【管理课件】corporate financial management 3e --emery finnerty stowe

12,Corporate Financial Management 3e Emery Finnerty Stowe,Options,Learning Objectives,Explain the importance of asset pricing models.Demonstrate choice of an investment position on the Capital Market Line (CML).Understand the Capital Asset Pricing Model (CAPM) and its uses.Describe the arbitrage pricing model and differentiate it from the CAPM.,Chapter Outline,12.1Options12.2Buying and Selling Parts of an Assets Return Distribution12.3Valuing an Option12.4Some Important Generalizations about Options12.5Places to Look for Options12.6A Simple Model of Option Valuation12.7Combining Option Values,Options and the Principles of Finance,OptionsLook for options that significantly affect value.Two-Sided TransactionsAlways consider both sides.Incremental BenefitsMeasure the impact of options on an incremental basis.,Options and the Principles of Finance,Time-Value-of-MoneyInclude its impact on the value of an option.Risk-Return Trade-OffAn option splits the assets returns and alters participant risk.Self-Interested BehaviorOptions can provide incentives that can influence behavior.,Options: Basic Terminology,An option is the right to do something, without the obligation to do it.A call option is the right to buy an asset at a fixed price, within a fixed time period.A put option is the right to sell an asset at a fixed price, within a fixed time period.,Options: Basic Terminology,The price at which the exchange is made is called the strike or exercise price.Exercising the option involves exchanging cash for the underlying asset.When a call option is exercised by the holder, the underlying asset is purchased by paying the exercise price.When a put option is exercised by the holder, the underlying asset is sold for the exercise price.,Options: Basic Terminology,An option is in-the-money if exercising it provides an advantage over directly buying or selling the underlying asset in the open market.A call option is in-the-money if the open market price of the underlying asset is more than the exercise price.A put option is in-the-money if the open market price of the underlying asset is less than the exercise price.,Options: Basic Terminology,An option is out-of-the-money if directly buying or selling the underlying asset in the open market provides an advantage over exercising it.A call option is out-of-the-money if the open market price of the underlying asset is less than the exercise price.A put option is out-of-the-money if the open market price of the underlying asset is more than the exercise price.,Options: Basic Terminology,The exercise value is the amount of advantage that an in-the-money option provides over buying or selling the asset at the open market price.The exercise value of out-of-the-money options is zero.,Options: Basic Terminology,Options have a finite life.Upon expiration, the option contract is null and void.An American option can be exercised at any time prior to expiration.A European option can only be exercised at maturity, not before.,The Lottery Ticket as an Option,A lottery ticket is a call option on the underlying prize.It is a European option.It has a strike price of zero.It has an exercise value of zero during its life.If it is the winning ticket, it is in-the-money at expiration; otherwise it is out-of-the-money.,Payoff Profile for an Asset,Suppose Carla buys some land for $60,000.,Value of Land,Gain,Loss,A Call Option on an Asset,If the land value is $68,000 1 year later, Alex would gain $3,000 by exercising his option.If the land value is $62,000 1 year later, Alexs option would expire worthless.,Suppose Carla buys some land for $60,000 and immediately sells a 1-year European call option on it to Alex. The option has an exercise price of $65,000.,A Call Option on an Asset,Carlas value = minMarket Value; $65,000Exercise value of Alexs call option = max(Market Value $65,000); $0,Exercise Value of Call Option at Maturity,Value of Asset at Expiration,$65,000,Gain,A Call Option on an Asset,Suppose Alex bought the call option from Carla for $2,000. Compute the dollar profit (or loss) for Carla and Alex at various land values at option maturity.,Profit of Call Option at Maturity,Value of Land at Expiration,loss,Gain,A Call Option on an Asset,Suppose the market value of the land is $55,000 when the option matures.Alex would not exercise the option. Thus, he would lose all of the $2,000 that he invested in the option for a 100% rate of return.,A Call Option on an Asset,Carlas net profit would be = Net profit on land + Amount received for the option= ($55,000 $60,000) + $2,000= ($3,000) (a loss)Her net investment was $60,000 $2,000 = $58,000Her rate of return is $3,000/$58,000 = 5.2%,A Call Option on an Asset,Suppose the market value of the land is $68,000 when the option matures.Alex would exercise the option:He would buy the land from Carla for $65,000 and sell it in the open market for $68,000.His net profit would be $3,000 $2,000 or $1,000.His rate of return would be $1,000/$2,000 or 50.0%,A Call Option on an Asset,Carlas net profit would be = Net profit on land + Amount received for the option= $65,000 60,000 + 2,000= $7,000Since her net investment was $58,000, her rate of return is $7,000/$58,000 = 12.1%,Gain or Loss at Call Option Expiration,Alex and Carla at Maturity,Value of Land at Expiration,$65,000,$2,000,Gain,loss,$67,000,$58,000,Carlas “covered” call,Alexs Call option,$58,000,Call Options on Assets,By selling a call option on an asset that is already owned, you give up the future “good” outcomes in exchange for the option price which is received immediately.This is called writing a covered call.By buying a call option, you are buying the future “good” outcomes by paying the option price today.,Carlas Covered Call,Value of Land at Expiration,Loss,Gain,A Put Option on an Asset,Suppose Carla buys some land for $60,000 and immediately buys a 1-year European put option on it from Paul. The option has an exercise price of $60,000.,A Put Option on an Asset,If the market value of the land is more than the exercise price ($60,000), Carla would sell the land in the open market, and the option would be worthless.The put option will be exercised by Carla only if the market value of the land is less than the exercise price of $60,000.At maturity, the value of the option would be the difference between the exercise price and the market value of the land.,Exercise Value of Put Option at Maturity,Value of Asset at Expiration,$60,000,Gain,$60,000,A Put Option on an Asset,Suppose Carla bought the put option from Paul for $2,000. Compute the dollar profit (or loss) for Carla and Paul at various land values at option maturity.,Profit of Put Option at Maturity,Value of Asset at Expiry,Gain,Loss,Break even = $58,000,$58,000,$58,000,Alex,Carla,A Put Option on an Asset,Suppose the market value of the land is $55,000.By exercising the put, Carla sells the land to Paul for $60,000.Her net profit would beProfit on land sale cost of put option= $0 $2,000 = $2,000 (a loss),A Put Option on an Asset,With a land value of $55,000, Paul pays $60,000 when Carla exercises the put.He thus loses $5,000 on the land transaction, but he received $2,000 when he sold the put a year ago.His net profit is thus($55,000 $60,000) + $2,000 = -$3,000 (a loss),Gain or Loss at Put Option Expiration,Alex and Carla at Maturity,Value of Land at Expiration,$60,000,$2,000,Gain,loss,$62,000,$58,000,Alex,Carlas synthetic Call option,$58,000,Carlas protective put,=,Writing a Covered Call,Long position in a stock; bought at $KShort position in a call; strike price $K; option premium c0, K,K,K + c0,ST,K c0,This is also known as writing a synthetic put,Synthetic Put,Short position in a stock at $K Long position in a call strike price $K; option premium c0,K,K,K c0,K c0,ST,Protective Put (Synthetic Call),Long position in a stock; bought at $K Long position in a put; strike price $K; option premium p0, K,K,K p0,ST,Synthetic Call,Short position in a stock Short position in a put; strike price $K; option premium p0,K,K,ST,Put Options on Assets,By buying a put option on an asset that is already owned, you are purchasing an insurance policy.Your losses are limited.By selling a put option, you are willing to accept the “bad” outcomes in exchange for the put price today.,Put-Call Parity,Every situation that can be described in terms of a call option has a parallel description in terms of a put option.Compare the case where Alex bought a call from Carla to the case where Carla purchased the put option from Paul.Alexs profits, as a function of land value, show a pattern similar to Carlas profits when she bought the put option from Paul.,Put-Call Parity,PhilosophicallyThe RIGHT to buy a stock together with the ABILITY to buy it. (A call option plus the present value of the exercise price.)Should be worth the same asThe RIGHT to sell a stock together with the ABILITY to sell it. (A put option written on a stock that you own.)This notion can be formalized as Put-Call Parity,Put-Call Parity,The following two portfolios have the same payoffs at expiry:One European call plus an amount of cash equal to present value of the exercise price .One European put plus one share of stock.This means that at time zero, two portfolios should have the same value.The following slide shows the payoffs.,Long 1 call, and PV of exercise price,Long 1 share, long 1 put,Put-Call Parity: Payoffs at Expiry,Valuing an Option,At maturity, the value of an option is eitherzero (if the option is out-of-the-money) or the positive difference between the value of the underlying asset and the options exercise price (if the option is in-the-money).Prior to maturity, the value of the option is generally greater than its exercise value.This excess value is called the “time premium” of the option.,The Time Premium of an Option,It arises since the option gives the holder the right to claim certain outcomes and reject others.It depends onthe time until expiration of the optionthe risk of the underlying assetriskless rate of return (think put-call parity),Time-to-Expiration and Option Values,The longer the time to expiration, the higher the time premium.You can never be worse off with an option that has a longer time to expiration.More time allows more chance for an option to be in-the-money at expiration.,Asset Risk and Option Values,The higher the risk of an asset, the greater the time premium.With higher risk, the probability of extremely good outcomes increases.This increases the probability that the option will be in-the-money at expiration.Even though the probability of extremely bad outcomes increases, the option will be worthless anyway.,Riskless Return and Option Values,The higher the riskless rate of return, the lower the present value of a known future amount.Exercising the option involves either the payment of the exercise price by the option holder (in the case of a call), or the receipt of the exercise price (in the case of a put).,Riskless Return and Option Values,A call holder will pay the exercise price to receive the asset.With higher riskless returns, the present value of this payment is lower and the call option value is higher.A put holder will receive the exercise price to receive the asset.With higher riskless returns, the present value of this payment is lower and the put option value is lower.,Maximum Option Values,The maximum value of an option can never be greater than the value of the underlying asset.The right to buy (or sell) the asset can never be worth more than the asset itself.,Total Value of Call Option,Value of Asset at Expiration,Gain,Total Value of Call = time premium + exercise value,Exercise value of call,Time premium,Exercise value,Total Value of Call Option,Value of Asset at Expiration,Put option value,Exercise value of put,Time value,Exercise value,Total Value of Put = time premium + exercise value,Some Generalizations about Options,The largest time premium occurs when the underlying assets value equals the exercise price.At this point, the uncertainty about whether the option will expire in- or out-of-the-money is the greatest.The time premium declines as the option becomes more in- or out-of-the-money.At this point, there is little uncertainty about whether the option will end up in- or out-of-the-money.,Some Generalizations about Options,An American option is never worth less than a comparable European option.The American option gives you everything that a European option does, plus the added feature of possible exercise prior to maturity.An options time premium is generally positive.An out-of-the-money option can never have a negative value.,Some Generalizations about Options,In-the-money American options would always have a positive time premium.If not, arbitrage is possible: buy the option and immediately exercise it.In-the-money European options could have a negative time premium.Immediate arbitrage is not possible since these options cannot be exercised prior to expiration.,Some Generalizations about Options,It is generally better to sell the option than exercise it.By exercising it prior to maturity, you are giving up the time premium.If you sell the option, you get both the exercise value and the time premium.,Some Generalizations about Options,The further an option is out-of-the-money, the less it is worth.The entire value of the “deep” out-of-the-money option is derived from the time premium.The time premium decreases as the options gets further out-of-the-money.,Places to Look for Options,Publicly traded optionsInsuranceReal estate optionsConvertible bondsWarrantsEmployee stock optionsCall provisions in bonds,Hidden Options,Common stock as a call option on the firms assets.The exercise price is the amount due to the debtholders.Common stock as a put option on the firms assets.The stockholders can “sell” the assets to the debtholders for an exercise price equal to the amount owed.,More Hidden Options,Stakeholder relationships in financial contracting.Refunding a home mortgage.Tax-timing options.Options connected with capital investments.Variable cost reduction.,A Simple Model of Option Valuation,Consider the call option sold by Carla to Alex. The option has one year to maturity, and an exercise price of $65,000. At the time of the sale, the land value was $60,000. Assume that in one year, the land value can be either $67,870 (up by 13.12%) or $48,000 (down by 20%) in one year. If the risk-free rate is 4% per year, and assuming that the land should yield this rate, what is the value of the call option on this land?,A Simple Model of Option Valuation,If the land value goes up to $67,870, the value of the call option would be$67,870 $65,000 or $2,870.If the land value declines to $48,000, the call option would expire out-of-the-money and be worthless.,A Simple Model of Option Valuation,Let pu denote the probability that land will go up in value. Then the probability that the land value will decline is (1 pu).Since the land is to yield the riskless rate of return of 4%,4% = pu (13.12%) + (1 pu) (20.0%)Solving this for pu, we get pu = 72.5%.The probability of a decline in land value is thus 27.5%,A Simple Model of Option Valuation,The expected value of the call option at maturity is:pu (Value of call if land goes up) +(1 pu) (Value of call if land goes down)= (0.725) ($2,870) + (0.275) ($0)= $2,080The present value of this is the value of the call option today:$2,080/1.04 = $2,000,An Arbitrage Option Valuation,We can get the same result with a completely different insight.We can replicate the payoff of the call option with a levered position in the land.That levered real estate portfolio can be valued.Once we have that number, we can back out the value of the call option.,An Arbitrage Option Valuation,A call option on this land with exercise price of $65,000 will have the following payoffs. We can replicate the payoffs of the call option. With a levered position in the stock.,Landt = 1,Landt = 0,Callt = 1,$2,870,$0,$60,000,$ 48,000,$ 67,870,An Arbitrage Option Valuation,Borrow the present value of $ 48,000 today and buy the land.The net payoff for this levered equity portfolio in one period is either $19,870 or $0.,Landt = 1,Landt = 0,Callt = 1,$2,870,$0,$60,000,$ 48,000,$ 67,870,debt, $ 48,000,=,=, $ 48,000,portfolio,$19,870,$0,An Arbitrage Option Valuation,The call option represents $2,870/$1,9870 =14.44% of the value of the land with borrowing. If we find the value of that portfolio, we can find the value of the call option at t = 0. The land at t = 0 is worth $60,000The present value of $48,000 is $46,153.84The value of the call is thus:,Arbitrage Option Valuation,The replicating portfolio intuition.,Many derivative securities can be valued by valuing portfolios of primitive securities when those portfolios have the same payoffs as the derivative securities.,Combining Option Values,The value of two or more hidden options cannot be greater than the sum of their individual option values.Consider buying insurance on the same car from two different insurance companies simultaneously.In the event of loss, you cannot get more than the total damages.The firms will split the repair bill.The added insurance premium for the second policy is not worth it.,Portfolios of Options,The value of an option on a portfolio of assets cannot be greater than the sum of the values of options on the individual assets.The risk of a portfolio is less than the sum of the risks of the individual assets.The Diversification PrincipleOption values decrease as the risk of the underlying asset decreases.,Portfolios of Options,As a proof, consider two portfolios:The first portfolio is two call options with a strike price equal to the average of K1 and K3 The other is a portfolio of 2 call options:one call with a strike of K1 , an