FNCE30007 Securities Sample Notes

Topic 1 – Introduction to Derivatives/Futures and Forward Markets

Derivative security – an instrument (or contract) whose payoff and, thus, value, depends on the values (or prices) of one or more other variables (known as underlying assets e.g. commodities, stocks, bonds, currencies, interest rates, live cattle and weather)

Derivatives trading • Exchanges ▪ Products and trading terms are standardised ▪ Traditionally derivative contracts have been traded using the open outcry system where traders physically meet on the floor of the exchange ▪ Increasingly this is being replaced by electronic trading where a computer matches buyers and sellers • Over-the-counter (OTC) ▪ Decentralised market where the participants trade with one another directly, without the oversight of an exchange ▪ A telephone- and computer-linked network of dealers who do not physically meet ▪ Trades are usually between financial institutions, corporate treasurers and fund managers ▪ A key advantage of the OTC market is that the terms of a contract do not have to be those specified by an exchange (flexibility); market participants are free to negotiate any mutually attractive deal ▪ A disadvantage is that there is usually some credit risk in an OTC trade (i.e. risk that the contract is not honoured)

There are three broad categories of traders: • Hedgers – use futures, forwards and options to reduce the risk that they face from potential future movements in a market variable (treasury/risk management) • Speculators – use derivatives to bet on the future direction of a market variable (engage in leveraged bets) • Arbitrageurs – take offsetting positions in two or more instruments to lock in a profit (proprietary trading exploiting mispricing across related securities)

Dangers of derivatives When a trader has a mandate to use derivatives for hedging or , but then switches to speculation, large losses can result.

Futures and Forward Markets

Futures – an agreement to buy or sell a specified quantity of a specified asset at a specified time in the future for a specified price (delivery price) Examples Agreement made today to: • Buy 5,000 bushels of wheat @ US $4.50/bushel on December 2, 2018 (CBOT) • Sell £62,500 @ 1.4800 US$/£ on March 15, 2019 (CME) • Sell 1,000 bbl. Of WTI oil @ US$50/bbl. on April 20, 2019 (NYMEX)

Topic 6 – Trading Strategies

By combining option positions (or combining a single option and a stock), investors can generate a variety of payoff functions (i.e. profit/losses profiles with many different shapes). The chosen strategy (and, thus, payoff profile) reflects views (bets) on the evolution of the underlying, either directionally or on its . For most strategies we will focus on payoff profiles at options (European options). Note that the profit/loss will be simply final payoff subtracted by initial cost, without discounting for the time value of money (since these options strategies are typically implemented over very short time horizons it does not make a huge difference).

Three types of options trading strategies • Strategies involving a single options and a stock – combines a position in an option with a position in the underlying o Writing covered calls – combines a long position in a stock plus a short position in a The long stock position ‘covers’ or protects the investor from the payoff on the short call that becomes necessary if there is a sharp rise in the stock price. Recall the put-call parity: −푟푇 푝 + 푆0 = 푐 + 퐾푒 This can be rearranged: −푟푇 푆0 − 푐 = 퐾푒 − 푝 This shows that a long position in a stock combined with a short position in a call is equivalent to a short put position plus a certain amount (퐾푒−푟푇) of cash. The reason why writing a covered call is not the same as writing a put is because you get certain amount of cash on top of the profit/loss from the short put.

The aggregate payoff looks like a short put (put-call parity).

In anticipation of a price rise, investor A might go long the stock and investor B might write a covered call. In the end, if the price goes up by a lot, investor A would be better off. If the price goes up by a little or goes down, the covered call writer would be better off. Therefore, writing a covered call limits the investor’s losses on the downside.

Box spreads A is a combination of a bull call spread with strike prices 퐾1 and 퐾2 and a bear put spread with the same two strike prices. The payoff from a box spread is always 퐾2 − 퐾1. −푟푇 The value of a box spread is therefore always the PV of this payoff, or (퐾2 − 퐾1)푒 . If it has a different value, there is an arbitrage opportunity.

Payoff from a box spread Stock price range Payoff from bull call Payoff from bear put Total payoff spread spread 푆푇 ≤ 퐾1 0 퐾2 − 퐾1 퐾2 − 퐾1 퐾1 < 푆푇 < 퐾2 푆푇 − 퐾1 퐾2 − 푆푇 퐾2 − 퐾1 푆푇 ≥ 퐾2 퐾2 − 퐾1 0 퐾2 − 퐾1

If the market price of the box spread is too low, it is profitable to buy the box. This involves buying a call with 퐾1, buying a put with strike price 퐾2, selling a call with strike price 퐾2 and selling a put with strike price 퐾1.

It is important to note that a box spread arbitrage only works with European options.

Butterfly spreads A spread involves positions in options with three different strike prices.

Butterfly spreads using calls It can be created by buying a call option with a relatively low strike price, 퐾1, buying a call option with a relatively high strike price, 퐾3, and selling two call options with a strike price 퐾2, hallway between 퐾1 and 퐾3. Generally, 퐾2 is close to the current stock price.

Topic 6 – The Black-Scholes-Merton Model

Example of BSM Telstra stocks (TLS) are trading at 푆 = 5.1. The expected (annualised) volatility of continuously compounded TLS returns is 휎 = 0.30. 67 A TLS call option has an price 퐾 = 4.4 and expires on November 24 (푇 = ). TLS pays no 365 dividends until March 2017. The current risk-free interest rate in Australia is 1.5% p.a.

What should the current price of the 4.4 TLS calls be according to the BSM model?

1. Find 푑1 and 푑2: 푆 휎2 ln ( 0) + (푟 + ) 푇 퐾 2 푑1 = 휎√푇 5.1 0.32 67 ln ( ) + (0.015 + ) ( ) 4.4 2 365 = 67 0.3√ 365 = 1.2343

푆 휎2 ln ( 0) + (푟 − ) 푇 퐾 2 푑2 = = 푑1 − 휎√푇 휎√푇 67 = 1.2343 − 0.30 × √ 365 = 1.1058 2. Use table of normal distribution probabilities and find: 푁(1.2343) = 0.8915 푁(1.1058) = 0.8656

Using normal tables: 푁(0.7512) = 푁(0.75) + 0.12 × [푁(0.76) − 푁(0.75)] 푁(−푥) = 1 − 푁(푥)

3. Use the BSM formula: −푟푇 푐 = 푆0푁(푑1) − 퐾푒 푁(푑2) 67 −0.015× = 5.1 × 0.8915 − 4.4푒 365 × 0.8656 = $0.7483

Volatility The volatility 휎 is the annualised standard deviation of the continuously compounded rate of return on the underlying asset over the life of the option.

The standard deviation (volatility) of the continuously compounded return over a time interval ∆푡 is 휎√∆푡.