Unformatted text preview: and Related Strategies Table 3. T Zeros 1. Synthetic Forward Loan: {BKM §15.6} Year T ry% f% 2009 1 2.00 2.00 a) Assume that it is December 2008. 2010 2 2.15 2.30 1) Current T Zero and implied forward rates are in Table 3. 2011 3 2.47 3.11 2) Assume that large investors can borrow/lend at these zero 2012 4 2.76 3.63 rates (probably true in normal times). 2013 5 3.05 4.21 b) A company wants to borrow $10,000 in 2011 for 1 year, and wants to lock in an interest rate today. What can it do? One possibility is to create a synthetic forward loan. By doing so, it can then lock in the 2011 forward rate f2011 = 3.11%, and it can do this at no initial cost and no matter what the 2011 short rate r2011 turns out to be. c) Procedure and result. 1) Action today (t = 0): • Buy N = 10 zeros maturing at the end of 2010, paying 10,000e–0.0215(2) = $9,579. • Issue N × exp(f11) = 10e0.0311 = 10.316 zeros maturing at the
32nds of 100% in the WSJ. Dec 108 067 6.5 700,234 2) The contracts involve 30 Day Fed. Funds (CBT)  $5,000,000; 100 – daily avg. bonds and bond prices, Nov 99.610 .040 96,983 but are used to hedge Dec 99.555 .025 69,945 against interest rate risk. 1 Month Libor (CME)  $3,000,000; pts of 100% Nov 98.6625 .1325 23,063 b) The T Bond contract is the Jan ‘09 98.5350 .1450 1,320 most popular and widely traded of all interest rate futures. 1) Each contract calls for the nominal delivery of 100 $1,000 par Treasury bonds paying 6% coupon interest semiannually with 20 years remaining to maturity. 2) Futures prices are expressed as percent and 32nds of a percent of par, as follows: • The March 2009 settlement price F0 is 116 105 or 116 10.5/32 % of par, so the futures price of the bond F0 = 1.16328125×1000 = $1,163.28 per bond. • This price increased by 1 09.0 = 1 9/32 % of par from the day before. c) How T bond futures work if delivery takes place. 1) Technically, T Bond futures permit the short position to determine exactly which Treas ury bonds to deliver. At minimum they must not be callable and must have at least 15 years remaining to maturity. Beyond that, the short position will choose the bonds that are cheapest to deliver. 2) At delivery, the short position delivers 100 $1,000 par T bonds per contract and is paid cash for each bond according to the formula below (where accrued interest is computed by actual/actual day count): • (Most recent settlement price FT × Conversion Factor) + Accrued Interest 3) The conversion factor is bond price per dollar of M as of the first day of the delivery month if coupon interest is semiannual and YTM ry = 6%. 4) Example. • Contract settlement price at delivery is FT = 109 10/32% of M, or $1,093.13. • Short position decides to deliver T bonds paying rc = 8%, with T = 16 ¼ yrs. • At ry = 6%, these bonds are worth $1,205.62 (net of accrued interest), so the con version factor = 1.20562. Assume that accrued interest = $20.22. • The long position will accept delivery of 100 of these bonds and will pay the short position (1093.13 × 1.20562) + 20.22 = $1,338.11 per bond, or $133,811. 5) Of course, things are much simpler if the positions are closed before delivery! •
• Long initial position π L = (Fτ – F0) × 100 bonds × no. contracts Short ini...
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 Winter '08
 Foster,C
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