Description
This is a PPT explaining money market futures.

Part-05
Money Market Futures

Eurodollar Futures
• These contracts are traded in Chicago • The underlying interest rate is LIBOR • Each contract is for a Time Deposit with
– A principal of 1,000,000 USD – And 3M to maturity

ED Futures (Cont…)
• The quarterly cycle is March, June, September, and December • On the CME a total of 40 quarterly futures contracts spanning 10 years are listed at any point in time • In addition the four nearest serial months are also listed

Illustration
• Assume that we are on 25 June 2008
– The four serial months will be July, August, October and November 2008 – The other available months will be SEP 2008, DEC 2008,, March, June, September, and December of 2009-17, March 2018, and June 2018

ED Futures (Cont…)
• Contracts expire at 11:00 a.m. London Time
– On the second London bank business day before the third Wednesday of the contract month – The contracts are cash settled to the BBA 3-M LIBOR

• Prices are quoted in terms of an IMM index for Eurodollars and implies an interest rate

ED Futures (Cont…)
• Quoted ED Futures Price = 100.00 – Implicit Interest Rate • The implicit rate is an actual or add-on interest rate and not a discount rate like in the case of T-bills

Illustration
• A discount rate of 5% means that for a 90 day loan with a maturity value of $1,000,000 the initial investment is 1,000,000[1 – 0.05x90/360] = $987,500 • The actual rate of return is (1,000,000-987,500)/987,500 x 360/90 = 5.06%

Illustration (Cont…)
• An add-on interest rate of 5% per annum means that if $1MM is invested for 90 days, the investor will get 1,000,000[1+0.05x90/360] = $1,012,500 after 90 days

Profits on ED Futures
• Assume that the futures price is 96
– The implicit interest rate is 4% per annum – Or 1% per quarter

• The implied quarterly interest payment on a time deposit of $1MM is
– .01x1,000,000 = $10,000

• If the price were to fall to $95 at the end of the day then it would represent a quarterly interest payment of $12,500 on a deposit of $1MM

Profits (Cont…)
• Take the case of an investor who goes long at $96
– He is obviously agreeing to lend at 1% per quarter

• The logic is the same as for contracts on other debt securities such as T-bills
– A long position means that you are willing to buy the debt security – In the case of ED futures, a long position means that you are willing to make a time deposit of 3-M – In either case you are a lender

Profits (Cont…)
• If interest rates were to rise to 5%, that is the futures price falls to 95, the long will lose $2,500 while marking to market
– Because when the contract is MTM it is as if he is offsetting by going short – In this case it would mean that he is agreeing to borrow at 1.25% per quarter

• So when interest rates rise the longs will lose • When rates fall the shorts will lose

Logic
• Now we can appreciate the logic of quoting prices in terms of an index and not in terms of an interest rate • What if prices were to be quoted in terms of rates?
– Longs would gain when prices fall – Shorts would gain when prices rise

• In all other futures market however it is just the opposite

Logic (Cont…)
• So to make money market futures consistent with other futures markets
– We quote prices in terms of an index and not a rate – When the index rises the longs will gain – When it falls the shorts will gain

• A second reason for quoting prices in terms of an index is to ensure that the bid is lower than the ask

Logic (Cont…)
• For an investor, the borrowing rate will be higher than the lending rate
– The rate underlying a short position is higher than the rate underlying a long position – If we quote the prices in terms of an index the bid will obviously be lower than the ask

Calculations
• Assume that the futures price changes from F0 to F1 • The profit for a long is as given below

Calculations (Cont…)

Minimum Price Move

Bundles and Packs
• A bundle entails the simultaneous purchase or sale of one each of a consecutive series of ED contracts
– The first contract of the bundle is normally the first quarterly contract available – Thus a 3 year bundle will consist of the first 12 ED contracts – On the CME 1, 2, 3, 5, 7, 10 year bundles are available

Bundles and Packs (Cont…)
• There is also a five year forward bundle
– Consist of 20 ED contracts starting from the first quarterly contract of year 6

• Packs also involve the purchase or sale of an equal number of consecutive ED futures
– But the number of contracts in a pack is fixed at 4

• Assume that today is 1 March 2008
– The 2-year pack will consist of one each of MAR, JUN, SEP, DEC contracts of 2009

Locking in a Borrowing Rate
• Today is 15 July 2009 • Ranbaxy is planning to borrow $1MM on 14 September for 90 days • The company can borrow at LIBOR • SEP 14 is the last day of trading for September futures • The company is worried that rates may rise by then

Locking…(Cont…)
• The current futures price is 94 • The current LIBOR for a 90-day loan is 5.85% • The company requires a short hedge since it is going to borrow • Assume that the firm goes short in one futures contract
– We will consider two different scenarios for September 14

Case A LIBOR = 4%
• The interest payable on a loan of $1MM is: 0.04x1,000,000x90/360 = $10,000 • Gain/Loss from the futures market is:
1,000,000x(F0-F1)/100x90/360 = 1,000,000x(94-96)/100x90/360 = (5,000)

• Effective interest paid is: 10,000+5,000 = $15,000

Case B LIBOR = 7%
• The interest payable is:
0.07x1,000,000x90/360 = $17,500

• Profit/loss 1,000,000x(94-93)/100x90/360 = $2,500 • The effective interest paid is 17,500 – 2,500 = $15,000

Locking…(Cont…)
• The company can lock in a payable of $15,000 irrespective of the prevailing LIBOR • This corresponds to a rate of: 15,000/1,000,000 x 360/90 = 6% this is the rate implicit in the initial futures price of 94

Important Issue
• Since the ED contract is cash settled the profit/loss from the futures contract will be received on September 14 when the contract expires • But the interest on the loan has to be paid only 90 days hence • Thus a futures profit can be re-invested for 90 days • On the other hand a futures loss would have to be financed

Important Issue (Cont…)
• If adjustments are made for the interest on such profits/losses • The effective interest paid
– Will be higher than 6% in Case A – And lower than 6% in Case B

• In our illustration we are ignoring such interest on profits/losses

Cash and Carry Arbitrage
• We are on 15 August 20XX • Futures contracts expiring on 18 September are priced at 94 • The 90 day ED deposit made on 18 September will mature on 17 December • The rate for an ED deposit between 15 August and 17 December is 6.75% • The rate for a loan between 15 August and 18 September is 4%

Cash and Carry (Cont…)
• Consider the following strategy • Borrow 1MM for 34 days
– 34 is the number of days between 15 Aug and 18 SEP

• Go short in a futures contract to borrow the maturity amount for a further period of 90 days • Invest the borrowed money in a 124 day deposit
– 124 is the number of days between 15 AUG and 17 DEC

Cash and Carry (Cont…)
• Amount due after 34 days is 1,000,000(1 + 0.04x34/360) • The futures contract will lock in a rate of 6% when this amount is rolled over for 90 days • The amount payable after 124 days will be:

Cash and Carry (Cont…)

Reverse Cash and Carry
• Assume that all the other variables have the same value except for the futures price which we will assume is 92 • Borrow 1MM for 124 days • Invest it for 34 days • Go long in a futures contract to rollover the maturity amount for a further 90 days

Reverse (Cont…)
• The amount repayable after 124 days is: 1,000,000x(1+0.0675x124/360) = 1,023,250 • The investment in a 34 day deposit will yield 1,000,000(1+.04x34/360) • The futures contract will lock in a rate of 8% for this amount • The amount receivable after 124 days is:

Reverse (Cont…)

No-Arbitrage Price
• We will derive a futures price that rules out both forms of arbitrage • We are standing on day t • The contract expires at T • The ED rate for a T-t day loan is s1 • The borrowing/lending rate for a T+90-t day loan is s2.

No Arbitrage Price (Cont…)

Hedging Rates for Periods Not Equal to 90 Days
• ED futures can be used to lock in a borrowing or a lending rate for a 90 day loan to be made on the expiration date of the contract • ED futures can also be used to lock in the rate for an N-day loan if N is close to 90 • The necessary condition is that the rate for an N-day loan should move closely with the rate for a 90-day loan

The Hedge Ratio

The Hedge Ratio (Cont…)

Illustration
• Assume that we are on 15 July 2009 • Ranbaxy will borrow 10MM on 14 September for 117 days • September futures price is 95.75 • The firm can borrow at the prevailing LIBOR on 14 September

Illustration
• Obviously Ranbaxy requires a short position • The hedge ratio is: Qf = 10x117/90 = 13

LIBOR = 4%
• Actual interest paid: 0.04x10,000,000x117/360 = $130,000 • Futures profit/loss is: 13x1,000,000x(95.75 -96)/100x90/360 = -8125 • So the effective interest paid is: 138,125

LIBOR = 4.5%
• Actual interest paid is: 0.045x10,000,000x117/360 = 146,250 • Profit/loss from the futures position is: 13x1,000,000x(95.75-95.50)/100x90/360 = 8125 • The effective interest paid is $138,125

Illustration (Cont…)
• Irrespective of the prevailing LIBOR on 14 September the company has locked in $138,125 • This corresponds to a rate i such that: 10,000,000[1+ix117/360] = 10,138,125 • i is equal to 4.25% which is the rate implicit in the initial futures price

Creating a Fixed Rate Loan
• YES Bank is able to borrow at LIBOR for 3-M at a time • Thus the interest payable is variable • It has a client who wishes to borrow at a fixed rate for 1 year • So the interest receivable is fixed • The bank would like to use futures contracts to mitigate the risk

Creating…(Cont…)
• ED futures can be used to hedge the funding risk • And to determine a suitable rate for the fixed rate loan • Assume that the borrower wants a loan for 100MM USD for a period of one year from 15 SEP 20XX at a fixed rate

Creating…(Cont…)
• • • • • The 90 day LIBOR on 15 September is 3.80% December contracts are available at 97.10 March contracts are available at 96.60 June contracts are available at 97 Assume that the rollover dates for the 3-M borrowings are the same as the expiration dates of the futures contracts for the respective months

Creating…(Cont…)
• Each contract is for $1MM • So the bank needs a short position in 100 each of
– December – March – And June contracts

Creating (Cont…)
• The interest expense for the first quarter is: 100,000,000x0.038x90/360 = $950,000 • There is no uncertainty about this for it is based on the current LIBOR • The short position in December futures will lock in a rate of 2.90% for a period of 90 days – from December to March • The corresponding interest expense is: 100,000,000x0.029x90/360 = $725,000

Creating (Cont…)
• The short position in March futures will lock in: 100,000,000x0.034x90/360 = $850,000 for a 90 day period from March • The June contracts will lock in: 100,000,000x0.03x90/360 = $750,000

Creating…(Cont…)
• The total interest payable for the 12-M period is:
950,000 + 725,000 + 850,000 + 750,000 = 3,275,000

• This corresponds to an annualized rate of:
3,275,000/100,000,000 x 100 = 3.275%

• The bank can now quote a fixed rate based on this effective cost of funding after factoring in
– Hedging costs – And a suitable profit margin

Stack and Strip Hedges
• We assumed that that the bank would hedge using 100 contracts for each of the expiration months • A hedge where the same number of contracts are used for each expiration month right from the outset is called a STRIP Hedge • However if the maturity of a contract is far away it may not be liquid

Stack…(Cont…)
• Illiquidity could be a deterrent for a hedger
– He would seek to enter and exit at a price close to the true or the fair value of the asset

• It is conceivable that in September when the hedge is initiated the June contract may not be liquid • So the bank may initiate the hedge with an unequal number of December and March contracts without taking a position in the June contract

Stack…(Cont…)
• When the December contracts expire it will take a position in the June contract • A hedge where the number of contracts for each maturity is not equal at the outset is called a STACK Hedge

Illustration
• Assume that June contracts are illiquid in September • The bank therefore hedges using 100 December contracts and 200 March contracts • The December contracts will lock in a rate for the planned borrowing in December • 100 of the March contracts will lock in a rate for March • The remaining are for hedging the June exposure

Illustration (Cont…)
• On 15 December the bank will partially offset its March position and go short in 100 June contracts
– The assumption is that June contracts would have begun to be actively traded by December

• Which is better – STRIP or STACK?
– It would depend on the movement of rates between September and December

Case-A: The Two are Equivalent
• Assume that the price of the March contract moves from 96.6 to 96 between September and December • While the price of the June contract moves from 97 to 96.40 • When the 100 extra March contracts are offset in December the profit will be:
100,000,000x(96.60-96)/100x90/360 = $150,000

Case-A (Cont…)
• The 100 June contracts will lock in 100,000,000x0.036x90/360 = $900,000 • The effective interest expense for the last quarter is: 900,000 – 150,000 = 750,000 • This is exactly what was locked in by the STRIP Hedge

Conclusion
• If the 3-M ED rate as contained in the March futures price, changes by the same magnitude and direction as the yield contained in the June futures price
– Then STRIP and STACK hedges will be equivalent

• Technically speaking, if there is a parallel shift in the yield curve, the two will be equivalent

Case-B: The Strip Outperforms
• If the increase in the March yield is less than the increase in the June yield then the STRIP hedge will outperform • Assume that the March price moves from 96.6 to 96 • While the June price moves from 97 to 96.20

Case-B (Cont…)
• The profit when the 100 March contracts are offset is $150,000 • The interest expense for the last quarter is: 100,000,000x0.038x90/360 = $950,000 • The effective interest for the last quarter is $800,000 • This is greater than the $750,000 locked in by the STRIP hedge

Case –B (Cont…)
• The same would be true if the decline in the March yield is more than the decline in the June yield • Assume that the March price moves from 96.60 to 96.90 while the June price moves from 97 to 97.10 • The profit from the March position is: 100,000,000x(96.60-96.90)/100x90/360 = (75,000)

Case-B (Cont…)
• The interest expense for the last quarter is:
100,000,000x0.029x90/360 = 725,000

• The effective interest is $800,000 • Which is greater than what was locked in by the STRIP hedge

Case-C: The Stack Outperforms
• In the increase in the March yield is more than the increase in the June yield, the STACK will outperform • Assume that the March price moves from 96.60 to 96 • And the June price moves from 97 to 96.60 • The effective interest for the last quarter is: 100,000,000x0.034x90/360 – 150,000 = 850,000 – 150,000 = $700,000

Case-C (Cont…)
• The same would be true if the decrease in the March yield is less than the decrease in the June yield • Assume that the March futures price moves from 96.6 to 96.9 • While the June price moves from 97 to 97.5 • The loss from the March position is $75,000

Case-C (Cont…)
• The interest expense for the last quarter is: 100,000,000x0.025x90/360 = $625,000 • The effective interest paid i: 625,000 + 75,000 = $700,000

LIBOR Futures
• The underlying asset is a time deposit with a principal of $3MM and one month to maturity • The contracts expire at 11:00 a.m. London time on the second bank business day before the third Wednesday of the contract month • At any point in time, contracts for the next 12 consecutive months are listed • So on 25 June 2008: July -08 to June -09 will be available • All contracts are cash settled

Euroyen Futures
• The underlying asset is a time deposit with a principal of $100MM JPY and three months to maturity • The contract settles to TIBOR and is cash settled • At any point 20 contracts are listed from the March quarterly cycle • So on 2 January 2009 the available months will be: March, June, September and December of 2009-2013

Euroyen LIBOR Futures
• The underlying asset is the same as that for Euroyen futures and the available contract months are identical • However the contract settles to LIBOR

T-bill Futures
• The underling asset is a 13-week (91 day) T-bill with a face value of $1MM • The contract cash settles into the auction rate on the business day of the weekly 91-day T-bill auction in the week of the third Wednesday of the contract month • At any point four months from the March cycle plus two serial months are listed • So on 25 June 2008: July 08, August 08, September 08, December 08, March 09, and June 09 will be listed

T-bill Futures (Cont…)
• The auction is conducted on a Monday for a bill to be issued on a Thursday • The rate that is set at the auction is the forward rate for a 91-day bill • There is an auction of a 13-week bill every week • So there will be a bill maturing 3 days after the auction and a bill maturing 94 days after the auction

Creating a Synthetic 91-day Forward Bill
• Assume that we are at t • Contract expires at T • There is a bill maturing at T+3
– Call this the SHORT Bill

• There is a bill maturing at T+94
– Call this the LONG Bill

• s1 is the rate of return on the short bill and s2 is the rate of return on the long bill
– These are not annualized rates

Creating…(Cont…)
• The 91 day forward rate is f1,2 • To rule out arbitrage (1+s1)(1+f1,2) = (1+s2) • That is:
(1+f1,2) = (1+s2)/(1+s1)

• Let P(t,T+3) be the price of a short bill with a face value of $1 • P(t,T+94) is the price of a long bill with a face value of $1

Creating…(Cont…)
• • • • P(t,T+3) = 1/(1+s1) P(t,T+94) = 1/(1+s2) So 1/(1+f1,2) = P(t,T+94)/P(t,T+3) To preclude arbitrage the forward bill implicit in the futures contract should track the price of this synthetic forward bill

No-arbitrage
• The quoted T-bill futures price is: Price = 100.00 – Implicit T-bill Yield • The implicit yield is a discount yield • And is based on a 360 day year • Let the futures price be F. The invoice price is: 1,000,000 – 1,000,000x(100-F)/100x91/360

No-arbitrage (Cont…)
• Let the discount rate for the short bill be d1 • And the rate for the long bill be d2 • To rule out arbitrage, we require that:

No-arbitrage (Cont…)

Illustration
• • • • • • • A futures contract has 14 days to expiration The short bill has 17 days to maturity The long bill has 108 days to maturity The quoted rate for the short bill is 4% The quoted rate for the long bill is 5% The price of the short bill ($1 FV) is 0.9981 The price of the long bill ($1 FV) is 0.9850

Illustration (Cont…)

The TED Spread
• It is a spread using both T-bill futures and ED futures • To set it up the investor needs to hold opposite positions in the two contracts but with the same expiration month • To go long in the TED spread he requires
– A long position in T-bill futures – And a short position in ED futures

• To go short in the spread he requires
– A short position in T-bill futures – And a long position in ED futures

TED Spread (Cont…)
• The TED Spread = T-bill Futures Price – ED Futures Price = (100-Implied T-bill rate) – (100-Implied ED rate) = Implied ED rate – Implied T-bill rate

Speculation
• A speculator expects the spread between the two rates to widen • He can operationalize his view by going long in the TED spread • If he is right and the spread does indeed widen, he will make a profit

Illustration
• On 15 July 2009 the September T-bill contract is priced at 96.70 • The September ED contract is priced at 96.10 • The TED spread is 96.70 – 96.10 = 0.60 • On 1 September T-bill futures are at 96.80 while ED futures are at 96 • The TED spread is 96.80 – 96 = 0.80

Illustration (Cont…)
• The profit from the T-bill position is: 1,000,000x(96.80-96.70)/100x90/360 = $250 • The profit from the ED position is: 1,000,000x(96.10-96)/100x90/360 = $250 • The total profit is $500 • This represents a widening of 20b.p in the spread 1,000,000x.20/100x90/360 = $500

Speculation (Cont…)
• If a person expects the spread to narrow he can go short in the spread • Assume that on 1 September T-bill futures are at 96.80 while ED futures are at 96.35 • The spread is therefore 0.45 • If an investor goes short in the spread: the profit from the T-bill futures is 1,000,000x(96.7-96.8)/100x90/360 = (250)

Speculation (Cont…)
• The profit from the ED position is: 1,000,000x(96.35-96.10)/100x90/360 = 625 • The total profit is $375 which represents a narrowing of 15 basis points

Fed Funds Futures
• The underlying asset is Federal Funds with a value of $5MM • Prices are quoted as 100 – overnight Fed Funds rate • At any time contracts are available for the next 24 consecutive months. • The contracts are cash settled



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