Findings

INTERNAL USE

What is the distribution of asset sizes in the index? (2000-2020)

> summary(size_dat$Size)
     Min.   1st Qu.    Median      Mean   3rd Qu.      Max. 
2.139e+03 2.205e+07 1.070e+08 6.319e+08 4.531e+08 4.468e+10


2019 only

PY

size_dat=data_equity_prices_bo0ty_usd %>% select(ValueDate,Size=Value) %>% filter(Size>10^3)
  
hist(log(size_dat$Size), breaks = 100, main = "Histogram of Index Constituent Sizes (USD)", xlab="USD Size (log scale)", xlim = c(10,25), probability = T, xaxt="n")  
lines(density(rnorm(100000, mean=mean(log(size_dat$Size), na.rm = T),sd=sd(log(size_dat$Size), na.rm = T))), col="red")
legend("topleft",c("Gaussian Distribution"), lty = 1, bty = "n", col="red")
axis(1, at=c(10,15,20,25),labels=format(round(as.numeric(c(exp(10),exp(15),exp(20),exp(25))),0),nsmall=0, big.mark=","), col.axis="black", las=0)

size_dat_ts=size_dat %>% group_by(ValueDate) %>% mutate(Size=log(Size)) %>%
  summarise(mean=mean(Size),median=median(Size), sd=sd(Size)) %>%
  mutate(upper=mean+1.97*sd, lower=mean-1.97*sd)
attach(size_dat_ts)
par(mar = c(5, 10, 5, 5))
plot(ValueDate,mean,type="l", main = "Average Constituent Size (USD, log sacle)", ylim = c(10,25), yaxt="n", xlab="", ylab="")
axis(2, at=c(10,15,20,25),labels=format(round(as.numeric(c(exp(10),exp(15),exp(20),exp(25))),0),nsmall=0, big.mark=","), col.axis="black", las=2)
lines(ValueDate,upper, col="red", lty=2)
lines(ValueDate,lower, col="red", lty=2)

What is the average leverage in the index? (Q4 2019)

> summary(lev_dat$lev_m)
   Min. 1st Qu.  Median    Mean 3rd Qu.    Max. 
 0.7249  0.7789  0.7827  0.7805  0.7879  0.8022 
> summary(lev_dat$lev_med)
   Min. 1st Qu.  Median    Mean 3rd Qu.    Max. 
 0.7776  0.8373  0.8444  0.8470  0.8570  0.8765 
> summary(lev_dat$lev_mw)
   Min. 1st Qu.  Median    Mean 3rd Qu.    Max. 
 0.5240  0.7270  0.7388  0.7201  0.7633  0.7732

PY

lev_dat= data_equity_prices_bo0ty_usd_fixed %>% select(ReportID,ValueDate,weight=Value) %>%
  mutate(CompanyID=substr(ReportID,5,13)) %>%
  left_join(select(equity_premia_sys_pred,CompanyID,ValueDate,Leverage_logXplus), 
            by=c("CompanyID"="CompanyID","ValueDate"="ValueDate")) %>%
  mutate(leverage=exp(Leverage_logXplus)-0.1) %>% 
  group_by(ValueDate) %>% 
  summarise(lev_m=mean(leverage), lev_med=median(leverage), lev_mw=weighted.mean(leverage, weight))

attach(lev_dat)
plot(ValueDate,lev_med,type = "l", ylim = c(0.5,0.9), main="Average leverage factor loading (Senior Liabilities/ Total Assets)", ylab="Senior Leverage", xlab="")
lines(ValueDate,lev_m, col="red")
lines(ValueDate,lev_mw, col="blue")
legend("bottomright",c("Median","Mean","Value Weighted Mean"), col=c("black","red","blue"), lty=1, bty = "n")