MGMT 41150 - Exam 1
one contract is the rate earned on
$1 million
contract size is
$100,000
a change of one basis point (0.01) in a Eurodollars futures quote corresponds to a contract price change of
$25
The value of a long forward contract:
(F0 - K)*e^(-rT)
The value of a short forward contract
(K - F0)*e^(-rT)
once the trader with the short position chooses a bond, the cash they receive for each $100 of face value is given by:
(P * conversion factor) + accrued interest p is the most recent futures settlement price
the short trader will choose the bond that maximizes the difference:
(P * conversion factor) - Quoted price
Asset with certain income: forward price (F0) =
(S0 - I) * e^(r * T) I is the present value of the income during life of forward contract
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. There are then 2 components to basis. This is known as cross hedging
treasury futures contracts allow the trader with the short position to deliver bonds of different maturities at delivery: - for T-bond futures, bond can be between ____ and ____ years to maturity - for 10-year T-note futures, any bond with ____ to ____ years to maturity will suffice
- 15 and 25 - 6.5 and 10
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.
Price manipulation: Hunt brothers
- Hunt brothers accumulated gigantic futures positions and demanded delivery on those contracts as they came due - they concurrently bought a huge quantity of physical silver and held it off the market - silver price jumped from $6/ounce to $48/ounce -CFTC imposed liquidation-only trading: traders are only allowed to trade to close a futures position -known as "Silver Thursday" -Hunt brothers went bankrupt afterwards
Since 2008 ...
- OTC market has become regulated - In the US and some other countries, standardized OTC products must be traded on swap execution facilities (SEFs) which are similar to exchanges - CCPs must be used for standardized transactions between dealers in most countries - All trades must be reported to a central registry
futures contracts categories
- Physical futures (agricultural, electricity, petroleum, metals, lumber) - Financial futures ( >50% of futures market volume)
Arguments against hedging
- Shareholders are usually well diversified and can make their own hedging decisions - It may increase risk to hedge when competitors do not - Explaining a situation where there is a loss on the hedge and a gain on the underlying can be difficult
Futures contract
- agreement to buy or sell an asset for a certain price at a certain time - similar to forward contract
forward contract
- an agreement between two parties to exchange a given quantity of an asset for a given price at a specific date in the future - these trade OTC and are usually negotiated between two large institutions
Futures contracts
- available on a wide range of assets - exchange traded - specifications need to be defined: what can be delivered, where it can be delivered, when it can be delivered (month long contracts0 - settled daily
Arguments for 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 - company can likely hedge for a lower cost than shareholders
at time T
- deliver underlying, and make payment - zero sum game: the winner's profit is the loser's loss
forward price
- delivery price that would be applicable to the contract if it were negotiated today (i.e., it is the delivery price that would make the contract worth exactly zero) - the forward price may be different for contracts of different maturities
mutual funds must:
- disclose investment policies - make shares redeemable at any time - limit use of leverage
forward market is self-regulated:
- forward contracts are traded OTC - forward contracts are not standardized - forward contracts don't have explicit margin requirements
The OTC market prior to 2008
- largely unregulated - banks acted as market makers quoting bids and offers - master agreements usually defined how transactions between two parties would be handled - But some transactions were handled by central counterparties (CCPs). A CCP stands between the two sides to a transaction in the same way that an exchange does
Reasons to hedge a stock portfolio
- may be out of the market for a while. Hedging avoids the costs of selling and repurchasing the portfolio - suppose 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 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
How derivates are traded
- on exchanges such as the Chicago Board Options Exchange - In the over-the-counter (OTC) market where traders working for banks, fund managers and corporate treasurers contact each other directly (these exchanges are privately negotiated)
basis risk
- risk attributable to uncertain movements in the spread between a futures price and a spot price - usually defined as the spot price of the asset being hedged minus the futures price of the contract used for the hedge - arises because of the uncertainty about the basis when the hedge is closed out
important features of futures
- settled daily - closing out a futures position involves entering into an outsetting trade - most contracts are closed out before maturity - 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
not the spot price
- spot price is the price for delivering the underlying right now - forward price is the price for delivering in the future
At time t
- the counterparties enter the contract - the value of the contract is zero at t, so no money changes hands - net number of outstanding contracts is always zero in the market: Number of long = number of short
not the value of the forward contract
- the value of the forward contract is the current value fo final payoff and it changes over the life of forward - forward price is fixed over the life of the forward
How derivates 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 without incurring the costs of selling one portfolio and buying another
Dangers
- traders can switch from being hedgers to speculators or from being arbitrageurs to speculators - it is important to set up contracts to ensure that trades are using derivatives in for their intended purpose
liquidity concerns
-in any hedging situation there is a danger that losses will be realized on the hedge while the gains on the underlying exposure are unrealized -this can create liquidity problems
types of orders
-market order -limit order -stop-loss order -stop-limit order -market-if-touched order
if Q is the quoted price of a Eurodollar futures contract, the value per contract is:
10,000 * [100 - 0.25(100 - Q)] this equation corresponds to the $25 per basis point rule
the final settlement price is
100-R, where R is the actual 3-month LIBOR on that day
day count - corporate and muni bonds
30/360
treasury bonds are quoted in _____ of a dollar
32nds
Optimal Number of Contracts if no adjustment for daily settlement
= (h* Qa) / Qf Qa = size of position being hedged (units) Qf = size of one futures contract (units)
Optimal number of contracts after "tailing adjustments" to account for daily settlement of futures
=(h^ * Va) / Vf Va = value of position being hedged (=spot price * Qa) Vf = value of one futures contract (=futures price * Qf)
American vs. European Options
An American option can be exercised at any time during its life A European option can be exercised only at maturity
if a stock is trading at a different price in New York and Tokyo what should you do?
Arbitrage trade is: buy at the lower price and immediately sell at the higher price
Hedging Using Index Futures: to hedge the risk in a portfolio, the number of contracts that should be shorted is
B*(Va / Vf) Va = value of the portfolio B = portfolio beta Vf = value of one futures contract
stock going up?
Buy a call
How are forward contracts usually closed?
By delivering the asset
PV =
CF * e^(-r * t)
FV=
CF * e^(r *t)
the forward price equation:
F = S(1 + r)^T
Forward price
F(t,T) = K
Asset with a known yield: forward price (F0) =
F0 = S0 * e^((r-q)*T) q is the average yield during the life of the contract (expressed with continuous compounding)
the futures price and spot price relationship is
F0 = S0*e^((r - q) *T) q is the average dividend yield on the portfolio represented by the index during the life of the contract
currency forward and futures equation
F0 = S0e^(r - rf)T rf is the foreign risk-free interest rate F and S are in USD / foreign currency
Short Hedge for Sale of an Asset: gain on futures
F1 - F2
F1 = F2 = S2 = b2 =
F1: futures price at time hedge is established F2: futures price at time asset is purchased S2: asset price at time of purchase b2: Basis at time of purchase
Long Hedge for Purchase of an Asset: gain on futures
F2 - F1
Types of traders
Hedgers, Speculators, Arbitrageurs
forward price notation
K
Short payoff =
K - ST
Types of hedge funds
Long/Short Equities, Convertible Arbitrage, Distressed Securities, Emerging Markets, Global Macro, Merger Arbitrage.
Size of OTC and Exchange traded markets
OTC market is much larger
Stack and roll
Procedure where short-term futures contracts are rolled forward so that long-term hedges are created.
Spot price of the underlying at maturity
S(T)
Spot price of the underlying at initiation
S(t)
the forward price (F0) =
S0 * e^(r * T)
Long Hedge for Purchase of an Asset: cost of asset
S2
Short Hedge for Sale of an Asset: cost of asset
S2
Short Hedge for Sale of an Asset: Net amount received
S2 + (F1 - F2) = F1 + b2
Long Hedge for Purchase of an Asset: net amount paid
S2 - (F2 - F1) = F1 + b2
spot price of asset on the delivery date
ST
Long payoff =
ST - K
basis =
St - Ft
maturity time (delivery time)
T
what is a Eurodollar?
a dollar deposited in a bank outside the USA
conversion factor
a parameter equal to the quoted price of the bond using a 6% interest rate, and the bond's maturity and time until coupon payment is rounded down to the nearest three months
arbitrage
a risk-free trade that results in a profit
this means changes in the index must correspond to changes in the value of
a tradable portfolio
day count - money market instruments
actual/360
Day count - treasury bonds
actual/actual
What is a Derivative?
an instrument whose value depends on, or is derived from, the value of another asset Ex: futures, forwards, swaps, options, exotics
stock index futures can be viewed as
an investment asset paying a dividend yield
investment assets
assets held by significant numbers of people purely for investment purposes ex: stock market index, bonds, gold
consumption assets
assets held primarily for consumption ex: corn, soybeans, copper, oil
delivery can be made at
at any time during the month
When is K (delivery price / forward price) established?
at the time the contract is established
what does your broker do in this scenario?
borrows the securities from another client and sells them on your behalf in the market the usual way
who establishes a margin account
both the long and short investor
at some stage you must _______ the securities so they can be replaced in the account of the client
buy
when F0 < S0e^((r-q)*T) an arbitrageur
buys futures and shorts or sells the stocks underlying the index
when F0 > S0e^((r-q)*T) an arbitrageur
buys the stocks underlying the index and sells futures
Eurodollars futures are settled in
cash
margin
cash or marketable securities deposited by an investor with his or her broker
Because delivery can involve many possible bonds, the trader with the short position will receive money based on the _______________ of the bond they choose to deliver
conversion factor
the balance in the margin account is adjusted to reflect
daily settlement
to find accrued interest:
day count * coupon payment
hedge funds use complex trading strategies and are big users of _________ for hedging, speculation, and arbitrage
derivatives
you must pay _______ and other benefits the owner of the securities receives
dividends
trader also has a potential wild card play
futures contract settlement price is the bond price at 2 pm Chicago time, but bonds continue to trade after this. If prices decline, they can buy them at the spot price and deliver, if not, roll it to the next day
optimal hedge ratio (h*) =
h* = (coefficient of correlation between change in S and change in F) * ((SD of the change in the spot price during the hedging period) / (SD of the change in the futures price during the hedging period))
optimal hedge ratio (h^) =
h^ = (correlation between percentage daily changes for spot and futures) * ((SD of percentage daily changes in spot) / (SD of percentage daily changes in futures))
margin calls
if the balance in the margin account falls below the maintenance margin level, then the trader will get a margin call, and has to deposit money to bring the margin account up to the initial margin level
for the formula to hold, the index must represent an
investment asset
a _______ futures hedge is appropriate when you know you will purchase an asset in the future and want to lock in the price
long
To raise the beta risk from B to B*, you need to ______ the following amount of contracts
long (B* - B) * (Va / Vf)
what do margins do
minimize the possibility of a loss through a default on a contract
hedge funds are not subject to the same rules as _____ _______ and cannot offer their securities publicly
mutual funds
Whereas a forward contract is traded OTC, a futures contract is traded ....
on an exchange - Chicago Board of Trade and Chicago Mercantile Exchange are two of the biggest exchanges for futures contracts
when do Eurodollar futures expire
on the 3rd Wednesday of the delivery month
the cost of the bond is
quoted price + accrued interest
the price you actually pay for the bond (cash price) =
quoted price + accrued interest
The _____ ________ approach to assessing capital investment decisions has become widely accepted
real options
a _______ futures hedge is appropriate when you know you will sell an asset in the future and want to lock in the price
short
To lower the beta risk from B to B*, you need to ______ the following amount of contracts
short (B - B*) * (Va / Vf)
The underlying assets include ...
stocks, currencies, interest rates, commodities, debt instruments, electricity, insurance payouts, the weather, etc
initiation time
t
what are Eurodollars based on?
the 3-month Eurodollar deposit rate (essentially the same as the 3-month LIBOR)
a strong negative correlation between interest rates and the asset price implies that
the forward price is slightly higher than the futures price
a strong positive correlation between interest rates and the asset price implies that
the futures price is slightly higher than the forwards price
volume of trading
the number of trades in one day
Call option
the option to buy a certain asset by a certain date (known as the expiration date) for a certain price (the strike price)
Put option
the option to sell a certain asset by a certain date (known as the expiration date) for a certain price (the strike price)
long position
the party that has agreed to buy the asset
short position
the party that has agreed to sell the asset
settlement price
the price just before the final bell each day used for daily settlement process
later it may have a positive or negative value depending on ...
the price of the asset
open interest
the total number of contracts outstanding equal to number of long positions or number of short positions
limit order
trade can be executed only at specified limit price or a more favorable price
market order
trade immediately at the best available price (Buy ASAP, sell ASAP)
market-if-touched order
trade is executed at the best available price after a trade occurs at the specified price (or better). For example, a sell MIT order would be at a price above the current market price
stop-loss order
trade is executed immediately once a specified price (or worse) is reached. For example, a market sell order is placed once the price is at or below the stop-loss price (which is less than the current price) "stopping the bleeding"
stop-limit order
trader specifies stop price and limit price: a limit order is submitted as soon as the price hits the stop price (for example, if current price is 30, the stop price could be 35 with a limit price of 37)
Derivatives play a key role in ...
transferring risks in the economy
speculators
use derivative to take bets on an asset moving up or down
arbitrageurs
use derivatives to lock in risk-free profits
hedgers
use derivatives to lower their overall risk
when the maturity and asset price are the same, the forward and futures prices are
usually assumed to be equal
short selling involves selling securities ________
you do not own
A forward contract is worth _______ when it is first negotiated
zero
Forward price is chose to make the contract's initial value ...
zero
The basis converges to ______ as the maturity of the futures contract approaches
zero