The P&G/BT 5/30 Leveraged Swap

P&G and BT entered a five-year (its tenor) swap on November 2, 1993. The NP was $200MM and the periodicity was s.a. BT was long in the sense that it paid fixed at 5.30% p.a. P&G paid floating, namely the average 30-day CP rate(measured daily with arithmetic averaging and equal-weighting) minus 75 bps plus a spread. Said spread was zero for the first settlement/payment date of May 2, 1994. After that, that is, for the nine remaining payment dates, the spread was computed as follows:

Max{0,[98.5 x [(5-year CMT)/5.78%] - (30-year TSY price)]/100}

Where 5-year CMT is the 5-year constant-maturity Treasury, and 30-year TSY price is the midpoint of the bid and offer cash bond prices for the 6.25% Treasury bond maturing on August 2023.

P&G hoped that the spread would be zero, thus permitting it to earn 5.30% on a payment of CP less 75 bps. But rates moved against P&G and it got crushed. A similar deal was done between BT and Gibson Greetings.

P&G sued BT for sell-side abuse and was partly successful. BT was fined and disciplined by the SEC. BT’s image was harmed. The court case and SEC action together established modern standards for sell-side conduct.

Notice that P&G could have achieved the same gamble (get it?) through trading an interest rate spread option. But embedding (read “hiding”) the option in a swap made the position off-balance sheet and therefore not obvious to analysts and the like. FAS133makes swaps - like other derivatives - on-balance sheet, to curb this sort of thing.

Note: Paine-Webber MMMF “breaking the buck” case.

A Generic Swap Application: “Sophistication Arbitrage”

Suppose that you invent an interest rate swap where the floating amount paid on the payment date is determined by the rate observed on the payment date itself - rather than say twelve-months ago (assuming an annual swap and ignoring the typical Actual/360 day count convention).

Define the reset dates in the swap as t(i) for i = 0, 1, 2, ..., n, with T(i) = t(i+1) - t(i). Define R(i) as the LIBOR rate for the period between t(i) and t(i+1), F(i) as the forward value of R(i), and vol(i) is the volatility of this rate, that is, the standard deviation of its natural logarithm. Vol(i) would come from a caplet or LIBOR option price.

In your swap, the floating payment at time t(i) is based on R(i), rather than the traditional R(i-1). It can be proven that the valuation of this swap should be based on the assumption that the forward rate is not F(i), but instead is

F(i) + {[F(i)^2(vol(i)^2)(T(i)t(i))]/[1 + F(i)T(i)]}.

The term in { } represents a type of convexity adjustment.

For example, let the NP be $100MM, let the fixed swap rate be 2%, payments are annual, the tenor is 2 years, the LIBOR curve is flat at 2% per annum (with annual compounding), and the vol curve is flat at 20% per annum. Ignore day count conventions. Here, a typical swap would have a zero value. But the floating payments in your swap would be estimated at a convexity-adjusted rate of

.02 + {(.02^2)(.20^2)(t(i))/(1.02)} = .02 + .0000156t(i).

So the floating payments at the end of years 1 and 2 should be based on rates of 2.00156% and 2.00312%. The value of the long swap is positive $4,528.

You are successful at marketing this swap, and you load up on long positions and engage in offsets by shorting plain-vanilla swaps.

Is this sell-side abuse?

Do you think you would be caught? If so, by the time you get your bonus and retire to Paris by way of say Morrocco?

• Credit Derivatives Lecture Outline

• NP = $180B in 1997 and $5100B in 2004

• CDS about 75% of market

• Banks about 50% of end-users (regulatory capital relief and diversification of loan portfolios)

• Underlying credits 44% North America, 40% Europe, 11% Asia

• Hull (Chapter 27, 5th ed.) provides coverage of:

– CDS valuation

– Implying default probabilities of reference credit assets from CDS’s

– Variations of CDs’s including binary and basket CDS’s

– Total Return Swaps

– Credit Spread Options

– CDO’s

• We focus on applications

– Synthetic CDO’s

– Diversification of concentrated credit risk

Note: See “Credit Derivatives” file.

But first a simple one: In the beginning of 2001 Enron was rated Baa1/BBB+ and swap rates on 5-year CDS’s were running around 115/135 bid/offer. So one could have insured $100MM for $1.35MM per year. Of course, Enron was in default by the end of 2001.