find the arbitrage free forward rate first (by the way are these rates in LIBOR?)
F0 = 0.85 x (1.18/1.12)90/365 = 0.861
since the quoted forward rate is underpriced (lower than the arbitrage free forward), you would borrow SF, use the proceed to buy USD at spot, invest USD, enter into the forward at 0.8. 3 months later, collect USD investment and convert it at the agreed forward rate at 0.8 and pay off the loan on SF
assuming a SF1,000,000 loan.
borrow SF1,000,000 convert to USD -> USD850,000 (at spot rate of 0.85)
USD850,000 invested for 3 months -> USD885,408 (at 18% interest rate, ending value rounded up, assuming 30-365 day convention and annual compounding)
convert USD885,408 back to SF (at the agreed forward rate of 0.8) -> SF1,106,850
loan amount need to be repaid in SF (again, assuming 30-365 day convention and annual compounding) -> SF1,028,338
collect a net difference of SF78,551 (1,106,850 - 1,028,338)
note that in step 3, if the agreed forward rate is 0.861 (the arbitrage free forward), there would be no profit (there might still be negative or positive arbitrage profit due to rounding errors)
if quoted forward rate is underpriced, you buy and invest the price currency (USD) at spot
if quoted forward rate is overpriced, you buy and invest the base currency (SF) at spot
if the question asks you to start with a currency, you just have to mix it around.
for example, if in my explanation you have to start with USD. you enter into a forward agreement at 0.8 first, borrow SF at SF rate, convert it into USD and use the proceed to invest in USD. 3 months later, convert the necessary amount of USD back to SF to repay SF loan and keep the leftovers.
same thing really but the ending profits will be in USD instead of at SF.
For this part, you would use the forward rate to convert back to SF, but how will the ending profits be in USD? Are you saying you would convert the one-year-ahead borrowed SF amount to USD using the forward rate?
Awesome, thanks. I was trying this conversion (bolded), but used the expected spot (instead of the forward) to go back and forth between the profit in SF and the profit in USD.
Since the market forward rate of $ 0.8/SF is lower than that implied by interest rate parity, $0.861/SF, then SF is undervalued vs dollar (we are supposed to buy more dollars in the future than now with one unit of SF currency), then we should borrow SF and invest in USD because it is relatively cheaper to do that taking into account both the forward price and the forward rates of both currencies that will prevail in the near future.