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Derivative securities

Fundamentals of risk management

Using derivatives to reduce interest rate risk

CHAPTER 18Derivatives and Risk Management

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If volatility is due to systematic risk, it can be eliminated by diversifying investors’ portfolios.

Why might stockholders be indifferent to whether or not a firm reduces the

volatility of its cash flows?

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Increase their use of debt.

Maintain their optimal capital budget.

Avoid financial distress costs.

Utilize their comparative advantages in hedging, compared to investors.

Reduce the risks and costs of borrowing.

Reasons Risk Management Might Increase the Value of a Corporation

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Reduce the higher taxes that result from fluctuating earnings.

Initiate compensation programs to reward managers for achieving stable earnings.

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An option is a contract that gives its holder the right, but not the obligation, to buy (or sell) an asset at some predetermined price within a specified period of time.

What is an option?

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It does not obligate its owner to take any action. It merely gives the owner the right to buy or sell an asset.

What is the single most importantcharacteristic of an option?

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Call option: An option to buy a specified number of shares of a security within some future period.

Put option: An option to sell a specified number of shares of a security within some future period.

Exercise (or strike) price: The price stated in the option contract at which the security can be bought or sold.

Option Terminology

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Option price: The market price of the option contract.

Expiration date: The date the option matures.

Exercise value: The value of a call option if it were exercised today = Current stock price - Strike price.

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Covered option: A call option written against stock held in an investor’s portfolio.

Naked (uncovered) option: An option sold without the stock to back it up.

In-the-money call: A call option whose exercise price is less than the current price of the under-lying stock.

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Out-of-the-money call: A call option whose exercise price exceeds the current stock price.

LEAPS: Long-term Equity AnticiPation Securities are similar to conventional options except that they are long-term options with maturities of up to 2 1/2 years.

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Stock Price Call Option Price$25 $ 3.00 30 7.50 35 12.00 40 16.50 45 21.00 50 25.50

Exercise price = $25.

Consider the following data:

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Create a table which shows (a) stockprice, (b) strike price, (c) exercise

value, (d) option price, and (e) premium of option price over the exercise value.

Price of Strike Exercise ValueStock (a) Price (b) of Option (a) –

(b)$25.00 $25.00 $0.00 30.00 25.00 5.00 35.00 25.00 10.00 40.00 25.00 15.00 45.00 25.00 20.00 50.00 25.00 25.00

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Exercise Value Mkt. Price Premium

of Option (c) of Option (d) (d) – (c)

$ 0.00 $ 3.00 $ 3.00

5.00 7.50 2.50

10.00 12.00 2.00

15.00 16.50 1.50

20.00 21.00 1.00

25.00 25.50 0.50

Table (Continued)

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What happens to the premium of the option price over the exercisevalue as the stock price rises?

The premium of the option price over the exercise value declines as the stock price increases.

This is due to the declining degree of leverage provided by options as the underlying stock price increases, and the greater loss potential of options at higher option prices.

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Call Premium Diagram

5 10 15 20 25 30 35 40 45 50

Stock Price

Option value

30

25

20

15

10

5

Market price

Exercise value

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The stock underlying the call option provides no dividends during the call option’s life.

There are no transactions costs for the sale/purchase of either the stock or the option.

kRF is known and constant during the option’s life.

What are the assumptions of theBlack-Scholes Option Pricing Model?

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Security buyers may borrow any fraction of the purchase price at the short-term, risk-free rate.

No penalty for short selling and sellers receive immediately full cash proceeds at today’s price.

Call option can be exercised only on its expiration date.

Security trading takes place in continuous time, and stock prices move randomly in continuous time.

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V = P[N(d1)] – Xe -kRFt[N(d2)].

d1 = . t

d2 = d1 – t.

What are the three equations thatmake up the OPM?

ln(P/X) + [kRF + (2/2)]t

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What is the value of the following call option according to the OPM?

Assume: P = $27; X = $25; kRF = 6%;t = 0.5 years: 2 = 0.11

V = $27[N(d1)] – $25e-(0.06)(0.5)[N(d2)].

ln($27/$25) + [(0.06 + 0.11/2)](0.5)

(0.3317)(0.7071)

= 0.5736.

d2 = d1 – (0.3317)(0.7071) = d1 – 0.2345

= 0.5736 – 0.2345 = 0.3391.

d1 =

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N(d1) = N(0.5736) = 0.5000 + 0.2168 = 0.7168.

N(d2) = N(0.3391) = 0.5000 + 0.1327 = 0.6327.

Note: Values obtained from Table A-5 in text.

V = $27(0.7168) – $25e-0.03(0.6327) = $19.3536 – $25(0.97045)(0.6327) = $4.0036.

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Current stock price: Call option value increases as the current stock price increases.

Exercise price: As the exercise price increases, a call option’s value decreases.

What impact do the following para-meters have on a call option’s value?

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Option period: As the expiration date is lengthened, a call option’s value increases (more chance of becoming in the money.)

Risk-free rate: Call option’s value tends to increase as kRF increases (reduces the PV of the exercise price).

Stock return variance: Option value increases with variance of the underlying stock (more chance of becoming in the money).

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Corporate risk management relates to the management of unpredictable events that would have adverse consequences for the firm.

What is corporate risk management?

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All firms face risks, but the lower those risks can be made, the more valuable the firm, other things held constant. Of course, risk reduction has a cost.

Why is corporate risk managementimportant to all firms?

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Speculative risks: Those that offer the chance of a gain as well as a loss.

Pure risks: Those that offer only the prospect of a loss.

Demand risks: Those associated with the demand for a firm’s products or services.

Input risks: Those associated with a firm’s input costs.

Definitions of Different Types of Risk

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Financial risks: Those that result from financial transactions.

Property risks: Those associated with loss of a firm’s productive assets.

Personnel risk: Risks that result from human actions.

Environmental risk: Risk associated with polluting the environment.

Liability risks: Connected with product, service, or employee liability.

Insurable risks: Those that typically can be covered by insurance.

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Step 1. Identify the risks faced by the firm.

Step 2. Measure the potential impact of the identified risks.

Step 3. Decide how each relevant risk should be handled.

What are the three steps of corporate risk management?

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Transfer risk to an insurance company by paying periodic premiums.

Transfer functions that produce risk to third parties.

Purchase derivative contracts to reduce input and financial risks.

What are some actions thatcompanies can take to minimize

or reduce risk exposure?

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Take actions to reduce the probability of occurrence of adverse events.

Take actions to reduce the magnitude of the loss associated with adverse events.

Avoid the activities that give rise to risk.

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Financial risk exposure refers to the risk inherent in the financial markets due to price fluctuations.

Example: A firm holds a portfolio of bonds, interest rates rise, and the value of the bonds falls.

What is a financial risk exposure?

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Derivative: Security whose value stems or is derived from the values of other assets. Swaps, options, and futures are used to manage financial risk exposures.

Futures: Contracts that call for the purchase or sale of a financial (or real) asset at some future date, but at a price determined today. Futures (and other derivatives) can be used either as highly leveraged speculations or to hedge and thus reduce risk.

Financial Risk Management Concepts

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Hedging: Generally conducted where a price change could negatively affect a firm’s profits.

Long hedge: involves the purchase of a futures contract to guard against a price increase.

Short hedge: involves the sale of a futures contract to protect against a price decline in commodities or financial securities.

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Swaps: Involve the exchange of cash payment obligations between two parties, usually because each party prefers the terms of the other’s debt contract. Swaps can reduce each party’s financial risk.

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The purchase of a commodity futures contract will allow a firm to make a future purchase of the input at today’s price, even if the market price on the item has risen substantially in the interim.

How can commodity futures marketsbe used to reduce input price risk?