Question

• • The risk-free rate in the US is 5% and the UK risk-free rate is 8%. The spot quote is $1.80/£ while the one year forward quote is $1.78/£. You can borrow either $1,000,000 or £555,556. According to IRP, is the forward quote correct? If not, what should it be?

If the forward quote is not correct, lay out the steps to implement an arbitrage.

• The annualized US risk-free rate is 8% and the Germany risk-free rate is 5%. Assume that any period rates less than a year can be interpolated (i.e. if you invested for 6 months then you would receive 4% in the US). The spot quote is €0.80/$ while the 3-month forward quote is €0.7994/$. You can borrow either $1,000,000 or €800,000. According to IRP, is the forward quote correct? If not, what should it be?

If the forward quote is not correct, lay out the steps to implement an arbitrage.

• A trader believes that the euro will appreciate versus the pound. Currently, the spot is €1.2/£ and the forward is €1.3/£. Lay out the steps that the trader would implement if she wants to potentially profit (using forwards) from her view.

What if spot finished at £0.8696/€

What if spot finished at £0.7143/€

• Below are quotes from JPMorgan
• Bid - Ask
• €/$ 0.8- 0.85
• £/$ 0.7- 0.75
• £/$

Calculate the £/€ quote. Explain what each trading desk at JPMorgan is doing so that the bank can arrive at that quote

Answer 1

Answering the first question out of multiple questions listed above.

• The risk-free rate in the US is 5% and the UK risk-free rate is 8%. The spot quote is $1.80/£ while the one year forward quote is $1.78/£. You can borrow either $1,000,000 or £555,556.

Forward rate as per IRP (Interest rate parity) = Spot rate * (1+Rd) / (1+Rf) where Rd is domestic currency and Rf is foreign currency

Spot quoted as $1.80/£ indicates that $ is domestic currency and £ is foreign currency

Future quote will be $1.8*1.05/1.08 = $1.75/£. But 1 year forward as $1.78/£. Since this is different from the value calculated, there exists an arbitrage opportunity.

Since pound is more strong (as compared to IRP calculations) we will sell the forward pound. Which means we will enter a future contract to Sell pounds for $1.78 today.

Now today we borrow USD $1,000,000, convert in into Pounds at $1.8/pound i.e. £555,556 and invest it in 8% interest rate which will give you £600,000 (i.e.555,556*1.08) at the end of 1 year. Now convert this pounds to USD @$1.78/pound

i.e. $1,068,000 (600,000*1.78)

Now Borrowed USD of $1,000,000 1 year ago would have interest accumulated of $1,000,000*5% = $50,000

SO total that we need to return to the creditor is $1,050,000 and remaining is our risk free arbitrage profit of $1,068,000 - $1,050,000 = $18,000

Thus, we get an arbitrage profit of $18,000