1.Breif Introduction

The SFC in Hong Kong has now given guidelines for the listing of leveraged ETFs based on non-China indices. click here for SFC leveraged product guideline

While initially only funds tracking non-Hong Kong and non-Mainland foreign equity indices can be included, it is likely that the authorization will extend to equity indices in Hong Kong. The most probable one in the future is the Heng Seng Index. Leveraged ETF,as its name implies,features a leveraged payoff(in percentage) in responce to the underlying asset.However,this leverage multiplier could be either positive or negative,depends on the long or short position the investors want to hold.Many interesting factors embedded in this product,it can be quite exiting when investing since the leverage amplifis your P&L,it can also be extremly risk,without you even notice where the real risk lies.

Following the theoretical performance of the following funds based on the Hang Seng Index (HSI), assuming there is no slippage on the tracking.
1: \(+2\) times the daily performance of HSI Fund
2: \(-2\) time the daily performance of HSI
note:all the synchronized performances are in percentage form

2.Backtesting performance

#2 year data
HSI<-read.table(file = "C:\\Users\\Steven\\Desktop\\hsi.txt",header = T)

suppose we invest 100 initially in the product. So the Net Asset Value at time 0 is 100.

2.1 Time scale: 1 year

HSI.1Y<-HSI[1:248,]
HSI.ret.1Y<-diff(log(HSI.1Y))
temp<-HSI.ret.1Y*1+1
ret.1Y.NAV<-cumprod(temp)*100
summary(ret.1Y.NAV)

##    Min. 1st Qu.  Median    Mean 3rd Qu.    Max. 
##   95.48  102.20  104.70  104.90  107.50  113.80

return of \(+2\) multiplier is just like 1:1 leverage during the Chinese stock market burst in 2015. Its cumulative returns is as follows.

temp<-HSI.ret.1Y*2+1
ret.1Y.pos2<-cumprod(temp)*100
summary(ret.1Y.pos2)

##    Min. 1st Qu.  Median    Mean 3rd Qu.    Max. 
##   90.82  103.90  108.20  109.20  113.90  128.10

return of \(-2\) multiplier

temp<-HSI.ret.1Y*-2+1
ret.1Y.neg2<-cumprod(temp)*100
summary(ret.1Y.neg2)

##    Min. 1st Qu.  Median    Mean 3rd Qu.    Max. 
##   74.90   82.76   88.10   88.68   93.80  108.40

here the camparison on plots.

library(reshape2)
library(ggplot2)
perform.1Y<-cbind(ret.1Y.NAV,ret.1Y.pos2,ret.1Y.neg2)
perform.1Y<-as.data.frame(perform.1Y)
names(perform.1Y)<-c("HSI", "2HSI", "-2HSI")
perform.1Y$ID<-seq.int(nrow(perform.1Y))
per1<-melt(perform.1Y,variable.name = "instrument", id=c("ID"))

ggplot(data = per1)+
  geom_line(aes(x = ID,y = value,colour=instrument),size=0.8)+
  scale_colour_manual(values=c("gray4","chocolate1","cornflowerblue"))+
  xlab("days")+
  ylab("NAV")+
  ggtitle("1 year backtesting")

Above is the performance of 1 year. The market is going up in 2014-2015, so people who take long position in the index will overall make some money,if the leverage ratio is 2,your profit will be enhanced. Also we can spot that more or less, it exhibits a “mirror” pattern between these products’ performance,the magnititude might just be the difference of mutiplier.This is a tricky thing,as will be illustrated below.(you might have noticed that the “symmetry” axis is not 100)

2.2 Time scale: 2 year

ret.HSI<-diff(log(HSI$HSI))
temp<-ret.HSI*1+1
ret.2Y.NAV<-cumprod(temp)*100
summary(ret.2Y.NAV)

##    Min. 1st Qu.  Median    Mean 3rd Qu.    Max. 
##   81.03  100.00  105.00  105.50  110.40  126.80

\(+2\) mutiplier

temp<-ret.HSI*2+1
ret.2Y.pos2<-cumprod(temp)*100
summary(ret.2Y.pos2)

##    Min. 1st Qu.  Median    Mean 3rd Qu.    Max. 
##   61.44   96.96  108.60  109.30  119.40  156.70

\(-2\) multiplier

temp<-ret.HSI*-2+1
ret.2Y.neg2<-cumprod(temp)*100
summary(ret.2Y.neg2)

##    Min. 1st Qu.  Median    Mean 3rd Qu.    Max. 
##   57.52   78.16   85.66   84.90   92.35  125.20

here the camparison on plots.

library(reshape2)
library(ggplot2)
perform.2Y<-cbind(ret.2Y.NAV,ret.2Y.pos2,ret.2Y.neg2)
perform.2Y<-as.data.frame(perform.2Y)
names(perform.2Y)<-c("HSI", "2HSI", "-2HSI")
perform.2Y$ID<-seq.int(nrow(perform.2Y))
per2<-melt(perform.2Y,variable.name = "instrument", id=c("ID"))

ggplot(data = per2)+
  geom_line(aes(x = ID,y = value,colour=instrument),size=0.8)+
  geom_rect(aes(xmin=400, xmax=480, ymin=-Inf, ymax=Inf),fill=alpha("gray",0.02),color="red")+
  scale_colour_manual(values=c("gray4","chocolate1","cornflowerblue"))+
  xlab("days")+
  ylab("NAV")+
  ggtitle("2 year backtesting")

Not so “mirror”,right? Focus on the red rectangle band region,where both \(+2\) and \(-2\) have a massive drop down below the initial value 100,whether you take a long position in HSI or short position in HSI,you are going to suffer a big loss. The risk lies in volatility,if the market is jumping up and down all the time,chances are low that you would not bleeding chip. The characteristic of this product here resembles options. No matter you short call or short put,the delta you take on is positive or negative,but the gamma you take is always negative,and as we know gamma=\(\frac{d^2P}{dS^2}\),is the stock price changes frequently, your position will always cause you money.

3.Result Explaination

The little trick here can be explained in intuitive way.If the market moves up \(x%\) (x not equal to 0) today and moves down \(x%\) tomorrow,or vise versa. One loses money in both senarios since \((1+x)(1-x)<1\).In the long run,even if the days of going up and going down are the same,even if the overall percentage of going up or going down are the same,one still loses money.
In fact,works by Cheng and Madhavan (2009) and Avellaneda and Zhang (2009) has shown that under the assumption of a geometic brownain motion of stock price,the NAV has following relations: \[\frac{NAV_t}{NAV_0}=C \times [\frac{S_t}{S_0}]^x\] where \[C=exp[\frac{(x-x^2)\sigma^2 t}{2}]\] \(C\) is always less than 1 since \((x-x^2)\) is negative(x not zero nor 1,which means buy nothing or buy just index). In the long term,volatility would increase since there’s little chance that the market is a quiet pool with no wind for years. As time goes by,\(C\) is becoming smaller and smaller thus reducing the positive return generated by \(\frac{S_t}{S_0}\),of course,if there is any positive return is itself a big question.

4.Risks and caution

So the leveraged ETF would always claim in the prospectus that this product is based on daily.But still we as retail investor do not do just a few days trading since most of people look forward to long term investment rather than short term “speculate”. In some cases,even professors and well trained practitioners would be blinded by the huge risk lies with in this product.

Leveraged ETF