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The Benefits of Buying Options

Filed Under Beginner Options Trading 

Chart
In Chapter Five, the put-call parity formula showed us that if you were absolutely certain that a stock was going to rise that you should either buy the shares with borrowed funds or buy the call and sell the put. Figure 8-4 shows why. The reason is that the long call buyer will always underperform the long stock buyer by the amount of the time premium for all regions above the strike price. Notice that above the $75 stock price, the two profit and loss curves run parallel to each other. Those two lines will never meet at any higher stock price and that’s a way of showing that the long call buyer will never get the time premium back. However, since we don’t know for sure whether a stock will rise, the call option provides a lot of protection by removing all of the downside risk that we showed in Figure 8-3. The time premium is the cost of that protection.
 
If the call buyer performs worse than the stock buyer by the amount of time premium then why would anybody buy the call option? Because it’s that same $3.84 time premium that provides the downside protection. Option traders give up a little bit of upside profit potential in exchange for greatly reducing the downside risk.
 
If you look to the left of the crossover point in Figure 8-4 you’ll see that if the stock falls below $75, the call owner will lose less than the long stock owner. With the stock below $75 at expiration, the call owner loses all intrinsic value in the option but also loses the $3.84 time premium, which means the total loss would be $75 - $3.84 = $71.16, which is exactly the crossover point that we previously calculated.
 
So protection is one of the big benefits of buying options. Call options provide protection from the downside risk of the stock. In this example, you can spend $79.46 per share today for the 200 shares of IBM and take a very big chance that the stock’s price will fall by more than the $8.30 cost of the $75 call option. Or you can spend $8.30 today for the call option and fully benefit if the shares rise or even if they fall below $71.16 at expiration.
 
How does the call option protect us from the large downside risk of a stock? Our put-call parity formula showed us that it comes from the fact that call options are really leveraged long stock plus a put option in disguise:
 
C = S – Pv (E) + put
 
If you own a call option, you are effectively borrowing money to buy stock, S – Pv (E), and then buying a put option to protect your downside. Long stock owners do not have the put option, which is why they have a much bigger downside risk.
 
Let’s see if the put-call parity formula holds true. At this time, the risk-free rate is roughly 3%, which means the effective interest rate for 230 days is .03 * (230/360) = .0192. Therefore, the present value of the exercise price is $75/1.0192 = $73.59. Using the quotes in Table 8-1 we see the $75 put is worth $2.45. Using our put-call parity formula, the value of the call must be S – Pv (E) + P, or $79.46 - $73.59 + $2.45 = $8.32, which is very close to the $8.30 quoted call price. This shows that when you pay the $8.30 price for the $75 call that the $75 put is included in that purchase.
 
This clearly demonstrates our first motivating factor for buying calls – protection from large losses. It also shows that call options with high deltas and long terms to expiration can be viewed as less risky than long stock purchases. Your maximum risk is much smaller and known up front and that is something we cannot say for stock owners.
 
 
Leverage
Leverage is our second motivating factor for buying call options. Leverage is a term borrowed from physics, which is simply defined as a mechanical advantage that allows the user to magnify a force. For example, if you need to change a car tire, you can lift a car off the ground with very little effort with a jack. The jack provides a tremendous mechanical advantage to the user making a seemingly impossible task easy enough to do with one hand.
 
In a similar way, options provide tremendous financial leverage to the user. For any given stock price movement, you can create a bigger “force” and get a bigger return from a fixed amount of money. For example, let’s revisit a comparison we made between the two investors in the last section. The stock investor buys shares of IBM at $79.46 while the option buyer pays $8.30. Now let’s assume that IBM closes at $85 at expiration. To the stock trader, that represents a return of $85/$79.46 = 1.069, which is approximately 7%. With the stock at $85 at expiration, the $75 call is worth the $10 intrinsic value. The return to the call trader is then $10/$8.30 = 1.205 = 20.5%, or roughly 21%. In other words, a 7% increase in the stock’s price led to a 21% return on the option. Just as with mechanical leverage, the option was able to take a tiny “force” of 7% and magnify it nearly three-fold.
 
Leverage is an elusive concept though. To many investors, it sounds as if the option trader performed better simply because of the higher returns. After all, it appears obvious that you would make more money with a 21% return on your money rather than only 7%. That would be true if we were investing the same dollar amounts. But if you work through the numbers, you’ll find that the dollar amounts are vastly different. In this example, we assumed the stock rose from $79.46 to $85, which is an increase of $5.54. The stock trader therefore makes a profit of 200 shares * $5.54 = $1,108. At expiration, the $75 calls are worth 200 * $10 = $2,000 and cost $1,660, which means the profit to the call buyer is only $340. If the option trade performs better in terms of percentages, why doesn’t it perform as well as the stock in terms of total dollar profit?
 
Again, this is a direct result of the $3.84 time premium in the option; that amount is never returned to you. If the option trader had this time premium returned when the option was sold then there would be an additional profit of 200 * $3.84 = $768. Notice that if we add this amount back to the $340 profit we get $768 + $340 = $1,108, which is exactly the same profit of the stock trader. We can look at this relationship another way. Assume there was no time premium in the option when it was purchased, which means it would have been trading for only the intrinsic value of $4.46 rather than $8.30. When it was sold for $10 at expiration, the net gain to the option trader would be $10 - $4.46 = $5.54, which is exactly the same dollar profit as the stock trader. This clearly shows that all intrinsic value is returned to you at expiration, which is why it is less risky to “pay” for intrinsic value. As long as the underlying stock does not move adversely then all intrinsic value remains with the option. The time value, however, is never returned to you under any circumstance.
 

In order to truly understand the leverage of an option, we must compare “dollar equivalent” exposure. For example, let’s assume the $75 call trading for $8.30 has a delta of 0.60. For the next one-dollar move, this option’s price will rise by the delta, or 60 cents, from $8.30 to $8.90. This 60-cent move is equivalent to $60 per contract. Now let’s see what a stock investor must spend to get this same $60 gain from a one-dollar move in the stock. A stock buyer must buy the delta equivalent number of shares, which is 60 shares of stock that would cost 60 * $79.46 = $4,767.60. So if an option trader buys the $75 call and a stock trader buys 60 shares of stock, then both will capture a $60 profit on the next one-dollar move in the stock. Now we just need to compare the costs of these dollar equivalent exposures. The stock trader spends $4,767.60 while the option trader spends $830, which means there is $4,767.60/$830 = 5.7 times as much leverage in the option as compared to the stock. (But keep in mind that this number will change as the delta of the option changes. We’re just saying this is how you’d need to calculate the leverage in the option at this point in time.)

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