Dr. Scott Brown Stock Options

Introduction Call & Put prices are highly inter-dependent and are not arbitrarily chosen. Put Call Parity is a strong mathematical relationship that describes the connection between calls and puts. Critical for understanding the mechanics of the options market and how options are priced. “Parity” – means equivalence. Parity Relationships simply shows the connections between two or more variables.

Put-Call Parity Equation Formula: S + P – C = Pv (E) S – Stock Price P – Put Price C – Call Price Pv(E) – Present Value of the Exercise Price. This formula says that values of long stock + long put + short call are equal to the present value of the exercise.

Put-Call Parity Equation (Cont.) Portfolio Strike PriceStock$50 Put$50 CallTotal Value The “total value” column shows this portfolio always sums to $50 no matter what happens to the stock’s price at expiration. Example:

Put-Call Parity Equation (Cont.) Formula: S + P = C + Pv (E) Left-hand side of equation: represents an investor who owns stocks plus a protective put. Right-Hand side of equation: represents an investor who owns a call option plus a deposit of cash, Pv (E). Formula tells us that an investor who buys stock and a put is financially doing the same thing as someone who buys a call and deposits sufficient cash to grow the value to the exercise price at expiration by earning the risk-free rate.

Put-Call Parity Equation (Cont.) Formula: C = S – Pv(E) + P Shows us that a long call option is the same thing as owning stock (+S), borrowing money, -Pv (E), and also owning a put (+P) When you buy a call, you are borrowing money to buy stock and also buying a put option.

Put-Call Parity Equation (Cont.) Portfolio A Stock Price$50 CallStockPay $50 Exercise Total Value The $50 call performs better than Portfolio A if the stock is below $50 at expiration since it doesn’t lose dollar-for-dollar with the stock, but both perform equally if the stock is at $50 or higher. Example:

Synthetic Options Not a type of option such as calls or puts. Are ways of creating positions that look, feel, and behave like one asset but are constructed from entirely different assets. The benefit of this is that one form may be more liquid or more efficient than another. To create a synthetic option all we need to do is refer to any of the put-call parity formulas and algebraically solve for the call option.

Synthetic Options (Cont.) Example: Original Formula: S + P – C = Pv (E) Synthetic Long Call Option: C = S – Pv (E) + P If you borrow the present value of the exercise price and buy stock plus buy a put, you have created a synthetic call option.

All Synthetic Combinations AssetSynthetic Equivalent Long StockLong Call + Short Put Short StockShort Call + Long Put Long CallLong Stock + Long Put Short CallShort Stock + Short Put Long PutShort Stock + Long Call Short PutLong Stock + Short Call

Real Applications for Synthetics When you are long the call, rather than exercising it, you could, instead, sell the same strike put. While the synthetic long stock position does not allow you to collect the dividend of the stock, it does let you collect the premium of the put. This put premium will be of greater value than the dividend on the stock while either choice exposes you to the same downside risk.

Creating a Call Option Assume you wish to buy a stock but are afraid to because of the recent volatility or because you don’t have enough money. So rather than buy stock, you decide to buy a call option. Once your order is received, the market maker must create a call option. In order to create that call, the market maker must buy stock and buy a put, which is a synthetic long call. He can then transfer that over to you by selling the call. When he sells you the call, he has effectively transferred the long stock plus long put positions over to you.

Are Options Bad for the Market? Many investors adamantly refuse to buy or sell options because they hear how “speculative” they are. They insist on holding only stocks. If you refuse to use options, you are speculating. By buying stocks, you are speculating that nothing will go wrong with your long stock position. It can be argued that investors who don’t use options are among the most speculative of investors.

Valuing Corporate Securities as Options Securities: Consider a firm that has issued a zero-coupon bond that matures to a value of $1,000,000 in five years. Payoffs for stockholders and bondholders at maturity: If value of the firm is less than $1M, say, $800k: Bondholders get: $800,000 Stockholders get: $0 Total Value of Firm: $800,000 If value of the firm is greater than $1M, say, $1.2M at maturity: Bondholders get: $1,000,000 Stockholders get: $200,000 Total Value of Firm: $1,200,000

Valuing Corporate Securities as Options (Cont.) Options: Assume you own 100 shares of stock and have sold, or written, a $100 call option against it. At expiration, if the value of the stock is less than $100, say $80: You get: $80 Call buyer: $0 Total value of your position is: $80 If the value of the stock is greater than $100, say $120 at expiration: You get: $100 Call buyer gets: $20 Total Value of positions is: $120

Using the Black-Scholes Model Recall the put-call parity formula: Stock + Put – Call = Present value of the exercise price. Rewritten for above corporation at maturity as: Stock + Put – Call = Total Value of Debt. Stock – Call = Total value of Debt – Put. So the Black-Scholes Option Pricing Model tells us the value of the covered call position (left side) is equal to the debt at maturity with a put written against it (right side). Options allow you to do what stockholders have always done – but for a lot less money. Why? Because they have strike prices. They allow you to partition the unlimited range of possible stock prices into segments that you wish to control.

Summary Stock + Put – Present value of the exercise price = Risk-free position (Conversion). The opposite of a Conversion is a Reversal (Short – Put + Present Value of exercise price). The value of a put option equals the time value of the call (above the cost-of-carry). Any synthetic position can be found by solving the formula S+P-C = Present value of E for a single variable. Buying calls is synthetically equivalent to buying stock on margin and buying a put for insurance.

Disclaimer DISCLAIMER: THE DATA CONTAINED HEREIN IS BELIEVED TO BE RELIABLE BUT CANNOT BE GUARANTEED AS TO RELIABILITY, ACCURACY, OR COMPLETENESS; AND, AS SUCH ARE SUBJECT TO CHANGE WITHOUT NOTICE. WE WILL NOT BE RESPONSIBLE FOR ANYTHING, WHICH MAY RESULT FROM RELIANCE ON THIS DATA OR THE OPINIONS EXPRESSED HERE IN. DISCLOSURE OF RISK: THE RISK OF LOSS IN TRADING FUTURES, FOREX AND OPTIONS CAN BE SUBSTANTIAL; THEREFORE, ONLY GENUINE RISK FUNDS SHOULD BE USED. FUTURES, FOREX AND OPTIONS MAY NOT BE SUITABLE INVESTMENTS FOR ALL INDIVIDUALS, AND INDIVIDUALS SHOULD CAREFULLY CONSIDER THEIR FINANCIAL CONDITION IN DECIDING WHETHER TO TRADE. OPTION TRADERS SHOULD BE AWARE THAT THE EXERCISE OF A LONG OPTION WOULD RESULT IN A FUTURES OR FOREX POSITION.HYPOTHETICAL PERFORMANCE RESULTS HAVE MANY INHERENT LIMITATIONS, SOME OF WHICH ARE DESCRIBED BELOW. NO REPRESENTATION IS BEING MADE THAT ANY ACCOUNT WILL, OR IS LIKELY TO, ACHIEVE PROFITS OR LOSSES SIMILAR TO THOSE SHOWN. IN FACT, THERE ARE FREQUENTLY SHARP DIFFERENCES BETWEEN HYPOTHETICAL PERFORMANCE RESULTS AND THE ACTUAL RESULTS SUBSEQUENTLY ACHIEVED BY ANY PARTICULAR TRADING PROGRAM. ONE OF THE LIMITATIONS OF HYPOTHETICAL PERFORMANCE RESULTS IS THAT THEY ARE GENERALLY PREPARED WITH THE BENEFIT OF HINDSIGHT. IN ADDITION, HYPOTHETICAL TRADING DOES NOT INVOLVE FINANCIAL RISK, AND NO HYPOTHETICAL TRADING RECORD CAN COMPLETELY ACCOUNT FOR THE IMPACT OF FINANCIAL RISK IN ACTUAL TRADING. FOR EXAMPLE, THE ABILITY TO WITHSTAND LOSSES OR TO ADHERE TO A PARTICULAR TRADING PROGRAM, IN SPITE OF TRADING LOSSES, ARE MATERIAL POINTS WHICH CAN ALSO ADVERSELY AFFECT ACTUAL TRADING RESULTS. THERE ARE NUMEROUS OTHER FACTORS RELATED TO THE MARKETS, IN GENERAL, OR TO THE IMPLEMENTATION OF ANY SPECIFIC TRADING PROGRAM WHICH CANNOT BE FULLY ACCOUNTED FOR IN THE PREPARATION OF HYPOTHETICAL PERFORMANCE RESULTS AND ALL OF WHICH CAN ADVERSELY AFFECT ACTUAL TRADING RESULTS. PS. In our opinion, we believe, it may be possible, that heavy smoking and drinking may be hazardous to your health. If you choose to smoke and drink while trading, The Delano Max Wealth Institute nor Dr. Scott Brown is liable for any damage it may cause. If you slip and fall on the ice, we're not liable for that either.