Protective Put Strategy Profits

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1 Chapter Part Options and Corporate Finance: Basic Concepts Combinations of Options Options Call Options Put Options Selling Options Reading The Wall Street Journal Combinations of Options Valuing Options An Option-Pricing Formula Capital-Structure Policy and Options Mergers and Options Investment in Real Projects and Options Summary and Conclusions Puts and calls can serve as the building blocks for more complex option contracts. If you understand this, you can become a financial engineer, tailoring the risk-return profile to meet your client s needs. Protective Put Strategy: Buy a Put and Buy the Underlying Stock: Payoffs at Expiration Protective Put Strategy Profits $5 Buy the stock Protective Put strategy has downside protection and upside potential $5 Buy a put with an exercise price of $5 $4 -$4 $4 $5 Buy the $4 Buy a put with Protective Put strategy has downside protection and upside potential 3 Covered Call Strategy Long Straddle: Buy a Call and a Put $4 Buy the $4 $4 $3 Buy a call with an $ -$3 -$4 $3 $4 $5 Sell a call with Covered call 4 -$ - $3 $4 $5 $6 $7 A Long Straddle only makes money if the stock price moves away from $5. Buy a put with an 5

2 Short Straddle: Sell a Call and a Put S P C E e $ -$3 -$4 A Short Straddle only loses money if the stock price moves away from $5. Sell a put with $3 $4 $5 $6 $7 Sell a call with an C Call option price S Current stock price r Risk-free rate Buy the stock, buy a put, and write a call; the sum of which equals the strike price discounted at the risk-free rate S P C Ee P Put option price E Option strike price T Time until option 6 7 Buy Stock & Buy Put Long Stock Buy Call & Buy Zero Coupon Risk-Free Exercise Price Long Call 8 9 Long Stock S P C Ee Long Call In market equilibrium, it must be the case that option prices are set such that: Otherwise, riskless portfolios with positive payoffs exist. a stock option is a function of 6 input factors:. Current price of underlying stock.. Strike price specified in the option contract. 3. Risk-free interest rate over the life of the contract. 4. Time remaining until the option contract expires. 5. Price volatility of the underlying stock. The price of a call option equals: r T C S N ( d ) E e N ( d )

3 Black-Scholes Model r T C S N ( d) E e N ( d ) Where the inputs are: S Current stock price E Option strike price r Risk-free interest rate T Time remaining until option s Sigma, representing stock price volatility, standard deviation Black-Scholes Model r T C S N ( d ) E e N ( d ) Where d and d equal: d ln ( S ) d d s s r T E s T T 3 Black-Scholes Models Remembering put-call parity, the value of a put, given the value of a call equals: S P C Ee P C S Ee Also, remember at : C S E P E S 4 Find the value of a six-month call option on the Microsoft with an $5 The current value of a share of Microsoft is $6 The interest rate available in the U.S. is r 5%. The option maturity is 6 months (half of a year). The standard deviation of the underlying asset is 3% per annum. 5 Assume S $6, X $5, T 6 months, r 5%, and σ 3%, calculate the value of a call. First calculate d and d ln( S / E) ( r.5s d σ T ) T C S N( d ) Ee rt N( d ) Then d, d d s T 6 7 3

4 Another Black-Scholes Example Assume S $5, X $45, T 6 months, r %, and σ 8%, calculate the value of a call and a put. From a standard normal probability table, look up N(d ).8 and N(d ).754 (or use Excel s normsdist function) 8 Levered Equity is a Call Option on the. The underlying asset are the assets of the. The strike price is the payoff of the bond. Two scenarios: greater in value than the debt: Shareholders have an in-the-money call, they will pay the bondholders and call in the assets of the. lower valued than the debt: Shareholders have an out-of-the-money call, they will not pay the bondholders and let the call expire. (i.e.the shareholders will declare bankruptcy) 9 Levered Equity is a Put Option on the. The underlying asset are the assets of the. The strike price is the payoff of the bond. Two scenarios: At the maturity of their debt, the assets of the are less in value than the debt: Shareholders have an in-the-money put and they will put the to the bondholders. (i.e. declare bankruptcy) greater in value than the debt: Shareholders have an out-of-the-money put they will not exercise the option (i.e. NOT declare bankruptcy) and let the put expire. It all comes down to put-call parity. C S P X e a call on the Stockholder s position in terms of call options a put on the the Stockholder s position in terms of put options a risk-free bond a call option on (to stockholders): a call on the assets (V) debt (B) Capital-Structure Policy and Options Recall some of the agency costs of debt: they can all be seen in terms of options. For example, recall the incentive shareholders in a levered have to take large risks. Why? Call V B Where B exercise price 3 4

5 Balance Sheet for a Company in Distress Low-Risk vs High-Risk Projects ( has $3 in debt outstanding) Assets BV MV Liabilities BV MV Cash LT bonds $3? Fixed Assets $4 Equity $3? Total $6 Total $6 State of Econ. Recession Boom Probability Low-Risk Project Firm $3 $7 Stock $4 Bond $3 $3 What happens if the is liquidated today? State of Econ. Recession Probability High-Risk Project Firm $ Stock Bond $ Boom $, $,7 $3 4 Which project is preferred by Bondholders? By Stockholders? Why? Firm with high-risk project has higher volatility, what does that do to the price of the call option (value of the )? 5 Investment in Real Projects & Options Real Options Classic NPV calculations normally ignore the flexibility that real-world s typically have. The next chapter will discuss this further. Whenever management can decide in the future how best to operate a project (expand, contract, delay, or abandon), the project contains a real option. Real estate developer buys 7 acres in a rural area. He plans on building a subdivision when the population from the city expands this direction. If growth is less than anticipated, the developer thinks he can sell the land to a country club to build a golf course on the property. The development option is a option. The golf course option is a option. How would these real options change the standard NPV analysis? 6 7 5

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