πŸ“Mathematical Foundations: The Sharpe Ratio

Why Is the Sharpe Ratio Our Primary Benchmark?

At Bitronix, we prioritize risk-adjusted return. The Sharpe Ratio β€” the ratio of average return to the standard deviation (volatility) of that return β€” is our primary metric for strategy quality.

A higher Sharpe Ratio signifies:

  • A smoother growth curve for your investments.

  • A higher statistical probability of achieving positive returns over any given time period.

Probability and the Sharpe Ratio

For a strategy with a Sharpe Ratio of 1, the probability of positive annual returns is approximately 84%. Over three years, this probability increases to ~96%. For comparison: the traditional "Buy & Hold" strategy for the S&P 500 index has demonstrated a Sharpe Ratio of approximately 0.3–0.4 over decades.

From Theory to Portfolio Mathematics

The strength of our uncorrelated ensemble is mathematically proven. The aggregate Sharpe ratio (S) for N strategies is calculated using the formula:

Where Ś is average Sharpe ratio of individual strategies, and Δ‡ is their average correlation coefficient.

With N=1000 and Δ‡ =0,01, the portfolio's Sharpe ratio is multiplied. This allows us to construct a portfolio with a high Sharpe ratio from many components, each of which has a modest individual metric.

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