Our Core Innovation
A fundamentally different approach to portfolio construction that accounts for the extreme events traditional models dangerously ignore.
The Critical Flaw
Modern Portfolio Theory (MPT), the foundation of virtually every portfolio optimization tool used today, assumes market returns follow a Gaussian (bell curve) distribution. This assumption is mathematically convenient — and catastrophically wrong.
Real market returns have "fat tails" — extreme events occur far more frequently than the bell curve predicts. The result? Traditional risk models systematically and dangerously underestimate the probability of market crashes, liquidity crises, and volatility spikes.
When your portfolio optimization framework cannot even acknowledge that a crash is possible, it certainly cannot protect you from one. Here is how badly the Gaussian model has failed at predicting real-world events:
Source: Analysis by Ron Piccinini, Ph.D., Head of Research at Dreams Investment Solutions. Past market events are not indicative of future results.
The HTO Solution
Heavy-Tail Optimization uses the Student-t distribution instead of the Gaussian. The Student-t distribution has heavier tails, meaning it assigns realistic probabilities to extreme market events — and optimizes portfolios accordingly.
Instead of pretending that crashes are statistically impossible, HTO builds portfolios that are prepared for them. The optimization target is not the Sharpe ratio — which relies on the same flawed Gaussian assumptions — but Expected Tail Loss (ETL), a measure that captures the average loss in the worst-case scenarios.
The result is a portfolio that may look similar to a traditional MPT portfolio in calm markets, but behaves very differently when markets turn violent. That difference is where HTO earns its edge.
“The Gaussian framework tells you the 2020 crash should happen once every 33.9 million years. We build portfolios that are ready for it to happen next Tuesday.”
Risk Measurement
Two fundamentally different ways to think about portfolio risk — and why the difference matters when markets crash.
ETL, also known as Conditional Value at Risk (CVaR), measures the average loss in the worst scenarios — typically the worst 5% of outcomes. Unlike the Sharpe ratio, ETL does not assume symmetry in returns. It specifically focuses on the left tail of the distribution, where the most damaging losses live.
By optimizing for ETL, HTO explicitly minimizes the expected damage from extreme drawdowns. This is the metric that actually matters when markets crash — and it is the cornerstone of our portfolio construction process.
The Sharpe ratio measures return per unit of volatility (standard deviation). The problem? Standard deviation treats upside and downside volatility equally and assumes returns are normally distributed. A portfolio that occasionally spikes upward is "penalized" the same as one that crashes.
HTO uses the Student-t distribution, which has heavier tails than the Gaussian. This means our portfolio allocations account for extreme events that occur far more frequently than normal models predict — without sacrificing return potential in normal markets.
Ready to Learn More?
Contact our team to learn how Heavy-Tail Optimization can improve risk management for your clients' portfolios.