# Covered Interest Arbitrage

Hi All, Does anybody know a systematic way of calculations for this as I end up in entangling the problem. S

Assuming all rates are in the form DC/FC: Let LHS = f / s RHS = (1+r_{D})/(1+r_{F}) Case 0: LHS = RHS. There is no arbitrage. Case 1: LHS > RHS. f/s x (1+r_{F}) - (1+r_{D}) > 0 implies borrow domestic, convert at spot, invest in foreign and convert back to domestic at forward. Case 2: LHS < RHS. 1/LHS > 1/RHS s/f > (1+r_{F})/(1+r_{D}) s/f x (1+r_{D}) - (1 + r_{F}) > 0 implies borrow foreign, convert at spot, invest in domestic and convert back to foreign at forward.

Have you checked the last question (120) in Exam 2 PM section of Schweser? Thanks

See p73 of Book 2. My calculation is like this: ( 1 + rd - (1 + rf) * F / S ) * initial amt borrowed = ( 1 + 0.0625*90/360 - (1 + 0.055*90/360) * 0.81/0.7901 ) * 1000000 = 23,658 Because this term is negative, you must borrow at the domestic risk free rate (i.e. borrow CAD), and short the forward (because its overpriced). Your profit should be 23,658. But then shouldn’t that give you CAD 23,658 profit ? I don’t see how they get 18,692 profit. Can anyone explain that ? Btw, using the same logic above gives the right answer for Q120 on Exam 2PM schweser. ( 1 + rd - (1 + rf) * F / S ) * initial amt borrowed = ( 1 + 0.05 - ( 1 + 0.03 ) * 2.1 / 2 ) * 1000 = 31.5 Profit is 31.5 which is correct there. And you’re borrowing the domestic currency in that one as well.

rDC vs “hedged rate” (1+rFC)*F/S-1 Borrow DC if rDC is lower. Buy FC Enter a forward contract (long FC) Buy bond in FC hold it, then (rewind) Sell bond (FC) Close contract(Sell FC, buy DC) Return borrowed money. Borrow FC if rDC is higher.

do you always borrow at the lower rate? either DC or FC rate? I don’t think so b/c of the currency impact… I always use 1+rdc > 1+rfc*(f)/(s) take the difference and multiply by the amount of the trade, this usually gets me the right answer…

I’m comparing rDC vs “hedged rate” (1+rFC)*F/S-1, not rDC vs rFC.

okay, so do you always borrow at lower of either the rDC or the hedged FC rate?

yes, borrow the lower, lend the higher

ah ha…got it now…thanks tvPM