In this workout, we are told that a company has just agreed to borrow 250 million euros at your arrival, plus 110 basis points for six months in three months time from its bank.

The treasury is concerned that rates might rise between now and then, and we are asked using the FRA information below, what is the rate the company could lock in by trading an FRA, and also do they need to buy or sell the FRA? We've got the current six month arrival fixing of 3.874%.

We then have the quotes for two different RAs.

We've got the bid and offer rates for three by six FRA and a three by nine FRA before we work out the all in rate.

Let's think about the trade direction.

As the company is a borrower and they are concerned about rates rising, they would need to buy an FRA because remember, the buyer under an FRA pays the fixed FRA rate.

The next question is then do they need to buy the three by six FRA or the three by nine FRA? And the answer is they need to buy the three by nine FRA, and that is because their loan is starting in three months time and then running for six months.

Next, to calculate the all in rate, we need to take the relevant FRA rate and add the spread of 110 basis points.

We've already established that we're going to be using the three by nine FRA.

So do we get the bid or the offer rate? And the answer is we get the offer because we are buying the FRA, so we get the higher of the two rates.

So our all-in rate would be the 3.31% FRA rate plus the spread of 110 basis points, which is 1.1%, and that gives us an all-in rate of 4.41%.

In summary, the treasurer should buy the FRA since that will generate a positive payout in the event your arrival rises.

Remember, if you buy an FRA, you pay the fixed FRA rate and receive the relevant reference rate.

And the relevant FRA that needs to be bought is the three by nine because the loan is against six month IOR and starts in three months time.

So the treasurer would buy at the offer of 3.31%, and as the loan is your IO plus 1.1%, this would lock them into a loan rate of 4.41%.