FRM-NOTES

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LECTURES ON FRM BY:

Dr. ARSHAD HASSAN

Dean Faculty of Management Sciences

MAJU ISLAMABAD

2015

WASEEM A. QURESHI

MM 141063

0344-5599155

[email protected]

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2

ACKNOWLEDGEMENT

I would like to express my sincere gratitude to Dr. Arshad Hassan, Dean, Faculty of

Management science Muhammad Ali Jinnah University, Islamabad for his guidance,

constant inspiration and valuable suggestions during writing of these notes on FRM

based on class lectures of the legend professor.

The completion of this task could not have been possible without the backing and

guidance of Sir Arshad Hassan whose contributions are gratefully acknowledged.

WASEEM AKHTER QURESHI MM 141063

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3 CONTENTS:

S.NO. PARTICULARS Page No.

1 Risk, Systematic & unsystematic 04

2 Risk Management, sources of risk 05

3 Exchange rate factors 08

4 Artificial Hedging 09

5 Financial derivatives 12

6 Margin Call 14

7 Hedging & speculation 20

8 Examples (forwards, futures ,options) 21-40

9 Assignment No. 1(Hedging) 41

10 Assignment No. 2(Hedging) 44

11 Pricing & Evaluation of Forwards 46

12 Commodity forward 49

13 Equity forward 51

14 Bond forward 55

15 Currency forward 54

16 Interest rate forward 55

17 Questions from book (forwards chapter) 56-68

18 Swap markets and contracts 69

19 Interest rate swap 70

20 Currency swaps 71

21 Equity swaps 75

22 Credit default, subordinate risk swaps 78

23 Options market & Evaluation 79

24 Concepts and basic strategies of options 79

25 Duration of bond 93

26 Valuation of options 93

27 Valuation of options (Binomial model, one period) 94 28 Valuation of options (Binomial model, Two period) 98

29 The Black-Scholes-Merton Model 100

30 The Merton model 104

31 Option Sensitivities (Greeks) 105

32 Assignment No. 3 (Option sensitivities) 109

33 Valuation at Risk (VaR) 111

34 Credit risk 117

35 Credit risk, Estimation Techniques 124

36 Operation Risk 143

37 Sovereign Risk 146

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4 RISK:

It is defined as uncertainty about future outcomes. Or it is the probability of loss, probability that actual return may differ from expected return. The risk may be categorized as Systematic risk and unsystematic risk.

A. SYSTEMATIC RISK: (β) beta

Risk which is common to an entire market because of the economic changes or other events that impacts large portion of the market. for example a significant political event may affect several securities. This risk is based on macro economic variables so no individual business can have control over it. Therefore it is unavoidable, uncontrollable and undiversifiable.

• (β) beta is the measure of systematic risk. • cov (Rm - Rf) / σ2m

• Volatility due to the overall stock market

• Since this risk cannot be eliminated through diversification, this is often called non diversifiable risk.

• it has four components. Business risk, financial risk, liquidity risk, country risk. B. UNSYSTEMATIC RISK:

It is company or industry specific risk that is inherent in each investment. It is also known as diversifiable, avoidable, controllable and specific risk.

• Volatility due to firm-specific events • Can be eliminated through diversification

• Also called firm-specific risk and diversifiable risk

• An investor can only reduce unsystematic risk. This can be done by spreading investments over a number of different assets

• REDUCING UNSYSTEMATIC RISK THROUGH DIVERSIFICATION:-

Risk management

Businesses, nonprofits, governments, and individuals engage in risk-taking activities. Although they may hedge their risks on occasion, they should not restrict their activities to those that are risk free. The fact that these entities engage in risky activities raises a number of important questions:

- How is risk defined?

- How does one recognize and measure risk?

- Which risks are worth taking on a regular basis, which are worth taking on occasion, and which should never be take?

- How are risks reduced or eliminated? What strategies should be used? - How are the processes of risk taking and risk elimination monitored?

0 Risk Number of Investments 8-12 30 Unsystematic Systematic 0 0 0 0 0 0 0 0 0 0

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5 These questions and many others collectively define the process of risk management. In short, how is risk managed? To understand this concept, we start with a formal definition of risk management.

“Risk management is the process of identifying the level of risk that an entity wants, measuring the level of risk that an entity currently has, taking actions that bring the actual level of risk to the desired level of risk, and monitoring the new actual level of risk so that it continues to be aligned with the desired level of risk. The process is continuous and may require alterations in any of these activities to reflect new policies, preferences, and information”.

An important thing to note is that, risk management not means always decreasing the risk, as it is done through hedging. Sometimes we need to increase the risk to go for some extra rewards. Risk management is a general practice that can entail reducing or increasing risk.

Risk Management Process:

Sources of Risk:

The sources of risk can be divided in two broad categories.

A. Financial risk. B. Non-financial risk

1. Exchange rate risk 1. Operational risk 2. Interest rate risk 2. Legal risk 3. Credit risk 3. Regulation risk 4. Equity risk 4. Accounting risk 5. Liquidity risk 5. Settlement risk 6. Commodity risk 6. Taxation risk

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6 Financial risk

Financial risk is an umbrella term for multiple types of risk associated with financing. It is a risk that a firm will be unable to meet its financial obligations. Five categories under financial risk are discussed below:

a. Exchange Rate Risk:

Uncertainty about future Changes in exchange rates of one currency in relation to another currency is exchange rate risk. It may be further classified in three categories.

Translation risk, transaction risk, economic risk.

i. Transaction risk: It is the risk that an exchange rate will change unfavorably over time. It deals with imports and exports. If rates move unfavorably, the receivables may decrease or payables may increase.

ii. Translation risk: A firm's translation exposure is the extent to which its financial reporting is affected by exchange rate movements. As all firms generally must prepare consolidated financial statements for reporting purposes, the consolidation process for multinationals entails translating foreign assets and liabilities or the financial statements of foreign subsidiary / subsidiaries from foreign to domestic currency. While translation exposure may not affect a firm's cash flows, it could have a significant impact on a firm's reported earnings and therefore its stock price. Translation exposure is distinguished from transaction risk as a result of income and losses from various types of risk having different accounting treatments.

Non-Financial _Company _Financial Accounting Taxes Legal Regulatio ns Settlement Mode l Operational Interest rate Equity Exchange rate Commodity Credit Liquidity

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7 iii. Economic risk: A firm has economic exposure (also known as forecast risk) to the degree that its market value is influenced by unexpected exchange rate fluctuations. Such exchange rate adjustments can severely affect the firm's market share position with regards to its competitors, the firm's future cash flows, and ultimately the firm's value. Economic exposure can affect the present value of future cash flows. Any transaction that exposes the firm to foreign exchange risk also exposes the firm economically, but economic exposure can be caused by other business activities and investments which may not be mere international transactions, such as future cash flows from fixed assets. A shift in exchange rates that influence the demand for a good in some country would also be an economic exposure for a firm that sells that good.

Example:

The cost of a product per unit is Rs. 100 in Pakistan. Sales price is cost plus 20%. The dollar rate is Rs. 100 / $ today. The international market price of the product is $1.3.

It means they want to sell it for Rs. 120 or $1.2 in the market which is feasible as it is below than international price of $1.3. suppose dollar price goes down to Rs. 80 / $ . Now the product cost becomes $ 1.25 and selling price will be cost plus 20%, i.e. $1.5 now it becomes more than $1.3 and cannot be sold in international market.

b. Interest rate risk:

The risk that an investment's value will change due to a change in the absolute level of interest rates, in the spread between two rates, in the shape of the yield curve or in any other interest rate relationship. Such changes usually affect securities inversely and can be reduced by diversifying (investing in fixed-income securities with different durations) or hedging).

c. Credit risk:

Credit risk refers to the risk that a borrower will default on any type of debt by failing to make required payments. The risk is primarily that of the lender and includes lost principal and interest, disruption to cash flows, and increased collection costs.

d. Market risk / equity risk:

Market risk is the risk that the value of an investment will decrease due to moves in market factors. Volatility frequently refers to the standard deviation of the change in value of a financial instrument with a specific time horizon.

e. Liquidity risk:

Liquidity risk is the risk that a financial instrument may not be traded without a significant concession in price due to the size of the market. This risk manifests itself much more on the sell side of a transaction than on the buy side.

NON FINANCIAL RISKS:

These are the risks that may not cause some direct financial losses but the results can cause some serious affects for the continuation of business and ultimately cause financial loss. Following are some sources of non financial risk faced by organizations.

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8 a. Operational risk:

Operational risk is defined as the risk of loss resulting from inadequate or failed processes, people and systems or from external events. This definition includes legal risk, but excludes strategic and reputational risk.

b. Regulation risk:

The risk that a change in laws and regulations will materially impact a security, business, sector or market. A change in laws or regulations made by the government or a regulatory body can increase the costs of operating a business, reduce the attractiveness of investment and/or change the competitive landscape.

c. Legal Risk:

The potential loss that may occur to an investment as a result of insufficient, improperly applie d, or simply unfavorable legalproceedings in the country in which the investment is made. For example, a country may have inadequate bankruptcy protection or, inan extreme circumstance, the government may be able to seize property without provocation. On the other hand, legal ri sk existseven in countries that operate under the rule of law: a court, for instance, may find aga inst a company in a given lawsuit, creating aprecedent for other companies with similar operati ons.

d. Taxation risk:

The risk that tax laws relating to dividend income and capital gains on shares and other securities might change, making stocks less attractive.

e. Accounting risk:

It is the risk associated with the financial statements of an organization that can be affected by exchange rate fluctuations. It is also called accounting exposure or translation risk.

f. Settlement risk:

The payments involved in swaps, forward contracts and options are referred to as settlements. The process of settlement involves one or both parties making payments. Any bankruptcy from any side can cause breach of agreement and creates risk of losses.

Exchange rate factors: / factors influencing exchange rates.

The exchange rate is one of the most important determinants of a country's relative level of economic health. It plays a vital role in trade, which is critical to most free market economies. But exchange rates matter on a smaller scale too. They even impact the real return of an investor's portfolio. Here we‘ll look at the main factors influencing exchange rates.

Factor 1: Differentials in Inflation. As a general rule, a country with a consistently lower inflation rate exhibits a rising currency value, as its purchasing power increases relative to other currencies. Those countries with higher inflation typically see depreciation in their currency's value in relation to the currencies of their trading partners.

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9 Factor 2: Differentials in Interest Rates. By manipulating interest rates, central banks exert influence over both inflation and exchange rates. Higher interest rates offer lenders a higher return relative to other countries. The impact of higher interest rates is mitigated, however, if a country's inflation is much higher than other countries', or if additional factors serve to drive their currency value down. The opposite relationship exists for decreasing interest rates.

Factor 3: Current-Account Deficits. The current account is the balance of trade between a country and its trading partners, reflecting all payments between countries for goods, services, interest and dividends. A deficit in the current account shows a country is importing goods and services more than it is exporting them. The country will then typically borrow capital from foreign sources to make up the deficit, causing its currency to depreciate relative to its trading partner.

Factor 4: Public Debt. Countries will engage in large-scale deficit financing to pay for public sector projects using governmental funding. While such activity stimulates the domestic economy, nations with large public deficits and debts are less attractive to foreign investors. This is because a large debt encourages more inflation, and higher inflation translates into lower currency value.

Factor 5: Terms of Trade. A country's terms of trade is a ratio comparing export prices to import prices. If the price of a country's exports rises by a greater rate than that of its imports, its terms of trade have favorably improved, which tends to show currency appreciation. However, if the price of a country's imports rises more than the rate of exports, their currency's value will decrease in relation to trading partners.

Factor 6: Political Stability and Economic Performance. Foreign investors inevitably seek out stable countries with strong economic performance in which to invest their capital. Political turmoil, for example, can cause a loss of confidence in a currency, and a movement of capital to the currencies of more stable countries.

Choices available to address instability in the exchange rate. 1. Invoice in home currency.

2. Invoice in some stable anchor currency.

3. Matching the imports and exports in same currency. 4. Artificial matching. / Money market hedge.

5. Financial derivatives. (forwards, futures, swaps, options)

What is artificial matching / money market hedging?

A hedge is an investment position intended to offset potential loss that may be incurred by a companion investment. In simple language, a hedge is used to reduce any substantial losses suffered by an individual or an organization.

It can also be defined as ―A risk management strategy used in limiting or offsetting probability of loss from fluctuation in the prices of commodities, currencies, or securities. In effect, hedging is a transfer of risk without buying insurance policies‖.

Hedging is always bidirectional. It has two positions in every case. It may be receivable and payable, buy or sell, long or short. When there is a receivable, hedger need to create a payable for the same amount to hedge that amount.

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10 Artificial matching is a three stage process.

1. Calculate Present value (PV)

2. Change the amount in home currency 3. Calculate future value (FV)

EXAMPLE 1:

UK Company is exporting $100 million goods receivable in 6 months. Spot rate 1£ = 1.5$. UK £ US $

Lending 5% 6% Borrowing 7% 8% What is effective conversion rate?

Solution:

Whenever a company needs to hedge, it must create receivable for every payable or payable for receivables to meet the hedge conditions, as hedge is always bilateral. Here we need to create a £ 100m payable account for the receivable amount.

Step 1: calculate PV of $100m using borrowing rate.

𝐹𝑉 = PV(1 + i)𝑛_{, 100 = PV(1 + .08)}1/2

𝑃𝑉 = 𝐹𝑉

(1+i)𝑛 PV = 100 / (1 + .08)

1/2_{= 96.2250m $}

Company should borrow 96.2250 m $ to pay 100m $ after 6 months.

Step 2: Change the amount in home currency ($ into £)

1£ = 1.5$ $ 96.2250m = £? , 96.2250 / 1.5 = £ 64.15m

Step 3: calculate FV for investable amount in the home currency at lending rate. 𝐹𝑉 = PV(1 + i)𝑛 , FV = 64.14(1 + .05)1/2 = £ 65.73m

What is effective rate at which it is actually replaced.

$ amount / £ amount = effective rate : $ 100 / £ 65.73 = $ 1.513 / £ It means £ 1 is replace with $1.5213

EXAMPLE 2:

A UK exporter has following transactions to be settled in following 6 months.

Exports Imports

A £ 500m ---

B $ 400m € 50m

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11 Following are the lending, borrowing and inflation rates.

US $ UK £

Lending 8% 10%

Borrowing 10% 13% Inflation 5% 8% Spot rate 1.5 = 1 Q 1. What is effective exchange rate.

Q 2. Do they need to hedge.

Solution:

£ 500m receivable is an amount in home currency, so we don‘t need to hedge for this amount. € 50m is receivable and at the same amount is payable, so no need to hedge for this amount. $ 400m is receivable and $ 200m is payable. So there is a need to hedge for this $ 200m difference amount.

Step 1: calculate PV of $200m using borrowing rate.

𝐹𝑉 = PV(1 + i)𝑛_{, 200 = PV(1 + .10)}1/2

PV = 200 / (1 + .10)1/2_{= 190.6925m $}

Company should borrow 190.6925 m $ to pay 200m $ after 6 months.

Step 2: Change the amount in home currency ($ into £)

1£ = 1.5$ $ 190.6925 m = £? , 190.6925 / 1.5 = £ 127.1283m

Step 3: calculate FV for investable amount in the home currency at lending rate. 𝐹𝑉 = PV(1 + i)𝑛_{, FV = 127.1283(1 + .10)}1/2_{= £ 133.33m}

What is effective rate at which it is actually replaced? 200 / 133.33 = 1.5

It means £ 1 is replace with $1.50

Whether we need to hedge for this or not. It can be calculated by the inflation rate. We see what will be effective exchange rate if we don‘t hedge.

𝐸𝑥𝑐𝑕𝑎𝑛𝑔𝑒 𝑟𝑎𝑡𝑒 = PV (1+𝑖𝑑)𝑛

(1+𝑖𝑓₎𝑛 =

1.5(1+.05)1/2

(1+.08)1/2 = $ 1.4790

HINT: 𝑖𝑑 is interest rate of domestic currency 𝑖𝑓 is interest rate of foreign currency

The rate calculated through inflation is $ 1.4790/£ which is lower than 1.5, means we don‘t need to hedge. If we convert $200 at 1.4790 per pound, we will get ($200 / 1.4790 = £ 135 m) which is more than £ 133.33

This is the formula we use to calculate the future prices of currency.

HINT 2: sometimes direction of the currency becomes basis for decision. In depreciation exporters don‘t need and importers must hedge to save their position.

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12

EXAMPLE 3:

Suppose for example 2, exports are replaced with imports. Do we need to hedge?

Imports Exports

A £ 500m ---

B $ 400m € 50m

C € 50m $ 200m

Following are the lending, borrowing and inflation rates.

US $ UK £ Lending 8% 10% Borrowing 10% 13% Inflation 5% 8% Spot rate 1.5 = 1 Solution:

Now we need to invest those $ 200m for future payables.

Step 1: calculate PV of $200m using lending rate.

𝐹𝑉 = PV(1 + i)𝑛 , 200 = PV(1 + .08)1/2

Pv = 200 / (1 + .08)1/2_{= 192.45m $}

Company should invest 192.45m $ to pay $200m after 6 months.

1£ = 1.5$ $ 192.45 m = £? , 192.45 / 1.5 = £ 128.30m

Step 3: calculate FV for investable amount in the home currency at borrowing rate. 𝐹𝑉 = PV(1 + i)𝑛 , FV = 128.30(1 + .13)1/2 = £ 136.3847m

What is effective rate at which it is actually replaced? 200 / 136.3847 = $ 1.4664

It means £ 1 is replaced with $1.4664

Decision: Importer should not hedge as it is lower than inflation exchange rate which is 1.4790

Financial Derivatives

Derivatives are the securities that extract their value from some underlying entity. This underlying can be an asset, index or interest rate and is often called the ―underlying‖.

Derivatives can be used for a number of purposes, including insuring against price movements (hedging), increasing exposure to price movements, for speculation or getting access to otherwise hard to trade assets or markets. Some of the more common derivatives include forwards, futures, options, and swaps.

The price of the underlying instrument, in whatever form, is paid before control of the instrument changes.

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13 Categories of derivative.

There are two categories of derivatives.

1. Forward commitments 2. Contingent claims

These are the obligations to be paid in the future. They have two main types on the basis of trading.

A. Over the counter (OTC)

These are traded over the counter and not in the exchange markets. (OTC options, also called "dealer options") are traded between two private parties, and are not listed on an exchange. The terms of an OTC option are unrestricted and may be individually tailored to meet any business need. In general, at least one of the counterparties to an OTC option is a well-capitalized institution.

B. Exchange traded.

These are traded in the market or different forums. It has two types. Exchange traded options have standardized contracts, and are settled through a clearing house with fulfillment guaranteed by the Options Clearing Corporation (OCC)

A. FORWARD COMMITMENTS

A forward commitment is an agreement between two parties in which one party agrees to buy and the other agrees to sell an asset at a future date at a price agreed on today. The three types of forward commitments are forward Contracts, futures contracts, and swaps.

1. FORWARD CONTRACT

Forward contract or simply a forward is a non-standardized / customized contract between two parties to buy or to sell an asset at a specified future time at a price agreed upon today, making it a type of derivative instrument.

This is in contrast to a spot contract, which is an agreement to buy or sell an asset on its Spot Date, which may vary depending on the instrument. A non-standardized or customized means according to the customer requirements.

Three things to be considered in contracts. Quantity, Rate and Date.

Settlements

The settlement is made by physical delivery or cash settlements. As physical deliveries are normally not carried out these days most of the settlements are done by cash settlements which is also called synthetic forward. In this case difference of the amount is to be paid to make the settlements. As a rule all the currency transactions are settled through cash settlements.

Example:

A contract is made today to buy 1000 ounce of gold at a price of $ 1350 after 60days.

Suppose on maturity the rate is $1370, seller will pay $20 to buyer and suppose the rate is $1310 the buyer will pay $40 to seller to settle the transaction.

It means buyer is gain is the loss of seller and vice versa, therefore the sum of derivative would always be zero.

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14 Long position and short position

The party agreeing to buy the underlying asset in the future assumes a long position, and the party agreeing to sell the asset in the future assumes a short position. The price agreed upon is called the delivery price, which is equal to the forward price at the time the contract is entered into.

Margin

All day trading markets have margin requirements which set the minimum amount of cash and/or securities that need to be deposited in a trading account in order to trade that market.

What is a Margin Call?

A margin call is when your day trading brokerage contacts you to inform you that the balance of your trading account has dropped below the margin requirements for one of your active trades. For example, if you have an active trade on the ZG (Gold) futures market, and your trading account goes below $4,455, your brokerage would contact you with a margin call.

An example:

Consider a futures contract in which the current futures price is $82. The initial margin requirement is 45, and the maintenance margin requirement is $2. You go long 20 contracts and meet all margin calls but do not withdraw any excess margin. Assume that on the first day, the contract is established at the settlement price, so there is no mark-to-market gain or loss on the day.

Following are the prices for 6 days.

DAY: 0 1 2 3 4 5 6 Future price 82 84 78 73 79 82 84 Solution: Day Beginning Balance Funds deposited Futures price Price change

Gain / loss Ending balance 0 0 100 82 - - 100 1 100 0 84 2 40 140 2 140 0 78 -6 -120 20 3 20 80 73 -5 -100 0 4 0 100 79 6 120 220 5 220 0 82 3 60 280 6 280 0 84 2 40 320

On day 0, you deposit $100 because the initial margin requirement is 45 per contract and you go long 20 contracts. At the end of day 2, the balance is down to $20, which is $20 below the $40 maintenance margin requirements ($2 per contract times 20 contracts). You must deposit enough money to bring the balance up to the initial margin requirement of $100. So on day 3, you deposit $80. The price change on day 3 causes a gain/loss of -100, leaving you with a balance of $0 at the end of day 3. On day 4, you must deposit $100 to return the balance to the initial margin level.

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15 A price decrease to $79 would trigger a margin call. This calculation is based on the fact that the difference between the initial margin requirement and the maintenance margin requirement is $3. If the futures price starts at $82, it can fall by $3 to $79 before it triggers a margin call.

Types of forwards

Following are the main types of forwards.

1. Equity forward

It is a forward contract where underlying is a stock, portfolio of stock or stock market index. 2. Commodity forward

It is a forward contract where underlying is commodity. 3. Currency forward

It is a forward contract where underlying is a currency or basket of currencies. 4. Bond forward

It is a forward contract where underlying is a bond or bond market index. 5. Interest rate forward / FRA forward

It is a forward contract where underlying is a loan. The FRA is written as 3 x 9. It means one will take a loan after 3 months for a period of 6 months. The transaction will take 9 months to be completed.

2. FUTURE CONTRACT

Future contract or simply a future is a standardized contract between two parties, to buy or to sell an asset at a specified future time at a price agreed upon today, making it a type of derivative instrument.

These contracts are standardized and market specific. Types of futures

All the forward contracts type is replaced with future contracts. 1. Equity future

It is a future contract where underlying is a Stock, Portfolio of stock or stock market index. 2. Commodity future

It is a future contract where underlying is a commodity. 3. Currency future

It is a future contract where underlying is a currency or basket of currencies. 4. Bond future

It is a future contract where underlying is a bond or bond market index. 5. Interest rate future.

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16 Differences:

The forward market is a private and largely unregulated market. Any transaction involving a commitment between two parties for the future purchase/sale of an asset is a forward contract. They are private transactions for a reason that, parties want to keep them private and want little government interference.

A future contract is a variation of a forward contract that has essentially the same basic definition but some additional features that clearly distinguish it from a forward contract.

Difference between forward and future.

Difference Forward Future

Contract size Customer specific Market specific

Maturity period Customer specific Market specific

In Pakistan it is last Friday of the following month.

Settlement On maturity Daily settlement

Marking to market Tradability No (Over the counter) Traded in market Risk management

mechanism

No mechanism, chance of default is greater

Mechanism available. e.g. Banks / clearing houses

Financial intermediary No Yes,

Liquidity No Yes

Marking to market No Yes/ Daily settlements

a. Contract specification / size

A forward contract is a customized and customer specific contract. The two parties establish all the terms of contract, including the identity of the underlying, the expiration date and the manner in which the contract is settled as well as the price. In a future contract price is the only term established by the two parties, the exchange established all other terms. The terms established by the exchange are standardized and exchange selects a number of choices for underlying, expiration dates and a variety of other contract-specific items.

b. Maturity Period

The period of a forward contract is decided at the time of its orientation with the consensus of parties involved while the period of a future contract is decide by the market in which it is traded. In Pakistan the normal maturity period of futures is 30 to 60 days. Futures are settled on the last Friday of the following month.

c. Settlements

All the forwards are settled on the maturity or where both the parties agree to settle their contract any time before the maturity period. Futures are settled through the exchanges that work like a clearing house on the daily basis. The clearing house requires that all the parties settle their gains and losses to exchange on the daily basis. This process, referred to as the daily settlement or marking to market is a critical distinction between future and forward contracts.

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17 An example:

Following is an example of marking-to-market process that occurs over a period of six days. We start with the assumption that the futures price is $100 when the transaction opens, the initial margin requirement is $5 and the maintenance margin requirement is $3. The trader takes a long position of 10 contracts on day 0, depositing $50. ($5 per contract).

Initial future price $100. Initial margin requirement $5. Maintenance margin requirement $3.

Day Beginning Balance Funds deposited Futures price Price change

Gain / loss Ending balance 0 0 50 100 - - 50 1 50 0 99.20 -.80 -8 42 2 42 0 96.00 -3.20 -32 10 3 10 40 101.00 5.00 50 100 4 100 0 103.50 2.50 25 125 5 125 0 103.00 -0.50 -5 120 6 120 0 104.00 1.00 10 130 d. Tradability

The forwards are not tradable and settled over the counter while futures are traded on the floor of exchange.

e. Risk management mechanism

The most important difference in management of default risk associated with the contracts. In a forward contract, the risk of default is a major concern. Specifically, the party with a loss on the contract could default. In a future contract, however, the future exchange guarantees to each party that if the other fails to pay, the exchange will pay.

f. Financial intermediary.

A forward is a customized contract between two parties and involves no intermediary while futures are actually contracts organized by exchanges or banks who work as intermediaries and clearing houses. They are the agents and guarantors of the futures.

g. Liquidity.

Futures are the contracts with generally accepted terms. Standardizing the instrument makes it more acceptable to a broader group of participants with the advantage being the instrument can then more easily trade in a type of secondary market. In contrast, forward contracts are quite heterogeneous because they are customized.

A futures contract is therefore said to have liquidity in contrast to forward contract, which does not generally trade after it has been created.

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18 3. SWAP

A swap is a derivative in which two counter parties exchange cash flows of one party's financial instrument for those of the other party's financial instrument. It is an agreement between two parties to exchange a series of future cash flows. Typically at least one of the two series of cash flows is determined by a later outcome. In other words, one party agrees to pay the other a series of cash flows whose value will be determined by the unknown future course of some underlying factor, such as interest rate, exchange rate, stock price or commodity price.

Types of SWAPS.

1. Interest rate swaps

2. Currency swaps / exchange rate swaps

3. Commodity swaps

4. Credit default swaps

5. Subordinate risk swaps

(Detailed discussion will be available in the following lectures)

B. CONTINGENT CLAIMS

A claim that can be exercised when certain specified outcome occurs. It depends on the state of nature of the financial claim. These claims may be OTC or exchange traded. Option is a type of exchange traded contingent claims.

OPTIONS:

An option is a contract which gives the buyer (the owner) the right, but not the obligation, to buy or sell an underlying asset or instrument at a specified strike price on or before a specified date. The seller has the corresponding obligation to fulfill the transaction – that is to sell or buy – if the buyer (owner) "exercises" the option. The buyer pays a premium to the seller for this right.

An option which conveys to the owner the right to buy something at a specific price is referred to as a call; an option which conveys the right of the owner to sell something at a specific price is referred to as a put. Both are commonly traded, but for clarity, the call option is more frequently discussed.

A. CALL OPTION

A Call Option is security that gives the owner the right to buy a fix no. of shares of a stock or an index at a certain price by a certain date. That "certain price" is called the strike price, and that "certain date" is called the expiration date.

The buyer of a call option is called ―long call‖ and the seller is called ―short call‖. A call option is defined by the following 4 characteristics:

 There is an underlying stock or index

 There is an expiration date of the option

 There is a strike price of the option

 The option is the right to BUY the underlying stock or index. This contrasts to a put option, which is the right to sell the underlying stock

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19 A call option is called a "call" because the owner has the right to "call the stock away" from the seller. It is also called an "option" because the owner has the "right", but not the "obligation", to buy the stock at the strike price. In other words, the owner of the option (also known as "long a call") does not have to exercise the option and buy the stock--if buying the stock at the strike price is unprofitable, the owner of the call can just let the option expire worthless.

B. PUT OPTION

A put option is the right to SELL a fix no. of shares of a stock or an index at a certain price by a certain date. That "certain price" is known as the strike price, and that "certain date" is known as the expiry or expiration date. A put option is a security that you buy when you think the price of a stock or index is going to go down.

The buyer of a put option is called ―long put‖ and the seller is called ―short put‖. A put option, like a call option, is defined by the following 4 characteristics:

 There is an underlying stock or index to which the option relates

 There is an expiration date of the put option

 There is a strike price of the put option

 The put option is the right to SELL the underlying stock or index at the strike price. This contrasts with a call option which is the right to BUY the underlying stock or index at the strike price.

It is called a "put" because it gives you the right to "put", or sell, the stock or index to someone else. A put option differs from a call option in that a call is the right to buy the stock and the put is the right to sell the stock.

C. EXOTIC OPTION

An exotic option is an option which has features making it more complex than commonly traded vanilla options. Like the more general exotic derivatives they may have several triggers relating to determination of payoff. An exotic option may also include non-standard underlying instrument, developed for a particular client or for a particular market. Exotic options are more complex than options that trade on an exchange, and are generally traded over the counter (OTC).

Option general categories

 European option – an option that may only be exercised on expiration.

 American option – an option that may be exercised on any trading day on or before expiry.

 Bermudan option – an option that may be exercised only on specified dates on or before expiration.

 Asian option – an option whose payoff is determined by the average underlying price over some preset time period.

 Barrier - option with the general characteristic that the underlying security's price must pass a certain level or "barrier" before it can be exercised.

 Binary option – An all-or-nothing option that pays the full amount if the underlying security meets the defined condition on expiration otherwise it expires worthless.

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20  Exotic option – any of a broad category of options that may include complex financial

structures.

 Vanilla option – any option that is not exotic.

(Further details on pricing and types of options is available in the topic of options at page 80)

HEDGING:

A hedge is an investment position intended to offset potential losses/gains that may be incurred by a companion investment. In simple language, a hedge is used to reduce any substantial losses/gains suffered by an individual or an organization.

A hedge can be constructed form many types of financial instruments, including stocks, exchange-traded funds, insurance, forward contracts, swaps, options and many types of over the counter and derivative products and future contracts.

SPECULATION:

Speculation is the practice of engaging in risky financial transactions in an attempt to profit from fluctuations in the market value of a tradable good such as a financial instrument, rather than attempting to profit from the underlying financial attributes embodied in the instrument such as capital gains, interest, or dividends. Many speculators pay little attention to the fundamental value of a security and instead focus purely on price movements. Speculation can in principle involve any tradable good or financial instrument. Speculators are particularly common in the markets for stocks, bonds, commodity, futures, currencies, fine art, collectibles, real estate and derivatives.

Hedger and Speculator

Hedger seeks to eliminate risk and need speculator to assume risk, but such is not always the case. Hedgers often trade with other hedgers and speculator often trade with other speculator. All one needs to hedge or speculate is a party with opposite beliefs or opposite risk exposure.

Why corporations need to hedge?

Hedgers shun the risk of price change and look for ways to transfer it, while speculators assume the risk of price change by taking one position (either long or short) in a market, and waiting for the price of their commodity to go in ―their‖ direction. Hedger, on the other hand, have a position, either long of short usually in the cash market, and attempt to limit their risk of price change loss by entering into an opposite and approximately equal position in another market (usually futures or options).

A short hedger is someone who has a long position (owns the commodity) in the cash market and transfer the risk of price decline by selling a futures contract or buying a put option. If the cash market price declines and the futures market price also declines, the loss he suffers in the cash market will be offset by the gain he realizes in the futures market.

Advantages and disadvantages of hedging:

The main advantage of hedge is that it lowers the risk of an investment significantly. If an investor makes an investment in which variables are out of his control, as is the case in nearly

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21 any investment—then he stands to lose money if things do not go as he planned. A hedge can help his offset these losses and thus reduce any unwanted risk.

The main disadvantage of a hedge is that, in reducing risk, the hedge is also cutting into the investor‘s potential reward. Hedges are not free, but must be purchased from another party. Like an insurance policy, a hedge costs money, and if the main position produces profits as planned, then the hedge will have been an unnecessary expenditure. Some investors would question the benefit of second-guessing the original investment in this way.

The relative advantages and disadvantages of a hedge will depend greatly on the situation in which the hedge is applied, as well as the hedge‘s cost. In some situations, a hedge will be absolutely necessary to make sure that an investor will remain financially solvent, regardless of what happens. In other cases, it merely signals an overcautious investor cutting into his own position.

Following are the main reasons for which corporations go for hedging.

Price risk transfer

Cash market prices change and there‘s nothing you can do about it. What‘s more, they

are going to keep changing, no matter what you do. So you have three choices: assume

the risk (be a speculator), transfer the risk of price change to a speculator (be a hedger),

or get out of the market.

Instead of waiting until you have the cash market product in hand, you can do a

―substitute sale‖ in the future market, this is called ―hedging‖. This means that you sell

now in the future market, substituting your actions in the future market today and

transfer the price risk.

Profit potential

It is possible (but not guaranteed) that after a short hedge has been put in place, both the

cash and futures prices will drop, with the futures price dropping more than the cash

price. This is a favorable change and a basis for profit potential.

Cash flow smoothing

If you establish a hedge six months before your cash market transaction and then prices

move unfavorably, your futures market position will start to earn you cash in the short

run. The reason is that futures positions are marked to market daily. If your futures

position has a gain during today‘s trading, the gained amount will be deposited to your

account at the close of business day. This cash may help your cash flow until your cash

market transactions.

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22

EXAMPLE 4:

Friends Co. is a UK based company that regularly trades with companies in the USA. Several large transactions are due in four months time. The transactions are shown below. The transactions are in ‗000‘ units of the currencies shown. Assume that it is now 1st_{July and that}

futures and options contracts mature at the relevant month end.

Friends Co. Exports $ 490 Imports $150 Exchange Rates: $ / £

Spot : 1.5166

3 months forward: 1.5286 6 months forward: 1.5401

CME $ / £ Currency futures (£ 75,500) , contract size

Future rates: September 1.5245 December 1.5586

CME currency options prices, $ / £ options £ 31,250 (cents per pound)

Strike price Call Put

September December September December

1.5200 3.55 4.50 2.30 4.50

1.5500 2.38 3.76 3.50 6.50

Required: prepare a report for the managers of Friends co. on how the five month risk should be hedged by using financial derivatives.

Solution:

We need to decide whether to hedge or not. If we need to hedge what is the best choice out the four available choices.

1. Hedge or not

2. Money market hedge 3. Forwards

4. Futures 5. Options

1. Hedge or not

Net exposure $490,000 - $150,000 = $340,000

An amount of $ 340,000 is receivable in four months time. So we need to hedge for this amount.

2. Money market hedge

We are not given the borrowing and lending rates, so we cannot use this money market hedge option.

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23

3. Forwards

First calculate 4 month future rate.

3 months forward: 1.5286 6 months forward: 1.5401

---

Increase in rates 0.0115

---

Average rate per month = 0.0115 / 3 = .0038

4 months forward = 1.5286 + 0.0038 = 1.5324

Conversion in £ with rate 1.5324 $ 340,000 / 1.5324 = £ 221,874

Forward option will give £ 221,874 for investment.

4. Futures

Spot rate: 1.5166

Future rates: September 1.5245 December 1.5586 4 month period ends October 31st

Position long call

First calculate 4 month future rate on Basis risk. Basis risk = spot rate – future rate

Basis risk = 1.5166 – 1.5586 = 0.0420 (rate is increasing in future time) Basis risk per month = 0.0420 / 6 = 0.0070

Expected future price = 1.5166 +4(.0070) = 1.5446 (used plus sign as rates increased) Conversion of amount in home currency £, 340,000 / 1.5446 = £220,121

Contract size = £75,500

No. of contracts = 220,121 / 75,500 = 2.91 means 2 or 3 contracts. Here we take 2 contracts: 75,500 x 2 = £ 151,000

Convert in dollars 151,000 x 1.5446 = $ 233,235

Unhedged amount = $ 340,000 – 233,235 = $ 106,765 (amount covered by forwards) Convert unhedged amount in £ = $ 106,765 / 1.5324 = £ 69,672

Total amount received through this choice =

Amount received in futures = £ 151,000 + Amount in forwards = £ 69,672

Total £ 220,672

Decision: £ 220,672 is amount received through futures and £ 221,874 is amount received using the choice of forwards calculate in previous situation. When there is a nominal or no difference in these two choice we will opt the forwards, as it more customized and bears less restrictions.

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24

5. options

1.5200 3.55 4.50 2.30 4.50

1.5500 2.38 3.76 3.50 6.50

Hint: while selecting the rates always use that rates which are in the benefit of the bank. Bank will charge higher rates we borrow and will give the lower rates when we lend or invest in the bank.

Contract size: £31,250 (cents per pound)

Exercise price: 1.5200 $ / £ ( we use this price as it is lower than 1.5324 of forwards) Position: long call (because we need to buy)

Contract used: December as the contracts mature in October) Amount in £ = 340,000 / 1.5200 = £ 223,684

No. of contracts = 223,684 / 31,250 = 7.16 contracts ( we take 7 contracts) Amount covered in options = 31,250 x 7 = £ 218,750

Convert in dollars = 218,750 x 1.5200 = $ 332,500 (option rate is used) Unhedged amount = 340,000 – 332,750 = $ 7,500 ( covered in forwards) Unhedged amount in £ = $ 7,500 / 1.5324 = £ 4,894 (forwards rate used) Cost of options (premium) = 218,750 x .045 = $ 9844

Convert option premium in £, $ 9844 / 1.5166 = £ 6491 (spot rate used) Net value received from options:

Amount covered in 7 contracts = £ 218,750 + Amount covered in forwards = £ 4,894 - Cost of options (premium) = £ (6,491) = Net amount receive in option = £ 217,153

Decision: amount received through options is £ 217,153 which is lower than all other choices, therefore forward is the best choice in all cases.

EXAMPLE 5:

Lammer Co. is a UK based company that regularly trades with companies in the USA.

Lammer co. has exported goods worth $ 120 m which is receivable in five months time. These are shown below. Assume that it‘s 1st June and that, future contracts mature at the relevant month end.

Exchange Rates: $ / £

Spot : 1.9156 – 1.9210

November forward: 1.9066 – 1.9120 December forward: 1.8901 – 1.8945

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25 Annual interest rates available to lamer co.

Borrowing Investing

UK 5.5% 4.2%

USA 4.0% 2.0%

Chicago money exchange $ / £ currency futures ( £ 62,500) September 1.9045 December 1.8986

Required: Prepare a report for the managers of Lammer Co. on how the five month currency risk should be hedged. Include in your report all relevant calculations relating to the alternative types of hedge.

Money market hedge is always based and calculated through borrowing and lending rates. Here the rates are available so we first check this option.

Annual interest rates available to ABC co.

Borrowing Lending

UK 5.5% 4.2%

USA 4.0% 2.0%

Following are three steps for money market hedge for $ 120,000,000 receivables.

Step 1: calculate PV of $120 using borrowing rate.4%

𝐹𝑉 = PV(1 + i)𝑛 , 120,000,000 = PV(1 + .04)5/12 Pv = 120,000,000 / (1.04)5/12_{= $ 118,054,886}

1£ = 1.9210$ $ 118,054,886 = £? , 118,054,886 / 1.9210 = £ 61,454,912

Hint: Here we use rate 1.9210 because we are taking loan and bank will charge higher rates.

Step 3: calculate FV for investable amount in the home currency at lending rate. 4.2% 𝐹𝑉 = PV(1 + i)𝑛_{, FV = 61,454,912(1.042)}5/12_{= £ 62,517,491}

Decision: final amount received through money market hedge is £ 8,866,897 we need to compare it with other choices, so we move to next calculations.

2. Forwards

Spot Rate: 1.9210

November forward: 1.9120

---

Decrease in rates 0.0090 Average rate per month = 0.0090 / 6 = .0015

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26 5 months forward = 1.9210 – 5(0.0015) = 1.9135

Conversion in £ with rate 1.9135 $ 120,000,000 / 1.9135 = £ 62,712,307

It means forward will give a sum of £62,712,307 which is better than amount of money market hedge that gives £ 62,517,491. Therefore forward is better choice than money market hedge.

3. Futures

CME $ / £ Currency futures (£ 62,500) , contract size Spot rate: 1.9156 – 1.9210

Position long call

Basis risk = 1.9210 – 1.8986 = 0.0224 (rate is decreasing in future time) Basis risk per month = 0.0224 / 7 = 0.0032

Expected future price = 1.9210 – 5(.0032) = 1.9050

Conversion of amount in home currency £ 120,000,000 / 1.9050 = £ 62,992,126 Contract size = £62,500

No. of contracts = 62,992,126 / 62,500 = 1007.87 means 1007 contracts. Here we take 2 contracts: 62,500 x1007 = £ 62,937,500

Convert in dollars 62,937,500 x 1.9050 = $ 119,895,938

Unhedged amount = $ 120,000,000 – 119,895,938 = $ 104,062 (amount covered by forwards) Convert unhedged amount in £ = $ 104,062 / 1.9135 = £ 54,383

Total amount received through this choice

Amount received in futures = £ 62,937,500 + Amount in forwards = £ 54,383

Total £ 62,991,883

Decision: future choice will give a sum of £ 62,991,883 that is best of all three choices. So we will consider the future option.

EXAMPLE 6:

ABC Co. is a UK based company that regularly trades with companies in the USA. Several large transactions are due in five months time. The transactions are shown below. The

transactions are in ‗000‘ units of the currencies shown. Assume that it is now 1st_{June and that}

futures and options contracts mature at the relevant month end.

Exports Imports

LMN Co. $ 890 £ 150

PQR Co. - $ 490

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27 Exchange Rates: $ / £

Spot : 1.9156 – 1.9210

3 months forward: 1.9066 – 1.9120 1 year forward: 1.8901 – 1.8945 Annual interest rates available to ABC co.

Borrowing Investing

UK 5.5% 4.2%

USA 4.0% 2.0%

Future rates: September 1.9065 December 1.8985

1.8800 4.70 5.90 1.60 2.95

1.9000 3.53 4.70 2.36 4.34

1.9200 2.28 3.56 3.40 6.55

Required: Prepare a report for the managers of ABC Co. on how the five month currency risk should be hedged. Include in your report all relevant calculations relating to the alternative types of hedge.

Solution:

1. Hedge or not

1. Hedge or not

£ 150 is receivable and the same amount is payable, so we don‘t need to hedge for that. In dollars $ 890 is receivable and $ 540 (490+50) is payable. A net of $ 350m (350,000) is receivable and it is the amount for which we need to hedge. Now we have to decide what the best available option for this hedge is.

Money market hedge is always based and calculated through borrowing and lending rates. Here the rates are available so we first check this option.

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28 Annual interest rates available to ABC co.

Borrowing Lending

UK 5.5% 4.2%

USA 4.0% 2.0%

Following are three steps for money market hedge for $ 350,000 receivables.

Step 1: calculate PV of $350m using borrowing rate.4%

𝐹𝑉 = PV(1 + i)𝑛_{, 350,000 = PV(1 + .04)}5/12

Pv = 350,000 / (1.04)5/12 = $344,328

1£ = 1.9210$ $ 344,328 = £? , 344,328 / 1.9210 = £ 179,243

Hint: Here we use rate 1.9210 because we are taking loan and bank will charge higher of the spot rates.

Step 3: calculate FV for investable amount in the home currency at lending rate. 4.2% 𝐹𝑉 = PV(1 + i)𝑛_{, FV = 179,243(1.042)}5/12_{= £ 182,343}

3. Forwards

3 months forward: 1.9120 1 year forward: 1.8945

---

Decrease in rates 0.0175

---

Average rate per month = 0.0175 / 9 = .0019

5 months forward = 1.9120 – 2(0.0019) = 1.9082

Conversion in £ with rate 1.9082 $ 350,000 / 1.9082 = £ 183,419

Hint: Here we use minus sign 1.9120

–

2(0.0019) because rates are decreasing. If the rates were increased we should use the + sign in this equation.

It means forward will give a sum of £ 183,419 which is better than amount of money market hedge that gives £ 182,343. Therefore forward is better choice than money market hedge.

4. Futures

CME $ / £ Currency futures (£ 62,500) , contract size Spot rate: 1.9156 – 1.9210

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29 First calculate 5 month future rate on Basis risk.

Basis risk = spot rate – future rate

Basis risk = 1.9210 – 1.8985 = 0.0225 (rate is decreasing in future time) Basis risk per month = 0.0225 / 7 = 0.0032 ( 7 months is total period June to Dec.) Expected future price = 1.9210 – 5(.0032) = 1.905 (used minus sign as rates decreased) Conversion of amount in home currency $ 350,00 / 1.905 = £183,727

Contract size = £62,500

No. of contracts = 183,727 / 62,500 = 2.93 means 2 or 3 contracts. Here we take 2 contracts: 62,500 x 2 = £ 125,000

Convert in dollars 125,000 x 1.9050 = $ 238,125

Unhedged amount = $ 350,000 – 238,125 = $ 111,875 (amount covered by forwards) Convert unhedged amount in £ = $ 111,875 / 1.9082 = £ 58629

Total amount received through this choice =

Amount received in futures = £ 125,000 + Amount in forwards = £ 58,629

Total £ 183,629

Decision: £ 183,629 is amount received through futures and £ 183,419 is amount received using the choice of forwards calculate in previous situation. When there is a nominal or no difference in these two choice we will opt the forwards, as it more customized and bears less restrictions.

5. options

1.8800 4.70 5.90 1.60 2.95

1.9000 3.53 4.70 2.36 4.34

1.9200 2.28 3.56 3.40 6.55

Hint: while selecting the rates always use that rates which are in the benefit of the bank. Bank will charge higher rates when we borrow and will give the lower rates when we lend or invest in the bank.

Contract size: £31,250

Exercise price: 1.8800 $ / £ ( we use this price as it is lower than 1.9082 calculated) Position: long call (because we need to buy)

Contract used: December ( as the contracts mature in October) Amount in £ = 350,000 / 1.8800 = £ 186,170

No. of contracts = 186,170 / 31,250 = 5.95 contracts ( we take 5 contracts) Amount covered in options = 31,250 x 5 = £156,250

Convert in dollars = 156,250 x 1.8800 = $ 293,750

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30 Unhedged amount in £ = $ 56,250 / 1.9082 = £ 29,478 (forward rate used)

Cost of options (premium) = 156,250 x .059 = $ 9219

Convert option premium in £ $ 9219 / 1.9156 = £ 4812 (used spot rate) Now see it on time line: (future value) = 𝐹𝑉 = PV(1 + i)𝑛

𝐹𝑉 = PV(1 + i)𝑛 = 𝐹𝑉 = 4812.46(1 + .042)5/12 = £ 4896 Net value received from options:

Amount covered in 5 contracts = £ 156,250 + Amount covered in forwards = £ 29,478 - Cost of options (premium) = £ 4896 = Net amount receive in option = £ 180,832

Decision: amount received through options is £ 180,832 which is lower than all other choices, therefore forward is the best option in all cases.

EXAMPLE 7:

Casasophia co, base in a European country that uses euro €, constructs and maintains advanced energy efficient commercial properties around the world. It has just completed a major project in the USA and is due to receive the final payment of us$ 20 million in four months.

Casasophia Co. is planning to commence a major construction and maintenance project in mazabia, a small African country, in six months time. This government owned project is expected to last for three years during which time Casasophia Co. will complete the construction of state of the art energy efficient properties and provide training to a local mazabian company in maintaining the properties. The carbon neutral status of the building project has attracted some grand funding from the European Union and these fund will be provided to the mazabian government in mazabian Shillings (MShs).

Casasophia co. intends to finance the project using the US# 20 million it is due to receive and borrow the rest through a € loan. It is intended that the US $ receipts will be converted into € and invested in short dated treasury bills until they are required. These funds plus the loan will be converted in t MShs on the date required, at the spot rate at that time.

Mazabia‘s government requires Casasophia co. to deposit the MShs 2.64 billion it needs for the project with mazabian central bank, at the commencement of the project. In return, Casasophia co. will receive a fixed sum of MShs 1.5 billion after tax at the end of each year. Neither of these amounts is subject to inflationary increases. The relevant risk adjusted discount rate for the project is assumed to be 12%. Following are the financial information available.

Exchange Rates: $ / € MShs / €

Spot : 1.3585 – 1.3618 MShs 116 – MShs 128

4 months forward: 1.3588 – 1.3623 Not available Futures:

CME $ / £ Currency futures (€ 125,000) , $ / € contract size Future rates: 2 months expiry 1.3633

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31 Options:

Contract size: € 125,000, exercise price quotation US$ per €, cents per Euro Calls, Puts.

exercise price Call Put

2 month expiry 5 month expiry 2 month expiry 5 month expiry

1.36 2.35 2.80 2.47 2.98

1.38 1.88 2.23 4.23 4.64

Casasophia co. local government base rate: 2.20% Mazabian government base rate: 10.80% Yield on short dated Euro treasury bills 1.80% Assume 360 days a year.

Mazabia‘s current annual inflation rate is 9.7% and is expected to remain at this level for the next six years. However, after that, there is considerable uncertainty about the future and the annual level of inflation and it could be anywhere between 5% and 15% for the next few years. The country where Casasophia co is based is expected to have a stable level of inflation at 1.2% per year for the foreseeable future. A local bank in mazabia has offered Casasophia co the opportunity to swap the annual income of MShs 1.5 billion receivable in each of the next three years for Euro, at the estimated annual MShs / € forward rates based on the current government base rates.

Required:

a. Advise Casasophia co on, and recommend an appropriate hedging strategy for the US$ income it is due to receive in four months. Include all relevant calculations.

b. Provide a reasoned estimate of the additional amount of loan finance Casasophia so needs to obtain to undertake the project in Mazabia in six months.

c. Given that Casasophia co agrees to the local bank‘s offer of the swap, calculate the net present value of the project in six month‘s time in €. Discuss whether the swap would be beneficial to Casasophia co.

Solution:

Query (a) Recommend the hedging strategy.

1. Hedge or not

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32

1. Hedge or not

An amount of $ 20,000,000 is receivable in four months time. So we need to hedge for this amount.

We are not given the borrowing and lending rates, so we cannot use this money market hedge option.

3. Forwards

As opposed to previous examples, here forward rates for future are given. So we not need to calculate these rates and use the higher rate to convert the dollar amount in Euro. Rates given are:-

Exchange Rates: $ / € MShs / €

Spot : 1.3585 – 1.3618 MShs 116 – MShs 128

4 months forward: 1.3588 – 1.3623 Not available

Convert $ amount in € = 20,000,000 / 1.3623 = € 14,681,054 4. Futures

CME $ / £ Currency futures (€ 125,000) , $ / € contract size Spot rate: 1.3585 – 1.3618

Future rates: 2 months expiry 1.3633 5 months expiry 1.3698

Period: 4 months

Contract period used: 5 months future 1.3698

Position: Long call

Basis risk = 1.3618 – 1.3698 = 0.008 (rate is increasing in future time) Basis risk per month = 0.008 / 5 = 0.0016

Expected future price = 1.3618 + 4(.0016) = 1.3682 (used plus sign as rates increased) Conversion of amount in home currency $ 20,000,00 / 1.3682 = €14,617,746

Contract size = €125,000

No. of contracts = 183,734 / 125,000 = 116.96 contracts.

Here we take 116 contracts: 125,000 x 116 = € 14,500,000 amount covered Convert in dollars € 14,500,000 x 1.3682 = $ 19,838,900

Unhedged amount = $ 20,000,000 – 19,838,900 = $ 161,100 (covered by forwards) Convert unhedged amount in € = $ 161,100 / 1.3623 = €118,255 (forward rate used) Total amount received through this choice =

Amount received in futures = € 14,500,000 + Amount in forwards = € 118,255