Derivatives notes PDF

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Comprehensive lecture notes from lectures 1-3...

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Why do derivatives exist?

Manage risk and speculate -

What is a derivative?

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We live in an uncertain and risky world Derivatives help us manage or hedge risks Invoicing in other currencies - If im a mining company selling gold, fluctuating prices create risk. Volatility in share markets - Fund managers hedge in the share market to eliminate the risk of the market dropping If im an importer who is voiced in USD will fear a decline in the value of the AUD An orange farmer – exposed to weather risks and the yield in oranges Instrument or security whose value depends on another variable or thing o Eg. Shares/ stock, market index, exchange rate, interest rate Other o Commodity, electricity, rainfall etc. They were invented in 1973

Trend Derivatives have increasingly become more exotic such as rainfall etc. Some people are affected by rainfall Wherever there is a danger derivatives pop up to hedge people against these risks Types -

of derivatives Forwards Futures Swaps Options

Derivatives can be bought on: Over the counter market Exchange traded market Buy derivatives on the over the counter market (OTC) Informal market where traders communicate by phone or computer Network of traders working at financial institutions

Why do people thing derivatives are evil?

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Haven’t been well regulated or there is a scandal where people lose a lot of money Derivatives are extremely complicated Warren Buffet doesn’t like derivatives – “weapons of mass financial destruction”

Read: Lehman Brothers bankruptcy  Bankrupt in GFC  Active participant in over the counter derivatives market Risks – Derivatives Airline

Forward contract

Has huge expenses to jet fuel Risks Jet fuel/ oil price Credit risk An agreement to buy or sell an asset at a specified price on a specified date Always two parties to a forward contract Long forward contract: making a legal obligation to buy the underlying asset Short forward position: the party who takes a short forward position is contracted to sell the underlying asset for a price of F at time T Contrast this to a spot contract Spot: Agreement to sell an asset today at the current market price or S0 Right now

F and T are the denotions (get an image of this) Eg.

Short forward position

 I think gold will go down  Enter a short forward position to sell gold at USD 1650 – obligation to sell gold  Buy gold a few months later at the spot price @ 1350  Forward contract exercised and make 330 USD per ounce of gold  Profit = 1000 ounces x 330 = 3300 What if it went up?  We are obliged to sell gold @ $1650 per ounce  Buy gold at the spot price $1800  Exercise forward contract and sell gold @ $1650  Loss = $150 USD per ounce  Loss = 150 x 1000 = 1500 Obligation to sell the underlying asset or thing Inset payoff diagram

Long forward position

Obligation to buy the underlying asset or thing -

Profit when the price of the underlying asset rises Loss if the underlying asset falls

Inset payoff diagram Over the counter market Exchange traded market Forward contract characteristics

Futures contracts

Highly customised o When is it delivered o Size, timing, delivery, underlying asset Each party bears credit risk o That the asset isn’t delivered An agreement to buy or sell an asset at a specified price on a specified future date -

Characteristics Can close them out early by taking an opposite position Futures contracts are traded on organised exchanges (eg. Through CBA/ ASX) and forwards are traded through banks o We do not have to find a counter party – its all done through the futures exchange o Forwards – need to find the counterparty o We never know the identity of the counter party o The clearing house guarantees the transaction will go through, the futures exchange will honour it if the counterparty doesn’t honour their side of the deal o The organised exchange make sure everything is spelled out in advance They are highly standardised o Very clear as to what sort of orange juice, what sort of cows -> very specific o Underlying asset, when it will be delivered, contract size, delivery date, delivery arrangements Futures exchanges are market to market o At the end of each day contracts are market to market – whether we made a profit or loss at the end of the day

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o If balance gets too low might call a margin call Option to close out position earlier o Forwards -> have to hold until expiry date

Closing out: a futures position means entering a new futures position equal in magnitude but opposite in direction to your original futures position The futures exchange would determine that the two positions cancel out each other and terminate the contracts Might close out early for a loss thinking that prices will go down more and lose money -

SPI200 futures

Difference between futures and forwards Spot contract Market index

Comments

Look at CME group website Always a standard $25 contract size per index point

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Portfolio of the 200 biggest stocks Costs = ounces x price Eg. 1000 ounces x 1320 USD = USD $1,320,000 -

Speculation

Hedging

Physical delivery at expiry o Rare that they are o Closed out before expiry date o If you hold until expiry, you have to deliver of buy the object so you close out before the delivery date and you don’t have to physically deliver o Convenient to close out earlier o ASX SPI200 futures are never physically delivered

Electricity prices are extremely volatile A lot of interest rate futures

A prediction or guess of the direction of price movements It’s a gamble, a guess Enter into a derivatives position that makes money when you guess correctly Usually a speculator doesn’t actually own the underlying asset/ have a position Always has exposure in the underlying asset Not guessing Don’t like the risk of being exposed to price fluctuations so they enter into a derivatives position to remove risks Provides a payoff that offsets price movements Makes money when prices move Being hedged means being locked into a price This is good if prices move against you but you don’t benefit or profit if they work with you Will always pay the same price/ provides an identical outcome Strategy: Identify the risk/ exposure in the asset Enter into a derivatives position that makes money when this unfavourable scenario occurs\

EG. Road construction project in China Spot price of bicherman now is RMB 2800 per ton Risk: Bicherman prices go up  Enter into a long futures contract : Hedging vs speculation Exchange rate hedging

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AUD/USD = 0.66 1 Australian dollar buys 66 USD

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1/0.66 = 1USD buys 1.5152 AUD

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When GBP 1 buys = 1.5 in 2020 and gbp 1 = 1.7 in 2019 – this means the currency has depreciated in 2020/ weakened

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Getting paid at a later date, compare the spot price and the forward price Other currency weakening is a risk Pick a derivatives position that will make money if the bad situation happens

Or

 Enter into a hedge, close out hedge  Buy at spot rate Try picturing yourself in one country to help work it out

Indexes

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Happy we hedged No matter which way bicherman price went we were shielded from it Same result

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A stock index tracks changes in hypothetical portfolio of stocks Reflection of overall market movements Futures contracts trade on the benchmark stock index

Index points = $25 standard contract Fund manager – managing $100m Thinks the market will drop Liquidate share portfolio and put it in cash – investors wouldn’t be impressed Hedge with SPI200 Stock portfolio has a beta of 1.2 – more risky than the average stock Example: Today is 1st Jan ASX200 currently at 6300 June2020 SPI200 futures for Jun 2020 are quoted at 6351 Beta – 1.2 Decision today: Risk is that the stock market will fall and falling portfolio value Enter into a short SPI200 futures contract Horizon of risk (time period)

How many contracts to we need?

If markets fall - 10% + 2% dividend yield = portfolio dropped = 8%

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Strategy

1. 2.

The fund manager locked in or hedged the price of the stock If the index went up, we would not benefit from that because our portfolio value would have been locked in Our portfolio would be exaggerated because our beta is higher than 1 or the average market return Identify risk/ exposure in the asset Enter a derivatives position that makes money when this unfavourable scenario occurs

3.

Replication Arbitrage

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Example

Money for nothing If two strategies always result in identical payoffs in the furture, they must have the same cost today or else there is an arbitrage opportunity A trading strategy that produces a fixed/ certain/ known outcome is essentially riskless and therefore must earn the riskless rate of interest (otherwise there is an arbitrage opportunity) You cant have something that costs you nothing today and has a payoff in the future (money doesn’t grow on trees) Shouldn’t have to pay anything today or at time 0 If capital F is priced properly there shouldn’t be a profit in the future Strategy that costs you nothing should deliver nothing in the future

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Underlying thing is Westpac shares What price should they enter into the contract? $28 dollars allows for arbitrage

Short forward contract: agreement to sell Westpac shares at the agreed upon price @28 Other party enters long forward: agreement to buy Westpac shares at $28 At time 0 Get my self prepared for time T (sell Westpac shares) Can either buy Westpac shares today and hold until time T and then sell (you then have the shares and you are prepared) (-$22) Or can borrow 22 from the bank (+$22) Net cash flow = 0 To arbitrage Shouldn’t have to pay anything today At time 1 We have a commitment to sell shares @28 dollars We receive $28 by selling Westpac shares The money borrowed from the bank will accrue interest so we have to pay that back for the 1 year horizon Pay back $23.13

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Costed us nothing at time 0 but managed to earn us $4.87 dollars per contract

This is an arbitrage opportunity. Case 2: F= 21 which his under-priced Enter into a long forward position – commitment to buy shares at time T Legal obligation to purchase Westpac share at $21

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Receive $22 from short selling Westpac shares Invest the $22 in the bank to receive interest over the horizon Return Westpac shares to owner @21 Money in bank grows from $22 to $23.13 Net profit is +$2.13

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There is money for nothing here as the cost at time 0 was 0 and the profit at time T was $2.13

There is only 1 correct forward price

$23.13 is the correct or no arbitrage forward price, the right price

Short selling

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Synthetic replication Riskless portfolio Carrying costs How to work out capital F (forward price)

Why? -

Involves selling an asset which you don’t actually own Borrowing an asset from someone Then straight away selling an asset at its market price. This raises money for you today. Someone who owns the stock and is willing to lend the shares – short seller then returns the shares to the original owner Commitment that in 1 year time the original owner will want their shares back

If you don’t know how to calculate this you can get ripped off We will calculate the no arbitrage capital F Valuable for an arbitrager to look for mispriced securities They can implement strategies to gain an arbitrage profit Pricing a forward contract, we really mean determining the correct delivery price F

Replication and arbitrage

Synthetic long

The way forward, futures and options are priced is somewhat different to how financial securities are priced (eg. Bonds, shares) This is because derivatives are based on underlying security Can replicate securities to calculate the capital F Borrow and buy Synthetically replicating a long forward contract If borrow and buy strategy replicates a long forward contract what happens if we also enter a short forward contract -

If we borrow and buy an asset and short a forward contract we will have Zero setup cost at time 0 Be totally riskless Should have zero cashflow at time T But it what if there’s an arbitrage opportunity

rT = paying back interest

Three piece strategy

Time 0 1. Long or short 2. Buy or sell underlying asset 3. Borrow or Invest proceeds Time 1...