Interpreting Probability and Value at Risk (VaR) Results
Monte Carlo simulation produces rich probabilistic outputs that require careful interpretation. Unlike single-number forecasts, these results describe ranges of possible outcomes with associated likelihoods. Understanding how to read and apply them separates sophisticated investors from those relying on hope or hype.
The simulation provides multiple perspectives on potential futures rather than one predicted path. Each metric tells part of the risk/reward story.
Probability of Success
This percentage shows how many simulated paths reached your target return. A 70% probability of doubling your money in one year suggests reasonable odds, while 15% indicates a long-shot bet. Context matters—high probability often comes with modest returns, while moonshot targets have low success rates.
Probability helps calibrate position sizing. Higher confidence outcomes can support larger allocations, while low-probability high-reward scenarios warrant smaller bets.
Expected Value and Median
Expected value is the average outcome across all simulations. In skewed cryptocurrency returns, it can be heavily influenced by rare but massive upside scenarios. Median outcome—the middle result when sorted—often provides a more realistic "typical" case.
When expected value significantly exceeds median, it signals positive skew: most outcomes are modest but occasional explosive wins pull the average higher.
Value at Risk Interpretation
95% VaR indicates the loss level that was exceeded in only 5% of simulations. If VaR shows potential 80% drawdown, you know extreme downside is possible even if unlikely. This metric quantifies tail risk crucial for capital preservation.
Best and worst case extremes show the full range of simulated possibilities, reminding investors that both extraordinary gains and losses remain within the realm of possibility.
Practical Decision Framework
Use probability for confidence assessment, expected value for theoretical edge calculation, VaR for risk budgeting, and median for planning realistic scenarios. No single number tells the whole story—together they provide comprehensive insight.
FAQ
Should I only take high-probability trades?
Not necessarily—portfolio construction often includes some low-probability high-reward positions for asymmetry.
What does negative expected value mean?
On average, the position loses money—though positive tail outcomes might still justify small allocation.
How often are extreme outcomes realized?
By definition rarely, but cryptocurrency markets have shown they occur more frequently than many models predict.
Probability is the language of rational investing.