Forwards&FuturesPricing

8/10/2019 Forwards&FuturesPricing

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Session 1Derivatives & Risk Management

Aparna Bhat

Forwards & Futures


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Forward Contracts- Meaning

Definitionan agreement between two parties that calls for the

delivery of an asset at a future point in time with a price agreed

upon today

Differ from spot contracts Spot contracts require immediate payment ; forward buyer

gains in terms of interest

Spot contracts require immediate delivery; forward seller earns

income on asset and incurs storage cost; short-selling possible Spot contract possible between unknown persons; forward

contracts possible only between known counterparties or

require mechanisms to protect against default


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Futures contracts

Why futures contracts? Forwards involve credit risk

Hence not suitable to small investors (example of Milton

Friedman)

Trading through an exchange can mitigate credit risk

which however requires standardization of contracts

Futures contract is a forward contract with standardized

terms traded on an organized exchange and follows a dailysettlement procedure whereby losses of one party to the contract are

paid to the other party


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Forwards and futures - distinction

Forwards Futures

Traded Over the counter

Custom-made contracts

Credit risk borne byparties

No margins

Settled by delivery; close-

out difficult No published price-

volume information

Exchange traded

Standardized contracts

Credit risk borne by theCCP

Initial margin and dailyMTM margins

Delivery rare; close-outeasy

Published price-volumedata


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Specifications of a futures contract

Contract Size

Quotation unit

Minimum price fluctuation (tick size)

Contract gradeTrading hours

Settlement Price

Delivery terms Daily price limits and trading halts


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Snapshot of a futures quote

nstrument Type Underlying Expiry Date Option Type Strike Price Market Lot

FUTIDX NIFTY 28JUL2011 - - 50

Price Information

Open Price 5668.00

High Price 5670.00

Low Price 5632.10

Last Price 5636.95

Prev Close 5665.85

Close Price -

Change from prev close -28.90

% Change from prev close -0.51

VWAP 5645.09

Underlying Value 5621.50

Number of contracts traded 93518

Turnover (In Lakhs) 263958.76

Open Interest 22744350

Change in Open Interest 914950

% Change 4.19

Order Book

Buy Qty Buy Price Sell Price Sell Qty

150 5636.65 5637.00 29250

100 5636.60 5637.45 50

100 5636.40 5637.80 400

100 5636.25 5637.90 450

50 5636.20 5637.95 50

719500 Total Buy Qty Total Sell Qty 573500

Cost of Carry

Best Buy Best Sell Last Price

Price 5636.65 5637.00 5636.95

Cost Of Carry 4.27 4.37 4.36

Other Information

Settlement Price Daily Volatility Annualised Volatility Client Wise Position Limits Market Wide Position Limits

5665.85 1.06 20.18 17851965 -


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Options given to the seller

Sellers are allowed various options in some futurescontracts (permissible variations in the specifications)

Timing option

Quality option

Location option

Quantity variation

Such options aimed at preventing market manipulation

of the deliverable through a short squeeze

Contract design requires a reconciliation of hedging

effectiveness with need to prevent market manipulation


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Why cash-settlement

A solution to problems associated with physicalsettlement

Parties settle difference in cash

Futures only for price-fixing and not for delivery

Cash settlement common for

Stock index futures

Weather derivatives

Single stock futures in some countries


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Applications of Forwards and Futures

Trading or speculationtaking a position in aforward or futures contract without any underlying

exposure and trying to profit from a directional

view

Hedgingtaking an opposite position in a

forward/futures contract in order to mitigate risks

to the underlying

Arbitragetaking a combined position in theforward/futures and the underlying in order to

profit from the mispricingof the forward/futures


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Trading in forwards and futures

Party entering into a buy contract = long

Party entering into a sell contract = short

A long position benefits from a rise in price of the underlying

Profit to long = Spot price at maturityOriginal futuresprice

A short position benefits from a fall in price of underlying

Profit to short = Original futures priceSpot price at

maturity

Forwards and futures have linearpayoffs


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Pricing of a forward contract

No arbitrage is the main assumption

The principle of replication

Cost of the replicating portfolio = cost of the

derivative


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Replicating a forward contract

Suppose you enter into a forward contract to buygold at time t at a delivery price F. What should bethe fair price at which to enter into this longposition?

At maturity of the forward contract you will receivegold at price F

This position can be replicated by buying goldtoday at spot price S by borrowing at a rate r%

p.a. and holding the gold till time t The cost of buying and holding gold till time t is

S*e^rt

No-arbitrage condition dictates that the forward

price F should be equal to S*e^rt


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Another argument An asset bought from 2 sources (spot market and futures market) must

be priced identically on delivery date; else arbitrage

Hence futures and spot price must converge on maturity date

A portfolio hedged with futures and both portfolio and hedge held till

maturity will be riskless

Eg- Consider an investment in Tata Motors today at Rs.304 hedged

with short 1-month future at Rs.305.

Final share price 280 290 300 310 320 330

Pay-off from short future 25 15 5 -5 -15 -25

Value of hedged portfolio 305 305 305 305 305 305

Current futures price 305 305 305 305 305 305


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Cost of Carry Model for pricing In the example the final value of hedged portfolio = Current

futures price

Portfolio value does not depend upon spot price at

maturity; i.e. overall position is riskless

A riskless position should earn the risk-free rate of return

Hence

Or

Where F0 =current futures price and S0 = current spot price

Thus forward price = Spot price + cost of carry


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Pricing with continuous compounding

Investment assets with no interim cash flows

Investment assets with known interim cash flows

Investment assets with known dividend yield

Consumption assets Where F= forward price,S=spot price, r=continuously

compounded interest rate, q=

dividend yield, I= PV of

known cash flow, u=storage

costs per unit of time, y=

convenience yield


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Assumptions of cost-of-carry model

No transaction costs

No restrictions on short sales

Same risk-free rate for borrowing and lending


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Violations of forward pricing formula.

Consider a non-dividend paying stock with spot price = 120, risk-

free rate=5%, period= 1 year

As F= S*e^ rt , F = 126.15

If actual F = 128 cash-carry arbitragepossible Buy stock today at 120 by borrowing at 5%

Sell stock one-year forward at 128

Hold stock for 1 year

At maturity, sell stock at 128 Repay borrowing with interest at 126

Net gain is Rs.2 (free lunch ?)

Hence F cannot be greater than S*e^rt


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Consider a non-dividend paying stock with spot price = 120, risk-

free rate=5%, period= 1 year

As F= S*e^ rt , F = 126.15

If actual F = 123 reversecash-carry arbitragepossible Sell stock today at 120 and lend proceeds at 5%

Buy stock one-year forward at 123

At maturity, get back loan with interest at 126

Receive delivery of stock at 123 Net gain is Rs.3 (free lunch ?)

Hence F cannot be less than S*e^rt


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Fair value of forward =

Current stock price = 900, known dividend after 4 months =40,

forward maturity =9 months, 4-month int rate= 3%, 9-month int rate=

4%

Fair value of forward = (900-39.60)*e^(0.04*9/12) = 886.60

If actual forward price = 910

Short forward contract at 910 and borrow to buy stock today

Borrow 39.60 for 4 months and 860.40 (900-39.60) for 9 months

After 4 months, pay off loan of 39.60 from dividend inflow At end of 9 months receive forward price of 910 and repay loan of 886.60

Gain = 23.40

If actual forward price is lower, reverse cash-carry arbitrage


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Cost of carry is offset by the known income yield q (q iscontinuously compounded)

Hence

Stock index futures priced as above

What is Index arbitrage?

When F > Se(rq)T an arbitrageur buys the stocks

underlying the index and shorts futures

When F < Se(rq)T an arbitrageur goes long in futures

and shorts the stocks underlying the index

Index Arb involves simultaneous trades in futures and many

different stocks; hence programmed trades


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Pricing of currency forwards

Pricing requires knowledge of spot exchange rate, domesticinterest rate and foreign currency interest rate

Interest rate parity requires that

Where rd=domestic interest rate and rf=foreign currency interest rate

Expressed in continuous compounding

Example:

Spot USD/INR =44.70, 1-year USD-libor = 5%, 1-year

INR rate =10%, 1-year USD/INR forward rate = 47.10What is the arbitrage implied?


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Forwards on consumption assets

Fair value of forward =Where u = storage costs as a % of value of asset and y =

convenience yield

Convenience yield measures benefit of holding

physical inventory of consumption asset instead of

forward contract on that asset

Is not observable or measurable directly

Can be estimated from past data Sophisticated models to determine it


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Why arbitrage not always feasible?

Implementing cash-carry arbitrage requires ability toborrow at risk-free rate

Only large institutional players have that ability

Reverse cash-carry arbitrage requires ability to borrow

the security

Owners may be unwilling to sell or lend especially in

case of consumption assets

Regulatory restrictions on short selling


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Contango and Backwardation

Normally futures price > spot price Known as Contango market

Non-income earning financial assets normally in

contango

Sometimes spot price > futures price

Known as backwardation or inverted market

Consumption assets in backwardation when

convenience yield exceeds cost of carry May be due to anticipated disruption in supply

Could be due to short squeeze


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Implied repo rate (IRR)

It is that interest rate which would make the observedforward or futures price equal to the theoretical price

predicted under conditions of no-arbitrage using given

values of the spot price and other variables

Implied repo rate is the rate at which an investor can

borrow synthetically by going short spot and long forward

invest synthetically by going long spot and short forward

There will be no arbitrage when

Lending rate < IRR < Borrowing rate


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Forward price and value

Value of a forward contract different from the forwardprice

Forward price = S*e^rt

Initial value of forward contract is zero

Contract gains or loses value at later stage

Value of forward on an non-income asset

f = (SK)*e^(-rt)


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Risk management with futures

Concept of hedging Why do companies hedge?

To reduce risk of bankruptcy

To enable company to focus on its core competence

Shareholders cannot hedge effectively

When hedging not profitable

When competitors dont hedge

When hedging is not selective


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Decisions in hedging

Whether a long hedge or short hedge Which futures contract

Which expiry month

Number of futures contracts to be used


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Short hedge and long hedge


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Basis risk

What is basis?

Spot price of asset to be hedged less futures price of contract

used

Hedging substitutes basis risk for price risk

P/L on hedged position = change in basis

Under a short hedge

Future sale price = Current futures price + future basis

Under a long hedge Future buy price = Current futures price + future basis

Hedge held till expiry results in perfect hedge

Examples


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Hedging profitability and basis


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Example of short hedge

An investor holds 10000 shares of X co. Spot price onMay 1 is Rs.100. Investor needs funds on June 11 to

meet his Advance tax liability on June 15. How can he

hedge against the volatility in the interim period? June X

Co. futures quoting at Rs.97 on May 1. (consider bothstrengthening and weakening of the basis)


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Example of long hedge

A businessman planning to travel to the US on Aug 22needs 50,000 USD for his trip. As on Aug 3 the

USD/INR spot rate is 59.23 and the Dollar-rupee

futures on NSE are quoting at 59.20. How can he hedge

against the dollar-rupee volatility?


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Computing the Hedge ratio

What is Cross hedging ? Hedge ratio = ratio of size of exposure to size of

futures position

Minimum Variance Hedge Ratio

Objective is to minimize the variance of hedgers position

= Correlation between spot & future * (Std Dev of spot/

Std Dev of

future)


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Hedging an equity portfolio

Compute beta of the portfolio Nifty future lot size 50

Nifty future price 5400

Portfolio to be hedged = Rs.10 lacs Portfolio Beta = 1.05


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Controlling Risk in Equity Portfolio

Diversification eliminates unsystematic risk in portfolio

Systematic risk remains; i.e. portfolio is sensitive to market riskalone

Strategy to outperform the overall market

Increase portfolio beta to more than 1 when market is expectedto rise; will ensure that portfolio will yield higher return thanmarket

Reduce portfolio beta to less than 1 when market is expected todecline; will ensure that portfolio will suffer lower loss thanoverall market

Portfolio beta needs to be changed when market trend is expectedto change


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How to alter portfolio beta

Portfolio rebalancing Involves replacing low-beta stocks with high-beta stocks when market

is expected to rise or vice-versa

Requires frequent buying and selling of stocks resulting in higher

transaction costs

Lending or borrowing

Switching between capital market and debt market

Reducing or increasing the debt component of the portfolio in order

to increase or reduce beta of overall portfolio

Using index futures Sell index futures to reduce beta

Buy index futures to increase beta


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Managing risk of futures contracts

Futures settlement will always result in loss to one party How to ensure that losing party does not default?

Tools to manage the default risk

Clearing House

Margin deposits

Marking to market


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Clearing House

Clearing house a part of the stock exchange Concept of Novation

Ensures settlement of the trade in case of default by

either party If buyer defaults, CH ensures that seller receives the funds

payout

If seller defaults CH ensures that buyer gets the securities

pay-out through auction mechanism


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Margin deposits

Both buyer and seller have to post margin Margins consist of initial margin and maintenance

margin

Margins determined in accordance with market volatility

The stock exchanges in India charge initial margin and

exposure margin for each contract and margins are

changed on an intra-day basis


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Marking to market

Accounting procedure that forces both sides of the contractto take their gains/ losses daily

Prevents build-up of large unrealized paper losses

Example:

A is long one lot of Nifty July future at 5560 and B is short thesame

That day Nifty future closes at 5508

As loss of Rs.2600 ((5560-5508)*50) is taken from his accountand moved to Bs account

As long position and Bs short position now re-priced at 5508 Repricing restarts the contract with a new base for

determining subsequent P&L.


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Case study - Metellgesellschaft

MG entered into long-term forward contracts to supply oil at

fixed prices to its customers

A fixed quantity to be supplied every month over a period of 10

years at prices fixed in 1992

Due to long-term short forward contracts the company faced the

risk of a rise in oil prices

Hedged the above risk by a stack and roll hedge

Entered into a long position in near-month oil futures contracts

for the entire quantity to be supplied over the 10 year period

On expiry of near-month contract the position was rolled over to

the next near-month contract for the remaining quantity of

exposure


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Case studycontd..

Oil prices were in normal backwardation when strategy wasadoptedbackwardation was expected to continue

Under conditions of backwardation futures price is below theexpected future spot price and hence futures prices rise toconverge with the spot at expiry

Hence MG expected to make MTM gains on its long futurespositions even as it lost on its forward sale commitments

However oil market changed to contango, i.e. spot pricesstarted declining and fell below the futures prices

Hence as MGs long futures contracts approached expiry, thefutures prices were declining and MG incurred huge MTMlosses


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Case studycontd

Due to its huge long position in the futures market, MGfaced margin calls and ran into funding problems

Although MG was making profits on its actual sales under the

forward contracts, these gains could not be recognized in

P&L under the German accounting rules while MTM losseson the long futures position had to be recognized

As a result MGs P&L was in a mess and adverse

consequences in the market

Eventual losses $1.5 billion Risks faced by MGbasis risk, liquidity risk and operational

risk


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Open Interest V/s VolumeDate Trade Open Interest

as on date

Trading Volume

for the day

Jan 1 A shorts 50 contracts

B goes long in 50 contracts

50 50

Jan 2 C goes long in 100 contracts

D goes short in 100 contracts

OI increases to 150

as new long and

short position are

created

50

Jan 3 A closes short position by

buying back 50 contracts

E shorts 50 contracts

OI remains at 150

because As short

position is replaced

by Es shortposition

50

Jan 4 C closes long position by

selling 100 contracts and D

closes short position by

buying back 100 contracts

OI falls to 50 as

existing long and

short positions are

closed

100


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Interpreting changes in OI

Open Interest Price InterpretationOI is increasing Price is increasing New buyers are coming in

and technically strong

market

OI is increasing Price is declining Indicates short-selling and

technically weak marketOI is declining Price is declining Indicates long liquidation

and technically strong

market

OI is declining Price is increasing Indicates short-covering

and technically weak

market


47/50

OI increasing; Price increasing

Increasing OI suggests creation of new positions. Also rising price

shows that new buyers are stronger than new sellers. Hence bullish for

the scrip

Scrip Date SettPrice OI Change in OIIDEA 14-Nov 96.05 8492000

IDEA 15-Nov 94.50 8688000 196000

IDEA 16-Nov 98.55 10804000 2116000IDEA 17-Nov 97.80 11452000 648000


48/50

OI increasing; Price declining

Increasing OI suggests addition of new positions. Falling price suggests

that new sellers are stronger than new buyers. Hence suggests short-

selling in the scrip

Scrip Date SettPrice OI Change in OIMUNDRAPORT 11-Nov 151.60 2766000

MUNDRAPORT 14-Nov 155.55 2562000 -204000

MUNDRAPORT 15-Nov 144.05 2784000 222000

MUNDRAPORT 16-Nov 132.05 4420000 1636000

MUNDRAPORT 17-Nov 131.55 5918000 1498000


49/50

OI declining; Price declining

Declining OI suggests closure of existing positions, i.e. old buyers are

now selling and old sellers covering up their short positions. Falling

price suggests that sellers (old buyers) are stronger than buyers (old

sellers). Hence implies liquidation of old long positions in the scrip

Scrip Date SettPrice OI Change in OI

IGL 11-Nov 428.65 213000

IGL 14-Nov 425.80 206500 -6500IGL 15-Nov 419.55 204000 -2500

IGL 16-Nov 413.40 180500 -23500


50/50

OI declining; Price increasing

Declining OI suggests closure of existing positions, i.e. old buyers are

now selling and old sellers covering up their short positions. Rising

price suggests that buyers (old sellers) are stronger than sellers (old

buyers). Hence implies short-covering in the scrip

Scrip Date SettPrice OI Change in OI

PATNI 16-Nov 391.15 806500

PATNI 17-Nov 422.45 564000 -242500

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