Hedging with options

The last section showed that options allow you to bend the profit and loss profiles so you can actively select the risks you want to accept. As you learn more about options, you’ll find you can mix and match calls and puts, longs and shorts, different expirations, different quantities and so on to create truly unique strategies and opportunities.

But would you believe that is not the true power of options? The true power is realized once you understand how to hedge with options to shift your profit and loss curves in different directions as the underlying stock is moving.

This section is not intended to be a full course on hedging but rather a way to close your introductory journey into the world of options. Once you understand how options allow you to hedge, we believe that you will be in a better position to make your own decision as to whether options are risky or not.

Hedging

To get started, let’s define what we mean by hedging. The word “hedge” is borrowed from early farmers who would plant shrubs along the perimeter of their farm to create a protective barrier or fence. In the world of finance, a hedge is an investment that is taken out specifically to reduce or cancel the risk of another investment. In other words, it’s an investment that forms a protective barrier around your portfolio.

To fully appreciate what it means to hedge, let’s assume you must take the following 10-question exam and match the answers in the right hand column to the questions in the left hand column. You must get a 90% or higher grade to pass the class:

1) Call option _____	A. Exercise price
2) Put option _____	B. Right to sell
3) Strike price _____	C. At-the-money options
4) Expiration date _____	D. ∂∆/∂s
5) Long options _____	E. In-the-money options
6) OCC _____	F. Right to buy
7) Highest time value _____	G. ∂c/∂s
8) Have intrinsic value _____	H. Third Friday
9) Formula for delta ______	I. Clearing firm
10) Formula for gamma ______	J. Convey rights

You start running through the questions: Number one, call option is F, the right to buy. Number two, put option is B, right to sell. Number three, strike price is A, exercise price and on down the list you go.

You easily move through the first eight questions apparently on your way to acing the test with a score of 100%. That is until you come to questions nine and ten: The formulas for delta and gamma? What is that?

You know they must correspond to answers D and G but have no idea which is correct so now you have a little dilemma. Either question nine is D and question ten is G or vice versa. If you guess correctly, you will score 100 on the quiz and get an A. But if you guess incorrectly, you will score an 80 and fail the class. Because you’re uncertain as to the answer, there is a 50-50 chance of either outcome. So now you’re thinking how unfortunate it is that passing the class has come down to a guessing game – effectively the toss of a coin. Is there anything you can do to improve your outcome? What would you do?

The correct answer is to hedge your bet and guess “D” for both questions nine and ten (or “G” for both). (For those who are curious, the correct answers for 9 and 10 are G and D respectively.) Doing so assures you that you will receive the necessary 90% and a passing grade. Notice what the hedge did for you. By sacrificing the 100%, you guaranteed the necessary 90%. If your goal is to pass the class then what difference is a 90% or a 100%? There is no difference. Yet many students lose sight of the true goal of passing the class and try to reach for the 100% grade.

There is no benefit in getting a 100% but there are big negative consequences for not getting 90%. It only seems rational that you should hedge yourself and sacrifice the 100% in exchange for the guaranteed 90%. Rather than take the 50-50 chance of passing, you have effectively bet against yourself – a hedge – and created guaranteed success.

If you can understand that analogy then you understand what it means to hedge your financial portfolios. All of you have some type of goal, whether it is to increase your account by so much per year, generate monthly income of a certain amount, or to have a certain amount at a future point in time, for examples. Whatever your goal happens to be, don’t lose site of it. Those who lost site that the goal was to pass the class (90% grade) on the exam may have ended up in failure by guessing at the correct answer. Guessing is no way to pass an exam. Investors who lose site of their goals and do not hedge their bets may end up missing their goals or even in bankruptcy by trying to reach for maximum profits. Guessing what will happen in the market is no way to accomplish your financial goals.

Betting Against Yourself

Any hedge, whether with investing, betting, insurance – or taking exams – serves the same purpose. Hedging means we give up some upside potential in exchange for less damage to the downside. For our exam, we gave up the chance of a 100% score in exchange for not getting 80% – we have hedged the score. With investing, hedging means we will give up some upside profits in exchange for removing some downside risk. In other words, a hedged portfolio means we bet against ourselves much like the exam. If we are bullish on the market, we may add a few bearish investments to hedge our bets.

Hedging is not a new concept for most fields but seems to be an elusive concept for many when it comes to finance. Here’s another simple example of the power of hedging. Does your office have a football pool? You can even hedge to give yourself an edge there too.

To make the example easy, assume there is only one game being played, which we’ll say is between the Tampa Bay Buccaneers and the Atlanta Falcons. It costs $5 to play. You have a small office and the only person willing to play so far is Sam, who has bet $5 on Tampa Bay. The sign-up sheet has made it to your office and you have a decision to make. You can either bet on Tampa or Atlanta. If you also bet on Tampa and they win there will be $10 in the pot, which will be split between Sam and you leaving you each with $5.

However, since you each put $5 in the pot, there’s no way you’ll make money from that bet. What happens if you bet on Atlanta? If Atlanta wins, you’ll win the entire $10 as Sam’s $5 will go to you. But if Tampa wins, your money will go to Sam and he’ll take the $10 pot. So if you bet on Atlanta, you’re faced with a 50-50 shot of winning (assuming the teams are equally matched). You’ll either double your money or lose it all. If you take the opposite side of Sam’s bet every week, you’ll end up breaking even in the long run, which doesn’t sound very appealing either.

Most people would see these two alternatives (either betting on Tampa or Atlanta) as their only choice. But there is a third choice you can do. You can hedge your bet by betting against yourself. Although it doesn’t sound like a way to make money, hedging is your best long-run alternative. Instead of betting on one team or the other, you simply put $10 in the pot and bet on both teams – you bet $5 on Tampa and $5 on Atlanta.

If Tampa wins, then you and Sam each hold a winning ticket and will split the $15 pot and each get $7.50 – you’ll lose $2.50 overall. If Atlanta wins, you’ll have the only winning ticket and keep the entire $15 pot thus making $5 overall. So half the time you’ll lose $2.50 and half the time you’ll win $5.

Mathematically, what can you expect to happen from this arrangement over the long run? We can find the answer by multiplying the probability of each outcome (50%, or 0.50) by the payoff:

0.5 * (-$2.50) = -$1.25
0.5 * (+5.00) = +$2.50
Expected value = +$1.25

By hedging your bet, you’ve changed your long-run average from zero to +$1.25. This means that you will make, on average, $1.25 per game in the long run (assuming you and Sam are the only ones betting and that Sam doesn’t catch on to your hedging scheme). Think about how powerful that is. If you bet on the same team as Sam, you’ll end up with nothing. If you bet against Sam, you may win some money in the short run, but over the long haul, you’ll end up with nothing. However, if you hedge your bet and bet against yourself, you can swing the odds in your favor. Strange, huh? Hedging is powerful because it works.

In this example, you put up 2/3 of the money pool in exchange for guaranteeing a winning ticket. You’ll either lose 25% of your money or gain 50% on your money, thus giving you a long run average gain of 12.5%. The more elaborate the football pool and the more people who bet, the harder it becomes to hedge.

For example, you may have to pick the winning team from among ten games that week. However, the idea is still the same. You’d just have to find the total number of combinations that could be made then find out which of those have been made. It’s not too hard from there to determine which combinations will hedge your bet.

Hedging is the key to making consistent money in the markets. But in order to further understand the importance of hedging, we need to find out what kind of risk takers we are.

What Kind of Risk Takers Are We?

Every day we’re faced with making decisions about risk. You may not realize that you do, but subconscious calculations are always taking place regarding which risks to take and which to avoid. Walking across the street is, technically, risking your life to get to the other side.

On one hand, you may think that sounds farfetched, but it is the worst thing that could happen from crossing the street. However, despite the risk, we walk across streets countless times because, intuitively, we know the probability of that worst-case scenario is very, very low. It’s an acceptable risk, so we choose to take it. Depending on the situation, people tend to avoid risk, accept risk, and in some cases, even seek to take risk.

Psychologists have created three general categories to classify these risks:

1) Risk-averse (those who avoid risk)
2) Risk-neutral (those who accept reasonable risks)
3) Risk-seeking (those who accept high-risk situations)

You are risk-averse if you buy insurance and you are a risk-seeker if you skydive. You are probably risk-neutral about crossing the street. In most cases, people have different attitudes toward risk and it’s not easy to say if they are risk-averse, risk-neutral, or risk-seeking for a particular event. That is, until it comes to money. When it comes to money, people become very predictable and display a consistent view of risk. It is this view of risk that causes many mistakes in trading. Do you fall into the same category as most people? Here’s how to find out: An eccentric millionaire asks you to choose between the following two choices. You only get to play the game once. Which would you choose?

A) $500 gain for sure
B) Flip a coin and get $1,000 if heads and nothing if tails

Both choices are similar in the sense they have the same long run average. In mathematical terms, they have the same expected payoff, or expected value, which is nothing more than a mathematical long-run average. If you were allowed to play this game thousands of times, you would expect to be up $500 per try regardless of which alternative you choose. Obviously, Choice A always yields $500 with each try. Choice B, on the other hand, yields $1,000 half the time and nothing half the time so, in the long run, you'd be up $500 per try. So even though both choices provide the same expected values over the long run, Choice B involves risk.

A risk-averse person will only take Choice A while risk-seekers will choose Choice B. A risk-neutral person would be indifferent between the two choices.

We Really Despise Risk

Dr. Robert Anthony said, “Most people would rather be certain they’re miserable, than risk being happy.” Sadly enough, most of the research in the field of behavioral finance shows this to be true. In fact, in 1979, two famous psychology researchers, Daniel Khaneman and Amos Tversky, published an influential paper in The American Psychologist showing our risk-averse natures – and with a remarkable twist. In that study, the researchers gave subjects a choice between the following two alternatives that we saw earlier:

A) $500 gain for sure
B) Flip a coin and get $1,000 if heads and nothing if tails

Most people picked Choice A without hesitation. This was no surprise to the researchers as they were aware of our risk-averse tendencies. However, the researchers added an interesting twist and asked the following intriguing question:

C) Take a $500 loss for sure
D) Flip a coin and lose $1,000 if heads and nothing if tails

By similar reasoning with the first set of choices, the second set encompasses an average loss of $500 regardless of which you choose. The difference here is that Choice C results in a guaranteed loss. Choice Dmay be a $1,000 loss, but it could also result in no loss, both with equal probability. The two researchers expected that if subjects displayed a risk avoidance behavior as with the first set of questions, they should still avoid risk and accept a $500 loss for sure.

But oddly enough, the researchers found that most subjects selected Choice D – they accepted the gamble to try and avoid the loss! This means that investors’ aversion to loss overcomes their aversion to risk. The paradox is that we detest risk so much that we’re willing to take risk to avoid it.

This is a fascinating observation about human nature that demonstrates why it’s so important to hedge trades. If a trade is moving against us, it’s our nature to try to gamble our way out. It goes against our makeup to take the for-sure loss. Likewise, when we have winning trades, it goes against our nature to hang on – we’re too afraid of losing the gains we already have. Hedging your positions prevents both of these behaviors and allows you to capture bigger profits.

How many times have you heard “you can’t beat the professionals” or “the market makers always win” or other similar phrases? The reason they are basically true is that professionals know how to hedge. Retail investors end up taking the risky side of the bet and are in trades too soon and out too early. They rely too much on timing and direction and end up losing. Add to this our risk aversion and willingness to gamble our way out of losing situations and you have the very reason so many investors and traders miss their goals with investing.

Hedging is a powerful tool and the key to financial success. Options were designed to hedge. It’s now time to discover the option secrets used by professional traders.

Stock Swap

Of all the hedging techniques, this is the probably the simplest and most useful for most traders so it is a great place to start. Unfortunately, it’s also the least used. Anybody who trades stocks needs to understand this strategy.

Let’s use eBay as an example. Between October and December 2002, eBay made a phenomenal run from around $50 to $70, which is shown by the area between the red arrows in Figure 10:

Figure 10

Assume you purchased this stock during the uptrend at $55; it would certainly be tempting to take the profit at $70. After all, eBay made a substantial move and it’s sensible to think it will pull back. But if you accept the fact that you’re probably not at the very top, the more prudent move is to stay in the trade but protect the existing unrealized profits. We can do that by utilizing a stock swap strategy. It’s very simple and here’s what you do:Sell all your shares and buy an equivalent share amount of call options. In effect, you are “swapping” your stock for calls.

Incidentally, these two trades, selling your stock and buying calls, can be executed simultaneously through most brokers. Let’s assume you originally purchased 300 shares of eBay at $55 and it’s now $70. That means you have an unrealized profit of $15, or $4,500. To execute the stock swap, you’d sell your 300 shares and simultaneously buy three calls. If our goal is to get a lot of cash off the table, we would probably consider buying the at-the-money $70 call. The actual quote for an eBay January $70 call at that time was $2.75.

Selling your shares will bring in $21,000 (300 shares * $70) cash and buying 3 $70 calls costs $825 (3 contracts * 100 * $2.75), which means you get a net credit of $20,175 cash to your account. The shares originally cost $16,500 ($300 * $55) so you’ve now locked in a profit of $20,175 - $16,500 = $3,675, or 22%. But not only did you lock in a profit, you are still effectively long 300 shares of stock. Any increase in eBay only increases your profit, and there is no risk of losing your original principal; it’s sitting safely in the money market. Figure 11 shows graphically the effect of our hedge:

Figure 11

The straight red line represents the original long stock position at $55. The blue hockey stick shaped line is our new long $70 call including the net credit we received from selling the stock. Effectively then, we own 300 shares of stock at a cost better than free; we cannot lose and we may make more.

Notice that the trade eliminates the downside risk at the expense of reducing the upside potential, which fits our definition of hedging. For instance, prior to the roll-up, you were exposed to the risk of the stock price falling below your $55 purchase price.

However, after the roll-up, the worst that can happen is that you make $3,675, which is shown by the solid blue arrow in Figure 12. No matter how low the stock’s price may fall, the blue profit and loss curve flattens out at $3,675:

Figure 12

At the same time, the blue profit and loss line runs parallel for all increasing stock prices above the $70 strike price as circled in Figure 12. However, notice that the blue line lies below the red line in this region, which means you’re not going to be as profitable as if you had just held the shares.  

In other words, for all stock prices in this range, we would be better off holding the stock as its profit and loss curve sits higher on the chart. The reason is simple: You must pay a time premium for the option and that reduces your profitability when compared to the original long stock position. But it’s not the fear of lost opportunity that drives us to get out early; it’s the fear of loss and the stock swap hedge removes all that fear. Now we’ve changed our perception of the trade and made it less risky. We can now stay in for much longer than we normally would and possibly catch a huge homerun trade.

Notice, too, that the hedge does not rely on timing. With the stock at $70, we are probably not at the very top of a peak. It’s much more likely that we didn’t sell the shares at the highest point. However, our risk-averse nature prods us to take the sure $15 profit and run. Rather than take the $4,500 gain, we hedged the position and captured a sure gain of $3,675. We now can stay in the position without fear and try for some real money.

Even if we are correct in our outlook and the stock continues higher, we are not done with our hedging. As the stock price climbs higher, we will use a similar trade called a roll up, which has the same effect of continually taking profits while maintaining exposure in the stock. Let’s take a look at the mechanics of a roll up.

The Roll-Up

The roll-up is philosophically the same as the stock swap. But rather than selling stock and buying call options, we are selling calls and buying calls. What does this do? If you recall from our earlier section on pricing principles, Principle #1 stated that lower strike calls must be more expensive. As the stock rises, you simply sell the call you own and simultaneously buy a higher strike call which must produce a net credit.

The reason is that the call you are selling (lower strike) must be worth more than the call you are buying (higher strike). Therefore, if you are selling the more valuable call and buying the less valuable call then you must end up with a credit from the trade.

Each roll-up generates more cash to your account and shifts the profit and loss curve higher. For example, assume that eBay moves from $70 to $75 and we roll the position up for a net credit of $3.50. While this is a hypothetical credit, it is very close to what you would see under these conditions and we talk about why this must occur in the Alpha Trader Certificate Course.

If you roll up for a net credit of $3.50 on 300 contracts, that will generate an additional 300 * $3.50 = $1,050 to your account. You had locked in $3,675 from the first roll to the $70 call and have now locked in another $1,025 from the second roll to the $75 call for a total guaranteed profit of $3,675 + $1,050 = $4,725. However, because you are still effectively long 300 shares (long 3 $75 calls) you will continue to profit if the stock price should continue to climb. The profit and loss graph will shift from the blue line to the green line as shown in Figure 13:

Figure 13: Effect of Rolling from $70 Call to $75 Call

Notice that the effect of the hedge is very similar as it is for the stock swap. In this case though, rather than eliminating all of the downside risk of the stock, you’re just increasing the amount you are preserving as shown by Arrow A.

The tradeoff is that the green line has been shifted to the right as shown by Arrow B. Again, this is due to the additional time premium you had to pay to acquire the $75 strike. For all stock prices above the $75 strike, the previous profit and loss curve would have performed better. But notice the relatively small space lost by the shift at Arrow B compared to the relatively large space gained by Arrow A. It is a small sacrifice of upside potential in exchange for a much higher guaranteed return. You have hedged your investment and it was done without losing control of the 300 shares.

What if you were more concerned about protecting profits? We could use other hedging strategies as well. For instance, when you rolled up to the $75 call, you could also sell the $80 call, which would make you long the $75 call and short the $80 call. This is a strategy called the vertical spread, and covered in detail in the Alpha Trader Certificate Course. For now, just understand that you can be long and short options at the same time.

Assume that you could sell the $80 call for $1. Selling three of these calls would generate an additional 300 * $1 = $300 profit but it would also limit your upside potential. If you rolled up to three of the $75 calls and sold three of the $80 calls then the profit and loss curve in Figure 13 would look like the one in Figure 14:

Figure 14: Effect of Rolling Up to Three $75 Calls and Selling Three $80 Calls

Figure 14 shows that you have increased your guaranteed return by another $300 at the expense of limiting your profits for all stock prices above $80. If you don’t think the stock price will rise above $80, why not sell that part of the range to someone else in the market? Try doing that with stock.

If the idea of completely capping your upside potential is unappealing, then you can hedge that bet, too, and roll up to three of the $75 calls but perhaps sell only two of the $80 calls. Your profit and loss curve would then look like Figure 15:

Figure 15: Effect of Rolling Up to Three $75 Calls and Selling Two $80 Calls

The blue line has shifted higher by $200 from the sale of the two $80 calls at $1 each. Because you control 300 shares and have sold off 200 shares, you are still net long 100 shares for all stock prices above $80 and that’s why the new green profit and loss curve doesn’t flatten out like it did in Figure 15. The possibilities are endless once you understand the fundamentals of options.

Figure 16 shows why hedging is usually the best choice. Trends usually last longer than most people expect and eBay was no exception. The red arrow shows the point where we were originally considered selling the stock. But the stock swap and subsequent roll-ups allowed us to capture a guaranteed profit and hold on through August to the price of $110 (eBay had a 2:1 split at this time, so Figure 16 only shows a $55 price):

Figure 16

No matter where you may decide to completely exit this trade, you are better off than if you sold the stock at $70. The stock swap and roll-up hedges allowed us to capture a profit of over $10,000 with no downside risk of principle. The cash from the stock swap and roll-ups was always sitting safely in money market.

Laddering Hedging Strategy

Hedging is so versatile that we can even create hedges where we get our money back and actually increase the amount of reward. Using the above example, when you originally sold the 300 shares of stock, you could have swapped it for a higher number of contracts, such as four $70 calls instead of three.

This still produces a guaranteed return to your account (although lower) but now adds some leverage if the stock should continue its bullish trend. When the stock hits $75, you could add more leverage and roll up from four $70 calls to say, five $75 calls.

When you swap or roll up to a higher number of calls (or down for puts), that’s called a laddering strategy, which implies that you’re changing the risk at each rung or step of the roll-up process. Each roll-up is still done for a net credit but just not as big of a credit. The tradeoff is that you are increasing the effective number of shares you own without any fear of losing your original principal.

There is no set amount or percentage that needs to be applied. As long as you are rolling up to a higher quantity of long positions, it’s a laddering strategy. Each choice presents a different set of risks and rewards, and it’s entirely up to you which is best.

Selling Spreads Against Stock

We mentioned previously that you can simultaneously be long and short an option at the same time, which is a strategy called a vertical spread. For example, if you buy a $55 call and sell a $60 call (same expiration) that is a $55/$60 vertical spread.

This strategy gives you the right to buy shares for $55 and the possible obligation to sell them for $60, which means the most you could ever make on the position is the $5 difference in strikes.

As with all option strategies, they can be applied in unimaginable ways and the vertical spread is a perfect example. How many people would think of selling spreads against a long stock position? And what do you suppose it would do to the shares of stock you own?

Case Study

He felt the stock was going to trend sideways for some time and may even fall substantially. He was obviously afraid of losses but didn’t want to pay for the put. Is there an option strategy we can develop that will profit from a sideways stock price and protect the downside risk? Table 10 shows the actual option quotes at the time:

Table 10: Wal-Mart Option Quotes

	Calls		Puts
	Bid	Ask	Bid	Ask
Aug $50	7.30	7.40	0.50	0.55
Aug $55	3.20	3.30	1.45	1.55
Aug $60	0.80	0.85	4.00	4.10

We purchased five puts to protect the downside risk he feared. In order to generate enough cash to pay for the put and provide a return in the event the stock price moved sideways we sold 10 – twice as many – $55/$60 vertical call spreads:

Buy 5 $50 puts at 0.55 = -$275
Sell 10 $55 calls at $3.20 = +$3,200
Buy 10 $60 calls at 0.85 = - $850
Net credit  = +$2,075

Figure 17 shows the effect of the previous three transactions against the long stock:

Figure 17

The long puts have completely protected the downside risk, and the sale of the vertical call spreads generated enough of a credit to shift the entire profit and loss curve above zero and create substantial profits if the stock price stays still as projected. As a bonus, the investor still maintains all of the upside potential. We must remember that these benefits did not come for free. If we overlay the original stock position, we can see the tradeoffs clearly in Figure 18:

Figure 18

Figure 18 shows that the investor hedged all of the downside risk and will profit nicely if the stock price stays still, which is exactly in line with his outlook. He accomplished this at the expense of giving up some (not all) of the upside potential. He has sacrificed the very best profit potential in exchange for a guaranteed return on his money and still has the opportunity to earn more money if the stock price rises.

The best news is that similar vertical spreads can be sold month after month, which allows the investor to continually shift the profit and loss curve higher, protect his downside, and still have the potential for unlimited gains.

What would happen if the investor sold 20 spreads instead of 10? Figure 19 shows the effect of buying the five puts but selling 20 $55/$60 vertical call spreads:

Figure 19

This type of a strategy can be used if the investor is far more bearish on the stock and willing to give up much more upside in exchange for more profit to the downside. What if the investor wanted to actually profit from a fall in the stock’s price? He can do that, too, by purchasing 10 puts rather than five. Figure 20 shows the effect of buying 10 puts and selling 10 $55/$60 vertical call spreads:

Figure 20

The purchase of 10 puts actually allows the investor to profit to the downside at the expense of profit at the center and to the upside. The possibilities are endless for those who take time to explore the world of options.

As stated at the beginning, this section is not designed to be a full course on hedging techniques as an entire book could be written on that subject. Instead, we wanted to introduce you to advantages that options provide by allowing you to buy and sell risk. For those who take the Alpha Trader Certificate Course, you will find that many other strategies will be self-evident if you understand the fundamental concepts presented in that course.

In order to succeed in the financial markets, you must invest relatively large dollar amounts and let the profits run. However, we also know that our risk-averse natures won’t allow that to happen. We feel much more comfortable placing small bets and being assured that it is the most we can lose – even if it means we will most likely lose it. By trying to avoid risk, most investors and traders actually place their money in maximum jeopardy.

All hope is not lost. In order to reach for bigger profits, you must remove the fear of loss. You must hedge your bets and bet against yourself. And the only way to do that is with options, since they are the only asset that allows you to buy and sell risk. Once you’ve locked yourself into a guaranteed winning position, hang on. Remember that trends last longer than we expect. Keep the position alive but continue to take profits and cover risk by additional hedges. Options remove fear. Use them conservatively to make money.

Edgar Watson Howe, a famous American writer, once said, “A good scare is worth more to a man than good advice.” If you learn to hedge your trades, you’ll never have to go through a good scare, and that is the best advice that we can give.