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Introduction
Chapter 1
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This first lecture has four main goals:1. Introduce you to the notion of risk and the role of derivatives in
managing risk.Discuss some of the general terms – such as short/long positions, bid-ask spread – from finance that we need.
2. Introduce you to three major classes of derivative securities.ForwardsFuturesOptions (calls and puts)
3. Introduce you to the basic viewpoint needed to analyze these securities.
4. Introduce you to the major traders of these instruments.
Basics
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Basics
Finance is the study of risk.How to measure itHow to reduce itHow to allocate it
All finance problems ultimately boil down to three main questions:What are the cash flows?When do they occur?What is the appropriate discount rate for those cash flows? I.e., how uncertain are those cash flows?
The difficulty, of course, is that normally none of those questions have an easy answer.
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BasicsRisk :
Diversifiable – risk that is specific to a specific investment – i.e. the risk that a single company’s stock may go down. This is frequently called idiosyncratic risk.Non-diversifiable – risk that is common to all investing in general and that cannot be reduced – i.e. the risk that the entire stock market (or bond market, or real estate market) will crash. This is frequently called systematic risk.
The market “pays” you for bearing non-diversifiable risk only – not for bearing diversifiable risk.
In general the more non-diversifiable risk that you bear, the greater the expected return to your investment(s).Many investors fail to properly diversify, and as a result bear more risk than they have to in order to earn a given level of expected return.
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Basics
In this sense, we can view the field of finance as being about two issues:
The elimination of diversifiable risk in portfolios;The allocation of systematic (non-diversifiable) risk to those members of society that are most willing to bear it.
Indeed, it is really this second function – the allocation of systematic risk – that drives rates of return.
The expected rate (in excess of the risk-free rate) of return is the “price” that the market pays investors for bearing systematic risk.
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Basics
So why do we have derivatives and derivatives markets?They permit transfer of risk (like insurance).They make risk transfer (and speculation, and investment) cheaper.
Lower transaction costsMinimize taxesAvoid regulatory constraintsSimplify credit problemsLump many transactions together
In other words, they get around market imperfections
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A First Example
There is a neat example from the bond-world of a derivative that is used to move non-diversifiable risk from one set of investors to another set that are, presumably, more willing to bear that risk.
Disney wanted to open a theme park in Tokyo, but did not want to have the shareholders bear the risk of an earthquake destroying the park.
They financed the park through the issuance of earthquake bonds.If an earthquake of at least 7.5 hit within 10 km of the park, the bonds did not have to be repaid, and there was a sliding scale for smaller quakes and for larger ones that were located further away from the park.
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A First Example
Normally this could have been handled in the insurance (and re-insurance) markets, but there would have been transaction costs involved. By placing the risk directly upon the bondholders Disney was able to avoid those transactions costs.
This was not a “free” insurance. Disney paid a premium on the bond--if the earthquake provision was not there, they would have paid a lower rate. Still, this premium was cheaper than the transactions costs of the alternative insurance strategy.
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A First Example
This example illustrates an interesting notion – that insurance contracts (for property insurance) are really derivatives!They allow the owner of the asset to “sell” the insured asset to the insurer in the event of a disaster.
Although the risk of earthquake is not diversifiable to the park, it could be to Disney shareholders, who (presumably) own well-diversified real estate portfolios.
They are like put options.
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Basics
Market Efficiency – We normally talk about financial markets as being efficient information processors.
Markets efficiently incorporate all publicly available information into financial asset prices.The mechanism through which this is done is by investors buying/selling based upon their discovery and analysis of new information.The limiting factor in this is the transaction costs associated with the market.For this reason, it is better to say that financial markets are efficient to within transactions costs. Some financial economists say that financial markets are efficient to within the bid-ask spread.Now, to a large degree for this class we can ignore the bid-ask spread, but there are some points where it will be particularly relevant, and we will consider it then.
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Basics
Before we begin to examine specific contracts, we need to consider two additional risks in the market:
Credit risk – the risk that your trading partner might not honor their obligations.
Familiar risk to anybody that has traded on ebay!Generally exchanges serve to mitigate this risk.Can also be mitigated by escrow accounts.
Margin requirements are a form of escrow account.Liquidity risk – the risk that when you need to buy or sell an instrument you may not be able to find a counterparty.
Can be very common for “outsiders” in commodities markets.
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The Nature of Derivatives
A derivative is an instrument whose value depends on the values of other more basic underlying variables
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Examples of Derivatives
Forward ContractsFutures Contracts SwapsOptions
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Derivatives Markets
Exchange tradedTraditionally exchanges have used the open-outcry system, but increasingly they are switching to electronic tradingContracts are standard there is virtually no credit risk
Over-the-counter (OTC)A computer- and telephone-linked network of dealers at financial institutions, corporations, and fund managersContracts can be non-standard and there is some small amount of credit risk
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Ways Derivatives are Used
To hedge risksTo speculate (take a view on the future direction of the market)To lock in an arbitrage profitTo change the nature of a liabilityTo change the nature of an investment without incurring the costs of selling one portfolio and buying another
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Forward Contracts
A forward contract is an agreement to buy or sell an asset at a certain time in the future for a certain price (the delivery price)It can be contrasted with a spot contract which is an agreement to buy or sell immediatelyIt is traded in the OTC market
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Foreign Exchange Quotes for GBP on Aug 16, 2001 (See page 3)
Bid Offer
Spot 1.4452 1.4456
1-month forward 1.4435 1.4440
3-month forward 1.4402 1.4407
6-month forward 1.4353 1.4359
12-month forward 1.4262 1.4268
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Forward PriceThe forward price for a contract is the delivery price that would be applicable to the contract if were negotiated today (i.e., it is the delivery price that would make the contract worth exactly zero)The forward price may be different for contracts of different maturities
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Terminology
The party that has agreed to buy has what is termed a long positionThe party that has agreed to sell has what is termed a short position
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Example (page 3)
On August 16, 2001 the treasurer of a corporation enters into a long forward contract to buy £1 million in six months at an exchange rate of 1.4359This obligates the corporation to pay $1,435,900 for £1 million on February 16, 2002What are the possible outcomes?
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Profit from aLong Forward Position
Profit
Price of Underlyingat Maturity, STK
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Profit from a Short Forward Position
Profit
Price of Underlyingat Maturity, STK
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Futures Contracts
Agreement to buy or sell an asset for a certain price at a certain timeSimilar to forward contractWhereas a forward contract is traded OTC, a futures contract is traded on an exchange
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Examples of Futures Contracts
Agreement to:buy 100 oz. of gold @ US$900/oz. in December (COMEX) sell £62,500 @ 1.5000 US$/£ in March (CME)sell 1,000 bbl. of oil @ US$100/bbl. in April (NYMEX) (a bbl. (barrel) of oil is 42 gallons.)
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1. Gold: An Arbitrage Opportunity?
Suppose that:- The spot price of gold is US$900- The 1-year forward price of gold is
US$1020- The 1-year US$ interest rate is 5% per
annumIs there an arbitrage opportunity?
(We ignore storage costs and gold lease rate)?
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2. Gold: Another Arbitrage Opportunity?
Suppose that:- The spot price of gold is US$900- The 1-year forward price of gold is
US$900- The 1-year US$ interest rate is 5%
per annumIs there an arbitrage opportunity?
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The Forward Price of GoldIf the spot price of gold is S and the forward price for a contract deliverable in T years is F, then
F = S (1+r )T
where r is the 1-year (domestic currency) risk-free rate of interest.In our examples, S = 900, T = 1, and r =0.05 so that
F = 900(1+0.05) = 945
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1. Oil: An Arbitrage Opportunity?
Suppose that:- The spot price of oil is US$95- The quoted 1-year futures price of oil
is US$125- The 1-year US$ interest rate is 5%
per annum- The storage costs of oil are 2% per
annumIs there an arbitrage opportunity?
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2. Oil: Another Arbitrage Opportunity?
Suppose that:- The spot price of oil is US$95- The quoted 1-year futures price of oil
is US$80- The 1-year US$ interest rate is 5%
per annum- The storage costs of oil are 2% per
annumIs there an arbitrage opportunity?
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Futures Exchanges in China
Shanghai Futures Exchange: copper, aluminum, natural plastics, fuel
petroleum, zinc and goldhttp://www.shfe.com.cn/contracts/secondpage.jsp?subjectpid=2&subjectmid=2
01&subjectid=2011&single=0&startpage=1
China Financial Futures ExchangeCSI 300 index futures
http://www.cffex.com.cn/wps/wcm/connect/cffex_dev/CFFEX_EN/SiteArea_Products/SiteArea_SHSZ300/
http://www.csindex.com.cn/sseportal/csiportal/en/zs/jbxx/hs300_en.jsp
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Options
A call option is an option to buy a certain asset by a certain date for a certain price (the strike price)
A put is an option to sell a certain asset by a certain date for a certain price (the strike price)
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Long Call on Microsoft (Figure 1.2, Page 7)
Profit from buying a European call option on Microsoft: option price = $5, strike price = $60
30
20
10
0-5
30 40 50 60
70 80 90
Profit ($)
Terminalstock price ($)
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Short Call on Microsoft (Figure 1.4, page 9)
Profit from writing a European call option on Microsoft: option price = $5, strike price = $60
-30
-20
-10
05
30 40 50 60
70 80 90
Profit ($)
Terminalstock price ($)
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Long Put on IBM (Figure 1.3, page 8)
Profit from buying a European put option on IBM: option price = $7, strike price = $90
30
20
10
0-7
90807060 100 110 120
Profit ($)
Terminalstock price ($)
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Short Put on IBM (Figure 1.5, page 9)
Profit from writing a European put option on IBM: option price = $7, strike price = $90
-30
-20
-10
70
90
807060
100 110 120
Profit ($)Terminal
stock price ($)
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Payoffs from OptionsWhat is the Option Position in Each Case?
K = Strike price, ST = Price of asset at maturity
Payoff Payoff
ST STKK
Payoff Payoff
ST STKK
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Types of Traders
• Hedgers
• Speculators
• Arbitrageurs
Some of the large trading losses in derivatives occurred because individuals who had a mandate to hedge risks switched to being speculators
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Hedging Examples (page 11)
A US company will pay £10 million for imports from Britain in 3 months and decides to hedge using a long position in a forward contractAn investor owns 1,000 Microsoft shares currently worth $73 per share. A two-month put with a strike price of $65 costs $2.50. The investor decides to hedge by buying 10 contracts
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Speculation Example
An investor with $4,000 to invest feels that Cisco’s stock price will increase over the next 2 months. The current stock price is $20 and the price of a 2-month call option with a strike of 25 is $1What are the alternative strategies?
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Arbitrage Example (pages 12-13)
A stock price is quoted as £100 in London and $172 in New YorkThe current exchange rate is 1.7500What is the arbitrage opportunity?
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Exchanges Trading Options
Chicago Board Options ExchangeAmerican Stock ExchangePhiladelphia Stock ExchangePacific Stock ExchangeEuropean Options ExchangeAustralian Options Market
