The Very Strange Chi­nese Yuan

In my pre­vi­ous post, I ex­plored the dis­tri­b­u­tion of price fluc­tu­a­tions for a va­ri­ety of dif­fer­ent mar­kets and time frames. Across all da­ta set­s, plot­ting the log re­turns in a his­togram ap­pears to rough­ly ap­prox­i­mate the den­si­ty func­tion of a Laplace dis­tri­b­u­tion. The in­tra­day prices of the Chi­nese yuan, how­ev­er, seem to ex­hib­it a dis­tinct­ly strange phe­nom­enon.

The ex­change rate be­tween the Chi­nese yuan and the US dol­lar is not an en­tire­ly mar­ket-driv­en rate the way many oth­er cur­ren­cy ex­change rates are. While the val­ue of the yuan is al­lowed to float to some de­gree, the Peo­ple’s Bank of Chi­na main­tains a cer­tain lev­el of con­trol over the yuan’s ex­change rate. Fur­ther­more, the yuan is quot­ed in two sep­a­rate mar­ket­s: an on­shore mar­ket and an off­shore mar­ket.

The On­shore Ex­change Rate

The on­shore ex­change rate, ac­cord­ing to my un­der­stand­ing, is de­ter­mined by a ref­er­ence rate set dai­ly by Chi­na’s cen­tral bank. The ex­change rate is al­lowed to float with­in a nar­row band above or be­low the ref­er­ence rate. Let’s look at an in­tra­day chart of the on­shore ex­change rate be­tween the Chi­nese yuan and the US dol­lar over a pe­ri­od of four days:

The chart above is based on one-minute in­tra­day data. This chart looks a bit odd to me. It seems to be sprin­kled with un­nat­ural spikes that quick­ly re­vert back to their pre­vi­ous val­ues. The price does­n’t zigzag the same way prices seem to move on oth­er price chart­s. But this is just a sub­jec­tive ob­ser­va­tion. Let’s look at a his­togram of price dif­fer­ences from one minute to the nex­t:

The two charts above show the same data; one plots the den­si­ty on a lin­ear scale and the oth­er shows it on a log­a­rith­mic scale. Em­ploy­ing the same tech­nique used in my pre­vi­ous post, the his­togram is over­laid with the den­si­ty func­tions of the fit­ted nor­mal and Laplace dis­tri­b­u­tion­s. No­tice that nei­ther one of these two fit­ted dis­tri­b­u­tions seem to mod­el the shape of the his­togram.

If you were to on­ly look at the cen­ter­most third of the chart, it would seem like the dis­tri­b­u­tion of price fluc­tu­a­tions might con­form to that of a Laplace dis­tri­b­u­tion just like the da­ta sets ex­am­ined pre­vi­ous­ly. How­ev­er, the out­er­most thirds of the chart tell a dif­fer­ent sto­ry. There is an out­sized clus­ter of large moves up and down.

The Off­shore Ex­change Rate

The off­shore ex­change rate is sup­pos­ed­ly a float­ing rate de­ter­mined by the mar­ket. While I’m no ex­pert on the spe­cif­ic de­tail­s, I pre­sume the Chi­nese cen­tral bankers ex­ert some form of in­di­rect in­flu­ence on the off­shore rate to keep it in par­i­ty with the on­shore rate. Here is a one-minute in­tra­day chart of the off­shore rate cov­er­ing a pe­ri­od of 24 hours:

This one al­so looks odd to me. It has those same un­nat­u­ral-look­ing spikes, most­ly in the down­ward di­rec­tion. If we ex­am­ine the dis­tri­b­u­tion of price move­ments for the off­shore rate, will the his­togram ex­hib­it the same triple peak pat­tern as the on­shore rate? Take a look:

In­deed, this strange phe­nom­enon ex­ists for both the off­shore rate and the on­shore rate. I don’t have a sol­id ex­pla­na­tion for this. It might sim­ply be an er­ror or anom­aly in­tro­duced by my da­ta provider. But I sus­pect it’s re­lat­ed to what­ev­er mech­a­nisms the cen­tral bankers are us­ing to put floors and ceil­ings on the yuan’s ex­change rate. I have al­so ob­served this phe­nom­enon in the US dol­lar ex­change rate against the Hong Kong dol­lar and, to a less­er ex­ten­t, the Tai­wan dol­lar.

The Eu­ro Ex­change Rate

Does the ex­change rate be­tween the yuan and the eu­ro ex­hib­it the same char­ac­ter­is­tics as the ex­change rate be­tween the yuan and the US dol­lar? Here is a chart of the off­shore ex­change rate be­tween the yuan and the eu­ro:

This da­ta set cov­ers the same 24-hour pe­ri­od as the US dol­lar off­shore rate ex­am­ined in the pre­vi­ous sec­tion. This price chart seems to be much clean­er, with few­er of those un­nat­ural price spikes. The dis­tri­b­u­tion of price fluc­tu­a­tions looks like this:

The triple peak pat­tern is not present in this da­ta set. I was­n’t ex­pect­ing this. Like the oth­er da­ta sets ex­am­ined in my pre­vi­ous post, the dis­tri­b­u­tion of price fluc­tu­a­tions for these da­ta rough­ly ap­prox­i­mates a Laplace dis­tri­b­u­tion.

Syn­thet­ic Ex­change Rates

With­out ob­serv­ing a quot­ed ex­change rate di­rect­ly, a syn­thet­ic ex­change rate be­tween two cur­ren­cies can be com­put­ed from the rates of two oth­er cur­ren­cy pairs. Sup­pose we know the off­shore ex­change rate be­tween the yuan and the eu­ro. And sup­pose we al­so know the ex­change rate of the eu­ro against the dol­lar. We can com­pute the off­shore ex­change rate be­tween the yuan and the dol­lar syn­thet­i­cal­ly us­ing the eu­ro as an in­ter­me­di­ary. Here is the re­sult of this com­pu­ta­tion:

As ex­pect­ed, this chart looks very sim­i­lar to the in­tra­day chart of the off­shore rate be­tween the yuan and the dol­lar shown ear­lier. In fac­t, I think this chart looks even bet­ter than the one based on the ac­tu­al quot­ed val­ues. It does­n’t have as many of those un­nat­u­ral-look­ing spikes. Here is what the dis­tri­b­u­tion of price move­ments looks like:

The his­togram based on the syn­thet­ic da­ta does­n’t show a trace of the triple peak pat­tern vis­i­ble in the his­togram based on the ac­tu­al quot­ed val­ues. Per­haps there might be an ar­bi­trage op­por­tu­ni­ty here worth ex­plor­ing.

Dai­ly Ex­change Rates

When an­a­lyz­ing the in­tra­day ex­change rates be­tween the Chi­nese yuan and the US dol­lar, we ob­served a triple peak pat­tern in the dis­tri­b­u­tion of price fluc­tu­a­tion­s. Does this triple peak pat­tern man­i­fest it­self if we ex­am­ine dai­ly da­ta in­stead of in­tra­day day? Here is the analy­sis of the on­shore ex­change rate us­ing dai­ly data:

It does not ex­hib­it the triple peak pat­tern char­ac­ter­is­tic of in­tra­day prices. The his­togram takes the shape of a Laplace dis­tri­b­u­tion, which is the com­mon pat­tern we see in oth­er da­ta set­s. Here is the analy­sis of the off­shore ex­change rate us­ing dai­ly data:

Again, we see the same thing. The his­togram takes the ap­prox­i­mate shape of a Laplace dis­tri­b­u­tion. The dai­ly price fluc­tu­a­tions of both the on­shore rates and the off­shore rates ex­hib­it the same be­hav­ior we have come to ex­pect from many oth­er da­ta set­s. The triple peak phe­nom­enon on­ly seems to man­i­fest it­self in small­er time­frames.

Ac­com­pa­ny­ing source code is avail­able on GitHub.