Reading 59- Risk Management Applications of Option Strategies
Consider a U.S. commercial bank that takes in one-year certificates of deposit (CDs) in its Hong Kong branch, denominated in Hong Kong dollars, to fund three-year, fixed-rate loans the bank is making in the U.S. denominated in U.S. dollars. Why would this bank wish to enter into a currency swap? The bank faces the risk that the Hong Kong dollar: A) decreases in value against the U.S. dollar and the risk that interest rates increase in Hong Kong. B) decreases in value against the U.S. dollar and the risk that interest rates decrease in Hong Kong. C) increases in value against the U.S. dollar and the risk that interest rates increase in Hong Kong.
C The bank faces two problems. First, if the Hong Kong dollar increases in value, it will take more U.S. dollars to repay the Hong Kong depositors. Indeed, if the Hong Kong dollar increases significantly, it may take more U.S. dollars to repay the Hong Kong depositors than the bank makes on the U.S. loan. Secondly, if the interest rate in Hong Kong rises, the bank pays more in interest on its CDs while the rate on the bank's U.S. loans does not change. In this case, interest expense would rise and interest income would remain the same, which narrows the bank's profits.
The put-call parity relation can be adjusted for dividend payments on a stock by which of the following methods? A) Add the present value of the expected dividend payments to the exercise price. B) Add the present value of the expected dividend payments to the current stock price. C) Subtract the present value of the expected dividend payments from the current stock price.
C The correct adjustment is to subtract the present value of the expected dividend payments from the current stock price.
Consider a $10,000,000 1-year quarterly-pay swap with a fixed rate of 4.5 percent and a floating rate of 90-day London Interbank Offered Rate (LIBOR) plus 150 basis points. 90-day LIBOR is currently 3 percent and the current forward rates for the next four quarters are 3.2 percent, 3.6 percent, 3.8 percent, and 4 percent. If these rates are actually realized, at the first quarterly settlement date: A) the fixed-rate payer will be required to make a payment of $7,500. B) the floating rate payer will be required to make a payment of $92,500. C) no payments will be made.
C The first floating rate payment is based on current LIBOR + 1.5% = 4.5%. This is equal to the fixed rate so no (net) payment will be made on the first settlement date.
DWR Services, Ltd., arranges a plain vanilla interest rate swap between RWDY Enterprises (pays fixed) and RED, Inc. (receives fixed). The swap has a notional value of $25,000,000 and 270 days between payments. LIBOR is currently at 7.0%. If at the time of the next payment (due in exactly 270 days), RWDY receives net payments of $93,750, the swap fixed rate is closest to: A) 7.500%. B) 6.625%. C) 6.500%.
C The net payment formula for the fixed-rate payer is: Fixed Rate Paymentt = (Swap Fixed Rate − LIBORt-1) × (# days in term / 360) × Notional Principal If the result is positive, the fixed-rate payer owes a net payment and if the result is negative, then the fixed-rate payer receives a net inflow. Note: We are assuming a 360 day year. We can manipulate this equation to read: Swap Fixed Rate = LIBORt-1 + [(Fixed Rate Payment / ( # days in term / 360 × Notional Principal) Note: the Fixed Rate payment will have a negative sign because we are told that RWDY receives a net payment. = 0.07 + [(-93,750 / (270 / 360 × 25,000,000) = 0.07 − 0.005 = 0.065, or 6.5%. Note: We know that the Swap Fixed Rate will be less than the floating rate, or LIBOR, because RWDY receives a net payment.
XYZ, Inc. has entered into a "plain-vanilla" interest rate swap on $5,000,000 notional principal. XYZ company pays a fixed rate of 8.5% on payments that occur at 180-day intervals. Platteville Investments, a swap broker, negotiates with another firm, SSP, to take the receive-fixed side of the swap. The floating rate payment is based on LIBOR (currently at 7.2%). At the time of the next payment (due in exactly 180 days), XYZ company will: A) pay the dealer net payments of $65,000. B) receive net payments of $32,500. C) pay the dealer net payments of $32,500.
C The net payment formula for the fixed-rate payer is: Fixed Rate Paymentt = (Swap Fixed Rate − LIBORt-1) × (# days in term / 360) × Notional Principal If the result is positive, the fixed-rate payer owes a net payment and if the result is negative, then the fixed-rate payer receives a net inflow. Note:We are assuming a 360 day year. Fixed Rate Payment = (0.085 − 0.072) × (180 / 360) × 5,000,000 = $32,500. Since the result is positive, XYZ owes this amount to the dealer, who will remit to SSP.
James Jackson currently owns stock in PNG, Inc., valued at $145 per share. Thinking that PNG is overbought and will decrease in price soon, Jackson writes a call option on PNG with an exercise price of $148 for a premium of $2.40. At expiration of the option, PNG stock is valued at $152 per share. What is the profit or loss from Jackson's covered call strategy? Jackson: A) gained $9.40. B) lost $4.60. C) gained $5.40.
C The option is in-the-money at expiration (MAX (0, S-X) and the PNG stock will be called away from Jackson at $148 per share, limiting Jackson's gain from owning the stock to $3 ($148-145). However, Jackson also gains the $2.40 from writing the call option. Therefore, Jackson's gain from the covered call strategy is $5.40 ($3.00+$2.40).
Al Steadman receives a premium of $3.80 for shorting a put option with a strike price of $64. If the stock price at expiration is $84, Steadman's profit or loss from the options position is: A) $23.80. B) $16.20. C) $3.80.
C The put option will not be exercised because it is out-of-the-money, MAX (0, X-S). Therefore, Steadman keeps the full amount of the premium, $3.80.
An investor purchases a stock for $40 a share and simultaneously sells a call option on the stock with an exercise price of $42 for a premium of $3/share. Ignoring dividends and transactions cost, what is the maximum profit that the writer of this covered call can earn if the position is held to expiration? A) $3. B) $2. C) $5.
C This is an out of the money covered call. The stock can go up $2 to the strike price and then the writer will get $3 for the premium, total $5.
stock price is denoted as
S
why is options trading called a zero-sum game?
because the sum of profits between buyer & seller of call and put option is ALWAYS zero
a put option is exercised when price of the stock is ____ strike price.
below
who profits when price of underlying asset increases?
buyer of call OR seller of put
who profits when price of underlying asset decreases?
buyer of put OR seller of call
strike price is also known as the
exercise price (X) price at which a derivative contract can be exercised The difference between the underlying security price & option strike price represents the amount of profit gained upon exercise or sale of option
at expiration, the value of call must be equal to
intrinsic value= max(0, S-X) the larger of 0, or the stock price- strike price
when buying either a call or put, the loss is
limited to the amount of the premium
a protective put has same shape profit diagram as a
long call
maximum loss for the buyer of a put is
loss of $5 premium (S>/X $50)
A put buyer believes underlying asset is ____
overvalued & will decline in price
uncovered call (naked call)
riskiest single-option transaction opposite to a covered call stock price could go up infinitely, and writer would be forced to buy the stock in the open market and deliver at strike price- potential losses are unlimited
the call holder will exercise the option when
stock price exceeds strike price at expiration date ($55> $50)
breakeven point for buyer & seller of call option is equal to
strike price + premium X + premium $50 + $5= $55 At $55, π=0
potential loss to writer of put=
strike price - premium $50-$5= $45
the greatest loss the put writer can have is
strike price- premium received
A call buyer believes underlying asset is ____
undervalued & will increase in price
maximum profit of a protective put=
unlimited
the potential loss to seller (writer) of option is
unlimited
the potential profit to the buyer of option is
unlimited
maximum gain to buyer of a put is
$5 strike price - premium $50-$5= $45
greatest profit to the writer of a put=
$5 premium (S>/$50)
the greatest profit the writer can make is
$5 premium (at any stock price S</ $50 strike) stock price < strike
maximum loss of a covered call=
(S0- premium)
maximum loss of a protective put=
(S0-X) + put premium paid
maximum profit of a covered call=
(X-S0) + call premium received
protective put analysis:
-cuts your downside losses by put purchase price ($4) -max loss occurs at an price below stock purchase price $100 -losses between $0 & $4 occur for stock prices between $100 and $104 -no profit until stock price exceeds breakeven point $104 -breakeven price= s0+ premium
The potential profits from writing a covered call position on a stock are: A) limited to the premium plus stock appreciation up to the exercise price. B) limited to the premium. C) greater than the potential profits from owning the stock.
A The covered call: stock plus a short call, or a short put. The term covered means that the stock covers the inherent obligation assumed in writing the call. Why would you write a covered call? You feel the stock's price will not go up any time soon, and you want to increase your income by collecting some call option premiums. To add some insurance that the stock won't get called away, the call writer can write out-of-the money calls. You should know that this strategy for enhancing one's income is not without risk. The call writer is trading the stock's upside potential for the call premium. The desirability of writing a covered call to enhance income depends upon the chance that the stock price will exceed the exercise price at which the trader writes the call. The owner of a stock has the rights to all upside potential. The profits for a short call are limited to the premium. For example, say that a stock owner writes a covered call at a stock price (S) of $50 and an exercise price (X) of $55 for a premium of $4. If at expiration, the price of the stock is more than $50 but less than $55, the buyer will not exercise, and the writer will "gain" the premium plus any stock appreciation between $50 and $55. If at expiration, the price of the stock is more than $55, the buyer will exercise and the writer's gain is limited to the premium.
An investor buys a 30 put on a share of stock for a premium of $7 and simultaneously buys a share of stock for $26. The breakeven price on the position and the maximum gain on the position are: Breakeven price Maximum gain A) $33 unlimited B) $21 $11 C) $37 $11
A To break even, the stock price should rise as high as the amount invested, $33 ($26 + $7). The maximum gain is unlimited, as the gain will be as high as the increase in the stock price.
Using put-call parity, it can be shown that a synthetic European call can be created by a portfolio that is: A) long the stock, long the put, and short a pure discount bond that pays the exercise price at option expiration. B) long the stock, long the put, and long a pure discount bond that pays the exercise price at option expiration. C) long the stock, short the put, and short a pure discount bond that pays the exercise price at option expiration.
A A stock and a put combined with borrowing the present value of the exercise price will replicate the payoffs on a call at option expiration.
The value of an interest-rate call option at expiration is zero or the: A) present value of, the market rate minus the exercise rate, adjusted for the period of the rate, times the principal amount. B) market rate minus the exercise rate, adjusted for the period of the rate, times the principal amount. C) exercise rate minus the market rate, adjusted for the period of the rate, times the principal amount.
A An interest rate call pays zero or the market rate at expiration minus the exercise rate. Since the payment is made at a date after expiration by the period of the reference rate, the value at expiration is the present value of this difference times the principal value.
Which transaction would least likely be classified as an interest rate swap? A) Receive AUD fixed, pay NZD floating. B) Receive U.S. fixed, pay U.S. commercial paper. C) Pay USD fixed, receive U.S. LIBOR.
A Because it involves two different currencies, this would be a currency swap.
Which statement best reflects the risk exposure of a put writer? A) Limited risk. B) No risk. C) Unlimited risk.
A Because stock prices cannot fall below $0, a put writer's risk is limited to the strike price.
Consider a quarterly-pay currency swap where Party A pays London Interbank Offered Rate (LIBOR) on $1,000,000 and Party B pays 4% on 900,000 euros. Current LIBOR is 3% and at the end of 90 days it is 4%. Which of the following statements regarding the first settlement date is most accurate? A) Party A must make a payment of $7,500. B) Party A must make a payment of $10,000. C) The payments made depend on the exchange rate.
A Floating rate payments in a swap are based on the reference rate for the prior period. The payment is: 0.03 × 90/360 × 1,000,000 = $7,500
Which of the following statements about long positions in put and call options is most accurate? Profits from a long call: A) are positively correlated with the stock price and the profits from a long put are negatively correlated with the stock price. B) are negatively correlated with the stock price and the profits from a long put are positively correlated with the stock price. C) and a long put are positively correlated with the stock price.
A For a call, the buyer's (or the long position's) potential gain is unlimited. The call option is in-the-money when the stock price (S) exceeds the strike price (X). Thus, the buyer's profits are positively correlated with the stock price. For a put, the buyer's (or the long position's) potential gain is equal to the strike price less the premium. A put option is in-the-money when X > S. Thus, a put buyer wants a high exercise price and a low stock price. Thus, the buyer's profits are negatively correlated with the stock price.
When one party pays a fixed rate of interest in an equity swap, which of the following is least accurate? A) The fixed-rate receiver will never get more than the fixed rate. B) The equity-return payer will gain if the equity return is zero. C) Unlike other swaps, in an equity swap the one-quarter-ahead payment is not known at the end of the previous quarter.
A If the periodic return on the equity is negative, the fixed-rate payer must pay the fixed rate plus the percentage of (negative) equity return, times the notional principal.
Consider a currency swap in which Party A pays 180-day London Interbank Offered Rate on $1,000,000 and Party B pays the Japanese yen riskless rate on 130,000,000 yen. Which of the following statements regarding the terms required at the initiation of the swap is CORRECT? A) Party A must pay 130,000,000 yen and receive $1,000,000. B) An exchange of principal amounts is not required at the initiation of the swap. C) Party A must pay $1,000,000 and receive 130,000,000 yen.
A Since Party A is paying in dollars, Party A must receive dollars in exchange for yen at the beginning of the swap.
The term notional principal refers to: A) the amount swapped. B) the period of time involved. C) the cash interest payment.
A The notional principal is the amount swapped. Note that the notional principal does not actually change hands with plain vanilla interest rate swaps, but is used to calculate the interest payment streams to be exchanged. Notional principal does exchange hands in a foreign currency swap.
The shape of a protective put payoff diagram is most similar to a: A) long call. B) short call. C) covered call.
A The payoff diagram for a protective put is like that of a call option but shifted upward by the exercise price of the put.
The profit/loss diagram for a covered call strategy looks like what other type of profit/loss diagram? A) Short put. B) Long put. C) Short call.
A The profit/loss diagram for the covered call looks like the profit/loss diagram for a short put position. Both option positions have limited profit potential, with the potential loss equal to the strike price less the premium.
For two European call options that differ only in time to expiration, the strongest statement we can make is that: A) the longer-term option must be worth at least as much as the shorter-term option. B) no relation can be established between the values of the two calls prior to expiration of the first. C) the longer-term option must be worth more than the shorter-term option.
A While longer-term options generally are worth more, for far in- or out-of-the-money options, the values could be equal.
protective put
A risk-management strategy that investors can use to guard against the loss of unrealized gains. reduces risk of losing money if the security declines in value
An increase in the riskless rate of interest, other things equal, will: A) increase call option values and decrease put option values. B) decrease call option values and increase put option values. C) decrease call option values and decrease put option values.
A. An increase in the risk-free rate of interest will increase call option values and decrease put option values.
writing covered calls [adds insurance]
An options strategy whereby an investor holds a long position in an asset and writes (sells) call options on that same asset in an attempt to generate increased income from the asset. For example, let's say that you own shares of the TSJ Sports Conglomerate and like its long-term prospects as well as its share price but feel in the shorter term the stock will likely trade relatively flat, perhaps within a few dollars of its current price of, say, $25. If you sell a call option on TSJ for $26, you earn the premium from the option sale but cap your upside. One of three scenarios is going to play out: a) TSJ shares trade flat (below the $26 strike price) - the option will expire worthless and you keep the premium from the option. In this case, by using the buy-write strategy you have successfully outperformed the stock. b) TSJ shares fall - the option expires worthless, you keep the premium, and again you outperform the stock. c) TSJ shares rise above $26 - the option is exercised, and your upside is capped at $26, plus the option premium. In this case, if the stock price goes higher than $26, plus the premium, your buy-write strategy has underperformed the TSJ shares.
A fiduciary call is a portfolio that is made up of: A) a call that is synthetically created from other instruments. B) a call option and a bond that pays the exercise price of the call at option expiration. C) a call option and a share of stock.
B A fiduciary call combines a call option and a bond that pays the exercise price of the call at option expiration.
A contract in which one party pays a fixed rate of interest on a notional amount in return for the return on a single stock, paid quarterly for four quarters, is a(n): A) returns swap. B) equity swap. C) plain vanilla swap.
B A swap contract in which at least one party makes payments based on the return on an equity, portfolio, or market index, is called an equity swap.
Consider a U.S. commercial bank that borrows funds in England for one year denominated in English pounds. Why would the investor wish to enter into a swap contract? As the: A) English pound decreases in value, it takes more U.S. dollars to pay off the English liability. B) English pound increases in value, it takes more U.S. dollars to pay off the English liability. C) U.S. interest rate increases, the value of the English liability increases.
B As the English pound increases in value, it takes more U.S. dollars to pay off the English liability, which increases the interest cost of borrowing funds denominated in English pounds.
Assume that the value of a put option with a strike price of $100 and six months remaining to maturity is $5. For a stock price of $110 and an interest rate of 6%, what value is closest to the corresponding call option with the same strike price and same expiration as the put option? A) $11.99. B) $17.87. C) $12.74.
B Call value = $110 + $5 - $100 / 1.060.5 = $17.87.
Compared to European put options on an asset with no cash flows, an American put option: A) will have the same minimum value. B) will have a higher minimum value. C) will have a lower minimum value.
B Early exercise of an in-the-money American put option on an asset with no cash flows can generate more, X − S, than the minimum value of the European option, X / (1 + R)T − S. The possibility of profitable early exercise leads to a higher minimum value on the price of the American put option.
For two European put options that differ only in their time to expiration, which of the following is most accurate? The longer-term option: A) can be worth more than the shorter-term option. B) can be worth less than the shorter-term option. C) can be worth at least as much as the shorter-term option.
B For European puts, it is possible that the longer term option can be less valuable than a shorter-term option.
Which of the following is NOT considered a reason for using the swaps market? To: A) reduce transactions costs. B) exploit market inefficiencies. C) maintain privacy.
B Historically, the two basic motivations for swaps were to exploit market inefficiencies and attempt to achieve cheaper financing. Today, the swaps market has matured and now offers few arbitrage opportunities to exploit market inefficiencies. In addition to seeking cheaper financing, current reasons for using swaps include reducing transactions costs, avoiding costly regulations, and maintaining privacy.
Which of the following statements about swaps is least accurate? A) Swaps are illiquid. B) Parties to swap contracts are often individual speculators. C) Swaps typically have zero value at initiation.
B Parties to swaps contracts are usually large institutions, rarely individual speculators or hedgers.
An investor who bought a floating-rate security and wishes to establish a minimum periodic cash flow on his investment could: A) sell an interest-rate floor. B) buy an interest-rate floor. C) sell an interest-rate cap.
B The buyer of a floor will receive a payment when the floating rate is below the floor rate, effectively establishing a minimum rate on the floating rate security.
Which of the following statements about uncovered call options is least accurate? A) The loss potential to the writer is unlimited. B) The most the writer can make is the premium plus the difference between the exercise price (X) and the stock price (S). C) The profit potential to the holder is unlimited.
B The most the writer can make is the premium. If the writer wrote a covered out of the money call, then the writer would make the premium plus the increase in the stock's price X-S.
An investor would exercise a put option when the: A) price of the stock is equal to the strike price. B) price of the stock is above the strike price. C) price of the stock is below the strike price.
C A put option gives its owner the right to sell the underlying good at a specified price (strike price) for a specified time period. When the stock's price is less than the strike price a put option has value and is said to be in-the-money.
An equity swap can specify that one party pay any of the following EXCEPT: A) the return on a specific portfolio of three stocks including dividends. B) the return on a single stock. C) the total return on a corporate bond.
C A swap involving the return on a bond would not be an equity swap.
Which of the following statements about the investors is least accurate? A) Grey's loss is unlimited. B) Kishiro's gain is limited to the strike price minus the premium. C) Grey's maximum gain and Kishiro's maximum loss sum to zero.
C Although options are a zero-sum game, it is the counterparty exposures that nets to zero. For example, the put buyer's maximum loss = put writer's maximum gain = the premium. The other statements are true. Note that the reason why Grey's loss is unlimited is that he does not currently own the stock. In other words, he has a naked position. If the stock were to rise, Grey would be forced to buy the stock in the open market to settle the exercise of the option. Because the potential for the stock to rise is unlimited, the potential loss for the naked call writer is also unlimited.
