e.g. sugar, grain, gold, oil, financial assets, e.g. stock indices, stock prices, and
Treasury ..... so that a profit of (2.1000 − 2.0470) × 250, 000 = 13, 250B is made.
Financial Markets and Products
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FRM 2013 Notes Preparation
Bibliography [1] John Hull, Options, Futures, and Other Derivatives, 8th Edition, Chapter 1: Introduction. New York: Pearson Prentice Hall, 2012. [2] John Hull, Options, Futures, and Other Derivatives, 8th Edition, Chapter 2: Mechanics of Futures Markets. New York: Pearson Prentice Hall, 2012.
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[3] John Hull, Options, Futures, and Other Derivatives, 8th Edition, Chapter 3: Hedging Strategies Using Futures. New York: Pearson Prentice Hall, 2012. [4] John Hull, Options, Futures, and Other Derivatives, 8th Edition, Chapter 4: Interest Rates. New York: Pearson Prentice Hall, 2012.
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[5] John Hull, Options, Futures, and Other Derivatives, 8th Edition, Chapter 5: Determination of Forward and Futures Prices. New York: Pearson Prentice Hall, 2012. [6] John Hull, Options, Futures, and Other Derivatives, 8th Edition, Chapter 6: Interest Rate Futures. New York: Pearson Prentice Hall, 2012.
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[7] John Hull, Options, Futures, and Other Derivatives, 8th Edition, Chapter 7: Swaps. New York: Pearson Prentice Hall, 2012. [8] John Hull, Options, Futures, and Other Derivatives, 8th Edition, Chapter 10: Properties of Stock Options. New York: Pearson Prentice Hall, 2012. [9] John Hull, Options, Futures, and Other Derivatives, 8th Edition, Chapter 11: Trading Strategies Involving Options. New York: Pearson Prentice Hall, 2012. [10] Robert McDonald, Derivatives Markets, 3rd Edition, Chapter 6: Commodity Forwards and Futures. Boston: Addison-Wesley, 2013. [11] Helyette Geman, Commodities and Commodity Derivatives: Modeling and Pricing for Agri-
culturals, Metals and Energy, Chapter 1: Fundamentals of Commodity Spot and Futures Markets: Instruments, Exchanges. West Sussex, England: John Wiley & Sons, 2005. [12] Anthony Saunders and Marcia Millon Cornett, Financial Institutions Management: A Risk Management Approach, 7th Edition, Chapter 14: Foreign Exchange Risk. New York: McGraw-Hill, 2011. [13] Frank Fabozzi, The Handbook of Fixed Income Securities, 8th Edition, Chapter 12: Corporate Bonds, by Frank Fabozzi, Steven Mann and Adam Cohen. New York: McGraw-Hill, 2012. [14] Caouette, Altman, Narayanan, and Nimmo, Managing Credit Risk, 2nd Edition, Chapter 6: The Rating Agencies. New York: John Wiley & Sons, 2008. 2
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1.1 Trading in the markets . . . 1.2 Derivatives . . . . . . . . . 1.2.1 Forward Contracts . 1.2.2 Futures contracts . . 1.2.3 Options . . . . . . . 1.3 Option and forwards payos 1.3.1 Forward payo . . . 1.3.2 Options payos . . . 1.4 Payos of hedging strategies 1.4.1 Forwards . . . . . . 1.4.2 Options . . . . . . . 1.5 Speculative payos . . . . . 1.5.1 Futures . . . . . . . 1.5.2 Options . . . . . . . 1.6 Arbitrage payos . . . . . . 1.7 Risks of the derivatives . . .
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1 Introduction
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4 5 5 5 5 6 6 8 10 10 10 11 11 11 12 13
Chapter 1
Introduction
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1.1 Trading in the markets
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AIM 1.1 Dierentiate between an open outcry system and electronic trading.
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An open out-cry system lets traders meet physically in the trade oor and execute their trades through shouting and hand signals. An electronic trading system lets traders enter their desired trades through a computer and then an algorithm matches the dierent trades, i.e. buyers and sellers.
AIM 1.2 Describe the over-the-counter market, how it diers from trading on
an exchange, and its advantages and disadvantages
A derivatives exchange is a market where individuals trade standardized contracts whose terms have already been de ned by the exchange market. The over-the-counter (OTC) market is a telephone and computer linked network of dealers where trades are given through the phonenetwork and they are usually taped/recorded in order to avoid any disputes that might arise. OTC market is not a formal exchange and there are no membership requirements for trading or listing requirements for securities. Security dealers quote prices at which they are willing to buy or sell securities and a broker executes a trade by contacting the dealer listing a quote. The basic dierences between OTC and exchange traded markets are: •
Size of trades: Trades are much larger in OTC markets than in exchange traded markets. 4
1.2. DERIVATIVES
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Format of contracts: In exchange traded markets are traded standardised contracts while in OTC are traded customised contracts which are set by the counterparties.
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Credit Risk: There is credit risk involved in the way contracts are traded in the OTC markets, i.e. contracts might not be honoured.
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Size of counterparties: In the OTC markets, usually the trading parties are large organ-
isations, while in exchange traded markets participate both organisations and individuals with scarce resources.
1.2 Derivatives
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AIM 1.3 Dierentiate between options, forwards, and futures contracts.
1.2.1 Forward Contracts
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A forward contract is the simplest form of a derivative contract, as it is an agreement to buy (sell) an asset at a speci ed time in the future, for a speci ed price. This type of contracts is traded usually in the OTC markets and they are used mostly in the foreign exchange market. For a forward contract there are required two parties: The party that assumes a long position and promises to buy the asset in the speci ed price at a speci ed time. And the party that assumes a short position and promises to sell the asset in the speci ed price and speci ed time. Forward prices are aected by supply and demand as in any other security. Forwards contracts are held till maturity.
1.2.2 Futures contracts
Futures contracts are similar to the forward contracts, that is they are also agreements between two parties to buy (sell) an asset in a speci ed time and price in the future. However, futures contracts are more standardized and they are traded in the exchange-traded market. The latter means futures contracts have less credit risk, as the exchange market speci es the characteristics of the futures contracts and they also make sure that the terms of the contracts will be honoured through a mechanism, i.e. clearing house . Futures contracts are used when trading commodities, e.g. sugar, grain, gold, oil, nancial assets, e.g. stock indices, stock prices, and Treasury bonds.
1.2.3 Options An option gives the right to its holder to buy or sell an asset at a speci ed time, at a speci ed price. When buying, the option is known as call option . An option that gives the right to its holder of selling an asset is known as put option . The speci ed price in the contract is known c Themellion 2012-2013 ⃝
6
1. INTRODUCTION
as the exercise or strike price and the speci ed date as maturity or expiration date . Options are traded on both the OTC and exchange traded markets. There are two broad categories of options: European and American options can be exercised any time before the expiration date while European can be exercised only at the maturity. A basic dierence between options and the other derivatives, i.e. forwards and futures, is the price the buyer needs to pay in order to acquire an option, i.e. option premium .
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1.3 Option and forwards payos
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1.3.1 Forward payo
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AIM 1.4 Calculate and identify option and forward contract payos.
The payo from a long position in a forward contract (on one unit of asset) is represented as the dierence between the spot price at maturity date, i.e. PT and the delivery price , i.e. K . PT − K
(1.1)
The holder of the forward contract is obligated to buy the asset underlying the forward contract in price K . If the spot price at the maturity date is higher than the delivery price he will achieve a gain equal to the dierence of these two prices, i.e. he can buy the asset in price K and sell it in price PT . However, if the spot price is less than the delivery price the holder will face a loss equal to the dierence between the two prices, i.e. he will buy an asset in price K while it is traded in the market in a lower PT price. Figure 1.1(a) shows that as long as the spot price at the maturity date is higher than the delivery price, i.e. values right of K , the holder of the forward contract will get a pro t. However, if the spot price at the maturity date is less than the delivery price, i.e. values left of K , then the holder of the contract will face a loss. c Themellion 2012-2013 ⃝
1.3. OPTION AND FORWARDS PAYOFFS
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Net P&L per share
Net P&L per share
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.
K
Share price at maturity (a) Forward Contract: Long Position
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Share price at maturity (b) Forward Contract: Short Position
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Figure 1.1: Forward contracts payos The payo from a short position can be de ned in a similar way: K − PT
(1.2)
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In this case, the holder of the asset is required to sell the asset in a speci ed price, at a speci ed time. So, if the delivery price is higher than the spot price at the maturity date, the holder is achieving a pro t as he sells the asset in a higher price than the current market price. However, if the delivery price is lower than the spot price the holder is having a loss as he sells the underlying asset in a lower - than the market - price. Figure 1.1(b) shows that when the spot price at the maturity date is higher than the delivery price, (values right of K ) the holder of the forward contract is facing a loss. When the spot price is lower than the delivery price, the holder will gain from this dierence.
Example 1.1 Forward Contract Payo
Table 1.1: Spot and forward quotes for the USD/EUR exchange rate, December 3, 2011 (EUR = Euro; USD = US Dollar; quote is number of EUR per USD). Bid Ask Spot 1.3407 1.3415 1-month forward 1.3380 1.3385 3-month forward 1.3360 1.3365 6-month forward 1.3354 1.3359 c Themellion 2012-2013 ⃝
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1. INTRODUCTION
Question: Based on Table 1.1, an investor can buy EUR in the spot market, on December 3,
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2011, at the rate of $1.3407 and sell EUR in the spot market at $1.3415 per EUR. Based on the same table, an investor is prepared to buy EUR in 1, 3 and 6 months at $1.3380, $1.3360 and $1.3354 respectively and to sell EUR in 1, 3, and 6 months at $1.3385, $1.3365 and $1.3359 per EUR respectively. Can you estimate the payos for a company that enters into a forward contract on December 3, 2011, to buy EUR 1 million after 6 months, assuming: (a) the spot price of USD/EUR at the end of the 6-month period is 1.35 and (b) the spot price of USD/EUR is 1.32. Answer: (a) If on December 3, 2011 company A enters into a forward contract to buy EUR 1 million after 6 months, that means that company A has agreed that it will buy EUR 1 million from the bank for $1.3359 million and the bank has agreed to sell EUR 1 million to Google for USD 1.3359 million. If at the end of 6 months the spot price of USD/EUR rose to 1.35 the forward contract would be worth (1.351.3359) × 1, 000, 000 = $14, 100 to company A as the later will buy EUR at a lower price. (b) If the spot price fell to 1.32 at the end of the 6 months then the forward contract will have a value equal to (1.321.3359) × 1, 000, 000 = −$15, 900 as company A will make the transaction on a price higher than the current market price.
1.3.2 Options payos
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In table 1.2 are given the bid and oer quotes for some of the American options trading on Google on December 2, 2011. The Google stock price at the time of the quotes was $620.36.
Example 1.2 Options Contract Payo Table 1.2: Prices of options on Google, December 3, 2011; stock price = USD 620.36. Calls Puts Strike Price ($) Dec-2011 Jan-2012 Mar-2012 Dec-2011 Jan-2012 Mar-2012 275.00 273.50 315.10 299.50 0.05 0.03 0.11 300.00 263.50 317.25 298.00 0.05 0.10 0.20 350.00 195.00 253.70 250.00 0.05 0.05 1.17 400.00 221.00 222.00 222.20 0.05 0.24 1.35 450.00 160.50 168.33 146.20 0.11 0.70 3.30 500.00 112.29 122.53 128.85 0.18 2.30 7.60
Based on Table 1.2 it can be said that: c Themellion 2012-2013 ⃝
1.3. OPTION AND FORWARDS PAYOFFS
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•
as the strike price increases the price of the call option decreases
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as the maturity date of the option is extended the call option becomes more valuable. The same eect is observed for the put option also
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as the strike price is increasing, the price of the put option is moving to the other direction.
Investors who buy call options are expecting that the price of the underlying asset will go up, and they will bene t from the dierence between the strike price of the option and the spot price at maturity date. For an example, an investor who buys one March call option on Google with a strike price of $500.00, will exercise this option only if the spot price raises above $500.00. If the spot price is $ then the pro t would be: ($650.00−$500.00) = ×100$15, 000.
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Investors who buy put options will exercise their contracts only if the spot price at the maturity date is lower than the strike price. An investor who purchases a March put option contract with a strike price $450.00, will exercise this contract only if Google share price falls below $450.00, e.g. $400.00, and the pro t would be (100 × $450.00 - $400.00) - $330 = $4,670.
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Net P&L per share
Net P&L per share
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Figure 1.2 below indicate the example payos when buying a call contract and selling a put option contract respectively. In Figure 1.2(a) is shown that as long as the share price at the maturity is below the strike price there is no reason to execute the call option. In Figure 1.2(b), it is shown that if the strike price is over the spot price at maturity there is a loss, while the spot price is over the strike price the investor who sold the put option can hold the revenues from selling the put contract.
Share price at maturity (a) Call option payo
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K
Share price at maturity (b) Put option payo
Figure 1.2: Forward Contract: Short Position c Themellion 2012-2013 ⃝
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1. INTRODUCTION
1.4 Payos of hedging strategies AIM 1.5 Describe, contrast, and calculate the payos from hedging strategies
involving forward contracts and options.
1.4.1 Forwards
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Using the data from table 1.1, let's assume that on December, 3, 2011 Amazon US knows that it will have to pay e10 million after 3 months, i.e. on March, 3, 2012, for goods it has purchased from a European supplier. Amazon US could hedge its foreign exchange risk by getting into a 3-month forward agreement and agreeing to buy e10 million for $13.365 million. If the exchange rate on March 3, 2012 is 1.25, the e10 million that Amazon has to pay will cost $12.5 million which is less than the hedged $13.365 million. If the exchange rate on March 3, 2012 is 1.45 then the e10 million will cost $14.5 million.
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Suppose that on December, 3, 2011 Amazon US knows that will receive e10 million 3 months later. Amazon US can hedge its currency risk by selling e10 million and entering a 3-month forward contract. According to table 1.1, Amazon US can sell e10 million at a rate of 1.3360. This would mean that Amazon US locks the amount to receive at $13.360 million. If the exchange rate on March 3, 2012 is lower than 1.3360 and Amazon US has not entered into a forward agreement in order to hedge the currency risk this will mean a loss. On the other hand, if the exchange rate on the expiration date is higher than 1.3360 and Amazon US has not entered into a forward agreement this will create a pro t. From the analysis above it can be said that use of hedging strategies does not guarantee the full protection of the hedger.
1.4.2 Options
Options can be used for hedging also. If an investor holds 1,000 stocks of Google on December 3, 2011 while the current price is $550.00 and expects it will be a drop of its share price in the following three months, in order to protect him he can buy 10 put option contracts of Google share with a strike price at $500.00 for $7.60 per option contract. The cost of his hedging strategy would be 7.60 × 100 × 10 = $7,600. The strategy costs $7,600 but it guarantees that each share cannot be sold less than $500.00. If the share price falls below $500.00 then the option is exercised. For example, if the share price falls to $480, then the investor can exercise the put option he holds and make a pro t of: ($500 − $480) × 1, 000 = $20, 000. If deduct the option premium paid then he has made a pro t of ($20, 000 − $7, 600) = $12,400. However, as long as the share price remains over $500.00 there is no meaning for exercising the option and the option expires worthless.
The main dierence between forward contracts and options contracts when used c Themellion 2012-2013 ⃝
1.5. SPECULATIVE PAYOFFS
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for hedging is that the former category is used to neutralise risk by locking the price of the underlying asset into a speci c level, while the option contracts are very similar to auto insurance, as they oer a way to investors to protect themselves against
adverse price movements in the future by paying a low premium. The insurance can be exercised only when it does make sense for the holder of the option.
1.5 Speculative payos AIM 1.6 Describe, contrast, and calculate the payos from speculative strategies
involving futures and options.
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1.5.1 Futures
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Speculation refers to the actions taken by traders in order to take advantage of future changes in asset prices. For example, a speculator who in time t expects currency A will be higher relative to currency B after 2 months and decides to buy currency A, has two options: (a) purchase currency A in the spot market and sell it after two months on a higher price, and (b) take a long position in N futures contracts on currency A (where each futures contract is for the purchase of Z currency A units). If the current exchange rate is 2.0470B per currency A and the futures price after two months is 2.0410B per currency A, then if the exchange rate in the spot market is 2.1000B per currency A after two months, under strategy (b) the futures contract alternative enables the speculator to realise a pro t of (2.100−2.0410)×250, 000 = 14, 750B . Under strategy (a) 250,000 units of an asset are being purchased for 2.0470B in time t and sold for 2.1000B after two months, so that a pro t of (2.1000 − 2.0470) × 250, 000 = 13, 250B is made. If the exchange rate falls to 2.000B per currency A, strategy (b) provides a loss of (2.0410 − 2.000) × 250, 000 = 10, 250B , whereas strategy (a) gives rise to a loss of (2.0470 − 2.0000) × 250, 000 = 11, 750B , assuming no interest received or paid. The main dierence of these two strategies is the amount required to be paid upfront, as strategy A requires a signi cant amount to be paid upfront while strategy B requires only a small amount of cash to be deposited by the speculator in what is termed a "margin account ". The futures market allows the speculator to obtain leverage.
1.5.2 Options Suppose that in time t a speculator considers that a stock will increase in value over the next 2 months. The stock price is currently $20, and a 2-month call option with a $22.50 strike price is currently selling for $1. Assuming there are two possible alternatives and that the speculator c Themellion 2012-2013 ⃝
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1. INTRODUCTION
is willing to invest $2,000: (a) purchase 100 shares, and (b) purchase 2,000 call options (i.e., 20 call option contracts). If the price of the stock rises to $27 after two months then under option (a) it yields a pro t of (100 × $27-$20)=$700.Under strategy (b) the total payo from the 2,000 options is 2, 000 × $4.50=$9,000 (or $7,000 when subtracting option premiun). In the same way potential pro ts from options can be big, so can be potential losses. So, if stock price after two months is 15$ then under strategy (a) the loss is $500 while under strategy (b) the loss is equal to the cost of options, i.e. $2,000, as there is no meaning to exercise the options.
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1.6 Arbitrage payos
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Futures and options are similar instruments for speculators as both oer some kind of leverage. In futures case, potential losses and pro ts are large, while for options contracts, losses are limited to the cost of the options.
AIM 1.7 Calculate an arbitrage payo and describe how arbitrage opportunities
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are ephemeral.
Arbitrage involves locking in a riskless pro t by simultaneously entering into transactions in two or more markets. Stocks that are listed in two stock markets usually become target of arbitrageurs. For example, a stock that is traded on two stock markets, e.g. New York and London, with a current stock price of $200 in New York and ¿100 in London at a time when the exchange rate is $2.0300 per pound, an arbitrageur could simultaneously buy 100 shares of the stock in New York and sell them in London to obtain a risk-free pro t of: [(100 × $2.03 × 100) − $200] or $300 in the absence of transactions costs. Arbitrage opportunities such as the one just described cannot last for long. As arbitrageurs buy the stock in New York, the forces of supply and demand will cause the dollar price to rise. Similarly, as they sell the stock in London, the sterling price will be driven down. Very quickly the two prices will become equivalent at the current exchange rate. Indeed, the existence of pro t-hungry arbitrageurs makes it unlikely that a major disparity between the sterling price and the dollar price could ever exist in the rst place. In practice only very small arbitrage opportunities are observed in the prices that are quoted in most nancial markets. c Themellion 2012-2013 ⃝
1.7. RISKS OF THE DERIVATIVES
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1.7 Risks of the derivatives AIM 1.8 Describe some of the risks that can arise from the (mis)use of deriva-
tives. •
Versatility: Due to their versatile nature, derivatives can be used for a dierent purpose than what was intended. For example, traders that have been asked to execute a hedging strategy can become speculators very easily.
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Underestimate potential losses: Due to the complex nature of derivatives and the
Summary 1 The basic points of this chapter are:
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interconnected global economy, rms can easily underestimate potential losses from trading derivative contracts.
Trades can be executed either on an open out-cry system or on an electronic trading. In the rst category traders are meeting in a trade- oor and through hand signals and shouting are looking to carry out their trades. Through electronic trading trades are being executed with the help of a computer and algorithm.
•
Derivatives are traded either in over-the-counter markets (OTC) or in exchange traded markets. In OTC markets, participants can buy or sell contracts in non-standardised form, while in exchange traded markets participants can only buy or sell contracts whose terms and conditions have already been prespeci ed by the market. OTC markets are popular for large traders from institutions. The fact that non-standardised contracts are being traded in the OTC markets, makes them of higher credit risk.
•
There are three main categories of derivatives: forwards, futures and options. First two are very similar. Their main dierences are that forward contracts are less standardised than futures and are being traded in the OTC markets while futures in the exchange traded markets. Also,forward contracts are held till maturity while futures are being rolled over forward. Forwards are being used mostly for currency while futures for commodities like gold, sugar, and oil.
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Options are being traded in both OTC and exchange traded markets. Their main dierence compared to the other two categories of derivatives is that option involves a fee, i.e. premium, and option holder is not obliged to exercise the contract in the maturity date unless it is pro table.
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c Themellion 2012-2013 ⃝
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1. INTRODUCTION
In forward contracts, when someone is going long, she can be pro table when the spot price in the delivery date is higher than the delivery price. Short positions are pro table when the spot price in the delivery date is less than the delivery price.
•
There are three main groups of derivative traders: hedgers, speculators, and arbitrageurs. Hedgers use either forwards or options to protect themselves from unexpected movements in the price of the underlying asset. The main dierence between options and forwards during a hedging strategy is that forwards lock the price in a speci c level, while options behave like auto insurance where the insurance can be exercised only if there is a need. Buying this insurance has a cost, i.e option premium, while forwards do not include this kind of cost, however they do not guarantee success of the hedging strategy.
•
Speculators can use futures or options to gain pro ts from speculating on an asset price. Potential gains or losses from the use of futures by a speculator are huge, while options' potential losses are limited to the cost of the options contracts. Also, through the use of futures it is only required to make a much smaller initial investment thatn when buying the same security in the spot market.
•
Arbitrage refes to the case where the same stock could be listed in two dierent stock markets, and traders could take advantage of "ine ciencies" between the currencies used in the two stock markets.
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•
c Themellion 2012-2013 ⃝
Index American options, 6 arbitrage, 12 call option, 5 clearing house, 5
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delivery price, 6 derivatives exchange, 4
forward contract, 5 futures contracts, 5
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margin account, 11 maturity date, 6
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electronic trading, 4 European options, 6 exercise price, 6
open out-cry, 4 option, 5 option premium, 6 over-the-counter (OTC) market, 4 put option, 5
short position, 7 spot price, 6
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