Probability of Breaching Price Target

How Often Should I Be Wrong?

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That was the basic question a client asked me last week. More specifically, they asked how often a stock should go above our upside target or below our downside target. (TLDR: It should happen at a rate of 50% of the Upside and Downside Probability – a 40% probability upside case should be breached 20% of the time).

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I knew the answer shouldn’t be 0% because that would imply a range of outcomes that was way too wide to be useful. But should it be 10%? 20%? More?

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For example, where will AAPL be in one year (currently ~$150)? If you give a range of $0 to $1,000, you’re not giving a lot of information, but you are almost certain to be right. A range of $110 to $225 is more meaningful but more likely to be wrong. How often should you be wrong?

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That depends on the forecast. Let’s use an example where an analyst forecasts five scenarios.

Imagine each of the areas between the targets is a bin with a cumulative probability. We’re trying to figure out bins #1 and #6 to tell us the probability of going below our lowest target, $20, and the probability of going above our highest target, $100.

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Step 1 is to figure out the cumulative probabilities in bins 2-5. $20 is a 10% probability, and $40 is a 20% probability, so the cumulative probability in bin 2 is 15% (avg (10%,20%)). Do that for each bin and you get a Sum of Bins of 90%, meaning that there is a 10% chance that the ultimate price should be outside the Upside or Downside targets.

Then, to figure out the Upside vs. the Downside, you allocate a 10% probability on a pro rata basis to each. Since the analyst assigned a probability of Upside and Downside of 10%, then the 10% probability of a breach of the Upside or Downside is split equally between the two.

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Here’s another example with different probabilities. Because the probability of Downside is 10% and Upside is 15%, the probability of a breach is skewed towards the Upside at 7.5% vs. the 5% probability of a Downside breach.

And a final example using a standard probability distribution for clients using Bear 30%, Base 50%, and Bull scenario of 20%. In this case, the probability of a Downside breach is 15% and 10% for the Upside. The portfolio manager should expect, in this case, that 25% of prices should fall outside of the range of forecasted outcomes with a slight skew towards the downside (15%).

Great questions are invaluable. Our clients ask many of them, allowing Alpha Theory and CenterBook Partners to continually push the knowledge of probabilistic fundamental investing.

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