Sharpe Ratio

Overview

The Sharpe Ratio measures risk‑adjusted return — how much excess return a portfolio generates for each unit of volatility. It connects return and risk into a single, intuitive number.

ClearLedger Analytics computes the Sharpe Ratio deterministically using excess average return and excess standard deviation, both derived from daily log excess returns and annualized using √252. This produces a stable, reproducible, transparent measure of risk‑adjusted performance.

1. What the Sharpe Ratio Represents

The Sharpe Ratio answers one question:

“How efficiently did this portfolio convert risk into return?”

Interpretation:

• Sharpe > 1.0 → strong risk‑adjusted performance

• Sharpe ≈ 1.0 → balanced, acceptable performance

• Sharpe < 1.0 → weak risk‑adjusted performance

• Sharpe < 0 → portfolio underperformed the risk‑free rate

The Sharpe Ratio is not about total return — it is about return per unit of risk.

2. Conceptual Definition

Sharpe Ratio represents the amount of excess return earned per unit of excess risk.

It isolates the portion of performance driven by efficient use of volatility, not just raw return.

3. ClearLedger Analytics Deterministic Implementation

ClearLedger Analytics computes the Sharpe Ratio using a precise, institutional‑grade method based on daily log excess returns.

Step‑by‑Step Calculation:

• Compute daily log excess returns — asset return minus risk‑free rate.

• Average the daily log excess returns — produces the mean excess return.

• Annualize the average excess return — using deterministic ClearLedger Analytics scaling.

• Compute excess standard deviation — standard deviation of daily log excess returns.

• Annualize excess standard deviation — using √252 scaling.

• Divide annualized excess return by annualized excess standard deviation — produces the final Sharpe Ratio.

Formula (ClearLedger Analytics implementation):

Sharpe Ratio = [Excess Avg Return] / [Excess StdDev]

This aligns with standard institutional risk‑engine practices while remaining fully deterministic and reproducible.

4. Why Sharpe Matters

The Sharpe Ratio helps advisors explain:

• whether the portfolio’s return justified the risk taken

• how efficiently the portfolio used volatility

• why two portfolios with similar returns may have different risk profiles

• how optimization improves risk‑adjusted performance

Clients understand Sharpe intuitively:

“For every unit of risk you took, you earned X units of return.”

It’s simple, powerful, and easy to communicate.

5. What Drives the Sharpe Ratio

The Sharpe Ratio changes when:

• volatility rises or falls

• diversification improves

• correlations shift

• weights change

• high‑conviction positions outperform or underperform

• the risk‑free rate changes

Sharpe is a portfolio‑level metric — not a security‑level metric — because risk is a property of the entire portfolio.

6. Sharpe Ratio in Optimization

ClearLedger Analytics uses the Sharpe Ratio to:

• evaluate optimized vs current portfolios

• highlight risk‑adjusted improvements

• support advisor explanations

• quantify the impact of weight changes

• show how diversification reduces volatility

The Sharpe Ratio is one of the clearest ways to demonstrate the value of optimization.

7. Sharpe Ratio vs Other Metrics

The Sharpe Ratio complements:

• Alpha → value added beyond market movement

• Beta → systematic risk

• Volatility → total risk

• Sortino Ratio → downside‑risk‑adjusted return

Sharpe is the most balanced, all‑purpose risk‑adjusted metric.

Conclusion

The Sharpe Ratio measures how effectively a portfolio converts risk into return.

ClearLedger Analytics computes Sharpe using deterministic excess‑return math, giving advisors a precise, transparent measure of risk‑adjusted performance.

This makes performance evaluation simple, explainable, and actionable.