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    Forwards & Futures

    Session 2Derivatives & Risk Mgt

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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-sellingpossible

    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 standardizedterms traded on an organized exchange and follows a daily

    settlement procedure whereby losses of one party to the contract

    are paid to the other party

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    Forwards and futures - distinction

    Forwards

    Traded Over the counter

    Custom-made contracts

    Credit risk borne by parties

    No margins

    Settled by delivery; close-out

    difficult

    No published price-volume

    information

    Futures

    Exchange traded

    Standardized contracts

    Credit risk borne by the CCP

    Initial margin and daily MTM

    margins

    Delivery rare; close-out easy

    Published price-volume data

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    Specifications of a futures contract

    Contract Size

    Quotation unit

    Minimum price fluctuation (tick size)

    Contract grade

    Trading hours

    Settlement Price

    Delivery terms

    Daily price limits and trading halts

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    Snapshot of a futures quotenstrument 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 futures

    contracts (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 physical

    settlement

    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 a

    forward or futures contract without any underlying

    exposure and trying to profit from a directional view

    Hedgingtaking an opposite position in aforward/futures contract in order to mitigate risks to

    the underlying

    Arbitragetaking a combined position in the

    forward/futures and the underlying in order toprofit

    from the mispricing of the forward/futures

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    Pricing of a futures contract 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 risk-less

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

    with short 1-month future at Rs.305. Assume that Tata Motors pays a

    dividend of Rs.2 in the next one monthFinal share price 280 290 300 310 320 330

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

    Dividend income 2 2 2 2 2 2

    Value of hedged portfolio 307 307 307 307 307 307

    Current futures price + dividend 307 307 307 307 307 307

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    Cost of Carry Model for pricing

    In the example the final value of hedged portfolio = Current

    futures price + Dividend income

    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

    OrWhere F0 =current futures price, S0 = current spot price and D= income

    on the underlying

    Thus forward price = Spot price + net 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=continuouslycompounded 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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    When asset pays no interim income..

    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 arbitrage possible 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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    When asset pays no interim income 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 arbitrage possible 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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    When asset pays known cash flow

    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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    When asset pays known yield Cost of carry is offset by the known income yield q (q is

    continuously 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 andshorts 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, domestic

    interest 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 INRrate =10%, 1-year USD/INR forward rate = 47.10

    What is the arbitrage implied?

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    Why arbitrage not always feasible?

    Implementing cash-carry arbitrage requires

    ability to borrow 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 lendespecially 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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    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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    Example of short hedge

    An investor holds 10000 shares of X co. Spot

    price on May 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 volatilityin the interim period? June X Co. futures

    quoting at Rs.97 on May 1. (consider both

    strengthening and weakening of the basis)

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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 risk

    alone

    Strategy to outperform the overall market

    Increase portfolio beta to more than 1 when market is

    expected to rise; will ensure that portfolio will yield higher

    return than market

    Reduce portfolio beta to less than 1 when market is expected

    to decline; will ensure that portfolio will suffer lower loss than

    overall market

    Portfolio beta needs to be changed when market trend is

    expected to change

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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 thesecurities pay-out through auction mechanism

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    Marking to market

    Accounting procedure that forces both sides of the contract to

    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 the

    same

    That day Nifty future closes at 5508

    As loss of Rs.2600 ((5560-5508)*50) is taken from his account and

    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 was

    adoptedbackwardation was expected to continue

    Under conditions of backwardation futures price is below the

    expected future spot price and hence futures prices rise to

    converge with the spot at expiry

    Hence MG expected to make MTM gains on its long futures

    positions even as it lost on its forward sale commitments

    However oil market changed to contango, i.e. spot prices started

    declining and fell below the futures prices

    Hence as MGs long futures contracts approached expiry, the

    futures prices were declining and MG incurred huge MTM losses

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    Case studycontd Due to its huge long position in the futures market, MG faced

    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 losses on thelong 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 150because 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 Interpretation

    OI 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 market

    OI 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

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    OI increasing; Price increasing

    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

    Increasing OI suggests creation of new positions. Also rising price

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

    the scrip

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    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

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    OI declining; Price declining

    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

    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

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    OI declining; Price increasing

    Scrip Date SettPrice OI Change in OI

    PATNI 16-Nov 391.15 806500

    PATNI 17-Nov 422.45 564000 -242500

    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