futures. futures contract a future contract is an agreement between to parties to buy or sell an...

Futures

Futures Contract A future contract is an agreement

between to parties to buy or sell an asset at a certain time in future for a certain price. The buyer of the contract, who is said to

be long the contract has agreed to buy (take delivery of) the goods in future.

The seller is said to be short the contract and has obligation to sell (deliver) the goods in the future.

Payoff for a buyer of Futures

6055 650

Spot price

Profit/Loss

Payoff for a seller of Futures

6055 650

Spot price

Profit/Loss

Futures Market in India Stock index futures launched on 12th June,

2000 and stock futures in 9th Nov, 2001. Futures on Stock Index and on individual stocks

NSE: S&P CNX Nifty Futures, CNXIT Futures, BANK Nifty,CNX 100, CNX IT,CNX Nifty Junior, Nifty Midcap 50, futures on 207 individual stocks

Commodity futures Currency futures Interest rate futures

NSE: Notional T – Bills, Notional 10 year bonds (coupon bearing and non-coupon bearing)

Futures Contract

Exchange traded products. A standardized, transferable,

exchange-traded contract that requires delivery of a commodity, bond, currency, or stock index, at a specified price, on a specified future date.

Forwards vs. Futures

A futures contract is like a forward contract: Both specify that a certain commodity will

be exchanged for another at a specified time in the future at prices specified today.

They represent zero net supply; for every buyer there is a seller.

Profit-loss profile realized in forwards and futures represent a zero sum game.


A futures contract is different from a forward: Futures are standardized; only the price in

negotiated: e.g. all December 2004 gold futures contracts are identical in that the amount of gold (contract size), quality of gold, delivery date and place of delivery are specified. Forwards are customized and all the aspects can be negotiated.

Forwards vs. Futures Offesetting (prior to delivery date) a trade is

possible in futures market while it is non-existent in most of the forward markets. For example, if you are long Dec 2004 gold futures contract you can close that position by later selling a Dec 2004 gold futures contract.

Default risk is least in case of futures. Since forward contracts are agreements between the two parties, each part face the counterparty default risk.


Most future positions are eventually offset and in many cases they are cash settled. In contrast, most forward contracts terminate with delivery of the specified good.

Margins and daily marking to market in case of futures.

Futures Contract: Standard Features

Contract specification Asset type

Exchange stipulates the grade of the asset. Contract size

Specifies the amount of the asset to be delivered under one contract.

Delivery agreement The place of delivery


Delivery months Futures are referred to by their delivery

months. Price quotes Daily price movement limits

Daily price movement limits, termed as limit move (limit up and limit down)

Position limits Maximum number of contracts that a

speculator may hold


Clearing house Clearinghouse of the exchange becomes

the opposite party to both buyers and sellers - thus guarantees the performance of the parties to each transaction.

Margin requirement When two parties trade a futures contract,

the futures exchange requires some good faith money (security) from both, to act as a guarantee.


Initial Margin Each exchange is responsible for setting the

minimum initial margin requirements. The initial margin is the amount a trader must deposit into his trading account (also called as margin account) when establishing a position.

Exchanges use SPAN (Standard Portfolio Analysis of Risk) to establish initial margin requirement.


Beyond the initial margin, if the equity in the account falls below a maintenance margin level, additional funds must be deposited to bring the account back up to the initial margin level. The process is known as margin call. The amount that is to be deposited is termed as variation margin.

Once a trader has received the margin call, he must meet the call, even if the price has moved in his favour.


For example, if the initial margin required to trade per gold futures contract is $1000, and the maintenance margin level is $750, then an adverse change of $2.60/oz. will result in a margin call. Because one gold futures covers 100 oz. of gold a decline of $2.60/oz in the futures price will deplete the long position by $260. The trader with losses must deposit sufficient funds to bring the margin to the initial level of $1000. The margin that is deposited to meet margin call is termed as variation margin.


Types of orders Market order

Trade to be carried out immediately at the best price Limit order

Specifies a particular price. The order can be executed only at this price or at one more favouarble to the investor.

Stop order or stop-loss order Also specifies a particular price. The order is

executed at the best available price once a bid or offer is made at a particular price or a less favorable price.


Stop-limit order A combination of stop order and limit order.

Market-if-touched order They are like limit orders, except that they

become market orders once a trade has occurred at the specified price.

Discretionary order/Market-not-held order Traded as a market order except that

execution may be delayed at the broker's discretion in an attempt to get a better price.


Time orders Unless specified, an order is a day order and

expires at the end of the trading day. Good-till-cancelled remains active till executed or cancelled by the customer. Some other time orders are Good-this-week, Good-this-month etc.

Spread order Specifies two trades that must be filled

together. The order can specify a difference in the prices or it can be a market order.


Offsetting the positions (squaring up) Most traders choose to close out their

position prior to delivery period specified in the contract by entering into the opposite type of the trade.

Open Interest Total number of contracts outstanding for a

particular delivery month. Open interest is a good proxy for demand

for a contract.


Settlement Physical settlement vs. Cash settlement Settlement month Settlement price


Marking to Market All futures traders’ positions are marked to

market daily. Also known as daily resettlement. It means

everyday, profits are added to, or losses are deducted from the trader’s account.

Profits and losses are based on the changes in the settlement prices or closing futures prices.

Contract specification: S&P CNX Nifty Futures

Underlying index S&P CNX Nifty

Exchange of trading National Stock Exchange

Security descriptor N FUTIDX NIFTY

Contract size 50 and multiples thereof

Price steps Rs. 0.05

Trading cycle Maximum three month trading cycle

Expiry date Last Thursday of the expiry month or the previous trading day if the last Thursday is a holiday

Settlement basis Mark to Market and final settlement is cash settled on T+1 basis

Settlement price Daily settlement price will be the closing price of the futures contracts for the trading day and the final settlement price will be the closing value of the underlying index on the last trading day


Marked to Market: An example In NSE all future contracts are marked to market

to the daily settlement price. The profit loss are computed as thus:

The trade price and the day’s settlement price for contracts executed during the day but not squared up

Previous’ days settlement price and the current day’s settlement price for brought forward contracts

Buy price and the sell price for contracts executed during the day and squared up


Trade details Quantity bought/sold

Settlement price

MTM

Brought forward from previous day

100@100 105 500

Traded during the day

Bought Sold

200@100100@102 102

200

Open position(Not squared up)

100@100 105 500

TOTAL 1200

Source: NSE

Basis and Convergence Basis and convergence explain the

relationship between futures price and cash price.

Basis Spot price (cash price) minus the futures

price In a normal market basis will be negative;

since future prices exceed spot prices and it is positive in an inverted market.

Basis approaches zero as the delivery month is approached.

Basis and Convergence

The process of basis moving towards zero is termed as convergence. Why does it happen?

It is due to arbitrage. For example, if future price is above spot price during the delivery period, the trader can

i. Short a futures contractii. Buy the assetiii. Make delivery

Pricing Futures

Do the quoted prices reflect true value of the underlying index?

Does there exist any opportunity for arbitrage?

Why should the basis be negative in normal markets?The dynamics lies in the Cost-of-carry model.

Cost of Carry Model Cost of carry measures the storage cost,

plus the interest that is paid to finance the asset less the income earned on the asset.

Cost of carry varies across the assets. For a non-dividend paying stock, the cost of

carry is the risk free rate because there are no storage costs and no income is earned.

For a commodity, storage cost is important.

Cost of Carry Model

The fair value of futures incorporates the ‘no-arbitrage’ limits on the prices. This is as thus

F = S + CC - CR F = Future prices S = Spot price CC = Holding costs or carry costs. CR = Carry returns

Cost of Carry Model For the stock index futures it can be

mentioned as

H(0,T) = rT/365, where r is the annual interest rate, T is the number of days until delivery date and [FV(divs)] is the future value of all dividends paid by the component of the stock index

FV(divs) - T)h(0,S S F

Cost of Carry Model If

traders will engage in a cash-and-carry arbitrage which calls for buying the spot index (it is relatively cheap) , ‘carrying‘ it, and selling the futures (relatively expensive).

If

Traders will engage in a reverse cash-and-carry arbitrage which calls for buying the futures and selling the spot, and investing the proceeds.



Normal Backwardation and Contango

Normal backwardation Futures prices are below expected future

spot prices, and futures price is expected to rise as the delivery date approaches

Contango A contango exists wherever the futures

price lies above the expected future spot price, and the futures price generally declines as the delivery date nears.

Buying a stock index futures contract and buying Treasury bills is frequently called a long synthetic stock position.

Buying shares of stock that replicates an index and also selling a futures contract on the stock creates a synthetic treasury bill.

Synthetic Stock and T Bills

Synthetic Stock

Illustration An investor owns $9,523,800 in one year

T-bills which will be worth $10 million one year hence.

Take long position in stock index futures with an underlying value equal to $9,523,800 (based on spot index).

Suppose that index futures price is 1375 and the spot is at 1325 and the futures contract multiplier is 250.

Synthetic Stock 28.7511 futures will be purchased

($9,523,800/1325*250 ) Now suppose after one year spot price and

futures price are at 1500. The value of the portfolio is

$10 million from T bills $898,472 in stock index futures profit (125 ×

250 × 28.7511) Gain is 14.434%, given that investor began

the year with $9,523,800

Synthetic Stock The 14.434% is identical to the return from

buying actual stocks, ignoring transaction costs.

The capital appreciation on the stock was 13.208%. (1500-1325/1325)

Had he purchased the stocks he would have received the dividends and interest on those dividends, and this dividend yield component would have been 1.2264%.

Total return is 14.434%

Synthetic T bill

The arbitrageur buys the stock and locks in a selling price by selling futures contract.

When performing a cash-and-carry arbitrage, the synthetic T-bill is created by borrowing at a lower rate and lending at a higher rate, which is risk less.

Hedging with Futures Hedgers use futures market to reduce a

particular risk that they face. A perfect hedge is one that completely

eliminates the risk. In practice, these are rare. When is the short futures position appropriate? When is a long futures position appropriate? Which futures contract should be used? What is the optimal size of the futures position?

Hedging: The Basic Principle

The objective is usually to take a position that neutralizes the risk as far as possible. Consider an investor who will gain Rs.10,000

for each rupee increase in the price of the commodity over the next three months and lose Rs.10,000 for each rupee decrease in the price during the same period. To hedge, the investor should take a short futures position that is designed to offset the risk.

Hedging with Futures

Short hedge Involves a short position in futures

contract. Appropriate when the hedger has already

owned the asset and expects to sell it in future.

Can also be used when an asset is not owned right now but will be owned at some time in future.


Short hedge illustration On May 15, 2004 an oil produces

negotiated a contract to sell 1 million barrels of crude oil. It has been argued that price that will apply in the contract is the market price on August 15. The oil producer is therefore in the position where it will gain $10,000 for each cent increase in the price and lose $10,000 for each cent decrease in the price.

Hedging with Futures Suppose that spot price on May 15 is $19

per barrel and August crude oil futures price is $18.75 per barrel. Each futures contract involves the delivery of 1000 barrels.

The company can hedge by shorting 1000 August futures contracts.

If the oil producer closes out his position on August 15, the effect of the strategy should be to lock in a price close to $18.75 per barrel.


Long hedge Long positions in a futures contract More appropriate when one needs to

purchase a certain asset in the future and wants to lock in a price now.

Hedging with Futures Long hedge illustration

On January 15 a copper fabricator knows it will require 100,000 pounds of copper on May 15 to meet certain contracts. The spot price of the copper is 140 cents per pound, and the May futures are priced at 120 cents per pound. Each contract is for the delivery of 25,000 pounds of copper.

The fabricator can hedge his position by taking a long position in four May futures contract.

Hedging with Stock Index Futures

Long security – Short index futures Every buy position on a security is

simultaneously a buy position on the index.

As a way out a long position on a security can be accompanied by sale of index futures.

One needs to know the beta of a security.


Illustration Shyam adopts a position of Rs.1 million

LONG MTNL on date 5th June 2001. He plans to hold the position till the 25th.

Suppose the beta of MTNL happens to be 1.2.

Hence he needs a short position of Rs.1.2 million on the index futures market to totally remove his Nifty exposure.


On date 5th June 2001, Nifty is 980 and the nearest futures contract (with expiration 28th June 2001) is trading at about 1000. Hence, each market lot of the futures (200 nifties) is worth Rs.200,000. To sell Rs.1.2 million of Nifty, we need to sell 6 lots (by rounding off to the nearest market lot).

He sells 6 market lots of Nifty (1200 nifties) to get the position:

LONG MTNL Rs.1,000,000SHORT NIFTY Rs.1,200,000


10 days later, Nifty crashed because of instability in the government.

On Thursday, Shyam unwound both positions. His position on MTNL lost Rs.120,000 since MTNL had dropped to 880,000. His short position on Nifty June futures earned Rs.141,600. Overall, he earned Rs.21,600.


Short security – Long index futures Every sell position on a security is a

simultaneous sell position on the index. A short position on a security must be

accompanied by a long position on the index futures.

A knowledge of beta is essential.


Illustration Shyam adopts a position of Rs.1 million

SHORT MTNL on date 1st April 1997. He plans to hold the position till Thursday the 24th.

The beta of MTNL happens to be 1.2. Hence he needs a long position of Rs.1.2

million on the index futures market to totally remove his Nifty exposure.


On date 1st April 97, Nifty is 980 and the nearest futures contract (with expiration 24th April) is trading at about 1000. Hence, each market lot of the futures (200 nifties) is worth Rs.200,000. To buy Rs.1.2 million of Nifty, we need to buy 6 lots (by rounding off to the nearest market lot).

He buys 6 market lots of Nifty (1200 nifties) to get the position:

SHORT MTNL Rs.1,000,000LONG NIFTY Rs.1,200,000


20 days later, Nifty rose because of stable political outlook.

On Thursday, Shyam unwound both positions. His position on MTNL lost Rs.120,000 since MTNL had gone up to 1,120,000. His short position on Nifty April futures earned Rs.93,600. Overall, he lost Rs.26,400.


Have portfolio – short index futures Every portfolio contains hidden index

exposure. Exposure can be minimized by using index

futures. Knowledge of beta of the portfolio is

essential.


Illustration On 25 May 2001, Shyam has a portfolio composed

of five securities: ITCHOTEL (100 shares, value Rs.112.00), ORIENTBANK (200 shares, value Rs.68.25), CIPLA (100 shares, value Rs.847.65), LUPINLAB (200 shares, value Rs.149.85), and SIEMENS (200 shares, value Rs.237.50). The total portfolio value is 187,085 and the fi ve securities have weights (5.98%, 7.29%, 45.31%, 16.02%, 25.40%). Shyam does not want to worry about budget-related fluctuations from 26 May 2001 till 10 June 2001.


The five securities have the following betas: ITCHOTEL (beta 0.59), ORIENTBANK (beta 0.90), CIPLA (beta 0.75), LUPINLAB (beta 1.13), and SIEMENS (beta 1.10). Hence the portfolio beta works out to (0.0598*0.59 + 0.0729*0.90 + 0.4531*0.75 + 0.1602*1.13 + 0.2540*1.10) or 0.90.

For complete hedging he will need to sell futures worth 0.90 * 187,085, i.e. Rs.168,376.50. On 25 May 2001, Nifty is at 1,122.95. So he decides to sell 200 Nifties.


Hence Shyam supplements his portfolio with a short position on the Nifty futures with expiry on 25th JUNE worth Rs.224,590.

On 10 June he buys back futures at a lower price and ends his hedge (see Table 5.1). His profits on the futures hedging was Rs.32,010 and his losses on the portfolio were Rs.32,990. Thus the net loss is Rs. 980. If he had not hedged, he would have lost 32,990.


Have funds – Long index futures Index futures can be used to hedge

against a rise in the index.


Illustration Iqbal obtained Rs.5 million on 17 Feb 1998. He

made a list of 14 securities to buy, at 17 Feb prices, totaling Rs.5 million.

At that time Nifty was at 991.70. He entered into a LONG NIFTY MARCH FUTURES position for 5000 nifties, i.e. his long position was worth 5,053,600.

From 18 Feb 1998 to 09 March 1998 he gradually acquired the securities (see Table 5.2). On each day, he

purchased one securities and sold off a corresponding amount of futures.


On each day, the securities purchased were at a changed price (as compared to the price prevalent on 17 Feb). On each day, he obtained or paid the ‘mark–to–market margin’ on his outstanding futures position, thus capturing the gains on the index.

By 09 Mar 1998 he had fully invested in all the shares that he wanted (as of 17 Feb) and had no futures position left.

The same sequencing of purchases, without the umbrella of protection of the LONG NIFTY MARCH FUTURES position, would have cost Rs.249,724 more.

Speculation with Index Futures

Bullish index – Long nifty futures On 1 July 2001, Milan feels the index will rise. He buys 200 Nifties with expiration date on 31st

July 2001. At this time, the Nifty July contract costs Rs.960

so his position is worth Rs.192,000. On 14 July 2001, Nifty has risen to 967.35. The Nifty July contract has risen to Rs.980. Milan sells off his position at Rs.980. His profits from the position are Rs.4000.

Speculation with Index Futures

Bearish index – Short nifty futures On 1 June 2001, Milan feels the index will fall. He sells 200 Nifties with a expiration date of 26th

June 2001. At this time, the Nifty June contract costs

Rs.1,060 so his position is worth Rs.212,000. On 10 June 2001, Nifty has fallen to 962.90. The Nifty June contract has fallen to Rs.990. Milan

squares off his position. His profits from the position work out to be

Rs.14,000.

Index Arbitrage A strategy designed to profit from temporary

discrepancies between the prices of the stocks comprising an index and the price of a futures contract on that index. By buying either the stocks or the futures contract and selling the other, an investor can sometimes exploit market inefficiency for a profit. Like all arbitrage opportunities, index arbitrage opportunities disappear rapidly once the opportunity becomes well-known and many investors act on it.

Index Arbitrage Index arbitrage can involve large transaction

costs because of the need to simultaneously buy and sell many different stocks and futures, and so only large money managers are usually able to profit from index arbitrage. In addition, sophisticated computer programs are needed to keep track of the large number of stocks and futures involved, which makes this a very difficult trading strategy for individuals.

Programme Trading Trading a stock portfolio in a single order

Index Arbitrage Suppose

i.e

How does one carry index arbitrage? Cash and Carry arbitrage


0 FV(divs) T)h(0,S S - F

Index Arbitrage

TODAY Buy the component of the index in

the appropriate weights, so that index is replicated

Borrow the forgoing amount for the number of days until the delivery date, at an annual interest rate of r% (h% annualized)

Sell one futures contract at its current futures price (F0)

Total Cash Flow

Cash Flow- S0

+ S0

0

0

Index Arbitrage

FIRST EX-DIVIDEND DATE Receive dividends Lend dividends from t1 to T

Total Cash Flow

SUBSEQUENT EX-DIVIDEND DATES Receive dividends Lend dividends from t2, t3,…T

Total Cash Flow

Cash Flow+ divs- divs

0

+ divs- divs

0

Index Arbitrage

ON THE DELIVERY DATE Offset the futures

contract Sell the stocks Repay loan and interest Receive dividends and

interest on dividends

Total Cash Flow

Cash FlowF0 – FT = F0 – STST-S0 – h(0,T)S0FV(divs)

0 FV(divs) T)h(0,S S - F

Arbitrage with Index Futures On 1 August, Nifty is at 1200. A futures

contract is trading with 27 August expiration for 1230. Ashish wants to earn this return (30/1200 for 27 days).

He buys Rs.3 million of Nifty on the spot market. In doing this, he places 50 market orders and ends up paying slightly more. His average cost of purchase is 0.3% higher, i.e. he has obtained the Nifty spot for 1204.

He takes delivery of the shares and waits.

Arbitrage with Index Futures While waiting, a few dividends come into his

hands. The dividends work out to Rs.7,000. On 27 August, at 3:15, Ashish puts in

market orders to sell off his Nifty portfolio, putting 50 market orders to sell off all the shares. Nifty happens to have closed at 1210 and his sell orders (which suffer impact cost) goes through at 1207.

The futures position spontaneously expires on 27 August at 1210 (the value of the futures on the last day is always equal to the Nifty spot).

Arbitrage with Index Futures

Ashish has gained Rs.3 (0.25%) on the spot Nifty and Rs.20 (1.63%) on the futures for a return of near 1.88%.

In addition, he has gained Rs.7000 or 0.23% owing to the dividends for a total return of 2.11% for 27 days, risk free.

Optimal hedge ratio Hedge ratio represents the ratio of the size of the

position taken in futures contracts to the size of the exposure.

Optimal hedge ratio may differ from 1. The optimal hedge ratio (h*) is given as

S = Standard deviation of change in spot price F = Standard deviation of change in futures price = Correlation coefficient between spot price and futures price

Optimal hedge ratio is also termed as Minimum variance hedge ratio.

F

Sh*

Optimal hedge ratio Optimal number of futures contracts is given

as thus:

NA = Size of the position being hedged (units) QF = Size of the futures contracts (units) N* = Optimal number of futures contracts for

hedging

F

A

Q

NhN

**

Optimal hedge ratio and Beta Stock index futures can be used to hedge an equity

portfolio. If the portfolio mirrors the index, a hedge ratio of

1.0 is appropriate. When the portfolio does not exactly match the

index, beta from the CAPM can be used to determine the appropriate hedge. This is as thus

P = Current value of the portfolio A = Current value of the stocks underlying one futures

contract

A

PN *

Beta Management Portfolio managers adjust their portfolio betas to

reflect changes in the perceived market risk and return

Bullish expectation increase beta (increase the exposure to the market)

Bearish expectation decrease beta (decrease the exposure to the market)

How to adjust beta? Reduce beta by selling part of an equity portfolio and buy

risk less securities Increase beta make additional investments on risky equity

portfolio through borrowing/selling risk less securities

Beta Management

Adjust beta by using stock index futures Sell stock index futures to reduce

exposure to market risk Buy stock index futures to have additional

exposure to market riskSee

illustration

Beta Management A portfolio manager owns following stocks:

Assume that the spot S&P 500 index is at 1350 and the S&P 500 futures price is 1357. The manager has invested $40, 70 and 50 million on the first, second and third stock respectively, thus making the total investment as $160 million. How can he decrease his portfolio’s beta to 0.83 or increase it to 1.66.

Stock

Umber of shares

Stock price ($) Beta

1 5 million 8 1.2

2 5 million 14 0.9

3 5 million 10 1.1

Beta Management Decreasing the current beta from 1.0375

to 0.83 Define the current portfolio of equities to be

asset 1 and the risk less security to be asset 2. The desired portfolio beta is 0.83. Thus

Therefore, a portfolio consisting of $128 million (0.80 × $160 million) invested in our portfolio of three risky equities, and $32 million in T bills would create a portfolio with a beta of 0.83 (0.80 × 1.0375 + 0.20 × 0).

0.80 or w )0w(1 (1.0375) w 0.83 111

Beta Management Size of the position being hedged =

$32,000,000 (=$32,000,000 / 1350 = 23703.7 units)

Size of one futures contract = 250 Beta of the portfolio = 1.0375 Optimal number of futures contracts =

98.370355

Interest Rate Futures

Interest Rate Futures Long term interest futures

T-Bond futures T-note futures

Short term interest rate futures T-Bill futures contract Eurodollars

Indian markets Futures contract on Notional 91 day T bill Futures contract on Notional 10 year coupon

bearing bond Futures contract on Notional 10 year zero coupon

bond.

T-Bond Futures The US Treasury Bond contracts at the CBOT Contract size

One U.S. Treasury bond having a face value at maturity of $100,000 or multiple thereof and coupon rate being 6%.

Deliverable grades U.S. Treasury bonds that, if callable, are not callable for at

least 15 years from the first day of the delivery month or, if not callable, have a maturity of at least 15 years from the first day of the delivery month. The invoice price equals the futures settlement price times a conversion factor plus accrued interest.

Tick size 1/32 of a point ($31.25/contract)

Contract months Mar, Jun, Sep, Dec

T-Note Futures (10yrs) One U.S. Treasury note having a face value at

maturity of $100,000 or multiple thereof. Deliverable grades

U.S. Treasury notes maturing at least 6 1/2 years, but not more than 10 years, from the first day of the delivery month.

Tick size One half of 1/32 of a point ($15.625/contract)

Contract months Mar, Jun, Sep, Dec

CBOT also trades on 5-yr and 2-yr Treasury note futures

Interest Rate Futures (IRF) in NSE

IRF underlyings in NSE Notional T – Bills (91 day) Notional 10 year bonds (coupon bearing

and non-coupon bearing) Trading cycle

The interest rate future contract shall be for a period of maturity of one year


Expiry day Interest rate future contracts shall expire on the

last Thursday of the expiry month. If the last Thursday is a trading holiday, the contracts shall expire on the previous trading day.

Further, where the last Thursday falls on the annual or half-yearly closing dates of the bank, the expiry and last trading day in respect of these derivatives contracts would be pre-poned to the previous trading day.


Contract size The permitted lot size for the interest rate

futures contracts shall be 2000. The minimum value of a interest rate futures contract would be Rs. 2 lakhs at the time of introduction.

The price steps in respect of all interest rate future contracts admitted to dealings on the Exchange is Re.0.01.


Settlement procedure and settlement price Daily Mark to Market settlement and Final Mark to

Market settlement in respect of admitted deals in Interest Rate Futures Contracts shall be cash settled by debiting/ crediting of the clearing accounts of Clearing Members with the respective Clearing Bank.

All positions (brought forward, created during the day, closed out during the day) of a F&O Clearing Member in Futures Contracts, at the close of trading hours on a day, shall be marked to market at the Daily Settlement Price (for Daily Mark to Market Settlement) and settled.


All positions (brought forward, created during the day, closed out during the day) of a F&O Clearing Member in Futures Contracts, at the close of trading hours on the last trading day, shall be marked to market at Final Settlement Price (for Final Settlement) and settled.

Daily settlement price shall be the closing price of the relevant Futures contract for the Trading day.

Final settlement price for an Interest rate Futures Contract shall be based on the value of the notional bond determined using the zero coupon yield curve computed by National Stock Exchange or by any other agency as may be nominated in this regard.

Conversion Factor and Invoice Amounts

The invoice amount, or invoice price, is the amount the short is paid, should they choose to deliver.

He invoice amount equals the futures settlement price times a ‘conversion factor’ plus ‘accrued interest’.

interest Accrued factor Convesrion

price settlementcontract Futures sizeContract amount Invoice

Conversion Factor Conversion factor

Conversion factor for a given bond is the value of the bond per dollar/rupee of face value as calculated on the first day of the delivery month, using an annual YTM of 6% and semi-annual compounding (T-bond futures).

Conversion factor (price factor) gives the price of an individual cash bond such that its YTM on the delivery day is equal to the notional coupon of the contract.

Accrued Interest Accrued interest

year halfin days ofNumber

couponlast since days ofNumber

deliversshort that thebonds theof valueface

$100,000on interest coupon Semiannual AI

Computing the Conversion Factor

Assume it is the first day of the delivery month, and calculate the time to maturity of the bond.

Round down this time to maturity to the nearest three-month period. For example, 18 years and 5.5 months becomes 18 years and 3 months.

If after rounding off the life of the bond is an integer multiple of semi-annual periods, then the first coupon is assumed to be paid after 6 months, otherwise assumed to be paid after 3 months.

Conversion Factor Example I We are short in a June futures contract and

that today is June 1, 2001. Consider a 7% T-bond that matures on 15 June, 2029 which is eligible for delivery under the futures contract.

On June 1, this bond has 28 years and 1.5 months to maturity. When rounded off to the nearest three months, we get a figure of 28 years.

The first coupon is then assumed to be paid after six months

Conversion Factor Example I The conversion factor is calculated as below:

1348.1100

1036.193791.94

100

)56,3(100)56,3(27

PVIFPVIFACF

Conversion Factor Example II Instead of the July 2029 bond, consider

another bond that is maturing on 15 September, 2029.

On June 1, 2001, this bond has 28 years and 3.5 months to maturity.

The life of the bond, when rounded off to the nearest three months, is 28 yrs and 3 months.

First coupon is assumed to be paid after three months.

Conversion Factor Example II First the price of the

bond three months from today, using a yield 6% is calculated.

Discount the price for another three months.

Subtract the accrued interest for three months, from the price obtained above.

116.982719.103694.37913.5

)56.3(100)56,3(2

7

2

7

PVIFPVIFAP

2665.115)03.1(

9827.1165.0

1352.1100

75.12665.115

75.12

1

2

7

CF

AI

Invoice Price

Let us assume that on 15 June, 2001 the 7% bond maturing on 15 September, 2029 will be delivered under June contract.

The actual delivery will be made two days later, that is, on 17 June.

How to calculate the invoice price?

Invoice Price The last coupon would have been paid on 15

March, 2001 and the next will be due on 15 September, 2001.

Accrued interest for a T-bond with face value of $100,000 is

The futures settlement price on 15 June is assumed to be 95-12.

This corresponds to a decimal futures price per dollar of the face value of

0435.1788100000184

94

2

07.0AI

95375.0100

32/1295

Invoice Price Invoice price

5110057.743

0435.17881000001352.195375.0 Price Invoice

T-Bond Futures Prices Cost-of-Carry model determines the T-Bond

futures prices. Because the short gets to choose which bond

to deliver, the futures price will reflect the spot price (S) of the bond that the market expects the short to select. This is called Cheapest-to-Deliver (CTD) bond.

The carry cost (CC) is the interest rate changes incurred when an trader borrows to buy the CTD.

Carry return (CR) is the accrued interest, actual coupon payments and the interest on coupons, if any.

Cheapest to Deliver T-Bond During the delivery month the CTD is

determined by computing the cost and the invoice amount. CTD is one that maximizes the inflows and minimizes the outflows for the short. CTD = max [invoice amount – (spot price +

accrued interest)] Before the delivery period, we can only

estimate which T-Bond will likely to be the CTD.

Cheapest to Deliver T-Bond Implied repo rate (IRR)

IRR is the rate of return earned by buying the deliverable spot asset and simultaneously selling a futures contract. Thus

0

00

S

S CRF IRR

Cheapest to Deliver T-Bond

Using duration If yields are above 6%, the CTD bond will

be the eligible bond with highest duration. If yields are below 6%, the CTD bond will

be the eligible bond with the lowest duration.

T-Bill Futures Contracts

Exchange International Money Market (IMM) segment

of Chicago Mercantile Exchange (CME) Underlying

3-month US T-bills having a face value at maturity of $1 million.

Delivery dates March, June, September and December

Eurodollar Futures

Underlying 3 month time deposits in dollars at banks

located outside the US mainly in Europe and in particular, in London.

Cash settled

futures. futures contract a future contract is an agreement between to parties to buy or sell an...

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