# Arbitrage Problem

First, I present the simple problem: “Suppose the 90-day int rate fo CAD is 6.25% and the 90-day interest rate for CHF is 5.5%. The current spot rate is CHF:CAD=0.7901, and the forward rate is 0.8100. Illustrate how you can earn an arbitrage profit if you deal in the equivalent of CHF 1 million.” How do I decide whether to lend CHF/borrow CAD or vice-versa based on the formula (1+domestic int rate)

If you deal in CHF, that means you’re starting from CHF. f you convert at spot, the CHF to CAD is 1/.7901 and you invest at CAD rate. Or, you could invest CHF and convert at fwd (1/.81). So IF my explanation is right, then you would have 1.0625 < 1.055*.7901/.8100 and which ever one is bigger and smaller, I think you lend at the higher and borrow at smaller, akin to saying you invest at the higher. Please correct me if i am wrong, because I wasn’t very clear when going through this section.

rellison I have a note card written out as if (rd-rf) < (F-S)/S then borrow domestic if (rd-rf) > (F-S)/S then borrow foreign rd=6.25, rf=5.5% rd-rf = 0.75% (F-S)/S = (0.81-0.7901)/0.7901=0.0252 so borrow foreign. 1000 CHF-> need to return 1013.29 after 90 days convert to CAD at spot -> 1265.66 lend forward->1284.72 in 90 days convert at forward-> 1040.62 CHF profit of 27.33 CHF

cpk123 Wrote: ------------------------------------------------------- > rellison > > I have a note card written out as > > if (rd-rf) < (F-S)/S then borrow domestic > if (rd-rf) > (F-S)/S then borrow foreign > > rd=6.25, rf=5.5% > > rd-rf = 0.75% > > (F-S)/S = (0.81-0.7901)/0.7901=0.0252 > > so borrow foreign. > 1000 CHF-> need to return 1013.29 after 90 days > convert to CAD at spot -> 1265.66 > lend forward->1284.72 in 90 days > convert at forward-> 1040.62 CHF > > profit of 27.33 CHF I am lost here: I know how to get which to borrow. But I forget which to convert at spot and then forward and then reconvert at which??? Ugh its giving me a freaking headache.

NM I figured this out. I am just stressed out so simple things are getting to me.

Maybe I have this wrong cpk, but if you start with 1000CHF let’s say, and the spot rate is CHF:CAD=0.7901, to convert to CAD, you get 1000 CHF=790.1 CAD because CHF:CAD=0.7901 is the same as 0.7901CAD/CHF, so when you multiply 1000CHF*0.7901CAD/CHF the CHF terms cancel out and you get 790.1 CAD… Why did you divide by 0.7901 instead of multiply?

do you have a question id for this. I am pretty sure that the convention that schweser follows is CHF/CAD=0.7901 – in which case the above calculation is correct. if it is the other way around … something is curiously wrong.

In book 2 of Schweser, they use the Base:Counter method, and then in book 3 through book 5 they switch to DC/FC. It’s frustrating, but to answer your question, it’s an example in Book 2, Page 73, in the blue box (you can’t miss it). Does this mean that your formula: if (rd-rf) < (F-S)/S then borrow domestic if (rd-rf) > (F-S)/S then borrow foreign doesn’t work though (I need to know so I can memorize it properly)? I kept it in the notation they use, which is Base:Counter=0.5, which means that 1 Base=0.5 Counters, or 0.5 Counter/Base.

They seem to be using 2 different things here: 1. 90/360 convention instead of 90/365 convention. 2. *90/360 convention instead of ^(90/365) convention. those few decimal pointing rounding throws this off.

So am I right about the translation cpk? And do those two formulas still hold up, considering that I think you should borrow domestic and lend foreign, otherwise you lose money on the arbitrage?

need someone with higher econ. knowledge to step in here. schweser notes and qbank seem to be at loggerheads with each other.

so whats the answer here? interest rate arb is rough on me. I get profit of 27,459 CHF on 1 million CHF.

Alright bros, this is how I think of it: you’re given the spot and interest rates calculate the forward rate pricing from the formula for no arbitrage pricing: so 0.7901 * (1+0.0625*(90/365)) / (1 + 0.055*(90/365))