#### options strategy

Knowledge of probability and statistics will allow traders to greatly increase profit possibilities while limiting risk. But knowledge of math is not required to enhance one’s trading.

Recognizing chart formations acts like recognizing opportunities. Both opportunities to profit, but also opportunity to avoid bloodbaths. Stock and option traders can either participate in major moves to their benefit or detriment. Numerous common technical patterns exist that can be employed to identify favorable entry and/or exit points.

Trend lines, support and resistance are required for any technical assessment. But these may be considered as just building blocks for more complex patterns. One of the simplest of these complex chart formations is known as a “Head-and-Shoulders.”

Made famous by Charles Dow, this major reversal pattern was and has appeared in every major market top or bottom in the last fifty years. This formation is a precursor to both market rallies and major corrections. It is accurately described as a “Head-and-Shoulders” top or bottom.

“Head-and-Shoulders Tops” look just like their name implies a “Head” (highest high) flanked by “Shoulders” (lower highs). Separating the head from either shoulder is the neckline. Made up of lows of similar time and price formation the “necks” do not have to be identical, but the closer to being a mirror version of each other, the higher the probability for a trend change in the other direction.

Double tops are widely considered as points of great resistance. Think of a “Head-and-Shoulders Top” as a triple top with the center top having a higher high. Add to that the fact that the neckline adds a point of support that if broken often foretells a stocks rapid decent.

As with any pattern, there can be a number of small variations. For example, there may be two or more left shoulders near the same price range, or two or more right shoulders. In any case, the most important component of the formation is the neckline. When it is broken, the pattern is complete and a significant change in character often follows. The following drop is often the most precipitous of the entire formation and occasionally will eclipse the height of the pattern (the top of the Head to the Neckline). As the new character evolves, successive rallies commonly fail at lower highs until the overall decline is far greater than the magnitude of the initial formation.

For the next paragraph either stand on your head or hold your monitor upside-down.

Once a trader learns “Head-and-Shoulders Tops,” they should have an easier time understanding “Head-and-Shoulders Bottoms.” Basically, bottoms are tops upside-down. That is, the shoulders are higher than the head and the necks are short-term highs not lows. “Head-and-Shoulders Bottoms” signal trend reversals with high probabilities of upward price appreciation, bullish reversals instead of bearish reversals.

It’s obvious you should never overlook the potential of a clearly formed and definitely broken trend. The historical traits of well know patterns demonstrate the ease in profiting from their analysis. But the difficulty may come from seeing the second shoulder before the opportunity has been diminished. Experience will help traders see them as they’re formed.

The Beauty of understanding chart patterns surrounds the fact traders can study them without risking their accounts by looking at existing charts. Study as many as possible. I hope that my examples have helped. I hope this article has also helped.

Some stocks went up. (Hopefully yours.) Some stocks traded lower. Some stock prices stayed the same. (A few flat lined dead on arrival, many roller coasted up and down back to the starting point.)

I was just recently in Las Vegas, for business of course. I enjoy going by the gaming tables. Market research, crowd psychology. Seeing how people bet their cash. Well chips anyway, if bettors had to use real money, they might recognize how much money they just lost.

Ever watch people learning to play craps? They’ll use real money. Haven’t they heard of paper trading? Maybe because the pit boss and the other casino employees are always willing to help. Lots of assistance available to make a bet. No matter what color the chips.

Gambling and specifically craps have much in common with options: complex risk reward curves. Since the IRS doesn’t allow deducting crap table loses from your income taxes, why would anyone want to throw dice. They can bet options, I mean trade options.

Many amateur options traders invest as if they were at a casino. No regards for the odds, just mesmerized by the big potential payoff.

Anyone who has been around Wall Street any length of time knows there isn’t many “sure things.” Truly, time’s passing is the only safe bet.

In this example we will trade based on Theta alone. We will consider the other “Greeks” asleep. In reality, they are NOT dormant. The fact is, you could set your trades up to minimize their effects. Remember it’s best not to awaken a sleeping giant if at all possible.

Our hypothetical example will be four At the Money (ATM) options on a single stock:

One month option = $ 1.00

Two month option = $ 1.41

Three month option = $ 1.73

Four month option = $ 2.00

With these hypothetical examples, let’s enter a simple time or **calendar spread**. We will buy the four month option for $ 2.00 while simultaneously selling the one month option for $ 1.00. Our net cost would be $ 1.00 ($ 2.00 less $ 1.00). Again for demonstration purposes we will not take commissions nor the bid/ask spread into consideration. And also ignore strike prices as well.

If everything remained the same except for time’s passage, after one month the option we sold (short position) would be worthless to the buyer. An At the Money (ATM) option has no value at expiration. A $ 1.00 profit to us, offset by the $ .27 loss on our four month turned three month option, brings our position value to $ 1.73.

Anyone who can find situations where all the variables remain constant for one month deserves to make 73% on their money.

In our perfect example situation, we could now sell another one month option for another Dollar. After the second month, the option we originally bought would have lost half its time, but only $ .59 of its value. Now priced at $ 1.41, the income would be equal to its original cost, $ 2.00. Our cost would be zero. Our profits infinite.

Closer to expiration, owning options costs more. Inversely, selling options closer to expiration can pay more.

If the one month ATM option is $ 1.00, and the four month equals $ 2.00, then the nine month option would be priced at $ 3.00. Continuing forward, the 16 month option’s price would be $ 4.00 and $ 5.00 would buy the 25 month option.

If we could sell one month of time for $ 1.00, we could pay for the 16 month option in four months. Giving us a year of potential for free.

Please don’t base trades on any one option pricing component, while ignoring the others. You’ve been given enough information to be dangerous. If you trade with blinders on, you tend to get blind sided.

Knowledgeable traders earn the right to have less money at risk and greater potential for profits. Knowledge comes with experience, and experience comes with time, regardless of real chips or paper trades.

The Big IF

The biggest battles of the Cold War were often fought during the Olympics. No matter what flag you saluted, it was US verses that “Evil Empire.” I don’t know about you, but I always felt the other country’s athletes used performance enhancing drugs. Not to mention their judge’s scores reflected definite political bias. Biased scoring could award a gold medal to a silver or bronze performance.

You’ve seen the kids who score and rank everything and anything. Holding up a card that is either a 6 or a 9, depending on which end is up. “Solid nines, but a six from the Russian Judge.” Simultaneously in Russia kids are jokingly scoring, “A six from the American Judge.” It’s all perspective.

Option pricing has its own “Russian Judge,” volatility. If you don’t understand volatility’s role in option pricing, your gold medal trades might not make it to the platform.

Option prices are based on a number of components; time, interest rates, dividends, price (stock & strike) and potential. Potential, also known as volatility, is the most subjective. Hence the ability to be the kink in our attempt for the gold.

Time is constant with all options. Three days from now or three weeks from now is the same, no matter if you are trading Amazon.Com or AOL.

Interest rates may change up or down, but it’s the same rate for every stock.

Dividends will vary stock by stock. General Electric’s dividend has nothing to do with General Motors. So dividends are figured on a stock by stock basis. The dividends will be the same no matter what strike price, no matter if it’s Puts or Calls, no matter if you’re buying or selling.

Options are priced as a snapshot in time. The math between price and strike prices at a given point in time is easily figured.

The simplicity of option pricing ends here. (As if you thought it was simple so far.)

**Volatility** is the **MOST IMPORTANT** component in option pricing. Simultaneously, it may be the **MOST DIFFICULT** to understand.

Mathematically speaking, volatility is the annualized standard deviation of daily returns. Translated, it measures the stock’s price fluctuation. The more the stock moves the higher the volatility.

Volatility scores potential movement of the underlying stock. The “Greek” symbol Vega measures volatility. Proving the point volatility is complex, Vega isn’t actually a Greek letter.

With me so far? It gets worse. Concerning option pricing, there are four types of volatility; Historical, Future, Expected, and Implied.

**Historical Volatility**

Simply stated, how much the price of a stock has moved in the past.

Without going deep into math, let me explain the concept. If you have two $ 50 stocks, the price is currently the same, but historical volatility may differ.

If one stock’s 52 week high/low is $ 40/60, while the other’s is $ 45/55, it is easy to see which stock trading range is greater. The more a stock’s price moves, the higher historical volatility.

If you have two $ 50 stocks with equal 52 week high/lows, their historical volatility may still be different. If one had a daily trading range of $ 5, its historical volatility would be higher than a stock with a daily trading range of $ 2. (Daily trading range equals the difference between the high and low during a one day period.)

Easily verified, historical volatility measures the actual prior price movement.

**Future Volatility**

An almost useless concept. Future volatility is historical volatility before it happens. Price movement before it moves. After it moves, it’s not in the future, it’s not in the present, it’s in the past. Confirmed after it happens. Future volatility is accurately measured in the future looking backwards, after it became fact. Of the four, it is the least important Volatility.

**Expected Volatility**

Expected volatility deals with the future. Generally based on prior price movements, it assumes the stock will move in a certain pattern. Not the what it’s moved, not the what it will move, but the what it should move.

Fairly valued options are calculated according to expected volatility. However, not all options are fairly valued. Some options are undervalued and many more are overvalued. As with anything, buy low sell high.

Certainly more important than future volatility, arguably more important than historic volatility, but definitely less important than implied volatility.

Volatility prices options, but as you will see option pricing determines volatility.

**Implied Volatility**

The Big IF, the “Russian Judge,” the other side of the coin, the pick pocket of option pricing. Call it what you want. Implied volatility costs option traders more money than anything else.

Understanding Implied volatility and Vega allows traders to win more often, but more important to potentially lose less often.

Next we will discuss implied volatility and its ramifications in greater detail.

**Time Passes**

Beginning traders go broke taking big losses. Novice traders fall victim to attrition through multiple small losses. Advance traders falter taking small profits. Where are you on the evolutionary chain of traders?

The ability to pick market direction reigns as the most important factor for success for all option traders. Understanding option pricing helps traders magnify gains, and avoid losses.

Many new option traders dig themselves such a deep hole they can’t climb out. At least, can’t climb out fast enough. Stock prices go up, they go down, they may end up where they started, but time always passes. Sometimes, there just isn’t enough time.

Have you heard the joke, “Convicts are the number one buyers of options, nothing makes time fly like owning an option.” If you break a Law of option pricing, you don’t go to the jail house, you go to the poor house!

What does all this mean?

An option’s rate of erosion shouldn’t surprise or scare anyone. Option buyers can calculate time’s expense before buying. This is done with the Greek called **Theta**. Option sellers can predetermine maximum returns. Traders can know the cost of carrying option positions, both long and short. Hedged position traders can profit from the continual and constant passage of time.

**Time’s Effect on Option Pricing:**

Time value and time decay ranks as one of the easiest components of option pricing to understand. The time value of an option includes everything but the intrinsic value. Time costs money! More time, more money. Less time, less money. It’s that simple.

But options can’t be simple, they have to have some complexity. Time passes rhythmically with the tick of a clock, but time value erodes at a different tempo. Time value decays at its square root.

The square of a number is the product of a number multiplied by itself. 1 x 1 = 1, 2 x 2 = 4, 3 x 3 = 9, etc. The square root is the other side of the equation. It’s the equal divisor. The square root of 1 is 1, the square root of 4 is 2, the square root of 9 is 3, etc.

The Laws of option pricing dictate time value is highest for the At the Money (ATM) option. Not sometime or most of the time but always. Time value drops as the strike prices move In and/or Out of the Money (ITM, OTM). Strike prices Deep In and/or Out of the Money (DITM, DOTM) have the lowest time value. Not sometime or most of the time but always.

To better understand time value and its rate of decay, one should think in price units and time units. Price units include dollars and cents; In the case of options, dollars and fractions of dollars. Time units can be days, weeks or months. You can even use hours, minutes or seconds. We won’t discuss an option’s blink of an eye decay rate, but we could mathematically figure it out.

A Hypothetical Example of At the Money (ATM) Call options, (All other option pricing components being constant):

One Time Period = The Square Root of One Price Unit

Two Time Periods = The Square Root of Two Price Units

Three Time Periods = The Square Root of Three Price Units

Four Time Periods = The Square Root of Four Price Units

Insert the time period of your choice, months, weeks, days. Insert the price unit of your choice dollars or fractions of dollars. For our example, lets make it months and dollars.

1 Month = $ 1.00 (Square Root of 1 = 1)

2 Months = $ 1.41 (Square Root of 2 = 1.41)

3 Months = $ 1.73 (Square Root of 3 = 1.73)

4 Months = $ 2.00 (Square Root of 4 = 2)

We could extrapolate, the nine month option would cost only $ 3.00 (Square Root of 9 = 3), the 16 month option’s price would be $ 4.00 (Square Root of 16 = 4).

We could replace months with weeks and dollars with fractions, such as 1/2. Therefore if the one week option were priced at $ .50, the four week option should be $ 1.00, the 16 week option would be $ 2.00.

If we assume four weeks per month, the consistency of the pricing of time becomes evident. We can see the one month option and the four week option are both priced at $ 1.00. $ 2.00 buys the four month option and/or the16 week option. Continuing the math, the 16 month/64 week (LEAP) option would be priced at $ 4.00.

Both equations provide an equal answer:

16 Time Periods = The Square Root of 16 Price Units.

16 Months = The Square Root of 16 Dollars.

16 Months = 4 Dollars.

64 Time Periods = The Square Root of 64 Price Units.

64 Weeks = The Square Root of 64 ½ Dollars.

64 weeks = 8 x .50. = 4 Dollars.

Stock prices go up, they go down, they may end up where they started, but time always passes. The passage of time can be a profitable journey.

Introducing: **Delta**

Options are complex! Their value being determined by a long mathematical equation, with many sub-equations and variables. I can’t write the formulas out for you. Not because they’re secret, but because my keypad doesn’t contain the crazy looking symbols used in the formulas.

Each aspect of option pricing is a separate component of the formula. To remove confusion, each component has a Greek title; Delta, Gamma, Theta, Vega, and Rho. Do you wonder? Should that last sentence read, “To ADD confusion?” Everyone knows Vega is not Greek. It’s a Chevrolet.

The first and most important of the “Greeks” is **Delta**. It is probably one of the most common known of the “Greeks,” but it can be looked at three ways. Two of which are widely accepted. The third is far less important and really only theoretical. Most quasi-knowledgeable traders only know one or two.

The first and most important way to look at Delta: Delta measures the rate of change in an option’s price compared to a one point ($1) movement in the underlying security.

Since the rate of change in the price of a stock is measured dollar for dollar, their movement is 100%. Stocks have a Delta of 1.00. Don’t worry; stock prices do not have any other “Greeks,” only Delta.

Option prices, which don’t move the same dollar for dollar as stock prices, have lower Deltas. Think of it as a percentage of the movement of the stock price. If a stock goes up $1 and an option on that stock went up 1/2, it had a Delta of .50.

Many times Deltas are not mentioned with decimals but as whole numbers. Since options trade 100 shares of stock per contract, the decimals are dropped. Example: .50 x 100 = 50.

Deltas can never be over 1.00 (one hundred). If you ever see an option move greater than the underlying, it was caused by another of the “Greeks.” In our examples, we will assume everything else remains constant. In reality, the other “Greek” forces are at work, but for explanation sake, they will remain silent.

The at the money (ATM) Call will typically have a delta of .50. In the money (ITM) will have a higher delta. The Delta is still higher on deep in the money (DITM). The opposite is true for out of the money (OTM) and deep out of the money (DOTM) options, their Deltas are lower.

An understanding of Delta helps option traders choose strike prices. To be profitable with small price movements, you will need to buy ATM or maybe even ITM options. The difference between the Bid/Ask spread may be too great to overcome with OTM options.

The parameters of our hypothetical example: $30 stock, $25 Call price $6 Delta .75, $30 Call price $2 Delta .50, $35 Call price $1 Delta .25. If the stock price increases $1 to $31, the $25 Call would increase .75 to $6.75. The $30 Call would rise to $2.50, the $35 Call would increase to $1.25.

Let’s say the Bid/Ask spread on the $35 Call was .75/1.00 when the stock was $30. After the $1 price rise in the stock the Bid/Ask spread might have become 1.00/1.25. If you buy @ $1 and can only sell @ $1, you lose the cost of commissions.

**Delta** is dynamic. When the stock price moves, the Delta changes. Delta will increase as the stock price increases. Delta will decrease if the stock price falls. This change is known as Gamma. Think of Delta as speed and Gamma as acceleration. We will go into Gamma later in much greater detail.

Delta also changes as time passes. As option expiration gets closer the Delta for the ITM option increases towards 1.00, and the Delta for the OTM option decreases towards .00, while the ATM option’s Delta will almost hold at .50, right until expiration.

OTM options are usually a bad deal. There’s generally not enough time for the price to rise and the Delta is too low, the exception is with Leaps. The Deltas on Leaps will be closer to .50. ITM Leaps will have lower Deltas than short term options. OTM Leaps will have higher Deltas than short term options. Most people are unaware of this phenomenon. It can be used to great advantage in calendar spreads.

Every option trader should know Delta! Its okay not to know Rho, but knowledge of Delta is essential. You will need to understand Delta before trying to grasp Gamma (my favorite).

In order to understand option strategies, especially using weekly options it is necessary to understand Delta – hopefully you do now. As always if you have any comments please leave them below.

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### Stock Option News

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- Patagonia Gold Corp. Grants Stock Options TSX Venture Exchange:PGDC - GlobeNewswire