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# How I Let Data Guide My Conclusions and Results Of Thousands Of Monte Carlo Simulated Trades!

I stand to you today to announce that I have used data and simulation to prove myself wrong. Call me a flip flopper if you like, but I view this as a constructive thing as I have chosen to take the most profitable and beneficial path rather than the most comfortable. While some remain attached to certain ideas, I let the data guide my conclusion whenever possible. The human mind is full of biases and often too rigid on our ideas. Be open to examining the assumptions that you take for granted on a daily basis just as testing the assumption that “the world was flat” was a productive one, it is possible you may make significantly greater progress than all of those around you who resist the change in your ideas.

My previous paradigm was guided by this understanding of the relationship of risk:

Unfortunately, every model has certain “assumptions” it must make to construct any particular generalized “model”. It is usually not the model itself you should test, but the assumptions within the model, as well as your own personal assumptions which can only be done by data first. After adjusting and testing these assumptions and thinking more dynamically I can see that this is simply not practical as you will also see in a bit.

At first I had a simulator created to calculate all possible permutations of theoretical trades, but realized the simulator could be improved. Rather than continuing down the direction I was headed, I “flip-flopped” again, instead opting for constant improvement. I instead came up with a spreadsheet that uses the random number generator and a “Monte Carlo simulator” plugin that I view as much more efficient and flexible in terms of the duration of trades in which I want to test. Although it lacks the same degree of precision, it is a productive tradeoff as you can still increase precision in exchange for a more timely monte carlo simulation (with more random iterations).

I used the spreadsheet to look at returns dynamically over a finite amount of time such as 300 trades. Out of a thousand traders for example, some percentage may gain 20% while another percentage gains 100% and another percentage loses 50%. Using this data, A histogram plotting all simulated results of each of the thousand random iterations of 300 trades was made for various levels of risk given a particular system. The simulation allows for a change of any one of these inputs (probability of 5 different “results” of the trade, the ROI given each of these 5 “results” the number of traders randomly selected and the number of trades they make). You can even look through random equity curves across all 300 trades at a given risk factor and refresh it with a push of a button to pull up another random trader to get a better sense of drawdown within different points of the system over the course of those 300 trades.

Without further ado, here are some results!

pX=probability of event X.

wX=win % (ROI) given event X.

System: p1-5=20% W1=150% W2=50% w3=0% w4=-50% w5=-100% A winning system is presented.

Risk defined as capital at risk since this is an option strategy and you can lose the entire premium.

“optimal F % / full kelly = 14% risk”

Note the severe skew right. This means as you increase risk extreme outliers begin to skew the average higher than what is “typical”. Skew right means the mean (average) is way higher than the median (average). The “worst case scenario” grows with risk. The probability that you end with a lower than average result (that is not a typo) increases as risk increases risk given a finite amount of time. Eventually the probability of a poor result is so great that as you increase risk the long term geometric return suffers. If you are a true cowboy looking to become an “outlier” and willing to put in the risk, then perhaps that is okay with you, but just know that going beyond the “optimal” amount is destructive as you approach “an infinite number of trades”. Just know the type of CRAZY account volatility you will have to endure, and a large probability that you actually will end down even after 300 trades. That’s almost 6 years at 1 trade a week!

Since I took the time to create this spreadsheet, I can simulate thousands, or if I like, tens of thousands of traders trading anywhere from 1 to 300 trades (or more if I take 5 minutes to set up more) with a given system with a push of the button. I can instantly adjust the expectations of the trading system and see how the results change.

In the next post Titled “Equity Curve of Risk – How Risk Influences Expectations” I show some example equity curve of a particular risk percentages.

## Game Theory and Investing

If you have an edge in the market, or are using an “exploitative” strategy, position sizing is supremely valuable. If not, you should position defensively (use an “equilibrium” strategy) to avoid being “exploited” yourself. As you increase position size and overall risk (with an edge) your geometric return functions like this (over an unlimited time period):

If we were to continue beyond double the amount that maximizes your geometric return, it would begin to look like this:

This is based upon a formula called the Kelly criterion. There are Kelly criterion spreadsheets available like this one. The exact percentage in which you reach the apex of returns depends upon your edge and odds. 50% of the “optimal” risk produces 75% of the results with 1/2 the volatility. Because of uncertainty over your edge, it statistically is better to err on the side of caution, not to mention better for reasons of psychologically, emotionally, and due to a “less than infinite” duration of one’s trading career, and “utility theory” among other things. Let me be clear… It is far more important to protect what you have while producing a positive return than maximizing the return. As such the exact application of this is perhaps not so important as recognizing that increasing the risk does not proportionally increase the geometric return.

Without fees involved, one single independently correlated position size at the apex of those charts produces a lower return than two independently correlated position sizes at HALF the apex.

We can pretty accurately conclude that uncertainty, randomness (or more accurately “chaos”) and portfolio volatility are usually the enemy of those who look to place wagers and handicap markets with a particular edge.

Illustrated numerically, it occurs because of this concept of the result of a loss not being equal to a gain:

loss gain | needed to get back to even
1.00% | 1.01%
2.00% | 2.04%
3.00% | 3.09%
5.00% | 5.26%
10.00% | 11.11%
20.00% | 25.00%
30.00% | 42.86%
40.00% | 66.67%
50.00% | 100.00%
60.00% | 150.00%
70.00% | 233.33%
80.00% | 400.00%
90.00% | 900.00%
95.00% | 1900.00%
99.00% | 9900.00%

The largest obstacle to overcome with this style of trading is that volatility will more often become your enemy. A conservative approach can still handle most expected volatility, but factor in your “black swan” and “10-sigma events”, and even a conservative strategy can be hit hard and fast by volatility to the point that it can destroy many otherwise profitable strategies. A robust approach that may do only a little better than break even in all environments, yet protect itself from the deadliest rare “black swans” in the long run may prove much better than the aggressive highly profitable approach. Fortunately their is a happy medium that may provide the best of both worlds.

If you have an edge, I believe a portfolio should still have a significant portion designed around mitigating the risks of volatility. The solution to volatility can be to try to adjust strategy based upon the “market type” you are in, but that can often be either retroactive (backward looking), and late to the party, or anticipatory and potentially inaccurate a high percentage of the time. As a result their are still substantial risks of not being able to significantly mitigate the risks of volatility ruining or greatly reducing a strategy’s profitability. In technical terms you might have a “balanced exploitative strategy”, that only slightly deviates from an “equilibrium strategy”.

Quick Primer on Game Theory – “Nash Equilibrium Theory” and “Exploitative Theory”
1)Imagine an alternate universe where there were only 2 investments “stock market” and “dollars” and no leverage where the “stock market” never goes to zero (although individual pieces might). If market were random or if the actual “edge” or expected direction were completely unknown, the “equilibrium solution” to play the market and produce gain based upon others mistake (who transfer capital from stock and cash unevenly causing changes in prices) without directly exploiting them would be 50% cash and 50% stock.
Example: Stocks are worth \$1000 and you have \$1000 in cash. Stocks double to \$2000. You sell 1/4th of your stock position so that you now have \$1500 cash, \$1500 stock (50% each). Stocks decline by half. You now have \$750 stock, \$1500 cash \$2250 total vs \$2000 you started with. \$250 more value than you started with or a 12.5% gain due to volatility after stocks “normalized” or “reverted to the mean”. The “equilibrium” strategy seeks not to handicap the market, but let others try to do so while over a very long period of time profit from volatility.
An “exploitative” strategy under the same “universe” is when you decide you have an edge and that the market has neglected “stocks” so you might buy somewhere between 50% and 100% stock (100% would be maximally exploitative, (and an “unbalanced” strategy) where as 50% would not be exploitative). The more “exploitative” you are, the more vulnerable to long term portfolio volatility, uncertainty, and “chaos” (I feel this is a much more accurate term than “randomness”). It’s important to realize that the farther the market is from “equilibrium”, the more an equilibrium strategy will gain. However, the proper exploitative strategy under the same circumstances will gain even more than equilibrium strategies if assumptions are correct in such situations. I will prove this with a brief example: If you had to choose heads or tails with a double sided coin (2 heads) with 3:1 payout (payout is far from equilibrium), calling 50% heads and 50% tails might still gain more than a 2:1 or 1.5:1 payout, but calling heads every time would be MORE profitable. However, if someone was able to switch to a double tailed coin or a regular coin at one point without you knowing, the more aggressively you bet your assumption and position for those assumptions, the more vulnerable to decline and even risk of ruin you are if your assumptions are proven wrong.

2)In the real world capital can migrate to and from multiple asset classes, credit can contract and expand, domestic capital flows can be very different than global ones and potentially move against the grain of global capital flow. Asset classes have components and sub components and so on all of which can receive capital inflows (rally) in the face of a broader capital outflow (gold going up or sideways as commodities go down. Rather than concentrate on a specific equilibrium solution, it’s more practical to just look at a simple one as part of a “core” strategy. One such as this:

If you want the technical jargon you can read about “modern portfolio theory” which basically attempts to maximize expected return for a given level of risk using the “efficient frontier” and using “beta” to define risk. To me “beta” is a backwards (retroactive) looking view on price volatility relative to the backwards looking view on the market’s price volatility. The assumption of an efficient market is also a “suboptimal” conclusion in my view. I am not interested in an overly technical portfolio that requires frequent management. Instead I am only looking to exploit the inefficiencies of the market one one hand, manage the risks to do so effectively, while mitigating risks via defending against chaos via a portion of capital that is in some pseudo-equilibrium solution that basically looks to establish a “baseline”

My portfolio composition will actually function more like this: (click on the image to see full size photo)

This is how the same concept could look and function with mostly leverage:

Depending on how low the correlation of each trades, you may be able to add a lot more individual short and long term trades as the natural “baseline” of risk, but it still must be monitored and have certain rules and “limits” in order to keep the exposure and risk in check at all times.

You might reduce cash and add in “long term income” based risk in your capital that could be anything from buying a 12 month cash CD every single month (so that every month you have a CD from a year ago pay out and become liquid), individual stocks that pay dividends, ETFs in any number of many categories that pay dividends and so on. The income will drip feed into the cash account, and because of a growing cash reserve that can be used to rebalance, their is less of a priority to have as much excess cash, provided the income is fairly robust. (A broad S&P ETF probably isn’t at risk to see its dividend get cut).

A basket of various income ETFs such as PFF,CORP,TLT,SPY,HYG,EWSS and SHY as a substitute for a large portion of that cash along with a 12 month CD purchased every month is an effective way to create liquidity without having so much capital tied up in 0 interest yielding cash on the side, yet without having an overly large amount of risk associated with it.

The philosophy is still about having an allocation based portfolio that can manage large swings in volatile capital flows, manage portfolio through large periods of expansion and contraction (inflation/deflation) and any number of unforeseen variables. This management of volatility in combination with individual positions and hedges provides a more stable portfolio overall, but still allows you to do plenty of “core” trading” in the short and long term.

The actual allocation should be dependent upon: your skill in each of the areas you allocate towards, your overall skill, your current market outlook/bias, risk tolerance and a few other variables. I’m not going to go any further in depth than that for now, but I hope this post is able to allow one to rethink their strategy and whether or not their strategy is properly prepared for different periods of volatility while still providing yourself with the flexibility to adapt.

You do NOT have to be a “game theorist” to invest and trade, but it is important that you understand that there is a basic “baseline”. Also, it is useful to know how one might adjust when approaching a market that is not at equilibrium and how to avoid significant risks that are detrimental to your long term returns. We will cover more on making adjustments to a basic balanced philosophy that I have presented.

## The Story Of Success: Do You Have The Hunger To Succeed?

I gave to you a great tool that can help you succeed in my last post.  “Jimmy Bob” asked a good question. The question was along the lines of “how much work do I do to reach success?”

This brings me to a story I have heard, but I will retell it anyways.

There once was a wise guru who had achieved enlightenment sitting on a mountain top

A young boy seeking enlightenment approached him and said, “I want to be successful like you, please teach me your secrets”.

“I will do anything it takes!” the kid responded.

“Anything? ” The guru questioned

“I would kill for the chance at success, I would die for it!”

The guru having been through the same routine of those who expected him to impart the wisdom over a brief 30 minute chat or less expecting their to be just those few “secrets” had grown tired of people coming to him asking for the quick solution and so often only claiming they would do anything. He knew the path to self improvement and personal development was a long road. Yet nevertheless he had an idea and said “meet me in Long Lake at 5a.m. tomorrow” and I will teach you what you need to know.

To the kid’s surprise, the next day when he came out to meet the guru, the guru was out in the lake already. The guru called to him, “come join me”

The kid said ” I am not prepared”

The guru said, “When you want success, you may not always be prepared, but you must continue on anyways”

The kid said, “But what I mean is, I didn’t bring my swimsuit.”

The guru responded “you may not always have the tools for the job at a particular time in your journey.

The kid said, “but the water is cold”

The guru replied “Life can be cold, and the journey to success can be even colder.”

The kid said “What does this have to do with success, I thought you were going to tell me the secrets? Or tell me a magic success formula? Or give me the magic pill to success?”

The guru replied “sometimes in life you have to make “the leap of faith”. Sometimes you have to trust that you’re in the right place and things don’t make sense. Sometimes you may have to rely on your training and experience to know the truth. Other times, to really know the truth and make the right decision, you sometimes have to go against everything you ever learned to find the truth even when it conflicts with your beliefs, and you must have the hunger to carry on anyways. Right now, entering cold water does not seem to have anything to do with success, and yet here we are. But a part of you inside knows that you are here for a reason. A part of you had enough wisdom to seek out someone who was successful and the courage to follow him. A part of you intuitively and instinctively knows that you must come to me now. I will not give you another chance, if you want to have success, join me immediately, no more questions”

As the kid finally decided to “take the journey” the guru said to him, “What I have heard from you is nothing but the typical excuses that is not all that much unlike the normal excuses that everyone makes that prevents them from success, “But I don’t have the money, but I don’t have the time, But I don’t know how, but this other guru who’s program I bought told me something different, but It’s too hard, it’s too cold, I don’t want to”. Inevitably some continue the march on, but of those people that try, many more will fail. I assure you, if you take the lessons I am here to teach you, you will succeed, but you have to trust me… Do you trust me?”

The kid approached the guru in water that went up to the kid’s neck.

He was a little nervous, but then he realized he did in fact trust the guru, so he said yes.

“Then allow me to baptize you in this lake.” Said the Guru

The kid nearly was confused, and caught himself from saying that he wasn’t religious and wasn’t interested. He thought perhaps it was a test. So he thought and realized that there were to be no more questions and that if he trusted the guru, he had to prove it. So he said okay.

As he was submerged under water, he realized the guru wasn’t letting up and was HOLDING him under water. The child began to become fearful, short of breath. He eventually realized he may have been wrong to trust the guru, he briefly calmed down and knew he could hold his breath longer so he still lay longer. But then he started to panic a bit and tried to stand up to which he was met with even more pressure.

“He’s trying to drown me, I am definitely wrong to have trusted the guru!” he thought, “I knew it”. He pushed and struggled even harder to come up for air but he couldn’t. full on panic set in. He finally started to leap out of the water when the guru covered his mouth and pushed him down one last time.

Just when he began to feel the intense struggle like he couldn’t take it anymore, and just when he reached maximum discouragement, his life started to flash before his eyes as he began to accept his fate and stopped struggling.

Just then the guru ripped him up out of the water and asked “Are you okay”.

The kid responded, “what the hell was that?! no I’m not okay, you almost killed me! I thought you told me to trust you, yet you could have killed me!”

The guru said, “Okay, now we shall do that 3 more times”, “Hell no!” the kid says.

The guru said to him, “ahhh… but I had had the impression you were willing to do anything… even die for a chance to achieve the success that allows you to truly live.”

“I didn’t mean I want you to kill me… How does that help anything anyways? Are you going to tell me what I need to know or just waste my time and practically kill me?!”

Then the guru imparted the most important lesson:

“I’ve already taught you everything you need to know, now only you can realize the lesson here. You see… No one can “tell you” how to succeed, only you can choose that path. It doesn’t matter what anyone says to you. It doesn’t matter who your guru is, without substantial desire and hunger for success, you will not succeed.

Yet when you want success like you want air, success is inevitable.

The guru continued, “The ‘old you’ is now metaphorically dead, and you are symbolically reborn and baptized into the mindset needed for success. You have endured what you have needed to in order to truly understand the hunger one must have. Having nearly accepted death, you probably had a few regrets, you probably thought of what was truly important to you. But if you still want success, it shall be yours… but only if you proceed with the same desire and passion of which you experienced when you wanted air.  So remember this feeling, and draw upon it when you aren’t content with where you are and truely know what it feels like to want something bad enough and know success is only a matter of time as long as you persist with this desire”

The kid grew up to be tremendously successful in all walks of life and continues to live a wonderful life.

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So there is only one question I have for you…