feature_events],
            DATASET_NEW$BUYBACK_DATA_TOOL$Event.Date[ Low_feature_events],Risk_Factors_Monthly,formula_used = five_factor_model)$results,
  car_table(DATASET_NEW$returns_by_event_monthly[, High_feature_events],
            DATASET_NEW$BUYBACK_DATA_TOOL$Event.Date[High_feature_events],Risk_Factors_Monthly,formula_used = five_factor_model)$results
),2)[reported_times,]

colnames(res) <- c("Low: CAR", "t-stat","p-value", "High: CAR", "t-stat","p-value")
feature_IRATStable = as.data.frame(res)

##
thesign = ifelse(characteristic_single_analysis_sign, -1, +1)
thefeature = thesign*DATASET_NEW$BUYBACK_DATA_TOOL[[which(names(DATASET_NEW$BUYBACK_DATA_TOOL) == characteristic_single_analysis)]]
thefeatureQ = thesign*BUYBACK_DATA_TOOL[[which(names(BUYBACK_DATA_TOOL) == characteristic_single_analysis)]]  
quantile_used_ind = as.numeric(quantile_used)

High_feature_events = !is.na(thefeature) & scrub(thefeature) >= quantile(scrub(thefeatureQ[!is.na(thefeatureQ)]),1-quantile_used_ind)
Low_feature_events  = !is.na(thefeature) & scrub(thefeature) <= quantile(scrub(thefeatureQ[!is.na(thefeatureQ)]),quantile_used_ind)

res = round(cbind(
  calendar_table(DATASET_NEW$returns_by_event_monthly[, Low_feature_events],
                 DATASET_NEW$BUYBACK_DATA_TOOL$Event.Date[Low_feature_events],Risk_Factors_Monthly,formula_used = five_factor_model, value.weights = DATASET_NEW$value.weights[Low_feature_events])$results,
  calendar_table(DATASET_NEW$returns_by_event_monthly[,High_feature_events],
                 DATASET_NEW$BUYBACK_DATA_TOOL$Event.Date[High_feature_events],Risk_Factors_Monthly,formula_used = five_factor_model, value.weights = DATASET_NEW$value.weights[High_feature_events])$results
),2)[reported_times,]

colnames(res) <- c("Low: CAL", "t-stat","p-value", "High: CAL", "t-stat","p-value")
feature_CALtable= as.data.frame(res)

##
thesign = ifelse(characteristic_single_analysis_sign, -1, +1)
thefeature = thesign*DATASET_NEW$BUYBACK_DATA_TOOL[[which(names(DATASET_NEW$BUYBACK_DATA_TOOL) == characteristic_single_analysis)]]
thefeatureQ = thesign*BUYBACK_DATA_TOOL[[which(names(BUYBACK_DATA_TOOL) == characteristic_single_analysis)]]  
quantile_used_ind = as.numeric(quantile_used)

High_feature_events = !is.na(thefeature) & scrub(thefeature) >= quantile(scrub(thefeatureQ[!is.na(thefeatureQ)]),1-quantile_used_ind)

High_feature <- apply(PNL_matrix_BB(start_date_event,"One.Year.After", High_feature_events,  DATASET_NEW$DatesMonth, DATASET_NEW$returns_by_event_monthly,event=1),1,non_zero_mean)
High_feature_Hedged_react = remove_initialization_time(suppressWarnings(scrub(alpha_lm(High_feature,Risk_Factors_Monthly[,pnl_hedge_factors],hedge_months,trade=1))),min_date=FirstTrade)

##
thesign = ifelse(characteristic_single_analysis_sign, -1, +1)
thefeature = thesign*DATASET_NEW$BUYBACK_DATA_TOOL[[which(names(DATASET_NEW$BUYBACK_DATA_TOOL) == characteristic_single_analysis)]]
thefeatureQ = thesign*BUYBACK_DATA_TOOL[[which(names(BUYBACK_DATA_TOOL) == characteristic_single_analysis)]]  
quantile_used_ind = as.numeric(quantile_used)

Low_feature_events  = !is.na(thefeature) & scrub(thefeature) <= quantile(scrub(thefeatureQ[!is.na(thefeatureQ)]),quantile_used_ind)

Low_feature <- apply(PNL_matrix_BB(start_date_event,"One.Year.After", Low_feature_events,  DATASET_NEW$DatesMonth, DATASET_NEW$returns_by_event_monthly,event=1),1,non_zero_mean)
Low_feature_Hedged_react = remove_initialization_time(suppressWarnings(scrub(alpha_lm(Low_feature,Risk_Factors_Monthly[,pnl_hedge_factors],hedge_months,trade=1))),min_date=FirstTrade)  

@

\clearpage

<<   eval = TRUE, echo=FALSE,message=FALSE,fig.pos='h',results='asis' >>=
tmp = cbind(feature_IRATStable,feature_CALtable)[reported_times,]
colnames(tmp)[1]<-colnames(tmp)[4] <-  "CAR"

printLatexTable(
  tmp,
  columns = c("IRATS CAR: LOW","HIGH","Calendar Time AR: LOW","HIGH"),
  title= paste("Buyback IRATS and Calendar Time Abnormals Returns for ",gsub("\\."," ", characteristic_single_analysis),sep=" "),
  caption= "The tables presents the abnormal returns for firms after repurchase announcements from the announcement date until $t$ months after the announcement. Left tables report monthly cumulative average abnormal returns (CAR) in percent using Ibbotson (1975) returns across time and security (IRATS) method combined with the Fama French (2015) five-factor model for the low and high prcentile sample of firms using the selected ctiretion that announced an open market share repurchase. The following regressions are run each event month~$j$:
\\begin{eqnarray*}
(R_{i,t} - R_{f,t}) &=& a_j + b_j (R_{m,t} - R_{f,t}) + c_j {SMB}_t + d_j {HML}_t + \\epsilon_{i,t}, \\\\
(R_{i,t} - R_{f,t}) &=& a_j + b_j (R_{m,t} - R_{f,t}) + c_j {SMB}_t + d_j {HML}_t + e_t {RMW}_t + f_t {CMA}_t + \\epsilon_{i,t},
\\end{eqnarray*}
where $R_{i,t}$ is the monthly return on security $i$ in the calendar month $t$ that corresponds to the event month $j$, with $j = 0$ being the month of the repurchase announcement. $R_{f,t}$ and $R_{m,t}$ are the risk-free rate and the return on the equally weighted CRSP index, respectively. ${SMB}_t$, ${HML_t}$, ${RMW}_t$, ${CMA}_t$ are the monthly returns on the size, book-to-market factor, profitability factor and investment factor in month $t$, respectively. The numbers reported are sums of the intercepts of cross-sectional regressions over the relevant event-time-periods expressed in percentage terms. The standard error (denominator of the $t$-statistic) for a window is the square root of the sum of the squares of the monthly standard errors. Right tables report monthly average abnormal returns (AR) of equally weighted Calendar Time portfolios using the Fama and French (2015a) five-factor model. In this method, event firms that have announced an open market buyback in the last calendar months form the basis of the calendar month portfolio. A single time-series regression is run with the excess returns of the calendar portfolio as the dependent variable and the returns of five factors as the independent variables. The significance levels are indicated by +, *, and ** and correspond to a significance level of $10\\%$, $5\\%$, and $1\\%$ respectively, using a two-tailed test.
",

label = "tbl:indcharacteristic",
titleontop=T,
metric = "Ret.",
scale=1,
lastSpecial=T#,
#dorotate=F
)
@

\clearpage

\begin{figure}[H]
\centering
<< BBISSpnl1, fig.width=10, fig.height=7, out.width='\\textwidth', echo=F >>=

plot(cumsum(100*Low_feature_Hedged_react),type="l",ylab="CAR", xlab = "",main = paste("Excess Returns of a Buyback Strategy based on ",gsub("\\."," ", characteristic_single_analysis),sep=" "), axes = FALSE, ylim=c(min(c(100*cumsum(Low_feature_Hedged_react),cumsum(100*High_feature_Hedged_react))), max(c(cumsum(100*Low_feature_Hedged_react),cumsum(100*High_feature_Hedged_react)))), cex.lab=1.1)
axis(1,at=seq(1,length(Low_feature_Hedged_react),length.out=10),labels=str_sub(names(Low_feature_Hedged_react)[seq(1,length(Low_feature_Hedged_react),length.out=10)], start = 1, end=4),cex.axis=1,las=3)
axis(2,cex.axis=1.1)
lines(cumsum(100*High_feature_Hedged_react), lty = 2,lwd=1.4)
for (iter in floor(100*min(c(cumsum(Low_feature_Hedged_react),cumsum(High_feature_Hedged_react)))/100):floor(100*max(c(cumsum(Low_feature_Hedged_react),cumsum(High_feature_Hedged_react)))/100))
  abline(h = 100*iter)
#plot_crisis_dates(Low_feature_Hedged_react) 
legend(x="topleft",
       c("High Quantile","Low Quantile"),
       lty=c("solid","dashed"),
       lwd=c(2,2),
       cex=1,bg="white",inset=0.01)

@
\caption{Buybacks: Returns of five-factor rolling hedged portfolio for only the buyback events for high and low percentile events. Solid line is ``high'' and a 12-months holding portfolio, dotted line is ``low'' and a 12-months holding portfolio. 
}
\label{fig:indcharacteristic}
\end{figure}


\clearpage

<<  eval = TRUE, echo=FALSE,message=FALSE,fig.pos='h',results='asis' >>=
latex_render_data_frame(
  pnl_matrix(remove_initialization_time(High_feature_Hedged_react,min_date=FirstTrade)), 
  title = paste("Monthly and Yearly Five Factor Abnormal Rerurns of a strategy investing in the high percentile buybacks defined using the event characteristic",gsub("\\."," ", characteristic_single_analysis), sep=" "),
  caption="Monthly and yearly five-factor rolling hedged abnormal returns of an equally weighted (with monthly rebalancing) portfolio of selected buybacks. The holding period for each buyback is 12 months per event.",
  label="tbl:indcharacteristicpnl", 
  columns=NULL,
  bigtitleontop = T,
  show_rownames=TRUE,
  scale = 0.9,
  digits=1,
  lastSpecial=F#,dorotate=F
)

@


\clearpage


\section{Customized Undervaluation Indicator and Excess Returns}

We define a customized Undervaluation index using the following event characteristics: \Sexpr{ifelse(characteristic_irats1 != "None",  paste(gsub("\\.", " ", characteristic_irats1), " (sign is ", ifelse(characteristic_irats1_sign, "-1","+1"),")",collapse = ""), "") } \Sexpr{ifelse(characteristic_irats2 != "None",  paste(",", gsub("\\.", " ", characteristic_irats2), " (sign is ", ifelse(characteristic_irats2_sign, "-1","+1"),")",collapse = ""), "") }  \Sexpr{ifelse(characteristic_irats3 != "None",  paste(",", gsub("\\.", " ", characteristic_irats3), " (sign is ", ifelse(characteristic_irats3_sign, "-1","+1"),")",collapse = ""), "") } \Sexpr{ifelse(characteristic_irats4 != "None",  paste(",", gsub("\\.", " ", characteristic_irats4), " (sign is ", ifelse(characteristic_irats4_sign, "-1","+1"),")",collapse = ""), "") } \Sexpr{ifelse(characteristic_irats5 != "None",  paste(",", gsub("\\.", " ", characteristic_irats5), " (sign is ", ifelse(characteristic_irats5_sign, "-1","+1"),")",collapse = ""), "") } \Sexpr{ifelse(characteristic_irats6 != "None",  paste(",", gsub("\\.", " ", characteristic_irats6), " (sign is ", ifelse(characteristic_irats6_sign, "-1","+1"),")",collapse = ""), "") }. For each of these characteristics we define the high and low events as those that are in the top or bottom \Sexpr{100*quantile_used_ind}$\%$ of the events. We then assign a score of 2 for the high, 0 for the low, and 1 for the rest of the events for each of these characteristics, and we add up these scores to create the customized undervaluation index. Figure \ref{fig:undervaluationindex} shows the number of events for each of the values of this customized index. 


We then consider the IRATS Cumulative Abnormal Returns (CAR) and Calendar Time method Abnormal Returns (AR) of the high/low quantiles of events defined using this customized Undervaluation Index. Table \ref{tbl:CUcharacteristic} shows the results. Figure \ref{fig:CUcharacteristic} shows the excess returns of a strategy that trades only the high or low percentile stocks for this customized undervaluation index (the strategy is designed as described in the paper). Table \ref{tbl:CUcharacteristicpnl} shows the monthly and yearly returns of the high percentile events strategy. 

<<   eval = TRUE, echo=FALSE,message=FALSE,fig.pos='h',results='asis' >>=

thesign = ifelse(characteristic_irats1_sign, -1, +1)
thefeature1 = (thesign==-1) + thesign*DATASET_NEW$BUYBACK_DATA_TOOL[[which(names(DATASET_NEW$BUYBACK_DATA_TOOL) == characteristic_irats1)]]  
thefeature1Q = (thesign==-1) + thesign*BUYBACK_DATA_TOOL[[which(names(BUYBACK_DATA_TOOL) == characteristic_irats1)]]  
High_feature_events1 = (scrub(thefeature1) >= quantile(thefeature1Q[!is.na(thefeature1Q)],1-as.numeric(quantile_used_ind)) & !is.na(thefeature1))
Low_feature_events1 = (scrub(thefeature1) <= quantile(thefeature1Q[!is.na(thefeature1Q)],as.numeric(quantile_used_ind)) & !is.na(thefeature1))

thefeature2 <- thefeature3 <- thefeature4 <- thefeature5 <- thefeature6 <- rep(0,length(High_feature_events1))
High_feature_events2 <- High_feature_events3 <- High_feature_events4 <- High_feature_events5 <- High_feature_events6 <- rep(FALSE,length(High_feature_events1))
Low_feature_events2 <- Low_feature_events3 <- Low_feature_events4 <- Low_feature_events5 <- Low_feature_events6 <- 
  rep(FALSE,length(Low_feature_events1))

if (characteristic_irats2 != "None"){
  thesign = ifelse(characteristic_irats2_sign, -1, +1)
  thefeature2 = (thesign==-1) + thesign*DATASET_NEW$BUYBACK_DATA_TOOL[[which(names(DATASET_NEW$BUYBACK_DATA_TOOL) == characteristic_irats2)]]  
  thefeature2Q = (thesign==-1) + thesign*BUYBACK_DATA_TOOL[[which(names(BUYBACK_DATA_TOOL) == characteristic_irats2)]]  
  High_feature_events2 = (scrub(thefeature2) >= quantile(thefeature2Q[!is.na(thefeature2Q)],1-as.numeric(quantile_used_ind)) & !is.na(thefeature2))
  Low_feature_events2 = (scrub(thefeature2) <= quantile(thefeature2Q[!is.na(thefeature2Q)],as.numeric(quantile_used_ind)) & !is.na(thefeature2))
}
if (characteristic_irats3 != "None"){
  thesign = ifelse(characteristic_irats3_sign, -1, +1)
  thefeature3 = (thesign==-1) + thesign*DATASET_NEW$BUYBACK_DATA_TOOL[[which(names(DATASET_NEW$BUYBACK_DATA_TOOL) == characteristic_irats3)]]  
  High_feature_events3 = (scrub(thefeature3) >= quantile(thefeature3[!is.na(thefeature3)],1-as.numeric(quantile_used_ind)) & !is.na(thefeature3))
  Low_feature_events3 = (scrub(thefeature3) <= quantile(thefeature3[!is.na(thefeature3)],as.numeric(quantile_used_ind)) & !is.na(thefeature3))
}
if (characteristic_irats4 != "None"){
  thesign = ifelse(characteristic_irats4_sign, -1, +1)
  thefeature4 = (thesign==-1) + thesign*DATASET_NEW$BUYBACK_DATA_TOOL[[which(names(DATASET_NEW$BUYBACK_DATA_TOOL) == characteristic_irats4)]]  
  High_feature_events4 = (scrub(thefeature4) >= quantile(thefeature4[!is.na(thefeature4)],1-as.numeric(quantile_used_ind)) & !is.na(thefeature4))
  Low_feature_events4 = (scrub(thefeature4) <= quantile(thefeature4[!is.na(thefeature4)],as.numeric(quantile_used_ind)) & !is.na(thefeature4))
}
if (characteristic_irats5 != "None"){
  thesign = ifelse(characteristic_irats5_sign, -1, +1)
  thefeature5 = (thesign==-1) + thesign*DATASET_NEW$BUYBACK_DATA_TOOL[[which(names(DATASET_NEW$BUYBACK_DATA_TOOL) == characteristic_irats5)]]  
  High_feature_events5 = (scrub(thefeature5) >= quantile(thefeature5[!is.na(thefeature5)],1-as.numeric(quantile_used_ind)) & !is.na(thefeature5))
  Low_feature_events5 = (scrub(thefeature5) <= quantile(thefeature5[!is.na(thefeature5)],as.numeric(quantile_used_ind)) & !is.na(thefeature5))
}
if (characteristic_irats6 != "None"){
  thesign = ifelse(characteristic_irats6_sign, -1, +1)
  thefeature6 = (thesign==-1) + thesign*DATASET_NEW$BUYBACK_DATA_TOOL[[which(names(DATASET_NEW$BUYBACK_DATA_TOOL) == characteristic_irats6)]]  
  High_feature_events6 = (scrub(thefeature5) >= quantile(thefeature5[!is.na(thefeature5)],1-as.numeric(quantile_used_ind)) & !is.na(thefeature5))
  Low_feature_events6 = (scrub(thefeature5) <= quantile(thefeature5[!is.na(thefeature5)],as.numeric(quantile_used_ind)) & !is.na(thefeature5))
}

Index_score = 
  2*High_feature_events1 + 1*(!High_feature_events1 & !Low_feature_events1) + 
  (characteristic_irats2 != "None")*(2*High_feature_events2 + 1*(!High_feature_events2 & !Low_feature_events2) ) + 
  (characteristic_irats3 != "None")*(2*High_feature_events3 + 1*(!High_feature_events3 & !Low_feature_events3) ) + 
  (characteristic_irats4 != "None")*(2*High_feature_events4 + 1*(!High_feature_events4 & !Low_feature_events4) ) + 
  (characteristic_irats5 != "None")*(2*High_feature_events5 + 1*(!High_feature_events5 & !Low_feature_events5) ) + 
  (characteristic_irats6 != "None")*(2*High_feature_events6 + 1*(!High_feature_events6 & !Low_feature_events6) ) 

Index_Score_rect = Index_score

###
thefeature = Index_Score_rect
High_feature_events = (scrub(thefeature) >= quantile(thefeature[!is.na(thefeature)],1-as.numeric(quantile_used_all)) & !is.na(thefeature))
Low_feature_events = (scrub(thefeature) <= quantile(thefeature[!is.na(thefeature)],as.numeric(quantile_used_all)) & !is.na(thefeature))

res = round(cbind(
  car_table(DATASET_NEW$returns_by_event_monthly[, Low_feature_events],
            DATASET_NEW$BUYBACK_DATA_TOOL$Event.Date[ Low_feature_events],Risk_Factors_Monthly,formula_used = five_factor_model)$results,
  car_table(DATASET_NEW$returns_by_event_monthly[, High_feature_events],
            DATASET_NEW$BUYBACK_DATA_TOOL$Event.Date[High_feature_events],Risk_Factors_Monthly,formula_used = five_factor_model)$results
),2)[reported_times,]
colnames(res) <- c("Low: CAR", "t-stat","p-value", "High: CAR", "t-stat","p-value")
feature_IRATStable_index = res

###
thefeature = Index_Score_rect
High_feature_events = (scrub(thefeature) >= quantile(thefeature[!is.na(thefeature)],1-as.numeric(quantile_used_all)) & !is.na(thefeature))
Low_feature_events = (scrub(thefeature) <= quantile(thefeature[!is.na(thefeature)],as.numeric(quantile_used_all)) & !is.na(thefeature))

res = round(cbind(
  calendar_table(DATASET_NEW$returns_by_event_monthly[, Low_feature_events],
                 DATASET_NEW$BUYBACK_DATA_TOOL$Event.Date[Low_feature_events],Risk_Factors_Monthly,formula_used = five_factor_model, value.weights = DATASET_NEW$value.weights[Low_feature_events])$results,
  calendar_table(DATASET_NEW$returns_by_event_monthly[,High_feature_events],
                 DATASET_NEW$BUYBACK_DATA_TOOL$Event.Date[High_feature_events],Risk_Factors_Monthly,formula_used = five_factor_model, value.weights = DATASET_NEW$value.weights[High_feature_events])$results
),2)[reported_times,]

colnames(res) <- c("Low: CAL", "t-stat","p-value", "High: CAL", "t-stat","p-value")
feature_CALtable_index = res

###
thefeature = Index_Score_rect
High_feature_events = which(scrub(thefeature) >= quantile(thefeature[!is.na(thefeature)],1-as.numeric(quantile_used_all)) & !is.na(thefeature))
High_feature <- apply(PNL_matrix_BB(start_date_event,"One.Year.After", High_feature_events,  DATASET_NEW$DatesMonth, DATASET_NEW$returns_by_event_monthly,event=1),1,non_zero_mean)
High_feature_Hedged_react_index = remove_initialization_time(suppressWarnings(scrub(alpha_lm(High_feature,Risk_Factors_Monthly[,pnl_hedge_factors],hedge_months,trade=1))),min_date=FirstTrade)

###
thefeature = Index_Score_rect
Low_feature_events = which(scrub(thefeature) <= quantile(thefeature[!is.na(thefeature)],as.numeric(quantile_used_all)) & !is.na(thefeature))
Low_feature <- apply(PNL_matrix_BB(start_date_event,"One.Year.After", Low_feature_events,  DATASET_NEW$DatesMonth, DATASET_NEW$returns_by_event_monthly,event=1),1,non_zero_mean)
Low_feature_Hedged_react_index = remove_initialization_time(suppressWarnings(scrub(alpha_lm(Low_feature,Risk_Factors_Monthly[,pnl_hedge_factors],hedge_months,trade=1))),min_date=FirstTrade)  
@

\clearpage

\begin{figure}[H]
\centering
<<  fig.width=10, fig.height=5, out.width='\\textwidth', echo=F >>=
#par(mfrow=c(2,1), mar=c(2.3,4,2.3,4))
#valuation_index_bb[which(valuation_index_bb==2)]<-3 # there is one company here. need to check why
tmp = table(Index_Score_rect)
tmp = structure(as.numeric(tmp), .Names = names(tmp))
barplot(tmp,main = "", ylab = "Number of Events", xlab = "",las=2,space=0.5, cex.names=1)
#tmp = table(valuation_index_iss)
#tmp = structure(as.numeric(tmp), .Names = names(tmp))
#barplot(tmp,main = "SEOs", ylab = "Number of Announcements", xlab = "SEO Overvaluation Index",las=2,space=0.5, cex.names=1)
rm("tmp")
@
\caption{Distribution of the Customized Undervaluation Index of all buyback events.}
\label{fig:undervaluationindex}
\end{figure}

\clearpage


<<   eval = TRUE, echo=FALSE,message=FALSE,fig.pos='h',results='asis' >>=
tmp = cbind(feature_IRATStable_index, feature_CALtable_index)[reported_times,]
colnames(tmp)[1]<-colnames(tmp)[4] <-  "CAR"

printLatexTable(
  tmp,
  columns = c("IRATS CAR: LOW","HIGH","Calendar Time AR: LOW","HIGH"),
  title= "Buyback IRATS and Calendar Time Abnormals Returns for the Customized Undervaluation Index",
  caption= "The tables presents the abnormal returns for firms after repurchase announcements from the announcement date until $t$ months after the announcement. Left tables report monthly cumulative average abnormal returns (CAR) in percent using Ibbotson (1975) returns across time and security (IRATS) method combined with the Fama French (2015) five-factor model for the low and high prcentile sample of firms using the customized undervaluation index that announced an open market share repurchase. The following regressions are run each event month~$j$:
\\begin{eqnarray*}
(R_{i,t} - R_{f,t}) &=& a_j + b_j (R_{m,t} - R_{f,t}) + c_j {SMB}_t + d_j {HML}_t + \\epsilon_{i,t}, \\\\
(R_{i,t} - R_{f,t}) &=& a_j + b_j (R_{m,t} - R_{f,t}) + c_j {SMB}_t + d_j {HML}_t + e_t {RMW}_t + f_t {CMA}_t + \\epsilon_{i,t},
\\end{eqnarray*}
where $R_{i,t}$ is the monthly return on security $i$ in the calendar month $t$ that corresponds to the event month $j$, with $j = 0$ being the month of the repurchase announcement. $R_{f,t}$ and $R_{m,t}$ are the risk-free rate and the return on the equally weighted CRSP index, respectively. ${SMB}_t$, ${HML_t}$, ${RMW}_t$, ${CMA}_t$ are the monthly returns on the size, book-to-market factor, profitability factor and investment factor in month $t$, respectively. The numbers reported are sums of the intercepts of cross-sectional regressions over the relevant event-time-periods expressed in percentage terms. The standard error (denominator of the $t$-statistic) for a window is the square root of the sum of the squares of the monthly standard errors. Right tables report monthly average abnormal returns (AR) of equally weighted Calendar Time portfolios using the Fama and French (2015a) five-factor model. In this method, event firms that have announced an open market buyback in the last calendar months form the basis of the calendar month portfolio. A single time-series regression is run with the excess returns of the calendar portfolio as the dependent variable and the returns of five factors as the independent variables. The significance levels are indicated by +, *, and ** and correspond to a significance level of $10\\%$, $5\\%$, and $1\\%$ respectively, using a two-tailed test.
",

label = "tbl:CUcharacteristic",
titleontop=T,
metric = "Ret.",
scale=1,
lastSpecial=T#,
#dorotate=F
)
@

\clearpage

\begin{figure}[H]
\centering
<< BBISSpnl2, fig.width=10, fig.height=7, out.width='\\textwidth', echo=F >>=

plot(cumsum(100*Low_feature_Hedged_react_index),type="l",ylab="CAR", xlab = "",main = "Excess Returns of a Buyback Strategy based on the Customized Undervaluation Index", axes = FALSE, ylim=c(min(c(100*cumsum(Low_feature_Hedged_react_index),cumsum(100*High_feature_Hedged_react_index))), max(c(cumsum(100*Low_feature_Hedged_react_index),cumsum(100*High_feature_Hedged_react_index)))), cex.lab=1.1)
axis(1,at=seq(1,length(Low_feature_Hedged_react_index),length.out=10),labels=str_sub(names(Low_feature_Hedged_react_index)[seq(1,length(Low_feature_Hedged_react_index),length.out=10)], start = 1, end=4),cex.axis=1,las=3)
axis(2,cex.axis=1.1)
lines(cumsum(100*High_feature_Hedged_react_index), lty = 2,lwd=1.4)
for (iter in floor(100*min(c(cumsum(Low_feature_Hedged_react),cumsum(High_feature_Hedged_react_index)))/100):floor(100*max(c(cumsum(Low_feature_Hedged_react_index),cumsum(High_feature_Hedged_react_index)))/100))
  abline(h = 100*iter)
#plot_crisis_dates(Low_feature_Hedged_react) 
legend(x="topleft",
       c("High Cusomized U-Index","Low Cusomized U-Index"),
       lty=c("solid","dashed"),
       lwd=c(2,2),
       cex=1,bg="white",inset=0.01)

@
\caption{Buybacks: Returns of five-factor rolling hedged portfolio for only the buyback events for high and low percentile events defined using the Customized Undervaluation Index. Solid line is ``high'' and a 12-months holding portfolio, dotted line is ``low'' and a 12-months holding portfolio. 
}
\label{fig:CUcharacteristic}
\end{figure}

\clearpage

<<  eval = TRUE, echo=FALSE,message=FALSE,fig.pos='h',results='asis' >>=
latex_render_data_frame(
  pnl_matrix(remove_initialization_time(High_feature_Hedged_react_index,min_date=FirstTrade)), 
  title = "Monthly and Yearly Five Factor Abnormal Rerurns of a strategy investing in the high percentile buybacks defined using the Customized Undervaluation Index",
  caption="Monthly and yearly five-factor rolling hedged abnormal returns of an equally weighted (with monthly rebalancing) portfolio of selected buybacks. The holding period for each buyback is 12 months per event.",
  label="tbl:CUcharacteristicpnl", 
  columns=NULL,
  bigtitleontop = T,
  show_rownames=TRUE,
  scale = 0.9,
  digits=1,
  lastSpecial=F#,dorotate=F
)

@


\clearpage

\end{document}