市值异象

Banz and Reinganum(1981)第一次记录了市值异象，发现小盘股收益高于大盘股收益，Fama and French(1992)将市值异象作为定价因子纳入定价模型。我们先评价市值异象在中国市场的表现，然后参考Fama and French(1992)的方法构造市值因子。

1、市值与价值策略表现

在t月将股票按t-1月的市值分为5组，分别统计当月等权收益和总市值加权收益，具体代码如下：

##加载软件包
pacman::p_load(data.table,plyr,stringr,dplyr,mongolite,future.apply,future,data.table,gt)

##建立R与MongoDB数据库的链接，collection为数据表对应的文件，db为数据库中的表
md<-mongo(collection = "tradedatadaily",db="stockdata")
mm<-mongo(collection = "monthlytrade",db="stockdata")
##查询字段有上市公司代码（symbol）、收盘价(close)、前收盘价(pre_close)，总市值(total_mv)，市净率（pb）
dailydata<-as.data.table(md$find(query = '{}',
                  fields = '{"symbol":"ture","trade_date":"ture","total_mv":"ture","pe":"ture","_id":"false"}'))[order(symbol,trade_date)][,yms:=gsub('^(\\d{4})(\\d{2})(\\d{2})$', '\\1-\\2',trade_date)][,.SD[.N],by=.(symbol,yms)][,-c(3,4)]
 

monthdata<-as.data.table(mm$find(query = '{}',
                  fields = '{"symbol":"ture","trade_date":"ture","close":"ture","pre_close":"ture","_id":"false"}'))[,yms:=gsub('^(\\d{4})(\\d{2})(\\d{2})$', '\\1-\\2',trade_date)][,-c(1,3)][dailydata,on=.(symbol,yms)][,':='(lmv=lag(total_mv),lbm=lag(1/pe),rets=close/pre_close-1),by=.(symbol)][!is.na(lbm)&!is.na(close)&yms>="1995-01",][,.(symbol,yms,lmv,lbm,rets)]

portfoli<-monthdata[,':='(gmv=cut(lmv,c(min(lmv)-10,quantile(lmv,seq(0.2,0.8,0.2)),max(lmv)+10),labels=1:5),
                          gbm=cut(lbm,c(min(lbm)-10,quantile(lbm,seq(0.2,0.8,0.2)),max(lbm)+10),labels=1:5))
                    ,by=yms][,':='(mveqrets=mean(rets),mvwret=sum(rets*lmv)/sum(lmv)),by=.(yms,gmv)
                             ][,':='(bmeqrets=mean(rets),bmwret=sum(rets*lmv)/sum(lmv)),by=.(yms,gbm)]

##序列均值t检验
ttest<-function(x){
  tt<-t.test(x)
  return(c(round(tt$estimate,4),paste0("(",format(tt$statistic,digits=2,nsmall=2),")")))
}
mvp<-rbind(dcast(unique(portfoli[,.(yms,gmv,mveqrets)]),yms~gmv,value.var = c("mveqrets"))[,-c(1)][,lapply(.SD, ttest)],dcast(unique(portfoli[,.(yms,gmv,mvwret)]),yms~gmv,value.var = c("mvwret"))[,-c(1)][,lapply(.SD, ttest)])%>%gt()%>%tab_header(
    title = "市值分组股票收益",
    subtitle = "1995-01-01 to 2021-04-01"
  )%>%
  tab_row_group(
    group = "等权收益",
    rows = 1:2
  )%>%tab_row_group(
    group = "加权收益",
    rows = 3:4
  )

mvp

cumret<-dcast(unique(portfoli[,.(yms,gmv,mveqrets,mvwret)]),yms~gmv,value.var = c("mveqrets","mvwret"))[,c("mveqrets_1","mveqrets_2", "mveqrets_3","mveqrets_4","mveqrets_5","mvwret_1","mvwret_2","mvwret_3","mvwret_4",  "mvwret_5"):=lapply(.SD, cumsum),.SDcols=c("mveqrets_1","mveqrets_2", "mveqrets_3","mveqrets_4","mveqrets_5","mvwret_1","mvwret_2","mvwret_3","mvwret_4",  "mvwret_5")]

plot(as.Date(paste0(cumret$yms,"-01")),cumret$mveqrets_1,type="l",ylim = c(-1,9),ylab = "累积收益",xlab = "时间",lwd=2,col="red")
lines(as.Date(paste0(cumret$yms,"-01")),cumret$mveqrets_2,lwd=2,col="orange")
lines(as.Date(paste0(cumret$yms,"-01")),cumret$mveqrets_3,lwd=2,col="green")
lines(as.Date(paste0(cumret$yms,"-01")),cumret$mveqrets_4,lwd=2,col="blue")
lines(as.Date(paste0(cumret$yms,"-01")),cumret$mveqrets_5,lwd=2,col="yellow")
legend(as.Date(paste0("2000-01","-01")),8,c("1","2","3","4","5"),col = c("red","orange","green","blue","yellow"),lty = 1,lwd=2,horiz = T)

portfoli<-monthdata[order(yms,lmv)][,lapply(.SD, head,5),by=yms][,':='(mveqrets=mean(rets),mvwret=sum(rets*lmv)/sum(lmv)),by=.(yms)
                             ][,':='(bmeqrets=mean(rets),bmwret=sum(rets*lmv)/sum(lmv)),by=.(yms)][yms>="2018-01",]