Derivative securities

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CHAPTER 18Derivatives and Risk Management

• Derivative securities
• Fundamentals of risk management
• Using derivatives to reduce interest rate risk

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Why might stockholders be indifferent to whether
or not a firm reduces the volatility of its cash
flows?

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

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Reasons Risk Management Might Increase the Value
of a Corporation

• 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.

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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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What is an option?

• 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.

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What is the single most important characteristic
of an option?

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

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Option Terminology

• 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.

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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 investors 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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Consider the following data
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.
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Create a table which shows (a) stock price, (b)
strike price, (c) exercise value, (d) option
price, and (e) premium of option price over the
exercise value.

• Price of Strike Exercise Value
• Stock (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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Table (Continued)

• 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

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What happens to the premium of the option price
over the exercise value 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
Option value
30 25 20 15 10 5
Market price
Exercise value
5 10 15 20 25 30 35
40 45 50
Stock Price
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What are the assumptions of the Black-Scholes
Option Pricing Model?

• The stock underlying the call option provides no
  dividends during the call options life.
• There are no transactions costs for the
  sale/purchase of either the stock or the option.
• kRF is known and constant during the options
  life.

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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 todays 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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What are the three equations that make up the OPM?

• V PN(d1) Xe -kRFtN(d2).
• d1 .
• s t
• d2 d1 s t.

ln(P/X) kRF (s2/2)t
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What is the value of the following call option
according to the OPM?Assume P 27 X 25
kRF 6t 0.5 years s2 0.11

• V 27N(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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What impact do the following para- meters have on
a call options value?

• Current stock price Call option value increases
  as the current stock price increases.
• Exercise price As the exercise price increases,
  a call options value decreases.

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• Option period As the expiration date is
  lengthened, a call options value increases (more
  chance of becoming in the money.)
• Risk-free rate Call options 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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What is corporate risk management?

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

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Why is corporate risk management important to all
firms?

• 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.

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Definitions of Different Types of Risk

• 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 firms products or services.
• Input risks Those associated with a firms
  input costs.

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• Financial risks Those that result from
  financial transactions.
• Property risks Those associated with loss of a
  firms 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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What are the three steps of corporate risk
management?

• 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.

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What are some actions that companies can take to
minimize or reduce risk exposure?

• 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.

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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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What is a financial risk exposure?

• 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.

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Financial Risk Management Concepts

• 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.

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• Hedging Generally conducted where a price
  change could negatively affect a firms 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 others debt
  contract. Swaps can reduce each partys
  financial risk.

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How can commodity futures markets be used to
reduce input price risk?

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