Arbitrage Problem

I hate everybody. Everyone needs to die.

good to know.

rellison Wrote: ------------------------------------------------------- > When using (1+Rd) rd, meaning 6.25%, or the 90-day version, meaning > 0.0625(90/360)? Does the CFA Institute use the > Year=360 convention or the 365 convention? —>Doesn’t make a difference for this question, because either way you are raising each one to the same power. For these the CFA uses the 365 day convention. The 360 day convention is used with FRAs. My rule of thumb is when I am raising something to a power I use the 365 day convention. But when I am multiplying a rate and then adding it to one I use the 360 day convention. Why do you hate us exactly? We are just trying to help. If you wanna hate someone hate Schweser…they Fing suck!

ok. after lunch I am at peace… cad=dc, chf=fc rd - rf – look for the period. (.0625 - 0.055)/4 = .001875 (f-s)/s = (0.81-0.7901)/(0.7901) = 0.002519 rd - rf < (f-s)/s so borrow domestic means borrow 1000 CAD 1000 CAD -> need to return 1015.625 CAD after 90 days convert to CHF at spot -> 1265.66 CHF @ 0.7901 CAD/CHF lend forward->1265.66 * (1+0.055/4) = 1283.06545 CHF in 90 days > convert at forward of 0.8100 CAD/CHF -> 1039.283002 Arbitrage profit = 1039.283 - 1015.625 = 23.658 CAD = 18.692 CHF (At Spot of 0.7901)

I just kiddin guys…love you mwah

Which do you use in order to calculate the currency to borrow or lend? 1)1+rd

please please please… read my post and see if it makes sense.

ah ok so TheAliMan just used the IRP formula to find the actual future spot rate E(s1) and then compared that to the forward rate trading now.

That’s right. Technically, you are applying the same formula as you have done, but this way, all you use is IRP and it’s intuitive.

CP - your methodology is sound. but one mistake. the problem at the top asked for 1mln CHF - so use 790 CAD to borrow at the start?

true, realized and corrected it later

This seems like a good problem to be able to solve for the test.

rellison Wrote: ------------------------------------------------------- > Which do you use in order to calculate the > currency to borrow or lend? > 1)1+rd 2)rd-rf RHS I want to be investing my money at that rate (said otherwise getting the domestic currency and depositing it in a bank in the DC country), this then equivalently implies that I need to borrow in the foreign country and convert to domestic country currency now, and later convert the proceeds at the forward rate (given) back into the foreign currency to pay back what I borrowed.

it took me a while to figure out these problems and decipher schweser’s solutions but i think i found a methodology. 1. figure out which is the base and which is the counter currency. we’re given CHF:CAD = 0.7901 for the spot. this ass backwards notation means you’re paying 0.7901 CAD for every CHF, so CHF is your base currency. 2. break down interest rate parity so you can compare borrowing rates at the base and counter currency. you basically want to separate terms so that the base rate is on one side of the equation and the counter currency is on the other side. start with S1 = S0*[(1+r counter)/(1+ r base)] and end up with (1 + r base) = (S0/S1)*(1 + r counter). then plug in the spot, forward and interest rates. in this case we see that the left side of the equation reduces to 1.0138 and the right side reduces to 0.9905. since the right side of the equation is less, it 's considered “cheaper” to borrow in the counter currency, ie IRP does not hold because the FX rate differential doesn’t offset the interest rate differential. the whole point of this is to figure out that you need to borrow in the counter currency, which we know to be CAD. 3. now you know you have to borrow CAD, but you deal in CHF. with 1,000,000, you can borrow 790,1000 CAD (at the spot rate). in three months, you’ll have to repay 790,100*(1+(0.065*(90/360))) = 802,445.3. 4. use the funds borrowed in the cheaper currency (the 790,100 CAD above) to invest in the more expensive currency. convert 790,100 to CHF at the spot (to get 1,000,000 CHF), and then lend that amount out at the CHF interest rate. at the end of three months, you’ll have (790,100 CAD /0.7901 CAD/CHF) = 1,000,000 CHF*(1+0.055*(90/360)) = 1,013,750 CHF. 5. convert the funds you lent and collected interest on to the currency in which you owe money. 1,013,750 CHF * fwd rate = 1,013,750 CHF * 0.81 CAD/CHF = 821,137.5 CAD. 6. calculate your arb profit by taking the difference of what you made from lending and what you paid back from borrowing. 821,137.5 CAD - 802.445.3 CAD = 18,692.5 CAD.