• Describe the basic characteristics of forward, futures and option contracts
• Overview exchange markets and over-the-counter markets
• Discuss futures markets
  • Explain the daily marking-to-market process
  • Discuss the margin process with reference to margin account transactions
  • Define and contrast normal markets and inverted markets – backwardation and contango
• Explain the activities of the derivatives users:
  • Hedgers • Speculators • Arbitrageurs
• Analyze basic arbitrage opportunities

• Explain the nature of futures and their relationship to forwards
• Understand how the futures market can be used by hedgers and speculators
• Explain the trading and settlement arrangements used by the SFE (Sydney Futures Exchange)
• Understand the following futures contracts and explain how they can be used for hedging
  • BAB futures (bank accepted bills)
  • SPI futures (Share Price Index)

• A derivative is a financial instrument whose value depends on (or derives from) the values of other, more basic underlying assets.
• Four fundamental derivative building blocks:
  • Futures contracts: Standardised exchange-traded agreements to buy/sell at a specified future date and price.
  • Forward contracts: Customised bilateral over-the-counter (OTC) agreements to buy/sell in the future.
  • Swaps: Private agreements between two parties to exchange periodic cash flows over multiple dates.
  • Options: Contracts conferring the right (without obligation) to buy (call) or sell (put) an asset.

• Financial Securities
  • Stocks, bonds, currencies, stock indices
• Commodities
  • Metals (copper, gold, silver)
  • Agricultural (corn, cotton, orange juice, coffee, cattle)
  • Wood
• Energy
  • Oil products, natural gas, electricity
• Other – Insurance, weather, credit

Investment Asset OR Consumption Asset ?

• Investment assets are held by many investors purely for investment (e.g. gold, silver).
• Consumption assets are held primarily for consumption (e.g. oil, copper).

• Advantages: provide standardized contracts on a range of delivery dates; no credit risk
• Disadvantages: attract margin requirements; no freedom to tailor contracts

• Important alternative to exchanges
• Telephone and computer-linked network of dealers who do not meet physically
• Trades are usually between financial institutions, corporate treasurers, and fund managers
• Advantages
  • More freedom – contract terms are tailored to the needs of the client (not exchange specific)
  • No need for margin payments
• Disadvantages
  • Credit risk (the risk that one of the parties will not honor the contract; documented under ISDA Master Agreements); this can be reduced by collateralization
• Since 2008 …
  • OTC markets have become regulated
  • Standardized OTC products trade on swap execution facilities (SEFs)
  • All trades must be reported to a central registry

Source: Bank for International Settlements. Chart shows total principal amounts for OTC markets and value of underlying assets for exchange markets.

• Notional principal: the reference dollar amount on which derivative cash flows are calculated.

A forward contract is an OTC agreement to buy or sell an asset at a certain time $T$ in the future for a certain price $K$ – the forward price.

• The party $A$ that has agreed to buy has a long position.
• The party $B$ that has agreed to sell has a short position.
• Entering a forward contract requires zero upfront cash flow (the contract value at initiation $f_0=0$). In the chart, $S_T$ is the spot price at maturity $T$.

A futures contract is an agreement to buy or sell an asset at a certain time $T$ in the future for a certain price – the futures price $F_t$ ($t$ is a point in time; $t=0$ is today).

• Futures prices are observed today but refer to transactions to be carried out in the future
  • Futures price is determined by supply and demand, in the same way as the spot price
• Futures contracts are traded on exchanges
  • The exchange specifies delivery date $T$ and settlement by delivery of the underlying (commodity futures) or by cash settlement (financial futures)
  • Are settled daily: marking-to-market
  • The clearinghouse guarantees both sides by novation (buyer to every seller, seller to every buyer)
• Most futures contracts are closed out before maturity, rather than settled by physical delivery. Closing out a futures position involves entering into an offsetting trade
  • resulting in a cash profit or loss

As time goes by, market participants continue trading futures contracts to buy/sell the asset at $T$.

• The spot price $S_t$ is the asset price at time $t$ for immediate delivery ($S_0$ is today's spot price)
• The futures price $F_t$ is the agreed delivery price for a futures contract initiated at $t$, for asset delivery at $T$

Note that $F_0=K$

• Since the seller of the futures contract can deliver the physical asset at maturity, the futures price and the spot price must be the same at that time ($F_T=S_T$). If not, arbitrageurs could make risk-free profits:
  • $F_T>S_T$: buy the asset spot, short futures, deliver; profit $F_T-S_T$
  • $F_T<S_T$: short sell the asset, buy futures, take delivery; profit $S_T-F_T$

• A margin is cash or marketable securities deposited by an investor with his/her broker; it is a performance bond, not a loan or down payment
  • Initial margin: deposited when the position is opened
  • Maintenance margin: the minimum balance before a margin call (typically about 75–80% of initial margin)
  • Margin call (variation margin): if the balance falls below maintenance margin, the investor must deposit funds to restore it to the initial margin
• The balance in the margin account is adjusted to reflect daily settlement (marking-to-market)
• Interest is earned on margin accounts
• Margins control credit risk, by reducing the loss in the event of default
• Clearinghouse (SFE Clearing Corporation)
  • Broker holds a clearing margin account with the Clearinghouse
  • Netting positions of all members and keep track of all transactions in one day

• On June 5: investor enters a long position in two December gold futures contracts
  • Contract size = 100 oz
  • Futures price = USD 400
  • Initial margin = USD 2,000 per contract or USD 4,000 in total
  • Maintenance margin = USD 1,500 per contract or USD 3,000 in total
• On June 26: investor closes out the position by entering a short position in two December gold futures contracts
  • Futures price = USD 392.30
• Investor loss = USD (392.30 − 400) × 200 = USD 1,540

The forward curve gives the futures prices on a given day, for a range of different maturities.

Figure: Listing for COMX gold futures contracts on 25 July 2011 (Source: ifs.marketcenter.com)

• Normal market
  • Forward curve is upward sloping
  • Futures prices for near months are lower than for later months
  • The market is in contango: futures prices trade higher than spot prices

Figure: Listing for NYMEX crude oil futures contracts on 4 July 2013 (Source: ifs.marketcenter.com)

• Inverted market
  • Forward curve is downward-sloping
  • Futures prices for distant months are lower than for near months
  • The market is in backwardation: futures prices trade lower than spot prices

• An option is a contract which confers a right (not an obligation) to buy/sell an underlying asset by (American) or at (European) a certain date ($T$) for a certain price ($K$, the option's strike price; here $K$ is no longer the forward delivery price)
  • The buyer pays the seller (writer) a premium for this right
  • European: exercised only on the expiration date; American: at any time up to and including it
• Options Matrix

• Hedging
  • Seek protection against unfavourable price changes in an asset already owned or planned to be bought/sold; reduce risk and lock in the price
• Speculation
  • Take a position in the market by betting on future price movements to earn profits from expected price changes
  • Take risk in the hopes of profit; leverage magnifies returns
  • Speculation provides liquidity in derivatives markets
• Arbitrage
  • Make risk-free profits by taking advantage of short-term market inefficiencies (simultaneous offsetting positions)
  • Eliminates market price discrepancies
• To change the nature of a liability (e.g. swaps)
• Types of traders
  • Hedgers, speculators, arbitrageurs
  • Market makers, mutual funds, hedge funds

• A US company will pay £10 million for imports from Britain in 3 months. The 3-month forward exchange rate is 1.6192.
• The company decides to hedge by using a long position in a forward contract
  • To lock in an exchange rate of 1.6192
  • Fixes the price paid in 3 months to USD 16,192,000 (10,000,000 × 1.6192)
• Hedging using forwards removes the uncertainty; there is no assurance that the outcome with hedging will be better
  • If exchange rate in 3 months < 1.6192: outcome without hedging is better
  • If exchange rate in 3 months > 1.6192: outcome with hedging is better

• An investor owns 1,000 Microsoft shares currently worth $28 per share. A two-month put with a strike price of $27.50 costs $1.
• The investor decides to hedge by buying 10 put option contracts (100 shares each).

• Stock price $20: exercise the puts, sell 1,000 shares at $27.50: $27,500 − $1,000 = $26,500
• Stock price $35: puts expire worthless, sell the shares for $35,000 − $1,000 = $34,000

• A US speculator believes that the £ will rise over the next 2 months and he is willing to speculate on £250,000.
• What are the alternative strategies?
  • Buy £250,000 today, invest them in an interest-bearing account and sell it later.
  • Long position in futures contracts on £.
• The profit/loss from both strategies is the same; the difference is that
  • Buying £ requires up-front investment (e.g. $360,000 at a spot rate of 1.4400)
  • The futures strategy requires less up-front investment (only margin): leverage to take a large speculative position (e.g. 4 CME contracts of £62,500 with $5,000 margin each = $20,000)

• An investor with $2,000 to invest expects the value of Amazon.com to 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 $22.50 is $1. What are the alternative strategies?
  • Buy 100 shares
  • Long 20 call option contracts (2,000 call options)

• $S_0=\mathrm{\$}20$; 2-month call with strike $K=\mathrm{\$}22.50$ costs $c=\mathrm{\$}1.00$. Budget $2,000.
• Strategy A: buy 100 shares for $2,000. Strategy B: buy 2,000 call options (20 contracts) for $2,000.
• Outcome scenarios at 2 months:

  Terminal Stock Price	Strategy A (100 Shares)	Strategy B (2,000 Calls)
  Drops to $15	Value $1,500 (Loss: -$500 / -25%)	Value $0 (Total Loss: -$2,000 / -100%)
  Rises to $27	Value $2,700 (Gain: +$700 / +35%)	Value $2,000\times \mathrm{\$}4.50=\mathrm{\$}9,000$ (Gain: +$7,000 / +350%)

• Futures Speculation:
  • Small upfront investment (only margin deposit required).
  • Linear payoff: Potential gain is unlimited, but potential loss is also unlimited and can exceed initial margin.
• Options Speculation:
  • Upfront cost is strictly limited to the option premium paid.
  • Non-linear payoff: Potential gain is unlimited, while downside loss is strictly capped at 100% of premium (limited loss); upside leverage can deliver explosive returns (>300%).
  • However, requires stock to move significantly beyond the strike price to overcome the time value paid.

• Assume: spot price of gold $S=\mathrm{\$}1,390$/oz, 1-year interest rate $r=5\mathrm{\%}$ per annum (simple interest), no income or storage costs for gold.
• Quoted 1-year futures price: $F_{\text{mkt}}=\mathrm{\$}1,485$.
• Theoretical forward price: $F_{\text{theor}}=\mathrm{\$}1,390\times (1+0.05)=\mathrm{\$}1,459.50$.
• Since $F_{\text{mkt}}>F_{\text{theor}}$, gold futures are overpriced! Is there an arbitrage opportunity? Yes: “cash-and-carry” arbitrage.

  Now ($t=0$)	After 1 year ($T=1$)
  Borrow $1,390 at 5% p.a. for 1 year	Repay the loan: $\mathrm{\$}1,390\times 1.05=-\mathrm{\$}1,459.50$
  Buy 1 oz of gold for $1,390	Deliver the gold under the futures contract
  Short a 1-year gold futures contract at $1,485	Receive the futures price: $+\mathrm{\$}1,485.00$
  Net cash flow today = $0	Arbitrage profit = $(1,485 − 1,459.50) = $25.50 per oz

• Assume: $S=\mathrm{\$}1,390$/oz, $r=5\mathrm{\%}$ per annum, no income or storage costs for gold; $F_{\text{theor}}=\mathrm{\$}1,459.50$.
• Quoted 1-year futures price: $F_{\text{mkt}}=\mathrm{\$}1,390$.
• Since $F_{\text{mkt}}<F_{\text{theor}}$, gold futures are underpriced! Is there an arbitrage opportunity? Yes: “reverse cash-and-carry” arbitrage.

  Now ($t=0$)	After 1 year ($T=1$)
  Sell (short sell) gold for $1,390	Take delivery of gold under the futures contract
  Invest $1,390 at 5% p.a. for 1 year	Investment grows to $\mathrm{\$}1,390\times 1.05=+\mathrm{\$}1,459.50$
  Long a 1-year gold futures contract at $1,390	Pay the futures price: $-\mathrm{\$}1,390.00$
  Net cash flow today = $0	Arbitrage profit = $(1,459.50 − 1,390) = $69.50 per oz

• What should the futures price be?
• If the spot price of gold is $S$ and the futures price for a contract deliverable in $T$ years is $F$, then
  $$F=S(1+r{)}^T$$
  where $r$ is the 1-year (domestic currency) simple interest rate.
• In our examples, $S=\mathrm{\$}1,390$, $T=1$ and $r=0.05$, so that $F=\mathrm{\$}1,390(1+0.05)=\mathrm{\$}1,459.50$.
• If $F>S(1+r{)}^T$: arbitrageurs borrow, buy spot, short futures (cash-and-carry).
• If $F<S(1+r{)}^T$: arbitrageurs short spot, lend the proceeds, buy futures (reverse cash-and-carry).
• With continuous compounding (Hull's notation) the same relation reads $F_0=S_0{e}^{rT}$.

• Setup: Spot oil $S=\mathrm{\$}85$, $r=5\mathrm{\%}$ p.a., storage cost $u=2\mathrm{\%}$ p.a.
• Scenario 1: Quoted 1-year futures $F=\mathrm{\$}93$:
  • Cost of carry upper bound: $F_{\text{max}}=85\times (1+0.05+0.02)=\mathrm{\$}90.95$.
  • Since $\mathrm{\$}93>\mathrm{\$}90.95$, cash-and-carry arbitrage WORKS (borrow, buy oil, store, sell futures → guaranteed profit).
• Scenario 2: Quoted 1-year futures $F=\mathrm{\$}82$:
  • Is there an arbitrage opportunity? NO!
  • Reverse cash-and-carry is not available: short-selling oil is not always possible because oil is a consumption asset – market participants cannot easily short sell physical crude oil, and commercial inventory holders will not sell stock due to operational convenience yield.