forward currency arbitrage currency, forward, problem, beyond

AndyNZ

Are we going to have to know how to do the exact arbitrage calculation for the forward currency derivative calcs? (ie. show the steps you would take to earn a risk-free profit based on a mis-priced currency forward)

I have no problem calculating the price/value of a currency forward. I can obviously tell if a forward is expensive or cheap. But the steps beyond that in these EOC to show that you earn a rate superior to the Rf make my head explode. Any ideas?

thx

WarrenB1

are you referring to the cash and carry or reverse cash carry arbitrage?

FinancialAnaly

i guess both.

OmarAdnan

Ok, heres how i think of it....

Theres two types of arbitrage, cash and carry and reverse cash and carry. Keep in mind, always want to buy low and sell high.

CASH AND CARRY
We use this method when the forward contract is trading at price that is too high. Since the forward is overpriced, we want to sell it (steps with same numbers and different letters are "simultanous".

1a. Sell the forward at the current price (means we will have to deliver asset in future)
1b. Borrow money at the current Risk free rate for the term of the contract
1c. Using the money borrowed, buy the asset the the current spot price

2a. At expiration of the forward contract, we need to deliver the asset. By buying the asset initially when we shorted the forward, we now own the asset and can deliver it. We deliver the asset to the long, and receive the forward price we agreed on in step 1a.

2b. We took a loan out to purchase the actual asset we delivered in 2a. We need to pay it back (Loan value(1+interest)^(days/365)) will be the amount we pay back. Because the forward price was too high when we originally sold it short, we end up making money on the difference between the loan repayment and the value we received for selling the forward short.



Reverse cash carry is the opposite. The forward is undervalued, so we buy it.

1a. Sell the asset short at spot price
1.b lend the proceeds at risk free rate for term of forward
1c. buy the forward contract

2a. At expiration, collect loan proceeds
2b. Use loan proceeds to purchase the asset at the forward price. The difference between that price and the loan proceeds is you arbitrage profit.


Hope this helps