# On the pricing of interest rate swaps

I\’m not sure that I believe these figures:

Take the example of a five-year loan for £1m taken out in 2007. In this example the customer wants to fix their rate for the duration of the loan. The bank, with its sophisticated pricing systems, would look at the swap market and get the price of buying the equivalent swap. The rate at the time might be 5.2pc, however the bank, wanting to make a profit and knowing the customer has no access to swap market prices, would quote the customer a cost of anything from 5.5pc to 6pc.

If the customer agreed to the swap, the bank would instantly lay off the risk by selling the swap in the market and locking in a profit for itself of between 30 basis points and 80 basis points. In the case of a £1m, five-year swap, the bank would effectively get a customer to buy a swap worth £200,000 for a cost of £225,000 to £250,000. The bank would immediately claim this profit by selling on the swap into the market, netting itself a gain of between £25,000 to £50,000.

OK, so this is a pretty simple swap. Moving floating rate money into fixed rate money.

I\’m happy enough that it costs 30 to 80 basis points to do this. But the numbers they are quoting there, 5.2% say, that\’s the total interest rate cost of the product, not the difference between the floating and fixed rate price.

I could of course be entirely wrong about this but surely no one sane is going to hand over a fee equal to the entire currently expected interest rate cost of the loan (that £250k over 5 years) just to make sure that the interest rate doesn\’t change?

The cost of the swap itself is going to be the difference between the fixed and floating rates. More like that 30 to 80 bps in fact. Or perhaps £40 k as the fee, not £250k.

This has nothing to do with whether the banls were charging excessive fees of course. But I do have this feeling that the Telegraph has got the actual costs of swas wildly wrong here.

Anyone care to enlighten me?

## 5 thoughts on “On the pricing of interest rate swaps”

1. Swaps usually trade with no up-front premium – there is no “cost” to the swap in the sense the article seems to suggest.

In the 30bp example, the bank’s profit would be 30bp a year for five years. Roughly £15,000 (actually a bit less because the future cash-flows should be discounted).

2. A simple interest rate swap is an agreement to exchange a fixed amount of interest in exchange for interest set using LIBOR.

At the outset the ‘Payer’ (not ‘buyer’) will agree to pay a per determined fixed rate, and ‘recieve’ the floating.

A 5 year GBP swap would generally be quoted ‘Semi/Semi’ meaning that the fixed rate would be paid every 6 months, whilst 6 month LIBOR woul be used to determine the floating cash flow. The cash would be exchanged at the end of each 6 month period, and subject to the number of actual days between the start/end (based on whatever date convention was agreed).

Note… No up front cash exchange…. Only exchanges of interest every six months. Although there are other formats such as ‘Annuals vs. 3s’ which is 1 fixed interest flow per year, against 4 floating flows set against 3 month LIBOR.

If the market rate was 5% at the time the trade was agreed at 5%, then the value of the swap is zero. If the agreed fixed rate was 5.8%, then the value of the swap is 0.8% * notional * day count / 365 * discount factor, for each leg, trotted up.

You could also agree ‘LIBOR plus’, but that would be compensated via a higher fixed rate.

Sometimes, in the wholesale market, you can agree an ‘off market’ fixed rate, but the loser would be compensated by an up front fee – this is quite rare.

However, the ways a bank can gauge the unsuspecting unsophisticated customer is something else… And they did….

3. The idea that the profit on a vanilla IRS is 30-80 bps is farcical.

Most big buy side participants have access to multiple swap dealers who have to compete for business. Just as I don’t know the cost a grocer or car manufacturer in incurs, the clients may not know the interdealer quote for the IRS, but they rely on competition to drive prices to costs. Less transparency may dampen competition some, but to the extent of 30-80 bps: please.

Moreover, clients have access to other information. They can look at spreads vs. gov’t bonds. They can also compute a synthetic swap price from the futures curve. For instance, you can calculate a USD swaps rate from Eurodollar futures prices.

The margins are razor thin on vanilla business. Dealers make more profit on more exotic products.

4. You’re all missing the point. Yes, in normal swap transactions with people who know what they are doing and understand the swaps marketplace banks would never get away with charging up-front fees and creating whopping spreads. But the clients were small businesspeople with no understanding of these things. It wouldn’t surprise me in the least to discover that banks not only sold them complex derivatives they didn’t need but also charged them hefty fees and ripped them off on interest rate spreads. Naive customers are always most at risk of being taken for a ride.

5. Because I’m a boring sod, I decided to work it out, properly discounting the cash flows.

If a bank were to make 80bp (6%-5.2%) on £1mio of 5 year semi/semi, with a prevailing market interest rate of 5.20%, then the profit would be just under £35,000, not £50k as the report seems to imply.

Probably of no use to anybody, but, there you are…