Currency and interest rate futures
Download
1 / 64

CURRENCY AND INTEREST RATE FUTURES - PowerPoint PPT Presentation


  • 67 Views
  • Uploaded on

CURRENCY AND INTEREST RATE FUTURES. CURRENCY FUTURES.

loader
I am the owner, or an agent authorized to act on behalf of the owner, of the copyrighted work described.
capcha
Download Presentation

PowerPoint Slideshow about ' CURRENCY AND INTEREST RATE FUTURES' - reid


An Image/Link below is provided (as is) to download presentation

Download Policy: Content on the Website is provided to you AS IS for your information and personal use and may not be sold / licensed / shared on other websites without getting consent from its author.While downloading, if for some reason you are not able to download a presentation, the publisher may have deleted the file from their server.


- - - - - - - - - - - - - - - - - - - - - - - - - - E N D - - - - - - - - - - - - - - - - - - - - - - - - - -
Presentation Transcript

Currency futures
CURRENCY FUTURES

  • A futures contract, like a forward contract is an agreement between two parties to exchange one asset for another, at a specified date in the future, at a rate of exchange specified up front. However, there are a number of significant differences.

  • Major Features of Futures Contracts

  • Organized Exchanges not OTC markets.

  • Standardization : Amount of asset, expiry dates,

  • deliverable grades etc.

  • Clearing House: A party to all contracts. Guarantees

  • performance. Mitigates/Eliminates Credit Risk

  • Daily mark-to-market and a system of margins.

  • Actual delivery is rare.


Foreign Currency Futures

  • Contract specifications are established by the exchange on which futures are traded.

  • Major features that are standardized are:

    • Contract size

    • Method of stating exchange rates

    • Maturity date

    • Last trading day

    • Collateral and maintenance margins

    • Settlement

    • Commissions

    • Use of a clearinghouse as a counterparty


FUTURES CONTRACTS

  • Global Futures Exchanges:

  • 1) IMM: International Monetary Market

  • 2) LIFFE: London International Financial Futures Exchange

  • 3) CBOT: Chicago Board of Trade

  • 4) SIMEX: Singapore International

  • Monetary Exchange

  • 5) DTB: Deutsche Termin Bourse

  • 6) HKFE: Hong Kong Futures Exchange


FUTURES CONTRACTS

  • B. Forward vs. Futures Contracts

  • Basic differences:

  • 1) Trading Locations

  • 2) Regulation

  • 3) Frequency of delivery

  • 4) Size of contract

  • 5) Transaction Costs

  • 6) Quotes

  • 7) Margins

  • 8) Credit Risk


Comparison of the Forward & Futures Markets

Forward MarketsFutures Markets

Contract size Customized Standardized

Delivery date Customized Standardized

Participants Banks, brokers, Banks, brokers,

MNCs. Public MNCs. Qualified

speculation not public speculation

encouraged. encouraged.

Security Compensating Small security

deposit bank balances or deposit required.

credit lines needed.

Clearing Handled by Handled by

operation individual banks exchange

& brokers. clearinghouse.

Daily settlements

to market prices.


Comparison of the Forward & Futures Markets

Forward MarketsFutures Markets

Marketplace Worldwide Central exchange

telephone floor with worldwide

network communications.

Regulation Self-regulating Commodity

Futures Trading

Commission,

National Futures

Association.

Liquidation Mostly settled by Mostly settled by

actual delivery. offset.

Transaction Bank’s bid/ask Negotiated

Costs spread. brokerage fees.


FUTURES CONTRACTS

  • Advantages of Futures:

  • 1) Easy liquidation

  • 2) Well- organized and

  • stable market.

  • 3) No credit risk

  • Disadvantages of Futures:

  • 1) Limited to a few

  • currencies

  • 2) Limited dates of

  • delivery

  • 3) Rigid contract sizes


FUTURES CONTRACTS ON IMM

  • Available Futures Currencies/Contract Size:

  • 1) British pound / 62,500

  • 2) Canadian dollar /100,000

  • 3) Euro / 125,000

  • 4) Swiss franc / 125,000

  • 5) Japanese yen / 12.5 million

  • 6) Mexican peso / 500,000

  • 7) Australian dollar / 100,000


Exchange traded currency futures were launched in India on August 29, 2008. As of now only USD-INR contracts have been permitted with contract size of USD 1000 with monthly maturities upto twelve months. The contracts will be cash settled in INR. Contracts will expire on the last working day of the month. Quotations will be given in rupee terms.

Unlike OTC forwards, no underlying exposure is required to trade in USD-INR futures. Individuals can also trade for purely speculative purposes.

Margins will be calculated using a VAR framework.

Contracts have started trading on NSE. Eventually, they will also be traded on MCX and BSE. Contracts between INR and other currencies will be introduced later based on perception of market interest.


FUTURES CONTRACTS August 29, 2008. As of now only USD-INR contracts have been permitted with contract size of USD 1000 with monthly maturities upto twelve months. The contracts will be cash settled in INR. Contracts will expire on the last working day of the month. Quotations will be given in rupee terms.

  • Transaction costs:

  • Commission payment to a floor trader; Brokerage, Bid-Offer Spreads

  • Leverage is high

  • Initial margin required is relatively low (less than 2% of contract value).


FUTURES CONTRACTS: SAFEGUARDS August 29, 2008. As of now only USD-INR contracts have been permitted with contract size of USD 1000 with monthly maturities upto twelve months. The contracts will be cash settled in INR. Contracts will expire on the last working day of the month. Quotations will be given in rupee terms.

  • Maximum price movements

  • 1) Contracts set to a daily price limit restricting maximum daily price movements.

  • 2) If limit is reached, a margin call may be necessary to maintain a minimum margin.


  • System of Margins August 29, 2008. As of now only USD-INR contracts have been permitted with contract size of USD 1000 with monthly maturities upto twelve months. The contracts will be cash settled in INR. Contracts will expire on the last working day of the month. Quotations will be given in rupee terms.

  • Initial margin: When position is opened

  • Variation Margin: Settlement of daily gains and losses

  • Maintenance Margin : Minimum balance in margin account. Balance falls below this, margin call issued. If not met, position liquidated.

  • Regulators specify minimum margins between clearing members and clearinghouse. Margins at other levels negotiated

  • Margins can be deposited in cash or specified securities such as T-bills. Interest on securities continues to accrue to owner. Margin is a performance bond.

  • Levels of margins may be changed if volatility increases.


  • System of Margins August 29, 2008. As of now only USD-INR contracts have been permitted with contract size of USD 1000 with monthly maturities upto twelve months. The contracts will be cash settled in INR. Contracts will expire on the last working day of the month. Quotations will be given in rupee terms.

  • With clearing house guarantee, buyer-seller need not worry about each other’s creditworthiness.

  • Standardized contracts with margin system increase liquidity.

  • Protects clearing house; enhances financial integrity of the exchange. Credit risk issues almost eliminated


CLEARING HOUSE August 29, 2008. As of now only USD-INR contracts have been permitted with contract size of USD 1000 with monthly maturities upto twelve months. The contracts will be cash settled in INR. Contracts will expire on the last working day of the month. Quotations will be given in rupee terms.

CLEARING MEMBER A

CLEARING MEMBER B

NON-CLEARING MEMBER

CUSTOMER

CUSTOMER

NON-CLEARING MEMBER

CUSTOMER

CUSTOMER


TYPES OF ORDERS IN FUTURES MARKETS August 29, 2008. As of now only USD-INR contracts have been permitted with contract size of USD 1000 with monthly maturities upto twelve months. The contracts will be cash settled in INR. Contracts will expire on the last working day of the month. Quotations will be given in rupee terms.

Market Orders : Execute at best available price

Limit Orders: Sell above or buy below stated limits

Market If Touched or MIT Orders: Become market orders

if price touches a trigger

Stop-Loss Orders : Sell if price falls below a limit; buy if it rises

above a limit. Used to limit losses on existing positions

Stop Limit Orders : Stop loss plus limit

Time of Day Orders, Day Orders, Good Till Canceled(GTC)

Orders

Participants : Brokers, Floor Traders, Dual Traders, Futures

Commission Merchants. Hedgers and speculators

both participate.


Currency Futures Contract Specifications August 29, 2008. As of now only USD-INR contracts have been permitted with contract size of USD 1000 with monthly maturities upto twelve months. The contracts will be cash settled in INR. Contracts will expire on the last working day of the month. Quotations will be given in rupee terms.

Exchange: IMM at Chicago Mercantile Exchange(CME)

British Pound Japan Yen

Size: £625000 ¥12,500,000

"Tick": $ 0002 per £ $0.000001 per ¥

(Per Contract) ($12.50) ($12.50)

Expiry Months: January, March, April, June, July, September, October, December, & Spot Month (Both GBP and JPY)

Limit: NO LIMIT FOR THE FIRST 15 MINUTES OF TRADING. A schedule of expanding price limits will be in effect when the 15-minute period is ended. (Both GBP and JPY)

“Tick” : Minimum size of price movement.


PRICE QUOTES OCTOBER 1, 2009 August 29, 2008. As of now only USD-INR contracts have been permitted with contract size of USD 1000 with monthly maturities upto twelve months. The contracts will be cash settled in INR. Contracts will expire on the last working day of the month. Quotations will be given in rupee terms.

JAPANESE YEN (CME)

USD PER 100 JPY

ContractOpen High Low Settle Chg Op Int

Dec 09 1.1153 1.1189 1.1095 1.1146 -.0016 117663

Mar 10 1.1140 1.1194 1.1109 1.1153 -.0017 107

Jun 10 1.1120 1.1185 1.1120 1.1167 -.0018 9

SOURCE : WALL STREET JOURNAL


OCTOBER 1, 2009 August 29, 2008. As of now only USD-INR contracts have been permitted with contract size of USD 1000 with monthly maturities upto twelve months. The contracts will be cash settled in INR. Contracts will expire on the last working day of the month. Quotations will be given in rupee terms.

BRITISH POUND (CME)

Contract Open High Low Settle Chg Op Int

Dec 09 1.6005 1.6024 1.5920 1.5946 -.0056 102389

Mar 10 1.5992 1.6009 1.5923 1.5945 -.0056 97

SOURCE : WALL STREET JOURNAL


OCTOBER 1, 2009 August 29, 2008. As of now only USD-INR contracts have been permitted with contract size of USD 1000 with monthly maturities upto twelve months. The contracts will be cash settled in INR. Contracts will expire on the last working day of the month. Quotations will be given in rupee terms.

SWISS FRANC (CME)

ContractOpen High Low Settle Chg OP INT

Dec 09 0.9658 0.9678 0.9571 0.9608 -.0052 45156

SOURCE : WALL STREET JOURNAL


USD/INR CONTRACT TRADED ON MCX-SX August 29, 2008. As of now only USD-INR contracts have been permitted with contract size of USD 1000 with monthly maturities upto twelve months. The contracts will be cash settled in INR. Contracts will expire on the last working day of the month. Quotations will be given in rupee terms.

OCTOBER 1, 2009 QUOTES

CONTRACT OPEN HIGH LOW CLOSE OP.INT NOTIONAL

VALUE

OCT 09 47.90 47.99 47.78 47.86 300000 522288.06

NOV 09 48.03 48.10 47.89 47.96 95700 139438.45

DEC 09 48.11 48.18 47.99 48.05 4800 1482.95

JAN 10 48.19 48.19 48.10 48.10 2000 15.01

CONTRACT SIZE : USD 1000 TICK SIZE : Rs.0.25

NOTIONAL VALUE: VALUE OF CONTRACTS TRADED RS.LAKH

EXPIRY DATE: 2 BUSINESS DAYS BEFORE THE LAST WORKING DAY

OF THE CONTRACT MONTH

Source: BUSINESS STANDARD


MCX-SX USD/INR FUTURES, November 25, 2008 August 29, 2008. As of now only USD-INR contracts have been permitted with contract size of USD 1000 with monthly maturities upto twelve months. The contracts will be cash settled in INR. Contracts will expire on the last working day of the month. Quotations will be given in rupee terms.

The MCX-SX INR December futures opened stronger and made a high of 49.96 on the back of overnight strength seen in US markets coupled with strong Asian markets in the morning. US rescue package of around $306 billion to Citigroup saw support being provided to stock markets.

One-month offshore Non-Deliverable Forward contracts were quoting at 50.62/77, weaker than the onshore spot rate, indicating the outlook for the currency continues to be bearish in the near term.

MCX-SX INR December futures towards the end of the session closed towards 50.33. Supports are at 50 followed by 49.7, while the resistances are seen around 50.60 followed by 50.95 levels.MCX-SX INR January futures closed towards 50.52 and registered a volume of 13.02cr and the open interest increased by 52.03% from the previous session.


Mumbai, Dec 2 The December futures contract today ended higher at 50.43 on the currency derivatives segment of the MCX Stock Exchange (MCX-SX).

The December contract resumed lower due to sharp losses seen in Asian stock markets. Looses in the market would see more outflows of funds, which would continue to pressure rupee in the near term.

RBI intervention was seen around 50.50 to arrest the rupee fall. But the inflows into the system are very less compared to outflows by the FIIs. Foreign fund outflows have been a key factor for the rupee's decline this year, which is 22 per cent down.

One-month offshore Non-Deliverable Forward contracts were quoting at 51.35/50, weaker than the onshore spot rate, indicating a bearish outlook for the currency.

Supports for December contract are at 50.15 followed by 4990, while the resistance are seen around 50.95 followed by 5120 levels and January futures closed towards 50.65 and registered a volume of 96.385 crore

Spot rupee closed stronger during the session. Supports hold between 49.55/65 followed by crucial support at 49.10, Resistance are around 50.90 followed by 5130 levels

The MCX-SX active December contract registered volume increase of around 21.16 per cent over the previous session.


  • FUTURES PRICES, SPOT PRICES AND EXPECTED SPOT PRICES higher at 50.43 on the currency derivatives segment of the MCX Stock Exchange (MCX-SX).

  • Basis = (Spot Price – Futures Price)

  • Normal Backwardation : Hedgers net short. Speculators must be net long; they would do so if they expect futures price to rise. Futures price rises as maturity approaches.

  • Contango : Hedgers net long. Speculators net short. Futures price expected to fall as maturity approaches

  • Net Hedging Hypothesis

  • Risk Aversion and behaviour of futures prices

  • Futures Price = Expected Spot Price ?


Backwardation higher at 50.43 on the currency derivatives segment of the MCX Stock Exchange (MCX-SX).

Contango

EXPECTED SPOT PRICE

FUTURES PRICE

FUTURES PRICE

Expiry

Expiry

Time

Time


  • FUTURES PRICES AND FORWARD PRICES higher at 50.43 on the currency derivatives segment of the MCX Stock Exchange (MCX-SX).

  • DETERMINISTIC INTEREST RATES: FUTURES PRICES EQUAL FORWARD PRICES

  • STOCHASTIC INTEREST RATES : FUTURES PRICES DIFFER FROM SPOT PRICES DUE TO DAILY GAINS AND LOSSES

  • SPOT PRICE AND INTEREST RATE POSITIVELY CORRELATED: FUTURS PRICE EXCEEDS FORWARD PRICE

  • NEGATIVE CORRELATION: FUTURES PRICE LESS THAN FORWARD PRICE


  • FUTURES PRICE AND SPOT PRICE higher at 50.43 on the currency derivatives segment of the MCX Stock Exchange (MCX-SX).

  • CASH-AND -CARRY ARBITRAGE

  • Spot Price of a dollar : Rs.44.00

  • 3-month Futures Price : 45.75

  • Rupee interest rate : 6% p.a.

  • Dollar interest rate : 4% p.a.

  • Borrow rupees, buy dollars and deposit, sell futures.

  • 3 months later, deliver, get rupees, repay loan.


Suppose contract size is $50000. higher at 50.43 on the currency derivatives segment of the MCX Stock Exchange (MCX-SX).

Must deposit $(50000)/(1.01) = $49504.95

Must borrow Rs.(49504.95)(44.0) = Rs.2178217.82

Must repay (2178217.82)(1.015) = 2210891.09

On expiry, liquidate deposit, deliver on futures collect Rs.2275000. Net profit: 64108.91

Futures Price “too high” : Buy asset in spot market, store, pay storage cost, sell futures, deliver at expiry.

Futures Price too low (e.g.44.60)

Reverse cash-and- carry arbitrage. Borrow dollars, convert to rupees and deposit, buy futures. Take delivery at expiry and repay dollar loan. Nothing but Covered Interest Arbitrage


Arbitrage and Theoretical Futures Price higher at 50.43 on the currency derivatives segment of the MCX Stock Exchange (MCX-SX).

Let C denote the present value of carrying costs, St the spot price, r the interest rate, and FUt,T the futures price for delivery at T, Then theoretical futures price is given by

FUt,T = (St + C)[1 + r(T-t)]

Actual futures price higher : cash-and-carry arbitrage

Actual futures price lower: reverse cash-and-carry arbitrage

For currency futures, futures prices are almost identical to forward prices.

A similar relation will hold between FUt,T1 and Fut,T2, T2>T1>t


In practice futures price does not exactly equal theoretical futures price. Reasons:

1 Transaction costs – bid-offer spreads, brokerage

2 In some cases, restrictions on short sales (Does not apply to currency futures)

3 Non-constant interest rates

4 Mark-to-market gains/losses.

5 “Convenience yield” (Commodity futures)

A band of variation around theoretical price.


  • Hedging with Currency Futures futures price. Reasons:

  • A corporation has an asset e.g. a receivable in a currency A.

  • To hedge it should take a futures position such that futures generate a positive cash flow whenever the asset declines in value.

  • The firm is longin the underlying asset, it should go short in futures i.e. it should sell futures contracts on A against its home currency.

  • When the firm is short in the undelying asset – a payable in currency A – it should go long in futures.

  • Cash Position: Receive A; Futures Position: Deliver A

  • Cash Position: Deliver A; Futures Position: Receive A

  • If no futures between A and HC, use futures between A and a currency closely correlated with HC.


Futures Hedge : An Example futures price. Reasons:

January 30. A UK firm has $250000 payable due on August 1.

£/$ spot:1.7550.

GBP Futures: September: 1.7125 December: 1.6875

Decides to hedge with September futures. GBP value of USD payable at futures price:

(250000/1.7125) = £145985.40.

Each GBP futures contract is for £62500.

Sells (145985.40/62500) = 2.3357 rounded off to 2 contracts.

Could be rounded off to 3 contracts.


On July 30 the rates are: futures price. Reasons:

July 30: £/$ spot: 1.6850 September futures: 1.6750

Firm buys USD spot. It has to pay

GBP(250000/1.6850) = £148367.95

Compared to the GBP value of payable at the spot rate at start this represents a loss of GBP 5917.81.

Buys 2 September futures contracts at $1.6750 to close out the futures position.

Gain on futures : $(1.7125-1.6750)(2)(62500) = £4687.50.

Not a perfect hedge. Basis narrowed.


  • Futures Hedge : Example (contd) futures price. Reasons:

  • Choice of contract underlying was obvious.

  • Firm chose a contract expiring immediately after the payable was to be settled. Is this necessarily the right choice?

  • The number of contracts chosen was such that value of futures position equaled the value of cash market exposure, aside from the unavoidable discrepancy due to standard size of futures contracts. Is this the optimal choice?

  • Futures hedge involves three considerations: Underlying, expiry date of the contract, number of contracts. The latter two problems do not arise with forwards. Why?


Three Decisions futures price. Reasons:

(1) Which contract should be used i.e. the choice of "underlying".

Home currency A; exposure in B; futures on B against A

available – Direct hedge.

Home currency A; exposure in C; no futures on C against

A. B and C are highly correlated; use futures on B – Cross

Hedge

(2) Choice of expiry date : In February A UK firm books a USD payable maturing on June 3. To hedge, must sell GBP futures (Buy USD futures). Which month? June or later?

(3) How many contracts? Choice of “hedge ratio”.

Value of futures position = Value of underlying exposure?


Choice of expiry date: As expiry date approaches, basis narrows. On expiry date futures price equals spot price. This is known as “Convergence”.

Does convergence help you or hurt you?

If convergence helps, choose near contract

If convergence hurts, choose far contract.

However, liquidity less in far contracts; bid-offer spreads are higher; basis volatility more.

Thumb rule followed by practitioners: Choose expiry date immediately after underlying exposure is to be settled.


Choice of Expiry Date narrows. On expiry date futures price equals spot price. This is known as “Convergence”.

Basis at the start

Positive Negative

Nature of hedge

Long F A

Short A F

Long Hedge: You must take delivery of underlying in your futures position. You have bought futures contracts.

Short Hedge : You must make delivery of underlying in your futures position. You have sold futures.

F: Convergence favours you. A: Convergence against you.

Positive Basis: Spot price > Futures Price


  • Choosing the Number of Contracts narrows. On expiry date futures price equals spot price. This is known as “Convergence”.

  • A Swiss firm has a USD payable of $500,000, maturing November 15.

  • It decides to sell December contracts priced at $0.74/CHF.

  • At this price, the CHF equivalent of $500,000 is CHF 675675.68.

  • Since one CHF contract is for CHF 125,000, it should sell : (675675.68/125000) = 5.4054 rounded off to 5 or 6 contracts.

  • Sounds logical but is it necessarily correct?

  • What is the objective of hedging?

  • To minimize the variance of the hedged position?

  • Define the "Hedge Ratio"(HR) as : VF/VH

  • = (Value of futures position/Value of cash position)

  • Should HR = 1.0 always?


  • Direct Hedge with a Timing Mismatch narrows. On expiry date futures price equals spot price. This is known as “Convergence”.

  • Choosing Hedge Ratio

  • A Swiss firm on February 28 has a USD 500,000 payable to be settled on July 1.

  • Cash market position short USD. Must buy USD futures or short CHF futures.

  • It chooses to hedge by selling September CHF contracts. This contract matures on September 18.

  • The spot rate is USD/CHF1.3335 or CHF/USD 0.7499

  • September futures price is USD/CHF 1.4518 or CHF/USD 0.6888

  • Each CHF contract is for CHF 125000.

  • Determine the number of contracts it should short.

  • .


Choosing Hedge Ratio narrows. On expiry date futures price equals spot price. This is known as “Convergence”. ….

VC : The value of the cash market position measured in the foreign currency.

St : The spot rate at the start stated as units of home currency(HC) per unit of foreign currency(FC).

T1 : The date when the cash position has to be settled.

T2 : The date when the futures contract expires, T2 > T1

VF : The value of the futures position measured in US dollars.

Ft,T2 : The price at time t of the futures contract maturing at T2 stated as units of HC per unit of FC.

In the example HC: CHF FC: USD

Vc = $500000 St = 1.3335 T1: July 1

T2: September 18 Ft,T2 = 1.4518


Choosing Hedge Ratio…. narrows. On expiry date futures price equals spot price. This is known as “Convergence”.

F~T1,T2 : The price of the same contract at time T1 (arandom variable)

 S~T1: The spot rate at time T1 when the hedge is lifted. Stated as units of HC per unit of FC. (Random variable)

The value of the hedged cash flow at time T1 is given by

V˜H,T1 = - VCS˜T1 + VF (Ft,T2 – F~T1,T2)

The variance of V˜H,T1is

(VC)22(S˜T1) + (VF)22(F˜T1T2)– 2VCVF COV(S˜T1 F~ T1,T2)

Let H = VF/VC be the hedge ratio


Then narrows. On expiry date futures price equals spot price. This is known as “Convergence”.

(VC)2 2(S˜T1) + (VF)22(F˜T1T2)– 2VCVF COV(S˜T1 F~T1,T2)

= (VC)2 [2(S˜T1)+ H2 2(F˜T1T2)– 2H COV(S˜T1 F~ T1,T2)]

To minimize this w.r.t. H

2 H 2(F˜T1T2)– 2 COV(S˜T1 F~T1,T2) = 0

This leads to

H = VF/VC = COV(S~T1, F~T1T2) / VAR(F~T1T2)

We need forward-looking estimates of these parameters.

Using past data estimate a regression equation:

S~T1 =  +  F~T1T2 + u

The estimate of  can be used as hedge ratio. But this would be a historical estimate.


  • Let us apply this result to the Swiss firm's case. narrows. On expiry date futures price equals spot price. This is known as “Convergence”.

  • Assume that we have somehow obtained estimates of the covariance of S˜T1 and F˜T1,T2 and the variance of F˜T1,T2.

  • Their ratio is 0.90.

  • Then the USD value of the futures position must be (500,0000.90) = USD 450,000.

  • At the futures price of $0.6888/CHF this translates into CHF 653310.10.

  • With each contract being CHF 125,000 this is equivalent to 5.23 contracts rounded off to 5 or 6 contracts.


The interest parity relation tells us that narrows. On expiry date futures price equals spot price. This is known as “Convergence”.

[1 + rB(T-t)]

Ft,T2(A/B) = St(A/B) ----------------- = k St(A/B)

[1 + rA(T-t)]

  [1 + rB(T-t)]

wherek = -----------------

[1 + rA(T-t)]

If the factor k remains constant, then

(FT1,T2-Ft,T2) = k(ST1 - St)

and a hedge ratio VF/VC = 1/k =  would give a perfect hedge.

But k does not remain constant. Optimal hedge ratio keeps changing


  • Dynamic hedging: As interest rates and spot rate keep changing, recalculate the optimal hedge ratio and rebalance the hedge by selling more futures or buying futures. How frequently?

  • Transaction costs must be considered. Any gain from frequent rebalancing must be weighed against increased transaction costs.

  • Large position, long duration of hedge, more frequent rebalancing warranted.

  • Standard-size problem cannot be circumvented.


  • SPECULATION WITH CURRENCY FUTURES changing, recalculate the optimal hedge ratio and rebalance the hedge by selling more futures or buying futures. How frequently?

  • Open Position Trading

  • In April Spot EUR/USD: 1.5750

  • June Futures : 1.5925

  • September Futures: 1.6225

  • You do not think EUR will rise. It will fall.

  • You do not think EUR will rise so much.

  • How to profit from this view? Sell September.


SPECULATION WITH CURRENCY FUTURES changing, recalculate the optimal hedge ratio and rebalance the hedge by selling more futures or buying futures. How frequently?

On September 10 the rates are :

Spot EUR/USD: 1.5940 September futures: 1.5950

Close out by buying a September contract.

Profit USD(1.6225-1.5950) per EUR on 125000 EUR

= USD 3437.50 minus brokerage etc.

First view was wrong; EUR did appreciate but not as much as implied by futures price.


  • SPREAD TRADING changing, recalculate the optimal hedge ratio and rebalance the hedge by selling more futures or buying futures. How frequently?

  • Intercommodity Spread

  • In April : Spot EUR/USD : 1.5500 GBP/USD: 1.9000

  • September Futures: EUR: 1.5800 GBP: 1.8580

  • Your view: GBP is going to rise against EUR.

  • What should you do?

  • Intracommodity Spread:

  • June EUR: 1.5800 September EUR : 1.7500

  • Your view: Between June and September EUR will not rise so much. What should you do?


Interest rate futures
INTEREST RATE FUTURES changing, recalculate the optimal hedge ratio and rebalance the hedge by selling more futures or buying futures. How frequently?

Treasury Bill Futures

A futures contract on US treasury bills is traded on the CME. Its specifications are as follows:

Product and Trading unit: 13 WEEK TREASURY BILL FUTURES

3-month (13-week) U.S. Treasury Bills having a face value at maturity of $1,000,000

 Point Description: ½ point = .005 = $12.50. A point here is one basis point or (1/100)th of 1 percent.


CME 13 WEEK US T-BILL changing, recalculate the optimal hedge ratio and rebalance the hedge by selling more futures or buying futures. How frequently?


  • T-Bill Futures Contract on CME…. changing, recalculate the optimal hedge ratio and rebalance the hedge by selling more futures or buying futures. How frequently?

  • The dollar value of a point represents interest at 0.01% p.a. on $1 million for a period of 3 months, which works out to $25.

  • Contract Listings: Mar, Jun, Sep, Dec,

  • Four months in March quarterly cycle plus 2 two months not in the March cycle (serial months).

  • The short must deliver a US T-bill with face value USD 1 mio, with 90, 91 or 92 days to maturity.

  • Futures price stated as: 100.000-Discount yield

  • Rates rise, price falls; rates fall, price rises.


Three Month Euro (EURIBOR) Interest Rate Futures changing, recalculate the optimal hedge ratio and rebalance the hedge by selling more futures or buying futures. How frequently?Contract (LIFFE)

Unit of trading: €1,000,000

Delivery months: March, June, September, December, and four serial months, such that 25 delivery months are available for trading, with the nearest six delivery months being consecutive calendar months

Quotation: 100.00 minus rate of interest

Minimum price movement (tick size and value): 0.005 (€12.50)

Last trading day: Two business days prior to the third Wednesday of the delivery month

Delivery day: First business day after the Last Trading Day

Trading hours: 07:00 – 21:00


  • THE EURODOLLAR DEPOSIT CONTRACT changing, recalculate the optimal hedge ratio and rebalance the hedge by selling more futures or buying futures. How frequently?

  • The underlying asset is a 3-month Eurodollar deposit of USD 1 million beginning on expiry date of futures.

  • Contract price is stated as (100-Implied Interest Rate)

  • May be cash settled only or both cash settled and physical delivery. If latter, long is actually assigned a deposit at a eurobank.

  • As interest rate rises, contract price falls. As rates fall, contract price rises.

  • To hedge against falling rates, buy futures; to hedge against rising rates sell futures


CME Eurodollar Futures changing, recalculate the optimal hedge ratio and rebalance the hedge by selling more futures or buying futures. How frequently?

Trade Unit : Eurodollar Time Deposit having a principal value of $1,000,000 with a three-month maturity.

Settle Method : Cash Settled

Point Size :1 point = 0.01 = $25.00

Tick Size (Min Fluctuations)

SGX : Half Tick 0.005=$12.50 Quarter 0.0025=$6.25 for nearest expiring month.

FLOOR : Half Tick 0.005=$12.50 Quarter 0.0025=$6.25 for nearest expiring month.

GLOBEX : Half Tick 0.005=$12.50 Quarter 0.0025=$6.25 for nearest expiring month.


DECEMBER 3, 2008 changing, recalculate the optimal hedge ratio and rebalance the hedge by selling more futures or buying futures. How frequently?


INTEREST RATE FUTURES DECEMBER 3, 2008 changing, recalculate the optimal hedge ratio and rebalance the hedge by selling more futures or buying futures. How frequently?


  • LONG TERM INTEREST RATE FUTURES changing, recalculate the optimal hedge ratio and rebalance the hedge by selling more futures or buying futures. How frequently?

  • The CBT contract on US T-bonds and T-notes; LIFFE contract on UK guilts. DTB contract on German Bunds etc.

  • The short must deliver a long term bond from among a set of eligible bonds -”Basket Delivery”

  • The CBT contract on US T-bonds: Underlying is a notional T-bond with 15 years to maturity and 8% YTM.

  • Exchange calculates a conversion factor for all eligible bonds.


LONG TERM INTEREST RATE FUTURES changing, recalculate the optimal hedge ratio and rebalance the hedge by selling more futures or buying futures. How frequently?

For US T-bond futures, price stated as % of face value with minimum 1/32% e.g.

Price : 103-18 means 103 and (18/32) percent of $100000

Long pays: Settlement Price × Conversion factor

+ Accrued Interest

Conversion Factor necessary because different bonds have different coupons and maturities.

An eligible bond has CF of 1.5 - Each of these bonds equals 1.5 of notional bonds.


30 Year U.S. Treasury Bonds Futures changing, recalculate the optimal hedge ratio and rebalance the hedge by selling more futures or buying futures. How frequently?


  • Hedging a Commercial Paper Issue changing, recalculate the optimal hedge ratio and rebalance the hedge by selling more futures or buying futures. How frequently?.

  • In January a corporation finalises its plans to make an issue of $50 million 90-day commercial paper around mid May.

  • Paper of comparable quality is now yielding 12.05%.

  • At this yield the company hopes to realise $48,493,750.

  • To protect itself against the possibility that rates may rise before its issue hits the market decides to hedge using EURO$ futures.

  • June futures currently quoted at 88.75

  • What should it do?


    • SPECULATION WITH INTEREST RATE FUTURES changing, recalculate the optimal hedge ratio and rebalance the hedge by selling more futures or buying futures. How frequently?

    • Open Position Trading

    • On September 1, December eurodollar futures on the IMM is trading at 89.25. A trader believes that short term interest rates are going to fall very soon. He buys a December contract at 89.25. On subsequent days, the prices and consequent losses/gains are :

    • Day 1: 89.35 (+$250) Day 2: 89.32 (-$75)

    • Day 3: 89.45 (+$325) Day 4: 89.47 (+$50)

    • Day 5: 89.45 (-$50) Day 6: 89.50 (+$125) Liquidates position.

    • Total gain: $625 minus brokerage commissions.


    • An Intra-Contract Spread Trade changing, recalculate the optimal hedge ratio and rebalance the hedge by selling more futures or buying futures. How frequently?

    • On February 25 the following prices are quoted for T-bill futures on the IMM :

  • March : 96.02

  • June : 95.25

  • September : 94.50

  • December : 93.00

    • A trader feels that the yield curve is going to become flatter. He has no particular ideas about how interest rates as a whole are going to change but he is confident that long term rates will be lower relative to short-term rates than they are now.


    • Intra-Contract Spread Trade….. changing, recalculate the optimal hedge ratio and rebalance the hedge by selling more futures or buying futures. How frequently?

    • If his prediction comes true the spread between near and far contracts will narrow. To profit from this he must sell a near contract and buy a far contract. (”sell a spread"). He sells a September contract at 94.50 and buys a December contract at 93.00.

  • By August 10, rates have fallen, yield curve is flatter:

  • September: 95.50 December: 94.75

  • Close out. Buy September sell December. Net gain 75 ticks or

  • USD 1875 minus brokerage.

  • Better strategy: Sell T-bill futures buy T-bond futures.


  • ad