CH 21: OPTIONS AND CORPORATE FINANCE

Derivatives and Derivatives Markets: Chapter 7

Derivative instruments (options, futures, forwards, and swaps) can be used to control asset price, FX and interest rate exposure and introduce certainty into an otherwise uncertain transaction.

Derivative An asset, such as a futures contract or an option contract, that derives its economic value from an underlying asset, such as a stock or a bond.

Hedge To take action to reduce risk by, for example, purchasing a derivative contract that will increase in value when another asset in an investors portfolio decreases in value.

Derivatives can serve as a type of insurance against price changes in underlying assets. Insurance plays an important role in the economic system: If insurance is available on an economic activity, more of that activity will occur.

Derivatives can also be used to speculate.

Speculate To place financial bets, as in buying futures or option contracts, in an attempt to profit from movements in asset prices.

A functional market in derivatives needs BOTH:

Some investors and policymakers believe that speculation and speculators provide no benefit to financial markets, but they provide two useful functions:

1. When a hedger sells a derivative to a speculator, they transfer risk to the speculator.

2. Speculators provide essential liquidity. Without speculators, there would not be a sufficient number of buyers and sellers for the market to operate efficiently.

Part I: OPTIONS

Introduction to Options "Gives the owner the right, without the obligation, to buy (or sell) a good at a specified price at (during) a specified time period." Unique because they are the right, but not the obligation, to exercise. Only exercised when it suits the option buyer.

TERMINOLOGY and NOTATIONCall option:The right, but not the obligation, to buy the underlying asset (e.g. a share of stock) at a specified price by a specifieddatee.g. you can buy the option to purchase 100 shares of Microsoft stock for $65/share before the close of trading on Oct 20, 2002. The price of Microsoft stock on May 28, 2002 was 64.1875, and the price of the call was $7 / share.Put option: The right, but not the obligation, to sell an asset (e.g. a share of stock) at a specified price by a specified date.Option Buyer: Purchases the right to buy or sell the assetOption seller:Grants the right to buy or sell to the option buyer (also called the option writer.)Premium:Fee paid by the buyer to the writer as compensation for the risk of selling (writing) the option.Spot price:The underlying stock (or asset) price Strike price: The specified price that the option is able to be exercised at (call this X)In-the-money:An option that would produce a profit if exercised today (i.e. has intrinsic value) - e.g., for call option, if spot > strike price.Out-of-the-money: Option has no intrinsic value - e.g., for call option, if spot < strike price.

OPTION MATURITIESExpiration date: Date that the buyers right to exercise the option ends American option: Can be exercised for spot value on any day between contract date and maturity date.European option: Can only be exercised on expiry date. But can be sold before maturity.

PROFIT (PAYOFF) PROFILES Value at expiration Buy a CallBuy a Put

Sell a CallSell a Put

Buying and selling a call option is a zero-sum game: The buyers gain is the sellers (or writers) loss, and vice versa. General strategy: Buy Calls to make money when the good rises General strategy: Buy Puts to make money when the good falls Options start to become valuable when the goods price moves past the strike price

Relationship between Call and Put values

Strategies in options markets may offset each other, resulting in riskless returns Assumptions Strategy Risk-free return = 10% (1) Buy Put Exercise price (put & call) = $55 (2) Sell Call Price of stock = $44 (3) Buy the Stock At expiration, stock = $58 or $34

Position Buy stockValue

55 Sum of strategies

Buy put

55 Value of stock at Expiration Sell call

P=58:P=34:

Stock = 58Stock = 34Put = 0Put = 55 34 = 21Call = -3Call = 0___________ Total = $55Total = $55

Result: Since you are guaranteed the $55 at year end, your total investment of (stock + put) (call premium) must earn the risk-free rate of return:

Assume: Value of put = $7Call premium = $1

Total investment today = $44 + $7 + (-$1) = $50The values of the call and put have to be such that the payoff ($55) is equal to the risk-free rate of return (o/w have arbitrage opportunities)

Put-call parity: Prices of puts and calls with the same exercise price and expiration date are precisely related to each other (due to arbitrage):

$44 + $7- $1 = 50 = 55/(1.10)

How are options priced? Pt = IV + TPWhere: Pt = option price period tIV = Intrinsic value (= spot price in period t strike price for call)TP = Time premium

TIME PREMIUM - always positive. A function of: Time remaining before maturity. Expected volatility. interest rates (higher rates you save more by not buying the stock) Volatility is the main influence. It represents risk for the writer so a premium is charged.

Hedging with Options

Firms, banks, and individual investors can use options, as well as futures, to hedge the risk from fluctuations in commodity or stock prices, interest rates, and foreign currency exchange rates.

Options are more expensive than futures, but have the important advantage that an investor who buys options will not suffer a loss if prices move in the opposite direction to that being hedged against.

A firm or an investor has to trade off the generally higher cost of using options against the extra insurance benefit that options provide.

As an options buyer, you assume less risk than with a futures contract because the maximum loss you can incur is the option premium.

The options seller does not have a limit on his or her losses. The seller of a put option is still obligated to buy at the strike price, even if it is far above the current market price.

Many hedgers buy options, not on the underlying asset, but on a futures contract derived from that asset.

Protective Put Strategy:

Part 2: Forwards, Futures, and Swaps

(1) FORWARD CONTRACT

= An agreement to buy or sell an asset at an agreed upon price at a future time.

Forward contracts give firms and investors an opportunity to hedge the risk on transactions that depend on future prices.

Generally, forward contracts involve an agreement in the present to exchange a given amount of a commodity, such as oil, gold, or wheat, or a financial asset, such as Treasury bills, at a particular date in the future for a set price.

Definitions:

Spot price The price at which a commodity or financial asset can be sold at the current date.

Settlement date The date on which the delivery of a commodity or financial asset specified in a forward contract must take place.

Counterparty risk The risk that the counterpartythe person or firm on the other side of the transactionwill default.

Features:1. The payoff profile for buying (going long) on a forward contract is as follows (Draw)

2. Default (or credit) risk of the contract is two sided. Either the buyer or the seller will lose the financial difference between the forwards price and the actual market price at settlement date. This amount is paid only at maturity - no payments are made at origination or during the term of the contract, this means a large loss position may build up and no liability fall due until maturity. In these circumstances, default risk can become considerable.

(2) FUTURES CONTRACTS

= A standardized contract to buy or sell a specified amount of a commodity or financial asset on a specific future date.

Futures contracts differ from forward contracts in several ways:1. Futures contracts are traded on exchanges, such as the Chicago Board of Trade (CBOT) and the New York Mercantile Exchange (NYMEX).

2. Futures contracts typically specify a quantity of the underlying asset to be delivered but do not fix the price.

3. Futures contracts are standardized in terms of the quantity of the underlying asset to be delivered and the settlement dates for the available contracts.

Margin requirement In the futures market, the minimum deposit that an exchange requires from the buyer or seller of a financial asset; reduces default risk.

For instance, on the CBOT, futures contracts for U.S. Treasury notes are standardized at a face value of $100,000 of notes, or the equivalent of 100 notes of $1,000 face value each. The CBOT requires that buyers and sellers of these contracts deposit a minimum of $1,100 for each contract into a margin account.

Marking to market In the futures market, a daily settlement in which the exchange transfers funds from a buyers account to a sellers account or vice versa, depending on changes in the price of the contract.Example: March 1 Buyer opens contract requiring delivery of a $1 million 90-day T-Bill at a price of $980,000.

If this were a forward : Buyer pays $980,000 on March 11 and gets the T-Bills(Market prices March 2 March 10 wouldnt matter)

But since its a futures contract : Cash positions of buyer and seller adjust each day toreflect changes in the futures price marked to market

Effect on the Account ofDATEFutures price (3/11) Buyer SellerMarch 1$980,000 ___ ___

March 2 981,250 $ 1,250 $ (1,250)

March 3 982,5001,250(1,250)

March 4 983,7501,250(1,250)

March 5 983,75000

March 6 No Trading

March 7 No Trading

March 8 981,250(2,500)2,500

March 9 980,000(1,250)1,250

March 10 979,375(625)625

March 11 978,750(625)625

Total:(1,250)1,250

Daily resettlements have to be paid in cash : Potential liquidity problem! Very high leverage: For $1 Million 90-day futures contract, initial margin is$1,500. Means 0.01 percent change in futures price of $1 Million equals a $1,000 change in margin. (Wipes out 67% of margin account)

Example of a gold futures contract

Its June 2011Agree with dealer to buy gold in Dec 31 @ $400/ounce One contract = 100 ouncesYou agreed to receive 100 oz of gold in Dec 31 @ $40,000

What do you pay today for this contract today ?

If in Dec 31 gold is selling @ $500/ounceYou take delivery & sell your 100 ozs in open mkt @ $50,000 Your gain $10,000If actual Dec 31 price is $350/oz, your loss $5,000If you do not want to wait until Dec and sell the futurescontract to someone else in Aug for $450/ounce, gain $5,000

HEDGING WITH COMMODITY FUTURES

Short position In a futures contract: the right and obligation of the seller to sell or deliver the underlying asset on the specified future date.

Long position In a futures contract: the right and obligation of the buyer to receive or buy the underlying asset on the specified future date.

Consider the case of a farmer who in March sows seed with the expectation that it will yield 10,000 bushels of wheat. The farmer is concerned that when she harvests the wheat in July, the price will have fallen below $2.00, so she will receive less than $20,000 for her wheat.

A manager who buys wheat at General Mills is concerned that in July the price of wheat will have risen above $2.00, thereby raising his cost of producing cereal. The farmer and the General Mills manager can hedge against an adverse movement in the price of wheat.

Hedging involves taking a short position in the futures market to offset a long position in the spot market, or taking a long position in the futures market to offset a short position in the spot market.*

As the time to deliver approaches, the futures price comes closer to the spot price, eventually equaling the spot price on the settlement date.

To fulfill her futures market obligation, the farmer can engage in either settlement by delivery or settlement by offset.[footnoteRef:1] [1: In greater detail, the spot price must equal the futures price on the settlement date because if there were a difference between the two prices, arbitrage profits would be possible.In using settlement by offset, rather than actually delivering wheat, she would close her position at the CBOT by buying two futures contracts, thereby offsetting the two contracts she sold in March. She sold the contracts for $20,000 (= $2.00 per bushel 10,000 bushels). By buying them back for $18,000 (= $1.80 per bushel 10,000 bushels), she earns a profit of $2,000 in the futures market. In the spot market, she sells her wheat for $18,000, thereby receiving $2,000 less than she would have received at the March spot price. Because this $2,000 loss is offset by her $2,000 profit in the futures market, she has succeeded in hedging the risk of a price decline in the wheat market.]

We can summarize the profits and losses of buyers and sellers of futures contracts:

Profit (or loss) to the buyer = Spot price at settlement - Futures price at purchase

Profit (or loss) to seller = Futures price at purchase - Spot price at settlement

Graphs:

Summary:

Speculating with Commodity Futures

Some investors who are not connected with the wheat market can use wheat futures to speculate on the price of wheat.If you were convinced that the spot price of wheat was going to be lower in July than current futures price, you could sell wheat futures with the intention of buying them back at the lower price on or before the settlement date.Notice, though, that because you lack an offsetting position in the spot market, an adverse movement in wheat prices will cause you to take losses.

Hedging with Financial Futures

Today most futures traded are financial futures. Widely traded financial futures contracts include those for Treasury bills, notes, and bonds; stock indexes; and currencies. An investor who believes that he or she has superior insight into the likely path of future interest rates can use the futures market to speculate. For example, if you wanted to speculate that future interest rates will be lower (or higher) than expected, you could buy (or sell) Treasury futures contracts.

Key Idea: Money you make (lose) in the spot market is lost (gained) in the futures market, so you come out the same.

Example: A financial services company lends $10 million for two years, at an interest rate of 10%. The cost of funds to the company is now 8% (so profit on first year is (10-8)% x $10 million = $200,000). The company is worried that rates may rise next year, to 12% (so would lose $200,000). In order to lock into a borrowing cost of 8.00% in the 2nd year, they undertake the following transactions:

MONEY MARKET TRANSACTIONSFUTURES MARKET

Today needs to borrow $10 million in one year, for one year (to be lent to another firm). The current rate (cost of funds) is now 8%, rate on loan = 10%. Profit in 1st year = +$200,000Today: Sells 10 futures contracts at a price of $926,000 (at rate = 8%) each in one year. Nominal Value: $9,260,000

In 1 year: Borrows $10m at 12%, loss on loan = (12 10 %) x 10m

----------------------------------------------Actual loss on borrowing in 2nd year: $ -200,000In 1 year: Positions expires, market value of contracts = 892,857 (at rate = 12%).Nominal value: 8,928,570------------------------------------------------Profit on hedge: $330,068

Bottom line: The financial services company has bought low, and sold high in the futures market to offset the loss in the spot market.

(3) SWAP CONTRACTS

= An agreement between two or more counterparties to exchange sets of cash flows over some future period.

Interest-rate swap A contract under which counterparties agree to swap interest payments over a specified period on a fixed dollar amount, called the notional principal.

With swaps, the interest rate is often based on the rate at which international banks lend to each other. This rate is known as LIBOR, which stands for London Interbank Offered Rate.

Why might firms and financial institutions participate in interest-rate swaps? One motivation is transferring interest-rate risk to parties that are more willing to bear it.

For example, suppose a company has issued 10-year floating rate debt this means its annual interest rate payments depend on how high or low the prevailing interest rate is. It can use a swap to convert its floating rate liability to a fixed rate liability. How? Find a second party that will accept fixed rate payments from the company; the second party then assumes the companys floating rate payments.

Who? Suppose theres a bank with fixed payments (interest on long term deposits) and floating returns (consumer loans). A fall in interest rates would reduce its returns and therefore its margin - it would therefore like to make its interest payments floating as well so its funding gap is not vulnerable. It should swap its fixed liability for floating.

Solution: The company assumes the banks responsibility to pay fixed rate payments, and the bank assumes the companys responsibility to pay floating rate payments. The swap has solved both parties risk of interest rate fluctuations.

Currency SwapsA basic currency swap has three steps:1. The two parties exchange the principal amount in the two currencies.2. The parties exchange periodic interest payments over the life of the agreement.3. The parties exchange the principal amount again at the conclusion of the swap.

Credit swap A contract in which interest-rate payments are exchanged, with the intention of reducing default risk.

Credit default swap A derivative that requires the seller to make payments to the buyer if the price of the underlying security declines in value; in effect, a type of insurance.

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Solved Problem7.4Why are the put options selling for higher prices than the call options?

b. Why does the April call sell for a higher price than the January call?

c. Suppose you buy the April put. Briefly explain whether you would exercise it immediately.

d. Suppose you buy the November call at the price listed and exercise it when the price of Amazon stock is $122. What will be your profit or loss?

e. Suppose you buy the April call at the price listed, and the price of Amazon stock remains $93.60. What will be your profit or loss?Interpreting the Options Listings

Options 2012 Pearson Education, Inc. Publishing as Prentice Hall# of 5035Interest-Rate SwapsFigure 7.2Payments in a Swap TransactionWells Fargo bank and IBM agree on a swap lasting five years and based on a notional principal of $10 million. IBM agrees to pay Wells Fargo an interest rate of 6% per year for five years on the $10 million. In return, Wells Fargo agrees to pay IBM a floating interest rate. In this example, IBM owes Wells Fargo $600,000 ($10,000,000 0.06), and Wells Fargo owes IBM $700,000 ($10,000,000 (0.03 + 0.04)). Netting the two payments, Wells Fargo pays $100,000 to IBM. Generally, parties exchange only the net payment.

Swaps 2012 Pearson Education, Inc. Publishing as Prentice Hall# of 50Swaps also offer more privacy, are not subject to government regulation, and can be written for long periods. However, with swaps, counterparties must be sure of the creditworthiness of their partners, and are not as liquid as futures and options.43Making the ConnectionReading the Options ListingsThe August contract listed in the first row has a Last price of $1.64. The Volume column provides information on how many contracts were traded that day, and the Open Interest column provides information on the number of contracts outstandingthat is, not yet exercised.

The higher prices of the call options reflect the fact that because the strike price is below the underlying price, so the call options are all in the money, while the put options are out of the money. For both the call options and the put options, the further away the expiration date, the higher the price.

Options 2012 Pearson Education, Inc. Publishing as Prentice Hall# of 5034