Constructing a Probability Map for Future Stock Returns

Each Monday I publish a weekly report “The Meta Strategy Derivatives Portfolio”, which includes a Probability Dashboard followed by a table with Probability Map Details that show return probabilities for the S&P 500 over different time frames. The main inputs and analysis that are used to reach these conclusions follows below these visualizations. 
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At the core of the weekly newsletter is a probability map for future returns of the S&P 500 over different time horizons. I translate these probabilities into a flexible portfolio exposure that tries to take advantage of market swings that tend to take place over roughly 1 to 8 weeks, while I stay invested tactically over the long term. 

To be transparent I want to lay out the process that leads to this probability map, so that anyone can emulate it and go about collecting information that contains a trading edge to integrate it into their trading process on their own.

Portfolio construction

The Meta Strategy Derivatives Portfolio is a holistic investing and trading portfolio constructed on the fundamental idea of the Meta Strategy. This strategy uses systematic fundamental and technical indicators to gradually rotate a portfolio between different asset classes according to long-term market conditions. The analysis here tells me whether to be long, short or neutral equity ETFs with the majority of my capital at any given time – over this basic allocation I then overlay a smaller derivatives sleeve to tilt the overall portfolio exposure.

Integrating information over different time horizons

Every day I collect pieces of information and strategy ideas which are more or less valuable for fine tuning a portfolio allocation. Long term return distributions of asset classes are very well researched and I consider them to be as reliable as anything is likely to be in the financial markets.
An expectation for a long-term positive return for owning an asset is the basic motivation to be an investor – if it didn’t exist the very species would die out over time.

Generic long-term strategies, e.g. factor exposure to value and momentum, carry strategies or trend-following, are next on the spectrum with lots of data and a fairly high reliability that there is some kind of return premium there.

The more we move down the ladder towards shorter time frames, the less reliable edges become (here is a good primer on possible “edges“) – for my intents and purposes they vanish into noise below one week.

The Probability Map

Here is where my concept of a probability map comes in: I want my net portfolio exposure to be the result of a stack of different edges and informational advantages, and am quite flexible in changing leverage and directional exposure frequently. I am willing to tolerate higher risk and volatility at the right time, if this results in higher returns.

I want to blend being a long term tactical investor, who is protected against big drawdowns, with being a nimble swing trader, who can take advantage of short- and medium-term shifts in return probabilities. For this I need a flexible framework that can deal with the constant evolution of the financial markets rather than a fixed ruleset of separate trading setups that may cease to work at anytime (I can still integrate these in the framework, if I want to).

To achieve this to the best of my ability I compile a current data driven estimate of the probabilities for future returns of the S&P 500 over the short term (1 – 8 weeks), medium term (3 – 6 months) and long term (6 – 18 months). I aggregate all the systematic edges I trust, include current market studies, and add the base rate — the basic historic probability distribution of the S&P 500 over the last 90 years.

As I think my long-term systematic strategy is the most reliable I invest 80% of my funds according to the Meta Strategy in simple, leveraged or inverse index ETF (the default is to be invested in stocks unless the strategy tells me to rotate into safe or alternative assets – e.g. as in February and March 2020).
The remaining 20% of my capital is then used to (over-)hedge this basic exposure or to add more leverage using a derivatives sleeve of options, CFD or futures. For those short-term trading decisions I blend the probabilities over my four basic time frames to reach an overall portfolio exposure.

In a bull market I might, for example, be invested long-term in an S&P 500 ETF, but temporarily be net short through the addition of put options, because my analysis perceives a high probability for a short-term pullback over the next month or so. During the pullback I then gradually sell these put options and add long exposure, and my net portfolio exposure shifts from short to leveraged long during this market swing.

Using probabilities to determine portfolio exposure

The highest possible conviction is around 80% – 90% probability (no certainty in financial markets) when all time frames align with high conviction. This will lead to a maximum one directional portfolio exposure and can only happen during a bull market because of the stock market´s upward bias – the static base rate needs to be aligned with all other time horizons. (Figuring out the right maximum exposure is tricky and every investor needs to find a comfortable volatility level individually.)

If, to use a common bull market situation as an example, the short and medium term probability estimate is opposing the long term bull market direction (the Meta Strategy is long equity ETFs), then the investment portfolio becomes over-hedged by the derivatives sleeve. Net exposure gradually moves from maximum exposure (all time frames align long) to hedged to neutral and finally to short.

Because the investment portfolio remains unchanged, this maximum short exposure will result in a comparatively small short tilt for me (about 60% – 65% short; with 50% being a market neutral exposure) — I want to stay aligned with the main trend as the best chances can be found there.

In a bear market the opposite happens, but the focus here lies on capital preservation rather than maximum returns, because high volatility environments are more difficult to trade.

The key to the process is that the less reliable medium- and short-term indications are always averaged with the strong return drivers of the base rate probabilities and long-term estimates. This avoids extreme positioning unless every time frame aligns for very high probability situations. Only then will the portfolio be at higher risk than a conventional buy-and-hold investment in stocks, because the potential reward is expected to be high and likely to materialize.


Basically any information, historic market study, strategic trading setup or other source of edge can be integrated (and adapted over time) through this process. My foundation is the analysis of the current long term market environment defined by economic fundamentals, trend and volatility – it leads to the investment part, the low maintenance Meta Strategy ETF Portfolios.
For the trading sleeve I have accumulated a number of my own analysis tools, market patterns and current market studies from trusted sources (e.g. by the excellent SentimenTrader service, Spotgamma or the Macrocharts blog– to name just a few of many).

I list the main inputs leading to my current market scenarios and outlooks below the probability map in the Meta Strategy Derivatives Portfolio newsletter.
There is some discretion involved which pieces of information, studies, market patterns and short term strategies I judge to be the key factors that drive the market at the moment, but each piece has to pass the test of providing a historical edge (a particular market condition that tilts the market’s return probabilities significantly away from the base rate when the historical data is analyzed).

How to translate a Probability Map into an optimal portfolio exposure

The amount of leverage used in a portfolio is crucial and must be decided on by each trader individually in advance (before a devastating loss happens!) through the lens of their risk tolerance. Risk and return will always be closely connected and there is no holy grail strategy that can severe that relationship. The probability map is simply a tool that weighs current risks and scales portfolio exposure accordingly. Nonetheless one must define the maximum risk level one is willing to accept in case things go wrong. I use a fraction of the Kelly Criterion as a tool to avoid risk of ruin and am willing to accept high levels of portfolio volatility for outsized returns.

This leads me to currently invest 80% of the capital dedicated to the Meta Strategy Derivatives Portfolio in index ETF over the long-term and the remaining 20% of my capital to the derivatives sleeve.

It helps to use maximum risk estimates to get to a good decision even when facing all the uncertainties of financial markets. I use the Meta Strategy’s stop loss level as my maximum pain point – it is about 15% to 20% below the stock market highs in a bull market (For example, in March 2020 the exit from stocks was signaled 16% below the high). This risk will be multiplied by the use of leverage or reduced when using a lower maximum leverage level than full stock market exposure.

In the high volatility regime of a bear market I reduce my position sizes as all moves tend to be faster and more violent.

Such a maximum risk estimate is very useful for any investor or trader with any kind of portfolio – it should be stress tested against worst case scenarios before they occur.

The question to ask is: could I live with this worst case loss?

I hope this gives some food for thoughts!


Do you like what you are reading? Consider becoming a basic or premium member, if you are ready for more:

You can follow how I invest according to the Meta Strategy in my own portfolio by subscribing to my monthly or weekly newsletters here.
A systematic monthly strategy for low maintenance, defensive and aggressive ETF model portfolios with all the ticker symbols and other details for US as well as EU investors.
A weekly Probability Map, that shows likely future stock returns over different time horizons, that is aimed at active traders.

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