No Options For Me!

(Think twice -- you may already be using them)

Speculation still seems to be a forbidden word with the financial press.  Magazines, television shows and many professionals alike will tell you that speculation is bad for the market and is the cause of the recent volatility.

There are so many investors who adamantly believe this and refuse to buy or sell options; they insist on holding only stocks.  But if you refuse to use options, you are speculating.  How?  Options were created as hedging tools.  Whenever you hedge, you give up some upside profits in exchange for some downside protection (the opposite if you are short the stock).  So if you buy stock and refuse to buy or sell options, you are speculating that nothing will go wrong with your long stock position.  You are willing to hold out for more profit at the expense of downside exposure to a price of zero.  In fact, it can be argued that investors who don't use options are among the most speculative of all!

If you're still in doubt, would you believe that stock can be viewed as an option?

Valuing corporate securities as options

When Black and Scholes developed their famous option-pricing model, they were certain there were many uses for it other than just valuing call options.  One of the uses they suggested was in valuing corporate securities.

Consider a firm that has issued one zero-coupon bond that matures to a value of $1,000,000 in five years.  With this money, the firm produces things and hopes to have a value in excess of this $1,000,000 in five years, and pays off their debt, leaving the stockholders with whatever remains in value.  However, if the firm's value is less than $1,000,000 at maturity of the bond, the stockholders will simply turn over the assets to the bondholders and will be free of further liability.

Let's look at the payoffs for stockholders and bondholders at maturity:

If value of the firm is less than $1,000,000, say, $800,000:
Bondholders get:  $800,000
Stockholders get:  $0
Total value of firm = $800,000

If the value of the firm is greater than $1,000,000, say $1,500,000 at maturity:
Bondholders get:  $1,000,000
Stockholders get:  $500,000
Total value of firm is $1,500,000

We see with the above payoffs that the total value of the firm is partitioned between the stockholders and bondholders.  Notice how the stockholders get nothing at expiration if the value of the firm is below the value of the matured debt.  But if the value of the firm is greater than the matured debt, stockholders receive the excess value.

Now compare this to options.

You own a $100 call option that someone has written as a covered position:

At expiration, if the value of the stock is less than $100, say $80:
Call writers get:  $80
Call owners get:  $0
Total value of firm is $80

In other words, if the value of the stock is below the strike at expiration, the covered call writer is left with the stock at its current value of $80.  The long call position receives nothing.

If the value of the stock is greater than $100, say $150 at expiration:
Call writers get:  $100
Call owners get:  $50
Total value of firm is $150

If the value of the stock is above the strike at expiration, the covered call writer will be assigned and receive the $100 strike price.  The call owners will receive the stock and pay the strike for a value of the stock price minus the strike price.  The stockholders, in this case, receive what's left over after the bondholders are paid.

If you look closely, you will see that the payoff for the call option above exactly resembles the payoffs to the stockholders for the corporation discussed earlier.

Using the Black-Scholes Model

If you read our section on synthetics, you may recall the put-call parity formula:

Stock + Put - Call = Present value of the exercise price

We can rewrite this for the above corporation as:

Stock + Put - Call = Present value of the debt

This can be rewritten at maturity as:

Stock - Call = Value of debt - Put

So the Black-Scholes Option Pricing Model tells us that the value of the covered call position (left side of equation) in our hypothetical firm is equal to the debt at maturity with a put written against it (right side of equation).

This means the bondholders have, in essence, written a put against the firm.  How?  In other words, if the value of the firm is less than the debt that is due at maturity, you "put" the firm back to the bondholders and walk away losing only what you paid for the stock -- just as when you buy a call option. 

The value of this put is part of what gives your stock its value! 

If you like owning stocks for this reason, you should consider using options in some fashion.  Options allow you to do exactly what you're doing with stock -- but for a lot less money.  They can also be used to create downside hedges in exchange for upside profits.  Because of these uses, you can create better risk-reward profiles that are simply not possible with stock alone.

There are many fascinating insights that can be learned from the Black-Scholes model.  Once you have a better understanding of options, you will start to see that stockholders are option players in disguise and the Black-Scholes Model can be used to value corporate securities too.  If you acknowledge this, you may start to open your eyes to the world of options, and create new trading opportunities that you never thought possible.