10/10/2018 Nattawoot Koowattanatianchai 1fin.bus.ku.ac.th/BA 747 Investment Analysis and... · 02-9428777 Ext. 1212 ... Pricing and valuation of bond and interest rate forwards Pricing

10/10/2018 Nattawoot Koowattanatianchai 1


Investment Analysis &

Portfolio Management

Assistant Professor

Nattawoot Koowattanatianchai,

DBA, CFA


Email:

[email protected]

Homepage:

http://fin.bus.ku.ac.th/nattawoot.htm

Phone:

02-9428777 Ext. 1212

Mobile:

087- 5393525

Office:

9th floor, KBS Building 4

http://fin.bus.ku.ac.th/nattawoot.htm


Lecture 4

Forward contracts

Discussion topics

Forward contracts

Nature of a forward contract

Types of forwards

Pricing and valuation of equity

forwards

Pricing and valuation of bond

and interest rate forwards

Pricing and valuation of currency

forwards

Credit risk in forwards


Readings

CFA Program Curriculum 2015 -

Level II – Volume 6: Derivatives

and Portfolio Management.

Reading 47

Don M. Chance and Robert

Brooks, An Introduction to Derivatives and Risk Management, 9th Edition, 2013,

Thomson.

Chapters 8-9


Derivative contracts

Definition

A derivative contract derives its value from the

performance of an underlying entity (e.g., asset,

index, or interest rate).

Derivative contracts covered in this course

Forwards

Futures

Options

Swaps


Forward contracts

Definition

A forward contract is an

agreement between two

parties in which one party, the

buyer or the long, agrees to

buy from the other party, the

seller or the short, an

underlying asset or other

derivative, at a future date at

a price established at the

start of the contract.


Forward contracts

Example

A pension manager, anticipating the receipt of

cash at a future date, enters into a commitment to

purchase a stock portfolio at a later date at a price

agreed on today.

The manager is hedged against an increase in stock

prices until the cash is received and invested.

The manager is also hedged against any decrease in

stock prices.


Forward contracts

Important features

Transaction price and quantity

are agreed today.

Neither long or short pays any

money at the start, although

some collateral may be

required to minimize the

default risk.


Delivery and settlement

At expiration

A deliverable forward contract stipulates that the

long will pay the agreed-upon price to the short,

who in turn will deliver the underlying asset to the

long.

Alternatively, a cash settlement forward contract

permits the long and short to pay the net cash

value of the position on the delivery date.


Delivery and settlement

Example

Two parties agree to a forward contract to trade a

zero-coupon at a price of $98 per $100 par.

At expiration, the underlying zero-coupon bond is

selling at a price of $98.25.

Delivery: The long is due to receive from the short an

asset worth $98.25, for which a payment to the short of

$98.00 is required.

Cash settlement: The long is due to receive $0.25 from

the short.


Default risk

Only the party owing the

greater amount can default.

Delivery: If the short is obligated

to deliver a zero-coupon bond

selling for more than $98, then

the long would not be obligated

to make payment unless the

short makes delivery.

Cash settlement: Since the

short is owing the greater

amount, he/she may default.


Termination of a forward contract

Assuming that the contract calls for a delivery

at expiration, and that the long decides that

he/she no longer wishes to buy the asset at

expiration.

The long can re-enter the market and create a

new forward contract expiring at the same time as

the original contract, taking the position of the

short instead. Doing so would mean that the long

has no further exposure to the price of the asset.



Example

Amy is originally long to buy at $40 and later short

to deliver $42.

At expiration, the short of the original contract delivers

the asset to Amy, and she pays him $40.

Amy then delivers the asset to the long of the

subsequent contract and receive $42.

Amy nets $2.



Example

Amy is exposed to a possibility of default from her

counterparty (credit risk).

The counterparty of her original contract defaults, she

has to buy the asset in the market and could suffer a

significant loss.

If the counter party of her subsequent contract defaults,

she would then not deliver the asset but would be

exposed to the risk of changes in the asset price.



Example

Amy can avoid the credit risk by

contacting the original

counterparty with whom she

engaged in the long forward

contract and go short the forward

this time.

If both agree to cancel both

contracts, the counterparty would

pay Amy the present value of $2.

The credit risk is eliminated.



Example

Amy could choose to deal

with the other counterparty

and leave the credit risk in

the picture.

She might receive a better price

from another counterparty.

She might perceive the credit

risk to be too high.


Types of forward contracts

Types of forward

contracts

Equity forwards

Bond and interest

rate forward

contracts

Currency forward

contractsOther types


Equity forwards

Definition

Equity forward is a contract

calling for the purchase of an

individual stock, a stock

portfolio, or a stock index at a

later date.


Equity forwards: Individual stocks

Example

A portfolio manager is responsible for the portfolio

of a high-net-worth individual. This individual is

heavily invested in the stock called Gregorian

Industries, Inc. (GII). The client notifies the

manager of her need for $2 million in cash in six

months. This cash could be raised by selling

16,000 shares at the current price of $125 per GII

share. For whatever reason, it is considered best

not to sell the stock any earlier than necessary.


Equity forwards: Individual stocks

Example

Portfolio manager’s actions:

Contacting a forward contract dealer and obtaining a

quote of $128.13 as the price at which a deliverable

forward contract to sell the stock in six months. Signing

the contract for the sale of 15,600 shares at $128.13

which will raise $1,998,828.

Possible consequences at expiration:

The client gains if the GII stock rises to a price above

$128.13 during the six-month period.

The client loses if the price falls below $128.13.


Equity forwards: Stock portfolios

Example

A pension fund manager needs to sell about $20

million of stocks to make payments to retirees in

three months. The manager has analyzed the

portfolio and determined the precise identities of

the stocks and number of shares of each that he

would like to sell.



Example

Pension fund manager’s

possible options:

Option 1: Entering into a forward

contract on each stock that he

wants to sell and incurring

administrative costs for each

contract.

Option2: Entering into a forward

contract on the overall portfolio

and incurring only one set of

costs.



Example

Pension fund manager’s actions:

Choosing Option 2 and providing a list of the stocks and

number of shares of each he wishes to sell to the dealer.

Obtaining a quote of $20,200,000 from the dealer.

If the stock is worth $20,500,000 at expiration.

Deliverable: The manager will transfer the stock to the

dealer and receive $20,200,000. This means that the

client effectively takes an opportunity loss of $300,000.

Cash settlement: The client will pay the dealer $300,000

and sell the stock in the market, receiving $20,500,000.


Equity forwards: Stock indices

Example

A UK asset manager wants to protect the value of

her Financial Times Stock Exchange 100 (FTSE

100) index fund. The manager wants to sell a

certain amount of UK blue chip shares at the later

date, but is unsure which stocks she will still be

holding then. She simply knows that FTSE 100 is

representative of the stock that she will sell. The

manager is also concerned with the systematic

risk associated with the UK stock market.



Example

Asset manager’s possible

options:

Option 1: Taking a specific

portfolio of stocks to a forward

contract dealer and obtaining a

forward contract on that portfolio.

Option 2: Obtaining a forward

contract on the FTSE 100 that has

a better price quote because the

dealer can more easily hedge the

risk with other transactions.



Example

Asset manager’s actions:

Assume that the manager

decides to protect

£15,000,000 of stocks. She

chooses Option 2 and

obtains a quote price of

£6,000 on a short forward

contract covering

£15,000,000 from the dealer.

The index contract is nearly

always cash settled.



Example

At expiration, the index is at £5,925.

The index declines by 1.25%. Thus, the manager should

receive 0.0125 × £15,000,000 = £187,500 from the

dealer.

If the portfolio perfectly matches a FTSE 100 index fund,

then it could be viewed that the loss of 1.25% of the

portfolio initially worth £15,000,000 (loss of £187,500) is

covered by the forward contract.

In reality, the portfolio is not an index fund and such a

hedge is not perfect.


Forward contracts on bonds

Definition

Bond forward is a contract calling for the purchase

of an individual bond, a bond portfolio, or a bond

index at a later date.

Similarities between equity forwards and

bond forwards

A bond may pay a coupon, which corresponds

somewhat to the dividend that a stock may pay.



Differences between equity forwards and bond

forwards

A bond matures. Thus, a forward contract on a bond must

expire prior to the bond’s maturity date.

Bonds often have many special features such as calls and

convertibility.

A bond carries the risk of default. So, a forward contract

written on a bond must contain a provision to recognize

how default is defined, what it means for the bond to

default, and how default would affect the parties to the

contract.



Example

Consider a forward contract on a default-free

zero-coupon bond (or a Treasury bill or T-bill) in

which one party agrees to buy the T-bill at a later

date, prior to the bill’s maturity, at a price agreed

on today.

Suppose the underlying is a 180-day T-bill, which is

selling at a discount of 4%.

Its price per $1 par will be 1- 0.04(180/360) = $0.98.

The bill will therefore sell for $0.98.

If purchased and held to maturity, it will pay off $1.



Example

Consider a forward contract that calls for delivery

of a 90-day T-bill in 60 days.

Suppose the contract sells for $0.9895. This implies a

discount rate of 4.2%.

$1 – 0.042(90/360) = $0.9895

T-bills are typically sold at a discount from par

value, a procedure called “discount interest”, and

the price is quoted in terms of the discount rate.

The use of 360 days is the convention in

calculating the discount.



Example

Consider a forward contract on a default-free

coupon-bearing bond, or a Treasury bond or T-

Bond.

The T-bond pays interest, typically in semiannual

installments, and can sell for more (less) than par value

if the yield is lower (higher) than the coupon rate.

Prices of T-bonds are typically quoted without the

interest that has accrued since the last coupon date. But

we shall always work with the full price – that is, the

price including accrued interest.

Prices are often quoted by stating the yield.


Interest rate forward contracts

Eurodollar

A dollar deposited outside the US.

Banks borrow dollars from other banks by issuing

Eurodollar time deposits, which are essentially

short-term unsecured loans.

The rate on such dollar loans is call the London

Interbank Rate.

The lending rate, called the London interbank offered

rate (Libor), is more commonly used in derivative

contracts.



Libor

Libor is the rate at which

London banks lend dollars

to other London banks.

Libor is considered to be

the best representative

rate on a dollar borrowed

by a private, i.e., non

governmental high-quality

borrower.



Example: Eurodollar time deposit

Suppose a London bank such as NatWest needs

to borrow $10 million for 30 days. It obtains a

quote from the Royal Bank of Scotland for a rate

of 5.25%.

30-day Libor is 5.25%.

If NatWest takes the deal, it will owe $10,043,750 in 30

days.

$10,000,000 x [1 + 0.0525(30/360)] = $10,043,750



Example: Eurodollar time deposit

Unlike the T-bill market, the interest is not

deducted from the principal. Rather, it is added on

to the face value, a procedure appropriately called

“add-on interest”.

The rates on Eurodollar time deposits are

assembled by a central organization and quoted

in financial newspapers.



Example: Other time deposit instruments

Eurosterling trades in Tokyo.

Euroyen trades in London.

A euro-denominated loan

One bank borrows euros from another.

There are two rates on such euro deposits.

EuroLibor is complied in London by the British Bankers

Association.

Euribor is complied in Frankfurt and published by the

European Central Bank.



Forward rate agreement

(FRA)

FRA is a contract in which the

underlying is neither a bond

nor a Eurodollar or Euribor

deposit but simply an interest

payment made in dollars,

Euribor, or any other currency

at a rate appropriate for that

currency.



Example: FRA

Consider an FRA expiring in 90 days for which the

underlying is 180-day Libor. Suppose the dealer

quotes this instrument at a rate of 5.5%. Suppose

the end user goes long and the dealer goes short.

The contract covers a given notional principal of

$10 million.

The end user will benefit if rates increase.

In contrast, the dealer will benefit if rates decrease.



Example: FRA

At expiration in 90 days, the rate on 180-day Libor

is 6%.

The 6% interest will be paid 180 days later.

The present value of a Eurodollar time deposit at that

point in time would be:



Example: FRA


is 6%.

The end user, the party going long the FRA, receives

the following payment from the dealer, which is the party

going short:



Example: FRA


is 6%.

The numerator indicates that the contract is paying the

difference between the actual rate that exists in the

market on the contract expiration date and the agreed-

upon rate, adjusted for the fact that the rate applies to a

180-day instrument.

The divisor appears because it is necessary to adjust

the FRA payoff to reflect the fact that the rate implies a

payment that would occur 180 days later on a standard

Eurodollar deposit.



FRA payoff formula (from the perspective of

the party going long)



FRA descriptive notation and interpretation


Notation Contract expires in Underlying rate

1×3 1 month 60-day Libor



3×6 3 moths 90-day Libor

3×9 3 months 180-day Libor



Currency forward contracts

Definition

A currency forward contract enables one party to

lock in a pre-agreed upon exchange rate at which

it will sell one currency and buy another currency

at a later date.

Use

Currency forwards are widely used by banks and

corporations to manage foreign exchange rate

risk.



Example

Suppose Microsoft has a European subsidiary

that expects to send it €12 million in three months.

When Microsoft receives the euros, it will then

convert them to dollars.

Microsoft is essentially long euros since it will have to

sell euros, i.e., Microsoft has euro-nominated assets that

exceed in value its euro-nominated liabilities.

Microsoft is essentially short dollars because it will have

to buy dollars.



Example

Microsoft’s actions

Obtaining a quote on a currency forward for €12 million

in three months.

JP Morgan Chase quotes a rate of $0.925.

Under this contract, Microsoft would know it could convert

its €12 million to 12,000,000 × $0.925 = $11,100,000 in

three months.

To hedge its position, Microsoft has to go short the

forward contract, i.e., goes short the euro and long the

dollar.



Example

At expiration, the spot rate for euros is $0.920.

Delivery: Microsoft is pleased that it is locked in a rate of

$0.925. It simply delivers the euros and receives

$11,100,000 at an exchange rate of $0.925.

Cash settlement: The dealer pays Microsoft

$12,000,000 × ($0.925 - $0.920) = $60,000. Microsoft

has to convert the euros to dollars at the current spot

exchange rate of $0.920, receiving 12,000,000 × $0.920

= $11,040,000.


Other types of forward contracts

Examples

Commodity forwards

The underlying asset is oil, a

precious metal, various sources of

energy (electricity, gas, etc.), or

some other commodity.

Forward contracts on whether

The underlying is a measure of the

temperature or the amount of

disaster damage from hurricanes,

earthquakes, or tornados.


Forward markets

Important characteristics

Forward contracts are private transactions,

permitting the ultimate customization.

Forward markets have only a light degree of

regulation. Default rates are high as a result.

Forward markets serve a specialized clientele,

specifically large corporations and institutions with

specific target dates, underlying assets, and risks.

Transactions in forward contracts typically are

conducted over the phone.


10/10/2018 Nattawoot Koowattanatianchai 5310/10/2018 Nattawoot Koowattanatianchai 53

4/6/2011 Natt Koowattanatianchai 53

Documents

10/10/2018 Nattawoot Koowattanatianchai 1fin.bus.ku.ac.th/BA 747 Investment Analysis and... · 02-9428777 Ext. 1212 ... Pricing and valuation of bond and interest rate forwards Pricing