forex and debt market derivatives-0496-raju
TRANSCRIPT
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Study on Forex and Debt Market Derivatives
Project report submitted toBangalore University
towards the partial fulfillment of the requirement forthe award of MBA Degree.
Submitted by GuideRaju.s Prof,Santhanam
Reg.No: 04XQCM6069
M.P. BIRLA INSTITUTE OF MANAGEMENTAssociate Bharatiya Vidya Bhavan
# 43, Race Course RoadBangalore 560 001
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Acknowledgement
Words are indeed and inadequate to convey my deep sense of
gratitude to all those who had made to this report successfully.
I wish to acknowledge with profound sense of appreciation to the
help and support I received from Prof,Santhanam and Guide, M.P.Birla
Institute of Management for providing the valuable guidance and
suggestions for completing this project report.
I owe a great debt of gratitude to my parents and other members of
my family for having helped me achieve my objective.
I would be failing in my duty if I do not acknowledge my friends
who have helped me in completing this report.
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Declaration
I Mr. Raju.s student of M.P.Birla Institute of Management,
Associate Bharatiya Vidya Bhavan, studying 4th semester MBA
hereby declare that this project report entitled Study on forex and
debt market Derivatives has been prepared by me during
academic year 2005-06 in the partial fulfilment of Master Degree of
Business Administration.
I also hereby declare that this project report has not been
submitted anytime to any other University or Institute for the award
of any Degree or Diploma.
Date:
Place: (Raju.s)
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PRINCIPALS CERTIFICATE
This to certify that this report titled Study on forex and Debt market
Derivatives has been prepared by Mr. Raju.s bearing the
registration No.04XQCM6069, under the guidance and supervision
ofPro.Santhanam, MPBIM, Bangalore.
Place:
Date: Principal
(Dr.N.S.Malavalli)
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GUIDES CERTIFICATE
This is to certify that mr Raju s,bearing reg no.04XQCM6069 has
prepared a report titled Study on forex and Debt market Derivetives
under my guidance. This has not formed the basis for the award of
any degree/diploma for any university.
Place:
Date: ( Raju.s)
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Executive Summary
Derivatives are one of the instruments in the hands of the investors which are useful
in fulfilling the needs of investors. This can be either to hedge the risk of the
underlying or to take a speculative view and make profits or losses and arbitrage
opportunities. This entirely speaks about the derivatives, its uses and the ways how
the individuals, banks and corporate use this instrument to make huge profit. To make
huge profit they want to take same amount of risk.
The topic of dissertation is Study on Forex and Debt market derivatives. This study
entirely speaks about the ways in which the interest rate risk is hedged like interest
rate futures, interest rate options, forward rate agreements and swaps, the reasons for
fluctuation in interest rates, the hedge ratio that is to be used and different ways of
calculating the hedge ratio like Market Value Nave Model, Face Value Nave Model,
Hedge Ratio, Regression Model, price sensitivity model and others.
Further the study carries towards the introduction of options, the ways how the
options are helpful in hedging the risk so that the profit is also reaped with less loss
which occurs by paying premium. The strategies used in the options like straddle,
strangle, bull spread, bear spread, and butterfly spread. It further carries towards the
Black Scholes Model and the assumption made by him for calculating the prices of
the options and it also speaks regarding the Delta, Gamma, Vega, RHO and Theta.
Then the study explains about the currency risk which is faced by most of the
exporters, importers and to those who deal in forex market and it gives a solution how
the currency risk can be hedged by using the currency futures and currency options.The factors which play the major role in determining exchange rate and the three
important theories on exchange rate i.e., Interest rate parity, Purchase power parity
and Fishers theory.
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Swaps, which are more efficient than interest rate futures, currency futures, interest
rate options and currency options. The various swaps used by the individual, banks
and corporate to hedge the interest rate risk and currency risks and the use of interest
rate swaps and currency swaps to corporate.
For most of the explanation there is a real life example how the interest rate futures
and currency futures are traded in Chicago Mercantile Exchange. Based on the study
there are two questioners for two different risks that is interest rate risk and currency
risk. This questioners speaks about the Indias position in interest rate futures and
options and currency futures and options.
At last with findings with the reasons as to why interest rate futures thinly traded in
India and reasons as to why the currency risk is the most unhedged risk in India. And
at the same time the conclusion which talks about the steps to be taken by the RBI and
SEBI in respect how to increase the trading in Interest rate futures and options and
currency futures and options
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TABLE OF CONTENTSDeclaration
Certificate by GuideAcknowledgementExecutive Summary
ChapterNo
Title Pageno
1 Introduction to derivatives 1
2 Introduction to Forward and Futures 3
2.1 Introduction to Forward contracts 3
2.2 Introduction to Futures 3
2.3 Distinction between futures and forwards 32.4 Futures Prices 4
2.4.1 Cost-of-carry model in perfect markets 4
2.4.2 The reverse cash-and-carry 5
2.4.6 Payoff for derivatives contracts 9
2.4.6.1 Payoff for a buyer of Nifty futures 9
2.4.6.2 Payoff for a seller of Nifty futures 9
3 Hedging Strategies 10
3.1 Face Value Naive Model 10
3.2 Market Value Naive Model 103.3 Conversion Factor Model 10
3.4 Basis Point Model 103.5 Regression Model 11
3.6 Price Sensitivity Model 11
4 Interest Rate Futures 13
4.1 Treasury-Bill Futures 13
4.2 Eurodollar Futures 14
4.3 Long term Treasury Futures 16
5. Currency Futures 185.1 Currency Exchange Risk 18
5.2 Currency Future with example 18
5.3 Three Theories of Exchange Rate 21
5.3.1 Purchase Power Parity (PPP) 21
5.3.2 International Fisher Effect (IFE) 21
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5.3.3 Purchasing Power Parity and Exchange Rate
Determination
22
5.3.4 Interest Rate Parity 23
5.3.5 IRP and Covered Interest Arbitrage 24
5.3.6 IRP and Hedging Currency Risk 24
5.3.7 IRP and a Forward Market Hedge 25
6 Options 26
6.1 Introduction 26
6.2 Option Terminology 27
6.3 The Four Basic Option Trades 28
6.3.1 Long Call 28
6.3.2 Long Put 29
6.3.3 Short Call (Nakedshort call) 31
6.3.4 Short Put 32
6.4 Introduction to Option Strategies 33
6.5 Black Scholes Option Model 34
7. Interest Rate Derivatives 37
7.2 Points of Interest: What Determines Interest Rates? 37
7.2.1 Supply and Demand 38
7.2.2 Expected Inflation 387.2.3 Economic conditions 39
7.2.4 Federal Reserve Actions 39
7.2.5 Fiscal Policy 39
7.3 Interest Rate Predictions 40
7.4 Forward rate agreement (FRA) 40
8. Interest rate options 42
8.1 Hedging Pre-Issue Pricing Risk for Fixed-Rate Debt 42
8.2 Hedging Solutions 43
8.2.1 Caps-Hedging against rising interest rate 43
8.2.2 Floors-Hedging against falling interest rate 44
8.2.3 Treasury collars 44
8.3 Hedging A Large Debt Issue 45
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8.4 Options on interest rate futures 45
8.5 Futures positions after option exercise. 47
8.6 Trading Example: Hedging with Options on CME Interest
Rate Futures
47
9. Currency Options 49
9.1 Introduction 49
9.2 Hedging with Options 49
10. Swaps 53
10.1 Introduction 53
10.2 Interest Rate Swap 53
10.3 Manage interest rate risk with a solution tailored to match a
specific risk profile
53
10.4 Why Use Swaps? 54
10.5 Interest Rate Swaps 54
10.6 An IRS can also be used to transform assets 56
10.7 Swaps for a comparative advantage 56
10.8 Swaps for Reducing the Cost of Borrowing 58
10.9 Currency Swaps 60
10.10 A plain vanilla foreign currency swap 61
10.11 Swaption 6111. Research Design 63
11.1 Questionnaire 64
12. Analysis and Interpretation 74
13. Findings 90
14. Conclusion 93
15. Bibliography 96
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Graphs
Figureno.
Particulars Pageno.
1. Depicts the ways in which Banks/Firms have hedged
there interest rates.
74
2 Depicts the counterparty risk faced by banks/firms 74
3 Depicts the reasons for the thin trade in the Indian Interestrate futures market.
75
4 Depicts that number of contracts has been increased due tothe CCILs proposal to settle FRA and IRS.
76
5 Depicts the different strategy used by the Banks andCorporate to Hedge the interest rate risk.
76
6 Depicts the various methods used by the Banks and
Corporate to reduce the duration of Portfolio/BalanceSheet
77
7 Depicts the favourable reasons given by respondents toenter with forwards than futures.
77
8 Depicts arbitrage opportunity exist with option pricing butdue to the transaction cost this disappears.
78
9 Depicts the various variables the respondents look at whiletrading in Option.
78
10 Depicts the basis points which the respondent expectsabove the term structure of interest rate because it does notaccommodate tax status, default risk, call option andliquidity risk
79
11 Depicts option adjusted spread will accommodate the riskswhich term structure does not consider.
79
12 Depicts the responses given by respondents when theyasked about if they would like to lend and borrow 6months down the line.
80
13 Depicts the various features which force the respondents toenter into swaps.
80
14 Comparison between to Interest rate swaps currencyswaps.
81
15 Depicts the factors which influence pricing the swaps. 81
16 Depicts the various derivative products used by the banks
and corporate to hedge the risks like default risk, basis risk,mismatch risk and interest rate risk.
82
17 Depicts most of the respondents agree that swaps aresuperior to interest rate futures and options.
82
18 Depicts swap dealers enter into Interest rate futures andoptions which has created more liquidity in bond markets.
83
19 Depicts the favourable reasons for the investorspreference to purchase structured notes.
83
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20 Depicts the favourable reasons for the issuers to issuestructured notes.
84
21 Depicts the features available in the interest rate swapswhich the respondents ranked according to therepreference.
84
22 Depicts the features available in the currency swaps which
the respondents ranked according to there preference
85
23 Depicts that 100% respondent banks and firms trade inforeign exchange.
85
24 Depicts the various type of arbitrage opportunity thebank/firms come across when they trade in foreigncurrency.
86
25 Depicts the exchange rate systems which the respondentsliked
86
26 Depicts the factors which are important in determining theexchange rate.
87
27 Depicts does FDIs and FIIs should be allowed to hedgethere foreign exchange in India.
87
28 Depicts does inflows will increase if FIIs and FDIs areallowed to hedge there foreign exchange in India
88
29 a Depicts the various reasons for the currency risk which ismost un hedged risk in India.
89
29b Depicts the various reasons for the currency risk which ismost un hedged risk in India.
89
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1. Introduction to derivatives
A derivative is a financial instrument which derives its value from some other
financial price. This other financial priceis called the underlying. A wheat farmer
may wish to contract to sell his harvest at a future date to eliminate the risk of a
change in prices by that date. The price for such a contract would obviously depend
upon the current spot price of wheat. Such a transaction could take place on a wheat
forward market. Here, the wheat forward is the derivativeand wheat on the spot
market is the underlying. The terms derivative contract, derivative product, or
derivativeare used interchangeably.
The emergence of the market for derivative products, most notably forwards, futures
and options, can be traced back to the willingness of risk-averse economic agents to
guard themselves against uncertainties arising out of fluctuations in asset prices. By
their very nature, the financial markets are marked by a very high degree of volatility.
Through the use of derivative products, it is possible to partially or fully transfer price
risks by lockingin asset prices. As instruments of risk management, these generally
do not influence the fluctuations in the underlying asset prices. However, by locking-
in asset prices, derivative products minimize the impact of fluctuations in asset prices
on the profitability and cash flow situation of risk-averse investors.
Derivative products initially emerged as hedging devices against fluctuations in
commodity prices, and commodity-linked derivatives remained the sole form of such
products for almost three hundred years. Financial derivatives came into spotlight in
the post-1970 period due to growing instability in the financial markets. However,
since their emergence, these products have become very popular and by 1990s, they
accounted for about two-thirds of total transactions in derivative products. In recent
years, the market for financial derivatives has grown tremendously in terms of variety
of instruments available, their complexity and also turnover. In the class of equity
derivatives the world over, futures and options on stock indices have gained more
popularity than on individual stocks, especially among institutional investors, who are
major users of index-linked derivatives. Even small investors find these useful due to
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high correlation of the popular indexes with various portfolios and ease of use. The
lower costs associated with index derivatives visavis derivative products based on
individual securities is another reason for their growing use.
1.1 Products: Forwards, Futures, Options and Swaps.
1.2 Participants: Hedgers, Speculators, and Arbitrageurs
1.3 Functions
1. Prices in an organized derivatives market reflect the perception of market
participants about the future and lead the prices of underlying to the perceived
future level. The prices of derivatives converge with the prices of the underlying
at the expiration of the derivative contract. Thus derivatives help in discovery of
future as well as current prices.
2. The derivatives market helps to transfer risks from those who have them but may
not like them to those who have an appetite for them.
3. Derivatives, due to their inherent nature, are linked to the underlying cash
markets. With the introduction of derivatives, the underlying market witnesses
higher trading volumes because of participation by more players who would not
otherwise participate for lack of an arrangement to transfer risk.
4. Speculative trades shift to a more controlled environment of derivatives market. In
the absence of an organized derivatives market, speculators trade in the
underlying cash markets. Margining, monitoring and surveillance of the activities
of various participants become extremely difficult in these kinds of mixed
markets.
5. An important incidental benefit that flows from derivatives trading is that it acts as
a catalyst for new entrepreneurial activity. The derivatives have a history of
attracting many bright, creative, well-educated people with an entrepreneurial
attitude. They often energize others to create new businesses, new products and
new employment opportunities, the benefit of which are immense
6. Derivatives markets help increase savings and investment in the long run. Transfer
of risk enables market participants to expand their volume of activity.
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2. Introduction to Forward and Futures
2.1 Introduction to Forward contracts
In a forward contract, two parties irrevocably agree to settle a trade at a future date,
for a stated price and quantity. No money changes hands at the time the trade is
agreed upon.
Suppose a buyerLand a seller Sagrees to do a trade in 100 grams of gold on 31 Dec
2005 at Rs.5, 000/ten gram. Here, Rs.5,000/tola is the forward price of 31 Dec 2005
Gold.
The buyerLis said to be long and the seller Sis said to be short. Once the contract
has been entered into, L is obligated to pay S Rs. 500,000 on 31 Dec 2005, and take
delivery of 100 gram of gold. Similarly, S is obligated to be ready to accept
Rs.500,000 on 31 Dec 2005, and give 100 gram of gold in exchange.
2.2 Introduction to Futures
A futures contract is an agreement between two parties to buy or sell an asset at a
certain time in the future at a certain price. Futures contract is same as forward
contracts. But unlike forward contracts, the futures contracts are standardized and
exchange traded.
2.3. Distinction between futures and forwards
Futures Forwards
Trade on an organized exchange OTC in nature
Standardized contract terms Customised contract terms
Hence more liquid Hence less liquid
Requires margin payments No margin payment
Follows daily settlement Settlement happens at end of
period
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2.4 Futures Prices
2.4.1 Cost-of-carry model in perfect markets
Assume that markets are perfect in the sense of being free from transaction costs and
restrictions on short selling. The spot price of gold is $370. Current interest rates are
10 percent per year, compounded monthly. According to the cost-of-carry model, the
price of a gold futures contract be if expiration is six months away is
In perfect markets, the cost-of-carry model gives the futures price as:
F0,t = S0 (1 +C)
F0,t= the future price at t=0 for delivery at t=1
S0= the spot price at time t=0
C = the cost of carry, expressed as a fraction of the spot price, necessary to carry the
good forward from the present to the delivery date on the futures.
The cost of carrying gold for six months is (1+.10/12)6- 1= .051053. Therefore, the
futures price should be: F0, t =$370(1.051053) = $388.89
2.4.2Consider the information of 4.1 given above.Now let us assume that futures
trading costs are $25 per 100-ounce gold contract, and buying or selling an ounce of
gold incurs transaction costs of $1.25. Gold can be stored for $.15 per month per
ounce. (Ignore interest on the storage fee and the transaction costs.)
What futures prices are consistent with the cost-of-carry model?
Answering this question requires finding the bounds imposed by the cash-and-carry
and reverse cash-and-carry strategies. For convenience, we assume a transaction size
of one 100-ounce contract.
2.4.2.1 For the cash-and-carry, the trader buys gold and sells the futures. This
strategy requires the following cash outflows:
Transactions Cash flow
Buy gold -$370(100)
Pay transaction costs on the spot -$1.25(100)
Pay the storage cost -$.15(100) (6)
Sell futures 0
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Borrow to finance these outlays -$37,215
Six months later, the trader must:
Pay the transaction cost on one future -$25
Repay the borrowing -$39,114.95
Deliver on futures ?
Net outlays at the outset were zero, and they were $39,139.95 at the horizon.
Therefore, the futures price must exceed $391.40 an ounce for the cash-and-carry
strategy to yield a profit.
2.4.2.2 The reverse cash-and-carry incurs the following cash flows. At the outset,
the trader must:
Particulars Cash flows
Sell gold +$370(100)
Pay transaction costs on the spot -$1.25(100)
Invest funds -$36,875
Buy futures 0
These transactions provide a net zero initial cash flow. In six months, the trader has
the following cash flows:
Collect on investment +$36,875(1+.10/12)6= $38,757.59
Pay futures transaction costs -$25
Receive delivery on futures ?
The breakeven futures price is therefore $387.33 per ounce. Any lower price will
generate a profit. From the cash-and-carry strategy, the futures price must be less than
$391.40 to prevent arbitrage. From the reverse cash-and-carry strategy, the price must
be at least $387.33. (Note that we assume there are no expenses associated with
making or taking delivery.)
2.4.3 Consider the information given in 2.4.1 and 2.4.2 above.Restrictions on short
selling effectively mean that the reverse cash-and-carry trader in the gold market
receives the use of only 90 percent of the value of the gold that is sold short. Based on
this new information, what is the permissible range of futures prices?
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This new assumption does not affect the cash-and-carry strategy, but it does limit the
profitability of the reverse cash-and-carry trade. Specifically, the trader sells 100
ounces short but realizes only .9($370)(100) =$33,300 of usable funds. After paying
the $125 spot transaction cost, the trader has $33,175 to invest.
Therefore, the investment proceeds at the horizon are:
$33,175(1+.10/12)6= $34,868.69.
Thus, all of the cash flows are:
Sell gold +$370(100)
Pay transaction costs on the spot -$1.25(100)
Broker retains 10 percent -$3,700
Invest funds -$33,175
Buy futures 0
These transactions provide a net zero initial cash flow. In six months, the trader has
the following cash flows:
Collect on investment $34,868.69
Receive return of deposit from broker $3,700
Pay futures transaction costs $25
Receive delivery on futures ?
The breakeven futures price is therefore $385.44 per ounce. Any lower price will
generate a profit. Thus, the no-arbitrage condition will be fulfilled if the futures price
equals or exceeds $385.44 and equals or is less than $391.40.
2.4.4 Consider allof the information about gold from 2.4.1 to 2.4.3. The interest
rate in question 2.4.1is 10 percent per annum, with monthly compounding. This is the
borrowing rate. Lending brings only 8 percent, compounded monthly. What is the
permissible range of futures prices when we consider this imperfection as well?
The lower lending rate reduces the proceeds from the reverse cash-and-carry strategy.
Now the trader has the following cash flows:
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Transactions Cash flow
Sell gold +$370(100)
Pay transaction costs on the spot -$1.25(100)
Broker retains 10 percent -$3,700
Invest funds -$33,175
Buy futures 0
These transactions provide a net zero initial cash flow. Now the investment will yield
only $33,175(1+.08/12)6= $34,524.31.
In six months, the trader has the following cash flows:
Transactions Cash flow
Collect on investment $34,524.31
Pay futures transaction costs $25
Receive delivery on futures ?
Return gold to close short sale 0
Receive return of deposit from broker $ 3,700
Total proceeds on the 100 ounces are $38,199.31. Therefore, the futures price per
ounce must be less than $381.99 for the reverse cash-and-carry strategy to profit.
Because the borrowing rate has not changed, the bound from the cash-and-carry
strategy remains at $391.40. Therefore, the futures price must remain within the
inclusive bounds of $381.99 to $391.40 to exclude arbitrage.
2.4.5 Consider all of the information about gold from 2.4.1 to 2.4.4 . The gold
future expiring in six months trades for $375 per ounce. Given all of the market
imperfections we have considered assuming that gold trades for $395.
If the futures price is $395, it exceeds the bound imposed by the cash-and-carry
strategy, and it should be possible to trade as follows:
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Cash-and-Carry Arbitrage
t =0 Borrow $37,215 for 6 months at 10%. +$37,215.00
Buy 100 ounces of spot gold. -37,000.00
Pay storage costs for 6 months. -90.00
Pay transaction costs on gold purchase. -125.00
Sell futures for $395. 0.00
Total Cash Flow $0
t =6 Remove gold from storage. $0
Deliver gold on futures. +39,500.00
Pay futures transaction cost. -25.00
Repay debt. -39,114.95
Total Cash Flow -$360.05
If the futures price is $375, the reverse cash-and-carry strategy should generate a
profit as follows:
Reverse Cash-and-Carry Arbitrage
t=0 Sell 100 ounces of gold short. +$37,000.00
Pay transaction costs. -125.00
Broker retains 10%. -3,700.00
Buy futures. 0
Invest remaining funds for 6 months at 8%. -33,175.00
Total Cash Flow $0
t=6 Collect on investment. -$34,524.31
Receive delivery on futures. -37,500.00
Return gold to close short sale. 0
Receive return of deposit from broker. +3,700.00
Pay futures transaction cost. -25.00
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Total Cash Flow +$699.31
2.4.6 Payoff for derivatives contracts
2.4.6.1 Payoff for a buyer of Nifty futures
The figure shows the profits/losses for a long futures position. The investor bought
futures when the index was at 1220. If the index goes up, his futures position starts
making profit. If the index falls, his futures position starts showing losses.
2.4.6.2 Payoff for a seller of Nifty futures
The figure shows the profits/losses for a short futures position. The investor sold
futures when the index was at 1220. If the index goes down, his futures position starts
making profit. If the index rises, his futures position starts showing losses.
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3. Hedging Strategies
Alex Brown has to hedge $500 million of long-term debt that his firm plans to issue in
May. The possible strategies Alex Brown could use to hedge his impending debt
issue.
3.1 Face Value Naive Model: In this method Alex would trade one dollar of nominal
futures contract per one dollar of debt face value. The major benefit of this method is
the ease of implementation. Unfortunately, it ignores market values and the
differential responses of the bond and futures contract prices to interest rates.
3.2 Market Value Naive Model: In this method Alex would hedge one dollar of debt
market value using one dollar of futures price value. That is, the hedge ratio is
determined by the market prices instead of nominal and face values. Unfortunately, it
does not consider the price sensitivities of the two instruments.
3.3 Conversion Factor Model: This model can be used when the hedging instrument
is a T-note or T-bond futures contract. The conversion factor adjusts the prices of
deliverable bonds and notes that do not have a 6% coupon to make them equivalent
to the 6% coupon bond or note that is called for in the contract. The hedge ratio is
determined by multiplying the Face Value Naive hedge ratio by the conversion factor.
The appropriate conversion factor to use is the conversion factor of the cheapest to
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deliver T-bond or T-note. This model still ignores price sensitivity differences
between the hedging and hedged instruments. The hedge ratio is calculated as below.
HR= - (Cash market principal/Futures market principal)*(Conversion
Factor)
3.4 Basis Point Model: This model uses the price changes of the futures and cash
positions resulting from a one basis point change in yields to determine the hedge
ratio. It is calculated as:
This model works well if the cash and futures instruments face the same rate
volatility. If they face different volatilities and that relationship can be quantified, then
the basis point model can be adjusted to account for the differing volatilities.
3.5 Regression Model: In the regression model the historic relationship between cash
market price changes and futures market price changes is estimated. This estimation is
accomplished by regressing price changes in the cash market on futures price
changes. The slope coefficient from this regression is then used as the hedge ratio.
Alex may not find this model useful, as he is trying to hedge a new debt issue. Even if
Alex had an historic price stream on 30-year corporate debt issues, the historic
relationship with the futures price might prove to be an unreliable indicator of the
present or future relationship. This stems from the fact that the price response of the
futures contract is determined by the cheapest-to-deliver bond. The cheapest-to-
deliver bond can vary in maturity from 15 years to 30 years. This means that the
futures contract can have very different price responses to interest rates at different
points in time.
For the RGR model the hedge ratio is:
HR= - (COVs,f/Variance of futures)
COVs,f = covariance between cash and futures.
3.6 Price Sensitivity Model: This may be a good model for Alex to use. It is designed
for interest rate hedging, and it accounts for the differential price responses of the
hedging and the hedged instruments. The model is duration-based so that it accounts
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for maturity and coupon rate differences of the cash and the futures positions. It is
computed as:
Where:
FPF and Pi are the respective futures contract and cash instrument prices; MDi and
MDF are the modified durations for the cash and futures instruments, respectively,
and RYC is the change in the cash market yield relative to the change in the futures
yield.
Let us look at an example. Alex Brown has just returned from a seminar on using
futures for hedging purposes. As a result of what he has learned, he re-examines his
decision to hedge $500 million of long-term debt that his firm plans to issue in May.
Face Value Naive hedge: In this model Alex current hedge is a short position of
5,000 T-bond futures contracts ($100,000 each). Currently Alex has employed a Face
Value Naive hedge. For each dollar of debt principal he plans to issue, he is short $1
of nominal T-bond futures. The benefit of the strategy is its ease of implementation.
The drawback is that cash instrument and the T-bond futures may have differential
price responses to interest rate changes.
Price sensitivity hedge: Alex feels that a price sensitivity hedge would be most
appropriate for his situation. The additional information is if the debt could be issued
today, it would be priced at 119-22 to yield 6.5%. With its 8% coupon and 30 years to
maturity, the duration of the debt would be 13.09 years. On the futures side, the
futures prices are based on the cheapest-to-deliver bonds, which are trading at 124-14
to yield 5.6%. These bonds have duration of 9.64 years.
The price sensitivity hedge ratio is:
FPF= 124.4375%*0.1 million MDF= 9.128788
Pi= 119.6875%_500 million MDi = 12.29108
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To hedge the risk, 6,475 contracts should be sold.
4. Interest Rate Futures
Interest rate futures were introduced in 1975 and were an immediate success. The
volume represents about one half of all future market activity. Almost all of the
trading in interest rate futures is at the Chicago Board of Trade and the International
Money Market (IMM) of the Chicago Mercantile Exchange.
4.1 Treasury-Bill Futures
The IMM T-Bill contract calls for the delivery of treasury bills with a face value of $1
million and 90 days to maturity at the expiration of the contract. The IMM uses a
special code for stating the price of T-bills; i.e., the price is given by the IMM index
which is 100-DY, where DY is the discount yield in percent. An alternative way of
stating this relation for bills having a year until maturity is:
PRICE OF CONTRACT = 1,000,000(1 - DY/100)
If the T-bills have DTM days to maturity the price is given by:
PRICE OF CONTRACT = 1,000,000(1 - (DY/100)(DTM/360))
For every change in the discount yield of one basis point (1/100 of 1 percent) the price
of the contract changes by $25.
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The price of a $1,000,000 face value 90-day T-bill has a discount yield of 8.75
percent.
Applying the equation for the value of a T-bill, the price of a $1,000,000 face value T-
bill is $1,000,000 -DY($1,000,000)(DTM)/360, where DY is the discount yield and
DTM= days until maturity. Therefore, if DY=0.0875 the bill price is:
Bill Price= $1,000,000-{(0.0875 ($1,000,000) (90))/360} = $978,125
Let us look at one more example. The IMM Index stands as 88.70. If you buy a T-bill
future at that index value and the index becomes 88.90, what is your gain or loss?
The discount yield = 100.00- IMM Index = 100.00- 88.70 = 11.30 percent.
If the IMM Index moves to 88.90, it has gained 20 basis points, and each point is
worth $25. Because the price has risen and the yield has fallen, the long position has a
profit of $25(20) = $500.
4.2 Eurodollar Futures
Eurodollars are any dollar denominated deposit in a bank outside of the U.S. Thus
dollar deposits in Singapore are still called Eurodollars. Eurodollar accounts are not
transferable but banks can lend on the basis of the Eurodollar accounts it holds. The
interest rate charged for Eurodollar loans is often based upon the London Inter bank
Offer Rate (LIBOR).
The Eurodollar contract on the IMM is also for $1 million. Since Eurodollar accounts
are not transferable it is not possible to actually make delivery on Eurodollar
contracts. Instead there is a cash settlement at the end of the contract period. In the
case of Eurodollar contracts the discount yield is replaced by an add-on yield which is
the interest earned in proportion to the original price. Thus,
Add-on Yield = DY/(1 - DY/100)
CME Eurodollar Interest Rate Futures Example
Suppose a financial manager of a company wishes to borrow US$10 million for 1
year at a fixed rate. She can ask a bank for a fixed rate for 1 year directly or a floating
rate and seek to hedge using an interest rate futures (eg: the CME Eurodollar futures).
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The value of a CME Eurodollar interest rate futures contract rises when interest rates
fall and vice versa, hence the manager would need a short position to hedge. Hence if
interest rates rise, the value of the contract falls and a short position is in the money
(sold high, can buy back low).
The notional principal of a CME Eurodollar interest rate futures contract is
US$1million. The price of the CME Eurodollar interest rate futures contract at the
maturity date is 100-RwhereRis the 90-day Libor interest rate that starts when the
contract matures on the 3rd Wednesday or each delivery month. This interest rate is
then the underlying variable for this contract.
The value of the CME Eurodollar interest rate futures contract on any given day
before it matures is given by the formula: 10000*[100-0.25(100-Z)] where Z is the
price of the futures contract at that time given by supply and demand! This implies
that for each basis point move in the price, the contract value changes by US$25.
E.g.: If Z = 94.32, V = 985,800
If Z = 94.33, V = 985,825
The contract is settled daily like any futures contract with variation margin payments.
Suppose the company does not hedge and interest rates and interest payments (using
90/360 convention) turn out to be:
Sep 15 1.89% 47250
Dec 15 2.44% 61000
Mar 15 2.75% 68750
Jun 15 2.90% 72500
Total interest rate cost = 249500
Suppose the financial manager hedges by selling US$10 million CME Eurodollar
interest rate futures short for maturities Sep, Dec and Mar and the relevant prices are
as follows:
Prices at Maturity
Today Sep Dec Mar
Spot 1.89%
Futs Sep 2.08% (97.92) 97.60 (2.4%)
Dec 2.54% (97.46) 97.31 (2.69%)
Mar 3.18% (96.82) 97.15 (2.85%)
This implies
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VToday/Sep=10*10000*[100-0.25(100-97.92)]=9948000
VSep/Sep= 10*10000*[100-0.25(100-97.60)]=9940000
Profit = 8000 = 10*25*(9792-9760)
VToday/Dec=10*10000*[100-0.25(100-97.46)]=9936500
VDec/Dec= 10*10000*[100-0.25(100-97.31)]=9932750
Profit = 3750 = 10*25*(9746-9731)
VToday/Mar=10*10000*[100-0.25(100-96.82)]=9920500
VMar/Mar= 10*10000*[100-0.25(100-97.15)]=9932750
Profit = -8250 = 10*25*(9682-9715)
Total costs
Interest costs as before Futures profit/loss
Sep 15 1.89% 47250
Dec 15 2.44% 61000 8000
Mar 15 2.75% 68750 3750
Jun 15 2.90% 72500 -8250
Total interest rate cost 249500 3500 (profit)
Total costs 249500-3500 = 246000
4.3 Long term Treasury Futures
Regardless of your market outlook, U.S. Treasury bond and note futures are the ideal
tools to help you adjust the risk/return characteristics of your fixed income securities.
Here are some of the many risk-management opportunities they offer.
Lock in a Purchase Price: If you plan to purchase fixed-income securities in the
futures and are concerned about the possibility of higher prices, you can buy Treasury
futures and secure a maximum purchase price.
Preserve Investment Value: By selling Treasury futures, you can lock in an attractive
selling price and protect the value of a portfolio or individual security against possible
decreasing prices.
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Cross-Hedge: U.S. Treasury bond and note futures can be used to control risk and
enhance the returns of non-U.S. government securities. Treasury futures can be
effective risk-management tools for corporate bonds, Eurobonds, and other fixed-
income instruments.
Trade Changes in the Yield Curve
Because Treasury futures cover a wide spectrum of maturities from short-term notes
to long-term bonds, you can construct trades based on the differences in interest rate
movements all along the yield curve.
Contract Specifications:
Trading Unit
T-bond Futures - One U.S. Treasury bond with $100,000 face value at maturity.
10-year T-note Futures - One U.S. Treasury note with $100,000 face value at
maturity.
5-year T-note Futures - One U.S. Treasury note with $100,000 face value at
maturity.
2-year T-note Futures - One U.S. Treasury note with $200,000 face value at
maturity.
Deliverable Grades
T-bond Futures-Bonds with at least 15 years remaining to maturity.
10-year T-note Futures- Notes with 61/2 to 10 years remaining to maturity.
5-year T-note Futures- Notes with 4 years 3 monthsto 5 years 3 months remaining
to maturity.
2-year T-note Futures- Notes with 1 year 9 months to 2 years remaining to maturity.
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Tick Size
T-bond Futures- 1/32
10-year T-note Futures - 1/32
5-year T-note Futures - 1/2 of 1/32
2-year T-note Futures - 1/4 of 1/32
5. Currency Futures
5.1 Currency Exchange Risk
How do currency fluctuations affect import/exporters?
Exchange rate volatility can work against an international company if a payment in a
foreign currency has to be made at a future date. There is no way to guarantee that the
price in the currency market will be the same in the future-it is possible that the price
will move against the company, making the payment cost more. On the other hand,
the market can also move in a business' favour, making the payment cost less in terms
of their home currency.
Generally, firms that export goods to other countries benefit when their home
currency depreciates, since their products become cheaper in other countries. Firms
that import from other countries benefit when their currency becomes stronger, since
it enables them to purchase more.
Hedging Against Currency Risk to Avoid the Volatility Trap
so how can a business protect against a risky currency? One way is to avoid the riskby minimizing their commercial involvement with countries that have volatile
currencies like the Japanese Yen. This is however not a practical solution. Another
way is to hedge in the spot currency market by taking a position that effectively
neutralizes the volatility in the pair.
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5.2 Currency Future:It is a futures contract to exchange one currency for another at
a specified date in the future at a price (exchange rate) that is fixed on the last trading
date. Typically, one of the currencies is the US dollar. The priceof a future is then in
terms of US dollars per unit of other currency. This can be different from the standard
way of quoting in the spot foreign exchange markets. The trade unitof each contract
is then a certain amount of other currency, for instance EUR 125,000. Most contracts
have physical delivery, so for those held at the end of the last trading day, actual
payments are made in each currency. However, most contracts are closed out before
that.
Example
Peter buys 10 September CME Euro FX Futures, at 1.2713 USD/EUR. At the end of
the day, the futures close at 1.2784 USD/EUR. The change in price is 0.0071
USD/EUR. As each contract is over EUR 125,000, and he has 10 contracts, his profit
is USD 8,875. As with any future, this is paid to him immediately.
More generally, each change of 0.0001 USD/EUR (the minimum tick size), is a profit
or loss of USD 12.5 per contract.
Investors use these futures contracts to hedge against foreign exchange risk. They can
also be used to speculate and, by incurring a risk, attempt to profit from rising or
falling exchange rates. Investors can close out the contract at any time prior to the
contract's delivery date.
Currency futures were first created at the Chicago Mercantile Exchange (CME) in
1972, less than one year after the system of fixed exchange rates was abandoned
along with the gold standard. Some commodity traders at the CME did not have
access to the inter-bank exchange markets in the early seventies, when they believed
that significant changes were about to take place in the currency market. They
established the International Monetary Market (IMM) and launched trading in seven
currency futures on May 16, 1972. Today, the IMM is a division of CME. In the
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second quarter of 2005, an average of 332,000 contracts with a notional value of USD
43 billion were traded every day. Most of these are traded electronically nowadays
A futures contract is like a forward contract it specifies that a certain currency will be
exchanged for another at a specified time in the future at prices specified today. A
futures contract is different from a forward contract. Futures are standardized
contracts trading on organized exchanges with daily resettlement through a
clearinghouse
The Standardizing Features
! Contract Size
! Delivery Month
! Daily resettlement
Initial Margin (about 4% of contract value, cash or T-bills held in a street name at
your brokers).
Suppose you want to speculate on a rise in the $/ exchange rate (specifically you
think that the dollar will appreciate).
Currently $1 = 140. The 3-month forward price is $1=150.
! Currently $1 = 140 and it appears that the dollar is strengthening.
! If you enter into a 3-month futures contract to sell at the rate of $1 = 150
you will make money if the yen depreciates.
! The contract size is 12,500,000
! Your initial margin is 4% of the contract value:
If tomorrow, the futures rate closes at $1 = 149, then your positions value drops.
Currency per
U.S. $ equivalent U.S. $
Wed Tue Wed Tue
Japan (yen) 0.007142857 0.007194245 140 139
1-month forward 0.006993007 0.007042254 143 142
3-months forward 0.006666667 0.006711409 150 1496-months forward 0.00625 0.006289308 160 159
150
$1012,500,00.04$3,333.33 !!"
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Your original agreement was to sell 12,500,000 and receive $83,333.33
But now 12,500,000 is worth $83,892.62
You have lost $559.28 overnight
! The $559.28 comes out of your $3,333.33 margin account, leaving $2,774.05
! This is short of the $3,355.70 required for a new position.
Your broker will let you slide until you run through your maintenance margin. Then
you must post additional funds or your position will be closed out. This is usually
done with a reversing trade.
5.3 Three Theories of Exchange Rate
5.3.1Purchase Power Parity (PPP)
Focuses on inflation and exchange rate relationship if the law of one price was true
for all goods and services, we could obtain the theory of PPP. It Postulates the
equilibrium exchange rate between currencies of two countries is equal to the ratio of
the price levels in the two nations. Prices of similar products of two different
countries should be equal when measured in a common currency
For example if nationAis US and nationBis the UK the exchange rate b/w dollar and
pound is equal to the ratio of US to UK prices. If the general price level in US is twice
to the general level in UK, then the absolute PPP theory postulates equilibrium rate to
be
Rab = S 2/Stg 1
5.3.2 International Fisher Effect (IFE)
IFE Uses Interest Rates rather than inflation rate difference to explain the changes in
interest rates over time. IFE is closely related to PPP because interest rates are
significantly correlated with inflation rates. The relationship b/w the percentage
change in the spot exchange rates in different national capital markets is known as
149
$1012,500,0062.892,83$ !"
149
$1012,500,00.04$3,355.70 !!"
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IFE. IFE suggests that given two countries, the currency with the higher interest rates
will depreciate by the amount of interest rate differential. This is with a country the
nominal interest rate tends to approximately equal the real interest rate plus the
expected inflation The proportion that the nominal interest rate varies directly with
the expected inflation rate, known as Fisher effect has subsequently been incorporated
into the theory of exchange rate determination.
IRP is an arbitrage condition that must hold when international financial markets are
in equilibrium. Suppose that you have $ 1 to invest over, say a one-year period.
Consider two alternative ways of investing your fund.
1. Invest domestically at the U.S interest rate or alternatively
2. Invest in a foreign country, say the U.K. at the foreign interest rate and hedge
the exchange risk by selling the maturity value of the foreign investmentforward.
An increase (decrease) in the expected rate of inflation will cause a proportionate
increase (decrease) in the interest rate in the country.
For the U.S., the Fisher effect is written as:
i$ = $ + E($)
Where,
$is the equilibrium expected realU.S. interest rate
E ($)is the expected rate of U.S. inflation
i$is the equilibrium expected nominal U.S. interest rate
If the Fisher effect holds in the U.S. i$ = $ + E($) and the Fisher effect holds in
Japan, i = + E() and if the real rates are the same in each country $ = then
we get the International Fisher Effect E(e) = i$ - i .
If the International Fisher Effect holds, E(e) = i$ - i and if IRP also holds
then forward parity holds.
5.3.3 Purchasing Power Parity and Exchange Rate Determination
S(F- S)-ii "$
S
(F - S)E(e) "
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The exchange rate between two currencies should equal the ratio of the countries
price levels.
S($/) =P$ #P
Relative PPP states that the rate of change in an exchange rate is equal to the
differences in the rates of inflation.
e= $ -
If U.S. inflation is 5% and U.K. inflation is 8%, the pound should depreciate by
3%.
The real exchange rate is
If PPP holds, (1 + e) = (1 + $)/(1 + ), then q= 1.
If q< 1 competitiveness of domestic country improves with currency depreciations.
If q> 1 competitiveness of domestic country deteriorates with currency depreciations.
5.3.4 Interest Rate Parity
IRP is an arbitragecondition. If IRP did not hold, then it would be possible for an
astute trader to make unlimited amounts of money exploiting the arbitrage
opportunity. Since we dont typically observe persistent arbitrage conditions, we can
safely assume that IRP holds.
Suppose you have $100,000 to invest for one year.
You can either
1. Invest in the U.S. at i$. Future value = $100,000(1 +ius)
2. Trade your dollars for yen at the spot rate, invest in Japan at i andhedge your
exchange rate risk by selling the future value of the Japanese investment
forward. The future value = $100,000(F/S)(1 + i)
Since both of these investments have the same risk, they must have the same future
valueotherwise an arbitrage would exist. (F/S)(1 + i) = (1 +ius)
Formally, (F/S)(1 + i) = (1 +ius) or if you prefer,
IRP is sometimes approximatedas
If IRP failed to hold, an arbitrage would exist. Its easiest to see this in the form of an
example.
)1)(1(
1
$
!
!
##
#
"
eq
S
F
i
i"
#
#
$
1
1
S
(F- S))-i(i
"$
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Consider the following set of foreign and domestic interest rates and spot and forward
exchange rates.
Spot exchange rate S($/) = $1.25/
360-day forward rate F360($/) = $1.20/
U.S. discount rate i$ = 7.10%
British discount rate i = 11.56%
5.3.5 IRP and Covered Interest Arbitrage
A trader with $1,000 to invest could invest in the U.S., in one year his investment will
be worth $1,071 = $1,000!(1+ i$) = $1,000!(1.071)
Alternatively, this trader could exchange $1,000 for 800 at the prevailing spot rate,
(note that 800 = $1,000$1.25/) invest 800 at i = 11.56% for one year to achieve
892.48. Translate 892.48 back into dollars at F360($/) = $1.20/, the 892.48 will
be exactly $1,071.
According to IRP only one 360-day forward rate, F360 ($/), can exist. It must be the
case that F360 ($/) = $1.20/Why?
If F360 ($/) $$1.20/, an astute trader could make money with one of the following
strategies:
Arbitrage Strategy IIf F360 ($/) > $1.20/
i. Borrow $1,000 at t= 0 at i$ = 7.1%.
ii. Exchange $1,000 for 800 at the prevailing spotrate,
(Note that 800 =$1,000$1.25/) invest 800 at 11.56% (i) for one year to
achieve 892.48
iii. Translate 892.48 back into dollars, if F360 ($/) > $1.20/ , 892.48 will
be more than enough to repay your dollar obligation of $1,071.
Arbitrage Strategy IIIf F360 ($/) < $1.20/
i. Borrow 800 at t= 0 at i= 11.56%.
ii. Exchange 800 for $1,000 at the prevailing spot rate, invest $1,000 at
7.1% for one year to achieve $1,071.
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iii. Translate $1,071 back into pounds, if F360($/) < $1.20/ , $1,071 will be
more than enough to repay your obligation of 892.48.
5.3.6 IRP and Hedging Currency Risk
You are a U.S. importer of British woolens and have just ordered next years
inventory. Payment of 100M is due in one year.
Spot exchange rate S($/) = $1.25/
360-day forward rate F360($/) = $1.20/
U.S. discount rate i$ = 7.10%
British discount rate i = 11.56%
IRP implies that there are two ways that you fix the cash outflowa) Put your self in a position that delivers 100M in one yeara long forward
contract on the pound. You will pay (100M)(1.2/) = $120M
b) Form a forward market hedge as shown below.
5.3.7 IRP and a Forward Market Hedge
To form a forward market hedge:
Borrow $112.05 million in the U.S. (in one year you will owe $120 million).
Translate $112.05 million into pounds at the spot rate S($/) = $1.25/ to receive
89.64 million.
Invest 89.64 million in the UKat i = 11.56% for one year.
In one year your investment will have grown to 100 millionexactly enough to pay
your supplier.
Forward Market Hedge
Where do the numbers come from? We owe our supplier 100 million in one year
so we know that we need to have an investment with a future value of 100 million.
Since i = 11.56% we need to invest 89.64 million at the start of the year.
How many dollars will it take to acquire 89.64 million at the start of the year ifS($/) = $1.25/?
1.1156
10089.64"
1.25
$1.0089.64$112.05 !"
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6. Options
6.1 Introduction:An option is a contract which gives its holder the right, but not the
obligation, to buy (or sell) an asset at some predetermined price within a specified
period of time. An option is a contract which gives its holder the right, but not the
obligation, to buy (or sell) an asset at some predetermined price within a specified
period of time.
A real life example
Suppose you are on your way to home one day and you notice that house at the end of
the street is for sale. Itsbigger then your current house and has a double bed room.
All this costs only $100,000. Youve just got to buy it! One problem is money: you
dont have anybut within a couple of months, you think you could get it. So what
do you do? Wait and risk losing the house to another buyer?
Here is something you could do: lets say you go down and see the owner of the
house and explain your situation. He feels for your predicament and suggests that you
pay a fee of $1,000. For that $1,000 he will hold the house for exactly two months and
no longer. Should you wish to buy it, you will have to pay $100,000. This means your
total cost is $100,000 + $1,000 = $101,000.
Youve just bought yourself a call option!
Within the two months you can raise the money and buy the house. You could forget
the deal all together and lose the $1000, but not be liable for anything else. Note
paying the $1000 gives you the right but not the obligation to buy the house. The
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owner of the house would be obliged to sell it to you should you so desire, but only
before the two months are up.
Lets fast forward. Two months are almost up and you have managed to secure some
finance. Paying the full price for the house is not a problem. However, you have just
read in the newspaper that housing prices in your area have fallen in the last two
months. Your dream house now has a $90,000 price tag.
What do you do? Take up the option to buy it for $10,000 for more than it s worth?
Certainly not! You would be happy to let your option expire, losing the $1,000
deposit. You could however go and buy the house at the current market price of
$90,000 and save the difference.
However lets say housing prices have increased and the house is really worth
$110,000. What do you do? You would take up your option to buy at $100,000 and
the seller would be obliged to sell it to you. In the markets, this is the same as
exercising a call option.
Hey, if you were so inclined, you could then sell the house at market price and make a
handsome $9,000 profit ($110,000 - $101,000 = $9,000). Then again you might just
want to live in it, but thats beside the point.
6.2 Option Terminology
! Call option: An option to buy a specified number of shares of a security within
some future period.
! Put option: An option to sell a specified number of shares of a security with in
some future period.
! Exercise (or strike) price: The price stated in the option contract at which the
security can be bought or sold.
! Option price: The market price of the option contract.
! Expiration date: The date the option matures.
! Exercise value (intrinsic value): The value of a call option if it were exercised
today = Current stock price - Strike price.
Note: The exercise (intrinsic) value is zero if the stock price is less than the strike
price.
! Seller of option is called Option Writer
! Covered option: A call option written against stock held in an investors portfolio.
Naked (uncovered) option: An option sold without the stock to back it up.
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! In-the-money call: A call whose exercise (strike) price is less than the current
price of the underlying stock.
! Out-of-the-money call: A call option whose exercise (strike) price exceeds the
current stock price.
! LEAPs: Long-term Equity Anticipation securities that are similar to conventional
options except that they are long-term options with maturities of up to 2 1/2 years.
Consider the following data:
Exercise (strike) price = $25.
Stock Price Call Option Price (Premium)
$25 $ 3.00
30 7.50
35 12.00
40 16.50
45 21.00
50 25.50
Price of Strike Exercise Value Intrinsic Value Mkt. Price Time Value
Stock(a) Price(b) of Option(a)-(b) of Option (c) of Option(d) (d) - (c)
25.00 $25.00 $0.00 $ 0.00 $ 3.00 $ 3.00
30.00 25.00 5.00 5.00 7.50 2.50
35.00 25.00 10.00 10.00 12.00 2.00
40.00 25.00 15.00 15.00 16.50 1.50
45.00 25.00 20.00 20.00 21.00 1.00
50.00 25.00 25.00 25.00 25.50 0.50
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6.3 The Four Basic Option Trades
These trades are described from the point of view of a speculator. If they are
combined with other positions, they can also be used in hedging.
6.3.1Long Call :A trader who believes that a stock's price will increase may buy the
stock or instead, buy the right to purchase the stock (a call option). He has no
obligation to buy the stock, only the right to do so until the expiry date. If the
stock price increases by more than the premium paid, he will profit. If the stock
price decreases, he will let the call contract expire worthless, and only lose the
amount of the premium.
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The figure shows the profits/losses for the buyer of a three-month Nifty 1250 call
option. As can be seen, as the spot Nifty rises, the call option is in-the-money. If upon
expiration, Nifty closes above the strike of 1250, the buyer would exercise his option
and profit to the extent of the difference between the Nifty-close and the strike price.
The profits possible on this option are potentially unlimited. However if Nifty falls
below the strike of 1250, he lets the option expire. His losses are limited to the extent
of the premium he paid for buying the option.
6.3.2 Long Put:A trader who believes that a stock's price will decrease can buy the
right to sell the stock at a fixed price. He will be under no obligation to sell the
stock, but has the right to do so until the expiry date. If the stock price
decreases, he will profit by the amount of the decrease less the premium paid.
If the stock price increases, he will just let the put contract expire worthless.
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The figure shows the profits/losses for the buyer of a three-month Nifty 1250 put
option. As can be seen, as the spot Nifty falls, the put option is in-the-money. If upon
expiration, Nifty closes below the strike of 1250, the buyer would exercise his option
and profit to the extent of the difference between the strike price and Nifty-close. The
profits possible on this option can be as high as the strike price. However if Nifty rises
above the strike of 1250, he lets the option expire. His losses are limited to the extent
of the premium he paid for buying the option.
6.3.3 Short Call (Nakedshort call): A trader who believes that a stock's price will
decrease can short sell the stock or instead sell a call. Both tactics are
generally considered inappropriate for small investors. The trader selling a call
has an obligation to sell the stock to the call buyer at the buyer's option. If the
stock price decreases, the short call position will make a profit in the amount
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of the premium. If the stock price increases, the short position will lose by the
amount of the increase less the amount of the premium.
The figure shows the profits/losses for the seller of a three-month Nifty 1250 call
option. As the spot Nifty rises, the call option is in-the-money and the writer starts
making losses. If upon expiration, Nifty closes above the strike of 1250, the buyer
would exercise his option on the writer who would suffer a loss to the extent of the
difference between the Nifty-close and the strike price. The loss that can be incurred
by the writer of the option is potentially unlimited, whereas the maximum profit is
limited to the extent of the up-front option premium of Rs.86.60 charged by him.
6.3.4 Short Put: A trader who believes that a stock's price will increase can sell the
right to purchase the stock at a fixed price. This trade is generally considered
inappropriate for a small investor. If the stock price increases, the short put
position will make a profit in the amount of the premium. If the stock price
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decreases, the short position will lose by the amount of the decrease less the
amount of the premium.
The figure shows the profits/losses for the seller of a three-month Nifty 1250 put
option. As the spot Nifty falls, the put option is in-the-money and the writer starts
making losses. If upon expiration, Nifty closes below the strike of 1250, the buyer
would exercise his option on the writer who would suffer a loss to the extent of the
difference between the strike price and Nifty-close. The loss that can be incurred by
the writer of the option is a maximum extent of the strike price( Since the worst that
can happen is that the asset price can fall to zero) whereas the maximum profit is
limited to the extent of the up-front option premium of Rs.61.70 charged by him.
6.4 Introduction to Option Strategies
Combining any of the four basic kinds of option trades (possibly with different
exercise prices) and the two basic kinds of stock trades (long and short) allows a
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variety of options strategies. Simple strategies usually combine only a few trades,
while more complicated strategies can combine several.
1. Covered Call:Long the stock, short a call. This has essentially the same payoff as
a short put.
2. Straddle: Long a call and long a put with the same exercise prices (a long
straddle), or short a call and short a put with the same exercise prices (a short
straddle).
3. Strangle: Long a call and long a put with different exercise prices (a long
strangle), or short a call and short a put with different exercise prices (a short
strangle).
4. Bull Spread: Long a call with a low exercise price and short a call with a higher
exercise price, or long a put with a low exercise price and short a put with a higherexercise price.
5. Bear Spread : Short a call with a low exercise price and long a call with a higher
exercise price, or short a put with a low exercise price and long a put with a higher
exercise price.
6. Butterfly: Butterflies require trading options with 3 different exercise prices.
Assume exercise prices X1 < X2 < X3 and that (X1 + X3)/2 = X2
Long butterfly -long 1 call with exercise price X1, short 2 calls with exercise price
X2, and long 1 call with exercise price X3. Alternatively, long 1 put with exercise
price X1, short 2 puts with exercise price X2, and long 1 put with exercise price X3.
Short butterfly -short 1 call with exercise price X1, long 2 calls with exercise price
X2, and short 1 call with exercise price X3. Alternatively, short 1 put with exercise
price X1, long 2 puts with exercise price X2, and short 1 put with exercise price X3.
6.5 Black Scholes Option Model
Black Scholes Model has been widely used but it is a complex option pricing model.
It is based on concept of risk less hedge. Investor buys stock & simultaneously sells
a call option on that stock. If stocks price rises, investor earns profit but holder of
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option will exercise it; that exercise will cost investor money. If stock price falls,
investor will lose on his investment in stock but gain from option (which will expire
worthless if stock price falls). Black Scholes model helps to set up so that investor
ends up with risk less position - no matter what stock does, investor s portfolio
remains constant. Risk less investment yields risk less rate; if return > risk free rate,
arbitrageurs will buy this risk less position & in process push rate of return down.
Black Scholes Model: Given price of stock, its potential volatility, options exercise
price, life of option & risk-free rate, there is but one price for the option if it is to meet
the equilibrium condition -- that a portfolio consisting of stock & call option will earn
risk free rate.
The assumptions of the Black-Scholes Option Pricing Model
1. The stock underlying the call option provides no dividends during the call
options life.
2. There are no transactions costs for the sale/purchase of either the stock or
the option.
3. kRF is known and constant during the options life.
4. Security buyers may borrow any fraction of the purchase price at the short-
term risk-free rate.
5. No penalty for short selling and sellers receive immediately full cash
proceeds at todays price.
6. Call option can be exercised only on its expiration date (European).
7. Security trading takes place in continuous time, and stock prices move
randomly in continuous time.
The three equations that make up the OPM are:
V = P[N(d1)] - Xe -kRFt[N(d2)].
d1 = ln (P/X) + [kRF + ($2/2)]t
$t
d2 = d1 - $t.
Terms in Black-Scholes equation
V = current value of call option
P = current price of underlying stock
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N (dio) = probability that a deviation < di will occur in a standard normal
distribution. Thus N (d1) & N (d2) represent area under a standard normal
distribution function.
X = exercise, or strike price of option
e = 2.7183
kRF = risk free rate
t = time until option expires (option period)
ln (P/X) = natural logarithm of P/X
%2 = variance of rate of return on the stock
What is the value of the following call option according to the OPM?
Assume: P = $27; X = $25; kRF = 6%; t = 0.5 years: $2 = 0.11
V = $27[N(d1)] - $25e-(0.06)(0.5)[N(d2)].
ln($27/$25) + [(0.06 + 0.11/2)](0.5)
d1 = (0.3317)(0.7071)
= (.07696 + .0575)/.2345 =0.5736.
d2 = d1 - (0.3317)(0.7071) = d1 - 0.2345
= 0.5736 - 0.2345 = 0.3391.
N(d1) = N(0.5736) = 0.5000 + 0.2168
= 0.7168.
N(d2) = N(0.3391) = 0.5000 + 0.1327
= 0.6327.
V = $27(0.7168) - $25e-0.03(0.6327)
= $19.3536 - $25(0.97045)(0.6327)
= $4.0036.
The impact of the following Para-meters have on a call options value
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! Current stock price: Call option value increases as the current stock
price increases.
! Exercise price (Strikeprice): As the exercise (strike) price increases,
a call options value decreases.
! Option period: As the expiration date is lengthened, a call options value
increases (more chance of becoming in the money.)
! Risk-free rate: Call options value tends to increase as kRF increases
(reduces the PV of the exercise price).
! Stock return variance (volatility): Option value increases with
variance of the underlying stock (more chance of becoming in the money).
! Premium (price pay) depends on:
" strike (exercise) price-
" market price (market - strike) = intrinsic value (intrinsic value =
economic value of exercising immediately)
" time until expiration = time value
" short term interest rates
" volatility
" anticipated cash payments on the underlying (div.)
Option Pricing
Effect of an increase of the factor on
$ Factors Call Price Put Price
" Current price of underlying + -
" Strike price - +
" Time to expiration of option + +
" Expected price volatility + +
" Short-term interest rate + -
" Anticipated cash payments - +
(dividends)
7. Interest Rate Derivatives:
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7.1 Introduction
An interest rate derivate is a derivative security where the underlying asset is the
right to pay or receive a (usually notional) amount of money at a given interest rate.
Interest rate derivatives are the largest derivatives market in the world. Market
observers estimate that $60 trillion dollars by notional value of interest rate
derivatives contract had been exchanged by May 2004.
According to the International Swaps and Derivatives Association, 80% of the world's
top 500 companies at April 2003 used interest rate derivatives to control their cash
flow. This compares with 75% for foreign exchange options, 25% for commodity
options and 10% for equity options.
The various interest rate futures contracts traded on exchanges worldwide provide an
array of portfolio hedging and cross-hedging mechanisms for financial instruments
such as mortgages or high-grade corporate bonds. A long hedge correlates to falling
interest rates, while a short hedge would be used for risk management when rising
interest rates are anticipated. For example, the manager of a bond portfolio who
foresees rising interest rates could hedge by selling T-Bond futures. As interest rates
raise, the price of the T-Bond contract falls, thus, short selling the appropriate number
of T-Bond contracts vis--vis the value of the bond portfolio would provide a hedge
against the de-valued portfolio. Similarly, a long-hedge can be used to by a fund
manager to lock in the price he/she will pay to add Treasury Bonds to the portfolio:
7.2 Points of Interest: What Determines Interest Rates?
Interest rates can significantly influence people's behaviour. When rates decline,
homeowners rush to buy new homes and refinance old mortgages; automobile buyers
scramble to buy new cars; the stock market soars, and people tend to feel more
optimistic about the future.
But even though individuals respond to changes in rates, they may not fully
understand what interest rates represent, or how different rates relate to each other.
Why, for example, do interest rates increase or decrease? And in a period of changing
rates, why are certain rates higher, while others are lower?
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An interest rate is a price, and like any other price, it relates to a transaction or the
transfer of a good or service between a buyer and a seller. This special type of
transaction is a loan or credit transaction, involving a supplier of surplus funds, i.e., a
lender or saver, and a demander of surplus funds, i.e., a borrower.
7.2.1 Supply and Demand
As with any other price in our market economy, interest rates are determined by the
forces of supply and demand, in this case, the supply of and demand for credit. If the
supply of credit from lenders rises relative to the demand from borrowers, the price
(interest rate) will tend to fall as lenders compete to find use for their funds. If the
demand rises relative to the supply, the interest rate will tend to rise as borrowers
compete for increasingly scarce funds.
7.2.2 Expected Inflation
Inflation reduces the purchasing power of money. Each percentage point increase in
inflation represents approximately a 1 percent decrease in the quantity of real goods
and services that can be purchased with a given number of dollars in the future. As a
result, lenders, seeking to protect their purchasing power, add the expected rate of
inflation to the interest rate they demand. Borrowers are willing to pay this higher rate
because they expect inflation to enable them to repay the loan with cheaper dollars.
If lenders expect, for example, an eight percent inflation rate for the coming year and
otherwise desire a four percent return on their loan, they would likely charge
borrowers 12 percent, the so-called nominal interest rate (an eight percent inflation
premium plus a four percent "real" rate).
7.2.3 Economic conditions: All businesses, governmental bodies, and households
that borrow funds affect the demand for credit. This demand tends to vary with
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general economic conditions. When economic activity is expanding and the outlook
appears favourable, consumers demand substantial amounts of credit to finance
homes, automobiles, and other major items, as well as to increase current
consumption. With this positive outlook, they expect higher incomes and as a result
are generally more willing to take on future obligations. Businesses are also optimistic
and seek funds to finance the additional production, plants, and equipment needed to
supply this increased consumer demand. All of this makes for a relative scarcity of
funds, due to increased demand. On the other hand, when sales are sluggish and the
future looks grim, consumers and businesses tend to reduce their major purchases, and
lenders, concerned about the repayment ability of prospective borrowers, become
reluctant to lend. As a result, both the supply and demand for credit may fall. Unless
they both fall by the same amount, interest rates are affected.
7.2.4 Federal Reserve Actions: As we have seen, the Fed acts to influence the
availability of money and credit by adjusting the level and/or price of bank reserves.
The Fed affects reserves in three ways: by setting reserve requirements that banks
must hold, as we discussed earlier; by buying and selling government securities
(usually U.S. Treasury bonds) in open market operations; and by setting the "discount
rate," which affects the price of reserves banks borrow from the Fed through the
"discount window."
7.2.5 Fiscal Policy: Federal, state and local governments, through their fiscal policy
actions of taxation and spending, can affect either the supply of or the demand for
credit. If a governmental unit spends less than it takes in from taxes and other sources
of revenue, as many have in recent years, it runs a budget surplus, meaning the
government has savings. As we have seen, savings are the source of the supply of
credit. On the other hand, if a governmental unit spends more than it takes in, it runs a
budget deficit, and must borrow to make up the difference. The borrowing increases
the demand for credit, contributing to higher interest rates in general.
7.3 Interest Rate Predictions
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General economic conditions, for example, cause all interest rates to move in the
same direction over time. Other factors vary for different kinds of credit transactions,
causing their interest rates to differ at any one time. Some of the most important of
these factors are:
1. Different levels and kinds of risk
! default risk
! liquidity risk
! maturity risk
2. Different rights granted to borrowers and lenders
! Coupon and zero-coupon bonds
! Convertible bonds.
! Call provisions
! Put provision
3. Different tax considerations
7.4 Forward rate agreement (FRA)
Let us assume that you have agreed to a loan with a floating interest rate. If the
general level of interest rates rose, you would normally be exposed to a higher interest
burden. But the purchase of a forward rate agreement (FRA) offers protection: if
money market rates rise, the FRA pays you the difference between the interest rate
fixed in the FRA and the prevailing market interest rate
You can protect your investment income against falling interest rates by selling the
FRA. If interest rates fell below the agreed threshold, FRA will compensate you for
the reduced return
Let us assume that you have taken out a two-year loan with a bank for EUR 5 million,
with interest payments linked to the six-month EURIBOR. The interest rate fixed for
the six-month period starting today is 4.0% p.a. The future development of the six-
month EURIBOR is uncertain today, which exposes you to risk. For that reason, you
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buy a FRA, with a six-month hedging period, starting in six months' time (a so-called
6x12 FRA) at a rate of 5.5%.
If, for example, over the next six months the six-month EURIBOR were to rise to
6.5%, without this contract you would be subject to 1.0% higher interest for this
interest period. Thanks to the FRA, which compensate you for these additional costs,
leaving your interest expense at 5.5% plus your loan margin. Contrary to your
expectations: in this case, your interest income will fall short of the anticipated level.
You can offset this risk by purchasing a floor. If, on the fixing day for your floor
contract, the prevailing EURIBOR rate is lower than the agreed floor rate, you will be
compensated to the extent of this differential.
When you buy a floor you pay only the option premium, with no subsequent costs
incurred.
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8. Interest rate options
8.1 Hedging Pre-Issue Pricing Risk for Fixed-Rate Debt
Many companies today are considering the issuance of fixed-rate debt to lock in cost-
effective funding and strengthen their capital base. Interest rates, however, don't
always cooperate. Fortunately, there are a number of hedging tools available which
can reduce the impact of interest rate fluctuations on prospective debt issues or private
placements during the structuring and marketing period before pricing.
The Challenge
Companies planning to issue fixed-rate debt are exposed to the risk of Treasury rate
movements until the new issue is priced. Even the briefest waiting period can
significantly increase exposure. To address this challenge, issuers can choose from a
variety of off balance sheet risk management techniques to synthetically hedge the
yield on the Treasury security on which the debt will be priced.
For Example
Consider a company that decides today to borrow $100mm for 10 years, with the
proposed issue to be priced in six weeks. The company does not want to speculate on
the direction of interest rates, and seeks to reduce its exposure until the issue is priced.
Until the debt is priced, the company faces exposure to changes in the underlying
Treasury rate; and un hedged interest rate exposure can translate into real money. For
example, on a $100 million 10-year Treasury with a current yield of 6.56%, the
present value of a one basis point change in rates is $72,000!
As you can see in the table below, the cost impact of even a small change in rates can
be extremely large - higher if rates go up, lower if rates fall. If in markets of even
average volatility, intraday rate movements alone can be as much as 15 basis points
up or down, consider how much is at risk over the typical 1 to 3 month pre-issue
period.
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Change in Treasury Rate Present Value of Interest Cost
(in basis points on $100 million Notional
0 $0
10 $720,000
20 $1,440,000
30 $2,160,000
40 $2,880,000
50 $3,600,000
8.2 Hedging Solutions
8.2.1 Caps-Hedging against rising interest rate
You plan to take out a loan, taking advantage of what are presently very attractive
interest rates. Despite the fact that you expect interest rates to rise, you still wish to
participate in the event of falling rates.
The solution for this is a cap. As the buyer of a cap you hedge against the risk of
rising money market rates. If, on the agreed fixing day for your cap, the prevailing
market interest rate, generally EURIBOR, exceeds the maximum interest rate agreed
in the cap contract, cap will pay you the difference between the prevailing market rate
and the agreed cap limit for the current interest period, based on the underlying
notional amount.
The particular advantage of this hedging method is that you continue to benefit
without restrictions from falling money market rates
Example let us assume that you intend to carry out some modernisation measures in
your company. As you do not wish to unnecessarily commit liquid funds, you decide
to take out an investment loan of EUR 1 million. A cap creates a ceiling on floating
rate interest costs. When market rates move above the cap rate, the seller pays the
purchaser the difference. A company borrowing on a floating rate basis when 3 month
LIBOR is 6% might purchase a 7% cap, for example, to protect against a rate rise
above that level. If rates subsequently rise to 9%, the company receives a 2% cap
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payment to compensate for the rise in market rates. The cap ensures that the
borrower's interest rate costs will never exceed the cap rate.
8.2.2 Floors-Hedging against falling interest rate
When investing liquid funds, an attractive return is a key criterion for your decision.
However, if money market rates decline this would, in practice, represent an actual
shortfall in revenue for your company. As a result, you could be missing out on
returns which you may have relied upon in your planning.
You can avoid the resulting uncertainty by buying what is known as a floor. A floor is
an agreement on a minimum inter