arbitrage opportunity

R

rbcc

Junior Member
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Nov 18, 2009
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Hi, I'm having trouble with this question,

spot rates:
r1 = 7%
r2 = 6%
r3 = 9%

Describe an arbitrage opportunity in each of the following cases
The bank quotes you a 1 year forward rate in 1 year of 4%

1 year forward rate in 1 year

(1.07)(1+f)=(1.06)^2
f=0.05

1) borrow 1 000 at 4%, then 1040 will be owing in year 2
2) lend 1000 at 6% and make 1060

arbitrage profit is $20

is that correct?

Thanks
 
I am having great trouble understanding your question. However, I am fairly confident your answer is wrong.

It LOOKS as though r[sub:2jum7mcy]1[/sub:2jum7mcy] = the current rate with principal due at the end of 1 year, r[sub:2jum7mcy]2[/sub:2jum7mcy] the current rate with principal due at the end of year 2, etc? Is that correct? How often is interest due?

I GUESS f is a guaranteed rate for a loan to be granted in one year and repayable one year after disbursement? Is that correct? How often is interest due?. What is the price for buying that option? Or perhaps f is the expected rate in one year for one year money? Not giving any definitions makes things a little hard.

Lend 1000 at 6% (per year??) for 2 years and make 60? I do not think so.
If you need to borrow money to fund your two-year loan in the second year, you also need to borrow it for the first year. So your cost is going to be higher than 40.
 
that's all the information I was given. I assumed that we are already in year one so lend 1000 at 6% for one compounding period, I'm not sure if that is a good assumption to make.
 
I am not sure. There is a whole lot of context missing here. It may be in the book or in what your teacher said in class, but I'd be guessing without that supplemetal information. "In each of the following cases" Just one case seems to be presented. Could you copy out the exact problem statement. Maybe there are some clues there that I have been unable to extract from your summary. Furthermore, if your book has standard definitions that would be good too. I mean r[sub:1uqztupa]1[/sub:1uqztupa] may mean a 1 year rate starting in year 1, r[sub:1uqztupa]2[/sub:1uqztupa] may be a 1 year rate starting in year 2 although that does not seem too likely on what the question (or questions) seem to be..
 
Describe an arbitrage opportunity in each of the following cases, assuming you can lend or borrow at the rates listed above


that's all the extra information. r1 is defined as being the interest rate at year one for funds invested in year one. There is also another "case" with a different interest rate. Now I'm thinking that a numerical solution is not intended.
 
rbcc said:
Describe an arbitrage opportunity in each of the following cases, assuming you can lend or borrow at the rates listed above


that's all the extra information. r1 is defined as being the interest rate at year one for funds invested in year one. There is also another "case" with a different interest rate. Now I'm thinking that a numerical solution is not intended.
Click to expand...
Ahh OK. No option cost (pretty unrealistic, but that eliminates that problem.)

ASSUMING that compounding is annual, and that the r's stand for current rates for r years

You can borrow for 1, 2, or 3 years now or invest now for 1, 2, or 3 years. You can also borrow in year 2 for 1 year. So to arbitrage MEANS to work with certain prices over equal periods so the only arbitrage possibility is to borrow now at 7% for a year with the right to borrow again for another year in one year at 4% and invest for two years at 6%. Now you can work out whether that is profitable or not.
 
Oh ok i think i know how to handle these types of problems now
 
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