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CHAPTER 7

FUTURES DERIVATIVES

Describe a derivativeDescribe the history of derivativeDescribe the development of derivative in MalaysiaExplain the difference between forward and futures contractExplain terms convergence, margins and marking to market

and basis riskExplain the terms hedging, speculating and arbitraging with

futuresDescribe the contract specification of FCPO and FKLIKnow how to hedge, speculate and arbitrage using FCPO

and FKLIExplain and understand the term single stock futures

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Learning Objectives

Chapter Outline• Introduction to Derivatives • Forward and Futures Contracts • The Key Elements of in Futures Trading • Hedging, Speculating and Arbitraging with

Futures Contract • The Crude Palm Oil (FCPO) and KLCI (FKLI)

futures • Single Stock Futures (SSF)

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What is a derivative? The word ‘derivative’ implies they derive their value from

something. It originates from mathematics and it is a variable that derives

from another variable. Derivatives on its own have little value but when it derives from

some other asset, known as the underlying, hence, it has its value.

The underlying can be share prices, prices of commodity, indices and interest rates.

For example, a derivative of Air Asia shares will derive its value from share price of Air Asia (underlying).

Similarly, a derivative contract on Crude Palm Oil depends on the price of palm oil and the derivative of Kuala Lumpur Composite Index (KLCI) will depend on the movement of the KLCI.

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Why do derivative markets exist?

• Largely to facilitate hedging.• The derivative markets are largely insurance

markets.• Firms, like individuals are risk averse and

would like to protect themselves against three main types of risk that businesses face: PRICE RISK, CURRENCY RISK and INTEREST RATE RISK.

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SPOT MARKET vs FORWARD/FUTURES MARKETS

• In the spot (cash) market, buyers and sellers agree on Price (P) and Quantity (Q) for immediate delivery (or within a few days).

• Example: Proton buys 1 million Japanese Yen in the spot market for currency, or it buys 100 tons of steel in the cash market for steel. MAS buys 500,000 gallons of gasoline in the spot market.

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FORWARD CONTRACT

• Private contracts between two parties (buyer and seller) for delivery sometime in the future (one month, one year).

• Not marketable securities and there is no secondary market.

• E.g. like the difference between a bank loan (not marketable) and a bond (marketable).

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Mechanics of Forward Contracts: An illustration

• Assume there are 2 parties – a cocoa farmer who has planted cocoa on his farm and is expecting to harvest the cocoa in 6 months and a confectioner who produces chocolate using cocoa powder.

• Assume further that the confectioner has in his inventory, sufficient cocoa to last him for the next 6 months, but would have to replenish his stock at the end of the sixth month. Clearly, both parties here are exposed to risk, in this case price risk.

• The cocoa farmer faces the risk that the spot price of cocoa could fall between now and 6 months from now, when he completes his harvest. Such a fall will obviously reduce his revenue and profits. Infact, if the fall in spot price is sharp enough, he could even face outright losses.

• The confectioner faces similar risk but in the opposite direction. The spot price of coca could increase between now and 6 months from now when he needs to replenish his inventory. Any increase in prices will increase his costs and reduce his profits.

• Since both parties face price-risk and neither party can tell which way prices would go, it would be in their interest to go into an arrangement that could protect them from this price-risk. Such an arrangement would be the forward contract. Under the forward contract, the farmer would agree to deliver and the confectioner to take delivery of cocoa of an agreed quantity on a mutually agreeable date and at a price determined now – i.e. at the time of initiation of contract.

Farmer(Short position)

negotiate

Agree on :Price, quantity, quality,

maturity delivery location etc.

Farmer(Short position)

Confection (Long Position)

The long position agrees to take delivery (buy) of the underlying asset while the short position agrees to make delivery (sell).

The long position agrees to take delivery (buy) of the underlying asset while the short position agrees to make delivery (sell).

Step 1 (at initiation of contract; day = 0)

Step 2 (on maturity date; day = 180)

Cocoa

Money

Confection (Long Position)

FORWARD CONTRACTS – EXAMPLE 1

• Giant Supermarket enters into a forward contract in May to purchase rice at harvest time in October, at a guaranteed price, from various rice farmers for their entire crop.

• Advantage: buyer (company) and seller (farmer) gave a guaranteed price. They are now protected from price swings in rice.

• They have eliminated price risk completely by hedging their position, locking in a price with a forward contract.

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FORWARD CONTRACTS – EXAMPLE 2

• Toyota Motors enters into a contract for British pounds with Bank One, to either buy pounds or sell pounds, in six months at a guaranteed exchange rate. By locking in, Toyota Motors has hedged currency risk.

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Advantages/Disadvantages of Forward Contract

• Advantage: They are very flexible and can be customized to the needs of the parties.

• Disadvantages:– There is no liquid market for forward contracts, no secondary

market. – Problem in price fixing. The party who has better negotiating

power may dictate an unfair price.– High default risk. One party may default (not fulfilling the

future obligation agreed upon earlier), resulting in losses for the other party. This risk is known as counterparty risk.

– Requires actual delivery to complete the contract..

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FUTURES CONTRACTS

• Are the same in principle as a forward contract, where two parties (buyer and seller) agree to trade/exchange something (rice, corn, oil, T-bills, Yen) in the future (one week, one month, one year), but they agree on P and Q now, for future delivery, using a futures contract from a futures exchange – an organized market for trading futures contracts.

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What is a futures contract?

• exchange-traded form of forward contract• Basically to overcome 3 problems of forward contract

– (1) multiple coincidence needs, – (2) unfair forward price and – (3) counterparty risk.

• Because they are exchange-traded, the contracts are standardised.

• Except for price the standardised contract would have specified the quantity (or the contract size), quality (or the grade) of the underlying asset, delivery date (or the expiry date) and location of delivery.

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Multiple Coincidence of Needs• At least three things must match before the two

parties in a forward contract can even begin to negotiate prices.(i) asset match(ii) maturity match(iii) quantity match

• There could be others such as delivery location etc. The result is that there could be substantial “search costs” involved. One party will have to search out the other thereby incurring costs in terms of time, advertisement etc.

Potential for Price Squeeze/Unfair Price• In a forward contract, the forward price is arrived at

through negotiation.

• The problem with negotiation is that, bargaining position matters. If one party is in a weak bargaining position, he could be squeezed by the other.

• However, if there is only one confectioner (potential buyer of cocoa) in the district but several cocoa farmers, the long position has the bargaining power and could dictate on price.

• In such a situation, even if the cocoa farmer feels the price offered may not be fair, he may have little choice but accept the price. This would be particularly so, if the product is perishable and could spoil shortly after harvest. The short position does not have much of an option to wait and see if he could fetch a better price post harvest.

Counterparty / Default Risk

• Counterparty risk or default risk, refers to the possibility that one of the parties to the transaction could default. Such default could happen not so much because the party is “dishonest” but rather due to the incentive to default given changes in the spot price.

• However, if spot prices subsequently begin to fall, the long position (confectioner) begins to hurt since he has agreed to forward price based on the higher previous spot price.

• The opposite is true if spot prices begin to rise after the forward contract is negotiated. Now, the short position, the farmer, begins to hurt since he would feel that his cocoa could now be sold at higher prices. He would regret having locked himself into the ‘low’ forward price.

• We assume that the two parties had agreed on a forward price of RM100 per ton. We examine what will happen if say, the spot price on maturity day is at RM70 per ton or RM120 per ton.

Advantages of futures contracts over forward contracts

• Liquid market, lots of buyers and sellers at organized exchanges all over the world.

• Active secondary market. Contract may trade hands many times before expiration.

• Minimal risk. The futures exchange requires an initial margin to open a position and they enforce daily settlement of all gains and losses to avoid default. There is maximum price movement, called daily limit, to minimize large losses. For example, daily price limit for palm oil futures is 10% above or below the settlement price of the preceding business day, trading stops for the day.

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Advantages of futures contracts over forward contracts

• The counterparty risk is reduced through a clearing house which take responsibility for ensuring the contract is brought through without any parties defaulting in the transaction.

• Cash settlement for most futures contracts, instead of settlement in the actual commodity.

• You can close your account anytime by taking an offsetting position. If your original position is to buy (go long) a futures contract, you can subsequently sell (go short) to close out your position, and vice versa. You can cash out without having to make or receive delivery.

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Disadvantages of futures contracts over forward contracts

• Less flexible since futures contracts are for fixed, standard amounts, e.g. palm oil futures contracts are for 25 metric tons per contract.

• Expiration dates are fixed: E.g. Jan, March, September and December. (only few delivery per year.

• The location for delivery are fixed (Port Kelang, Penang/Butterworth and Pasir Gudang (Johor)

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Examples of futures contracts traded in Bursa Malaysia Derivatives Bhd

• Stock Index Futures– KLCI (FKLI) Futures

• Single Stock Futures (SSFs)• Interest Rate Futures

– 3 Month Kuala Lumpur Interbank Offered Rate interest rate (FKB3)• Bond Futures

– 3-Year Malaysian Government Securities (FMG3) Futures– 5-Year Malaysian Government Securities (FMG5) Futures – 10-Year Malaysian Government Securities (FMGA) Futures

• Agriculture Futures– Crude Palm Oil (FCPO) Futures – Crude Palm Kernel Oil (FPKO) Futures – USD Crude Palm Oil (FUPO) Futures

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The Key Elements of Futures Trading

• Convergence of Futures and Cash Prices• Basis and Basis Risk • Margins and Marking to Market • Types of orders • The Clearing House

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Price Convergence• The futures price of a contract and the cash price (spot

price of the underlying) of the same commodity tend to converge, i.e. they will come together as the delivery month of the futures contract approaches. On maturity date, the futures price must equal spot price.

• When futures price > spot price = contango.• When futures price < spot price = backwardation.• Determined by market forces (ss and dd)

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The Convergence Property

• The convergence property states that the price of a futures contract on the day of its maturity must equal the spot price of the underlying on that day.

• The logic for this is that, on its maturity day, a futures contract is essentially a spot asset.

• The Spot Price and the Future Price must be equal otherwise there would be a riskless arbitrage opportunity. One could even argue that the existence of such arbitrage opportunity would ensure convergence.

Spot-Futures Convergence at Maturity

FuturesSpot

Maturity day

t

Spot/Futures Price

Basis and Basis Risk

• Basis is the difference between cash price (or spot price), S and Futures price, F.

• It reduces to zero at it approaches maturity of the futures contract.

• In a perfect hedge, the gains or losses in the futures contract exactly offset the losses or gains of the underlying asset being hedged.

• If do not perfectly cancel each other out, it is called basis risk. Due to mismatches of quality (grade), location, maturity, qty.

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Basis and Basis Risk

• The difference or spread between the futures and spot prices is often known as the basis. The basis should equal the net carrying cost.

• The basis narrows over time to reach zero at maturity. Prior to maturity however, the basis would be positive or occasionally negative.

oTt SFBasis ,

• Basis risk can be thought of as tracking error. Basis risk would be present whenever there is any of these three mismatches:

(i) Asset mismatch(ii) Maturity mismatch and(iii) Quantity (or contract size) mismatch.

Margins and Marking to Market• Example:

Consider an investor, contacts his broker on Tuesday, 2nd of June to buy two December crude palm oil futures contracts at Bursa Malaysia Derivative Berhad. One futures contract equivalent to 25 metric tons. Current market price is RM2,000 per ton.Therefore, the investor is contracted to buy 50 metric tons at this price. The total value of this transaction: = 2 contracts x 25 metric tons x RM2,000= RM100,000

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Margins and Marking to Market• The broker requires the investor to deposit some money

in a margin account (initial margin). Assume that the initial deposit is RM10,000 per contract = Initial Margin = RM20,000.

• At the end of each day, the margin account is adjusted to reflect the investor’s gain or loss.

• This is the additional margin payments that would have to be paid and is called the variation / maintenance margin.

• This practice is referred to as “marking to market” or (marked to market).

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Margins and Marking to Market

• Assume that at the end of the day, the palm oil futures price closes at RM1,850 per ton. This implies that the investor has made a loss = 2 contract x 25 metric tons x RM150 = RM7,500

• If the price for the following day closes at RM2,300 per ton, the balance of the margin account will increase by:2 x 25 x RM450 = RM22,500

• Hence for the last two days, the margin balance has become RM35 000 = (RM20,000 – RM7,500 + RM22,500)

• The investor is entitled to withdraw any balance in the margin a/c in excess of the initial margin (IM) = RM15 000

• To ensure that margin a/c does not become negative, a maintenance margin is set (usually lower than IM).

• If the balance falls < maintenance margin, the investor will receive a margin call. He is expected to top up the difference back to the initial margin the following day.

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DAY Price Variation gain/loss Balance

0 2000 Pay margin 20 000 20 000

1 1850 (7500) 12 500

2 2300 450 x 2 x 25 = 22500 35 000

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The Clearing House

• Acts as intermediary in futures transactions.• Guarantees the performance of the parties in

each transaction.• To ensure none of the parties are hurt by the

defaulting party.

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Crude Palm Oil (FCPO) Futures and KLCI (FKLI) Futures

• The Underlying Instrument of FCPO and FKLI• The Contract Specification FCPO – refer to

Table 7.1 page 192• The Contract Specification FKLI – refer to

Table 7.3 page 196

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Trading Practicalities• Long – bought futures contract

– Contract to receive delivery/contract to buy underlying asset

– eg: Long 2 August 2011 FCPO at RM1000/tonne[ Engage in contact to receive delivery of 50 tonnes of

CPO in August 2011 at RM1000/tonne]• Short – sell futures contract

– Contract to make delivery/contract to sell underlying asset

– Short 2 Aug 2011 at RM1000/t[ Engage in contract to deliver 50 tonnes of CPO in Aug

2011 at RM1000/t] 40

EXERCISE

• Long 3 Dec 2012 FCPO @RM1,200• TODAY:

• A contract to buy 75 tonnes of CPO in Dec 2012 at RM1,200

• At maturityDec 2012• BUY 75 tonnes of CPO and pay RM1,200 Physical

settlement• OR• SELL 3 Dec 2012 FCPO at price of Dec 2012 FCPO traded in

Dec 2012. cash settlement

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EXERCISE

• Long August FKLI @ 1120• Contract to buy KLCI in August @ 1120• SETTLEMENT

– CASH Settlement– Sell Aug FKLI @ price of AUG FKLI traded in Aug.

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Forwards, Futures; Zero sum Game

• In a world of limited/finite resources, most financial transactions, including all derivatives transactions are zero-sum games; that is one party’s gain is at another party’s expense.if spot prices riseProfit to Long = Spot price at Maturity – Original Futures Price (the short position’s implied loss equals this amount)if spot prices fallProfit to Short = Original Futures Price – Spot price at Maturity.(the long position’s implied loss equals this amount)

Types of Futures Markets Participants

• Hedgers• Speculators• Arbitrageurs

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Hedgers

• Futures traders who have a personal or business interest in the future commodity prices, exchange rate or interest rate.

• E.g. importers/exporters, corporations buying and selling in the future, farmers, portfolio managers, firms expecting to borrow money in the future, firms/investors expecting to invest money in the future, etc.

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Hedgers - Examples

• Farmers (sellers) and producers are worried about the price of their product going down in the future. They can use futures contract to lock in price now for future output of oil, corn, wheat, sugar, steel, gold etc by going SHORT on contracts for their product.

• Exporters (importers) receiving foreign currency (paying in foreign currency) can hedge risk by going short (long) on currency futures.

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• Given the KLCI is 1050 and the value of a portfolio is RM3 million. If the portfolio manager wishes to hedge 80% against a price decrease, how many contracts will the portfolio manager have to trade? Does the trader buy or sell?

• Suppose in February, a palm oil producer anticipates that he will have 180 metric tonnes of crude palm oil ready for sale in four months’ time. He would like to fix the price for his produce. The current market price (February) of the palm oil is about RM2,250 per metric tonne while the June crude palm oil futures (FCPO)is currently trading at RM2,265.

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Types of Hedging Hedging is taking a (1) future position in anticipation of

a later cash transaction or (2) taking a future position opposite to the current physical position held.

The former type is known as anticipatory hedging and the latter type is known as hedging the current market position.

An example of anticipatory hedging is the palm oil producer who intends to sell his palm oil in 2 months could lock in the price by selling the futures contract today.

An example of hedging current market position is the fund manager with a portfolio of shares could hedge against a fall in share prices by selling (taking a futures position opposite to the current position of holding a portfolio of shares) stock index futures contracts today.

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Strategy

• Number of contracts• Contract Month• Action

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Types of Hedging

• anticipatory hedging – - Refer to Table 7.5 page 199

• hedging the current market position

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An Anticipatory Hedge• Often, producers may not have an immediate position in an

underlying asset but a potential position. That is, they anticipate having a position in the underlying asset at a future point.

• Assume that the farmer is expecting to produce 120 tons of cocoa in 6 months and wishes to hedge his price-risk. Suppose further that cocoa futures are maturing in 6 months from now and have a standard size of 10 tons per contract. The current quoted price for 6 month cocoa is say RM100 per ton or RM1,000 per contract. For simplicity, assume that the confectioner also requires 120 tons in six months

• Notice that the cocoa farmer in our example did not have an immediate exposure. He is expecting to harvest cocoa in 6 months. Yet, he hedges the position today. This is what is known as anticipatory hedge.

• Each party could do their hedging through the futures market as follows. The farmer would call his futures broker and short (sell) 12 cocoa futures for 6 month delivery while the confectioner would instruct his broker to long 12 such contracts.

• At this point both parties would be fully hedged since in 6 months the confectioner knows he will have to pay exactly (RM1,000 x 12) = RM12,000 for the 120 tons of cocoa he needs while the farmer is assured of RM12,000 as payment for his cocoa.

• Notice that neither party needs to know who the counter party is. Yet, each party is assured of delivery/payment because the exchange (through its clearing house) becomes the counter party to both the farmer and confectioner.

• On registration of the trade, the clearinghouse guarantees the transaction. Assuming both parties hold their position to maturity, the cocoa futures contract will be settled on its maturity day (day 180) as follows.

Exchange DesignatedWarehouse

Cocoa Farmer(short)

Exchange(Clearing-

house)

Confectioner (Long)

Payment (4)

Cocoa

Warehouse receipt

(2)

(5)

(6)

Settlement of A Futures Contract

Numbers within brackets show the sequence of events

(3) w. receipt

Payment (4)

(3) w. receipt

Cocoa

Warehouse receipt

(1)

Example• Suppose in Feb, a crude palm oil producer anticipates that

he will have 200 metric tons of crude palm oil ready for sale in two months time. He would like to lock in the price of his crude palm oil. The current mkt price (Feb) is RM1,250 per metric ton. April crude palm oil futures is currently trading at RM1,265.

• His exposure to risk = price may fall between now (Feb) and the time of sale (April) = risk of price decline.

• Action: Sell futures (short position) of a specific number of contracts at a certain point in future

• = 200 tons/25 = 8 contracts• Contract Month: April

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• Assume in April the price of crude palm oil in the spot market has dropped to RM1,245/ton. So has the April futures (price convergence).

• The producer sells the CPO in the spot market for RM1,245 and also closes out the futures position by buying (long position) 8 futures contracts at RM1,245.

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Summary of the positions:Position Today Position at Maturity Gains/Loss

Cash Mkt Mkt price = RM1,250 Mkt price = RM1,245Action: sells 200 tons at RM1,245.Total sales = 200 x RM1,245 = RM249,000 RM249,000

Futures Mkt Mkt price = RM1,265Action: short futures = 8 contracts at RM1,265Total value of futures = 8 x 25 x RM1,265 = RM253,000

Close its position by buying 8 futures contract @RM1,245.Action: Long Futures = 8 x 25 x RM1,245= RM249,000 RM4,000

Total revenue RM253,000

Effective price per metric ton

RM1,265RM253,000 200 tons57

Example• Suppose in May, a crude palm oil refiner receives an order for a

800 met tons of refined PO to be delivered in Sept. He would like to lock in the price of his crude palm oil. The CPO futures for delivery in Sept is trading at RM1,270.

• Current spot price = RM1,265 (lower than futures price). However he does not have the available cash to buy now.

• His exposure to risk = price may increase in the future.• Action: Buy futures (long position) of a specific number of

contracts at a certain point in future • = 800 tons/25 = 32 CPO Sept futures contracts at RM1,270.• (he needs to pay only the initial margin)• This gives confidence to the oil refiner to quote the price to his

customers using known PO cost.

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Example

• In Sept, he purchases the 800 met tons of CPO in the spot market at RM1,278

• He closes out the futures position by selling (short position) 32 futures contracts at the current mkt price of RM1,278.

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Summary of the positions:Position Today Position at Maturity Gains/Loss

Cash Mkt Mkt price = RM1,265The refiner needs 800 met tons of CPO in Sept.

Mkt price = RM1,278Action: buys 800 tons at RM1,278.Total costs: = 800 x RM1,278 = RM1,022,400 (RM1,022,400)

Futures Mkt Mkt price = RM1,270Action: buy futures = 32 contracts at RM1,270Total value of futures = 32 x 25 x RM1,270 = (RM1,016,000)

Close its position by selling 32 futures contract @RM1,278.Action: sell Futures = 32 x 25 x RM1,278= RM1,022,400 RM6,400 (Pft)

Net costs (RM1,016,000)

Effective price per metric ton

RM1,270(RM1,016,000) 800 tons

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SPECULATORS• Have no personal or business interest in the commodity or

currency. They are trading futures contracts as a purely speculative investment or gamble.

• For example, an investor could take a position on a palm oil futures contract for March 2009 @ RM1,250 per metric ton, and they are not in the palm oil business, they have no interest in actually receiving or delivering palm oil at expiration. They are just taking a position on the price of palm oil in the future.

• Speculators can participate in futures trading because actual delivery is not required.

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SPECULATORS - EXAMPLE• If a speculator thinks that the cash price of

palm oil will go above RM1,250 sometime between now and June 2009, they take a LONG POSITION, and buy palm oil futures contracts. They are speculating that the P > RM1,250, and will make money if that happens. They buy @RM1,250 and hope to sell at P > RM1,250. Speculator is gambling (betting) that the price of palm oil will be > RM1,250.

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SPECULATORS - EXAMPLE

• If the speculator thinks that the cash price of palm oil will go below RM1,250/metric ton, he will take a SHORT POSITION, and sell palm oil futures. He will make money if P < RM1,250, they are betting that the price of palm oil will fall.

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Speculating with Futures Contract Speculators deal with price changes that occurred in

the market. They are motivated by the strong desire to make profit

on the transaction. They will buy the futures at low price and sell at high

price. The speculative traders in the futures market help to

fulfil a very important role. They provide the depth and volume of trading that allow hedgers and others to enter or exit the market easily.

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Three types of speculators

– The scalpers look out for minimum price fluctuations on heavy (large) volumes taking small profits at a time. They aim to make small profits on large volumes of transaction.

– The day traders do intraday trading and on small volumes of trade. The typical day trader would take long or short positions of a few contracts and would close-out their positions later in the day when the prices have moved.

– The position traders look for long-term price trends and may hold over weeks, or months before getting out.

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Using CPO Futures to Speculate

• Outright position speculative strategy – Takes a view of the change of the futures prices

and speculate on it– – refer to section 7.5.4.1 page 202

• Spread trading speculative strategy– Based on expectations of changes in relationship

between several futures contract– – refer to section 7.5.4.2 page 203

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EXERCISE:

• A trader takes a view that March FKLI which are currently trading at 1158.6 are about to enter a downtrend.– Should the trader go long or short futures.– Assuming that the trader maintains his position

until expiry and the cash settlement price is 1125.4, what will be the profit/loss.

• Profit = (1158.6-1125.5) x RM50 = RM1660

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EXERCISE• A palm oil producer firmly believes that the

price of crude palm oil is about to enter an uptrend. It is now October and the trader buys 6 November CPO futures at RM1,370. The margin for CPO is RM8,000 per contract.

• Calculate profit and loss on the transaction if the trader decides to close the contracts on day 5. The price of FCPO on day 1,2,3,4, and 5 are RM1,235, RM 1,350, RM1,370, RM1,400 and RM 1,398 respectively.

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EXERCISE

• Suppose in March, the April FCPO contract is trading at RM1,225 while the May contract is trading at RM1,100. Assume that between March and April, FCPO fell quite sharply. The trader anticipates that the spread to be narrowed.

• Outline the strategy that the trader should take.• Assume that April FCPO is traded at RM1140 upon

maturity, calculate the profit/loss if the spread between April FCPO and May FCPO is 70 points.

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• Spread Narrow

• Buy May FCPO and Sell April FCPO• Profit/Loss = (1210-1100) + (1225-1140)

= 195 X 25 = 4875

70

1225

1100

Spread 70 points

Price

Time

Arbitraging with Futures Contract

Arbitrage is simultaneous purchase and sale of the same instrument in different markets to profit from the temporary price differences or inconsistencies. How did arbitrage ensure price convergence? An arbitrage is a trade that involves buying in the physical market and selling at the futures market at a higher price. A trader who initiate the arbitrage if observes the prices are traded above the ‘fair values’ will act on by selling the futures where the prices are high and pushes the price back to the fair value as determined in the physical market. Provide liquidity and ensuring the price of cash and futures converges at the expiry date of the contract.

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Fair value of futures price using cost of carry model

tycrSF )1(

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whereF = futures price for a contract with maturity from

time t to T at maturityS = cash or spot price of the underlying assetr = annualised risk-free interest rate (a proxy for

opportunity cost)c = annualised cost of storage (%) (inclusive of

shipping, handling, shrinkage, spoilage or damaged, etc)

y = convenience yield on the cash commodityt = time to futures expiry expressed on yearly

basis

Fair value of futures price using cost of carry model

• Example:• Spot price = RM1,275• Storage = RM5 per month• Risk-free rate = 4%• 1-month Futures contract = RM1000

• Theoretical Fair price: F = RM1,275 (1 + 0.04 + 5x12/1,275) 30/365

= RM1,283.7873

• Is it possible to make a gain if the actual futures price is lower than the fair price? If so, describe the strategy a trader could use in this situation.

• If the 1-month FCPO is traded at RM1500. Calculate the PL if any.

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Using CPO Futures to Arbitrage

• Find the fair value of the futures price• If the actual futures price > fair value, overpriced position

– sell futures and buy the spot or physical market• If the actual futures price < fair value, underpriced

position – buy futures and sell the spot or physical market• An illustration of how to calculate fair value of the CPO

futures – page 204• Table 7.7 shows the outcome of arbitraging.

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Example

• In March, the spot price for CPO is RM975. If the cost of storage is RM 5 per month and the risk free rate is 5%, what is the upper limit for the April futures price assuming the contract expires in one month?

• FV = 975([1+(0.05 )] + [(5*12/975)])30/365

= 983.51 FV April FCPO[ April FCPO should trade above this limit]

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• Assume that April FCPO are currently trading at RM1000 per tonne.

• Arbitrage opportunity exist coz April futures are not correctly priced, OVERVALUE

• Strategy;Today;Sell April FCPO at RM1000/t coz overvalueBuy CPO at RM975/t; store at RM5 per month.Upon maturity, deliver CPO to buyer and receive RM1000/t.

Profit: 1000 – 975 – 5 = RM20/t

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EXERCISE

• Today is early October. You believe that quotations of FKLI are mismatched. Currently the spot index is quoting at 990 while November FKLI at 1060. You expect average dividend yield of 3.5% and risk free rate of 6.5% per annum, show your arbitrage activity and profit if both indices converged at 1020 in the last day of November for RM5 million funds.

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tycrSF )1(

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F = 990 (1+ 6.5% + 0 – 3.5%)61/365

F = 994.90

Overpriced:

Today: Sell 94 Nov FKLI @ 1060 Buy RM5 million shares @ 990. Hold temporarily

Later: Buy 94 Nov FKLI @ 1020 Sell shares that worth

( 5M + ( 1020-990/990)5M= 5151515.152

Arbitrage ProfitDescription Profit

Futures Profit (1060-1020) x 94 x 50 188000

Cash Portfolio profit

[(1020-990)/990 ] x 5M 151515

Interest exp 6.5% x 5 M x 61/365 (54315)

Div yield 3.5% x 5M x 61/365 29247

TOTAL 314447

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EXERCISE

• Your bank is willing to finance the purchase of physical shares for 3M through arbitrage activity. You observe that the spot index is currently trading at 965 while July FKLI at 1088. Assuming your cost of funds is 7.5% per annum and dividend yield of 4.5% for 90 day’s holding. Show your arbitrage profit (if any) if July FKLI converge with KLCI at 1050 upon maturity.

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• F = 972.05

• No of Contract = 3M /(1088 x 50) = 55 contracts• Today

– Sell 55 July @ 1088– Buy RM 3M shares on a borrowed funds CI 965

• Later– Buy 55 July @ 1050– Sell Shares @ [3M+(1050-965/965)x3M]= 3,264,248.70– Receive dividend for 90 days– Pay interest for 90 days

• Profit– (3,264,248.70 -3M) + (4.5% x 3M)90/365 – (7.5%x3M)90/365 +

(1088 – 1050)55 x 50– = 82

Example;

• Suppose you observe the following quotations today.• 3-month FKLI price = 1,210• Index value = 1,200 pts• rf rate = 4%• Dividend Yield = 2%• Time to maturity of SIF = 90 days

• To see if arbitrage is possible we first check for mispricing. The correct value of the 3-month FKLI should be;

• Ft = 1,200 (1+.04-.02)0.25= 1,200 (1.02)0.25 = 1,205.96 points

Given the above information, the futures is clearly overpriced relative to spot. The futures price should be 1,205.96 points, yet it is quoted at 1,210 points. Overpriced by approximately 4 points.

Since there is mispricing, arbitrage is possible. By using the following arbitrage strategy a riskless profit can be made. (Note that no cash outlay is needed today

we will look at 2 market scenarios. (Note: current stock index value is 1,200 pts)

• Index Rises to 1225 at maturity• Index Falls to 1175 at maturity

Scenario 1: Index Rises to 1225Cash & Carry Arbitrage

Action Position Today

Position At Maturity

Profit/Loss

(I) Short 1 FKLI Contract

60,500(1210 x 50)

(61,250) (750)

(I) Long Spot (60,000) 61,250 1,250

(I) Borrow RM60,000 @ 4% for 90 days.

60,000 (60,591.20) (591.20)

(I) Receive divs. and invest it @ 4% for 90 days.

0 303 303

Net = 211.80

Scenario 2: Index Falls to 1175Cash & Carry Arbitrage

Action Position Today

Position At Maturity

Profit/Loss

(I) Short 1 FKLI Contract

60,500 (58,750) 1,750

(I) Long Spot (60,000) 58,750 (1,250)

(I) Borrow RM60,000 @ 4% for 90 days.

60,000 (60,591.20) (591.20)

(I) Receive divs. and invest it @ 4% for 90 days.

0 303 303

Net = 211.80

Reverse Cash and Carry Arbitrage

Suppose in the above example, the Futures price today is quoted as;3-month SIF price = 1201

Now, the SIF is underpriced relative to spot. In order to arbitrage we need to do the reverse of the earlier strategy

The following reverse Cash and Carry arbitrage would be appropriate here

Index Rises to 1225

Action Position Today

Position At Maturity

Profit/Loss

(I) Long 1 SIF Contract 60,050 61,250 1,200

(I) Short Spot 60,000 (61,250) (1,250)

(I) Lend RM60,000 @ 4% for 90 days.

(60,000) 60,591.20 591.20

(I) Borrow RM300 @ 4% to replace divs. on borrowed shares (shorted).

0 (303) (303)

Net = 238.20

Index Falls to 1175

Action Position Today

Position At Maturity

Profit/Loss

(I) Long 1 SIF Contract 60,050 58,750 (1,300)

(I) Short Spot 60,000 (58,750) 1,250

(I) Lend RM60,000 @ 4% for 90 days.

(60,000) 60,591.20 591.20

(I) Borrow RM300 @ 4% to replace divs. on borrowed shares (shorted).

0 (303) (303)

Net = 238.20

Single Stock Futures (SSFs)

• SSFs are based on individual stocks listed in Bursa Malaysia and therefore, it tracks the movement of the individual underlying stock.

• As of now, there are 9 SSF contracts.• The contract specification – refer to Table

7.10 page 213.

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