p.26
Mark-to-Market Mechanism in Futures
What happens to the long position when the futures price falls to $3,800?
The long position incurs a loss calculated as ($4,200 - $3,800) × 250 × 10 = $1,000,000, which is deducted from the margin account.
p.5
Determining Forward Prices
What is the forward price for the contract that the hedge fund is considering?
The forward price is F0,T = $100.
p.28
Margin Requirements in Futures Trading
What is the initial margin in dollars if the initial margin is 10%?
The initial margin in dollars is 10% of the notional value, which is 0.10 * 9500 = 950.
p.26
Mark-to-Market Mechanism in Futures
What is the balance of the margin account at the end of tomorrow's trading after the loss?
The margin account balance is $3,000,000 × e^r × ∆t - $1,000,000 = $2,000,000, assuming an annualized interest rate r is zero.
p.20
Futures Contracts: Definition and Differences from Forwards
What are futures contracts?
Futures contracts are agreements between two counterparties to exchange a pre-specified amount of an asset at a pre-specified time for a pre-determined price.
p.28
Futures Contracts: Definition and Differences from Forwards
What is the notional value of your position if the XYZ index is at 950 and you buy 10 futures contracts?
The notional value of your position is 950 * 10 = 9500.
p.19
Payoff Structures in Forward Contracts
What is the payoff at time T for a short forward position?
The payoff at time T is F0,T - S0 × N0 × e^(r × T) = F0,T - S0 × e^(r - q) × T > 0.
p.19
Forward Contracts: Definition and Mechanics
What should be done if F0,T < S0 × e^(r - q)T?
The text does not specify the action for this scenario.
p.3
Forward Contracts: Definition and Mechanics
What is a forward contract?
A forward contract is an agreement between two counterparties to buy or sell a certain amount of an underlying asset on a future date for a specified unit price.
p.19
Payoff Structures in Forward Contracts
What is the total number of shares at time T if N0 = e^(-q × T) < 1?
The total number of shares at T is NT = N0 × e^(q × T) = 1.
p.26
Margin Requirements in Futures Trading
How does the margin account balance compare to the maintenance margin requirement?
The margin account balance of $2,000,000 is lower than the maintenance margin requirement of $2,600,000.
p.11
No Arbitrage Principle in Finance
What is the significance of identical payoffs at T for two portfolios?
If two portfolios have identical payoffs at T, they should have the same values today, ensuring no arbitrage opportunities.
p.29
Margin Requirements in Futures Trading
How does the margin account grow after a week with an initial margin of $237,500 and a 6% interest rate?
$237,500 × e^(6%) × (1/52) = $237,774.20.
p.19
Forward Contracts: Definition and Mechanics
What action should be taken if F0,T > S0 × e^(r - q)T?
Short the forward with forward price F0,T and borrow S0 × N0 to buy N0 shares.
p.5
Margin Requirements in Futures Trading
What collateral does the hedge fund need to put up for the forward contract?
$20 in cash as collateral.
p.13
Determining Forward Prices
What is the formula for the simple return of an asset from today till time T?
ret = (S_T - S_0) / S_0 = (S_T / S_0) - 1
p.21
Mark-to-Market Mechanism in Futures
What does mark-to-market mean in the context of futures contracts?
Mark-to-market means that at the end of each trading day, the exchange calculates traders’ losses, and if they are too large, the trader either receives a margin call or his position is immediately closed.
p.21
Mark-to-Market Mechanism in Futures
How does mark-to-market help control counterparty risk?
No exchange in the U.S. has ever defaulted on its payments because they have controlled counterparty risk via mark-to-market.
p.6
Forward Contracts: Definition and Mechanics
What are the main problems faced by the hedge fund in liquidating its position?
Large transaction costs, market liquidation issues, maturity mismatch with standardized bonds
p.5
Forward Contracts: Definition and Mechanics
What is the expected stock price movement for firm XYZ according to the hedge fund?
The hedge fund expects that the stock price will drop within the next year.
p.8
Synthetic Zero-Coupon Bonds
What is the total position in a synthetic zero-coupon bond?
The total position consists of the synthetic zero-coupon bond payoff, the short forward position payoff, and the original stock exposure payoff.
p.20
Futures Contracts: Definition and Differences from Forwards
What are the main differences between futures and forward contracts?
Futures are traded on an exchange, are standardized in terms of size, maturity, and underlying, and have profits and losses marked to market with daily settlement.
p.2
Spot Markets and Outright Purchases
What are spot markets?
Markets for outright purchases where all steps of the transaction occur simultaneously.
p.11
No Arbitrage Principle in Finance
What does it imply if F0,T > S0 × e^(r0 × T)?
Portfolio #2 is relatively underpriced, leading to a risk-free profit by going long on portfolio #2 and short on portfolio #1.
p.10
Determining Forward Prices
How is the forward price F0,T determined?
The forward price F0,T can be determined by creating a replicating portfolio that mimics the payoff of the forward contract, which involves borrowing zero-coupon bonds and purchasing the underlying asset.
p.3
Forward Contracts: Definition and Mechanics
What is the convention regarding the cost of entering into a forward contract?
It costs nothing to enter into a forward contract when initiated, although parties can choose other arrangements if preferred.
p.10
Payoff Structures in Forward Contracts
What is the payoff at time T for a long underlying position?
The payoff at time T for a long underlying position is N0 × (ST).
p.16
Determining Forward Prices
If the S&P 500 index spot price is 1100 and a 6-month forward price of 1115 is quoted, what do you do?
You would enter into the forward contract as the quoted price is lower than the expected future price based on the risk-free rate.
p.9
No Arbitrage Principle in Finance
What is the no arbitrage principle in finance?
The no arbitrage principle states that two securities with identical payoffs should have the same price in well-functioning markets; otherwise, arbitrageurs will exploit the price difference until the prices equalize.
p.9
No Arbitrage Principle in Finance
What constitutes an arbitrage opportunity?
An arbitrage opportunity is a trading strategy that either costs nothing today and yields a profit in the future or yields a profit today with guaranteed zero cash flows in the future.
p.2
Spot Markets and Outright Purchases
What occurs simultaneously in an outright purchase?
All three steps: setting the price, transferring cash, and transferring the share occur simultaneously.
p.10
Payoff Structures in Forward Contracts
What is the value at time 0 for a long forward position?
The value at time 0 for a long forward position is 0.
p.3
Forward Contracts: Definition and Mechanics
What does the expiration (maturity) date T represent in a forward contract?
The expiration date T is the date of the final purchase and payment.
p.13
Determining Forward Prices
What is the relationship between expected log-return and expected asset price?
μ_0 × T = ln(E_0[S_T] / S_0), leading to E_0[S_T] = S_0 × e^(μ_0 × T).
p.18
Payoff Structures in Forward Contracts
What is the value of Portfolio #1 at time 0 if it consists of a long forward and shares of stock?
The value at time 0 is 0.
p.18
Payoff Structures in Forward Contracts
What is the total value of the portfolio at time 0 when considering both long forward and short bonds?
Total value is S0 × e^(-q × T) - F0,T × e^(-r × T).
p.12
Determining Forward Prices
How is the expected log-return of the underlying calculated?
The expected log-return can be found from E0[ST] = S0 × e^(μ0 × T).
p.4
Payoff Structures in Forward Contracts
What is the payoff to a long forward contract at maturity T?
The payoff to a long forward contract is N0 × (ST − F0,T).
p.23
Futures Contracts: Definition and Differences from Forwards
What must be specified in the futures contract regarding delivery?
The delivery must occur at a given location, which is also specified by the contract.
p.8
Synthetic Zero-Coupon Bonds
What does the payoff of a synthetic zero-coupon bond depend on?
The payoff of a synthetic zero-coupon bond depends on the stock price at time T and the forward price.
p.2
Spot Markets and Outright Purchases
What are the three steps involved in buying a share of firm XYZ's stock?
1. Set the price to be paid 2. Transfer cash from the buyer to the seller 3. Transfer the share from the seller to the buyer
p.24
Margin Requirements in Futures Trading
What is the initial margin in futures contracts?
The initial margin is the collateral that both counterparties must set up with the exchange when entering a futures contract, allowing the exchange to control their risk.
p.18
Determining Forward Prices
What is the formula for the forward price on a stock with a known continuously-compounded dividend yield?
F0,T = S0 × e^(r - q) × T
p.14
Forward Contracts: Definition and Mechanics
What is the initial value of a forward contract?
The initial value of a forward contract is 0.
p.27
Margin Requirements in Futures Trading
What is the purpose of a margin call in futures trading?
The margin call is to restore the initial margin and ensure that the value of an existing futures position does not become too negative.
p.24
Mark-to-Market Mechanism in Futures
What is the daily 'mark to market' process in futures trading?
The daily 'mark to market' process involves traders paying losses or receiving gains at the close of each day, which are either deducted from or credited to their margin accounts.
p.3
Forward Contracts: Definition and Mechanics
Where are forward contracts typically traded?
Forward contracts are traded on OTC (over-the-counter) markets, not on exchanges.
p.14
Forward Contracts: Definition and Mechanics
What options does a hedge fund have if it wants to exit a forward contract at time t?
The hedge fund can either cancel the original contract with the original counterparty or enter into a reverse forward contract with a new counterparty.
p.27
Margin Requirements in Futures Trading
What is the remaining amount in the margin account after closing the long position?
$2,000,000 is the remaining amount in the margin account after the long position is closed.
p.14
No Arbitrage Principle in Finance
What must be true about the outcomes when exiting a forward contract?
The outcomes must be the same regardless of whether the fund deals with the original counterparty or a new one, to avoid arbitrage.
p.9
No Arbitrage Principle in Finance
How is the value of derivative securities determined?
The value of derivative securities is determined by assuming no arbitrage exists in the market.
p.4
Forward Contracts: Definition and Mechanics
What is the nature of a forward contract in terms of profit and loss?
A forward contract is a zero-sum game, meaning one party's gain is the other party's loss.
p.28
Margin Requirements in Futures Trading
What is the highest XYZ index futures price 1 week from today at which you will receive a margin call?
You will receive a margin call if the futures price drops below the maintenance margin, which is 80% of the initial margin. The maintenance margin is 0.80 * 950 = 760. Therefore, the highest futures price is 950 - (950 - 760) = 760.
p.17
Forward Contracts: Definition and Mechanics
What strategy is employed when the price of a six-month forward contract is $1115?
Short-sell one share and deposit the proceeds at the risk-free rate while buying the forward.
p.13
Determining Forward Prices
How is the annualized return calculated?
The annualized return is calculated as (1/T) * ret, where T is measured in years.
p.25
Mark-to-Market Mechanism in Futures
What is the notional value for 10 contracts of September 2023 S&P 500 futures?
$10,000,000 = 10 × 250 × $4,000
p.10
Payoff Structures in Forward Contracts
What is the total value of the portfolio that includes short bonds and a long underlying?
The total value of the portfolio is N0 × (S0 − F0,T × e−r0×T).
p.15
Forward Contracts: Definition and Mechanics
How is the value of the original short forward contract today calculated?
It equals the present value of the risk-free payoff at time T, which is e^−r × (T − t) × N0 × (F0,T − Ft,T)
p.9
No Arbitrage Principle in Finance
What is the Law of One Price?
The Law of One Price is the principle that in well-functioning markets, identical goods must sell for the same price, which is fundamental to derivative pricing.
p.4
Payoff Structures in Forward Contracts
What happens if ST > F0,T in a forward contract?
If ST > F0,T, the buyer (long position) makes a profit by paying only F0,T instead of ST.
p.11
No Arbitrage Principle in Finance
What action should be taken if F0,T < S0 × e^(r0 × T)?
Portfolio #2 is relatively overpriced, so one should short portfolio #2 and long portfolio #1 to achieve a risk-free profit.
p.8
Synthetic Zero-Coupon Bonds
What is the role of the short forward position in a synthetic zero-coupon bond?
The short forward position contributes to the overall payoff structure of the synthetic zero-coupon bond.
p.20
Futures Contracts: Definition and Differences from Forwards
Why is standardization important in futures contracts?
Standardization is important for reducing liquidity risk, but it may introduce a possible mismatch between the futures contract size or maturity and the actual needs of market participants.
p.29
Margin Requirements in Futures Trading
What is the notional value of the position when each contract is for 250 units of the XYZ index and the price is $950?
$950 × 10 × 250 = $2,375,000.
p.29
Margin Requirements in Futures Trading
How is the value of X determined in the margin call scenario?
By solving the equation: 950 × 8% × 250 × 10 = $237,774.20 − ($950 − X) × 250 × 10, resulting in X = $930.89.
p.12
Determining Forward Prices
What factors does the forward price depend on?
The forward price depends only on the interest rate (r0) and the current spot price (S0).
p.9
No Arbitrage Principle in Finance
Does the definition of arbitrage opportunity mention the magnitude of profit?
No, the definition does not specify the magnitude of profit because it focuses on the existence of a profit without any loss being possible.
p.23
Futures Contracts: Definition and Differences from Forwards
When can delivery of the asset occur in a futures contract?
Delivery of the asset can occur only during the specified delivery months and on specific dates.
p.10
Forward Contracts: Definition and Mechanics
What does a replicating portfolio do in the context of forward contracts?
A replicating portfolio replicates the payoff of the forward contract by using borrowed funds to buy the underlying asset.
p.3
Determining Forward Prices
What is the forward price in a forward contract?
The forward price is set to ensure that the value of the forward contract equals zero for both parties at the inception of the contract.
p.22
Various Underlying Assets for Futures Contracts
Which currencies are commonly traded in futures contracts?
USD/EUR, USD/GBP, USD/AUD, EUR/AUD.
p.21
Futures Contracts: Definition and Differences from Forwards
Who is the counterparty in a futures trade?
The exchange clearing house is the counterparty to both parties in the trade and does not take substantial risky positions.
p.14
Determining Forward Prices
What happens to the value of a forward contract at any point t between 0 and T?
At any point t, the value of the forward contract can be determined by the current stock price St and the forward price Ft,T.
p.27
Margin Requirements in Futures Trading
What amount was requested in the margin call example?
$1,000,000 was requested to restore the initial margin.
p.15
Determining Forward Prices
What is the forward price today (time t) for a forward contract?
Ft,T = St × e^r × (T − t)
p.23
Futures Contracts: Definition and Differences from Forwards
How are futures contracts referred to in terms of delivery?
Futures contracts are referred to by their delivery months, which are specified by the exchange.
p.24
Margin Requirements in Futures Trading
What happens if a trader's account falls below the maintenance margin?
If the amount in the trader’s account falls below a maintenance margin, the exchange issues a margin call, requiring the trader to post additional collateral to restore the initial margin or risk having their position closed by the exchange.
p.18
Forward Contracts: Definition and Mechanics
How many shares will you have at time T if you start with 1 share at time t=0 and have a continuously-compounded dividend yield q?
You will have 1 × e^(q × T) shares at T.
p.14
Payoff Structures in Forward Contracts
How is the value of a forward contract determined at maturity?
At maturity T, the value of a forward contract is equal to the payoff, which is F0,T - ST for a short position.
p.22
Various Underlying Assets for Futures Contracts
What are some equity indexes that have futures contracts?
S&P 500, NASDAQ 100, RUSSELL 2000.
p.16
Determining Forward Prices
What is the fair compensation required to sell a non-dividend paying security for 50 one year from now, if it is currently trading at 100 and the interest rate is positive?
Zero, because in expectation you neither gain nor lose from this trade.
p.16
Forward Contracts: Definition and Mechanics
What does it mean to sell short?
Selling short means borrowing a security and selling it with the intention of buying it back later at a lower price.
p.16
Forward Contracts: Definition and Mechanics
What does it mean to sell long?
Selling long means buying a security with the expectation that its price will rise, allowing you to sell it later for a profit.
p.12
Determining Forward Prices
What is the difference between the expected log-return and the forward price called?
The difference is called the 'risk premium'.
p.23
Futures Contracts: Definition and Differences from Forwards
What are the two types of settlement in futures contracts?
The two types of settlement in futures contracts are physical settlement and cash settlement.
p.22
Various Underlying Assets for Futures Contracts
What are some examples of commodities available for futures contracts?
Softs like corn, wheat, soybean, cocoa, coffee, orange juice; metals like gold and silver; energies like crude oil and natural gas.
p.21
Futures Contracts: Definition and Differences from Forwards
What does it mean to reverse a position in futures trading?
Reversing means to take a position opposite to the original one, such as taking a short position after having taken a long position.
p.3
Forward Contracts: Definition and Mechanics
How is the notional value of a forward contract calculated?
The notional value is calculated as N0 × S0, where N0 is the amount of the underlying asset and S0 is the spot price of the underlying.
p.27
Mark-to-Market Mechanism in Futures
How does mark-to-market benefit futures trading?
Mark-to-market ensures that the value of an existing futures position does not become too negative at any trading day.
p.21
No Arbitrage Principle in Finance
What would have mitigated the impact of Lehman Brothers' bankruptcy?
Lehman Brothers’ bankruptcy would not have been so devastating if its various derivative positions had been held at a clearinghouse.
p.29
Margin Requirements in Futures Trading
What condition must be met for a margin call to occur based on the margin account after marking to market?
The maintenance margin must be higher or equal to $237,774.20 − ($950 − X) × 250 × 10.
p.7
Synthetic Zero-Coupon Bonds
How is the continuously-compounded interest rate r_0 defined?
The continuously-compounded interest rate r_0 is defined as r_0 = 1/T ln(F_0, T/S_0) = 4.79%.
p.23
Payoff Structures in Forward Contracts
How does the daily Profit and Loss (P&L) for the buyer of a futures contract get calculated?
The daily P&L for the buyer is calculated as: Daily P&L = Contract Size × (b F t, T − b F t − 1, T).
p.23
Payoff Structures in Forward Contracts
What is the nature of the relationship between the gains and losses of the two parties in a futures contract?
The relationship is zero-sum; what one party gains, the other loses.
p.4
Forward Contracts: Definition and Mechanics
What are the two counterparties in a forward contract?
The two counterparties are the long position (buyer of the underlying at expiration date T) and the short position (seller of the underlying at expiration date T).
p.27
Margin Requirements in Futures Trading
What happens if you do not meet a margin call in futures trading?
If you do not meet the margin call, the exchange will close your long position and refund the remaining amount in your margin account.
p.13
Determining Forward Prices
How is the expected return of an asset estimated today?
E_0[ret] = (E_0[S_T] / S_0) - 1
p.16
Forward Contracts: Definition and Mechanics
Do you think people steal forwards? Explain.
While forwards are contracts and not physical assets, they can be manipulated or misrepresented. However, the concept of stealing a forward contract is more about fraud or breach of contract rather than theft in the traditional sense.
p.2
Spot Markets and Outright Purchases
Can you give examples of outright purchases?
Cash purchases of coffee, sandwiches, books, etc.
p.7
Synthetic Zero-Coupon Bonds
What is the outcome of a synthetic zero-coupon bond independent of the future stock price S_T?
The outcome is risk-free and is given by N_0 × F_0, T.
p.7
Synthetic Zero-Coupon Bonds
Why is the term 'synthetic' used in synthetic zero-coupon bonds?
It is called 'synthetic' because the outcome will be the same if the asset manager sells N_0 shares of stock ZYX at S_0 and uses the proceeds to buy a zero-coupon bond.
p.7
Synthetic Zero-Coupon Bonds
What is the simple interest rate r_S_0 in the context of synthetic zero-coupon bonds?
The simple interest rate r_S_0 is calculated as r_S_0 = 1/T [F_0, T/S_0 - 1] = 5%.
p.24
Margin Requirements in Futures Trading
How do exchanges adjust margin requirements?
Exchanges adjust margins frequently based on market volatility; they typically raise margins during volatile price moves and lower them when price moves become less volatile.
p.18
Forward Contracts: Definition and Mechanics
What does the variable q represent in the context of forward contracts on stocks?
q is the 'implied' continuously-compounded dividend yield.
p.22
Various Underlying Assets for Futures Contracts
What types of interest rate products are available for futures contracts?
Eurodollars, Treasury bonds and notes.
p.22
Various Underlying Assets for Futures Contracts
What are weather products in the context of futures contracts?
Products like heating degree days in cities such as Atlanta, Chicago, New York, and Las Vegas.
p.12
Determining Forward Prices
Does the forward price predict the future spot price?
No, the forward price typically differs from the expected future price due to the risk premium.
p.15
Payoff Structures in Forward Contracts
What does the fund receive at time T from the original short forward and reverse forward?
A risk-free payoff equal to N0 × (F0,T − Ft,T)
p.12
Determining Forward Prices
What is the formula for the forward price?
The forward price is given by S0 × e^(r0 × T).
p.12
Determining Forward Prices
When is the risk premium usually positive?
The risk premium is usually positive if the underlying is risky.
p.4
Payoff Structures in Forward Contracts
What is the payoff to a short forward contract at maturity T?
The payoff to a short forward contract is N0 × (F0,T − ST).
p.14
Determining Forward Prices
What is the forward price of the reverse contract at time t?
The forward price of the reverse contract at time t is Ft,T.
p.16
Determining Forward Prices
If the S&P 500 index spot price is 1100 and a 6-month forward price of 1135 is quoted, what do you do?
You would not enter into the forward contract as the quoted price is higher than the expected future price based on the risk-free rate.
p.23
Futures Contracts: Definition and Differences from Forwards
What is the futures price at time 0?
The futures price at time 0, denoted as b F 0, T, is the price at which the trader who shorts the futures agrees to sell the underlying asset to the trader who buys (is long) the futures.
p.23
Payoff Structures in Forward Contracts
What happens to the party who agrees to buy the asset at maturity when the price increases?
The party who agrees to buy the asset at maturity gains when the price increases and loses otherwise.
p.4
Payoff Structures in Forward Contracts
What happens if ST < F0,T in a forward contract?
If ST < F0,T, the seller (short position) makes a profit by receiving F0,T instead of ST.
