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CPA REVIEW PROGRAMMECPA REVIEW PROGRAMMEFINAL STAGE: MODULE FFINAL STAGE: MODULE F
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P17: INTERNATIONAL FINANCEP17: INTERNATIONAL FINANCEDERIVATIVE INSTRUMENTS: OPTIONSDERIVATIVE INSTRUMENTS: OPTIONS
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1. INTRODUCTION
Options are unique financial instruments that confer upon the holder the
right to do something without the obligation to do so. More
specifically, an option is a financial contract in which the buyer of
the option has the right to buy or sell an asset, at a pre-specified
price, on or up to a specified date if he chooses to do so; however,
there is no obligation for him to do so. In other words, the option
buyer can simply let his right lapse by not exercising his option. The
seller of the option has an obligation to take the other side of the
transaction if the buyer wishes to exercise his option. Obviously, the
option buyer has to pay the option seller a fee for receiving such a
privilege.
Options are available on a large variety of underlying assets including
common stock, currencies, debt instruments, and commodities. Also
traded are options on stock indices and futures contracts (the
underlying asset is a futures contract and futures-style options. While
over-the-counter option trading has had a long and chequered history,
option trading on organized options exchanges is relatively recent.
Options have proved to be a very versatile and flexible tool for risk
management in a variety of situations arising in corporate finance,
stock portfolio risk management, interest risk management and hedging of
commodity price risk. By themselves and in combination with other
financial instruments, options permit creation of tailor-made risk
management strategies.
Options also provide a way by which individual investors with moderate
amounts of capital can speculate on the movements of stock prices,
exchange rates, commodity prices and so forth. The limited loss
features of optios is particularly advantageous in this context.
2. CURRENCY OPTIONS
2.1 Currency Options Defined
A currency option may be defined as a contract which gives its holder
the right (not the obligation) to buy or sell, on or by a specified
date, a specified amount of a particular currency at an exchange rate
determined at the time of the signing of the contract. In December
1982, the Philadelphia Stock Exchange began trading options on the
pound. Currently, options are offered on the pound as well as the
Australian dollar, the Canadian dollar, the German mark, the French
franc, the Japanese yen, and the ECU. Currency options are also traded
on the Chicago Board Options Exchange and the London International
Financial Futures Exchange (LIFFE).
2.2 Categories of Currency Options
There are two categories of options, viz, American style options and
European style options. If an option can be exercised on any date during
its lifetime it is called an American style option but if it can be
exercised only on its expiration date, it is called a European style
option. American options offer buyers more flexibility in that they can
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be exercised on any date up to and including the maturity date of the
option. Also, the term European style has nothing to do with European
terms for quotations; rather, it has to do with when the option buyer
can exercise the option, that is, buy or sell the currency at the strike
price. European options can be exercised only on the maturity date of
the option. They cannot be exercised before that date.
Basic Option Concepts
Option Writer and Holder. An option is a contract, and there are
two sides or counter parties to each contract. The writer (or
seller) of the option sells to the holder (or buyer) the right to
buy or sell the amount of the currency specified in the contract.
In return for this privilege, the holder of the contract pays the
writer no matter what happens, that is, irrespective of whether
the holder decides to exercise or not. It is essential not to
confuse the buying and selling of the option with the buying and
selling of the underlying currency. The writer of the option
sells the right to buy or sell the currency, and hence is the
seller of the option who receives, in return, the premium. The
writer has an obligation to comply with the holder’s decision
should the latter decide to exercise the right of buying and
selling the currency. The holder of the option, on the other
hand, buys the right to buy or sell the currency, and hence is the
buyer of the option who pays the premium. If the holder chooses
not to exercise this right, then the premium will be lost (by the
holder)
Call and Put Options. An option gives the holder the right to buy
or sell a currency. A call option gives the holder the right to
buy a currency. In this case, the writer must comply by selling
the currency to the holder if the latter decides to exercise. A
put option, on the other hand, gives the holder the right to sell
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a currency. The writer must comply by buying the currency from
the holder if the latter decides to exercise.
Naked and Covered Option. An option is described as ‘naked’ if
there is no corresponding spot position in the underlying
currency. For example, if the writer of an Australian dollar call
option does not have a spot position in the Australian dollar, the
option in naked. This is because, if the holder of this option
decides to exercise, the writer cannot comply unless he or she
buys the required amount on the spot market. With a covered
option, the writer can comply without resorting to the spot market
as the writer can sell Australian dollar holdings. The writer of
a naked option is required to deposit a margin.
The Exercise Exchange Rate. Also called the strike exchange rate
(or price, in general), it is the exchange rate at which the
holder of the option buys (in the case of a call) or sells (in the
case of a put) should the holder choose to exercise. Let E be the
exercise exchange rate and S the actual spot exchange rate
prevailing when the decision whether or not to exercise is
considered. Assume also that these exchange rates are expressed
as the number of units of currency x per one unit of currency
y(x/y) where y is the currency to be bought or sold by the holder
of the option. Ignoring the premium for the time being, the
following rules hold:
The holder will exercise a call option if S>E. Profit is made by buying
currency y at E and selling it at S. Gross profit per unit of
currency y is S-E. if S<E, there is no point in exercising a call
option, since it is cheaper to buy currency y on the spot market.
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The holder will exercise a put option if S<E. Profit is made by buying
currency y in the spot market at S and selling it at the exercise
exchange rate, E. Gross profit per unit of currency y is E-S. if S>E,
there is no point in exercising the put option, since this will produce
a loss.
The difference between the actual and the exercise exchange rates (or
vice versa) is called ‘gross’ profit, as opposed to ‘net’ profit,
because the premium that is paid by holder to acquire the option is
not considered. Let us now reconsider the rules by introducing the
premium, . In the case of a call option, net profit per unit
currency y is S-(E+).
In the case of a put option, net profit per unit of currency is E-
(S+). Notice that while the profit obtained by the holder is
unlimited, there is an upper limit on the loss, which is the premium.
The worst that could happen is that the holder chooses not to
exercise, in which case the holder loses the premium only. On the
other hand, the maximum the writer of an option can gain is the
premium, while his or her loss is unlimited.
Long and Short Positions.
The holder or buyer of the option is described as holding a long
position, while the writer or the seller of the option holds a short
position on the same option. A long position gives a right, while a
short position creates a commitment. The following are various
possibilities:
1. A long call position gives the right to buy a currency;
2. A long put position gives the right to sell a currency.
3. A short call position implies a commitment to sell a
currency to the holder of the option if the latter decides to
exercise.
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4. A short put position implies a commitment to buy a
currency from the holder of the option if the latter decides
to exercise.
Expiry Date, American Options and European Option.
An option gives the holder the right to buy or sell a currency on or
before a certain date, known as the expiry (or expiration) date after
which the contract terminates, that is, the date after which the
holder’s right to buy or sell the currency will no longer be valid.
An American option can be exercised on or before the expiry date,
while a European option can be exercised only on the expiry date.
Because an American option gives a greater privilege than a
corresponding European option, the premium paid on the former must be
higher.
In the Money and Out of the Money. An option is in the money if
it can be exercised at (gross) profit. If S>E, then a call option
is in the money while a put option is out of the money.
Conversely, if S<E, then a put option is in the money while a call
option is out of the money. If S=E, then the option is at the
money. If an option is in the money this does not necessarily
mean that it can be exercised at net profit. This will only
happen if it is in the money by an amount that is greater than the
premium.
Intrinsic Value and Time Value. The intrinsic value of an option
is the extent to which the option is in the money. At any point
in time during the life of an option, the greater the difference
between the actual exchange rate prevailing then and the exercise
exchange rate (or vice versa), the greater is the intrinsic value
of a call (put) option. For a call option the intrinsic value is
given by.
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where Vi,t is the intrinsic value at time t, and St is the spot
exchange rate prevailing then. If St,<E, then Vi,t=0. For a put
option
Vi,t=E-Si and hence, if St>E, then Vi,t=O.
Over-the-Counter and Exchange Traded Option. An over the counter
(OTC) traded option is an option created by a writer to meet the
specific requirements of a buyer, given that such an option is not
generally traded on the floor of an exchange. An Example is an
option to buy AUD 242 000 by 12 May at an exercise exchange rate
of 0.7650 USD/AUD). This kind of option is obviously non-
standardised. On the other hand, an exchange traded option is
one of a class of standard options that have predetermined
specifications with respect to size, exercise price and expiry
date.
2.3 Pricing Currency Options.
Pricing currency options means determining the value of the premium, per
unit of the underlying currency, that must be paid by the buyer to the
writer of the option. The total cost of acquiring the option is,
therefore, equal to the product of the premium and the number of units
of the underlying currency in the option. If the underlying exchange
rate is x/y, then the premium is also expressed as units of x (normally
a fraction of one unit of x) per one unit of y. if the contract has Q
units of y, the total cost of the option is Q. Option dealers quote a
bid premium and an offer premium for each contract: the bid is what the
dealer is prepared to pay to buy the option, and the offer is what the
dealer must be paid to sell. The dealer must state whether the
underlying option is a call or a put, and whether is an American or a
European option, as well as the exercise price and the date of expiry.
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2.3.1 Factors Determining Option Prices
The following factors determine the premium or the price of a currency
option:
The Exercise Exchange Rate: The higher the exercise exchange
rate, the lower the premium on a call and the higher the premium on a
put. This is straightforward. A call option that gives the holder
the right to buy a currency at a lower exercise exchange rate should
be more valuable than when the right can be exercised at a higher
exchange rate. The lower the exercise exchange rate, the more likely
it is that it will be below the market exchange rate, in which case
the holder can exercise the option at a profit. The reverse argument
applies to the case of a put option
Time to Expiry: The longer the time to expiry, the greater is the
premium. This is because the probability that an out-of-the-money
option becomes in the money increases with the time to expiry. On or
very close to the date of expiry, an out-of-the-money option will be
worth nothing because there is a zero probability that it will be in
the money. Thus, it has a zero intrinsic value and a zero time
value, and hence the premium should be zero.
Intrinsic Value: The higher the intrinsic value – that is, the
more the option is in the money – the higher the premium. This is
because the greater the intrinsic value, the higher is the
probability that the option will be exercised at a profit.
Exchange Rate Volatility: An option is like an insurance policy,
and so it costs more where there is a greater underlying risk, which
in currency options arises from exchange rate volatility. If the
options are spot transactions, the relevant volatility is that of the
spot rate. If the options are on futures contracts, the relevant
volatility is that of the futures exchange rate. Since the
volatility of the spot rate determines the volatility of the futures
rate, it is the volatility of the spot rate that matters. Exchange
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rate volatility is normally measured by the standard deviation of the
exchange rate as calculated from historical data.
Type of Option: For a given exercise exchange rate, volatility
and time to expiry, the premium on an American option should be
higher than the premium on a European option.
Interest Rate on the Currency of Purchase: If the underlying
exchange rate is x/y, then y is the currency to be bought and sold in
accordance with the contract, while x is the currency of purchase,
that is, the currency in which the premium is valued and paid. The
higher the interest rate on the currency of purchase, the lower is
the present value of the exercise price. A higher interest rate,
therefore, has the same effect as a lower exercise price. Thus, a
higher interest rate is associated with a higher value of calls and a
lower value of puts.
The Forward Spread and the Interest Rate Differential: If
currency y is expected to appreciate, then a call option on y should
become more valuable while a put option becomes less valuable. For
reasons which will become clear in Chapters 10 and 11, the
possibility of currency y appreciating increases as the forward
spread and the interest differential increase
2.3.2 The pricing Formula
The Black-Scholes (1973) model was developed to explain the
determination of the premium on stock options. Garman and Kohlhagen
(1983) adapted the Black-Scholes formula to come up with a currency
option pricing formula. The price of a European call option, ’, is
given by
’= √T)
such that;
d= log(S/E)+T(i-i * + 2 /2)
√T
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where S is the actual spot rate prevailing at the time of trading, E is
the exercise exchange rate (both expressed as the price of one unit of
the option’s underlying currency in terms of the currency of purchase),
i is the interest rate on the currency of purchase, i* is the interest
rate on the underlying currency, is the standard deviation of the
exchange rate, T is the option’s maturity expressed as a fraction of a
year (365 days) and N(.) is the standard normal cumulative distribution
function. All the parameters of equation are readily available, except
, which can be estimated either from historical data or from a similar
option having the same maturity but a different exercise exchange rate.
’= √T)
which can be simplified to: ’=[FN(d)-EN(d-√T)eiT
where: d= log(F/E)+T 2 /2
√T
The relevance of the forward rate is that the spot rate, S, and the
interest rates, i and i* (which are related to the forward rate via
covered interest parity) appear in the formula. The price of a
corresponding put option, p, may be calculated from the put-call parity
relationship;
p=’+
Alternatively, the price of the put option can be obtained directly from
the following equation.
p=e-iTE[1-N(d-√T)]- [1-N(d)]
which can also be written in terms of the forward rate as
p={F[N(d)-1]-E[N(d--√T)-1]}eit
2.3.3 Measures of Sensitivity
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Obviously, the price of an option depends on several parameters. There
are various measures of the sensitivity of option prices with respect to
these parameters.
1. Delta (δ) : Delta measures the change in the premium
corresponding to a small change in the spot exchange rate, S. It
also reflects the probability that the option will expire in the
money. Thus, delta, ranges in value between zero for far out-of-
the-money option to 1.0 for deep in-the-money options. A delta
of 0.5 means that a one-point change in the spot exchange rate
will cause a 0.5-point change in the value of the option. Long
calls and short puts have positive deltas, because a rise in the
spot exchange rate leads to an increase in the value of the
option. Short calls and long puts have negative deltas. The
value of delta is affected by volatility and the time to expiry.
- Delta is given by : (δ)=ΔΔS
In general, the higher the delta, the greater the probability of
the option expiring in the money
2. Gama (γ) : This parameter measures the rate of change of delta
with respect to the spot exchange rate. Thus, a low gamma
reflects a stable delta. A positive gamma indicates that
profits increase when the exchange rate moves in a favourable
direction, and that the loss-making rate declines as more
losses are incurred if the exchange rate moves in an
unfavourable direction. Long options have positive gammas,
while short options have negative gammas.
- Gamma can be calculated as. γ=ΔδΔS
3. Theta (θ) : Theta measures the anticipated change in the
premium resulting from a change in the time to expiry. As the
time to expiry declines, so does the time value of the option.
Theta quantifies the change in the value of the option as the
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time to expiry declines. A theta of –1 means that each day
will cause a decrease in the option’s value of –1/365. Long
option positions have negative thetas, because as time passes
the holders lose some value of their investment in terms of the
premium. Short option positions have positive thetas for the
opposite reason.
- Theta is given by: θ= ΔΔt
Where t is time measured in days. The relationship between the
premium and the time to expiry is nonlinear, implying time-
varying θ. This means that option prices decline at an
increasing rate as the expiry date approaches. In general, the
option loses the bulk of its values in the final thirty days
prior to expiry.
4. Vega (ν) : This parameter is a measure of the rate of change
of the premium with respect to volatility. Long options have
positive Vegas, while short options have negative Vegas.
- Vega is calculated as ν = ΔΔ
The problem that arises here (and also in trying to implement the
option pricing formula) is that volatility is unobserved. Thus,
volatility is viewed as (i) historical, which is evaluated from
historical data, (ii) forward-looking, when historical volatility
is altered to reflect expectations about the future; and (iii)
implied, which is derivered from the pricing formula.
5. Rho (р): Rho meares the rate of change of the premium with
respect to the interest rate. Remember that the interest rate
is used as a discount factor, and so rho tends to be higher for
options with longer time to expiry. It is also possible to
distinguish between р and р*, depending on whether the
sensitivity is measured with respect to i or i*, ‘The effect of
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the two interest rates may also be viewed through the effect on
the forward rate. A change in either or both interest rates
leads to a change in the forward rate, and hence in the forward
premium as implied by equations (7.6 and 7.7) р and р* can be
calculated as
- р= Δ <0 Δi
- р*= Δ >0 Δi*
2.4 Uses of Currency Options
Currency options provide the corporate treasurer another tool for
hedging foreign exchange risks arising out of the firm’s operations.
Unlike forward contracts, options allow the hedger to gain from
favourable exchange rate movements, while being protected against
unfavourable movements. However, forward contracts are costless while
options involve up-front premium costs.
Investors may speculate in the currency options market based on their
expectations of the future movements in a particular currency. For
example, if the speculators expect that the Japanese yen will
appreciate, they will purchase Japanese yen call option. When the spot
rate of Japanese yen appraciate, they can exercise their option by
purchasing yen at the strike price and then selling the yen at the
prevailing spot rate.
For every buyer of a currency call option, there must be a seller.
A seller of a call option is obligated to sell aspecified currency at a
specified price (the strike price) up to a specified expiration date.
Sometimes, when the speculators expect the currency to depreciate in the
future, they may want to sell a currency call option. And the only way
a currency call option will be exercised will be when the spot rate is
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higher than the strike price. In this way, when the option is
purchased, the seller of the currency call option will receive the
premium. He can keep the entire amount if the option is not exercised.
Also, when it appears that an option will be exercised there will still
be sellers of options. But such options will sell for high premiums
because of the increased risk of the option being exercised at some
point.
2.5 Options Market Structure: Exchange Traded and OTC Options
Options are purchased and traded either on an organised exchange or in
the over-the-counter (OTC) market. Exchange traded options or listed
options are standardised contracts with predetermined exercise prices,
standard maturities (one, three, six, nine, and 12month), and fixed
maturities (March, June, September, and December).
OTC options are contracts whose specifications are generally negotiated
as to the amount, exercise price and rights, underlying instrument, and
expiration. OTC currency options are traded by commercial and investment
banks in virtually all-financial centers.
The OTC options market consists of two sectors:
(1) A retail market composed of nonblank customers who purchase
from banks what amounts to customised insurance against adverse
exchange rate movements and
(2) A wholesale market among commercial banks, investment banks,
and specialized trading firms; this market may include interbank
OTC trading or trading on the organised exchanges.
The interbank market in currency options is analogous to the interbank
markets in spot and forward exchange. Banks use the wholesale market to
hedge or ''reinsure'' the risks undertaken in trading with customers and
to take speculative positions in options.
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Exchange-traded and OTC options comparedExchange-traded OTC
Contract terms, includingamounts
Standardized Fixed to suitcircumstances; terms arenot standard
Expiration Standardized Determined byrequirements of customer
Transaction method Stock exchange typemedium
Bank-to-client or bank –to-bank.
Secondary market Continuous secondarymarket
No formal secondarymarket
Commissions Negotiable Negotiable, but usuallybuilt into the premium
Participants Exchange members andclients
Banks, corporations andfinancial institutions
Exchange Listed.
The other market for FX options is the exchange-listed market of the
various stock and futures exchange around the world. The principal
centres are Philadelphia, where the stock exchange lists options on spot
FX and Chicago, where theMerchantile Exchange lists options on its FX
futures contracts. In both cases, quotations are in the form of
currency (rather than volatility).
Access to the market is through brokers who impose commissions for each
contract traded. The market operates on the floor of the exchange where
brokers gather to reflect their clients’ orders with market makers or
specialists providing the prices. The markets have specified opening
and closing times for each currency contract. Also, the exchanges have
widened the availability by extending trading hours.
2.6 Advantages of Currency Options
Advantages
Options are used by buyers just like an insurance policy against
movements in rates. Thus, they are alternatives to using the
futures market or to the forward exchange market.
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The main advantages of using options are:
The option buyer, at the outset, judges the worst-case
scenario. Once premium is paid, no further cash is payable
and when the main objective is to limit downside risk, this
is a powerful advantage.
Since there is no obrigation to exercise an option, options
are ideal for hedging contingent cashflows which may or may
not materialise, such as tenders.
Options provide a flexible hedge offering a range of prices
where the option can be exercised, whereas forward or future
markets only deal at the forward prices which exist at the
time the deal is made.
Options provide major possibilities in the rang eof toools
available to treasures and traders. They can be used on
their own to hedge or they can be combined with the forward
and futures markets to achieve more complex hedges.
Futures require daily margins to cover credit risk while
forwards require bank credit line. An option buyer can
dispense with either depending on the specific market in
which he operates.
3 INTEREST RATE OPTIONS
3.1 Definitions and Types
A less conservative hedging device for interest rate exposure is
interest rate options. A call option on interest rate gives the holder
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the right to borrow funds for a specified duration at a specified
interest rate, without an obligation to do so. A put option on interest
rate gives the holder the right to invest funds for a specified duration
at a specified return without an obligation to do so. In both cases,
the buyer of the option must pay the seller an up-front premium stated
as a fraction of the face value of the contract.
3.2 Interest Rate Cap and Interest Rate Floor
An interest rate cap consists of a series of call options on interest rate or
a portfolio of calls. A cap protects the borrower from increase in
interest rates at each reset date in a medium-to-long-term floating rate
liability. Similarly, an interest rate floor is a series or portfolio
of put options on interest rate which protects a lender against fall in
interest rate on rate rest dates of a floating rate asset.
3.3 Interest rate Collar
An interest rate collar is a combination of a cap and a floor.
3.4 The Put-Call Option Parity
Interest rates parity relates the forward (and futures) rates
differential to the interest differential. Another parity conditions
relate options prices to the interest differential and, by extension, to
the forward differential. We are now going to derive the relation
between put and call option prices, the forward rate, and domestic and
foreign interest rates. To do this, we must first define the following
parameters:
C = call option premium on a one-period contract
P = put option premium on a one-period contract
E = exercise price on the put and call options (dollars per unit of
foreign currency)
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eo = Current spot rate (dollars per unit of foreign
currency)
e1 = End-of-period sot rate (dollars per unit of foreign
currency)
f1 = One-period forward rate (dollars per unit of foreign
currency)
rh = US. Interest rate for one period
rf = Foreign interest rate for one period
The parity relations are presented by the following equations:
C = e0/[1 + rf] – E/[1 + rh] + P
According to interest rate parity,
e0/[1 + rf] = f1/[1 + rh]
Substituting the Second Equation into Equation One yields a new
equation:
C = [f1 – E]/[1 + rh] + P
or C - P = [f1 – E]/[1 + rh]
These parity relations say that a long call is equivalent to a long put
plus a forward (or futures) contract. The term f1 - E is discounted
because the put and call premia are paid upfront whereas the forward
rate and exercise price apply to the expiration date.
3.5 Interest Rate Exposure
3.5.1 Nature and Measurement
Fluctuations in interest rate affect a firm’s cash flows by affecting
interest income on financial assets and interest expenses on
liabilities. To put it in another way, the market values of a firm’s
portfolio of financial assets and liabilities fluctuate with interest
rates. For a non-financial firm, fluctuations in interest rates causes
corresponding fluctuations in operating earnings and rates of return on
projects.
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Effective assessment and management of interest rate exposure requires
first of all a clear statement of the firm’s risk objectives. The
financial manager must then translate these into operational guidelines
for monitoring key parameters which will reveal the firm’s total
exposure. Leach (1988) has suggested a classification into primary and
secondary objectives as follows:
Primary Objective:
i. Net interest income, i.e. interest income on assets minus
interest expense on liabilities. Monitoring of this account
will of this account will reveal the sensitivity of the firm’s
profitability to changes in interest rates.
ii. Net equity exposure, i.e. sensitivity of the firm’s net worth
to interest rates
The first of these is more suitable for a non-financial corporation with
relatively few financial assets as the latter measure requires
estimating the changes in values of non-financial assets as interest
rates change. The second measure is more suitable for a financial
institution with predominantly financial assets and liabilities.
Secondary Objective.
i. Credit exposure which is really a measure of default risk.
Most firms would wish to limit their exposure to any one
individual or firm.
ii. Basis risk arises when interest rate exposure on one
instrument, e.g. commercial paper is offset with another
instrument, e.g. Eurodollar futures or when floating rate
assets tied to one index, e.g. prime rate are funded by
floating rate liabilities tied to another index, e.g.
Eurodollar CDs.
iii. Liquidity risk pertains to timing mismatches between cash
inflows and outflows, e.g. when a longer duration assets is
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funded by a shorter duration liability which will have to be
refunded at maturity, possibly at a higher cost.
The measure of exposure selected must incorporate these objectives.
The most often used device to assess interest rate exposure is Gap
Analysis. It focuses mainly on the liquidity risk. The entire planning
horizon is divided into sub periods. For each subperiod, the difference
between the assets and liabilities which mature or are repriced during
that interval is designated as the ‘gap’. If the gap is positive there
will be a net cash surplus while if it is negative there will be a
deficit.
A more sophisticated approach uses the concept of duration discussed in
detail in Appendices. Duration of an interest bearing security measures
the sensitivity of its market value to changes in yield. Another
interpretation brings out the tradeoff between reinvestment market
value. Consider a coupon bond. An increase in interest rate reduces
the market price of the bond but allows the coupons to be reinvested at
a higher rate of return.
Duration can be interpreted as the period over which these two effects
balance each other. Since durations obey additivity, the duration of a
portfolio is simply the weighted sum of the durations of components of
the portfolio. A firm with a portfolio of financial assets and
liabilities can minimize interest rate exposure by equating as nearly as
possible the duration of its assets and liabilities.
3.5.1.1 Forward Rate Agreement (FRA)
A Forward Rate Agreement (FRA) is an agreement between two parties in which
one of them (the seller of the FRA), contracts to lend to the other (the
buyer), a specified amount of funds, in a specific currency, for a
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