【正文】 LIBOR Date Days LIBOR % SP500 SP500 return LIBOR Payment SP Payment Net Payment Jan 2 Apr 2 90 % 225,000 190,106 34,894 Jul 2 91 231,292 580,003 348,711 Oct 2 92 238,944 319,803 558,747 Jan 2 92 221,056 140,498 80,558 The value of equity swap a. The value of this equity swap was zero on Jan 2, the time of initiation. The same is true for April 2, July 2, Oct 2 and Jan 2 immediately after the payment is made. Why? b. The value of this equity swap on, say March 1, will not be zero, however. Assume that the futures price of SP500 index futures contract maturing in April contract finished at on that day. The discount rate on March 1 for the maturity of April 2 is %. 1. What is the value of swap to the LIBOR payer? The LIBOR payment on April 2 is known to be 225,000. Its present value is 225,000*exp(*32/365)=223,212. The receipt on April 2 subject to the SP500 index performance is [(IA2IJ2)/%]*100m. Its present value is [(*)*100m/]*exp(*32/365)=2,137,166. The total value =223,2122,137,166=2,360,378. ? Commodity swaps In a typical modity swap, one counterparty makes periodic payments to the second counterparty at a fixed price per unit for a given notional quantity of some modity. The second counterparty pays the first counterparty a floating price for a given notional quantity of some modity. The modities are usually the same. The floating price is usually calculated as an average price. ? Credit Default Swaps Will be discussed in the section of credit risk. ? Procter Gamble – Bankers Trust Leveraged Swap 1 The story On November 2, 1993, PG and BT entered a five year, semiannual settlement, $200 million notional principal interest rate swap contract known as the “5/30” swap. BT pays a fixed rate of % and PG pays a floating rate depends on thirtyday mercial paper (CP) daily average rate less then 75 basis points, plus some spread. The key factors in the agreement are the spread and the 75 basis points – a plain vanilla swap would have been % versus the CP daily average rate flat. The swap was scheduled to lock in on May 4, 1994. Because the spread on the lockindate was 2,750 basis points, PG experienced significant losses and filed a lawsuit. An outofcourt settlement was reached in May 1996. BT agreed to absorb $157 million. 2 The PGBT leveraged swap Term: 5 year Frequency: Semiannual payments Fixed rate payer: Bankers Trust at % Floating payer: PG at 30day mercial paper daily average rates less 75 Basis points plus a spread. 3 The spread The spread is zero for the first 6month settlement period, and then would be fixed for the remaining nine semiannual periods, depending on Treasury yields and prices on the first settlement date, May 4, 1994, according to the formula. Spread = max{0, [(5year CMT%/% (30year TYS Price)]/100 } 5year CMT% is the yield on the 5year constantmaturity Treasury note. The 30year Treasury (TSY) bond price is the midpoint of the bid and offer prices on the % Tbond maturing in August 2023, not including accrued interest. The spread on November 2, 1993 was zero because [*%/% ]/100 = The spread on May 4, 1994 was Max {0, [*%/% ]/100} = Thus in return for receiving a fixed rate of %, the PG would have been obligated to pay the 30day CP daily average rate plus % (%%) for the next four and one half years on the $200 million swap if the formula had not been amended prior to May 1994. 4 The amendment The swap was amended in January 1994 to move the determination date of the spread from May 4, 1994 to May 19, 1994 in exchange for 13 basis points improvement in the floating rate side of the swap, ., 75 basis points has been changed to 88 basis points. Interestingly, there is a Federal Open Market Committee meeting scheduled on May 17, two days before the new spread determination date. PG decided in March 1994 to lock in the spread, instead of waiting for May 19 determination. This was done in three stages with $50 million on March 10, $50 on March 14, and the remaining $100 million on March 29 All in all, the spread was locked in at 15%. The loss can be estimated at about $ million in present value terms. 5 Was corporate treasury group at PG able to ascertain the risk it was beating upon entering the transaction? A loss of over $100 million on a swap with a notional principal of $200 million is extraordinary, a real testament to the power of leverage. The spread formula can be simplified to Spread = max(0, *5yearCMT% *30yearTSY price) ?Spread = *?CMT% *?TSY Price. Using % as the sixmonth forward yield in Nov. 1993 on the Tbond on August 1, 2023, we have