Notes from the lectures of week 1 to 3, and part of week 4 of Investment and Portfolio Theory 2 that is part of the specialization/major in Finance for Business Administration and Economics & Business Economics at University of Amsterdam
Derivatives
- Derivatives were once dubbed ‘financial weapons of mass destruction’ by Warren
Buffet.
- Securities whose prices ‘derive from’ the prices of other securities.
- These other securites are cash-flows (from business, in the broadest sense of the word)
or commodities (again, very broadly defined) that are brought tp the market and
traded.
- Derivatives are contingent claims giving a payoff only under specific circumstances –
mainly if the value of the underlying security differs from an ex ante agreed threshold.
o The payoff can be a lot bigger (due to leverage)
o Benefits of price exposure, but in a way that is more favourable than trading
directly the underlying asset.
Organization of markets and contracts
- Markets:
o Over-the-counter (OTC): tailor-made privately negotiated contracts;
conditions adapted to specific circumstances.
o Exchange traded: standardized contracts so one-size-fits-all; many trading
parties create liquid supply and demand.
- Contracts:
o Futures and forwards: both parties have the obligation to trade in the future
at a price that is fixed today in the contract.
o Options: one party has the right, but not the obligation, to buy or sell an asset
at a pre-specified price. If execution of the right is not favourable, this party
can walk away from the transaction.
Forwards and Futures Contracts
- Two parties agree a transaction at a fixed price today, but execute the sale (delivery) at
a later date:
o The buyer of the underlying securities has a long position, the seller has a
short position.
o The future price is fixed today, as well as the settlement date.
o Execution is compulsory, so the side that loses cannot get out of it (unlike
options, where one side can).
o The contract defines also the quantity of the underlying asset, and the delivery
method.
- Example: selling 1,000 tons of wheat with a delivery in 6 months at a price of €200 a
ton.
o If the price in 6 months is €150, then the seller gets a higher price for the
wheat than the spot market and makes a profit of €50,000.
o If the price 6 months from now is €240, the buyer gets a lower price and
makes a profit of €40,000.
, - Profits and losses are equal, so forwards and futures are zero-sum contracts.
o Each party has exposure to price changes (the value of the contract may
change over time).
Profits of forward and future contracts
- Profits and losses: depend on the difference between the price we fix for a future date
(future price, F0) and the price – as of yet unknown – that will prevail at the settlement
date (ultimate spot price PT)
- Profit is zero: when the ultimate spot price PT equals the initial futures price F0.
- Future contracts are traded on assets in four main categories:
o Agricultural commodities
o Metals and minerals
o Foreign currencies
o Financial futures
- Forward contracts can be established on a wider variety of assets.
Comparison of Forwards and Futures: Flexibility vs Additional Risks
Additional risks of forward contracts
- Liquidity risk:
o Suppose conditions have changed, and the shipment of iron ore you had - and
whose price you wanted to lock in using a forward – is not at the bottom of the
ocean.
o You want to get rid of the obligation to sell iron ore.
o With a forward, this means having to renegotiate with the other party, the other
party will charge you for this, as you have no other way to get out of the
contract.
, - Credit risk:
o Who says that the other party will honour its commitment?
o They might not have the money or be unwilling to pay.
- Delivery risk:
o Maybe we just thought of gold as a nice investment opportunity, and we like
to profit from price developments, but have no appetite for the costs of
physical delivery such as insurance and security.
How futures solve these additional risks?
- Organized markets with standardized contracts can eliminate many risks.
- Clearinghouse: intermediary that becomes the counter-party to all futures contracts.
o Seller of contracts for long position.
o Buyer of contracts for short position.
o Rather than paying or delivering to an unknown and potentially unreliable
party, the clearinghouse guarantees execution of trades.
- The clearinghouse provides liquidity, eliminates the credit risk, and enables investors
to reverse their trades.
Open interest and liquidity risk
- Some futures contracts are more liquid than others; especially contracts with relatively
short times to maturity (close settlement dates) are often popular:
o Most parties seek a short-term hedge or speculative position.
- The popularity (liquidity) of a contract is measured by open interest:
o The number of contracts outstanding (long and short contracts are not counted
separately).
o Open interest measures the nominal amount (quantity x F0)
o The actual sums changing hands are much smaller due to market-to-market.
- When a contract comes very close to delivery, the open interest drops dramatically.
o Depending on the market (commodity, currency, etc), 97 to 99% of the future
contracts do not result in delivery; the position are closed before the settlement
date by buying the opposite contract.
o For financial futures, it is 100%, as physical delivery excluded by the
exchange rules.
Market-to-market and credit risk
- Margin account:
, o Security account with cash or T-bills that ensures the trader can satisfy the
obligations of the contract.
o When establishing the futures contract both parties post an initial margin.
o The amount of initial margin depends on the size of the position and volatility
of the underlying assets.
- Market-to-market mechanism reduces credit risk:
o The mechanism by which profits or losses accrue to traders.
o Futures prices change daily, and the clearinghouse requires traders to
recognize profits or losses daily.
o The profits and losses accrue to the margin accounts of both long and short
traders through daily transfers.
- Margin calls protect the clearinghouse:
o If a trader accrues sustained losses from daily marking to market, the balance
on the margin account may fall below a critical value called the maintenance
margin.
o Margin call is a requirement to replenish the margin account or to reduce the
futures position.
o Positions are closed out before the margin account is exhausted and the
clearinghouse is not put at risk.
o Small potential losses as the outstanding balance is limited to the price
movements in a single day.
Pricing futures and market arbitrage
- The price of future depends on a no-arbitrage argument:
o If the price of buying the underlying asset now and storing it till the settlement
date, differs from the futures price, there is an arbitrage profit.
o The future price is equal to the spot price, corrected for storage costs.
- Storage costs are very broad:
o Include corrections for dividends and interest payments.
o Opportunity costs of having capital tied up in the underlying asset.
o Often the term ‘cost of carry’ is used.
- A position with certain payoffs should earn the risk-free rate over the invested
capital.
o A position in futures contract and a position in the underlying assets have risks
that cancel out.
- Example:
o Investor holds $1000 in a mutual fund indexed to the S&P500.
o Assume dividends of $20 will be paid on the index fund at the end of the year.
o A futures contract with delivery in one year is available for $1010.
o The investor hedges the exposure to market risk by selling (shorting) one
contract.
- Payoffs for different levels of the S&P500:
o Final value of S&P500 portfolio ST: 990 1010 1030
o Payoff on short futures (1010 – ST): 20 0 -20
o Dividend income: 20 20 20
o Total: 1030 1030 1030
- This return makes perfect sense with a rf of 3%.
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