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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