Options and Futures Markets Exam 1

Both "long" and "short" are

"delayed"

r

= Interest rate

m

= Periods per year

n

= Years

Basis

= spot price of asset to be hedged - futures price of contract used

American Option

An American option can be exercised at any time during its life. Options are to buy or sell 100 shares of stock.

Russell 2,000

An index of the prices of 2,000 of the smallest capitalization stocks in the United States.

NASDAQ - 100

Based on 100 stocks using the National Association of Securities Dealers Automatic Quotations Service

Long Calls

Betting on rising spot prices

Distressed Securities

Buy securities issued by companies in or close to bankruptcy

European Options

Can only be exercised at maturity.

Stop-limit order

Combination of stop and limit

S2

Final Asset Price

Examples of Derivatives

Futures contracts, forward contracts, swaps, options

S1

Initial Asset Price

b1

Initial Basis

Emerging Markets

Invest in debt and equity of companies in developing or emerging countries and in the debt of the countries themselves

Open order or Good-till-canceled order

Is in effect until executed or until the end of trading in a particular contract

Decrease in the basis

Leads to strengthening of the basis

Perfect hedge

One that completely eliminates the risk. They are rare, and your goal is to get as close as possible.

N star

Optimal number of futures contracts for hedging

PV

Present Value

K

Strike price, price paid for the underlying asset when executing option

RM

The actual LIBOR interest rate observed in the market at time T1 for the period between times T1 and T2

Margin Requirement

The cash balance (or security deposit) required from a futures or options trader.

Par Yield

The par yield for a certain maturity is the coupon rate that causes the bond price to equal its face (par) value.

Other key points about Futures

They are settled daily.

t

Time as % of year

Merger Arbitrage

Trade after a merger or acquisition is announced so that a profit is made if the announced deal takes place

b1 formula

b1 = S1 - F1

b2 formula

b2 = S2 - F2

Expectations Theory

forward rates equal expected future zero rates

Premium

price paid for an options contract

Market Segmentation

short, medium and long rates determined independently of each other

Spot price

the price for immediate, or almost immediate delivery

Continuous Compounding

A way of quoting interest rates, it is the limit as the assumed compounding intervals is made smaller and smaller. In the area of "derivatives" we use continuous compounding

Order is default set

An order is a day order and expires at the end of the trading day, unless otherwise stated

b2

Final Basis

Last trading day

Generally a few days before the last notice day

Examples of labels used for hedge funds together with trading strategies includes:

Long/Short Equities, Convertible Arbitrage, Distressed Securities, Emerging Markets, Global Macro, Merger Arbitrage.

QA

Size of position being hedged in units

Borrower (Valuation)

Value of FRA where a fixed rate is paid is: L(RF-RK)(T2-T1)e^-R2T2

A Clearinghouse and Clearing Margins

A clearinghouse acts as an intermediary in futures transactions. It guarantees the performance of the parties of each transaction. The clearinghouse has a number of members, who must post funds with the exchange. Brokers who are not members themselves must channel their business through a member. The main task of the clearinghouse is to keep track of all the transactions that take place during a day so that it can calculate the net position of each of its members. Just as an investor is required to maintain a margin account with a broker, the broker is required to maintain margin with a clearinghouse member and the clearinghouse member is required to maintain a margin account with the clearinghouse (clearing margin)

Forward Rate Agreement

A forward rate agreement (FRA) is an agreement that a certain rate will apply to a certain principal during a certain future time period. A FRA is equivalent to an agreement where interest at a predetermined rate ,RK is exchanged for interest at the market rate. A FRA can be valued by assuming that the forward interest rate is certain to be realized. Cash flows are "mirror images" for the two parties. Usually FRA's are settled prior to the period in question - requiring discounting at the market rate.

Futures Contracts

A futures contract is an agreement to buy or sell an asset at a certain time in the future for a certain price, by contrast in a spot contract there is an agreement to buy or sell the asset immediately (or within a very short period of time). Available on a wide range of underlyings. Exchange traded and specifications need to be defined: what can be delivered, where it can be delivered, when it can be delivered. Settled daily

Options vs. Futures/Forwards

A futures/forward contract gives the holder the obligation to buy or sell at a certain price. An option gives the holder the right to buy or sell at a certain price.

Short Hedge

A hedge that involves a short position in futures contracts. A short futures hedge is appropriate when you know you will sell an asset in the future (think already long the future) & want to lock in the price, already own it and know you will sell it in the future.

Long Hedge

A hedge that involves taking a long position in a futures contract. A long futures hedge is appropriate when you know you will purchase an asset in the future (think already short the future) and want to lock in the price.

Margins

A margin is cash or marketable securities deposited by an investor with his or her broker. The balance in the margin account is adjusted to reflect daily settlement. Margins minimize the possibility of a loss through a default on a contract.

Inverted Market

A market where futures prices decline with maturity

Treasury Notes

A marketable U.S. government debt security with a fixed interest rate and a maturity between one and 10 years

Treasury Bonds

A marketable, fixed-interest U.S. government debt security with a maturity of more than 10 years

U.S Dollar Index

A trade weighted index of the values of six foreign currencies: Euro, Yen, Pound, Dollar, Swedish Krona, Swiss Franc.

Zero Rates

A zero rate (or spot rate), for maturity T is the rate of interest earned on an investment that provides a payoff only at time T, or the n-year zero coupon interest rate is the rate of interest earned on an investment that starts today and lasts for n years.

Examples of Futures Contracts

Agreement to: Buy 100 oz. of gold @ US $1050/oz. in December. Sell 62,500 Euro @ 1.5500 US$/Euro in March. Sell 1,000 bbl of oil @ US$75/bbl. in April.

Russell 1,000

An index of the prices of the 1,000 largest capitalization stocks in the United States.

LIBOR, HIBOR, Eurobor, etc.

An interest rate at which banks can borrow funds, in marketable size, from other banks in the London interbank market. An interest rate stated in Hong Kong dollars on the lending and borrowing between banks in the Hong Kong market

To avoid risk of having to take delivery...

An investor with a long position should close out his or her contracts prior to the first notice day.

Call Option

An option to buy a certain asset by a certain date for a certain price (the strike price). The price of a call option decreases as the strike price increases. Both options become more valuable as their time to maturity increases.

Put Option

An option to sell a certain asset by a certain date for a certain price (the strike price). The price of a put option increases as the strike price increases. Both options become more valuable as their time to maturity increases.

Arbitrage

Arbitrageurs take offsetting positions in two or more instruments to lock in a profit.

Convergence of Futures Price to Spot Price

As the delivery period for a futures contract is approached, the futures price converges to the spot price of the underlying asset. When the delivery is reached, the futures price equals, or is very close to the spot price.

Dow Jones Industrial Average

Based on a portfolio consisting of 30 blue-chip stocks in the United States. The weights given to the stocks are proportional to their prices.

Standard & Poor's 500 (S&P 500)

Based on a portfolio of 500 different stocks: 400 industrial, 40 utilities, 20 transportation companies, and 40 financial institutions. Their weights in the portfolio at any given time are proportional to their market capitalizations.

Basis RIsk

Basis is the difference between spot & futures. Basis risk arises because of the uncertainty about the basis when the hedge is closed out. Problems that lead to more complexity of hedging and basis risk. The asset whose price is to be hedged may not be exactly the same as the asset underlying the futures contract. The hedger may not be certain of the exact date the asset will be bought or sold. The hedge may required the futures contract to be closed out before its delivery month.

Beta

Beta is the slope of the best-fit line when the return on the asset is regressed against the return on a well-diversified stock index. When β = 1.0, the return on the portfolio tends to mirror the return on the index. When β = 2.0, the changes in the return on the portfolio tend to be twice as great as the corresponding changes in the return from the index. When β = 0.5, they tend to be half as great.

Long Puts

Betting on spot prices falling

Short Puts

Betting on spot prices not falling

Short Calls

Betting on spot prices not increasing

Options Buyers and Sellers

Buyers are referred to having long positions. Sellers are referred to having short positions. Selling an option is also known as writing the option.

Exchanges Trading Futures

CBOT and CME (now CME Group), intercontinental exchange, NYSE Euronext, Eurex, BM&FBovespa (Sao Paulo, Brazil), and more.

Global Macro

Carry out trades that reflect anticipated global macroeconomic trends

Exchanges Trading Options

Chicago Board of Options Exchange, International Securities Exchange, NYSE Euronext, Eurex (Europe), and more.

Choice of Contract

Choose a delivery month that is as close as possible to, but later than, the end of the life of the hedge. When there is no futures contract on the asset being hedged, choose the contract whose futures price is most highly correlated with the asset price. This is known as cross hedging (no contract on jet fuel, but heating oil is very correlated with it).

Arguments in Favor of Hedging

Companies should focus on the main business they are in and take steps to minimize risks arising from interest rates, exchange rates, and other market variables.

Rc

Continuously compounded rate

Reasons for Hedging an Equity Portfolio

Desire to be out of the market for a short period of time. (Hedging may be cheaper than selling the portfolio and buying it back.) Desire to hedge systematic risk (Appropriate when you feel that you have picked stocks that will outperform the market.)

Zero Bonds

Determining Zero Rate, there are two methods: (1) observe yields on "strips" - synthetic bonds with only principal payments and (2) use coupon bonds and the "bootstrap method"

Long Hedge Basis

During a long hedge, you hedge the future purchase of an asset by entering into a long futures contract. The price realized for the asset is S2, and the profit on the futures position is F2 - F1. Cost of Asset = S2 - (F2 - F1), or F1 +b2. Basis strengthens unexpectedly, the hedger's position worsens; if the basis weakens unexpectedly, the hedger's position improves.

Short Hedge Basis

During a short hedge, you hedge the future sale of an asset by entering into a short futures contract. The price realized for the asset is S2, and the profit on the futures position is F1-F2. Price realized = S2 + (F1 - F2), or F1 + b2. Basis strengthens (i.e., increases) unexpectedly, the hedger's position improves; if the basis weakens (i.e., decreases) unexpectedly, the hedger's position weakens.

Market-if-touched order

Execute and order at the best price, once a price is touched

Limit Order

Execute at a price, or better

Market Order

Execute at market price

Stop order

Execute order once a particular price is hit -- it becomes a market order

e

Exponential

Annual compounding

FV = Amount * (1+ r)^n

Less than Annual

FV = Amount * (1+(r/m))^n*m

Continuous Compounding Formula Future and Present Value

FV = P e^rt, PV = FV*e^-rt

F2

Final Futures Price

Futures Commission Merchants

Follow the instructions of their clients and charge a commission for doing so

Downward Sloping Yield Curve

For a downward sloping yield curve, Par Yield (R1) > Zero Rate (R2) > Forward Rate (RF)

Upward Sloping Yield Curve

For an upward sloping yield curve, forward rate (RF) > Zero Rate (R2) > Par Yield (R1)

Forward Contracts vs. Futures Contracts

Forward - private contract between two parties, not standardized, usually one specified delivery date, settled at end of contract, delivery or final settlement usual, and some credit risk. Forward - traded on an exchange, standardized, range of delivery dates, settled daily, usually closed out prior to maturity, virtually no credit risk.

Forward Contracts

Forward contracts are similar to futures except that they trade in the over-the-counter market. Forward contracts are popular on currencies and interest rates. A forward contract is an OTC agreement to buy or sell an asset at a certain time in the future for a certain price. There is no daily settlement (but collateral may have to be posted). At the end of the life of the contract one party buys the asset for the agreed price from the other party.

Forward Rates

Forward rates are the implied interest rates for a period of time, based on current zero rates. If one year and two year zero rates are 3% and 4%, respectively; then 5% is the forward rate for year 2. It is the rate when combined with the year 1 rate of 3%, that results in the 4% zero rate for year 2.

Liquidity Preference Theory

Forward rates higher than expected future zero rates

FT

Forward/Future price, price paid for the forward/future

FV

Future Value

Trader Types

Futures Commission Merchants, Locals, Hedgers, Speculators, Arbitrageurs.

Foreign Exchange Quotes

Futures exchange rates are quoted as the number of USD per unit of the foreign currency. Forward exchange rates are quoted in the same way as spot exchange rates. This means that GBP, EUR, AUD, and NZD are USD per unit of foreign currency. Other currencies (e.g., CAD and JPY) are quoted as units of the foreign currency per USD.

Corporate Bond Rates

Generally, corporate bond interest rates are based on a "spread" over the US Treasury Security interest rate

Hedge Funds

Hedge funds are not subject to the same rules as mutual funds and cannot offer their securities publicly. Mutual funds must: disclose investment policies, make shares redeemable at any time, limit use of leverage, take no short positions. Hedge funds are not subject to these constraints. The investment strategy followed by a hedge fund manager often involves using derivatives to set up a speculative or arbitrage positions. Once the strategy has been defined, the hedge fund manager must: evaluate the risks to which the fund is exposed, decide which risks are acceptable and which will be hedged, and devise strategies (usually involving derivatives) to hedge the unacceptable risks.

Hedging

Hedgers use futures, forwards, and options to reduce the risk that they face from potential future movements in a market variable.

Three Reasons for Trading Derivatives

Hedging, Speculation, and Arbitrage. Hedge funds trade derivatives for all three reasons. When a trader has a mandate to use derivatives for hedging or arbitrage, but then switches to speculation, large losses can result.

Position traders

Hold their positions for much longer periods of time, they hope to make significant profits from major movements in the markets.

Delivery

If a futures contract is not closed out before maturity, it is usually settled by delivering the assets underlying the contract. When there are alternatives about what is delivered, where it is delivered, and when it is delivered, the party with the short position chooses. A few contracts (for example, those on stock indices and Eurodollars) are settled in cash. When there is cash settlement contracts are traded until a predetermined time. All are then declared to be closed out.

Rolling the Hedge Forward

If the expiration dates of a hedge are later than the delivery dates of all the futures contracts that can be used, the hedger must roll the hedge forward by closing out one futures contract and taking the same position in a futures contract with a later delivery date. We can use a series of futures contracts to increase the life of a hedge. Each time we switch from 1 futures contract to another we incur a type of basis risk. If a company wishes to use a short hedge to reduce the risk associated with the price to be received for an asset at time T, he can: t1 = short futures contract 1, t2 = close out futures contract 1, short futures contract 2, t3 = close out futures contract 2, short futures contract 3, ... , tn = close out futures contract n-1, short futures contract n. Time T = close out futures contract n.

Hedging Using Index Futures

If the portfolio mirrors the index, a hedge ratio of 1.0 is appropriate. N star = VA / VF. When the portfolio does not exactly mirror the index, we can use (β) Beta from the capital asset pricing model to determine the appropriate number of contracts to short.

Hedging Outcomes

If we assume a perfect hedge - no basis - then the hedge result offsets the physical result - so the net result is "zero". If you make $ on the hedge, you will lose the exact same $ on the physical. If you make $ on the physical, you will lose the exact same $ on the hedge.

F1

Initial Futures Price

r

Interest rate

Collateralization in OTC Markets

It is becoming increasingly common for contracts to be collateralized in OTC markets. Counterparties post margin with each other to reflect changes in the value of the contract. Consider two companies, A and B, that have entered into an over-the-counter contract. A collateralization agreement would typically require them to value the contract each day. If, from one day to the next, the value of the contract to company A inceases, company B is required to pay cash (or other collateral) equal to this company A. But if the value of the contract to company A decrease, company A is required to pay cash equal to the decrease to company B. Interest is paid on outstanding cash balances. Regulators are now insisting that clearinghouses (similar to those used for futures) be used for some OTC standards.

Accounting & Tax

It is logical to recognize hedging profits (losses) at the same time as the losses (profits) on the item being hedged. It is logical to recognize profits and losses from speculation as they are incurred. Roughly speaking, this is what the accounting and tax treatment of futures in the U.S. and many other countries attempts to achieve.

Increase in the basis

Leads to strengthening of the basis

Options are everywhere

Many of you will not be traders, but as "financial types" knowing derivatives are important. How to: hedge expenses or sale prices, negotiate contracts, value capital projects via real options

Why Hedge Equity Returns

May want to be out of the market for a while. Hedging avoids the cost of selling and repurchasing the portfolio. Suppose the stocks in your portfolio have an average beta of 1.0, but you feel they have been chosen well and will outperform the market in both good times and bad times. Hedging ensures that the return you earn is the risk-free return plus the excess return of your portfolio over the market.

h star

Minimum variance hedge ratio. It can be shown that h star is the slope of the best-fit line from a linear regression of ∆S against ∆F

Opening and Closing Futures Positions

Most contracts are closed out before maturity. Reason is that most investors choose to close out their positions prior to the delivery period specified in the contract. Making or taking delivery under the terms of a futures contract is often inconvenient and in some instances quite expensive. This is true even for a hedger who wants to buy or sell the asset underlying the futures contract. Such a hedger usually prefers to close out the futures position and then buy or sell the asset in the usual way. Closing out a futures position involves entering into an offsetting trade.

Fill-or-kill order

Must be executed immediately on receipt or not at all

Optimal Number of Contracts

N star = (h starQA)/QF. The futures contracts should be on h star x QA units of the asset. Round to the nearest whole number. Use this equation for forwards because there is no daily settlement price, it is only at the end of the contract.

Tailing the Hedge

N star = (h starVA)/VF. When futures are used for hedging, a small adjustment, known as tailing the hedge, can be made to allow for the impact of daily settlement.

Cross-Hedging

Occurs when the two assets are different. For example, an airline that is concerned about future price of jet fuel. Since jet fuel futures are not actively traded, it might choose to use heating oil futures contracts to hedge its exposure.

Repo Rates

One party sells Treasury securities to another party, usually on an overnight basis, and buys them back the following day. For the party selling the security (and agreeing to repurchase it in the future) it is a repo; for the party on the other end of the transaction, (buy the security and agreeing to sell in the future) it is a reverse repurchase agreement

Arguments Against Hedging - Explaining a situation when there is a loss, when you use a long hedge

Price decrease means that you will be buying the physical at a lower price and profiting, but the futures position will have led to selling at a lower price and buying back (closing) at a higher price, opportunity cost is the profit you could have made from buying the physical at the lower price. Company is in a "worse position". Price increase means that you will be buying the physical at a higher price, but the future will result in selling the asset at a higher price, then buying it back at a lower one. Company is in a better position because it locked in a price.

Arguments Against Hedging - Explaining a situation when there is a loss, when you use a short hedge

Price decrease will lead to losing money on the sale of the physical, but the futures position leads to an offsetting gain. Company is in the same position as normal. Price increase will lead to gaining money on the sale of the physical, but the futures position leads to an offsetting loss. Company is in a worse off opportunity cost than normal. Hard to explain to executives why we lost money.

Short Call Profit equation

Profit = - Max(St - K, 0) + Premium

Short Put Profit equation

Profit = -Max(K - St, 0) + Premium

Short Forward (Futures) Profit equation

Profit = FT - St

Long Put Profit equation

Profit = Max(K - St, 0) - Premium

Long Call Profit equation

Profit = Max(St - K, 0) - Premium

Long Forward (Futures) Profit equation

Profit = St - FT

Calculating Minimum Variance Hedge Ratio

Proportion of the exposure that should optimally be hedged is: h star = ρ(σS/σF).

You can ..... forward/futures

Purchase or sell

Long/Short Equities

Purchase securities considered to be undervalued and short those considered to be overvalued in such a way that the exposure to the overall direction of the market is small.

Optimal Hedge Ratio

Ratio of the size of the position taken in futures contracts to the size of the exposure. When the asset underlying the futures contract is the same as the asset being hedged, it is natural to use a hedge ratio of 1.0. Hedger's exposure was on 20,000 barrels of oil, and futures contracts were entered into for the delivery of exactly this amount of oil.

Continuous Compounding - Compounding m times per year Conversion formula

Rc = m* ln[1+(Rm/m)], Rm = m(e^Rc/m -1)

Regulation of Futures

Regulation is designed to protect the public interest. Regulators try to prevent questionable trading practices by either individuals on the floor of the exchange or outside groups.

When the underlying asset is different than the asset, gives rise to the hedger's exposure of risk.

S2 * - price of the asset underlying the future contract at time t2. As before, S2 is the price of the asset being hedged at time t2. The price paid (or received) for the asset is S2 + F1 - F2. Can be written as: F1 + (S2* - F2) + (S2 - S2 *). (S2 * - F2) = the basis that would exist if the asset being hedged were the same as the asset underlying the futures contact. (S2 - S2*) = the basis arising from the difference between the two assets.

Rm

Same rate as continuously, but with m times per year

Types of Speculators

Scalpers, Day traders, position traders

Normal Market

Settlement prices increase with the maturity of the contract

Arguments Against Hedging - Individuals do their own hedging

Shareholders are usually well diversified and can make their own hedging decisions. This assumes that the individual shareholders' have as much available information about the company's risks as does management. This also ignores the idea of commissions and other transaction costs. Hedging is less expensive per dollar for large transactions than small transactions. Although a shareholder with a well-diversified portfolio, owning a company that uses copper, and a company that produces copper, will not be subject to copper price variances, so they would not want the company to hedge.

Treasury Bills

Short-term debt obligation backed by the U.S. government with a maturity of less than one year. T-bills commonly have maturities of one month, or six months (4, 13, or 26 weeks)

Hedging Price of an Individual Stock

Similar to hedging a portfolio. Does not work as well because only the systematic risk is hedged. The unsystematic risk that is unique to the stock is not hedged.

QF

Size of one futures contract in units

Special Warning

Some companies hedge when they are "worried". This results in hedging at the wrong time - locking in a loss. This is particularly prevalent when hedging physical commodity positions - think oil, natural gas, electricity, feeds stocks.

Speculation

Speculators use futures, forwards, and options to bet on the future direction of a market variable.

St

Spot price, current price of the underlying asset

Convertible Arbitrage

Take a long position in a convertible bond combined with an actively managed short position in the underlying equity.

Bond Yield

The bond yield is the discount rate that makes the present value of the cash flows on the bond equal to the market price of the bond. More than likely need to use an iterative ("trial and error") method - solver in excel.

∆F

The change in the futures price during the hedging period

∆S

The change in the spot price during the hedging period

ρ

The coefficient of correlation between ∆S and ∆F

More about Delivery

The decision on when to deliver is made by the party with the short position (investor A). When investor A decides to deliver, investor A's broker issues a notice of intention to deliver to the exchange clearinghouse. This notice states how many contracts will be delivered and, in the case of commodities, specifies where delivery will be made and what grade will be delivered. The exchange chooses a party with a long position to accept delivery. Suppose that investor B was the party on the other side of investor A's futures contract when it was entered into. It is important to realize that there is no reason to expect that it will be investor B who takes delivery. Investor B may well have closed out his or her position by trading with investor C, investor C may have closed out his or her position by trading with investor D, and so on. The usual rule chosen by the exchange is to pass the notice of intention to deliver on to the party with the oldest outstanding long position. Parties with long positions must accept delivery notices. However, if the notices are transferable, long investors have a short period of time, usually half an hour, to find another party with a long position that is prepared to accept the notice from them. In the case of a commodity, taking delivery usually means accepting a warehouse receipt in return for immediate payment. The party taking delivery is then responsible for all warehousing costs. In the case of livestock futures, there may be costs associated with feeding and looking after the animals. In the case of financial futures, delivery is usually made by wire transfer. For all contracts the price paid is usually the most recent settlement price.

Net Interest Income

The excess of the interest received over the interest paid

First notice day

The first day on which a notice of intention to make delivery can be submitted to the exchange

RF

The forward LIBOR interest rate for the period between times T1 and T2

RF (FRA Valuation)

The forward rate for the period

Futures Price

The futures price for a particular contract is the price at which you agree to buy or sell. It is determined by supply and demand in the same way as a spot price

Options

The holder has the right, not the obligation to exercise

Last notice day

The last day on which a notice of intention to make a delivery can be submitted to the exchange

Volume of trading

The number of trades in 1 day

Over-the-Counter Markets (OTC)

The over-the counter market is an important alternative to exchanges. It is a telephone and computer-linked network of dealers who do not physically meet. Traders are usually between financial institutions, corporate treasurers, and fund managers.

Terminology

The party that has agreed to buy has a long position (close out by selling). The party that has agreed to sell has a short position (close out by buying).

L

The principal underlying the contract

RK

The rate of interest agreed to in the FRA

σF

The standard deviation of ∆F

σS

The standard deviation of ∆S

Open Interest

The total number of contracts outstanding. This equals to number of long positions or number of short positions.

Ways Derivatives are used

To hedge risks, to speculate (take a view on the future direction of the market), to lock in an arbitrage profit, to change the nature of a liability, to change the nature of an investment incurring the costs of selling one portfolio and buying another

To account for a portfolio with varying betas:

To hedge the risk in a portfolio the number of contracts that should be shorted is: N star = β(P/A). Where P is the value of the portfolio, β is the beta, and A is the value of the assets underlying one futures contract.

Locals

Trade on their own account

Discretionary order or Market-not-held order

Traded as a market order, except that execution may delayed at the broker's discretion in an attempt to get a better price

Convergence example, Futures price is above spot price during delivery period

Traders have a clear arbitrage opportunity, sell (i.e., short) a futures contract, buy the asset, make the delivery. As traders exploit this arbitrage opportunity, the futures price will fall.

Convergence example, Futures price is below spot price during delivery period.

Traders interested in acquiring the asset will find it very attractive to buy the future and wait for delivery. As traders do so, the futures price will rise.

Electronic Trading

Traditionally futures contracts have been traded using the open outcry system where traders physically meet on the floor of the exchange. This is increasingly being replaced by electronic trading where a computer matches buyers and sellers.

Types of Interest Rates

Treasury Bills, Treasury Notes, Treasury Bonds, LIBOR, HIBOR, Eurobor, etc., Repo Rates

Arguments Against Hedging - Increase risk to hedge when competitors do not

Two companies, TakeaChance Co. and SafeandSure Co.. SafeandSure Company chooses to hedge, while TakeaChance Company does not. If the price of gold increases, economic pressure will tend to lead to a corresponding increase in the wholesale price of jewelry, so that TakeaChance Company's gross profit margin is unaffected. In contrast, SafeandSure Company's profit margin will increase after the effects of the hedge have been taken into account. If the price of gold decreases, economic pressures will lead to a corresponding decrease in the wholesale price of jewelry. Again, TakeaChance Company's profit margin is unaffected. However, SafeandSure Company's profit margin could become negative as a result of the "hedging" carried out!

Measuring Interest Rates

Type of interest rate depends on application and "custom". Compounding - daily, monthly, quarterly, semi-annual, annual ... Continuous. For example, for corporate bonds, interest is paid 2 times per year: for term loans interest may be paid monthly, quarterly, semi-annual or annual - for capital evaluation we normally use annual

General Process of Hedging when you will be Acquiring Asset/Commodity

Use a long hedge, at inception - buy forward (long, agree to buy), at termination - buy asset (normal business activity), close out forward by offsetting it, short forward (sell). Cost = Asset Price - (Short Forward - Long Forward)

General Process of Hedging when you will be Selling Asset/Commodity

Use a short hedge, at inception - short forward (agree to sell), at termination - sell asset (normal business activity), close out forward by offsetting it, long forward (buy). Profit = Asset Price - (Short forward - Long Forward)

Derivative Contract Instructions

Use the standard formulas to calculate payoff (does not reflect option premium) and profit (does reflect option premium). See Options and Futures examples Spreadsheet

Lender (Valuation)

Value of FRA where a fixed rate (RK) will be received on a principal L between times T1 and T2 is: L(RK-RF)(T2-T1)e^-R2T2

VF (A)

Value of one futures contract in dollars (the future price times the contract size)

VA (P)

Value of the position being hedged in dollars, or Current value of the portfolio

Day traders

Watching for very short term trends and attempt to profit from small changes in the contract price, hold their positions for less than one trading day, unwilling to take the risk that adverse news will occur overnight.

Scalpers

Watching for very short term trends and attempt to profit from small changes in the contract price, usually only hold their positions for only a few minutes

Discrete Compounding

We compound based on "desire". Annual, and less than Annual. The frequency of compound impacts the future value amount

To calculate the cash price of a bond..

We discount each cash flow at the appropriate zero rate (think of zero rates as PV factors)

Maintenance Margin

When the balance in a trader's margin account falls below the maintenance margin level, the trader receives a margin call requiring the account to be topped up to the initial margin level.

Principal of hedging

When you are "short" physical, go "long" future, when you are "long" physical, "short" future.

When you purchase

You are "long"

When you sell

You are "short"

The nature of derivatives

a derivative is an instrument whose value, depends on the values of other more basic underlying variables

Time-of-Day order

specifies a particular period of time during the day when the order can be executed

Settlement Price

the price just before the final bell each day. This is used for the daily settlement process.

Futures price

the price of the contract, the price for delivery at some time in the future

R2 (FRA) Valuation

the zero rate for maturity T2

Long futures position

this is termed what the person who agreed to buy, close by selling

Short futures position

this is termed what the person who agreed to sell, close by buying