Finals Preparation Notes Week 9 - Chapter 15 - Forex Markets 11,12,13

11. A toy manufacturer in Thailand is exporting goods to New Zealand. In order to

ascertain the firm’s exposure to foreign exchange risk the company needs to calculate

the THB/NZD cross-rate. An FX dealer quotes the following rates:

USD/NZD 1.3241–47

USD/THB 30.32–48

Calculate the THB/NZD cross-rate. (LO  15.5)

• Most currencies are quoted against the USD, therefore it is necessary to calculate the

cross rate to obtain the THB/NZD quote

• Crossing two direct FX quotations:

o place the currency that is to become the unit of the quotation first

o divide opposite bid and offer rates, that is:

o to obtain the bid rate: divide the base currency offer into the terms currency bid

o to obtain the offer rate: divide the base currency bid into the terms currency offer.

• Therefore, place the USD/THB quote first:

USD/THB 30.32 - 48

USD/NZD 1.3241 - 47

To determine the THB/NZD cross rate:

1.3241 / 30.48 = 0.0434

1.3247 / 30.32 = 0.0437

THB/NZD 0.0434 - 37

12. An Australian manufacturer generates receipts in JPY from exports to Japan. At

the same time, the company imports component parts from the USA, incurring

commitments in USD. The company needs to determine its net open position to the

JPY. Rates are quoted at:

USD/JPY 83.43–47

AUD/USD 1.0246–54

Calculate the AUD/JPY cross-rate. (LO  15.5)

• It is possible to use two methods to calculate this cross-rate; first

transpose the AUD/USD rate to a direct USD/AUD rate and then use

the two direct quote method (see question 11). Alternatively, use the

direct and indirect quote method.

• Crossing a direct and an indirect FX quotation:

o to obtain the bid rate—multiply the two bid rates

o to obtain the offer rate—multiply the two offer rates.

• To determine the AUD/JPY cross rate:

83.43 x 1.0246 = 85.48

83.47 x 1.0254 = 85.59

AUD/JPY 85.48 – 85.59

13. An importer has entered into a contract under which it will require payment in

GBP in one month. The company is concerned at its exposure to foreign exchange risk

and decides to enter into a forward exchange contract with its bank. Given the

following (simplified) data, calculate the forward rate offered by the bank. (LO 15.6)

AUD/GBP (spot): 0.6456–76

One-month Australian interest rate: 6.75% p.a.

One-month UK interest rate: 4.25% p.a.

• The quote is from the perspective of the dealer relative to the base currency.

• The importer needs to buy GBP therefore it will sell AUD to the dealer. The dealer is

therefore buying AUD, so need to use the bid rate.

• Note: both countries use a 365 day year; assume 30 day contract.

S [1 + (It x contract days/days in year)]

[1 + (Ib x contract days/days in year)]

where: S = spot rate

Ib = interest rate of base currency

It = interest rate of terms currency

Therefore, based on the above data:

0.6456 [1 + (0.0425 x 30/365)]

[1 + (0.0675 x 30/365)]

= 0.6456 (1.003493 / 1.005548)

= AUD/GBP0.6443 Week 9 - Chapter 16 - Forex Markets 5,6,8

5. Draw a chart and explain in words what is expected to happen to the Indian rupee

demand and supply curves (USD/INR) if there is a forecast increase in India’s inflation

rate while the inflation rate remains stable in the USA. (LO 16.2)

• Purchasing power parity contends that exchange rates will adjust to ensure prices on the

same goods are equal between countries.

• A sustained surge in Indian inflation will increase the costs of local goods

• USA demand for the Indian goods would fall

• Therefore there would be a reduction in the demand for the Indian rupee

• The demand curve would move from D0 to D1

• At the same time Indian would seek relatively cheaper goods from overseas

• The supply of the INR would increase as importers purchased the USD

• The supply curve would move from S0 to S1

• The net result would be a depreciation in the INR to and exchange rate of USD/INR48.25

49.50  

48.25  

D1   D0  

S0  

S1  

USD/INR  

Indian  Rupee  (billion)    

6. Draw a chart and explain in words what is expected to happen to the New Zealand

dollar demand and supply curves (USD/NZD) if there is a forecast increase in New

Zealand’s national income relative to a stable growth rate in the USA. (LO  16.2)

• New Zealand’s demand for imports would increase

• Increase in supply of NZD in order to purchase USD to pay for imports

• The supply curve would move from S0 to S1

• With USA national income unchanged the USA demand for New Zealand goods, and

thus the NZD, will remain unchanged

• The demand curve is therefore unchanged

• The net effect is a depreciation in the NZD

However, as discussed in question 7 we need to consider the impact of increased investment

on the exchange rate as well.

8. Draw a chart and explain in words what is expected to happen to the Indonesian

rupiah demand and supply curves (USD/IDR) if there is a forecast increase in

Indonesia’s interest rates relative to interest rates in the USA. (LO  16.2)

• If Indonesian interest rates rise, while those in the USA remain relatively stable, overseas

residents and institutions can be expected to place some of their excess cash in interest-

bearing instruments in Indonesia in order to obtain the higher rate of return. This is

represented by an increase in demand for IDR.

D0  

S0  

S1  

USD/NZD  

Quantity  NZD    

• At the same time, Indonesian businesses are likely to keep their surplus funds in banks

and instruments in Indonesia rather than in the lower rate of return overseas.

• With fewer IDR being placed overseas there is a reduction in the supply of IDR in the FX

market.

• The combined effect is that the increase in interest rates has resulted in an increase in the

demand for IDR, and a reduction in the supply of IDR, and consequently the IDR has

appreciated.

However, as discussed in question 9 we need to consider the reason for the higher interest

rates in Indonesia.

D0   D1  

S1  

S0  

USD/IDR  

Quantity  IDR    

Week 10 - Chapter 13 - Interest Rate Determination 7,8,9,11,15 7. A number of theories attempt to explain the term structure of interest rates. The

expectations theory provides a foundation for our understanding of interest rate

determination. Outline the expectations theory approach to the determination of

interest rates. In your answer, explain the relationships that the theory contends will

exist between short-term and longer-term interest rates. (LO13.3)

• Expectations theory refers to the shape of a yield curve as a function of the current and

future short-term interest rates; that is, the return received on a continuous series of short-

term investments should be the same as that received for a longer-term investment.

• An investor will therefore be indifferent as to whether they invest for a short period of a

longer period; for example, an investor has two options (1) invest today for a one-year

period at 4% per annum and reinvest the funds in twelve months time, or (2) invest the

funds today for a two-year period at 4.5% per annum. The expectation theory will

contend that the one-year investment rate in twelve months time should be 5% per annum

(that is, 4.5% x 2 = 9% - 4% = 5%).

Assumptions of the expectations theory:

• There are a large number of financial investors who hold reasonably homogeneous

expectations about the future values of short-term interest rates.

• There are no transaction costs, and so investors can move into and out of instruments at

no cost as they change their expectations and as they see market rates that are

inconsistent with their expectations.

• There are no impediments to market rates moving to their competitive equilibrium levels.

• The goal of investors is to maximise their expected rate of return, that is, if all bonds as

perfect substitutes for each another, regardless of their term to maturity, then longer-term

interest rates paid on bonds will be equal to the average of the short-term interest rates

expected to prevail over the longer-term period.

8. Within the context of interest rate determination, the expectations theory attempts to

explain the various shapes of the yield curve. How is the existence of a normal yield

curve and an inverse yield curve explained by the theory? (LO  13.3)

Normal yield curve:

• will result from expectations that future short-term rates will be higher than current short-

term rates

o the central bank may reduce short-term rates, but since the market believes that future

short-term rates will be higher than current short-term rates, longer-term rates will not

fall as far as the policy-induced cut in short-term rates; therefore, the yield curve will

be upward-sloping (that is, if E1i1 > 0i1, then the yield curve will be normal).

Inverse yield curve:

• will result if the market expects future short-term rates to be lower than current short-

term rates

o even though the central bank may increase rates at the short end of the yield curve to

achieve its monetary policy objectives, market participants expect that once those

objectives have been achieved, short-term rates will be lowered again; in this

circumstance, long-term rates will not rise to the same extent as the policy-induced

change in short-term rates, and therefore the yield curve will slope downwards.

9. The segmented markets theory challenges two of the assumptions of the expectations

theory.

(a) Identify the two assumptions challenged, and explain the segmented markets

approach.

The segmented markets theory rejects two expectation theory assumptions:

• that all bonds are perfect substitutes for one another

• that investors are indifferent between holding instruments with a short term to maturity

and holding instruments with a long term to maturity.

Segmented markets approach to explaining the yield curve:

• Securities in different maturity ranges, for example a 1 to 3 year range versus a 9 to 10

year range, are not viewed by various market participants as being perfect substitutes for

one another.

• Whereas bonds with a very short term to maturity may well be close substitutes for each

other, and likewise for bonds with long terms to maturity, a one-month-to-maturity bond

is unlikely to be seen as a close substitute for a 10-year bond.

• Some market participants have a preference for short-dated securities, and others have a

preference for longer-term maturities; that is, different investors have preferences for

different segments of the market.

• The particular preferences are motivated out of a desire by the various participants to

reduce the riskiness of their portfolios.

• Investors will seek to minimise their exposure to fluctuations in the prices and yields

associated with their assets and liabilities by matching the cash flows and maturities of

their assets and liabilities; for example, life offices have mainly long-term liabilities and

therefore tend to hold more longer-term assets.

• The implication of the segmented markets approach is that it is the relative demands for

and supplies of securities in the various maturity ranges that determine yields.

• The shape and slope of the yield curve are determined by the relative demand and supply

conditions that exist along the maturity spectrum.

(b) It may be argued that the segmented markets approach is negated by modern risk

management practices, arbitrage and speculation. Explain what is meant by this

assertion. (LO 13.3)

• The segmented markets approach emphasises the risk management motivation of market

participants; that is, the matching of cash flows and maturities of assets and liabilities in

order to minimise associated risk exposures. By implication, this approach would cause

discontinuities in a yield curve thus exposing significant speculation and arbitrage

opportunities.

• Arbitrageurs, who are indifferent about the maturity of the bonds they hold, will sell and

buy to take advantage of the discontinuities along the yield curve. Their actions will

smooth out the yield curve; that is, remove the segmentation distortions.

• Therefore, it may be reasonable to argue that certain investors do have segment

preferences along a yield curve, but those preferences are balanced by investors with

different preferences, arbitrageurs and speculators.

11. The liquidity premium theory seeks to extend our understanding of the expectations

theory and the determination of interest rates.

(a) Outline the principal contention of the liquidity premium theory.

• A criticism of the pure expectations approach is its assumption that investors are

indifferent as to whether they hold long-term or short-term bonds.

• There is one important characteristic that distinguishes short-term and longer-term

securities that may result in a violation of the assumption of indifference.

• Longer-term-to-maturity bonds are susceptible to a greater risk of larger price

fluctuations than are shorter term instruments.

• Given the greater price risk associated with longer term securities, it may be hypothesised

that investors require a premium if they are to be enticed away from the shorter end of

the maturity spectrum.

• If this is the case, then the expectations hypothesis explanation of the level of longer term

rates may be presented as being approximately:

0i2 = (0i1 + E1i1 ) + L

2

• Where L is the liquidity premium that is demanded in order to hold the higher risk,

longer-term security.

• The size of L is likely to increase the longer the term to maturity of the particular

instrument.

• The effect of the liquidity premium on the expectations hypothesis is shown below:

(b) How does the historic prevalence of a normal yield curve provide indirect evidence

of the existence of a liquidity premium?

• Support for the addition of the liquidity premium to the expectations hypothesis is

derived from observations of the shape of the yield curve over time.

• The positive or upward-sloping curve is labelled as the ‘normal’ yield curve.

• The normal yield curve is typically the shape most frequently observed over the years.

• The combination of the expectations theory and the liquidity premium explains the

observed dominance of the normal curve.

Yield    %  

Time  

observed  yield  curve  

expectations  yield  curve  liquidity  premium  

• At times, even though the pure expectations outcome is an inverse curve, when the

liquidity premium is added to the curve it results in a positive or normal curve.

• At other times, the slope of an inverse yield curve will become flatter as a result of the

effect of the liquidity premium; that is, the inverse curve will move upward.

• The combined expectations and liquidity premium theories provide a useful framework

for understanding the behaviour of the yield curve.

(c) Does the existence of an inverse yield curve indicate a violation of the liquidity

premium contention? (LO 13.3)

• No; an inverse yield curve is still possible.

• In this instance, the downward slope of the inverse yield curve will be reduced by the

liquidity premium effect. That is, the yield curve will become flatter, but still retain an

inverse slope.

Extended learning question

15. This question requires calculations relating to the yield curve and the expectations

theory. (LO 13.5)

(a) If an investor possesses the following information, and expectations on Treasury

bond yields are:

0i1 = 7.50% p.a.

E1i1 = 8.80% p.a.

calculate the yield on a two-year bond (0i2) that would result in the investor being

indifferent between placing funds in a one-year bond now, to be followed by a one-year

bond in a year’s time, or placing the funds in a two-year bond now.

(1) Calculation using arithmetic average:

Yield    %  

Time  

observed  yield  curve  

expectations  yield  curve  

liquidity  premium  

0i2 = (0i1 + E1i1 )

2

= 7.5 + 8.8

2

= 8.15 %

(2) Calculation using geometric average:

0i2 = [( 1 + 0i1 ) ( 1 + E1i1 )] 0.5 - 1

= [( 1.075 ) ( 1.088 )] 0.5 - 1

= [ 1.1696 ] 0.5 - 1

= 8.148 %

(b) You are given the following data:

0i1 = 10.00% p.a.

E1i1 = 12.00% p.a.

E2i1 = 13.00% p.a.

E3i1 = 13.00% p.a.

On the basis of the expectations theory of the yield curve, complete the following.

• Calculate the 0i2, 0i3 and 0i4 rates.

formula: 0in = [(1 + 0i1) (1 + E1i1) (1 + E2i1) ... (1 + En - 1i1)]1/n - 1

(i) 0i2 = [(1 + 0.10) (1 + 0.12)]1/2 - 1

= 11.00%

(ii) 0i3 = [(1 + 0.10) (1 + 0.12) (1 + 0.13]1/3 - 1

= 11.66%

(iii) 0i4 = [(1 + 0.10) (1 + 0.12) (1 + 0.13) (1 + 0.13]1/4 - 1

= 11.99%

• Explain what is meant by implicit forward rates of interest.

On the basis of the expectations theory, a yield curve provides information on what

the on-balance expectations of market participants are concerning a large range of

future interest rates. That is, implicit in the yield curve there are indicators, or

information, on a series of expectations about future interest rates.

• List the full range of one-year implicit rates of interest that could be calculated on

the basis of the yield curve data that provide the current rates on bonds with one,

two and three years to maturity.

Implicit interest rates that could be calculated on the basis of the above yield curve are 1i1 , 1i2

and 2i1.

• Given the following yield curve data, calculate the 2i2, 1i2 and 3i1 implicit rates:

0i1 = 8.00% p.a.

0i2 = 9.00% p.a.

0i3 = 10.00% p.a.

0i4 = 11.00% p.a.

Yield    %  

1   2   3  0   Years  

0i1  0i2  0i3  

1i1  1i2  

2i1  

Actual  rates  

Implicit  rates  

formula: nik = [(1 + 0in+ k)n + k]1/k -1

[ (1 + 0in)n ]

(i) calculate 2i2 where: n = 2; k = 2

= [(1 + 0.11)4]1/2 -1

[(1 + 0.09)2]

= 13.04%

(ii) calculate 1i2 where: n = 1; k = 2

= [(1 + 0.10)3]1/2 -1

[(1 + 0.08)1]

= 11.01%

(iii) calculate 3i1 where: n = 3; k = 1

Yield    %  

1   2   3  0   Years  

0i1  0i2  0i3  

1i1  1i2  

2i1  

Actual  rates  

Implicit  rates  

4  

0i4  

1i3  

2i1  3i1  

8%  9%  

10%  11%  

= [(1 + 0.11)4]1/1 –1

[ (1 + 0.10)3]

= 14.06%

                                                                                   

Week 11 - Chapter 19 - Forwards and Futures Contracts 8,10,14,15

8. A business plans to borrow approximately $20 million in short-term funding through

the issue of commercial paper in three months’ time. The business does not have a view

on what is likely to happen to interest rates over the next three months, but it would be

very satisfied if it could obtain its funding at the current yield.

(a) Using the following data, show how 90-day bank-accepted bills futures contracts can

be used to hedge the interest rate risk to which the business is exposed. Show the

calculation and timing of all transactions and cash flows (ignore transaction costs and

margin requirements).

Today’s data:

(i) current commercial paper yields 8.00 per cent per annum

(ii) 90-day bank-accepted bills futures contract 91.75.

Data in three months:

(iii) commercial paper yields 9.00 per cent per annum

(iv) 90-day bank-accepted bills futures contract 91.25

Cash or Physical Market Futures Market

Today:

The company expects to borrow $20

million in three months; it notes that

current yields are 8.00%, but is

exposed if yields rise before the

commercial paper is issued

Today:

Sell twenty 90-day bank accepted bills

futures contracts at 91.75 (yield 8.25%)

Use discount securities formula

P = 365 x $20 million

365 + (0.0825 x 90)

= $19,601,262

pay initial margin

Three months time:

Sell commercial paper with a face

value of $20 million – yield 9.00%

P = $19,565,800.05

Three months time:

buy twenty contracts at 91.25

P = $19,577,606.44

Hedge outcome:

• cost of borrowing increased over

three-month period by $47,311.18

• profit received from the futures

transactions is $23,655.56

• the profit is used to offset the

• profit received from futures

transactions is $23,655.56

• borrower was not able to perfectly

hedge risk because of initial and

final basis risk

additional cost of borrowing in the

physical market when the company

issues commercial paper

(b) What is the effective cost of funds achieved with this hedging strategy? What would

the cost of funds have been had the hedge not been put in place? Explain your answer,

showing your calculations. (LO  19.5)

Effective cost of funds 90365 x

available fund ofamount totalfunds ofcost net

⎥⎦

⎤⎢⎣

⎡=

= 90365 x

profit futures borrowedamount profit futures - bills ofcost

⎥⎦

⎤⎢⎣

⎡

+

annumper 8.49%

90365 x

23,655.56 0.05$19,565,80$23,655.56 - 5$434,199.9

=

⎥⎦

⎤⎢⎣

⎡+

=

• If the hedging strategy had not been put in place then the cost of issuing the commercial

paper would have been 9.00 per cent per annum.

10. A funds manager currently manages a diversified Australian share portfolio valued

at $25 million. The manager decides to use the S&P/ASX 200 Index futures contract to

manage an exposure to a forecast decline in share prices. The S&P/ASX 200 Index is

currently at 4500. In three months’ time the S&P/ASX 200 is at 4265.

(a) Today: set up a hedging strategy to manage the risk exposure.

• The price of the futures contract equals the S&P/ASX200 Index multiplied by $25

• To establish the hedging strategy, the funds manager can sell 222 S&P/ASX200 futures

contracts

• Value = 222 x 4500 x $25

= $24,975,000

• Note: the manager wishes to protect a selling position in the future so will sell futures

contracts today

• Pay initial margin.

(b) In three months’ time: close out the open position.

• To close an open position, take opposite contracts

• Buy 222 S&P/ASX200 futures contracts

• Receive return of margin payments and futures strategy profits.

(c) Show the net valuation effect of the hedging strategy. (LO 19.5)

• Buy 222 S&P/ASX200 futures contracts

• Value = 222 x 4265 x $25

= $23 670 750

• Net profit = $1,304,250

• Net profit will be used to offset the fall in value of the share portfolio in the stock market.

14. (a) What is a forward rate agreement?

• The FRA is a contractual agreement, between two parties, relating to an interest rate level

that will apply at a specified future date. A borrower that needs to borrow funds in seven

months can lock-in an interest rate today that will apply in seven months.

• The FRA effectively allows the parties to the agreement to lock-in a rate of interest that

will apply at the specified future date based on a notional principal amount.

(b) What are the main features of an FRA? Explain how a corporation that needs to

borrow funds in seven months can use an FRA to fix the cost of funds today.

• The agreement relates to the interest rate; no exchange of principal takes place.

• The final settlement between the parties to the agreement is the value of the difference

between the FRA agreed interest rate and the reference interest rate that exists on the

settlement date.

• An FRA can usually be entered into for periods of up to two years.

• An FRA is a compensation agreement; one party will compensate the other party, based

on the notional principal amount, for any adverse movement in the FRA settlement rate

relative to the FRA agreed rate.

The FRA will specify:

• the  FRA  agreed  rate;  fixed  at  the  start  of  the  FRA  

• the  notional  principal  amount  of  the  interest  cover  

• the  FRA  settlement  date  when  compensation  is  paid  

• the  contract  period  on  which  the  FRA  interest  rate  cover  is  based  (end  date)  

• the  reference  rate  to  be  applied  at  settlement  date.  

(c) What are the main differences between an FRA and a futures contract? (LO  19.7)

• The FRA is an over-the-counter product.

• A futures contract is an exchange traded contract. Futures contracts are standardised.

• An FRA can be negotiated to meet a risk manager’s specific needs in relation to amount

and contract period

• Futures contracts require margin payments; the FRA does not

• Futures contracts are guaranteed by the clearing-house; with the FRA counterparty risk is

evident

15. You know that in seven months’ time your company is going to borrow $5 million

for six months. You obtain the following quotes from an FRA dealer:

6Mv7M (23) 10.35 to 25

7Mv13M (23) 10.50 to 20

You enter into an FRA with the dealer:

(a) What will be the FRA agreed rate?

• The FRA quote 7Mv13M states that the dealer is quoting seven months forward on 6-

month money (therefore disregard first quote). Also the FRA quote of 10.50 - 20 means

that the dealer is prepared to buy (lend) at 10.50% per annum and sell (borrow) at

10.20% per annum.

• In this case, the company is the borrower and therefore will accept the buy rate from the

dealer (10.50%).

• Note: the contract will be settled on the 23rd of the specified month. We have not been

advised of the FRA settlement reference rate; for example, it may be BBSW or LIBOR.

(b) If the reference rate on the settlement date is 9.75 per cent per annum, what is the

compensation amount?

)i (D 365P 365

)i (D 365P 365

rate agreedFRA theminus rate settlementFRA

cs ×+

×−

×+

×

where:

is = 0.0.975

ic = 0.1050

D = assume 182 days (reasonable to assume 180 or 183 days also)

P  =  $5  000  000  

944.57 $16 243.13 751 $4 187.70 768 $4

0.1050) (182 365000 000 5 365

0.0975) (182 365000 000 5 365 settlement

=

−=

×+

×−

×+

×=

• The FRA compensation amount, or settlement amount, is $16 944.57

(c) Which party to the FRA will make the compensation payment? (LO 19.7)

• Company is a borrower and wished to hedge the cost of funds

• The company locked in a rate of 10.50% per annum in the FRA contract

• At settlement date rates have fallen to 9.75% per annum

• The company will be able to borrow at the lower rate in the physical market

• Therefore, the company will pay the compensation amount of $16 944.57 to the writer of

the FRA, the bank.

                   

Week 12 - Options - Chapter 20 -3,4,5,9,10

3. (a) Explain the differences between American-type options and European-type

options.

• An American [type] option is an option that can be exercised by the holder any time

between its origination and expiration.

• A European [type] option gives the option buyer the right to buy or sell at the exercise

price only at a specified date or dates.

(b) What are the advantages of each option contract for both the buyer and the seller of

a contract?

• The American type option is a much more flexible product; for example, the holder of an

American type option to buy Westpac Banking Corporation shares at $20.35 may

exercise the right to buy at any time during the life of the option, particularly if Westpac

shares are trading in the market above the $20.35 exercise price.

• Exchange traded option contracts are often American type options.

• The European type option is relatively cheaper in that a lower premium is payable; for

example, the buyer of a put option to sell BHP Billiton shares at $30.00 will hold the

option to exercise that right on the expiration date specified in the option contract.

• This lower cost type of option may be attractive to risk managers who have a specific

date related risk to hedge.

(c) Discuss the effect of each option type on the pricing of the premium. (LO 20.1)

• The buyer of an American type of option will be required to pay a higher premium than

would otherwise be payable for the same European type option. The higher premium on

the American type option, or the lower premium on the European type option, reflects the

relevant risk relationships.

• The writer of the American type option will be compensated for providing a much more

flexible risk management product.

4. Suncorp Group shares currently trade at $6.98. An investor enters into a long call

option on Suncorp Group with an exercise price of $8.05 per share in two months, and

a premium of $0.15 per share.

(a) Calculate the break-even price for the short call position.

• The short call position is held by the writer of the option. The writer of the option

receives the $0.15 premium. The break-even for the writer is the exercise price plus the

premium.

• That is, $8.05 + $0.15 = $8.20

(b) Draw a fully labelled diagram of the long call and short call positions.

(c) At what minimum stock price will the option buyer exercise the option on the

expiration date? (LO 20.2)

• The option buyer will exercise the option when the share price in the stock market is

above $8.05

• While the share price is between $8.05 and $8.20, the buyer will exercise the option in

order to recover some of the premium already paid.

5. Wesfarmers shares currently trade at $29.66. A funds manager is holding a large

number of Wesfarmers shares in an investment portfolio and wishes to protect the

value of the investment. The manager buys a long put option with an exercise price of

$29.45 per share and pays a premium of $1.20 per share.

(a)  Buyer  of  option  

(b)  Seller  of  option  Profit   Profit  

Break-­‐even  

Break-­‐even  

Premium  

Premium  

Exercise  price  Loss   Loss  

Market  price  

Exercise  price  

+$0.15  

$8.05  $8.20   $8.05  

$8.20  

-­‐$0.15  

0  

(a) By entering into this options strategy, explain whether the funds manager will

exercise the option if the spot price is above or below the exercise price.

• The funds manager has bought the right to sell Wesfarmers shares at $24.95

• The manager will exercise the option if the share price is below the option exercise price

of $24.95

(b) Calculate the break-even price for the long put position.

• The break-even point for the buyer of the option (long put) is the exercise price less the

premium; that is: $24.95 - $1.20 = $23.75

• Note: the option holder will exercise the option when the share price is between $23.75

and $24.95 as he/she will be able to offset the cost of at least part of the premium that has

already been paid. If the share price falls below $23.75 the option holder will be in-the-

money.

(c) Draw a fully labelled diagram of the long put and the short put positions. (LO 20.2)

9. Discuss the relationship between the exercise price of an option, the current market

price of the underlying asset and the intrinsic value of the option. In your answer

explain the money position of an option. (LO 20.4)

(a)  Buyer  of  option  

(b)  Seller  of  option  Profit   Profit  

Break-­‐even  

Break-­‐even  

Premium  

Premium  

Exercise  price  Loss   Loss  

Market  price  

Exercise  price  

+$1.20  

$23.75  $24.95   $23.75  

$24.95  

-­‐$1.20  

0  

• The relationship between the current market price of the underlying asset and the

exercise price of an option determines whether or not the option actually has a value if

the option was exercised immediately. This value is referred to as the intrinsic value of

the option.

• If an option could be exercised immediately and a profit made, the price that would be

paid to buy such an option should be equal to the intrinsic value of the option.

• The greater the intrinsic value of the option, the higher is the value of the option, that is,

the larger the premium.

• The relationship between the price of an asset and the option exercise price determines

whether an option is in-the-money or not. An option is in-the-money if it can be

exercised at a profit, that is, if it has a positive intrinsic value.

• If the exercise price is equal to the price of the asset in the physical market, the option is

said to be at-the-money.

• In the situation where an option would not be exercised, the option is described as being

out-of-the-money.

10. Within the context of the pricing of an option, explain the relationship between:

(a) the volatility of the price of the underlying asset and the value of an option

• The higher the volatility of the price of the asset the greater is the chance that the holder

of the option will be able to exercise for a larger profit. Thus, on average, the value of an

option is higher for an asset that demonstrates a higher price volatility compared with one

that displays a low volatility.

• The relationship of volatility and the value of the option is also impacted by the type of

option. It is to be expected that a European option that exhibits the same level of

volatility over the contract period as an American option will have less value.

(b) the time to the expiration date and the value of an option. (LO 20.4)

• Options possess time value. It is the time value of an option that, in part, explains why

options most frequently are valued at a premium greater than the intrinsic value.

• The reason the expiration date is important in determining the option’s premium is to be

found in the fundamental nature of an option.

• The option gives the holder the future chance to make a profit by exercising the contract

under favourable conditions.

• On the assumption that the price of the underlying asset will fluctuate in the future, the

longer the time until expiration the greater is the chance that the option will be able to be

exercised at a profit; for example, if the exercise price for a call option is currently above

the spot price, the longer the time to expiry the greater is the chance that the spot price

will move above the exercise price.

• It must be acknowledged also that the longer the time to expiry the greater is the risk that

the spot price may move adversely. In that situation, however, the loss sustained by the

holder of the call option would be limited to the premium paid.

• What is important in valuing the option is that the longer the time to expiry the greater is

the probability of there being a favourable spot price movement.