Introduction to Derivative Securities

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FINA 6219Professor Andrew Chen

• Introduction to Derivative Securities
• Lecture Note 1

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Outline

• What are Derivative Securities (of Derivatives)
  and what are they used for?
• Types of Derivative Securities
• Forward and Futures Contracts
• Specification
• Hedging Examples
• Options
• Basic Specification
• Speculation and Hedging Examples
• Other Types of Options
• Swaps
• Swap Mechanisms
• Terminology of Interest Rate Swaps
• Simple example of Interest Rate Swaps

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What are Derivatives?

• A derivative security (or contingent claim) is a
  security whose value is wholly based on the price
  of underlying or primitive assets.
• Derivatives are useful and powerful tools for
  risk management. They are not dangerous.
• Derivatives do not kill companies, people do!

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Forward Contracts

• A forward contract is an agreement between two
  parties to buy an underlying asset at a set time
  in the future at an agreed-upon price.
• Long forward position.
• Short forward position.
• Not traded on exchanges.
• Contract Specification
• Amount and quality of the underlying asset to be
  delivered
• Delivery price (K)
• Time of delivery (T) and location
• Forward contracts are zero-sum games

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Example Using Forward contracts to hedge
exchange-rate risk

• A U.S. company is exporting goods to Britain and
  in six months knows it will collect one million
  British pound (GBP).
• The company wants to hedge its exposure to
  USD/GBP exchange rate risk.
• Assume that the current spot and forward prices
  for USD/GBP are as follows
• Date Forward Price ()
• Spot 1.8927
• 1-mth 1.8882
• 3-mth 1.8784
• 6-mth 1.8638

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Example (continued)

• To hedge its foreign exchange risk, the company
  enters into a forward contract to sell one
  million British pounds in six months at a
  delivery price of 1.8638 per GBP.
• The company will have fixed the U.S. dollars to
  be realized at 1,863,800 (1,000,000 GBP x
  1.8638 per GBP).
• The company commits to converting its GBP revenue
  into dollars at the agreed-to rate.
• The company's profit/loss on the short forward
  position in the forward contract (which is equal
  to K ST ) will offset its foreign-exchange
  loss/profit in the spot market.

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Example (continued)

• Suppose USD/GBP spot exchange rate in 6 months is
  ST 1.8835.
• The net dollar revenue to the company will be the
  payoff on the forward contract plus the foreign
  exchange transaction.
• (1,000,000)(1.8638-1.8835) (1,000,000)(1.8835)
  1,863,800
• Hedge or dont hedge?

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Example (continued)

• Questions
• Suppose the 6-month GBP forward price appreciates
  to 1.8645 per GBP soon after the company signs
  the forward contract. Has the company's short
  position on the forward contract made or lost
  money?
• Does the delivery price of the company's forward
  contract change overtime as the market forward
  rate fluctuates?
• Determination of the market value of previously
  established forward contracts will be discussed
  later.

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Another Example (Long Hedge)

• Suppose another U.S. company knows that it will
  have to pay five million British pounds in three
  months for goods it has purchased from a British
  supplier.
• The company can hedge its foreign exchange risk
  by taking a long position in five million British
  pounds for a price of 1.8784 per GBP in three
  months.
• This has the effect of fixing the price to be
  paid to the British exporter at 9,392,000.
• Alternatively viewed, the gain/loss on the long
  forward contract (ST - K) offsets the loss/gain
  from having to buy British pounds in the spot
  market in three months.

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Example (continued)

• Suppose the British pound spot exchange rate in
  three months is 1.8796.
• The net dollar cost to the company will be the
  foreign exchange transaction minus the payoff on
  the forward contract.
• (5,000,000)(1.8796) - (5,000,000)(1.8796 -
  1.8784) 9,392,000
• Hedge or dont hedge?

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Payoff Diagram for Long and Short positions
Payoff
Long Position ST - K
0
ST
K
Short Position K - ST
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Futures Contracts

• Futures contracts are similar to forward
  contracts
• Major differences
• Exchanged traded and regulated
• Standardized
• Futures Traders
• Marked-to-market
• Margin requirements (performance bonds) are also
  a significant feature of futures contracts
• Taxation of Futures Transactions

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Futures Contracts

• Standardized Contracts
• Amount and quality of the underlying asset to be
  delivered
• For commodities there is usually a range of
  grades that can be delivered (by the short
  party), but the price received is adjusted
  according to grade.
• Contract size (Examples)
• Soybeans - 5,000 bushels (bu)
• Pork bellies - 40,000 pounds (lbs.)
• Orange juice - 15,000 pounds (lbs.)
• Gold - 100 ounces (oz)
• Silver - 5,000 ounces (oz)
• Japanese Yen - 12.5 million Yen

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Futures Contracts

• Delivery Arrangements
• Future price quotas (example)
• Soybeans cents per bu
• Pork bellies cents per lb.
• Daily Price Limits
• The futures exchanges typically impose daily
  price limits on futures prices. Trading stops for
  the day when an up or down limit is reached.
• Position Limits
• Maximum number of contracts held at any one time
  in an asset and by contract month.

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Futures Traders

• Classified by Trading Strategy
• Hedgers
• Speculators
• Spreaders
• Arbitrageurs

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Futures Traders

• Classified by Trading Style
• Scalpers
• Day Traders
• Position Traders

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Futures Traders

• Daily Settlement
• The clearinghouse uses margins and the daily
  settlement of the accounts to help ensure its
  survivals.
• Initial Margin
• The amount that must be deposited on the day the
  transaction is opened.
• Maintenance Margin
• The amount that must be maintained every day
  after the transaction.

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Marking to Market

• By tradition, the forward or futures price is
  initially set so the current market value of the
  contract is equal to zero.
• The terms of a futures contract, on the other
  hand, are revised every day to maintain a zero
  market value for the contract.
• Suppose that you entered into 5 futures contracts
  to sell gold for 410 in 30 days.
• The next day the futures price of identical
  contracts for sale in 29 days is being negotiated
  at a futures price of 405.

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Marking to Market

• As a futures contract, the futures price of your
  contract would be revised to 405.
• You would have added to your account the
  difference between the futures price yesterday
  and today, multiplied by the number of futures
  contracts you have outstanding
• Your account would be credited by 2,500 5x 100
  x (410-405).
• If your contract were a forward contract, it
  would take on a positive market value. Why?
• This everyday process is called marking to
  market.

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Step by Step example

• Suppose on Dec 1, 2008, an investor contacted a
  broker to buy (take a long position) three (3)
  March 2009 silver futures contracts on the New
  York Commodity Exchange (COMEX).
• At the time the order was executed, the futures
  price was 488.0 cents per ounce. The size of each
  contract is 5,000 ounces.
• The broker required the investor to post an
  initial margin of 1,250 per contract or 3,750
  in total. The broker also informed the investor
  that the maintenance margin was 900 per contract
  or 2,700 in total.

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Example (continued)

• If the balance in the margin account falls below
  the maintenance margin, the investor receives a
  margin call (or a house call) and is expected to
  add funds to the margin account to bring the
  balance back to the initial margin.
• The additional funds deposited in the margin
  account are called variation margin, they usually
  are required to be deposited on the day you
  receive the margin call.

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Example (continued)

• In most cases, an investor earns interest on the
  balance in a margin account. In addition, an
  investor may be able to meet the initial margin
  by depositing securities instead of cash.
• At the end of each trading day (starting with the
  close of trading on the first trading day) each
  contract is marked to market and the margin
  account is adjusted to reflect the investor's
  gain or loss.
• By the end of trading on December 1, the March
  futures price for silver was 491.0 cents per
  ounce. The investor's account was credited 450
  3x 5,000 x (4.91 - 4.88). Why? The 15,000
  ounces of March silver, which the investor
  contracted to buy at 4.88 per ounce, could be
  sold for 4.91 per ounce.

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Example (continued)

• The investor can withdraw any balance in the
  margin account in excess of the initial margin.
  Thus, by the end of December 1, the investor
  could withdraw 450.
• The gain or loss on a futures position is
  determined by the settlement price, which is the
  average of the futures prices at which the
  contract traded immediately prior to the close of
  trading for the day. The settlement price for
  December 1 was 491.0 cents per ounce.
• At the close of each subsequent day that the
  investor maintained the long position in March
  silver, his margin account was marked to market.

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Example (continued)

• Consider the following example
• Initial margin - 3,750 Maintenance Margin -
  2,700
• Margin call (or House call) Closing out
  position

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Example (continued)

• Gain/loss on futures position
• Profit 4,650 - (3,750 1,200) - 300
• Under the futures contract, the gain/loss is
  realized day by day because of the daily
  settlement procedures.
• Gain/loss on forward contract
• 15,000 x (4.86 - 4.88) - 300
• Under the forward contract, the whole gain/loss
  is realized at the end of the life of the
  contract.

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Taxation on Futures Transactions

• Investors' and traders' profits from most futures
  contracts, as well as index options are
  considered to be 60 percent capital gains and 40
  percent ordinary income.
• Capital gains are taxed at the ordinary income
  tax rate, but subject to a maximum of 15 percent.
  
• Therefore, an investor in the 31 percent tax
  bracket would have futures profit taxed a blended
  rate of 60(15) 40(31) 21.4

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Taxation of Futures Transactions

• In addition, all futures and index options
  profits are subject to a market-to-market rule in
  which accumulated profits are taxable in the
  current year even if the contract has not been
  closed out.
• For example, assume that you bought a futures
  contract on October 15 at a price of 1,000 and
  your account of course would be mark-to-market
  daily.
• Suppose that at the end of the year, the
  accumulated profit of your futures position was
  400 and the futures price at the end of the year
  was 1,400.
• You would be required to pay the tax that year on
  400 even though you had not closed out the
  contract.
• In other words, realized and unrealized profits
  are taxed and losses are recognized.

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The Exchange Clearinghouse
What is the significance of the Clearinghouse??
Trading Pit
Broker
Broker
Clearinghouse
Seller
Buyer
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Options

• Specifications
• Call options
• Put options
• Terminology
• Option premium
• European versus American options
• The purchaser of an option is not obligated to
  buy or sell the asset. The holder will not
  exercise the option unless his or her payoff is
  positive.
• It costs nothing to enter a forward or futures
  contract (except commissions and margin
  requirements).
• By contrast, an investor must pay an up-front fee
  or premium for an options contract.

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Example of Speculating with Options

• Bullish Outlook
• On March 4, 2009, the common stock of TWX was
  trading at 17.28.
• If your outlook for TWX is positive, you could
  buy TWX July 16 call options for 2.15 per
  option. Suppose you buy 10 contracts for a total
  cost (ignoring commissions) of 2,150 10 x 100 x
  2.15. Note that buying a TWX July 16 call option
  contract gives you the right to purchase 100
  shares of TWX common stock at a cost of 16.00
  per share at any time before the option expires
  in July in 2009.
• If the price of TWX stock climbs to 30 before
  your option expires and the value of one call
  option rises to 16.50, you have two choices if
  you want to dispose of your options

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Bullish Outlook example (continued)

• Option 1
• You can exercise your option and buy stock for
  16.00 per share for a total cost of 16,000 10
  x 100 x 16.00, and simultaneously sell the
  shares on the stock market for 30,000 10 x 100
  x 30.
• Your net profit (ignoring commissions) is 11,850
  30,000 - 16,000 - 2,150.

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Bullish outlook example (continued)

• Option 2
• You can close out your position by selling the 10
  options contracts for 16,500, yielding a net
  profit of 14,350 16,500 - 2,150.
• In this case, you earn a return on investment of
  667.44 (14,350/2,150), whereas the return on
  an outright stock purchase, given the same price
  movement, would be only 65.29 (30,000-16,000-2,1
  50)/(16,000 2,150).

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Example of Speculating with Options

• Bearish Outlook
• On March 4, 2009, MAC closed at 38.93.
• If your outlook MAC is negative, you could buy
  July 37.50 put options for 2.25 per option.
  Suppose you buy 5 contracts for a total cost
  (ignoring commissions) of 1,125 5 x 100 x
  2.25. Note that buying the MAC July 37.50 put
  option contract gives you the right to sell 100
  shares of its common stock at a price of 37.50
  per share at any time before the option expires
  in July, 2009
• If the price of MAC falls to 31.00 before your
  options expire in July and the price of one put
  option rises to 8.50, you have two choices if
  you want to dispose of your options

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Bearish outlook example (continued)

• Option 1
• You can buy 500 shares of MAC stock at 31 per
  share and simultaneously exercise your put
  options to sell the stock at 37.50 per share.
• Profits would be 2,125 18,750 - 15,500 -
  1,125, representing a rate of return for the
  investment of 12.78.

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Bearish outlook example (continued)

• Option 2
• Sell the put option contracts, and collect the
  difference between the price paid and the price
  received,
• Profits would be of 3,125 4,250 1,125,
  representing a rate of return for investment of
  177.78.

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Hedging with Options

• Important differences with Forwards/Futures
• It costs nothing to enter a forward/futures
  contract (except for margin requirements). By
  contrast, an investor must pay an up-front fee
  (the premium) for an options contract.
• Forward/Futures contracts are designed to
  neutralize risk by fixing the price that the
  hedger will pay or receive for the underlying
  asset. By contrast, put options provide
  insurance. They offer a way for investors to
  protect themselves against adverse price
  movements in the future while allowing them to
  benefit from favorable price movements.

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Hedging with options example

• Protective put for portfolio insurance
• Consider an investor who on March 4, 2009 owns
  1,000 shares of JCP. The closing share price is
  59.90 per share and the investor's portfolio
  position in JCP is worth 59,900.
• The investor is concerned about downside risk and
  purchases 10 April 60 put contracts at a premium
  of 3.20 per option.
• The cost of this portfolio insurance is 3,200
  10 x 100 x 3.20.

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Hedging with options example (continued)

• Therefore, the protective put (S P) position
  preserves upside potential and limits downside
  risk to the put exercise price minus the premium,
  i.e., 56,800 1,000 x (60.00 - 3.20).

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Real-Life Example

• Enron Story
• 25,000 shares (85/share) valued at 2,125,000
• 10 months later, shares drop to 0.25/share,
  portfolio valued at 6,250.
• Had he used a protective put, he would have
  preserved his position
• The Option Clearinghouse Corporation (OCC), an
  AAA insurance company, would guarantee the
  performance of the put options.

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One-Step Binomial OPM

• Given the following binomial stock price trees,
  what are the values of a 3-month call option with
  strike price 50, and a 3-month put option with
  strike price 50?
• Assume that the stock price may go up by 10 (u
  1.10) or down by 10 (d 0.90), and the
  risk-free interest is 5 in 3-month.

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One-Step Binomial OPM (continued)

• Solution technique (Pricing a Call Option)
• Find the risk-neutral probability
• As Cu max(Su K, 0) 5, and Cd max(Sd k,
  0) 0.
• Apply formula for the one-step binomial OPM for
  call
• Thus, we have
• C (0.5629)(5) (1 0.5629)(0)e-0.05(3/12)
  2.78

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One-Step Binomial OPM (continued)

• Solution technique (Pricing a Put Option)
• Find the derived probability p 0.5629
• Derive Pumax(K Su,0) 0, and Pdmax(K Sd, 0
  ) 5
• Apply the formula for one-step binomial OPM for
  put
• Thus, we have
• P (0.5629)(0) (1 0.5629)(5)e-0.05(3/12)
  2.13

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Multi-Step Binomial OPM

• If we want to use a two time-step binomial OPM to
  evaluate a six-month European call option with a
  strike price of 50.
• Assume that the stock price starts at 50 and in
  each of two time steps may go up by 10 (u
  1.10) or down by 10 (d 0.90).
• Since each time-step is three months in length,
  ?t 3/12 0.25, and the risk-free interest rate
  is 5 per year with continuous compounding (r
  0.05).

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Multi-Step Binomial OPM (continued)

• We know the risk-neutral derived probability of
  an increase in the stock price in each time step
  is
• The stock price tree is illustrated in the
  following slide.

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Stock Price Tree
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Solution Techniques

• Method 1 Working backwards period by period
• At node D Cuu max(60.5 50, 0) 10.5 
• At node E Cud max (49.5 50, 0) 0
• At node F Cdd max(40.5 50, 0) 0
• At node B
• Cu
• At node C
• Cd
• At node A

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Solution Techniques

• Method 2 Applying the 2 step binomial-tree OPM
  for call
• If we know the following formula for two-step
  binomial OPM for call option, we can directly use
  the formula to compute the call value as follows
• where
• Cuu Max (Suu K, 0) 10.5
• Cud Max (Sud K, 0) 0
• Cdd Max (Sdd K, 0) 0
• C(0.5629)2(10.5)2(0.5629)(0.4371)(0)(0.4371)2(
  0)e-2(0.05)(0.25)
• 3.2449.

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Pricing of a European Put Option

• Consider a new example of a six-month European
  put option with a strike price of 70 on a stock
  whose current price is also 70.
• We suppose there are two time steps of three
  months (?t 0.25) and in each time step the
  stock price either moves up by 15 (u 1.15) or
  down by 20 (d 0.80).
• We assume that the risk-free interest rate is 5
  per year with continuous compounding (r 0.05).
  
• For this case, the risk-neutral probability of an
  increase in the stock price is

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Solution Techniques

• Method 1 Working Backwards period by period

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Method 1 (continued)

• As before, we work backward in the tree to
  compute the initial put option price of 6.39317.

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Solution Techniques

• Method 2 Applying the two-step binomial-tree
  model for European put option
• The value of a two-time-step European put option
  is the present value of its expected terminal
  value based upon the risk-neutral probabilities
  and discounted at the risk-free rate of interest.
  Notice again that the discounting takes place two
  time-step in this case
• P(0.6074)2(0)2(0.6074)(0.3926)(5.6)(0.3926)2(2
  5.2)e-2(0.05)(0.25)
• 6.39317.

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From Theory to Practice

• Coming up with u, d, and p.

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Case Example

• Defensive strategies following a stock merger for
  Cardinal Health, Inc.
• On November 27, 1996 Owen Healthcare, Inc.
  (OWN) and Cardinal Health, Inc. (CAH) announced
  a definitive agreement to merge.
• The merger was to be accounted for as a
  pooling-of-interest and to be recognized as a
  tax-free reorganization for holders of OWN and
  CAH.
• The target date for closing was March 18, 1997.
• The following are hedging strategies for CAH
  shares.

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Case Example

• Protective Put Options
• The investor owned CAH stock and was unable to
  sell the shares due to tax limitations.
• Downside risk could be reduced by buying
  protective puts.
• Given the market price of CAH stock was 61 per
  share at the time. Investors could purchase a
  two-year European-style, cash-settled protective
  put option with strike price of 55 from Morgan
  Stanley for 4.50 per share.
• The hedging outcomes with buying protective puts
  at option expiration are as follows

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Case Example

• Protective Put Options

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Case Example

• Hedging with Protective Put

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Case Example

• Zero Cost Collar
• Investors could use zero-cost collar to reduce
  the downside risk without paying any option
  premium.
• Essentially the investors purchase a two-year,
  European style, cash-settle put options with
  strike price of 55.00 from Morgan Stanley and
  finance the put premium by selling a two-year,
  European style, cash-settled call options with
  strike price of 77.00 from Morgan Stanley.
• The hedging outcomes with zero-cost collar are as
  follows

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Case Example

• Zero Cost Collar

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Case Example

• Hedging with Zero-cost Collar

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Case Example

• Advantages of zero-cost collar
• Investors hedge equity position below the put
  strike while retaining ownership, voting rights
  and dividends.
• No net upfront out-of-pocket expense to the
  investors.
• Cash-settlement of options defers any sale of the
  underlying shares.
• Option strike prices and maturities may be
  customized to meet investors risk/reward
  parameters.
• Disadvantages
• Investors relinquish upside above call strike
  price.
• Investors must post stock and put options as
  collateral against short call options.
• Investors are exposed to Morgan Stanley credit
  risk.

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Case Example

• Zero Cost Call Spread Collar
• In the zero-cost collar hedging strategy,
  investors give away all future upside to fund the
  downside protection. Investors can have downside
  protection without giving away all future upside
  potential.
• Given the current market price of CAH stock at
  61 per share, investors could enter into a call
  spread collar with Morgan Stanley by buying a
  two-year cash-settled put option with strike
  price of 52 and a two-year cash-settled call
  option with strike price of 75 per share with
  Morgan Stanley and finance the premiums by
  selling a two-year cash-settled call option with
  strike price of 61 per share.
• The hedging outcomes with zero-cost call spread
  collar are as follows

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Case Example

• Zero Cost Call Spread Collar

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Case Example

• Hedging with Call Spread Collar

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Other Types of Options

• Stock Index Options
• Settled in cash
• Popular contracts such as options on SP 500 are
  traded on CBOE
• Foreign Currency Options
• Mostly traded on PHLX
• Futures Options (i.e. Options on Futures)
• When exercised, investor receives a futures
  contract plus cash difference between the futures
  price and the exercise price.
• OTC Options
• Exotic options such as calls on max, calls on
  min, chooser, compound options, etc.
• Embedded Options
• Options that are part of another security, such
  as convertible bonds, LYONs, PERCS, etc.

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Swaps

• According to the market survey of ISDA (the
  International Swaps and Derivatives Association),
  the swap markets are huge and growing

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Swaps

• Terminology
• Interest Rate Swap An arrangement to exchange
  interest-rate payments between two
  counterparties.
• Two counterparties
• Fixed-rate payer Pays fixed and receives
  variable rate of interest in the swap. It has a
  long position in the swap.
• Floating-rate payer Pays variable rate and
  receives fixed rate of interest in the swap. It
  has a short position in the swap.
• Plain vanilla (the fixed/floating interest rate
  swap)
• Two counterparties exchange their interest
  payments on the notional principal for a
  specified length of time. The first party pays
  the fixed amount and receives a floating amount
  of interest in the swap while the second party
  pays the floating amount and receives a fixed
  amount of interest in the swap.

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Fixed/Floating Rate Swap

• Example Costs of Borrowing

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Fixed/Floating Rate Swap
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Fixed/Floating Rate Swap
8.9
BBB
AAA
T-Bill
T-Bill 0.75
8.8
(Floating Rate Market)
(Fixed Rate Market)
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Fixed/Floating Rate Swap

• Effective Costs of Borrowing

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