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#153: Probability Does Not Equal Profitability

#153: Probability Does Not Equal Profitability

micksonmatch
September 26, 2024

S2N Spotlight

A few days ago, I produced a chart that showed the probability of an asset maintaining its current performance using the Z-Score as the indicator. The Z-Score in our case is the monthly rolling 12-month return less its mean, divided by the standard deviation of the return. To calculate the probability, we use a normal distribution of the cumulative distribution function of Z-Scores. Here is the Python code:

data['Z-Score'] = (data['YOY'] - mean_return) / std_dev_return
data['Probability'] = 1 - norm.cdf(data['Z-Score'])

With the SP500 in the chart below, we have a Z-Score producing a probability of 6.65% that the current price action will remain at its current levels. This is a low probability because the current return is significantly higher than its mean, producing a high Z-Score and, in turn, a low probability of remaining above average. Picture it like stretching an elastic band; eventually you will grow tired of holding the band stretched out as you are fighting its natural tension.

This is where things get a little interesting. Yesterday I used regression analysis to make the point that investing when markets are overvalued will produce below-average returns versus investing when markets are undervalued. This seems so obvious. What is not so obvious is that investing in the real world following a linear time horizon doesn’t necessarily produce the returns that you think. Let’s dig in a bit.

I created a backtest. I am not trying to create an optimised strategy. I am simply following the principle of investing when there is an 80% chance or more that price action will be above average, implying current price action is underperforming. I sell when there is a 20% chance or less of the price action continuing to be above average, implying the current price action is overperforming.

The surprising part is you are much better off buying and holding versus trying to time the market. You can see the numbers on the chart. The Z-Score strategy produces a Sharpe Ratio of 0.27 versus 0.58 for buy and hold, which is more than double the risk-adjusted return.

I applied the same backtest criteria to gold and got an even worse performance result.

I am not suggesting that you cannot use these indicators to build a better strategy. What is clear for the eye to see in the above 2 examples is that this strategy tends to miss out on many of the big moves. If you think it is better to make the buy and sell probability thresholds less extreme, you are wrong as well.

If your head is now spinning, that is not a bad thing; I think it makes us better traders / investors to respect how hard it is to beat buy and hold or time the market.

S2N Observations

I couldn’t help but notice a story in the Wall Street Journal today.

Google wrote Character a check for around $2.7 billion, according to people with knowledge of the deal. The official reason for the payment was to license Character’s technology. But the deal included another component: Shazeer agreed to work for Google again.

Within Google, Shazeer’s return is widely viewed as the primary reason the company agreed to pay the multibillion-dollar licensing fee.

Shazeer was one of Google’s early hires and regarded as an AI genius. He left the company because they didn’t put one of his projects into production. This kind of excessive spending is a warning sign to me that the whole AI complex is getting too far ahead of itself.

Staying on topic, the rumour in the WSJ is that Open AI is about to become a for-profit company and give Sam Altman 7%. I am not too sure what to make of this. I am all for capitalism so no problem there. I just think once again this whole AI complex is becoming something bigger than it is.

Another story that caught my eye was the financial trouble Sotheby’s is in. Apparently the billionaire new owner of Sotheby’s has a penchant for leverage. Turnover at the luxury auctioneer is down significantly this year, causing major cash flow problems. Some managers were getting their bonuses in the form of IOU’s. You can see that the companies bond price was trading at nearly 70 cents on the dollar before the Abu Dhabi sovereign wealth fund stepped in. Maybe this is another early warning sign that the excessive spending on the back of excessive monetary stimulation is over and there may be some high-profile casualties to come.

I got quite a lot of interested feedback when I included Ray Dalio’s 10-year GDP forecast for major nations. I don’t yet have the report in full, but here is another brilliant visualisation by Visualist Capital