Short selling, volatility and bubbles

Yesterday, I wrote a post (in French) about short-selling in financial market since some journalists claimed that it was well-known that short -selling does increase volatility on financial market. Not only in French speaking journals actually, since we can read on http://www.forbes.com that  « in a market with restrictions on short-selling, volatility is reduced ». But things are not that simple. For instancehttp://www.optionsatoz.com/ explains it from a theoretical point of view. But we can also look at the data. For instance, we can compare the stock price of Air China, exchanged in Shanghai in blue (where short-selling is forbidden) and in Hong Kong in rouge (where short-selling is allowed), since @Igor gave me the tickers of those stocks

library(tseries)
X<-get.hist.quote("0753.HK")
Y<-get.hist.quote("601111.SS")
plot(Y[,4],col="blue",ylim=c(0,30))
lines(X[,4],col="red")

But as @alea_ pointed out, one asset is expressed here in Yuans renminbi, and the other one in HK dollars. So I downloaded the exchange rate fromhttp://www.oanda.com/

Z=read.table("http://freakonometrics.blog.free.fr/public/
data/change-cny-hkd.csv",header=TRUE,sep=";",dec=",")
D=as.Date(as.character(Z$date),"%d/%m/%y")
z=as.numeric(Z$CNY.HKD)
plot(D,z,type="l")
X2=X[,4]
for(t in 1:length(X2)){
X2[t]=X2[t]*z[D==time(X2[t])]} 
X2=X[,4]
plot(Y[,4],col="blue",ylim=c(0,30))
lines(X2,col="red")

Now both stocks are expressed in the same currency. To compare returns volatility, a first idea can be to use GARCH models,

RX=diff(log(X2))
RY=diff(log(Y[,4]))
Xgarch = garch(as.numeric(RX))
SIGMAX=predict(Xgarch)
Ygarch = garch(as.numeric(RY))
SIGMAY=predict(Ygarch)
plot(time(Y)[-1],SIGMAY[,1],col="blue",type="l")
lines(time(X2)[-1],SIGMAX[,1],col="red")

But volatility is here too eratic. So an alternative can be to use exponentially-weighted moving averages, where simple recursive relationships are considered

https://perso.univ-rennes1.fr/arthur.charpentier/latex/vol-04.png

or equivalently

https://perso.univ-rennes1.fr/arthur.charpentier/latex/vol-05.png

The code is not great, but it is easy to understand,

moy.ew=function(x,r){ 
m=rep(NA,length(x))

for(i in 1:length(x)){ 

m[i]=weighted.mean(x[1:i], 
         rev(r^(0:(i-1))))}

    return(m)} 

sd.ew=function(x,r,m){

sd=rep(NA,length(x))

for(i in 1:length(x)){
    
sd[i]=weighted.mean((x[1:i]-m[i])^2,
          rev(r^(0:(i-1))))}

    return(sd)} 
q=.97
MX=moy.ew(RX,q)
SX=sd.ew(RX,q,MX)
MY=moy.ew(RY,q)
SY=sd.ew(RY,q,MY)
plot(time(Y)[-1],SY,col="blue",type="l")
lines(time(X2)[-1],SX,col="red")

And now we have something less erratic, so we can focus now on the interpretation.
It is also possible to look on the difference between those two series of volatility, areas in blue means that in Shanghai (again, where short-selling is forbidden) returns are more volatile than in Hong Kong, and areas in red are periods where returns are more volatile in Hong Kong,

a=time(X2)[which(time(X2)%in%time(Y))]
b=SY[which(time(Y)%in%time(X2))]-
  SX[which(time(X2)%in%time(Y))]
n=length(a)
a=a[-n];b=b[-n]
plot(a,b,col="black",type="l")
polygon(c(a,rev(a)),c(pmax(b,0),rep(0,length(a))),
        col="blue",border=NA)
polygon(c(a,rev(a)),c(pmin(b,0),rep(0,length(a))),
        col="red",border=NA)

So clearly, there is nothing clear that can be said… Sometimes, volatility is higher in Hong Kong, and sometimes, it is higher in Shanghai. But if we look at the price, instead of looking at volatility,

a=time(X2)[which(time(X2)%in%time(Y))]
b=as.numeric(Y[which(time(Y)%in%time(X2)),4])- 
  as.numeric(X2[which(time(X2)%in%time(Y))])
n=length(a)
a=a[-n];b=b[-n]
plot(a,b,col="black",type="l")
polygon(c(a,rev(a)),c(pmax(b,0),rep(0,length(a))),
        col="blue",border=NA)
polygon(c(a,rev(a)),c(pmin(b,0),rep(0,length(a))),
        col="red",border=NA)

Here, it looks like bans on short-selling creates bubbles. Might not not be a goodthing.


4 thoughts on “Short selling, volatility and bubbles”

  1. This is really interesting, You’re a very skilled blogger. I’ve joined your feed and
    look forward to seeking more of your excellent post. Also, I’ve shared your website in my social networks!

  2. @Igor oui, mais je crois que pas mal de monde utilise ces deux places pour faire des analyses comparatives sur la règle d’interdiction de la vente à découvert… Je fais un peu comme tout le monde car je ne sais pas comment faire proprement une étude comparative sur le sujet.

    @Eric sur le dernier point je ne pense pas qu’il faille regarder la composant idiosyncratique, en enlevant la tendance de marché. Il existe une forme d’opportunité d’arbitrage puisque le même titre (exprimé dans la même unité monétaire) a des prix différents. Mais je vais essayer de refaire un billet propre et plus formelle sur les bulles et l’absence d’opportunité d’arbitrage.

  3. Le dernier argument m’aurait davantage convaincu si le prix des actions avait été corrigé de l’évolution de (l’indice de) chacune des places financières

  4. Besides the exchange rate, there could be all kinds of additional constraints to the Shangai market that do not exist on HK, why focus on short selling ? Why not focus on the illiquidity of one market over another ? Etc… Arthur, I am not discounting your great analysis but there ought to be a stronger case in light of this argument taking so much bandwidth in the media.

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