Probably the greatest discovery ever (3)

In my previous post probably greatest discovery ever-2 I lightly touched on the role of probability plays in option strike picking. I also compared the three alternatives on the access to the probability of option strike. In this post I am going to explore why probability is so important in option trading from another perspective. 

Option trading can be fun and could be profitable as long as one knows what option is all about. Option is a derivative of an underlying asset like stock or index. As explained in the previous post, some traders use option trading simply as a speculative tool especially those standalone Long traders who solely wish their trades can go into ITM to enjoy the exponential growth of the premium while the Short traders are usually less aggressive and just hope their trades can remain OTM so that they can earn some humble profit, ie., the already known premium amount received as soon as the trade is established. 

However, apart from the speculative application, option actually has a more functional purpose or usage. For some big investors with a huge portfolio or the fund managers who have an enormous holding under their management, the constant market fluctuation is a headache to trying to maintain the value of their holding in a comparative stable level. This is when hedging comes into play and option is a good hedging tool particularly the Long Put option against the anticipated market plummet. The profit from the Long Put position hopefully can off-set part of, if not all, the loss on the portfolio in case of a market crash. 

Unlike the speculators who hold their Long position solely for a speculative profit, the hedging Long Put is a kind of protection against an anticipated or unexpected market plummet. Just like any trade on earth that there must be counterparts for either the buyer or seller, whenever there is a Long then there is inevitably a Short in the option trading. That is to say, when one, due to the need on hedging, longs put say a stock option then s/he needs a short put counterpart so that the trade can be made. Naturally in the real world there are market makers so the counterparts might not be the same like those in the property transaction that a house owner matches with a house hunter. Anyway as a whole in the market, all the Longs must be equal to all the Shorts.

While there are at least two different types of long put traders, ie., speculators and hedge-seekers, but their counterpart, ie., the short put traders are rather unanimous. They all want to receive the profit, ie., premium, by shorting put. Short traders receive the profit upfront when the trade is made but at the same time they assume the risk of their position going into ITM if the underlying asset plummets prior to the expiry of the option and they will face potential huge loss if the ITM is very deep. As option trading is a zero sum game so the loss of the short traders is exactly the profit of the long traders and this is what and when a speculative long trader makes profit and a hedge-seeker can be protected. 

To the hedging Long trader's eye, the Short trader is just like his/her insurer whom will pay him/her back his/her loss on the fall of value on his/her portfolio. While from the fact that Short Put traders receive premium and assume the risk if there is a plummet and their loss could compensate the Long Put traders then they are really acting like an insurance company, an individual though. 

Everybody know that the business of the insurance industry is fundamentally a business based on probability. The probability of the event that being underwritten dictates the details of the policy especially the premium payable. With the perspective of the nature that Short traders are insurer underwriting the risk of their Long traders counterpart, this explains how important it is to look at the probability of the strikes of their position if they want to play safe. After all, Short traders are no different from running an insurance company. Shouldn't probability be treated as the most fundamental determinant when committing on any option trading, when the potential loss could be huge?

Probably the greatest discovery ever (2)

In the earlier post probably greatest discovery ever I said, as being a option trader, that probability is such a good thing especially on the strike picking because apart from reviewing all the technical indicators on the supports and resistances and the analysis on the open interest of other derivatives like the Futures and CBBC, the decision on a strike boils down to whether the strike will become ITM or OTM at the settlement day. Notwithstanding there are Straddle, Strangle, Butterfly...and many other option strategies but boiling it down to the most foundamental components there are only Long and Short while Long prefers ITM vs Short avoids ITM. Therefore the tool that helps predict whether a particular strike will go ITM is paramount to an option trade.

In that post I have slightly touched on the saying that in option trading shorting at a strike with p=0.1 of being ITM is usually safe in a normal market situation. Perhaps not every reader is familiar with option trading so I am going to explain a little bit that in the option trading world, some traders use option as a hedging of their positions in assets holding like stock while some just trade for profit without any need on the hedging of whatsoever. For the latter, profit could be from receiving the premium on their short position or the price difference after the settlement of their initial long position. Long position traders is betting on the strike(s) of their trades will go into in-the-money (ITM) so their profit can grow exponentially but Short traders just prefer the opposite because basically they are the counterparts of the Long traders despite not necessarily be of any of a particular trade concerned. Simply speaking when a Long trader makes money there must be a Short trader losing money in a particular trade because option trading is a zero sum game . Therefore Short traders never want to see the strike(s) of their position go into ITM.

I hope the above little explanation can shed some light on why I said a tool that helps to predict whether a particular strike will go into ITM is so important to all option tradings. That also explains why probability is so helpful because when the probability of a particular strike is known then it is just all about a trader's discretion on whether the risk of the trade is justified. In that earlier post I said luckily the probability of a particular strike in option trading is, unlike some other events which their probabilities are difficult to tell, rather easy to be determined, scientifically and objectively. 

For any seasoned option traders, they should be well versed in the jargon in option trading like Delta, Theta, Gamma and Vega...etc. Among these jargon, Delta is defined as the ratio of the change in the price of an underlying asset with the change in the price of a derivative or option. However on the other hand, it is also known as the probability. For example, a strike with 0.2 Delta means p=0.2 or 20% possibility being ITM. One must understand that the Delta of a particular strike does change along with the price movement of the underlying asset though so that probability is better seen as a snapshot of the moment concerned only. Therefore it is rather risky to make a trade base on the Delta reading of a strike to assume it will remain the same till the settlement day especially when there is still a long way to go. 

Considering the drawback of the Delta, some traders resort to the option pricing theory  to use the Implied Volatility (IV) to work out how likely a particular strike of an option will be exercised, ie., being ITM. In real life, IV is quoted by market makers who are usually more market intellectual to judge the riskiness of a particular strike so supposedly to be able to assign the corresponding IV. Basing on the quoted IV, traders can work out the likelihood of an option will be exercised at the expiration according to the formula of the pricing model. However, apart from other elements, the underlying asset price is also one of the variables used in the formula. Therefore using the IV on the calculation of probability literally has the same drawback as the using of Delta. Meanwhile, to the contrary to the Delta, market makers often quote a higher IV when the market is volatile but then when an higher IV is used to be the variable on the calculation in a specific market volatile moment the result tends to be fluctuant thus making it less reliable.

In light of the pitfall of the Delta and option pricing model, I prefer to refer to the historical data. For example for a spot month trading, the past record of the percentage of the monthly closing price vs opening price is used. These past percentage figures, say for the last 10 years, are ranked from smallest to biggest then it is easy to find out which percentage is within the 10% of the smallest as well as the 10% biggest. Those 10% smallest should be negative representing the most extreme adverse months while those 10% biggest are positive representing those extreme good months in the past 10 years. The thresholds right before these 10% smallest and 10% biggest biggest are what I am looking for and are used to become the risk determinants. That is to say, the strike is chosen at the same percentage of these thresholds comparing to the month opening price of any particular spot month trading. Naturally whether it is 10% smallest/biggest or whatever percent just rest on the risk appetite of the trader at their own discretion. 

The above methodology is the application of the probability based on historical data. This idea might not be most scientific but it has taken the history into account. Some argue that history is something happened in the past and it is not necessarily able to predict the future. As Mark Twain puts it that history doesn't repeat itself but it rhymes. Those good months or bad months could be as the result of different causes but the magnitude of their impact in the market were clearly marked in the history which can be used as a reference to whatever happening or going to happen in the future. For example if there will be a black swan event in this month which is not bigger in scale than the financial crisis in October of 2008 then it is quite reasonable to assume the plunge should not exceed the magnitude in that month which falls into the 10% adverse months bracket. Therefore any strike with smaller decline percentage than was that in October, 2008 should be a safe one no matter what the black swan event is.

Having said, the application of probability based on historical data doesn't come without pitfall of its own. The prerequisite of this methodology is the binomial distribution of the past data. Meanwhile even if this criteria is met, if the black swan event is so big and bigger than any past events throughout the statistical measured period, ie., 10 years in the example, then the assumption is simply not applicable. Luckily an as longer as possible period in question should be able to address the issue, largely if not completely. What still makes this methodology fails is that if there will be a mega crisis in scale which has never happened in human's history before like the outbreak of a worldwide nuclear war then the historic statistical data just fails to do their job. However, the point is, if there will be such a devastating nuclear war, then do we still exist? So do we still care about the option traded?

Probably the greatest discovery ever

I have to admit that I have not been a fan of mathematics since my school days. The scores on this subject were low and sometimes fell below the pass grade. I particularly had problem with the abstract calculation on advanced mathematics like algebra and calculus which after tons of brain work yet the answers are still x, y or z which fails to correlate nothing in the real world. Having said that, it does not mean I do not like mathematics though. What I need is to relate the calculation with somethings, better be tangible, that I know after hardworking then I shall get the answers that can be visualized.

I forgot the name of the man whom once said investing does not need a great mathematician. Anyone with basic understanding of simple addition, subtraction and a little multiplication will do well. I do agree with such saying because a Maths idiot like me have never come across any problem in the calculation of my investments. Unless for those who work in the Quant Investing or Algo Trading need advanced mathematical knowledge as well as programming skills, common folks with basic understanding on Maths do not need to be shied away from investing.

Having said, an extra knowledge on top of the basic mathematical calculation does help on a better informed investing decision. This knowledge is not rocket science though. Actually many of us have learned it in our college studying because Statistics is the backbone of many sciences so all graduates must have studied it no matter what subject they are major in. Despite I did have some difficult time during my study in Statistics but I did find that it is interesting because most of the issues that Stat is trying to solve are not abstract idea. In fact many terms that we come across daily are the result of statistics like average minimum wage, households income, queuing time, life expectancy...etc. They are all intimate to our daily life but not just x, y or z.

Among all knowledge within statistics, I think the concept of Probability is the most valuable piece of discovery that mankind has made ever, at least to all investors. In English, probability is about the chance of the happening or not happening in percentage or in decimal point. This is the reason I said Probability is the greatest discovery ever. In most cases, all things on earth will end up to the fact at the extreme polarity of probability of 0 or 1 where in between lies a range of ambiguity and this is the fun part of the world, ie., how likely the result will be. Excuse me for a juicy analogy that someone once said the sexiest woman is not a nude but the one with partially revealing.

In investing world, probability also plays a very important role. We all want to know what direction the Dollar is going to go say by the end of this year, the result is very simple either goes up or down but how likely it is up vs down? This is a billion dollars question and it is all about probability. Likewise, what the chance is that a particular company's debt will be defaulted is of most concern of its bond investors. For option traders, it has nothing more important than the probability of their positions will go into ITM or stay OTM no matter they are Longs or Shorts at the settlement day.

In my previous posts I wrote quite a lot relating to the importance of probability to trading is-a trade-worthwhile and the series of index-option-trading-with-statistic5. I found that probability is really the essence of the option trading because at the end of the day what a option trader cares about is whether s/he can be benefited by her/his premium received from the credit trades or by the trade profit of the long position. Unlike something on earth that probability is somewhat difficult to be determined, luckily how likely a particular strike will go ITM or OTM is rather somehow predictable so making a option trade decision is a lot more logical and reasoned. For example, based on the past settlement data, by shorting a position at a strike which is with 0.1 probability of going ITM will most likely let the trader be exposed at only 10% risk which is quite safe in the normal market situation. Naturally the risk level is completely at the trader's discretion according to his/her risk appetite but the key point is by knowing the probability it allows a trader to pick a strike under an informed decision.

As a option trader, I would say probability is probably the greatest discovery ever!

Index option trading with statistic(5)

I did not intend to make this topic as a series despite I have made four posts about it already. However, since I have also written another related post regarding probability on trading and it is closely related to what I term it probability trading so it is good to supplement some more info about this idea in this post.

Every short side option trader knows that option trading boils down into three key estimations prior to position building,
1. Direction of index movement, ie., above or below the rollover point at the settlement day
2. Range of volatility and the peak and valley of the month
3. settlement point

Naturally there are also concern on position size, strike picking, time of position building and long or short which are more on the risk management and trade strategy which varies from one person to another.

In my first post I mentioned that as long as one believes the index movement is the manifestation of the combat between bearish and bullish master players so it follows a structured pattern which history will repeat in somewhat similarity. Therefore probability from the past statistic could be a good reference for the inference of the future. This is the basis of my idea of probability trading, ie., decision based on the likelihood on what things will/will not happen.

The application of probability on the above mentioned three key aspects does not share equal weighing. In fact probability shows little implication on the first aspect, ie., direction of movement, because whether the spot month index will end up higher or lower than the rollover point is indeed random and is affected by the key events happen in that month which probability data fails to predict. Having said so, statistic does reveal that for HSI when the previous month has experienced a more than 10% fall then there is a 0.78 probability that the spot month will see a higher than rollover point settlement.

Probability does it job best on the second aspect, ie., the prediction on the monthly volatility and peak/valley. Statistic shows that 0.87 probability monthly volatility is below 3000 points and 0.73 probability below 2000 points respectively in the past 18 years. Naturally how accurate the probability data for a particular month can be depends on the design of the database which I mentioned in my first post. A sophisticated database which incorporates well designed sorting parameters does reveal a reliable probability of the volatility of a month for a given pattern.

Although probability data cannot predict the exact settlement point for a particular month but just like what it does for the volatility, it can show the probability of the how many points deviation from the rollover point. For example, it is 0.05 probability that any given month the settlement is more than  1800 points above the rollover point.

In my post  "is a trade worthwhile?", I raised the concept of odds and probability for the basis of whether a trade should be made at all. A well structured database can provide probability for the volatility and settlement point. The information of odds for index option trading for short side trader is even easier. Basically the profit for a short position is known when it is built. The potential loss depends on how the hedging is or what strike the protective long is put. The odds is just a simple maths.

As Charlie Munger puts it, value investing is all about looking for bets with 0.5 probability but with 3:1 odds. Through the use of database and the application of probability, index option trading can be more secured. The risk (probability of settlement beyond the strike of position) is foreseen and how much the profit is also known right at the time of position building. No more torture from the fear and greed. This is the essence of my idea of probability trading.

Good luck in trading!