Interest Rate Futures

July 2011

1

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 20115

6

7

Volume by geographical zone

8

• 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

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

Pricing futures

)1(0, CSF to

CS

F t1

0

,0

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

DTM discount yield Face value discount Price A B C D        [B*(A/360)]*C C-D

77 6% 100,

0000, 128,

3333. 987

167

167 10% 100,

0000, 463,

8889

953 611

90 125. % 100,

0000, 312,

5000. 968

750

167 days

90 days

77 days6%

10%

12.5%

Jan 5

Mar 22

12

Interest rate futures and arbitrage

167 days

90 days

77 days8%

10%

12.5%

Jan 5

Mar 22

DTMdiscount

yield Face value discount Price A B C D        [B*(A/360)]*C C-D

77 8

10000,

00

17,111

11 982889,

16

7 10%

10000,

00

46,388.

89 953611,

90

125.%

10000,

00

31,250.

00 968750,

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 953611 = 968750-(96850*(x)*(77/360)) 953611/968750 = 1-(.213889x) X = .73063

DTM discount yield Face value discount Price A B C D        [B*(A/360)]*C C-D

77 6% 100,

0000, 128,

3333. 987

167

167 10% 100,

0000, 463,

8889

953 611

90 125. % 100,

0000, 312,

5000. 968

750

14

Financing cost and implied repo rate

CS

F t1

0

,0

1+C = 968,750/953611 = 1.015875

DTM discount yield Face value discount Price A B C D        [B*(A/360)]*C C-D

77 6%

100,000,

0 128,

3333. 98

7167,

167 10%

100,000,

0 463,

8889

95 3611,

90125. %

100,000,

0 312,

5000. 96

8750

implied repo rate >financing costcash n carry

borrow fund buy cash bond , sell futures, hold bond n deliver against futures

implied repo rate <financing cost

reverse 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

instrument Lending rate Borrowing rate77 day T-bill 73063. 75563

167day t-bill 10 1025

Unequal borrowing and lending rate

DTM discount yield Face value discount Price A B C D        [B*(A/360)]*C C-D

77 6

100000 0 12833

9871, 67

167 10% 100000

0 46389, 9536,

11

90 12.29% 100000

0 30725, 9692,

75

16

Interest rate futures and arbitrage

instrument Lending rate Borrowing rate77 day T-bill 73063. 75563

167day t-bill 10 1025

Unequal borrowing and lending rate

DTMdiscount

yield Face value discount Price A B C D  

     [B*(A/

360)]*C C-D

77 8% 1000,

000

1711, 111.

982, 889

167 10% 1000,

000

4638, 889.

953, 611

90

1297.%

1000, 000

3242, 500.

967, 575

17

The futures yield and forward rate of interest

1.048646 = x * 1.015875 X = 1.032259 ; forward rate =3.2559%

167 days

90 days

77 days

7.3063%

10%

12.5%

953,611 968,750

953,611 1,000,000

1.015875

1.048646

18

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 519.71

24

Delivery process

25

Conversion factor

26

The cost of carry model for T-bond futuresCash 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 for 10169

2

Borrow 100103 for 77 days @7.3063%Buy 8% t-bond for 100103         

Mar-22      

Deliver T-bond against futures get10169

2

Paid debt    10169

2

    profit 0

invoice amount = accrued interest + cost    

interest =(7 7 /1 8 2 )* 4 %*100000,    

 

1 ,69

2        

invoice amount in next 77 days  

101

,692      

cost of buy T-BondPV of invoice amount    

   - 101692 73063 *(( . %

77360*101692

   

100

,103      

Assume perfect market no seller options27

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.

Date Futures Market

September 20 Sell 1 Dec Eurodollar futures at 90.30

September 25 Buy 1 Dec Eurodollar futures at 90.12

Profit : 90.30-90.12

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.

.

Date Futures Market

Mar 20 Buy the DEC Eurodollar futures at 86.50Sell the SEP Eurodollar futures at 87.50

September 25 Sell the DEC Eurodollar futures at 88.14Buy 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$

TTM Futures contract Futures Yield (%)

Futures quotation

3 month JUN 12.00 88.00

6 month SEP 12.50 87.50

9 month DEC 13.50 86.50

29

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.

.Date Futures Market

Feb 17 Sell 1 DEC Eurodollar futures at 90.29Buy 1 DEC T-bill Futures at 91.18

Oct 14 Buy 1 DEC Eurodollar futures at 89.91Sell 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

Hedging with interest rate futures

Date Cash Market Futures Market

Dec 15 Fund manager learns he will receive 970,000 in six month to invest in T-billMarket yield 12% is attractive and want to lock in yieldFace value of bill to purchase is 1 million

Buy T-bill futures to mature in six monthFutures prices = 1 Mil – (1 mil*(.12*(90/360))) = 970,000

June 15 Receive 970,000 to investMarket 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

Hedging with interest rate futures

Date Cash Market Futures 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

Date Cash Market Futures 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

DTM discount yield Face value discount Price A B C D        [B*(A/360)]*C C-D

90 18%

10,000,

00

45,000.

00

9550,

00

90 16%

10,000,

00

40,000.

00

9600,

00

90

185.0%

10,000,

00

46,250.

00

9537,

50

90

162.5%

10,000,

01

40,625.

04

9593,

76

33

Thank you

34