1. Definition

  • A risk forecast is a prediction about the probability and potential impact of adverse outcomes.
  • Unlike a standard forecast (which predicts the “most likely” future), a risk forecast focuses on tail events (worst-case or low-probability but high-impact scenarios).

In short: not just “what will happen?” but “how bad could it get, and with what probability?”

2. Key Characteristics

  • Based on probabilistic forecasting (not just point forecasts).
  • Often expressed as quantiles or distributions that highlight risk levels.
  • Emphasizes uncertainty and extremes, rather than averages.

3. Examples

Finance

  • Value-at-Risk (VaR):
    • The maximum expected loss at a given confidence level (e.g., 5% quantile of returns).
    • Example: “1-day 5% VaR = –\$10M” → 5% chance of losing more than \$10M in a day.
  • Expected Shortfall (Conditional VaR):
    • The expected loss if losses exceed the VaR.

Weather & Natural Hazards

  • Hurricane forecasts:
    • Not just average path, but probabilities of wind speed exceeding thresholds.
  • Flood risk forecasts:
    • Probability that water level > danger level within 7 days.

Energy & Infrastructure

  • Electricity demand risk forecast:
    • Probability of demand exceeding system capacity.
  • Grid management uses tail forecasts for blackout prevention.

Healthcare / Epidemiology

  • Forecasting probability of extreme patient loads (hospital overflow).
  • Pandemic modeling: probability of exceeding a threshold of daily infections.

4. Methods Used

  • Quantile forecasts: estimate tails (e.g., 5th or 95th percentile).
  • Full distribution forecasts: model the entire outcome distribution.
  • Extreme value theory (EVT): specialized for modeling rare events.
  • Bayesian approaches: posterior predictive distributions naturally quantify risk.
  • Simulation & stress testing: generating scenarios under different assumptions.

5. Evaluation of Risk Forecasts

  • Pinball Loss (quantiles): evaluates accuracy of quantile risk levels.
  • CRPS: measures distributional accuracy.
  • Backtesting (finance): check if actual extreme losses exceed VaR more often than expected.
  • Calibration: ensure “5% probability events” actually happen ~5% of the time.

6. Why Risk Forecasts Matter

  • Traditional forecasts may look good on average but miss rare but costly events.
  • Risk forecasts guide decision-making under uncertainty:
    • Banks → capital reserves.
    • Energy → safety capacity.
    • Governments → disaster response.

Summary:
A risk forecast focuses on predicting uncertain and extreme outcomes rather than just averages. It is probabilistic, often expressed through quantiles (VaR, Expected Shortfall) or full distributions, and is crucial in finance, weather, energy, and healthcare. Evaluation uses proper scoring rules and backtesting to ensure risks are neither underestimated nor exaggerated.