# Probability of Breaching Price Target

How often should a stock go above our upside target or below our downside target? In this article, Alpha Theory CEO Cameron Hight discusses his insights on probabilistic fundamental investing.

How Often Should I Be Wrong?

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).

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?

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?

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.

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.

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.