Foreign currency exchange loss math

[Noah Balmer]

Since it's been coming up in other forums, and was just touched on here as well, this might be an opportune time to address a topic that many people are confused about.  I've seen several incorrect interpretations of the forex loss math floating around lately.  The correct description is in the help text on "currency exchange loss", linked from any borrower profile page:

" Kiva offers Field Partners the option to protect themselves against severe currency fluctuations (a US dollar appreciation of over 20% relative to the Local Currency). "

The math for this is actually pretty simple, but it's very hard to visualize without examples, and it's very easy to jump to inaccurate conclusions.

Here are some hypothetical examples that might help.

Example one:

On date one, 1USD=1Shilling.  I lend 100USD, which is converted to 100 shillings.

On date two, 1USD=1.1Shilling.  The partner wants to repay me.  In order to buy 100 USD , they'll have to spend 110 shillings.  They'll be paying an extra 10% due to currency fluctuation... that 10% was not over the 20% threshold of USD appreciation that we expect partners to bear, so the partner has to pay it. They pay 110 shillings, I get all 100USD back

Example two:

Date one is the same as in the last example. 1USD=1Shilling. I lend 100USD, which is converted to 100 shillings.

On date two, 1USD=1.2Shilling.  The partner wants to repay me.  In order to buy 100 USD , they'll have to spend 120 shillings.  They'll be paying an extra 20% due to currency fluctuation... that's exactly on the 20% threshold of USD appreciation that we expect partners to bear, so the partner has to pay it. They pay 120 shillings, I get all 100USD back

Example three:

Date one is the same as in the other examples. 1USD=1Shilling. I lend 100USD, which is converted to 100 shillings.

On date two, 1USD=1.5Shilling.  The partner wants to repay me, but the USD has appreciated by 50%.  In order to buy 100USD, they'd have to spend 150 shillings. That's above the 20% threshold, so here's what happens. They buy 120 (100+20%) shillings worth of dollars.  At today's exchange rate, they can get 80USD for their 120 shillings (120*(1/1.5)), so they spend 20% more than they got, and pay me just 80USD.  It's less than I lent them in USD, but more than I lent them in shillings.  

Example four:

Date one is the same as in the other examples. 1USD=1Shilling. I lend 100USD, which is converted to 100 shillings.

Somewhere along the way, there's a catastrophic currency devaluation in the partner's country.

On Date two, 1USD=10,000Shillings. The Partner wants to repay me, but the USD has appreciated by 1,000,000%.  The math is the same as before.  They pay what they got in shillings, plus 20%.  Now (120*1/10,000)=.012, or 1.2 cents.  That's what their money, that used to be worth 120USD back on day one, is worth today.  

Now I, as the lender, might think it's unfair that I lent 100USD and I'm now only owed 1.2 cents, but imagine being on the other side of the transaction.  Imagine that you, one day, borrowed $100.  A while later, it's time to repay, but you're told that in order to repay your $100 loan, you have to come up with one million dollars (100*10,000).  On top of this, you now live in a country that's in the middle of a major economic crisis, and very likely a war, too.

Assuming you were someone who needed that $100 loan, you're going to have one heck of a time coming up with a million dollars.

The thing to notice here is that the 20% is not 20% of any USD amount.  It's limit, at 20%, of appreciation of USD over the partner's local currency.  Any attempt an an explanation that talks about limits at  N dollars, whether N is 20%, or 120%, or 80%, or 116%  of the USD amount that was originally lent, is in error.  The limit is calculated from the other currency's perspective, and since the exchange rate can fluctuate to arbitrary magnitudes in any direction, the USD equivalent of that limit can be literally any positive value.  

I hope these examples are helpful.

-Noah