deriv mark/fwd mark/futures/options/swap/risk Flashcards
Define a deriviative and distinguish between exchange-traded and over-the-counter derivatives
A derivative has a value that is derived from the value of another asset or interest rate.
Exchange-traded derivatives, notably futures and some options, are traded in centralized locations and are standardized, regulated, and default risk free.
Forwards and swaps are customized contracts (over-the-counter derivatives) created by dealers and by financial institutions. There is very limited trading of these contracts in secondary markets and default (counterparty) risk must be considered.
Contrast forward commitments and contingent claims
A forward commitment is a binding promise to buy or sell an asset or make a payment in the future. Forward contracts, futures contracts, and swaps are all forward commitments
A contingent claim is an asset that has value only if some future event takes place (e.g. asset price is greater than a specified price). Options are contingent claims.
Define forward contracts, futures contracts, options (calls and puts), and swaps and compare their basic characteristics.
Foward contracts obligate one party to buy, and another to sell, as specific asset at a predetermined price at a specific time in the future.
Swaps contracts are equibalent to a series of forward contracts on interest rates, currencies, or equity returns.
Futures contracts are much like forward contracts, but are exchange-traded, quite liquid, and require daily settlement of any gains or losses.
A call option gives the holder the right, but not the obligations, to buy an asset at a predetermined price at some time in the future.
A put option gives the holder the right, but not the obligation to sell an asset at a predetermined price at some time in the future.
The owner of a call can “call the asset in” (i.e. buy it); the owner of a put has the right to “put the asset to” the writer of the put
Describe purposes of an controversies related to derivative markets.
Deriviative markets are criticized for their risky nautre. However, many market participants use derivatives to manage and reduce existing risk exposures.
Derivative securities play an important role in promoting efficient market prices and reducing transactions costs.
Explain arbitrage and the role it plays in determining prices and promoting market efficiency.
Riskless arbitrage refers to earning more than the risk-free rate of return with no risk, or earning an immediate gain with no possible future liability.
Arbitrage can be expected to force the prices of two securities or portfolios of securities to be equal if they have the same future cash flows regardless of future events.
Explain delivery/settlement and default risk for both long and short positions in a foward contract.
A deliverable forward contract on an asset specified that the long (the buyer) will pay a certain amount at a future date to the short, who will deliver a certain amount of an asset.
Default risk in a forward contract is the risk that the other party to the contract will not perform at settlement, because typically no money changes hands at the initiation of the contract.
Describe the procedures for settling a forward contract at expiration, and how termination prior to expiration can affect credit risk.
A forward contract with cash settlement does not require delivery of the underlying asset, but a cash payment at the settlement date from one counterparty to the other, based on the contract price and the market price of the asset at settlement.
Early termination of a forward contract can be accomplished by entering into a new forward contract with the opposite position, at the then-current expected forward price. This early termination will fix the amount of the gain or loss at the settlement date. If this new forward is with a different counterparty than the original, there is credit or default risk to consider since once of the two counterparties may fail to honor its obligation under the forward contract.
Distinguish between a dealer and an end user of a forward contract
An end user of a forward contract is most often a corporation hedging an exisiting risk.
Forward dealers, large banks, or brokerages originate forward contracts and take the long side in some contracts and the *short side *in others, with a spread in pricing to compensate them for actual costs, bearing default risk, and any unhedged price risk they must bear.
Describe the charaacterisitics of equity forward contracts and forward contracts on zero-coupon and coupon bonds.
An equity forward contract may be on a single stock, a customized portfolio, or an equity index, and is used to hedge the risk of equity prices at some future date.
- equity forward contracts can be written on a total return basis (including dividends), but are typically based solely on an index value
- index forwards settle in cash based on the notional amount and the percentage difference between the index value in the forward contract and the actual index level at settlement
Forward contracts in which bonds are the underlying asset may be quoted in terms of the discount on zero-coupon bonds (e.g. t-bills) or in terms of the yield to maturity on coupon bonds. Forwards on corportate bonds must contain special provisions to deal with the possibility of default as well as with any call or conversion features. Forward contracts may also be written on portfolios of fixed income securities or on bonds indexes.
A portfolio manager desires to generate $10 million 100 days from now from a portfolio that is quite similar in composition to the S&P 100 index. She requests a quote on a short position in a 100-day forward contract based on the index with a notional amount of $10 million and gets a quote of 525.2. If the index level at the settlement date is 535.7, calculate the amount the manager will pay or receive to settle the contract.
The actual index level is 2% above contract price, or:
535.7/525.2 - 1 = 0.02 = 2%
As the short party, the portfolio manager must pay 2% of the $10 million notional amount, $200,000, to the long.
Alternatively, if the index were 1% below the contract level, the portfolio manager would receive a payment from the long of $100,000, which would approximately offset any decrease in the portfolio value.
A forward contract covering a $10 million face value of T-bills that will have 100 days to maturity at contract settlement is priced at 1.96 on a discount yield basis. Compute the dollar amount the long must pay at settlement for the T-bills.
The 1.96% annualized discount must be “unannualized” based on the 100 days to maturity.
0.0196 * 9100/360) = 0.005444 is the actual discount
The dollar settlement price is (1-0.005444) * $10 million = $9,945,560
Please note that when market interest rates increase, discount increase, and T-bill prices fall. A long, who is obligated to purchase the bonds, will have losses on the forward contract when interest rates rise, and gains on the contract when interest rates fall. The outcomes for the short will be opposite.
Describe the characterisitcs of the Eurodollar time deposit market, and define LIBOR and Euribor
Eurodollar time deposits are USD-denominated shot-term unsecured loans to large money-center banks outside the US
The London Interbank Offered Rate (LIBOR) is an international reference rate for Eurodollar deposits and is quoted for 30-day, 60-day, 90 day, 180-day, 360-day (1 year) terms.
Euribor is the equivalent for short-term Euro denominated bank deposits (loans to banks)
For both LIBOR and Euribor, rates are expressed as annual rates and actual interest is based on the loan term as a proportion of a 360-day year.
Describe forward rate agreements (FRAs) and calculate the gain/loss on a FRA
Forward rate agreements (FRAs) serve to hedge the uncertainty about short-term rates (e.g. 30 or 90 day LIBOR) that will prevail in the future. If rates rise, the long receives a payment at settlement. The short receives a payment if the specified rate falls to a level below the contract rate.
Calculate and interpret the payoff of a FRA and explain each of the component terms of the payoff formula
The payment to the long at settlement on an FRA is:
The numerator is the difference between the rate on a loan for the specified period at the forward contract rate and the rate at settlement, it’s the interest savings in percent
and the denominator is to discount this interest differential back to the settlement date at the market rate at settlement.
Consider an FRA that:
- expires/settles in 30 days
- is based on a notional principal amount of $1 million
- is based on 90-day LIBOR
- specifies a forward rate of 5%
Assume the actual 90-day LIBOR 30-days from now (at expiration) is 6%. Compute the cash settlement payment at expiration, and identify which party makes the payment
If the long could corrow at the contract rate of 5%, rather than the market rate of 6%, the interest saved on a 90-day $1 million loan would be:
(0.06 - 0.05)(90/360) * 1 million = 0.0025 * 1 million = $2,500
The $2,500 in interest savings would not come until the end of the 90-day loan period. The value at settlement is the PV of these savings. The correct discount rate to use is the acutal rate at settlement, 6% not the contract rate of 5%.
The payment at settlement from the short to the long is:
2,500 / 1+[(0.06) * 90/360)] = $2,463.05
Describe the characterisitcs of currency foward contracts
Currency forward contracts specify that one party will deliver a certain amount of one currency at the settlement date in exchange for a certain amount of another currency.
Under cash settlement, a single cash payment is made at settlement based on the difference between the exchange rate fixed in the contract and the market exchange rate at the settlement date.
Gemco expects to receive EUR50 million three months from now and enters into a cash settlement currecny forward to exchange thes euros for US dollars at USD1.23 per euro. If the market exchange rate is USD1.25 per euro at settlement, what is the amount of the payment to be received or paid by Gemco?
Under the terms of the contract Gemco would receive:
EUR 50 million * USD/EUR 1.23 = USD61.5 million
Without the forward contract, Gemco would receive:
EUR 50 million * USD/EUR 1.25 = USD62.5 million
The counterparty would be disadvantaged by the difference between teh contract rate and the market rate in an amount equal to the advantage that would have accrued to Gemco had they not entered into the currency forward
Gemco must make a payment of USD1.0 million to the counter party.
A direct calculation of the value of the log (USD) position at settlement is:
(USD/EUR 1.23 - USD/EUR 1.25) * EUR50 million = -USD1.0 million
Describe the characteristics of futures contracts
Compare futures contracts and forward contracts
Like forward contracts, futures contracts are most commonly for delivery of commodities and financial assets at a future date and can require delivery or settlement in cash
Compared to foward contracts,futures contracts:
- are more liquid, trade on exchanges, and can be closed out by an offsetting trade
- do not have counterparty risk; the clearing house acts as coutnerparty to each side of the contract
- have lower transactions costs
- require margin deposits and are marked to market daily
- are standardized contracts as to asset quantity, quality, settlement dates, and delivery requirements
Distinguish between margin in the securities markets and margin in the futures markets, and explain the role of initial margin, maintenance margin, variation margin, and settlement in futures trading
Futures margins deposits are not loans, but deposits to ensure performance under the terms of the contract.
- Initial margin* is the deposit required to initiate a futures position
- Maintenance margin* is the minimum margin amount. When margin falls below this amount, it must be brought back up to its initial level by depositing varation margin.
Margin calculations are based on the daily settlement price, the average prices for trades during a closing period set by the exchange.
Describe price limits and the process of marking to market, and calculate and interpret the margin balance, given the previous day’s balance and the change in the futures price.
Trades cannot take place at prices that differ from the previous day’s settlement prices by more than the price limit and are said to be limit down (up) when the new equilibrium price is below (above) the minimum (maximum) price for the day.
Marketing-to-market is the process of adding gains to or subtracting losses from the margin account daily, based on the exchange in settlement prices from one day to the next.
The mark-to-market adjustment either adds the day’s gains in the contract value to the long’s margin balance and subtracts them from the short’s margin balance, or subtracts the day’s loss in contract value from the long’s margin balance and adds them to the short’s margin blaance.
Consider a long position of five July wheat contracts, each of which covers 5,000 bushels. Assume that the contract price is $2.00 and that each contract requires an initial margin deposit of $150 and a maintenance margin of $100. The total initial margin required for the 5- contract trade is $750. The maintenance margin for the account is $500. Compute the margin balance for this position after a 2-cent decrease in price on Day 1 , a 1-cent increase in price on Day 2 , and a 1-cent decrease in price on Day 3.
Each contract is for 5,000 bushels so that a price change of $0.01 per bushel changes the contract vlue by $50, or $250 for the five contracts: (0.01)(5)(5,000) = $250,000
The following figure illustrates the change in the margin balance as the price of this contract changes each day. Note that the initial balance is the initial margin requirement of $750 and that the required deposit is basedon the previous day’s price change.
(figure)
At the cose on Day 1, the margin balance has gone below the minimum or maintenance margin level of $500. Therefore, a deposit of $500 is required to bring the margin back to the initial margin level of $750. We can interpret the margin balance at any point as the amount the investor would realize if the position were closed out by a reversing trade at the most recent settlement price used to calculate the margin balanace.
Describe the concept of moneyness of an option.
Moneyness for puts and calls is determined by the difference between the strike price (X) and the market price of the underlying stock (S)
- in the money*
- out of the money*
Descirbe interest rate caps, floors, and collars
Interest rate caps put a maximum (upper limit) on payments on a floating-rate loan and are equivalent (from the borrower’s perspective) to a series of long inerest rate calls at the cap rate.
Interest rate floors put a minimum (lower limit) on the payments on a floating-rate loan and are equivalent (from the borrower’s perspective) to a series of short interest rate puts at the floor rate.
Interest rate collar combines a cap and a floor. A borrower can create a collar on a floating-rate loan by buying a cap and selling a floor.
Define intrinsic value, and time value, and explain their relationship.
The intrinsic value of an option is the payoff from immediate exercise if the option is in the money, and zero otherwise
The time (speculative) value of an option is the difference between its premium (market price) and its intrinsic value. At expiration, time value is zero.
intrinsic value of a call option = (S-X) or 0
intrinsic value of a put option = (X-S) or 0
Determine the minimum and maximum value of European options and American options
Calculate and interprest the lower prices of European and American calls and puts based on the fules for minimum values and lower bounds.
(figure)
- an american call is worth as least as much as a European call to claim*
- the lower bound on an American call is a least as much as the lower bound on European call*
- the lower bound on a European put is below that of an American put option (i.e. max[0,X-S0]}. This is because when it;s in the money, the American put option can be excised immediately for a payoff of X - S0*
Compute the lowest possible price for 4-month American and European 65 puts on a stock that is trading at 63 when the risk-free rate is 5%.
Compute the lowest possible price for a 3-month American and European 65 calls on a stock that is trading at 68 when the risk-free rate is 5%
Explain put-call parity for European options, and explain how put-call parity is related to arbitrage and the construction of synthetic options.
fiduciary call (a call option and a risk-free zero-coupon bond that pays the strike pirce X at expiration) and a protective put (a share of stock and a put at X) have the same payoffs at expiration, or arbitrate will force thses positions to have equal prices:
c + X / (1 + RFR)T= S + p
This establishes the put call-parity
Based on the put-call parity relation, a synthetic security (stock, bond, call or put) can be creaed by combining long and short positions in the other three securities
Explain how cash flows, on the underlying asset affect put-call parity and the lower bounds of option prices
When the underlying asset has positive cash flows, the minima, and maxima, and put-call parity relations are adjusted by subtracting the present value of the expected cash flows from the assets over the life of the option. That is, S can be replaced by (S - PV of expected cash flows)
Determine the directional effect of an interest rate change or volatility change on an option’s price
An increase in the risk-free rate will increase call value and decrease put values (for options that do not explicitly depend on interest rates or bond values).
Increased volatility of the underlying asset or interest rate increases both put values and call values.
Describe, calculate, and interpret the payments of currency swaps, plain vanilla interest rate swaps, and equity swaps
In an equity swap, the returns payer makes payments based on the return on a stock, portfolio or index, in exchange for fixed- or floating-rate payments. If the stock, portfolio, or index, declines in value over the period, the returns payer receives the interest payment and a payment based on the percentage decline in value
In a currency swap, the notional principal (in two different currencies) is exchanged at the inception of the swap, periodic interest payements in two different currencies are exchanged on settlement dates, and the same notional amounts are exchanged (repaid) on the termination date of the swap.
In plain vanilla (fixed-for-floating) interest-rate swap, one party agrees to pay a floating rate of interest on the notional amount and the counterparty agrees to pay a fixed rate of interest.
The formula for the net payment by the fixed-year rate payer, based on a 360-day year and the number of days in the settlement period is:
(figure)
Calculating the payments on an interest rate swap
Bank A enteres into a $1,000,000 quarterly-pay plain vanilla interest rate swap at a fixed-rate of 6% based on a 360-day year. The floating-rate payer agrees to pay 90-day LIBOR plus a 1% margin; 90-day LIBRO is currently 4%.
(figure)
Calculate the amounts Bank A pays or receives 90, 270,, and 360 days from now.
The payment 90 days from now depends on current LIBROR and the fixed rate (don’t forget the 1% margin).
Fixed-rate payer pays:
(figure)
270 days from now, the payment is based on LIBOR 180 days from now, which is 5%. Adding the 1% margin makes the floating-rate 6%, which is equal to the fixed rate, so there is not net thrid quarterly payment.
The bank’s “payment” 360 days from now is:
(figure)
Because the floating-rate payment exceeds the fixed-rate paymet, Bank A will receive $1,250 at the fourth payment date
Ms. Smith enters into a 2-year $10 million quarterly swap as the fixed payer and will receive the index return on the S&P 500. Fixed rate is 8%, and the index is currently at 986. At the end of the enxt three quarters, the index level is: 1030, 968, and 989.
Calculate the net paymet for each of the next thtree quarters and identify the direction of the payement
The percentage change in the index each quarter, Q is: Q1 = 4.46%, Q2 = -6.02%, and Q3 = 2.17%. The index return payer will receive 0.08/4 = 2% each quarter and pay the index return, there fore:
(figure)
Determine the value at expiration, the profit, maximum profit, maximum loss, breakeven and underlying price at expiration, and payoff graph of the strategies of buying and selling calls and puts and determine the portential outcomes for investors using these strategies
Call option value at expiration is Max (0, S - X) and profit (loss) is Max (0, S - X) - option cost.
(figure)
Put value at expiration is Max (0, X - S) and profit (loss) is Max (0, X - S) - option cost
(figure)
A call buyer (call seller) aniticpates an increase (decrease) in the value of the underlying asset.
(figure)
A put buyer (put seller) anticipates a decrease (increase) in the value of the underlying asset.
(figure)
Determine the value at expiration, profit, maximum profit, maximum loss, breakeven underlying price at expiration, and payoff graph of a covered call strategy and a protective put strategy, and explain the risk management application of each strategy.
A covered call position is a share of stock and a short (written) call, Profits and losses are measured relative to the net cost of this combination (S0 - premium).
- The purpose of selling a covered call is to enhance income by trading the stock’s upside potential for the call premium
- The upside potential on a covered call is limited to (X - S0) + call premium received. The maximum loss is the net cost (S0 - premium).
A protective put consits of buying a share of stock and buying a put. Profits and losses are measured relative to the net cost (S0 + premium).
- A protective put is a srategy to protects against a decline in the value of the stock
- Maximum gains on a protective put are unlimited, but reduced by the put premium paid. Maximum losses are limited to (S0 - X) + put premium paid.
