However, you can still model an entire portfolio over a time period with given assumptions. Just be sure you also test the extreme end of assumptions that would be an unprecedented result. For instance, although we've had a 20% loss in a day in 1987 crash, what about a 60% decline in a month? This sort of decline would be very very very rare, but if an event like this wipes you out erasing decades of gains, your system may not even be profitable at all in the long run due to the very rare event.
Let's start with a hypothetical coinflip to keep things simple. Heads you net double what you risk. Risk 1, win 3, profit 2. Tails you lose 1.
If we flipped a coin and then adjusted our bet based upon the new position size we can calculate our return over several flips very simply. Assume 50 heads and 50 tails.
Let's calculate the win result for 50 heads. For a position size of 1%.
It's 1.02^50 or 1 plus the win ratio times the position size. This equals your multiplier factor. The result is 2.691588. in other words, over 50 wins your wealth will have multiplied by ~2.7 or an increase of ~170%.
Now we also have 50 losses. Since each loss we will adjust our position size, the wealth will decrease by a factor of .99 per loss and size will be adjusted downwards. .99^50=0.60500607 or about 60% of what we started with if we lose 50 times in a row or a loss of about 40%.
So now we can combine them ~2.7*~.60=~1.62 or a 62% gain over 100 flips.
But hold on just a second, it's very possible that you only get 40 heads or perhaps only 30. We need to test the outliers in terms of number of flips as well as the magnitude of the results (how big each individual win or loss can be). Since this trade is fixed (the upside does not change and the downside does not change) we don't have to adjust the magnitude of the win. But we should test for what sort of drawdown we are looking at at 1% position size if we lose 70/100. The results are (1.02^30)*(.99^70=~.896 or a loss of ~10.4%. What about 20/80? THe loss would be closer to 33.5% in a year. what about 10/90? Results are a loss of about 51%. You can see how even modest positioning with limited upide and a clear edge can still produce a lot of volatility over time if you go through a rough streak. We can test the upside as well if you'd like. 90 heads to 10 tails would be 437.5%. 80/20=299% 70/30=195.85%.
This is similar to a hypothetical system, but it is not equal. Before we go looking at more complex outcomes with multiple outcomes, let's look at smaller as well as larger position sizes. For now let's summarize 1% position size.
Expected results (50/50)=62.8% gain per 100 flips
outside range results 40/60 to 60/40= 20.8% to 119.5%
extreme range (30/70 to 70/30) = -10.37% to 195.8%
very extreme range 20/80 to 80/20 = -33.5% to 298.8%
unprecedented extreme 10/90 to 90/10 = -50.67 to 437.48%
I'll go ahead and do the work to summarize 5% position sizes and 0.25% position sizes, but for those looking to make sure they do it right, it's position size times expectation plus starting portfolio for one trade. For instance starting portfolio in this case will always be 100% or 1. expectations in this system will always be either minus a full position or plus 2 full positions. So if position size is 5% a 5% loss from the 100% will leave us with 95% of what we started with or .95. A win will leave us with 10% plus what we started with of 1.10. So now we can build out the results table for 5%
Expected results (50/50)=803% gain per 100 flips
outside range results 40/60 to 60/40= 8.5% to 3812%
extreme range (30/70 to 70/30) = -51.86% to 16851%
very extreme range 20/80 to 80/20 = -88.89% to 733.32%
unprecedented extreme 10/90 to 90/10 = -97.43% to 318010%
The biggest problem with this strategy in real life is there is very little ability to separate a broken system from an extreme outcome and by the time you figure it out, the damage can already be done.
The other extreme of 0.25% positions will see .9975 of what we started with per trade or 1.0050
Expected results (50/50)=13.27% gain per 100 flips
outside range results 40/60 to 60/40= 5.1% to 22%
extreme range (30/70 to 70/30) = -2.5% to 31.5%
very extreme range 20/80 to 80/20 = -9.50% to 41.75%
unprecedented extreme 10/90 to 90/10 = -16.1% to 52.78%
We can see the dramatic difference in outcomes. Just for fun, let's see what happens if we position size way too large at 60%.
expected gain at 50/50=~-100%*. Even a winning strategy with less than 100% going as expected results in ruin if we bet too large. *The exact loss is 99.83%
While we could simulate more realistic trades with options and more than 2 possible results to more accurately model the outcomes there is another problem we run into comparing reality to the theory as currently modeled. In reality you won't wait until one trade is done to start another. So we will stick to the coinflip argument until we resolve it.
This simultaneous trading provides both benefits (in that you can put more capital to work while less is at risk since the odds of a lot of small trades simultaneously not working out at once is less than if all that capital were tied up in one trade) as well as a hindrance (In that while losing 40 1% positions over 40 trades will only lose you 1-(.99^40)=.33 or 33%, 40 losses simultaneously will lose you 40. In addition while 40 1% coinflips that win one at a time will compound and win you 1.02^40=~2.2 or 120%, when placed all at once they will only win you 40%.
Still, it's far less riskier with far better results to bet 1% on 40 coinflips than 40% of the capital on a single coinflip. Even as we will transition into a model that models actual trades, no two trades are exactly correlated, so there is still a bennefit for diversification (before fees) that can act to reduce risk if used properly.
Nevertheless, we have to change the calculation entirely to how many simultaneous trades over a period to where it adds up the sum of all results as opposed to multiplying. For instance, if we have 1% position with 30 wins and 20 losses simultaneously, rather than (30^1.02) * (20^.99)=1.48 or 48% return, the calculation is (1.02*30)-(.01*20)=.40 or 40% return if we have multiple overlapping periods like this we can add the separate periods. For instance if we had 2 periods of 30 wins and 20 losses, we can still adjust position sizes after a period so the result is 1-(1.4^2)=.96 or 96% instead of just 40%*2 or 40%+40%=80%.
In reality, a very important variable determining success or failure when using overlapping trades is how correlated each trade is to another. For instance, if all you have are calls in each individual S&P stock expiring at the same time, you are going to be very exposed to a broad market sell off during that time, and you might as well have a single call in the S&P. There is no real diversification of risk if you are exposed to the same correction in the broad market or rotation out of it. Having 40 1% of various S&P stocks is about the same as having a 40% position on for the S&P over that period. If instead you have a variety of strike prices across a variety of time periods and each are in a variety of underlying stocks in different sectors of the market as well as focusing on the underowned stocks, then a rotation from the overowned into the underowned or the big cap into the small or the index correlated to the uncorrelated can actually be your gain as the market declines. However, 40 1% positions bought over approximately the same way (within the same price range or time range) with approximately the same expiration date (within a month of each other) even if you are seeking out underowned names is still vulnerable to the type of everything down correlated sell off common during major corrections (down 15-20%) and bear markets. Although there will be numerous sell offs where you are not impacted by uncorrelated sell offs, the selloffs that are correlated can do enough damage where you better plan for a strategy that can weather multiple extreme moves over a few years and still be profitable over a time period, otherwise you will need to position differently or adjust your strategy. One such adjustment may be buying insurance in the form of index puts over a long period of time to pay the minimum and then rolling that time premium as needed. This doesn't protect against a long period where your individual trades fail to gain traction or where the market doesn't ever rotate into underowned names and instead is lead by the names leveraged to the index.
Consider that when modeling against all extremes which I will show you how to do briefly. Remember when I showed you the table of expected return, outside range, outside extreme etc? One thing you may wish to do is run a calculation for a 10 year period that contains a couple outside extremes to the downside, one to the upside and the rest either in the normal or outside range or results. You can test different position sizes over this time period. Keep in mind that it will be very easy and possibly appropriate to adjust following a significant decline as you don't know whether or not that was just an extreme or representative. You don't know if your expectations moving forward will equal the past, be better than or worse than the past. Emotionally, you may also determine you've had enough. For this reason, your effective bankroll may actually be smaller than you calculated and your proportional risk to that bankroll may be higher than you realize.
We are ultimately going to seek out a balance between multiple strategies across multiple portfolios to try to mitigate risk of our overall wealth and obtain our goals.
For instance one such overall wealth building strategy may look something like this.
1)401k aims to capture the very long term wealth effect over multiple credit cycles (usually 7-11 years) as well as overall movement from and to stocks and other assets like bonds, and may reposition to try to capitalize off of moves lasting months to years.
2)Roth IRA aims to bennefit from swings in stocks lasting weeks to months.
3)Individual option account combined with individual stock accounts aim to insure against the longer term moves when insurance is relatively cheap and in appropriate times, while primarily seeking the non-correlated moves and counter moves and spotting individual bullish and bearish setups when appropriate. The taxible individual trading accounts will dynamically adjust position size by having some exposure to the index and some exposure to cash and hedges and increasing or decreasing that exposure as the short term and long term trades swell up in size to maintain a proportional bias consistent with expectations and avoid overexposure to any one period of time or expiry or overallocation to risk.
This is just one such possible idea, but another involves complex rotation. Another variable is market condition. certain strategies do better during sideways markets, others during quiet markets, others during choppy markets, others during bull and others during bear market and combination of the 2 variables of volatility and trend/direction (or no direction if it's a sideways correction through time).
Here is one such strategy I sort of tentatively mapped out. The idea is you get some market correlated names and perhaps include owning companies run by money managers like Warren Buffett like birkshire hathaway shares. At the time I made this I mistakenly thought WCC (Westco Financial) was still run by Charlie Munger, but there may be some sort of publicly held company that has a large float of investible securities that is run by a quality asset manager. The idea is to own market correlated names that you believe in over the long run to equal perform or outperform. Your 401k might also be allocated into long term outperform but in a more permenant sort of way so you may view that separately. Then you may consider a basket of commodities that start as a very small position and you might buy for the long term at historically significant prices when possible. You might have a currency trading account or just trade calls/puts in currency ETFs to place trades that move differently from the market itself. You also may want to own some proportion of long term corporate bond and treasury bonds, however, we are at a historical period where rates are probably rising so keeping this percentage very small or finding some way to hedge against rising rates on the extreme end (perhaps long term puts in TLT) may be appropriate.
Then you have your stock timing portion of your portfolio that tries to maintain a mixture across varying strike prices. And finally you have some hedging capital and cash, and since you won't need all of your cash at even extremes, some percentage can be held in income.
The goal of holding commodities and bonds is to capture rotations in capital into and out of the stock market as well as provide the buffer for your individual stock timing/outperforming portion of your account(s). The goal of having large cash and income amount is both for future opportunity of better prices as well as some degree of protection from deflation as well as reducing account volatility to desirable size, particularly if you are seeking maximum volatility. The goal of having market correlated names is to both have something to balance out growth in stocks and to generally add lower and reduce higher while options are by design going to increase exposure higher and decrease lower and some trading strategies involving stocks or options may stop out lower and add higher.
In order to optimize the portfolio according to risk tolerance and our goals we will need to run several calculations like the calculations that we already did stress testing the portfolio against hypothetical extremes and determining the blend that we desire. That will be for another time.
The goal will be to accomplish a goal of return (or better) while keeping max drawdown limited to a particular amount (or less)... or else over a time period to maximize the probability of an event with a secondary time period where an amount must be reached. This may put less focus on the drawdown in a given month or year, but ultimately the drawdown must be limited such that you are able to recover and obtain your goal.
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