【正文】 ?TSY Price = * *?YLD% ?Spread = *?CMT% +*?YLD%. A parallel shift in term structure (yield curve) will cause the spread to move by a factor of . One basis point increase raises the spread by basis points, a very big leverage. A move of only 58 basis points from November 2, 1993 curve would be able to cover the 75 basis point cushion. Each additional basis point move drives the market value of the leverage swap down by about $ million. In addition, PG is facing both the CP rate and the spread. Both ponents are positively related to the interest rte level. PG get hit twice if the interest rate moves together. This swap is, therefore, poorly structured. 6 Is the swap a fair deal? In its “5/30” leveraged swaps with BT, PG stood to gain if fiveyear and thirty year Treasury yields remained steady between Nov. 1993 and May 1994. PG’s upside gains were limited to the 75 basis points per period (later amended to 88 basis points). Its downside risk was unlimited. This payoff pattern is consistent with an interpretation that the leveraged swap consists of a plain vanilla receive fixed interest rate swap and written options on Treasury securities. PG’s strategy was to use the premium on the written option to reduce it cost of borrowed funds. Using information on put options on Tbond futures one can see the deal was not fair to PG. For the amount of risk borne on transaction. PG received no more than onethird the value of the written options via the swap than if the puts had been written on the exchange directly. 7 Aggressive corporate finance PG’s objective in the Fall of 1993 was to lower the anticipated cost of borrowed funds by writing options on Treasury securities. Corporations take positions on interest rates all the time when structuring their debt liabilities. Managers’ view on future market conditions arises when they select a maturity and coupon structure, as well as decide whether to include call, put, or other instruments. The difference in the accounting treatments is in timing of the recognition of ine and expense. If PG had written the exchangetraded put options, there would have been nondeferred current ine or expenses, regardless of the motivation for transaction. PG, however, probably anticipated synthetic alternation treatment on the leveraged swap. Embedding the written options would allow the “premium” received to be amortized over the fiveyear tenor of the swap. Moreover, if the speculative bet lost, the losses would be amortized as well. Even better, the higher cost of funds experienced for the five years as a result of a positive spread would be buried in the overall cost of borrowed funds and not appear as a separate line item in balance sheet. ? 靜夜四無鄰，荒居舊業(yè)貧。 Floating rate used in time t=Rt1(LIBOR at time t1). NET payment at time t: Fixed rate at time t: Fixedrate payer receives (Rt1Qk) and floatingrate payer receives (kRt1Q). The following is a possible scenario of cash flows for the fixedrate payer under a $100 million, 5year swap at % with semiannual cash flow exchanges. Time (years) LIBOR Floating Payment Fixed Payment Net 0 1 2 3 4 5 6 7 8 9 10 + + + + + + + What is the implication of ting about credit (default risk)? Pricing interest rate swaps: a. Set the fixed rate of swap so that the swap has a zero value at the time of initiation. This is called par swap. b. Suppose that payment dates are t1,t2,…,tn. The value of a swap at time t, Vt, from the perspective of the floatingrate payer: Vt=B1tB2t c. B1t: value of fixedrate bond underlying the swap when ti?t?ti+1, B1t= ?nj=i+1ker(t,tj)(tjt)+Qer(t,tn)(tnt). d. B2t: value of floatingrate bond underlying the swap. At the floating rate resetting day, ., t=t1,t2,…,tn, immediately after the payment is made, B2t=Q. Why? In between, ., titti+1, B2t=(Q+k*)exp[r(t,ti+1)(ti+1t)], where k* is the floating rate payment at time ti+1 already known at time t. Determining the swap rate at time 0: V0(k) = ?ni=1kexp[r(0,tj)tj]+Qexp[r(0,tn)tn] Q=0 ? Q=?ni=1kexp[r(0,tj)tj]+Qexp[r(0,tn)tn]. That is, set an appropriate coupon rate so that the bond is priced at par. e. Example: Counterparty A in a threeyear swap pays 6month LIBOR and receives a fixed rate on a notional principal of $100 million. The swap has years to maturity. (The swap rate was determined one year and ninemonth ago.) At the time of initiation, 3year 8% bond was priced at par. The LIBOR at the last payment date was % (semiannual pounding). Discount rates for 3month, 9month and 15month maturities are 10%, %, and 11%, respectively. The fixed rate =8% per annum. B1=*+4e*+104e * =, B2=(100+)e*===(million) to A and