Probability-Weighted Investing
Value investments by weighing bear, base, bull, and black-swan outcomes
- Difficulty
- Advanced
- Time to result
- ~ongoing to results
- Steps
- 6
- Confidence
- 97%
Probability-Weighted Investing begins by rejecting certainty about the future and replacing a single forecast with a distribution of outcomes. The investor defines bear, base, and bull cases, adds relevant black-swan possibilities, estimates the value under each case, and assigns an evidence-based probability to each. Multiplying each outcome by its probability produces an expected value that can be compared with the current market price. The mechanism also explains why prices move: new information changes investors' collective probability estimates, sometimes too much and sometimes too little. The framework is especially useful in complex situations because careful scenario construction can reveal opportunities that investors avoiding uncertainty or detail have mispriced.
Origin
Dan Chung linked the method to the probability theory background he absorbed from his father, a professor of probability theory, and to Alger Asset Management's fundamental investment process.
Core principles
- 01Nobody can reliably predict the future
- 02Investment outcomes form a range rather than a point estimate
- 03Market prices aggregate participants' changing probabilities
- 04Upside matters only when weighed against downside and extreme events
- 05Complexity can create opportunity when others avoid the analysis
How to run it
- 1
Reject the point forecast
Start from the assumption that nobody knows the future with certainty. Frame the investment as a range of possible outcomes rather than one predicted result.
Pro tip Treat unusually confident forecasts as claims requiring stronger evidence, not as safer estimates.
Watch out Do not disguise a preferred outcome as the only realistic forecast.
- 2
Construct the core cases
Describe distinct bear, base, and bull cases using operational assumptions such as demand, margins, competition, and capital needs. Estimate the asset value under each case.
Pro tip Make the cases internally consistent rather than merely changing the valuation multiple.
Watch out Cases that differ only cosmetically will understate uncertainty.
- 3
Add extreme scenarios
Identify low-probability events that could materially alter the investment, including technological disruption, regulation, financing failure, or unexpected breakthroughs.
Pro tip Include both harmful and beneficial surprises where appropriate.
Watch out Do not use the black-swan label for routine volatility already represented in the core cases.
- 4
Assign probabilities
Give each scenario an explicit probability based on available evidence, comparable situations, and base rates. Ensure the probabilities sum to 100 percent.
Pro tip Record why each probability was chosen so it can be challenged and updated.
Watch out False numerical precision can conceal weak assumptions.
- 5
Calculate expected value
Multiply each scenario value by its probability and sum the results. Compare this probability-weighted value with the market price and required margin of safety.
Pro tip Test how sensitive the conclusion is to modest probability changes.
Watch out A high expected value can still conceal an unacceptable chance of permanent loss.
- 6
Update as facts change
Revise scenarios, values, and probabilities when material information arrives. Distinguish genuine fundamental changes from temporary shifts in market sentiment.
Pro tip Keep the original model to see whether changing conviction reflects facts or emotion.
Watch out Do not change probabilities solely to rationalize price movement.
In the wild
An investor models a bear case in which growth falls sharply, a base case in which customer demand remains durable, and a bull case in which geopolitical threats accelerate adoption. A low-probability competitive disruption case is added. After weighting each valuation, the expected value remains above the depressed market price, but the investor waits for sufficient downside protection before increasing the position.
→ The decision reflects both long-term upside and the possibility of further near-term deterioration.
A pharmaceutical and agricultural company faces uncertain litigation liabilities alongside improving operating prospects. The investor separates the remaining legal downside, a normalized base case, and a stronger agricultural-cycle outcome, then updates probabilities as liabilities become better defined.
→ Shrinking uncertainty can reveal value before every legal case is resolved.
Common mistakes
Treating the base case as certain
A base case is the most representative scenario, not a guaranteed forecast. Ignoring the tails defeats the framework's purpose.
Assigning probabilities by instinct alone
Probabilities should be tied to evidence, base rates, and explicit assumptions. Unsupported numbers create an illusion of rigor.
Ignoring changes after purchase
Scenario weights must change when facts change. Anchoring to the original model can turn disciplined analysis into rationalization.
Is it for you?
Best for
It is best for fundamental investors evaluating companies with several plausible operating or valuation paths.
Not ideal for
It is not ideal for decisions where no credible scenarios, valuation ranges, or evidence-based probabilities can be developed.
From the transcript
“investing is basically first recognizing that nobody knows anything about the future.”
“So the only way really do pro at least from my perspective and algers, is where the probabilities of a bearer case, the base case,…”
“the price of of any asset in the stock market is essentially the combined probabilities of everybody bullish, bearish, neutral, ignorant, highly informed insiders outsiders.”
From the episode
Daniel C. Chung on Probability Theories for Investors
Daniel C. Chung