solution manual for 《investment analysis and portfolio management》 ch24.doc

24 - 1 chapter 24 swap contracts, convertible securities, and other embedded derivatives answers to questions 1.cfa examination iii (1994) l(a). an interest rate swap is a customized risk-management vehicle. in a pension portfolio (i.e., investment) context, an interest rate swap would be represented by an agreement between two parties to exchange a series of interest money cash flows for a certain period of time (term) based on a stated (notional) amount of principal. for example, one party will agree to make a series of floating-rate coupon payments to another party in exchange for receipt of a series of fixed-rate coupon payments (or vice versa, in which case the swap would work in reverse). no exchange of principal payments is made. l(b). strategies using interest rate swaps to affect duration or improve return in a domestic fixed-income portfolio can be divided into two categories: duration modification. swapping floating- for fixed-rate interest payments increases portfolio duration (and vice versa, decreases duration when the portfolio is the floating-rate recipient). this method of modifying duration can be used either to control risk (e.g., keep it within policy guidelines/ranges) or to enhance return (e.g., to profit from a rate anticipation bet while remaining within an allowed range). seeking profit opportunities in the swap market. opportunities occur in the swap market, as in the cash markets, to profit from temporary disequilibrium between demand and supply. if, in the process of exploiting such opportunities, portfolio duration would be moved beyond a policy guideline/range, it can be controlled by using bond futures contracts or by making appropriate cash-market transactions. if a strategy calls for a large-scale reorientation of the portfolios characteristics in a manner that swaps could achieve, their use for implementation of the strategy would act to reduce transaction costs (thus improving portfolio return) and might also permit transactions to be effected more quickly or completely than through conventional trading mechanisms. 2.an interest rate swap is an agreement to exchange a series of cash flows based on the difference between a fixed interest rate and a floating interest rate on some notional amount. a fixed rate receiver would get the difference between a fixed rate and a floating rate if the fixed rate was above the floating rate, and pay the difference if floating was above fixed. the fixed rate is set so that no cash changes hands upon initiation of the deal. this can be thought of as: 24 - 2 i. a series of forward contracts on the floating rate because forward contracts also have no initial cash flow and will net the difference between the floating rate and the forward rate (which acts like a fixed rate). to make the analogy precise, only one forward rate is chosen but it is chosen such that the sum of the values of all the contracts are zero. the fixed rate receiver is like the short position in the interest rate forwards, because if interest rates go up, she loses. ii. a pair of bonds, one with a floating-rate coupon the other with a fixed-rate coupon (both selling at par with the same face value and maturity). being the fixed-rate receiver in the swap is the same as being long the fixed-rate bond and short the floating-rate bond. as long as the floating rate is less than the fixed rate, the coupon payment from the fixed-rate bond will cover the interest due on the floating rate bond and the difference is profit. if the floating rate is above the fixed rate then the fixed- rate receiver must make up the difference. since the bonds are of the same face amount, there is no net cash flow at the beginning or end of the agreement. 3.to have zero value at origination, the present vale of the expected cash flows from the swap must be zero. this implies that if there is an upward sloping yield curve, the expected cash flows to the floating payer will come at the beginning of the swap and be offset by expected payments by the floating payer at the end of the swap. the only way this is possible is if the fixed rate is somewhere between the current floating rate (low) and the implied floating rate later in the contract (high). 4.you are essentially holding a two-year swap agreement that requires you to pay 7% in exchange for floating. since the market rate for the same swap is 6.5%, if your counterparty defaulted you would be able to replace the swap at a lower rate. thus, it would be to your benefit for your counterparty to default, and you would realize an economic gain. 5.you have created an off-market swap where you are paying a fixed rate of 7%. this is seen by analyzing the portfolio of long a 7% cap and short a 7% floor. if interest rates are above 7%, then the cap pays the difference between 7% and the floating rate, and the floor is out-of-the money. if interest rates are below 7%, then you must pay the difference between floating and 7%, and the cap is out-of-the-money. since the market rate is a fixed rate of 8% for the same maturity and you only have to pay 7%, you will have to pay money up-front to get the cap and floor. in other words, the cap costs more than you will get from selling the floor. 6. cfa examination iii (1995) 6(a). the problem here is to sell equities and reinvest the proceeds with the skilled fixed- income manager, without changing the split between the existing allocations to the two asset classes. the solution is to turn to derivative financial instruments as the means to the end: selling enough of the existing fixed-income exposure and bringing in enough of the equity exposure to get the desired mix result. 24 - 3 the following are distinct derivatives strategies that the board could use to increase the funds allocation to the fixed-income manager without changing the present fixed- income/equity proportions: strategy 1 - use futures: one strategy would be to sell futures on a fixed-income index and buy futures on an equity index. selling the futures eliminates the fixed-income index return and risk, while keeping the skilled fixed-income managers extra return. by being long the equity index, the portfolio obtains the index return and risk, keeping its exposure to the equity market. strategy 2 - use swaps: a second strategy would be to use over-the-counter (otc) swaps. bi would swap a fixed-income index return for an equity index return in a notional amount large enough to keep the skilled managers extra return while eliminating the fixed-income market return and replacing it with the equity market return. strategy 3 - use option combinations: a third strategy would use put and call options to create futures-like securities. buying put options and selling call options on a fixed-income index, while selling put options and buying call options on a stock index, would achieve the same result as the appropriate futures position. 6(b). the following are advantages and disadvantages of each strategy identified and explained in part a: strategy 1 - use futures advantages: 1. futures contracts are liquid instruments. 2. transaction costs are low. 3. credit risk is negligible because the securities are marked to market daily. disadvantages: 1. if the holding period is long, rollover (transaction) costs are incurred. 2. standard contract forms are limited, so contracts may not exist on the index or instrument needed. tracking errors may create basis risk between the index and the performance benchmark. strategic 2 - use swaps advantages: 1. swaps can be tailored to fit the desired investment horizon, eliminating (or reducing) rollover costs. 2. swaps can be contracted for a specific index (like the performance benchmark) even if there is no futures contract on it. 3. the desired adjustment goal can be accomplished through a single transaction. 24 - 4 disadvantages: 1. a counterparty credit risk is created that can be much larger than with other types of instruments. 2. swap agreements are illiquid instruments, and disposals can be both difficult and expensive. 3. transaction costs are large because of typical “tailoring” of a given swap. strategy 3 - use option combinations buying put and call options on fixed income index (synthetic short position) and buying call and selling puts on stock index (synthetic long position) advantages: 1. transaction costs are low. 2. credit risks are small. disadvantages: 1. rollover(s) may be necessary. 2. the “right” option may not be available when needed or at all. 3. holders may exercise the put option and end the hedge. a generic disadvantage of any strategy is that returns are automatically eroded by the costs of establishing and maintaining the strategies, of meeting margin requirements, if any, and of unwinding them, if necessary. 7.cfa examination iii (1995) 7(i). from bis perspective, the major risk it would eliminate under this transaction is represented by participation in the eafe index (to the extent that this participation has been reduced), the return on which is now being paid to the counterparty bank. bi has reduced its international equity exposure. the market risk, formerly present in that part of the total participation that has now been swapped out in exchange for s at maturity, however, a unit holder receives the orginal issue price plus a supplemental redemption amount, the value of which depends on where the equity index settled relative to a predetermined initial level. 11(a).ii. commodity-linked bear bond unlike traditional debt securities that pay a scheduled rate of coupon interest on a periodic basis and thee pr amount of principal at maturity, the commodity-linked bear bond allows for an investor to participate in a delcine in a commoditys price. in exchange for a lower than market coupon, buyers of a bear tranche will receive a redemption value that exceeds the puchase price if the commodity price has declined by the maturity date. 11(b).i. a dual currency bond is a debt instrument that has coupons denominated in a different currency than its principal amount. these bonds can be viewed as a combination of two simpler financial instruments: (1) a single-currency fixed-coupon bond in the home currency, and (2) a forward contracct to exchange the bonds principal into a predetermined amount of a foreign currency. dual currency bonds are generally sold to 24 - 8 investors who are willing to “take a view” over the longer term in the foreign exchange market. 11(b).ii. first the effective forward exchange rate could be valued appropriately through the price premium, so the bond is properly priced. for a dual currency bond to be properly priced, the nominal forward exchange rate implied by the promised exchange of principalat maturity is actually favorable, and the price premium brings the effective forward exchange rate to a fairly priced level. alternatively, the investor might be “paying up” for the convenience and the desirable foreign currency exposure that cannot be acquired in any other way. that is, the usd fixed income investor is willing to pay a premium to acquire a forward exposure in chf, taking a longer term view that the chf will appreciate against the usd. 11(b).iii. if the bonds coupon pays in usd and the principal pays in chf. then the annual coupon payment will remain unchanged over the life of the bond. the principal payment due at maturity (in chf) would have been fixed by the forward contract rate at the time the dual currency bond was purchased, but the principal payment revalued in usd terms will be higher to the usd investor because of the strengthening of the chf against the usd. in other words, the chf principal payment due at maturity, expressed in usd, will be higher because of the chf appreciation. 24 - 9 chapter 24 answers to problems 1.from exhibit 24.4, we find that the fixed rate receiver will get the bid rate for the two year swap, viz., 3.34%. datefixed-liborfixed-ratefloating-rate ratereceipt payment 2/19/023.34%3.60%- - 8/19/023.34%3.90% $375,750$407,250 2/19/033.34%4.45%$375,750$448,500 8/19/033.34%4.60%$375,750$503,406 2/19/043.34%4.20%$375,750$529,000 8/19/043.34%3.95%$375,750$477,750 2/19/053.34%4.05%$375,750$454,250 the values for the receipts and payments are found using: fixed-rate receipt = swap fixed rate x (180/360) x notional principal floating-rate payment = reference ratet-1 x (#days/360) x notional principal the number of days is given in exhibit 24.6. 2(a). company w will want to enter into a receive-fixed pay-floating swap with semiannual payments for 5 years with a notional principal of usd 35m. the current quote on this swap is 4.82%. company x will want to enter into a pay-fixed receive- floating swap with semi-annual payments for 4 years with a notional principal of usd 50m. the current quote on this swap is 4.51%. 2(b). the two swaps are not matched perfectly. the first mismatch is the size of the notional principal. since company ws swap is for usd 15m less than company xs the dealer is exposed to a usd 15m receive-fixed swap for the first four years. the second mismatch is maturity. company ws swap is one year longer, so after four years, the dealer will be exposed to a usd 35m pay-fixed swap. 3.the key is to recognize that the combination of buying the cap and writing a floor at the same strike rate generates the same settlement cash flows as a pay-fixed swap. the fixed rate on the swap would equal the strike rate on the cap and floor. consider first the 8 percent cap-floor combination. the treasurer could buy the cap for 413 basis points (the market makers offer) and sell the floor for 401 basis points (the 24 - 10 market makers bid). the net is an up-front outflow of 12 basis points (times the notional principal). because the 8 percent pay-fixed swap would not entail an initial payment, the 8 percent cap-floor combination can be rejected. consider next the 7 percent cap-floor combination. the treasurer could buy the cap for 597 basis points and sell the floor for 320 basis points, resulting in a net up-front outflow of 277 basis points. the fixed rate on the synthetic swap would be 7 percent however, not 8 percent. the attraction of the cap-floor alternative turns on the trade-off of a present value of 277 basis points versus a three-year annuity of 100 basis points (actually a 12- period annuity of 25 basis points per quarterly period). using the three-year fixed rate of .20 percent, the present value of the savings is 263.57 basis points; that is, 12 25 = 263.57 t=1 (1+ .00820/4)t because the 263.57 basis points are less than the up-front cost of 277 basis points, the 7 percent cap-floor combination can be rejected as well. consider finally the 9 percent cap-floor combination. the treasurer could buy the cap for 220 basis points and sell the floor for 502 basis points, resulting in a net up-front inflow of 282 basis points. the fixed rate on the synthetic swap would be 9 percent. because the initial receipt exceeds the present value of the higher swap coupon (i.e. 282 263.57), this combination should be considered. is it definitely better? perhaps so in terms of cash flow and the time value of money, but the treasurer would also have to consider the tax and accounting treatment of the difference in the options premiums to confirm the benefit. 4(a). issue the traditional frn and enter one pay-fixed swap: (libor + 0.10%) x (365/360) + 6.38% - libor x 365/360) = 6.38% + (0.10% x 365/360) = 6.3814% issue the bull floater and enter one receive-fixed swap: (12.75% - libor) x (365/360) + (libor x 365/360) 6.34%) = (12.75% x 365/360) 6.34% = 12.9271% - 6.34% = 6.5871% issue the bear floater and enter two pay-fixed swaps (or one with twice the notional principal): (2 x libor - 6.40%) x (365/360) + 2 x 6.38% - (libor x 365/360) = -6.4889% + 12.74% = 6.2511% 24 - 11 4(b).note that the bull/swap combination is fixed only for libor 12.75% while the net settlement payout on the swap increases. the bear/swap combination is fixed only for libor 3.20%. if libor 8 percent, the return will be (3 x libor - 24 percent) + (3 x 13.35 percent - 3 x libor). the libor flows net out by design, and the return is 16.05 percent. if libor 166 3 3 103 + 100 x (ny3 - 166)/166 thus, you receive the same cash flows as a straight bond which pays a 3% coupon and is redeemable at par plus the additional cash flows associated with 0.60241 (=100/166) units of a call option on the nyse index which pays a dollar for each point the index exceeds 166 at maturity. 13(b). a regular bond without the embedded index option would have to sell for 71.65%, or: p = 3/(1.0765)+ 3/(1.0765)2 + 103/(1.0765)3 = $87.94 guinness was able to sell the spel for 100.625, meaning that the value of the option feature must satisfy: 100.625 = 87.94 + (bonds option value) so that the bonds option feature is worth $12.685. (recall that this represents only about 60% of a regular nyse index call option struck at 166.) the bonds option value is purely a time premium since the option is currently out of the money (i.e., the index value of 134 is less than the exercise price of 166). 14(a). d1 = ln(35/50) + .052 + (.342/2) (5) = -0.3567 + .052 +.0578(5) = 0.1923/.7603 .34 (5).5 .7603 = .25 d2 =.25-.34 (5).5 = -.51 n(.25) =.5987 n(-.51) =.3050 c(t) = 35(.5987)- 50e-.052(5)(.3050)= 20.9545- 50.7711)(.3050) = 20.9545 11.7593 = 9.195 q = 10,000/100,000= 0.1 w(t) = 9195/1.1 = 8.36 14(b). since the stock price before exercise must be $5,200,000/100,000 = $52, then all warrants will be exercised. then the warrant holder will purchase 10,000 shares at $50 per share, thus injecting $500,000 of new capital into the firm. then the firm will be worth $5,700,000/10,000 = $51.82. 14(c). the warrant was originally worth $8.36. at expiration, the warrant was only 2 points in- the-money and with the dilution effect, it was worth only 2/1.1 = 1.82. this is a 24