Why the RMB USD swap is set at 7.85

Macroblog (via Simonworld) noted WSJ's report on a swap transaction for RMB between PBoC and the state banks. As the strike price was set at 7.85 12 months later, some interpret this as an indication for potential appreciation and some thought PBoC was testing the water.

Macroblog has also kindly provided some link to the definition of swap. So let's try to understand whether it is fair deal to the banks, or if not who is going to be benefited if RMB appreciates (or depreciates).

A swap is basically an exchange of interests earned by the two parties involved.

  1. Say, A has USD1, in 12 months, he will earn interest based on US interest rate, i.e. 4.74%. (see here, but number might change slightly every day)
  2. But if he changes this into RMB and puts it into the bank, he could only earn the RMB interest rate, at 1.8%. (note: PBC's website shows 金融机构存款利率 is 2.25% set on Oct/2004, which is what i used initially, so there is a smaller basis point adjustment. According Jorge (see update below), after 20% tax the effective return is 1.8%.)
  3. The difference in interest rate is 2.84%, which is quite significant (this is one of the reason that speculators believe the exchange rate could change)
  4. The state banks have RMB8.0805, they have two options to invest
    • (A) earn 1.8% interest, have 8.0805 x 1.018 in 12 months;
    • (B) exchange to USD with PBoC, earn 4.74% interest in 12 months, then exchange USD1.0474 back to RMB, if at the same rate of 8.0805, it will make 1.0474x8.0805 in 12 months
    • (B) is obviously a better option for the state banks, but a bad deal for PBoC
  5. PBoC is not stupid, so it enters into a swap contract with the state banks, making sure it is a fair deal. i.e. the state banks will earn exactly the same return of 8.08x1.018. Therefore, the exchange rate for this particular trasnsaction 12 months later should be 8.0805x1.018/1.0474=7.8537! Now option (B) will become 1.0474 x7.85 = 8.0805x1.018, same as (A)

In short, this is just a simple mathematical exercise. If the swap contract is for 24 months, the strike price wil be 8.0805x(1.0216/1.0486)^2=7.67. (2-year rate for USD is 4.86%; 2-yr rate for RMB is 2.70% in PBC's site with 20% tax applicable)

This tells us NOTHING about the expectation of RMB excahnge rate. Because the return for PBoC and the statebanks are not affected by any change in the currency market.

P.S. In reality PBoC should take into account the volatility (though there is no historical data) and charge a premium if it expects USD to appreciate, and a discount if otherwise. PBoC probably wants to use some RMB to cope with the capital inflow (FDI + speculator) and expect the flow may reverse in future, so it is willing to do the swap. This provides an additional avenue to sterilize the USD (vs issuing RMB bonds).

Update (Nov 29 evening): Standard Chartered Bank's Wang Zhihao apparently did the same calculation in a report titled "RMB Silent and important move 人民币:沉默而重大的举措" It was also reported that NDF contract converged from 7.74 up to 7.77 immediately after the news was heard. Wang commented that traders correctly interpreted the signal that the x-rate will be more stable.

Update (Nov 30) to explain the 1.8% RMB interbank yield: Jorge explained the tax (at 20% of the interbank rate 2.25%) in a comment; Dan Slater of loomberg said "China's banks are being squeezed by deposit rates of around 2.25%, compared to money market rates, which are just over 1.5%."



Anonymous said...

Sun Bin,
Great post. I'm linking to it right away. Thanks for the comment on my blog as well.

Simon said...

Exactly right, Sun bin. You should come work in a bank! Send me your CV asap...

Sun Bin said...

then write to Mr Schumer :)

you missed the good old pre-Plaza days to travel to japan as well (so did i)

Sun Bin said...

only about 2.5% change up to now, still in 8+.

Sun Bin said...


in theory yes.
there should be an implied volatility if one reverses the black-scholes formula. and this derived volatility can be used to calculate the NDF premium.

in my first calculation (before I saw Wang Zhihao's 1.8% adjusted value) I used 2.25% as RMB interbank rate, that implies a 0.45% premium is charged, and hence a very small implied volatility -- one that would be much much smaller than what the NDF contracts used. i.e. the PBoC anticipated appreciation should be much smaller than those in Singapore believe.
Therefore, NDF strike price in Singapore increased a little after hearing this deal (as noted in my 'update'), but only a little because the traders then decided this is only one of the many data points.

If one use 1.8%, the "basis" is that PBoC and the state banks believed valatility was zero.

Sun Bin said...

Thanks, but banking is not my expertise, it was some time ago when I learned these financial instruments. And as you can see, I just tried to make these things understandable to everyone.

the idea has been tossed around. but i do not see good rationale other than that it is simple and convenient. tourists and retailers definitely like that.

Sun Bin said...

here are the reaons why I think 1:1 for RMB:HKD is not the target

1) There is nothing magic other than a coincidence in number.
And it is doubly silly if afterweard HKD is pegged and RMB is going to be "more flexible", because the convenience will be destroyed when it departs from 1:1.
2) If RMB is pegged to HKD, it will destroy the basket-peg it has been promoting. even worse, it will destroy the confidence of 'one country, two system" and HK's financial independence and autonomy
3) Tourists and retailers on both sides of Shenzhen River would love it, as it reduced transaction cost. But many retailers are doing this already, absorbing the 3-4% difference (same for Macau). (credit card takes 2-2.5%, so not a big deal)

Sun Bin said...

To further elaborate on why the swap is not a short position, here is what I said in response to Joe's question.

...it is a wash between the state banks and PBoC. it is neither a long or a short position. because the difference in strike price is neutralized by the difference in interest rates.

Why PBoC is not on a short position? because it ends up exactly at the same amount of USD it has (6bn) as it has in the beginning. (and the banks end up with exactly the same amount of RMB it has in the beginning).

the contract might have been drafted in this way.
1) PBoC lends $6bn to banks
2) banks lends $6x8.0805bn to PBoC
3) however, each party will keep the interests earned as if without this transaction
4) after 12 months, reverse the 2 lending with at the exact amount, with no interests.

this is exactly the same as the swap contract announced.

1) PBoC still have exactly $6bn in USD after 12 months. it is unable to get rid of it in this transaction. therefore, it is not a short position. a short position would involve no buy-back

2) pboc does not make one cent more than if it has not entered this contract. it could have made the extra 2.89% if it put the 6bn USD into 12 month deposit with a bank in London.

Anonymous said...

Two points:

1) This seems to be a straight currency forward rather than a swap. A currency swap is technically when someone pays interest in one currency in exchange for interest in another.

2) Black-Scholes is irrelevant in currency forwards.


Sun Bin said...


thanks for the clarification.

yes, it was simple maths for this particular contract. 'swap' was a lazy name used by WSJ and others.
but if you replace the deal with the 'equivalent contract' in my comment above, it does appears to be a swap of interests with the spot rate kept at 8.0805.