Forward Arbitrage Stalla Question identify, exchange, 120, forward

SeanWest

Spot Exchange Rate: $1.5/pound
60-day forward exchange rate: $1.47/pound
120-day Forward Exchange Rate: $1.45/pound
60 day rate 120 day rate
U.S. 4% 4.5%
U.K. 5% 5.6%
Assume that the no-arbitrage, 120-day forward price is $1.4948/pound. After borrowing GBP, identify the most appropriate arbitrage transactions to earn an arbitrage profit from the misvaluation of the forward contract.
A. Sell USD for GBP forward and buy USD for GBP spot
B. Sell USD for GBP spot and buy USD for GBP forward
C. Sell USD for GBP forward and buy GBP for USD spot
Now, I used the formula [1+rdomestic)(120/360)] to determine which to borrow/lend, but it gave me the wrong answer; it said to Sell USD for GBP forward and buy USD for GBP spot. The answer seems simple (buy $1.45/pound and sell $1.4948/pound) and maybe their answer choices confused me…does this formula still work?

NakedPuts00

Whats the question number?

Nishant1

Since no-arb price =1.4948 $/P and the market price = 1.45 $/P. The Forward contract seems to be undervalued. Means you buy the $/P contract forward and sell the $/P spot.
So A?

jmh530

The answer is A, and it’s just the way the answers are posed that throws me off.
It’s in the workbook they give to people when they have the free problem session. It’s in the 24-problem workbook, so I don’t know what “number” it is, sorry.

domani

US unannualized rate:
= 0.045*120/360 = 0.015
UK unannualized rate
= 0.056*120/360 = 0.0187
Calculate what no arbitrage forward price is:
FP = SP * (1 + rate US)/(1 + rate UK)
= 1.5 $/GBP * (1.015)/(1.0187)
FP = 1.4946 $/GBP
Now compare to the quoted forward of 1.45 $/GBP
Note that the quoted price shows that GBP is undervalued compared to the arbitrage price (the GBP converts to less US dollar)
The result? If the forward shows GBP is undervalued, then the US is overvalued.
So we want to sell US forward using the quoted forward price
In order to sell USD in the future, we’ll need to buy US today (converting from GBP at the spot price)
A. Sell USD for GBP forward and buy USD for GBP spot
It’s all about thinking what currency you’ll need to sell at the forward price to decide what currency you need to hold and invest at the risk-free rate today.