1. Interest Rate Futures July 2011 1

2. Introduction  Interest rate Futures  Short term interest rate futures (STIR)  Long term interest rate futures (LTIR) 2

3. World interest rate contracts 3

4. 2010 Break down of interest rate contract volume by product group 4

5. Source: FIA Magazine March/April 2011 5

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8. Volume by geographical zone 8

9. Principle value of 1 Mil with a three-month maturity Quote : 100 - yield yield = (discount/price)(360/day to maturity) price = 1 mil – discount yield(%)*1 Mil*DTM 360 9

10. Short term interest rate futures  Eurodollar  Assume discount yield is 8.32 % with 90 days to maturity what is the price? price = 1 mil – discount yield(%)*1 Mil*DTM 360 Price = 1,000,000 - [(.0832*1,000,000*90 )/360] = 979,200  Quotation = 100-.0832 = 91.68 10

11. Pricing futures Cost of carry model in perfect market market is perfect financing cost is the only carrying charge ignore the different between forward and futures prices ignore the options the seller may possess 11

12. Interest rate futures and arbitrage DTMdiscount yieldFace valuediscountPrice ABCD [B*(A/360)]*CC-D 776% 1,000,000 12,833.33 987,167 16710% 1,000,000 46,388.89 953,611 9012.5% 1,000,000 31,250.00 968,750 167 days 90 days77 days 6% 10% 12.5% Jan 5 Mar 22 12

13. Interest rate futures and arbitrage 167 days 90 days77 days 8% 10% 12.5% Jan 5 Mar 22 DTMdiscount yieldFace valuediscountPrice ABCD [B*(A/360)]*CC-D 778% 1,000,000 17,111.11 982,889 16710% 1,000,000 46,388.89 953,611 9012.5% 1,000,000 31,250.00 968,750 13

14. Interest rate futures and arbitrage  For no arbitrage to happen:  Holding 167 days t-bill(10%) must give equal yield to hold 77 days t-bill followed by 90days t-bill (12.5%) from futures delivery  Only yield that prevent arbitrage is  953611 = 968750-(96850*(x)*(77/360))  953611/968750 = 1-(.213889x)  X =.73063 DTMdiscount yieldFace valuediscountPrice ABCD [B*(A/360)]*CC-D 776% 1,000,000 12,833.33 987,167 16710% 1,000,000 46,388.89 953,611 9012.5% 1,000,000 31,250.00 968,750 14

15. Financing cost and implied repo rate 1+C = 968,750/953611 = 1.015875 DTMdiscount yieldFace valuediscountPrice ABCD [B*(A/360)]*CC-D 776% 1,000,000 12,833.33 987,167 16710% 1,000,000 46,388.89 953,611 9012.5% 1,000,000 31,250.00 968,750 implied repo rate>financing costcash n carry borrow fund buy cash bond, sell futures, hold bond n deliver against futures implied repo rate<financing costreverse cash n carry Buy futures, sell bond short, invest proceed until futures expires take delivery and repay short sales 15

16. Interest rate futures and arbitrage instrumentLending rateBorrowing rate 77 day T-bill7.30637.5563 167day t-bill1010.25 Unequal borrowing and lending rate DTMdiscount yieldFace valuediscountPrice ABCD [B*(A/360)]*CC-D 776% 1,000,000 12,833 987,167 16710% 1,000,000 46,389 953,611 9012.29% 1,000,000 30,725 969,275 16

17. Interest rate futures and arbitrage instrumentLending rateBorrowing rate 77 day T-bill7.30637.5563 167day t-bill1010.25 Unequal borrowing and lending rate DTMdiscount yieldFace valuediscountPrice ABCD [B*(A/360)]*CC-D 778% 1,000,000 17,111.11 982,889 16710% 1,000,000 46,388.89 953,611 9012.97% 1,000,000 32,425.00 967,575 17

18. The futures yield and forward rate of interest  1.048646 = x * 1.015875  X = 1.032259 ; forward rate =3.2559% 167 days 90 days77 days 7.3063% 10% 12.5% 953,611968,750 953,6111,000,000 1.015875 1.048646 18

19. Longer maturity interest rate futures  Treasury bond Futures  Treasury Note futures 19

20. US Treasury Note & Bond Futures 20

21. US Treasury Note Futures 21

22. Delivery of Bond futures  Majority of position will be liquidated or rolled forward and only tiny amount resulted in delivery 22

23. Deliverable grade  Deliverable grade is defined in contract specification and is varied by contract.  Several bonds could be delivered against the contract. Seller will choose the cheapest to deliver bond to deliver.  Conversion factors will adjust for the differences in coupons and maturity among the deliverable bonds. (approximate from assume face value of bond is 1$ and discounted the CF from bond at 6% using bond pricing equation)  When delivery, invoice piece will equal converted futures price + accrued interest  converted futures price = contract scale factor (1000)* settlement price *conversion factors 23

24. Invoice price If accrued interest is 519.71 24

25. Delivery process 25

26. Conversion factor 26

27. The cost of carry model for T-bond futures Cash and carry arbitrage for a T-bond  T-bond that is deliverable on a futures contract has an 8% coupon and cost 100$.  Financing rate 7.3063% on a discount basis for 77 days until futures contract is deliverable. Jan-05 Sell one T-bond Futures for101692 Borrow 100103 for 77 days @7.3063% Buy 8% t-bond for 100103 Mar-22 Deliver T-bond against futures get101692 Paid debt 101692 profit0 invoice amount = accrued interest + cost interest =(77/182)*4%*100,000 1,692 invoice amount in next 77 days 101,692 cost of buy T-Bond PV of invoice amount 101692- ((7.3063%*77/360)*101692) 100,103 Assume perfect market no seller options 27

28. Speculating with interest rate futures  Outright position  Long trader: betting interest rate will fall and futures prices will rise  Short trader: betting interest rate will rise and futures prices will fall Example : Trader Expect short term interest rate will rise. DateFutures Market September 20Sell 1 Dec Eurodollar futures at 90.30 September 25Buy 1 Dec Eurodollar futures at 90.12 Profit : 90.30-90.12 Total gain 18 basis points *25 = 450$ 28

29. Speculating with interest rate futures  Spread position  Intra-commodity : speculate on the term structures of interest  Example : Trader expects that the current very steep upward sloping yield curve would flatten within six month. (not sure whether rates were going to rise or fall.. DateFutures Market Mar 20Buy the DEC Eurodollar futures at 86.50 Sell the SEP Eurodollar futures at 87.50 September 25Sell the DEC Eurodollar futures at 88.14 Buy the SEP Eurodollar futures at 89.02 Profit : (88.14-86.50)+(87.50-89.02)=1.64-1.52=12 Total gain 12 basis points *25 = 300$ TTMFutures contractFutures Yield (%)Futures quotation 3 monthJUN12.0088.00 6 monthSEP12.5087.50 9 monthDEC13.5086.50 29

30. Speculating with interest rate futures  Spread position  Inter-commodity : speculate on shifting risk level between instrument  Example : International debt crisis, bank involved in international lending has more risk. May expect to find a widening of yield spread between T-bill and Eurodollar deposit.. DateFutures Market Feb 17Sell 1 DEC Eurodollar futures at 90.29 Buy 1 DEC T-bill Futures at 91.18 Oct 14Buy 1 DEC Eurodollar futures at 89.91 Sell 1 DEC T-bill futures at 91.02 Profit : (90.29-89.91)+(91.07-91.18)= 0.38-0.11 =0.27 Total gain 27 basis points *25 = 675$ 30

31. Hedging with interest rate futures DateCash MarketFutures Market Dec 15Fund manager learns he will receive 970,000 in six month to invest in T-bill Market yield 12% is attractive and want to lock in yield Face value of bill to purchase is 1 million Buy T-bill futures to mature in six month Futures prices = 1 Mil – (1 mil*(.12*(90/360))) = 970,000 June 15Receive 970,000 to invest Market yield drop to 10% 1 million face value of T0bill now cost 975,000 Loss = -5000 Offset position by selling T-bill at futures yield 10% or futures prices 975,000 (1,000,000- (1,000,000*(.1*90/360))) Profit =5,000 Net wealth change = 0 Long hedge 31

32. Hedging with interest rate futures DateCash MarketFutures Market March A bank makes a 9 month fixed rate loan to a client. Financed by a six month CD at 3% but need to rolled over for 3 month at the expected rate of 3.5% bank is vulnerable to the rate rising over the expected rate. Short SEP Eurodollar at 96.5 futures prices reflecting 3.5% futures yield September 3 month LIBOR is now 4.5% Bank’s cost of fund is 1% over the expected rate of 3.5% Additional coats equal (90/360)*.01*1,000,000 =2,500 Offset position by long Eurodollar at futures yield 4.5% or futures prices 95.5 Profit 100 basis points *25 =2,500 Net after hedge = 0 Short hedge 32

33. Hedging with interest rate futures DateCash MarketFutures Market T=0 A company decides to sell 90day commercial paper in 3 months in the amount of 1,000 million, at the expected yield of 18%, which should net the firm 955 million. Short 1000 T-bill futures contracts to mature in 3 months with a yield of 16% futures prices per contract is 960,000 T= 3 months market view changes and perceived CD has more risk ; yield widen to 2.25% CD rate is now 18.5% instead of 18% sale of CD thus get the firm of 953.750 million Opportunity loss 955-953.75 = -1.25 million T-bill futures about to matures T-bill futures rate = spot rate =16.25% (raised as expected more inflation) futures prices is 959,375 per contract Gain 625 per contract or total gain 625,000 $ Net after hedge = -625,000$ Cross hedge DTMdiscount yieldFace valuediscountPrice ABCD [B*(A/360)]*CC-D 9018% 1,000,000 45,000.00 955,000 9016% 1,000,000 40,000.00 960,000 9018.50% 1,000,000 46,250.00 953,750 9016.25% 1,000,001 40,625.04 959,376 33

34. Thank you 34