# covered interest arbitrage

can someone explain this question

Spot rate \$0.85 / SF

Three month forward for SF \$0.80 / SF

Three month Interest rate for SF annualized 12%

Three month Interest rate for USD annualized 18%

1 million USD

What is the question?

to find the covered interest arbitrage using a carry trade

I believe that to find the arbitrage profit you need to find the expected forward rate using interest rate parity spot multiply (1+int rate price currency)3/12 divided (1+ int rate base currency)3/12, and multiply the difference between the answer you get and the given forward by 1 million and you get the profit

Carry trade is a method of borrowing money from currency with lower interest and investing in higher -yield currency.

Firstly, you should be able to calculate how much SF you want to borrow, base on above assumption

1000000*0.85 (spot ex rate) = 850000

Secondly, you calculate interest receipt and payment for SF and USD

interest receipt for USD: 18%/4 * 1000000

interest payment for SF: 12%/4 * 850000

after that you convert total USD (principal + interest receipt) into SF (multiply forward rate 0.8 SF). Subtracting these amount from initial amount of SF, you can get gain/loss

Edit: DO NOT READ THE POST ABOVE MINE - HE IS WRONG. If you have to BUY a million USD at a rate of 0.85 USD/CHF then it will cost you MOOOOOORE THAN 1 million CHF. In order to buy 1 million USD it will cost you 1,176,471 francs (NOT 850,000).

I’m happy to explain. This question, is totally made up and routed deeeeeeeep in something we call “la la land”.

You’re not going to find a market where someone’s willing to take the contra side of that forward contract when the price currency interest rate is 6% higher than the base. The market would swoop on those arbitrage profits soooooooo fast.

In your example you understand that swiss francs are trading at a forward discount, when given the laws of uncovered interest rate parity they ought to be trading at a premium.

18% - 12% = 6% that we would expect the dollar to weaken by over this time frame not STRENGTHEN.

Now, all that aside, you really shouldn’t struggle to understand that if you borrow in swiss francs, invested in USD markets, and then bought that forward contract to convert back to francs for a notional of 1million US you earn a riskless profit of 92,529.07 swiss francs. I used the quarterly compounding method and not simple interest to get this number btw - on the exam, either way is sufficient.

It’s weird that they’re asking you to calculate this in terms of a million dollars. You obviously wouldn’t be borrowing in the US market if those rates were higher. So, to be fair, they should have told you to start in francs.

Also, understand that for a carry trade to work out, the currency of the higher interest rate country needs to depreciate by LESS than dictated by uncovered interest rate parity.

attempting this type of Qs after few years

As per covered int rate parity = 0.861 /SF should be the forward rate however you can book the trade at 0.8 /SF, which means you should sell \$ in futures market. Implies:

Forward Mkt —> Buy SF ----> Sell USD

Spot Mkt --> Sell SF --> Buy USD

As you need to long 1m USD (as per the qs I will assume) you need borrow equivalent Francs @12% i.e. 1/0.85 = 1.76471 m

Invest USD @18% => 1.18 m USD after 1 yr

Convert to 1.475 m CHF at the forward market, return 1.317m to your lender, Keep 0.157m CHF as gain

Try again next year. It says for only three months.

Simple interest = 94,485.29 francs gain Compounded = 92,529.07 francs gain