Interest Rate Futures July

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

World interest rate contracts 3

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

Source: FIA Magazine March/April

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Volume by geographical zone 8

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

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 = =

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

Interest rate futures and arbitrage DTMdiscount yieldFace valuediscountPrice ABCD [B*(A/360)]*CC-D 776% 1,000,000 12, , % 1,000,000 46, , % 1,000,000 31, , days 90 days77 days 6% 10% 12.5% Jan 5 Mar 22 12

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, , % 1,000,000 46, , % 1,000,000 31, ,750 13

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  = (96850*(x)*(77/360))  / = 1-( x)  X = DTMdiscount yieldFace valuediscountPrice ABCD [B*(A/360)]*CC-D 776% 1,000,000 12, , % 1,000,000 46, , % 1,000,000 31, ,750 14

Financing cost and implied repo rate 1+C = 968,750/ = DTMdiscount yieldFace valuediscountPrice ABCD [B*(A/360)]*CC-D 776% 1,000,000 12, , % 1,000,000 46, , % 1,000,000 31, ,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

Interest rate futures and arbitrage instrumentLending rateBorrowing rate 77 day T-bill day t-bill Unequal borrowing and lending rate DTMdiscount yieldFace valuediscountPrice ABCD [B*(A/360)]*CC-D 776% 1,000,000 12, , % 1,000,000 46, , % 1,000,000 30, ,275 16

Interest rate futures and arbitrage instrumentLending rateBorrowing rate 77 day T-bill day t-bill Unequal borrowing and lending rate DTMdiscount yieldFace valuediscountPrice ABCD [B*(A/360)]*CC-D 778% 1,000,000 17, , % 1,000,000 46, , % 1,000,000 32, ,575 17

The futures yield and forward rate of interest  = x *  X = ; forward rate =3.2559% 167 days 90 days77 days % 10% 12.5% 953,611968, ,6111,000,

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

US Treasury Note & Bond Futures 20

US Treasury Note Futures 21

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

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

Invoice price If accrued interest is

Delivery process 25

Conversion factor 26

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 % on a discount basis for 77 days until futures contract is deliverable. Jan-05 Sell one T-bond Futures for Borrow for 77 Buy 8% t-bond for Mar-22 Deliver T-bond against futures get Paid debt 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 ((7.3063%*77/360)*101692) 100,103 Assume perfect market no seller options 27

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 September 25Buy 1 Dec Eurodollar futures at Profit : Total gain 18 basis points *25 = 450$ 28

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 Sell the SEP Eurodollar futures at September 25Sell the DEC Eurodollar futures at Buy the SEP Eurodollar futures at Profit : ( )+( )= =12 Total gain 12 basis points *25 = 300$ TTMFutures contractFutures Yield (%)Futures quotation 3 monthJUN monthSEP monthDEC

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 Buy 1 DEC T-bill Futures at Oct 14Buy 1 DEC Eurodollar futures at Sell 1 DEC T-bill futures at Profit : ( )+( )= =0.27 Total gain 27 basis points *25 = 675$ 30

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 = 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

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

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 million Opportunity loss = 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, , % 1,000,000 40, , % 1,000,000 46, , % 1,000,001 40, ,376 33

Thank you 34