Managing Market Risk Unit

8/2/2019 Managing Market Risk Unit

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PONDICHERRY UNIVERSITY

Department of Commerce

Assignment

On

Managing Market Risk in Derivatives

SUBMITTED TO : Dr.D.LazarAssociate ProfessorDepartment of CommerceSchool of ManagementPondicherry University

Submitted by,

P.Hemapriya,

II M.com (B.F)
http://images.google.co.in/imgres?imgurl=http://www.pondiuni.edu.in/regular/results/uni_logo.gif&imgrefurl=http://www.pondiuni.edu.in/regular/results/btechcmc170708.php&usg=__yET4n7MXUjJYe5i577EmZr8U3MM=&h=1027&w=1024&sz=170&hl=en&start=16&um=1&tbnid=OOFw_ui7xW1kyM:&tbnh=150&tbnw=150&prev=/images%3Fq%3DPONDICHERRY%2BUNIVERSITY%26hl%3Den%26sa%3DN%26um%3D1


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CONTENTS

MEANING OF MARKET RISK

HEDGING INTRODUCTION

PURPOSES OF HEDGING

OBJECTIVES AND BENEFITS OF HEDGING

HEDGING PROCESSSS

HEDGING SITUATIONS

STRATEGIES FOR HEDGING

HEDGING SCHEMES

PORTFOLIO INSURANCE


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Market risk is the risk that the value of a portfolio, either an investment portfolio or a trading

portfolio, will decrease due to the change in value of the market risk factors. The four standard

market risk factors are stock prices, interest rates, foreign exchange rates, and commodity prices.

The associated market risks are:

Equity risk, the risk that stock prices and/or the implied volatility will change.

Interest rate risk, the risk that interest rates and/or the implied volatility will change.

Currency risk, the risk that foreign exchange rates and/or the implied volatility will change.

Commodity risk, the risk that commodity prices (e.g. corn, copper, crude oil) loss amount

due to market risk.

As with other forms of risk, the potential loss amount due to market risk may be measured in a

number of ways or conventions. Traditionally, one convention is to use Value at Risk. The

conventions of using Value at risk are well established and accepted in the short-term risk

management practice.

However, it contains a number of limiting assumptions that constrain its accuracy. The first

assumption is that the composition of the portfolio measured remains unchanged over the specified

period. Over short time horizons, this limiting assumption is often regarded as reasonable.

However, over longer time horizons, many of the positions in the portfolio may have beenchanged. The Value at Risk of the unchanged portfolio is no longer relevant.

The Variance Covariance and Historical Simulation approach to calculating Value at Risk also

assumes that historical correlations are stable and will not change in the future or breakdown under

times of market stress.

In addition, care has to be taken regarding the intervening cash flow, embedded options, changes in

floating rate interest rates of the financial positions in the portfolio. They cannot be ignored if their

impact can be large.
http://en.wikipedia.org/wiki/Riskhttp://en.wikipedia.org/wiki/Equity_riskhttp://en.wikipedia.org/wiki/Equity_riskhttp://en.wikipedia.org/wiki/Implied_volatilityhttp://en.wikipedia.org/wiki/Interest_rate_riskhttp://en.wikipedia.org/wiki/Currency_riskhttp://en.wikipedia.org/wiki/Commodity_riskhttp://en.wikipedia.org/wiki/Value_at_Riskhttp://en.wikipedia.org/w/index.php?title=Variance_Covariance&action=edit&redlink=1http://en.wikipedia.org/wiki/Historical_Simulationhttp://en.wikipedia.org/wiki/Historical_Simulationhttp://en.wikipedia.org/wiki/Historical_Simulationhttp://en.wikipedia.org/wiki/Equity_riskhttp://en.wikipedia.org/wiki/Implied_volatilityhttp://en.wikipedia.org/wiki/Interest_rate_riskhttp://en.wikipedia.org/wiki/Currency_riskhttp://en.wikipedia.org/wiki/Commodity_riskhttp://en.wikipedia.org/wiki/Value_at_Riskhttp://en.wikipedia.org/w/index.php?title=Variance_Covariance&action=edit&redlink=1http://en.wikipedia.org/wiki/Historical_Simulationhttp://en.wikipedia.org/wiki/Risk


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Managing risk is important to a large number of individuals and institutions. The most

fundamental aspect of business is a process where we invest, take on risk and in exchange earn a

compensatory return. The key to success in this process is to manage your risk return trade-off.

Managing risk is a nice concept but the difficulty is often measuring risk. There is a saying what

gets measured gets managed. To alter this slightly, What cannot be measured cannot be

managed. Hence risk management always requires some measure of risk. Risk in the most general

context refers to how much the price of a security changes for a given change in some factor.

In the context of Equities,Beta is a frequently used measure of risk. Beta measures the

relative risk of an asset. High Beta stocks or portfolios have more variable returns relative to the

overall market than low Beta assets. If a Beta of 1.00 means the asset has the same risk

characteristics as the market, then a portfolio with a Beta great than one will be more volatile than

the market portfolio and consequently is more risky with higher expected returns. Conversely

assets with a Beta less than 1.00 are less risky than average and have lower expected returns.

Portfolio managers use Beta to measure their risk-return trade-off. If they are willing to take on

more risk (and return), they increase the Beta of their portfolio and if they are looking for lower

risk they adjust the Beta of their portfolio accordingly. In a CAPM framework,Beta or market risk

is the only relevant risk for portfolios. For Bonds, the most important source of risk is changes in

interest rates. Interest rate changes directly affect bond prices. Modified Duration is the most

frequently used measure of how bond prices change relative to a change in interest rates.

Relatively higherModified Duration means more price volatility for a given change in interest

rates. For both Bonds and Equities, risk can be distilled down to a single risk factor. For

Bonds it is Modified Duration and for equities it is Beta. In each case, the risk can be measured

and adjusted or managed to suit ones risk tolerance.

The various ways to manage the market risk are:

1. Investment in Portfolio;

2. Managing through Hedge.

We shall discuss in detail about the ways in which hedging can be effectively used to

manage the market risk.

HEDGING


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INTRODUCTION

Hedging is undertaken to reduce the price risk of a cash or forward position. The

managerial goals of a hedging programme are to make a hedging decision and to manage the

programme. A hedge is a position that is taken as a temporary substitute for a later position in

another asset or liability or to protect the value of an existing position in an asset or liability until

the position can be liquidated. Mostly hedging is done in derivative instruments. The instruments

most often used for hedging are futures, forwards, options and swaps. Futures, forwards and swaps

are off-balance sheet instruments. That is they are not shown up on either the assets side or on the

liabilities side of the users balance sheet.

Example:

In the month of March 2003, a Jute mill anticipates a requirement of 10,000 candies

of Jute in the month of July, 2003.Current price of jute is Rs.1000 per candy. Based on this price,

the company has entered into other financial arrangements. It is of great importance to the mill

that, at the time of jute is actually purchased, price is not changed substantially higher than

Rs.1000 per candy. To avoid this, it buys 10,000 candies of jute on the jute futures market, where

current price of jute is Rs.1050 per candy. In the month of July, the price of jute has risen sharply

with the current spot price being Rs.1500 per candy. The corresponding futures price for July jute

is found to be Rs.1470 per candy.

At this point of time jute mill has two options:

1. It can sell its futures contract on the market at prevailing rate of Rs.1470, and buys its

requirements from spot market. Profit/Loss profile of this transaction will be as

follows:

Jute purchased = Rs.1000 per candy

Sale proceeds = Rs.1470 per candy

Profit from sale = Rs.470 per candy and current price of jute Rs.1500 per candy to

be paid and net cost of candy to mill is Rs.1030 per candy.

So futures transaction has ensured the minimization of upward price risk a mere for

Rs.30 per candy.

2. The mill could take delivery of jute directly from futures market. In this case the mill

would pay Rs.1000 per candy, but for taking delivery there may be possibilities of not

delivery of same variety of jute.


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It is observed from the above example that by buying futures the firm has hedged against

the upward price risk

PURPOSES OF HEDGING

Earlier hedging was taken to be only one kind (known as routine or nave hedging),

whereby the trader always hedged all his transactions purely for covering all the price risks.

According to this concept, the hedging can be used for many other purposes:

Carrying charge hedging According to this approach, the stockiest watch the price

spread between the spot and futures prices, and if the spread covers even carrying costs then the

stockiest buy ready stocks. It means that the traders may go for hedging if the spread is adequate to

cover carrying costs whereas earlier view was that hedges are used to protect against loss on stock

held.

Operational hedging According to this view, hedgers use the futures market for their

operations and use the same as substitute for cash or forwards transactions. They think that the

futures market are more liquid and have lower difference between bid and ask prices.

Selective or discretionary hedging As per this concept, the traders do not always hedge

themselves but only do so on selective occasions when they predict adverse price movements in

futures. Here the objective is to cover the risk of adverse price fluctuation rather to avoid price risk.

Anticipatory hedging This is done in anticipation of subsequent sales or purchases. For

example, a farmer might hedge by selling in anticipation of his crop while a miller might hedge by

buying futures in anticipation of subsequent raw material needs.

OBJECTIVES AND BENEFITS OF HEDGING.

1. Hedging is done to reduce risk.


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2. Hedging is desired by the shareholders simply to find a more acceptable combination of

return and risk.

3. Firms go for hedging to get tax advantages.

4. Firms choose hedging because its managers livelihood may be heavily tied to the

performance of the firm. Thus the managers benefit from reducing the firms risk.

5. Hedging is a tool to offset the market (systematic) risk of stock portfolios.

6. Hedging is important for the proper functioning, long term liquidity and open interest

of a futures market.

THE HEDGING PROCESS.

Hedging is to take a position in futures that offsets the price changes in the cash asset.

Hence, hedging a current long cash position consists of taking a short futures position. In order to

determine whether one should sell or buy futures to initiate a hedge, a potential hedger can follow

a two-step process:

1. Determine the exposure of the cash position to potential losses; thus a loss occurs for a

current long cash position when prices decline, whereas a loss occurs for a short cash or

anticipated cash position when prices increase.

2. Determine whether a short or a long futures position is needed to offset the potential

loss in the cash position.

SHORT HEDGE

A hedger who holds the commodity and is concerned about a decrease in its price might

consider hedging it with a short position in futures. If the spot price and future price move

together, the hedge will reduce some of the risk. For example, if the spot price decreases, the

futures price also will decrease. Since the hedger is short the futures contract, the futures

transaction produces a profit that at least partially offsets the loss on the spot position. This is

called a short hedge because the hedger is short futures.


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Example:

A US exporter who knows that he will receive German mark in three months from a

German company. Exporter will realize gain if the mark increases its value in relation to the US

dollar and a loss if the mark decreases its value relative to the US dollar. A Short futures position

leads to a loss if mark increases in value and a gain if it decreases in value. It has the effect of

offsetting the exporters risk.

LONG HEDGE.

This is another type of anticipatory hedge involves an individual who plans to purchase a

commodity at a later date. Fearing an increase in the commoditys price, the investor might buy a

futures contract. Then, if the price of the commodity increases, the futures price also will increase

and produce a profit on the futures position. That profit will partially offset the higher cost of

purchasing the commodity. This is a long hedge, because the hedger is long in the futures market.

Example:

A farmer anticipates a bumper crop amounting to 150 quintals, which he expects to harvest

in the month of January. It is October and current price of crop is Rs.10, 000 per quintal. This price

is acceptable to the farmer and gives him a sufficient return. But he is apprehensive of a fall in

price by the time crop will be ready. He, therefore, sells 150 quintals on the commodity futures

market at a current price of Rs.9500 per quintal. In the month of January, price of crop have in fact

risen. Current spot price is Rs.11, 000 per quintal. Now, farmer has two alternatives:

1. He can buy back 200 quintals of January crop on the futures market at a present futures

price of Rs.10, 500.He can then deliver his actual crop of pepper in spot market at the

ruling rate of Rs.11, 000 per quintal. As a result farmer will have following profit/loss:

January contract sale @ Rs.9500per quintal. January contract buys @ Rs.10, 500.

So, there is a net loss of Rs.1000 per quintal. Further he sells his output @ 11,000 in the

spot market and by deducting the loss on futures market position of Rs.1, 000; net price

obtained by former is Rs.10, 000 per quintal.

2. He can deliver in the futures market @ Rs.9500 per quintal.


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These situations where sale of futures by those hedging against price fall is called

short hedge and taken guarding against downward price movements.

Hedging Situations

Conditions today Risk Appropriate Hedge

Hold asset Asset price may fall Short hedge

Plan to buy asset Asset price may rise Long hedge

Sold short asset Asset price may rise Long hedge

Issued floating-rate liability Interest rates may rise Short hedge

Plan to issue liability Interest rates may rise Short hedge

STRATEGIES FOR HEDGING.

Hedging is typically associated with reducing risk (reducing price volatility). However,

those who employ futures market have different strategies and different goals in order to

implement a hedging programme. Market participants practice following strategies:

Reduction of risk the primary use of futures for hedging is to reduce the price

variability associated with the cash asset position.

Selective hedging hedging only during those time periods when a forecast

determines that the cash position will lose money is called selective hedging.

Speculating on the basis when the returns form the hedge are a consideration in

whether the hedge will be undertaken, then this approach is equivalent to predicting

the changes in the basis during the hedge period.

Optimum risk return hedging-the optimal hedge decision considers both the

reduction in risk and the return from the combined cash-futures position

HEDGING SCHEMES


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The Greeks

The term Greeks refers to 5 basic measures of risk. They are called Greeks because the risk

figures are denoted by Greek letters Delta (), Gamma (), Theta (), Vega (V) and Rho ().

Each Greek symbolizes a single component of risk as follows:

DELTA (): The change in price or value of a derivative in relation to the change in price or

value of the underlying security, index, or rate. For an equity option, this would be the dollar

option price change per underlying dollar stock price change. For an interest rate cap, this would

be the dollar cap price change per basis point move in the reference interest rate (e.g. LIBOR). For

call options or long positions in other derivatives, delta is positive. For put options or short

positions in other derivatives, delta is negative. Hedging Delta requires matching the trade with

another position with the same total Delta in the opposite direction, for example a long call option

hedged with a short future, both with equal but opposite Deltas (and possibly some convexity

adjustment to the future contract hedge).

An example of IBM call options, the March 105 call with the stock trading at 100 will have a

higher delta than the 110 call because it is closer to realizing its value. Using the example with a

put option, a 100 put would have a greater delta than the 95 put.

Traders will often use the terms in the money, out of the money when discussing delta. Generally

the following can be stated.

If delta < .30 then it is out of the money

If delta = .50 then it is at the money

If delta > .70 then it is in the money

The first form of hedging is known as delta hedging.

Rough Formula: Delta () = (DP0 DP1) / (UP0 UP1)

Where: DP0 = derivative price now


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DP1 = derivative price previous

UP0 = underlying price or value now

UP1 = underlying price or value previous

Example-use of delta hedging: An investor has sold 20 option contracts, i.e., options to buy 2000

shares. Suppose the option price is Rs.10 and the stock price is Rs.100 per share. Assume a call

option whose delta is 0.7. The investor wishes to hedge the position.

The investor will immediately buy 0.7*2000 = 1400 shares. The gain (loss) on the option

position would tend to be offset by the loss (gain) on the stock position. For example, if stock

price goes up by Re.1, then the stock will produce a gain of Rs.1400 on the shares purchased, the

option price will tend to go up by 0.7*1 = Rs.0.70,again producing a loss of Rs.1400 on the option

written and vice versa.

The value of a delta is subject to change as per the market conditions. If the delta of the

asset is 1.0 then the delta of the option position. A position with a delta of zero is referred to as

being delta neutral...Further, when the delta hedging is implemented in practice, the hedge has to

be adjusted periodically. This is known as rebalancing. The stock price is increased at the end, and

then it will also lead to an increase in delta. For example, if delta rises from 0.70 to 0.80, this

would mean that an extra 0.10*2000 = 200 shares would have to be bought to maintain the hedge.

Slope =

()


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As the time passes, the delta will change and the position in the stock will have to be adjusted.

These hedging schemes which involve frequent adjustments are known as dynamic hedging

schemes.

Delta of European Calls and puts:

In a European call option on a non-dividend paying stock, it can be shown that

= N(d1

Using delta hedging for a short position in a European call options therefore involves keeping a

long position of N (d1) shares at any given time. Similarly, using delta hedging for a long position

in a European call option involves maintaining a short position of N (d1) shares at any given time.

For a European put option of a non-dividend paying stock delta is given by

= N(d1) 1

This is negative which means that a long position in a put option should be hedged with a long

position in the underlying stock and vice versa. In brief, put option have negative deltas because

they become more valuable as a stock price falls. Deep out- of- the-money options have deltas

close to zero at-the-money options have deltas close to -0.05 and deep in-the-money options have

deltas that approach 1.

The variation of the delta on a call option and a put option with the stock prices is shown below:


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GAMMA (): The change in Delta in relation to the change in price or value of the underlying

security, index, or rate. As this is the rate of change of the rate of change, then it must be the

second derivative. Unlike delta, which has values bounded by 0 to 1,gamma can vary from

-10,000 to 10,000.Most Gamma values are around + /- 500.Gamma is highest when an option is at

the money and lowest when the option is either in or out of the money.

Gamma is only applicable to non-linear option-type derivatives like basic vanilla options,

swaptions, caps/floors, convertible bonds, callable bonds, etc. Gamma represents the estimated

slope or curve of the Delta profile over a range of underlying prices or values. Calculating

Gamma requires two Delta calculations as inputs. The Gamma formula is the same for both calls

and puts. Hedging Gamma requires going long or short a security with the same or similar delta

and delta slope values, but in the opposite direction. Hedging Gamma is an imperfect science, andmust be done on a continual basis as prices change.

Rough Formula: Gamma () = ( 0 1) / (UP0 UP1)

Where: 0 = Delta now


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1 = Delta previous

UP0 = underlying price or value now

UP1 = underlying price or value previous


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THETA (): The change in price or value of a derivative in relation to units of time (usually 1

day). Theta primarily applies to option-type derivatives like basic vanilla options, swaptions,

caps/floors, convertible bonds, callable bonds, etc. Theta represents the change in time value of an

option as time progresses to an expiration date. Theta is almost always negative, because the

probability of an option being in the money decreases as time to expiration decreases since there is

less time for large price swings to occur. Theta typically has an exponentially decreasing value,

with the slope of Theta increasingly negative (probability of going in the money increasingly less

possible) as expiration nears. Hedging Theta of a long call option position requires

shorting/selling/writing a same or similar call, or buying a put with the same strike and expiration.

Lets go back to the IBM example.

The March 110 calls sell for 1 and the June 110 calls sell for 2. As each day passes, the life of

the option diminishes giving a reduced possibility for a payoff. Since March comes before June the

March option will decay faster than the June option.


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Rough Formula: Theta = (DP0 DP1) / (T0 T1)


DP1 = derivative price previousT0 = time now

T1 = time previous


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spo


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Vega (V): The change in price or value of a derivative in relation to the unit volatility of the

underlying security price, index value, or rate. Vega applies to non-linear option-type derivatives

like basic vanilla options, swaptions, caps/floors, convertible bonds, callable bonds, etc. Vega also

applies to options and futures on volatility indexes such as the VIX. As volatility of the underlying

price, value, or rate increases, an options theoretical value also increases because there is greater

probability that it will go in the money. The opposite is also true; as underlying volatility

decreases, an options price should also decrease. Volatility of an underlying price, index, or rate

is measured in standard deviations over a chosen look back period.

For example, estimating the volatility of an underlying stock price would typically require

calculating the standard deviation of price over the previous years trading days. Likewise,

estimating the volatility of an underlying interest rate (e.g. Fed Funds) would require calculating

the standard deviation of interest rates over the previous year. The Vega calculation is the same

for both calls and puts. Hedging Vega requires going long or short volatility in the opposite

direction as the derivative position. For example, a long call or put option is long volatility


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either a long call or long put option increases in value if the underlying reference volatility

increases. To hedge this, you would go short volatility by shorting/selling/writing equivalent

call or put options.

Vega is also known as omega, lambda, kappa or sigma. To understand this concept, let us look at

the IBM example.

Assume that on Thursday, IBM 105 call settled at 3 with the stock at 100.Then on Friday morning,

IBM schedules a press conference to introduce a revolutionary new product. Since investors might

be unsure of the products viability (it could be a huge success or a cash drain), they will bid up the

volatility of the stock. That is, the chance of higher or lower stock performance is now increased so

the option price will rise through a higher Vega, independent of the movement in the stock price.

Rough Formula: Vega (V) = (DP0 DP1) / (V0 V1)


DP1 = derivative price previous

V0 = underlying volatility now

V1 = underlying volatility previous


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RHO (P): The change in price or value of a derivative in relation to the risk-free discount rate

used to NPV the future value of the derivative to present value. Lower risk-free discount rates

imply a higher present value, and vice-versa. Short-term derivatives like listed equity options (


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Other Risk Measures

PV01 (a.k.a. DV01): The change in the dollar present value of a bond or interest rate trade in

relation to a 1 basis point (0.01%) move in the underlying interest rate. PV01 is equivalent to

Delta, where the underlying rate is an interest rate.

Rough Formula: PV01 = PVr0 PVr1

Where: PVr0 = present value of bond or trade using rate now

PVr1 = present value of bond or trade using rate previous

Duration:The approximate percentage of value the bond or trade will lose for a 1% increase in

interest rates. Duration is roughly equivalent to the time in which the purchase price of a bond will

be repaid by its internal cash flows. Duration is considered an alternative to PV01 or Delta.

Convexity: The curvature of how the price of a bond changes as the interest rate changes.

Convexity is essentially the same as Gamma, and measures changes in Duration over different


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interest rates.

SOLVED PROBLEMS

1. Calculate the delta of an at-the-money six-month European call option for a non-dividend

paying stock when the risk-free interest rate is 10%p.a.and the stock price volatility is 25%

p.a.

Solution:

In this problem, following informations is available:

Stock price S = X

Risk-free return R = 0.1

Standard deviation = 0.25

Time to maturity T = 0.5

So, d1 = {In(s/x)+[(0.1+0.25)2 / 2] *0.5} / 0.250.5 = 0.3172

N (d1) = 0.64

2. Calculate the delta of an at-the-money six month option on a non-dividend paying stock

when the risk-free interest rate is 5% p.a and the stock price volatility is 12.5% p.a.

Solution:

Here in this problem, the following informations are given:

Stock price S = X

Risk-free return R = 0.05

Standard deviation = 0.125

Time-to-maturity T = 0.05

So, d1= {ln(s/x) + [(0.05+0.125)2 / 2] *0.5} / 0.1250.5 = 0.1856

N (d1) = 0.6103

3. An investor has sold 20 option contracts (2000 options) on Infosys shares. The option price

is 500. The stock price is 5000 and the option delta is 0.6.If the delta has changed from 0.6


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to 0.65. The investor wishes to hedge the position. Show how an investor can hedge his

position.

Solution:

The investor will immediately buy 0.6*2000 = 1200 shares. Over the next short

period of time the call price will tend to change by 60% of the stock price (loss) on call

option will be offset by the loss (gain) on call stock. As time passes Delta will change and

the position in the stock will have to be adjusted.

For example, if increases to 0.65 a further 0.05*2000 = 100 shares will have to be

bought.

HEDGING EXAMPLES FOR FIXED INCOME DERIVATIVE TRADES

EXAMPLE #1: Plain Vanilla Swap

The first example uses a $100 million notional vanilla swap paying USD Fixed and receiving USD

LIBOR.

How to hedge this trade 5 STEPS TO HEDGING:

First, choose a point on the curve to hedge. This can be all points on the curve, all points in a

segment of the curve (MM, futures, AIC swaps, etc.), or just a single point. To keep things simple,

lets select the 2Y point. The As of Date of this trade is 9/1/05, so we are looking to hedge the risk

associated with 9/1/07, which is conveniently on the 2Y point of the curve.

Second, select the direction (up or down) you are hedging. Lets hedge a +1bp change in the

curve.

Third, identify the type of risk you want to hedge. Here we only have the USD LIBOR rate risk to

hedge.


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Fourth, identify the total dollar value of risk to hedge. For a +1bp change on the 2Y point of the

curve, our model says we need to hedge -$0.48 x $1M notional = -$480,000 (this is the DV01). To

determine how much is required to hedge the entire trade, simply add up the dollar risk for each

point in the money market segment, futures segment, and AIC swap segment separately. Here we

have risk by segment of -$386.44 money market, -$6,266.54 futures, and $76,853.69 AIC swaps.

These should add up roughly to the value change of the swap if you perturb the entire curve up

+1bp in a parallel shift.

Fifth, calculate the required number of units, contracts, or notional of the hedging instrument you

are going to use.

Since we are looking to hedge a point 2Y out on the curve, we cannot use futures. We need a

longer term instrument such as a 2Y AIC swap to hedge the 2Y point. Here, we choose a 2Y

RECEIVER Swap paying 3M LIBOR and receiving FIXED with an expiration date on 9/2/07 and

notional of approximately $100 million. This trades risk profile is the mirror image of the

existing PAYER Swap paying FIXED and receiving 3M LIBOR. This is known as a "back to

back" trade, and is commonly used by sell side broker-dealers and trading desks of mutual fund

companies looking to hedge their fund portfolios.

For most trades, hedging a single point on the curve does not make sense. Rather, each segment ofthe curve, or the entire trade, would be hedged. By segment, the risks to hedge are: -$386.44

money market, -$6,266.54 Eurodollar futures, and $76,853.69 AIC swaps.

The -$386.44 money market risk is minimal, so it probably would not make sense to hedge this

part of the curve.

The -$6,266.54 futures risk can be hedged by using the required = risk / BPV formula. Eurodollar

futures trade at -$25 per +1bp, so we need -$6,266.54 / -$25 = 250.66 = +/- 251 contracts.

To determine the notional of a USD LIBOR Receiver Swap needed to hedge the $76,853.69 AIC

swap segment risk, use the following formula: Notional of hedge swap = $76,853.69/DV01 of

hedge swap.


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EXAMPLE #2: USD LIBOR cap

The second example uses a $5 million notional cap on USD LIBOR. A cap is essentially a series

of European call options on an interest rate. A cap is made up of multiple caplets, each with a reset

rate (strike) and its own expiration date. The value of a cap reflects the probability of an interest

rate being in or out of the money at the expirations of all caplets. This probability is non-linear for

a cap so there is delta, gamma (curvature), volatility (Vega), and time (theta) risk.



segment of the curve (MM, futures, AIC swaps, etc.), or just a single point. Lets select the 6M

point here. The As of Date of this trade is 9/1/05, so we are looking to hedge the risk associated

with 3/1/06, approximately the MAR06 point on the curve.

Second, select the direction (up or down) you are hedging. Since this is a long cap, we will profitif USD LIBOR goes up and incur losses if it drops, so we need to hedge a -1bp change in USD

LIBOR. Also, because we are long a cap (call option), we will profit if USD LIBOR volatility

rises and lose if volatility falls, so we need to hedge a -100bp change in forward USD LIBOR

volatility. (NOTE: For convenience, we are going to assume perfect symmetry in sensitivities

between USD LIBOR caps and floors with the same strike (3% here). This assumption is highly

simplified and does not take into account the natural volatility skew built into Cap vs. Floor

prices. Here we assume the dollar effect of a -1bp move in rate or volatility is simply the inverse

of a +1bp move.)

Third, identify the type of risk you want to hedge. Lets hedge both the USD LIBOR rate risk and

the USD LIBOR forward volatility risk.

Fourth, identify the total dollar value of risk to hedge.


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Our model shows a +$108.15 move in cap value for a +1bp move in USD LIBOR rate at the 6M

point on the curve. Inverting this we get -$108.15 move in value for a -1bp shift at 6M.

Our model also shows a +$130.67 move in cap value for a +100bp move in USD LIBOR volatility

at the 6M point (remember the vole sensitivity is set to a 100bp shift.) Inverting this, we get -

$130.67 move in value for a -100bp move in USD LIBOR volatility at 6M.


are going to use.

To hedge the USD LIBOR rate risk, we need to sell (go short) the following number of futures

contracts. This is an imperfect hedge. Required number of Eurodollar contracts = -$108.15 dollar

risk / $25 per BP per contract = -4.33 contracts.

The 6M USD LIBOR forward volatility risk is more difficult to hedge. To cleanly hedge the -

$130.67 volatility risk associated with the 6M curve point, we need to find an instrument strictly

designed for USD LIBOR volatility. For example, we could buy an OTC USD LIBOR volatility

put or short an OTC USD LIBOR volatility future. We could also write (go short) a similar USD

LIBOR cap or floor, although this would also have delta effects that would interact with the futures

delta hedge above. Buying another USD LIBOR cap or floor would be incorrect, as this would

make us further exposed to USD LIBOR volatility.

EXAMPLE #3: Bermudan Swaption

The third example uses a Bermudan Swaption exercisable into a $100 million notional

Fixed/Floating USD LIBOR swap, with the option to pay fixed rate payments and receive LIBOR

floating payments (a Payer Swaption). The value of a swaption reflects the probability of the swap

rate being in or out of the money on the exercise date. A Bermudan Swaption has multiple

exercise dates, with each normally aligned with a reset date for the floating rate (here USD

LIBOR). Valuation of a Bermudan Swaption is therefore very similar to valuing a Cap. The

probability of the Bermudan Swaption being in or out of the money is non-linear so there is delta,

gamma (curvature), and volatility (Vega) risk.


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segment of the curve (MM, futures, AIC swaps, etc.), or just a single point. Lets select the 10Y

point here, since our model says this is where the greatest LIBOR rate sensitivity lies.

Second, select the direction (up or down) you are hedging. Since this is a long Payer Swaption,

we will profit if USD LIBOR rises since we will be able to exercise and enter into a swap where

we pay a fixed rate of 3% and receive a higher LIBOR rate. Lets assume we are taking adirectional position (long) on USD LIBOR and hedge a -1bp change in USD LIBOR. Also,

because we are long an option on an interest rate (call option), we are long volatility. We will

profit if USD LIBOR volatility rises, and lose if it falls. So we could hedge a -100bp change in

USD LIBOR volatility.

Third, identify the type of risk you want to hedge. Lets hedge both the USD LIBOR rate risk and

the USD LIBOR volatility risk.

Fourth, identify the total dollar value of risk to hedge. For a -1bp change at the 10Y point, we

need to hedge -$49,841.44 of USD LIBOR rate risk and -$9,678.80 of USD LIBOR volatility risk

on this swaption.


are going to use.

The problem with hedging such a long-dated swaption is finding an appropriate instrument tohedge it with. There are no liquid exchange traded futures or options with a 10Y tenor. Therefore

any hedge must be done in the OTC market. There are several potential choices available:

A combination of a 3M LIBOR volatility put and a floor on 3M LIBOR.

A forward-starting Receiver Swap receiving fixed and paying 3M LIBOR.


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Long a 10Y Treasury Bond receiving LIBOR+

A Total Return Swap using this Bermudan Swaption as the reference asset you would give up

the total returns of the Swaption for a set period in exchange for receiving payments of LIBOR +/-

a spread and an offsetting payment (insurance) on any capital losses of the Swaption.

Others

Each of these positions has its own unique delta, gamma, Vega, theta, and rho. Thus the selection

and sizing of any hedge would require a fair amount of what if analysis and computing power.

PORTFOLIO INSURANCE

Portfolio insurance is a method of hedging a portfolio ofstocks against the market riskby

short selling stock index futures.

Portfolio Insurance is the term assigned to the practice of limiting the losses or even

eliminating the losses, for a position which you take in stocks or bonds or in any other set of

investments. It is a method of hedging a portfolio of stocks against the market risk by short selling

stock index futures.

This hedging technique is frequently used by institutional investors when the market

direction is uncertain orvolatile. Short selling index futures can offset any downturns, but it also

hinders any gains.

Portfolio insurance is based only on the principal of risk transfer. One persons

protection is another persons liability. The cost of portfolio insurance is the mechanism to

equilibrate its demand with supply.

SIPC is an insurance that provides brokerage customers up to $500,000 coverage for cash

and securities held by a firm.

Mark Edward Rubinstein along with fellow Berkeley finance professor Hayne E. Leland,

Rubinstein developed the portfolio insurance financial product in 1976. This strategy would later

become associated with the October 19, 1987, Stock Market Crash.
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How is Portfolio Insurance achieved?

Portfolio Insurance is achieved by using Financial Derivatives or Options. So basically,

you buy a stock, as long as it is above its buy price, you are in profit. The risk or loss comes when

the price of the stock goes below your buy price. Hence, the practise of eliminating this loss is

known as Portfolio Insurance. Some financial experts also claim that risk can never be eliminated

from a Portfolio, only its effects can be mitigated. Hence, the practise of mitigating the risks from

the Portfolio is known as Portfolio Insurance.

Graph illustrating portfolio insurance

Portfolio Insurance Today

Portfolio Insurance was blamed by investors

Brady Commission said PI contributed to severity

Much less popular today, although still very widely used

Black Monday (1987)

In finance, Black Monday refers to Monday, 19 October, 1987, when stock markets

around the world crashed, shedding a huge value in a very short time. The crash began in Hong

Kong, spread west through international time zones to Europe, hitting the United States after other
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markets had already declined by a significant margin. The Dow Jones Industrial Average (DJIA)

dropped by 508 points to 1738.74 (22.61%).

Losses

By the end of October, stock markets in Hong Kong had fallen 45.5%, Australia 41.8%,

Spain 31%, the United Kingdom 26.45%, the United States 22.68%, and Canada 22.5%. New

Zealand's market was hit especially hard, falling about 60% from its 1987 peak, and taking several

years to recover. (The termsBlack Monday andBlack Tuesday are also applied to October 28 and

29, 1929, which occurred afterBlack Thursday on October 24, which started the Stock Market

Crash of 1929. In Australia and New Zealand the 1987 crash is also referred to as Black Tuesday

because of the time zone difference.)

The Black Monday decline was the largest one-day percentage decline in stock market

history. Other large declines have occurred after periods of market closure, such as, in the USA, on

Monday, September 17, 2001, the first day that the US market was open following the September

11, 2001 attacks. (Saturday, December 12, 1914, is sometimes erroneously cited as the largest one-

day percentage decline of the DJIA. In reality, the ostensible decline of 24.39% was created

retroactively by a redefinition of the DJIA in 1916).

Interestingly, the DJIA was positive for the 1987 calendar year. It opened on January 2,

1987, at 1,897 points and would close on December 31, 1987, at 1,939 points. The DJIA did not

regain its August 25, 1987 closing high of 2,722 points until almost two years later.

Mysteriousness: A degree of mystery is associated with the 1987 crash.

Important assumptions concerninghuman rationality, the efficient-market hypothesis, and

economic equilibrium were brought into question by the event. Debate as to the cause of the crash

still continues many years after the event, with no firm conclusions reached.

In the wake of the crash, markets around the world were put on restricted trading primarily

because sorting out the orders that had come in was beyond the computer technology of the time.
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This also gave theFederal Reserve and other central banks time to pumpliquidityinto the system

to prevent a further downdraft. While pessimism reigned, the DJIA bottomed on October 20.

Following the stock market crash, a group of 33 eminent economists from various nations

met in Washington, D.C. in December 1987, and collectively predicted that the next few years

could be the most troubled since the 1930s. In fact, calendar year 1987 had an overall gain, as did

1988 and 1989.

CASE ILLUSTRATION: MARKET RISK MANAGEMENT AT HSBC

Introduction

Like any other global bank, HSBC is affected by market risk. HSBC separates exposures to market

risk into trading and non-trading portfolios. Trading portfolios include those positions arising from

market-making, proprietary position-taking and other marked-to-market positions. Non-trading

portfolios primarily arise from HSBCs retail and commercial banking assets and liabilities,

financial investments classified as available for sale and held to maturity.

Organisation and responsibilities

An independent unit within Group Risk, develops the Groups market risk management policies

and measurement techniques. Each major operating entity has an independent market risk

management and control function which is responsible for measuring market risk exposures in

accordance with group policies and monitoring and reporting them on a daily basis.

Each operating entity is required to assess the market risks which arise on each product in its

business and to transfer these risks to either its local Global Markets unit for management, or to

separate books managed under the supervision of the local Asset and Liability Management

Committee. This way all market risks are consolidated within operations which have the necessary

skills, tools and management capabilities to handle such risks professionally. Each operating unit

must ensure that market risk exposures remain within the limits specified for that entity. The nature

and degree of sophistication of the hedging and risk mitigation strategies performed across the

Group corresponds to the market instruments available within each operating jurisdiction.
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Measurement and monitoring of market risk

Sensitivity analysis

Sensitivity measures are used to monitor the market risk positions within each risk type, for

example, for interest rate risk, the present value of a basis point movement in interest rates.

Sensitivity limits are used to monitor diversification of risk both across and within asset classes.

Interest rate risk

Interest rate risk arises principally from mismatches between the future yield on assets and their

funding cost as a result of interest rate changes. HSBC uses a range of tools to monitor and limit

interest rate risk exposures. These include the present value of a basis point movement in interest

rates, VAR, stress testing and sensitivity analysis.

Foreign exchange risk

HSBC controls foreign exchange risk within the trading portfolio by limiting the open exposure to

individual currencies, and on an aggregate basis. VAR and stress testing are also used to measure

and control this kind of risk.

Foreign exchange exposures also arise from net investments in subsidiaries, branches or associated

undertakings, the functional currencies of which are currencies other than the US dollar. HSBCs

aim is to ensure that consolidated capital ratios and the capital ratios of individual banking

subsidiaries are protected from the effect of changes in exchange rates. For each subsidiary bank,

the ratio of structural exposures in a given currency to risk-weighted assets denominated in that

currency must broadly equal the capital ratio of the subsidiary in question. HSBC hedges structural

foreign exchange exposures only in limited circumstances.

Specific issuer risk

Specific issuer (credit spread) risk arises from a change in the value of debt instruments due to a

perceived change in the credit quality of the issuer or underlying assets. Besides VAR and stress


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testing, HSBC manages such exposure through the use of limits referenced to the sensitivity of the

present value of a basis point movement in credit spreads.

Equity risk

Equity risk arises from the holding of open positions, either long or short, in equities or equity

based instruments. Besides VAR and stress testing, HSBC controls the equity risk within its

trading portfolios by limiting the net open equity exposure.

Equity risk within the non-trading portfolios typically arises as a result of investments in private

equity and strategic investments. Investments in private equity are subject to limits on the total

amount of investment. While evaluating potential new commitments, HSBC attempts to ensure

that industry and geographical concentrations remain within acceptable levels for the portfolio as a

whole.

References:

1. Derivatives & Risk Management, S.P.Gupta.

2. Derivatives & Risk Management, John.C.Hull.

3. Derivatives, Valuation and Risk Management, David A. Dubofsky and Thomas W. Miller,

JR.

4. Investment Management, Security Analysis and Portfolio Management by V.K.Bhalla.

5. Security analysis and Portfolio Management by Fischer and Gordon.

6. A case study on delta hedging: futures versus Underlying spot Antoine a. Kotze.

Managing Market Risk Unit

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