forex and debt market derivatives-0496-raju

8/10/2019 Forex and Debt Market Derivatives-0496-Raju

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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)


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:



Broker retains 10 percent -$3,700


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


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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Broker retains 10 percent -$3,700


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:


Collect on investment $34,524.31

Pay futures transaction costs $25


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.


maturity.


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

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