risk and options

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Risk Management

by Binam Ghimire

In risk Management, we talk

“what risks to take”. We don’t

talk “No risk to take”

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3

Objectives

Commodity Price and Interest Rate Risk

Derivatives

Option

Forward

Futures

Swaps

Insurance

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Risk – What did we learn so

far?

Risk: Do we like?

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5

Why Hedging?

19 September 2010, Man Utd 3 - 2 Liverpool Picture Source: Barclays Premier League, www.premierleague.com

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Why Hedging?

When the firm reduces its risk exposure with the use of financial instruments it is said to be hedging

Hedging offsets the firm’s risk, such as the risk in a project, by one or more transactions in the financial markets.

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Hedging using Derivatives

A derivative is a financial contract

The value of the contract is derived from the price of some underlying asset

So the value of derivative changes when there is a change in the price of an underlying related asset

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Hedging using Derivatives

Derivatives are FINANCIAL PRODUCTS THAT ENABLE PARTICIPANTS TO TRADE RISK, OFTEN WITHIN AN ORGANISED MARKET

We are able to hedge because market is imperfect

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“Derivatives are to

finance what

scalpels are to

surgery”

Options

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Option Terminology

An option is a security that gives the holder the right to buy or sell a particular asset at a specified price, on or before, a specific date.

A call option would be created, for example, if on Feb. 1st, Ms. B paid $1000 to Mr. A for a contract that gives Ms. B the right, but not the obligation, to buy ABC properties from Mr. A for $20,000 on or before July 1st.

A put option would be created if Mr. A sold Ms. B a contract for the right, but not the obligation, to sell ABC properties to Mr A at a specific price on or before a certain date.

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Option Terminology

Depending on the parties and types of assets involved, options can take on many different forms. Certain features are common to all options.

With every option contract there is a right, but not the obligation, either to buy or to sell.

a call is the right to buy a specific asset or security

a put is the right to sell a specific asset or security.

Every option contract has a buyer and a seller.

the option buyer is referred to as the holder and has a long position in the option.

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Option Terminology

the holder buys the right to exercise or evoke the terms of the option claim.

the seller often referred to as the writer, has a short position and is responsible for fulfilling the obligations of the option if the holder exercises.

Every option has an option price, an exercise price, and an exercise date.

The price paid by the buyer to the writer is referred to as the option premium.

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Option Terminology

The exercise price or strike price is the price specified in the option contract at which the underlying asset can be purchased or sold.

The exercise date is the last day the holder can exercise.

A European option is one that can be exercised only at the exercise date, while an American option can be exercised at any time on or before the exercise date.

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In the Money: Strike Price> stock Price (A call option is in the money if the stock price is above the strike price. A put option is in the money if the stock price is below the strike price.)

At the Money: Strike Price= Stock Price (a strike price that is equal to the current market price of the underlying stock)

Out of the Money= Strike Price< stock price ( A call option is out of the money if the stock price is below its strike price)

Option Terminology

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NYSE Euronext

Euronext (http://www.euronext.com) trades a wide variety of options.

Details of the individual equity contracts traded at Euronext may be found at:-

http://www.euronext.com/trader/contractspecifications/wide/contractSpecifications-3084-EN.html?docid=47378

Current market prices for equity options are available at http://www.euronext.com/trader/priceslistsderivatives/derivativespriceslists-1830-EN.html?cha=1830&lan=EN&mep=7

http://www.euronext.com/







http://www.euronext.com/trader/priceslistsderivatives/derivativespriceslists-1830-EN.html?cha=1830&lan=EN&mep=7






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Option Strategies

We will briefly cover four fundamental option strategies:

call and put purchases.

call and put writes.

The features of these strategies can be seen by examining the relationship between the price of the underlying asset and the profit/loss.

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Call Purchase

Suppose an investor buys a call option on ABC stock with an exercise price (X) of $50 at a call premium (C) of $3.

In simple terms this option gives the holder the right, but not the obligation, to buy ABC stock for $50.

What we have to determine is what factors will lead to the option being exercised or thrown away.

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Exercise - Yes/No ???

If the stock price is $30 on the expiration date will the investor exercise his call option ?

Of course not ! Why would he buy the stock for $50 in the option market if he could buy it for $30 in the cash market.

If the stock price is $40 on the expiration date will the investor exercise his call option.

Again of course not. And so on for $41, $42...$49.

Note that regardless of whether the option is exercised or not the investor must still pay the premium - $3.

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However, if the stock price is $50 the investor is indifferent between buying the stock in the cash marker and the options market

What about stock prices above $50 ?

At stock prices above $50 such as $51 and $52 it is advantageous for the investor to buy the stock from the options contract rather than buy it in the cash market.

But the investor paid $3 for the option so he is effectively paying $53 for the stock. So although it is advantageous for the investor to exercise his option in reality it would have been better not to have purchased the option at all.

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If the stock price is above $53 on expiration not only is it advantageous for the option to be exercised it is in fact profitable.

For example, if the stock price is $60 the investor could purchase the option for $50 by the terms of the option contract then sell the stock in the cash market for $60, thus making a profit of $10.

The profit net of the premium is then $7.

Following this logic it is possible to map out a relationship between the stock price and profit/loss from exercising the option.

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Stock Price Exercise? Premium Profit from Exercing Net Profit

$40 No $3 0 -$3

$45 No $3 0 -$3

$50 Yes/No $3 0 -$3

$55 Yes $3 $55-$50=$5 $2

$60 Yes $3 $60-$50=$10 $7

$65 Yes $3 $65-$50=$15 $12

This relationship can best be described graphically. We refer to this relationship as a profit profile.

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Profit Profile of a ABC call option with a strike price of

$50 and a premium of $3

-5

0

5

10

15

40 45 50 55 60 65

Stock Price ($'s)

Pro

fit

($'s

)

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-5

0

5

10

15

40 45 50 55 60 65

Stock Price ($'s)

Pro

fit

($'s

)

13

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-5

0

5

10

15

40 45 50 55 60 65

Stock Price ($'s)

Pro

fit

($'s

)

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-5

0

5

10

15

40 45 50 55 60 65

Stock Price ($'s)

Pro

fit

($'s

)

14

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The profit profile highlights two important features of call purchases.

the position provides an investor with unlimited profit potential.

losses are limited to an amount equal to the call premium.

These two features help explain why speculators prefer buying a call rather than the stock itself.

Features of the Call Purchase

Strategy

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Options are highly leveraged

In our example, suppose that the price of ABC stock could range from $30 to $70 at expiration.

If a speculator purchased the stock for $50, the profit from the stock would range from -$20 to $20, or in percentage terms, from -40% to +40%.

On the other hand the return from the option would range from +567% to -100%.

Thus the potential reward to the speculator from buying a call instead of a stock can be substantial, 567% compared to 40%; but the potential loss is also large, -100% vs 40%.

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Call Write

The second fundamental option strategy involves the sale of a call in which the seller does not own the underlying stock.

Such a position is known as a call write.

Again assume that the exercise price on the call option on ABC stock is $50 and the call premium is $3.

The profits/losses associated with each stock price from selling the call are depicted in the following table.

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Holder Premium Writers

Stock Price Exercise? Received Action from writer Profit/Loss

$40 No $3 Nothing $3

$45 No $3 Nothing $3

$50 Yes/No $3 Nothing $3

$55 Yes $3 Buy ABC for $55 sell at $50 $3 - $5 = -$2

$60 Yes $3 Buy ABC for $60 sell at $50 $3 - $10 =-$7

$65 Yes $3 Buy ABC for $65 sell at $50 $3 - $15=-$12

Note the profit to the writer is the inverse to that of the holder.

Holder Exercise, Action from

Writer and pay off to Writer

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Profit profile for the writer of an ABC call option

with a strike price of $50 and a premium of $3

-12

-10

-8

-6

-4

-2

0

2

4

40 45 50 55 60 65

Stock Price ($'s)

Pro

fit

($'s

)

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-12

-10

-8

-6

-4

-2

0

2

4

40 45 50 55 60 65

Stock Price ($'s)

Pro

fit

($'s

)

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-12

-10

-8

-6

-4

-2

0

2

4

40 45 50 55 60 65

Stock Price ($'s)

Pro

fit

($'s

)

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-12

-10

-8

-6

-4

-2

0

2

4

40 45 50 55 60 65

Stock Price ($'s)

Pro

fit

($'s

)

18

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-12

-10

-8

-6

-4

-2

0

2

4

40 45 50 55 60 65

Stock Price ($'s)

Pro

fit

($'s

)

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As highlighted in the profit profiles, the payoffs to a call writer are just the opposite to those of the call purchase; that is, gains/losses for the buyer are exactly equal to the losses/gains of the seller.

The call write position provides the investor with only a limited profit opportunities, equal to the value of the premium, with unlimited loss possibilities.

While the limited profit and unlimited loss feature of a call write may seem unattractive, the motivation for an investor to write a call is the cash or credit received and the expectation that the option will not be exercised.

Features of the Call Write

Strategy

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Put Purchase

Suppose an investor buys a put option on ABC stock with an exercise price (X) of $50 at a put premium (P) of $3.

In simple terms this option gives the holder the right, but not the obligation, to sell ABC stock for $50.

What we have to determine is what factors will lead to the option being exercised or thrown away.

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Exercise - Yes/No ??

If the stock price is $70 on the expiration date will the investor exercise his put option ?

Of course not ! Why would he sell the stock for $50 in the option market if he could sell it for $70 in the cash market.

If the stock price is $60 on the expiration date will the investor exercise his call option.

Again of course not. And so on for $59, $58...$51.

Note that regardless of whether the option is exercised or not the investor must still pay the premium - $3.

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However if the stock price is $50 the investor is indifferent between selling the stock in the cash marker and the options market

What about stock prices below $50 ?

At stock prices below $50 such as $49 and $48 it is advantageous for the investor to sell the stock in the options contract rather than sell it in the cash market.

But the investor paid $3 for the option so he is effectively receiving $47 for the stock. So although it is advantageous for the investor to exercise his option in reality it would have been better not to have purchased the option at all.

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If the stock price is below $47 on expiration not only is it advantageous for the option to be exercise it is in fact profitable.

For example, if the stock price is $40 the investor could buy the stock in the cash market for $40 then sell the option for $50 by the terms of the option contract.

The profit net of the premium is then $7.

Following this logic it is possible to map out a relationship between the stock price and profit/loss from exercising the option.

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Holder Premium Holders

Stock Price Exercise? Paid Action from Holder Profit/Loss

$40 Yes $3 Buy stock for $40 sell at $50 -3 + 10 = $7

$45 Yes $3 Buy stock for $45 sell at $50 -3 + 5 = $2

$50 Yes/No $3 Nothing -3

$55 No $3 Nothing -3




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Profit Profile to the holder of an ABC Put Option with a strike

price of $50 and a premium of $3

-4

-2

0

2

4

6

8

$40 $45 $50 $55 $60 $65

Stock Price

Pro

fit

($'S

)

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-4

-2

0

2

4

6

8

$40 $45 $50 $55 $60 $65

Stock Price

Pro

fit

($'S

)

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-4

-2

0

2

4

6

8

$40 $45 $50 $55 $60 $65

Stock Price

Pro

fit

($'S

)

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Put Purchase

Thus, similar to a call purchase, a long put position provides the buyer with potentially large profit opportunities (not unlimited, since the price can never be below zero), while limiting the losses to the amount of the premium.

Unlike the call purchase strategy, the put purchase position requires the stock price to decline before profit is realized.

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Put Write

The exact opposite to a put purchase (in terms of profit or loss and stock price relations) is the sale of a put, known as a put write.

This positions profit and loss figures are shown below.

Stock Exercise Put Premium Action Put Writers

Price Yes/No ? Paid/Received by Writer Profit

40 Yes $3 Buy stock for 50 (real value 40) +$3 + 40 - 50 = -7

45 Yes $3 Buy stock for 50 (real value 45) +$3 + 40 - 45 = -2

50 No/Yes $3 Nothing 3

55 No $3 Nothing 3

60 No $3 Nothing 3

65 No $3 Nothing 3

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Profit profile to the writer of an ABC Put Option with a

strike price of $50 and a premium of $3

-8

-6

-4

-2

0

2

4

$40 $45 $50 $55 $60 $65

Stock Price

Pro

fit

($'s

)

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Black-Scholes Option pricing

Model

What is the price of an option

Can we use NPV technique?

Black-Scholes - Pioneered by Fischer Black and Myron Scholes (1973)

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Black-Scholes Option Pricing

Model (BSOPM)

The Black-Scholes equation for valuing call options is:-

C SN d Xe N drT

1 2

d

SX

r T

T1

21

2ln

d d T2 1

T = time to expiration (years),

N(.) = cumulative normal probability,

C = fair value of the option,

S = the current price of the stock,

r = the risk free rate of interest,

X = exercise price of the option,

= annualised standard

deviation of the stock return.

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Model (Explaining in simple)

First thing it is remarkably simple to price an option when there is no time to expiration.

Let us assume that there is only a fraction of time available before expiration. We got a call option say right to buy the share at $100 of IBM and if the price of the Stock is $115, then the option is worth $ 15. So the price of the option at expiration is the underlying stock price– the exercise price (We can give mathematical notation S and K similar to Black-Scholes). Hence the price of the call option at expiration is £15

The real question is how to price option before expiration?

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Model

We know the option will pay off if the underlying asset achieves a final value above the exercise price. So how can we actually put this into a pricing formula? If you check Black-Scholes pricing formula given above there is similarity with the formula for value of call option at expiration.

Value of a call option at expiration is S – K = $15. Or 15, 0 take the maximum of two

If it is the case that the stock price at expiration is $ 90. The Call option finishes at out of the money. Then S –K is a negative number and it will take 0. Look Black-Scholes. Without going into detail it is something similar to S – K. We have S the current stock price and instead of K we have present value of the exercise price

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Model

Agreed: the formula is more complicated than this.

Because - We need to mathematically determine the probability that a call option finishes in the money i.e. underlying commodity price > exercise price at the time of maturity.

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Black-Scholes Model to

option pricing

Black and Scholes (1973) made some assumption how the stock price behaves.

Need to think in terms of a normal distribution: Mean return that we expect and the volatility. With that information we can actually calculate what is the probability the stock price finishes above the strike price. For this the model uses cumulative normal distribution.

Using, in particular, volatility of the underlying assets, we can calculate the probability that stock price finishes in the money.

The above are the essential ingredients of Black-Scholes model.

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Black-Scholes Model to

option pricing

Note the above is a very simple explanation of Black-Scholes Model but should provide a fair amount of idea on the formula/ model.

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Forward Contract

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Forward Contract

A Forward Contract is the most basic derivative contract. It is an agreement between 2 parties to carry out a trade (buy/sell asset) in the future at a price agreed now.

The buyer takes a long position. The counterparty agreeing to make future delivery takes a short position.

The contract will specify the delivery date, the settlement date and the delivery price.

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Forward Contract

A Simple Example: Agreement made on 20th October with a butcher to buy (take delivery) 5 Kilograms turkey on the 24th of December for an agreed price of £10 (say £2/kg)

The butcher is selling the forward contract. The butcher is making the delivery. The price and conditions of the agreement set on the 20th October. However, no cash transaction is made on the 20th October.

Forward contract is not an option. Here both the buyer and seller are obliged to perform (In option, the buyer may choose not to exercise)

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Forward Contract: Example

Real business example:- Suppose on 12th December

Company X sells £1m of goods to a USA customer to be delivered after 1 month. Buy and Sell rated quoted is $/£ 1.6656-1.6660. So rate of 1.6660, Company X can invoice $1.6660 million payable in 1 month

The problem is that the exchange rate may move

The spot and forward exchange rate is shown next

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59 Source: ft.com, 2/12/2009, Pound Spot Forward

$/£ SPOT AND FORWARD RATES (02/12/09)

SPOT 1 MONTH 3 MONTHS 1 YEAR

1.6658 1.6655 1.6648 1.6616

The spot rate is quoted for (almost) immediate delivery.


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The calculation of the forward exchange rate must take into account the differences in the interest rates prevailing in each country at the time the deal is struck. So the formula for Forward Exchange Rate:

Where,

F= Forward Exchange Rate, S = Spot rate of £1 in units of a foreign currency; (1.6658), rf = the risk-free rate of interest in the foreign currency; (0.31%), rd = domestic risk-free rate of interest; (0.46%), t = the number of days until maturity of the contract; (90), T = number of days in the year. (360)

T

tx

100

rdrf1SF


For the 1 month contract:

= 1.6656, which is close (Actual 1.6655)

The difference in the spot and forward rate should reflect the differences in interest rates (interest rate parity). If interest rate parity did not hold then arbitrage opportunities would arise.

360

30x

100

46.00.3111.6658F


1 + r$ = F$/£

1 + r£ S$/£

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The company wants to sell $1.6660 m. in 1 month time at an exchange rate agreed now.

The 1 month forward rate is $/£1.6655. (02/12/09)

Guaranteed to receive:

$1.6660m = £1,000,300.21

$/£1.6655

As with all forward contracts the price (exchange rate) is fixed.


Futures

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Evolved from forward contract (Dojima, Japan – 1963)

Similar concept to forward, except:

Futures trade on futures exchanges (CME, CBOT, LIFFE, etc.)

Futures are standardized contracts

this increases their liquidity

but sometimes firms prefer precise, custom made (OTC) forward contracts

Futures Contracts

Default risk for futures is lower because:

The clearinghouse of the exchange guarantees payments.

An initial margin is required.

Futures contracts are “marked to market” daily (daily resettlement)

Futures contracts are traded anonymously on an exchange at a publicly observed market price and are generally very liquid.

Both the buyer and the seller can get out of the contract at any time by selling it to a third party at the current market price.

Futures Contracts

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Swaps

Swaps are contractual agreements between 2 parties to exchange cash flows.

The cash flows to be swapped may be determined on the basis of:

Interest rates

Exchange rates

The price of indices

Commodity prices

Most swaps involve two counterparties, typically firm and a swap dealer

We cover interest rates swap

Meaning

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If interest rates rise the fixed rate payer gains as the amount of floating rate interest received will increase.

The floating rate payer will obviously lose a similar amount.

Normally the floating rate is linked to LIBOR and is set one period before the payment is to be made.

Interest Rate Swap

A pays fixed and receives floating. Notional principal = £40m . The fixed rate = 7%. The floating rate is 6-months LIBOR

MONTH 6 12 18 24 30 36 42

LIBOR 6.5 7.0 7.3 7.7 7.0 6.2 5.9

Standard swaps have semi annual coupons. At the first coupon date in 6 months fixed coupon is £40m x 7% x ½ = £1.4m. And floating coupon (same as 7% again) is £40m x 7% x ½ = £1.4m.

Interest Rate Swap, Example

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Subsequently A’s cash flows are as follows (Fixed for Floating Interest Rate SWAP):

MONTH PAYS RECEIVES NET

12 £1.4m £1.4m 0

18 £1.4m £1.46m £60,000

24 £1.4m £1.54m £0.14m

30 £1.4m £1.4m 0

36 £1.4m £1.24m -£0.16m

42 £1.4m £1.18m -£0.22m


Note that as LIBOR rises the fixed payer gains.

However, as LIBOR falls the fixed payer loses. In this way a swap can be used to hedge against interest rate movements.


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Companies use interest rate swaps routinely to alter their exposure to interest rate fluctuations.

The interest rate a firm pays on its loans can fluctuate for two reasons.

First, the risk free interest rate in the market may change.

Second, the firm’s credit quality, which determines the spread of the firm must pay over the risk free interest rate, can vary over time.

By combining swaps with loans, firms can choose which of these sources of interest rate risk they will tolerate and which they will eliminate.

Combining Swaps with

Standard Loans

Bolt Industries is facing increased competition and wants to borrow $10 million in cash to protect against future revenue shortfalls.

Currently, long-term AA rates are 10%. Bolt can borrow at 10.5% given its credit rating.

The company is expecting interest rates to fall over the next few years, so it would prefer to borrow at short-term rates and refinance after rates drop.

However, Bolt’s management is afraid that its credit rating may deteriorate as competition intensifies, which may greatly increase the spread the firm must pay on a new loan.

How can Bolt benefit from declining interest rates without worrying about changes in its credit rating

(Example Source: Berck and DeMarzo (2007) Corporate Finance, Pearson International Edition, Boston, page 959)


Standard Loans, Example

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Bolt wants to convert its long-term fixed rate into a floating rate (one that will decline if market interest rates decline). It can do this by entering into a swap where it will receive a fixed rate (which can then be used to pay its fixed long-term obligation) and pay a floating rate. Its net exposure will be the floating rate.



Execute: Bolt can borrow at the long-term rate of 10.5% and

then enter into a swap in which it receives the long-term AA fixed rate of 10% and pays the short-term rate Its net borrowing cost will then be

In this way, Bolt locks in its current credit spread of 0.5% but gets the benefit of lower rates as rates decline. The tradeoff is that if rates increase instead, it is worse off.



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The discussion from this point forward follows the following text book on Corporate finance, page 925-967

Berck and DeMarzo (2007) Corporate Finance, Pearson International Edition, Boston

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Insurance

Insurance is the most common method firms use to reduce risk

Protects against hazards such as fire, storm damage, vandalism, earthquakes, and other natural and environmental risks

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Insurance

Business liability insurance, which covers the costs

that result if some aspect of the business causes harm to a third party or someone else’s property

Business interruption insurance, which protects the firm against the loss of earnings if the business is interrupted due to fire, accident, or some other insured peril

Key personnel insurance, which compensates for the loss or unavoidable absence of crucial employees in the firm

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Insurance Pricing in a Perfect

Market

The insurance company in a perfect market should compete until they are just earning a fair return and the NPV from selling insurance is zero. The NPV is zero if the price of the insurance equals the present value of the expected payment; in that case we call the price is actuarially fair

Where rL is the cost of capital

Lr1

Loss)ofeventthein(PaymentEx Pr(Loss)PremiumInsurance

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Example: Insurance Pricing

and the CAPM

Problem: As the owner of a landmark Chicago skyscraper,

you decide to purchase insurance that will pay $1 billion in the event the building is destroyed by terrorists.

Suppose the likelihood of such a loss is 0.1%, the risk-free interest rate is 4%, and the expected return of the market is 10%.

If the risk has a beta of zero, what is the actuarially fair insurance premium? What is the premium if the beta of terrorism insurance is –2.5?

Solution:

The expected loss is 0.1% x $1 billion = $1 million. If the risk has a beta of zero, we compute the insurance premium using the risk free interest rate ($ 1 million/ 1.04 = $ 961,538)

If the beta of the risk is not zero, we can use the CAPM to estimate the appropriate cost of capital. Given a beta for a loss, BL, of -2.5, and an expected market return, rmkt, of 10%.


and the CAPM

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Solution:

In this case, the actuarially fair premium is ($1 million)/ (1-0.11) = $ 1.124 million.

Although this premium exceeds the expected loss, it is fair price given the negative beta of the risk.


and the CAPM

%11%)4%10(5.2%4)( fmktLfL rrrr

The Value of Insurance

In a perfect capital market, insurance will be priced so that it has an NPV of zero for both the insurer and the insured.

But if purchasing insurance has an NPV of zero, what benefit does it have for the firm?

Modigliani and Miller provided us with the answer to this question:

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In a perfect capital market, there is no benefit to the firm from any financial transaction, including insurance.

Insurance is a zero-NPV transaction that has no effect on value.

Although insurance allows the firm to divide its risk in a new way (e.g., the risk of fire is held by insurers, rather than by debt and equity holders), the firm’s total risk—and, therefore, its value—remains unchanged.

Thus, just like a firm’s capital structure, the value of insurance must come from reducing the cost of market imperfections on the firm.


Bankruptcy and Financial Distress Costs When a firm borrows, it increases its chances of

experiencing financial distress.

Issuance Costs When a firm experiences losses, it may need to

raise cash from outside investors by issuing securities. Issuing securities is an expensive endeavor


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Example : Avoiding Distress

and Issuance Costs

Problem: Suppose the risk of an airline accident for a major

airline is 1% per year, with a beta of zero. If the risk-free rate is 4%, what is the actuarially fair

premium for a policy that pays $150 million in the event of a loss?

What is the NPV of purchasing insurance for an airline that would experience $40 million in financial distress costs and $10 million in issuance costs in the event of a loss if it were uninsured?

Example : Avoiding Distress

and Issuance Costs

Solution: The expected loss is 1% x $150 million = $1.50

million, so the actuarially fair premium is $1.50 million/ 1.04 = $ 1.44 million

The total benefit of the insurance to the airline is $ 150 million plus an additional $ 50 million in distress and issuance costs that it can avoid if it has insurance.

Thus the NPV from purchasing the insurance is

NPV = -1.44 + 1% x (150+50)/ 1.04 = $0.48 million

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Commodity Price Risk

For many firms, changes in the market prices of the raw materials they use and the goods they produce may be the most important source of risk to their profitability

Hedging with Vertical Integration Hedging with Storage Hedging with Long-Term Contract

By locking in its fuel costs through long-term supply contracts, Virgin Atlantic Airlines has kept its earnings stable in the face of fluctuating fuel prices.

For example, with a long-term contract at a price of $23 per barrel, Virgin would gain by buying at this price if oil prices go above $23 per barrel.

If oil prices fall below $23 per barrel, Virgin would lose from its commitment to buy at a higher price.

Commodity Price Risk

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Example :Hedging with Long-

Term Contracts

Problem: Consider a chocolate maker that will need 10,000

tons of cocoa beans next year. The current market price of cocoa beans is $1,400

per ton. At this price, the firm expects earnings before interest and taxes of $22 million next year.

What will the firm’s EBIT be if the price of cocoa beans rises to $1950 per ton?

What will EBIT be if the price of cocoa beans falls to $1200 per ton?

What will EBIT be in each scenario if the firm enters into a supply contract for cocoa beans for a fixed price of $1,450 per ton?

Example :Hedging with Long-

Term Contracts

Solution: If the price of cocoa beans increases to $1,950 per

ton, the firm’s costs will increase by (1950-1400) x 10,000 = $5.5 million.

Other things equal, EBIT will decline to $22 million – (1200 -1400) x 10,000 = $24 million.

Alternatively, the firm can avoid this risk by entering into the supply contract that fixes the price in either scenario at $1,450 per ton, for an EBIT of $22 million – (1450-1400) x 10,000 = $21.5 million

risk and options

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