ATLASRecovery probability
Investing glossary · Models and probabilities
The chance that a stock which has fallen climbs back to a previous level, such as its high or your purchase price, within a given time.
Definition
Recovery probability answers the least comfortable question in investing: if I am down, what is the chance the stock gets back to where it was within a certain time? Mathematically it is a "first-passage" probability: the chance that the price touches a target level at any time before a deadline, not only at the end.
It depends on three things: how far the price must climb, how volatile the stock is, and how much time you allow. A bigger gap makes recovery less likely, a higher volatility makes it more likely to touch the level (and to fall further), and more time helps. A model can give an honest number, but it cannot say whether the reasons for the fall have gone away.
Formula
P(reach H within T) = Φ((−b+νT)/(σ√T)) + e^(2νb/σ²) · Φ((−b−νT)/(σ√T)), b = ln(H/S), ν = μ − σ²/2
H = target (e.g. the previous high), S = current price, b = ln(H ÷ S), μ = drift, σ = volatility, ν = μ − σ²/2, T = time in years, Φ = standard normal cumulative distribution.
Worked example
Nike (NKE) is 46% below its 52-week high of $69.14: it would need to gain 84% to get back there. With an annual volatility of 29% and a long-run drift of 7%, the chance that it touches that high at some point within a year is about 4%.
This is a probability of touching the level, not of staying above it; and it assumes the past volatility is a fair guide to the next twelve months.
How ATLAS uses it
The Recovery product in ATLAS applies exactly this calculation to your own purchase price or to a stock's high, so you see the odds instead of a hope.
Related in ATLAS: Recovery →Browse all ATLAS tools →See it on a real stock
The example above uses these companies. Open their pages for the full numbers:
Frequently asked questions
Does a stock that fell always recover?
No. Many do not return to the old high for years, and some never do. The probability depends on the size of the fall, the volatility and the time allowed.
What is a first-passage probability?
The chance that a random process touches a given level at least once before a deadline. It is higher than the chance of simply being above that level at the deadline.
Related terms
Put the idea to work on your own stocks
Open any company in ATLAS to see its fair value, its odds of rising and its risk numbers side by side.
Try ATLAS →Not investment advice. ATLAS estimates are produced by statistical models from public data; they can be wrong and past performance does not predict future results. Consider your own situation before investing. Disclaimer