Carry Trade

Does anyone have any tricks on how to solve for the profit in a carry trade?

Yeap, what I do is first identify the currency that is more depreciated in the forward than it should be. This is the currency on which you will borrow the money.

eg. suppose the spot EUR/DOL is 2.00, and the forward for 1 year is 2.10. Let`s suppose that the 1 year EURO risk-free is 4%, while the DOL risk-free is 1%. 2.00 x 1.04/1.01 = 2.06. So the 1 year EUR/DOL forward should be 2.06, right?

So here we have a carry trade opportunity. In this case, the forward is saying that the EUR will depreciate more than it actually will, according to the arbitrage price theory. Bingo, now that I know that the forward is pricing a more depreciated EUR in the future that should be, I will borrow money on EUR, change my EUR for DOL, invest for 1 year, than change back, and profit.

Solving:

I’ll borrow EUR 1.000. One year from now I’ll have to pay back 1,000 x 1.04 = 1,040 EUR.

I’ll exchange my EUR 1,000 for DOL 500, using the spot rate.

I’ll invest this DOL 500 using the risk-free rate. 1 year from now I’ll have 500 x 1.01 = 505.

Now I’ll exchange my DOL 505 for EUR, using the exchange rate of 2.10 (that was the exchange rate of the forward one year ago).

505 x 2.10 = 1,060.5

Since I owe 1,040 EUR -> 1,060.5 - 1,040 = 20.5 = Profit.

Like I said, borrow in the currency that the forward is saying that will depreciate more than it actually should, and the rest is simple math.

This is a good example, an easier way i would remember how to do the carry trade is this formula.

Once finding out there is a carry trade opportunity and which currency you will investing/borrowing from:

net profit = (Forward rate x investing currency Rf rate) / Current spot rate ] - investing currency Rf rate

= {(2.10 x 1.01) / 2} - .04 = .0205

Multiplying this with the amount invested will give you the profit from the carry trade.

Recheck your formula.

You mean funding currency interest rate in the latter end of your formula?

Yep and should be 1+funding currency %. So should read: = {(2.10 x 1.01) / 2} - 1.04 = .0205

you dont have to do any calculations. find out how much the funding currency appreciated, add that to the funding currency’s rate. thats your loss. your gain is the high yield currency rate. net the two. bam

“I’ll exchange my EUR 1,000 for DOL 500, using the spot rate.”

Shouldn’t it be EUR 1,000 for DOL 2,000? Using the “Up and multiply” rule i.e 1,000 EUR x 2.00 = 2,000 DOL?

No, it shouldn’t.

The exchange rate is EUR/DOL 2.00, which means that EUR2.00 = DOL1.00.

Got my ups and downs confused lol

Has been many ups and downs in this exam prep!!!

Thank you

I don’t know any tricks, but it’s pretty straightforward:

  • Borrow some amount of currency A at its risk-free rate
  • Convert currency A to currency B at today’s spot rate
  • Invest currency B at its risk free rate
  • Later, convert currency B to currency A at the then prevailing spot rate
  • Pay off the currency A loan amount plus interest
  • Whatever’s left over is profit