# Performance Ratios – Sharpe vs. Sortino vs. Treynor vs. Information vs. Bias

We look at the differences in various types of performance ratios:

We’ll also look at the concepts of Active Return and Active Risk.

## Key Takeaways: Performance Ratios – Sharpe vs. Sortino vs. Treynor vs. Information vs. Bias

• Sharpe Ratio: Measures the excess return per unit of total risk (standard deviation). Assesses risk-adjusted performance compared to a risk-free asset. Common for both single asset classes and overall portfolios.
• Sortino Ratio: Focuses on downside risk by measuring excess return per unit of downside deviation. Emphasizes harmful volatility.
• Treynor Ratio: Assesses returns earned above the risk-free rate per unit of market risk (beta).
• Information Ratio: Evaluates the active return of a portfolio relative to its benchmark, adjusted for the volatility of those excess returns.
• Omega Ratio: Measures the probability of achieving a threshold return. Focuses on entire distribution of returns rather than just mean and variance.
• Bias Ratio: The Bias Ratio is a financial metric that identifies valuation bias or price manipulation in investment portfolios by analyzing return distributions for abnormalities. Used most commonly in the subjective pricing of illiquid assets, such as private equity or private real estate.
• Active Risk: Represents the volatility of the active return relative to a benchmark.
• Active Return: The difference between a portfolio’s return and its benchmark’s return.

## Sharpe Ratio

The Sharpe Ratio, developed by Nobel laureate William F. Sharpe, is a measure used to assess the performance of an investment by adjusting for its risk.

It is calculated as the difference between the returns of the investment and the risk-free return, divided by the standard deviation of the investment returns, which represents total risk.

### Significance

This ratio is used in understanding how much excess return is being generated for the additional risk taken compared to a risk-free asset.

A higher Sharpe Ratio indicates better risk-adjusted performance.

It is still widely used in the asset management industry to understand value-additive performance.

For example, if a manager beats the index by 2x but is doing so with 2x the volatility, the risk-adjusted performance is the same.

## Sortino Ratio

The Sortino Ratio modifies the Sharpe Ratio by considering only downside risk (harmful volatility) instead of total risk.

It is computed as the difference between the portfolio’s return and the risk-free return, divided by the standard deviation of negative asset returns.

### Significance

This ratio is especially useful for traders/investors who are concerned about downside risk.

Unlike the Sharpe Ratio, the Sortino Ratio does not penalize positive volatility (volatility that leads to gains).

It focuses only on the negative variance.

## Treynor Ratio

Developed by Jack Treynor, this ratio measures the returns earned more than the risk-free rate per unit of market risk (beta).

It is calculated by subtracting the risk-free rate from the portfolio return and dividing by the portfolio’s beta.

### Significance

The Treynor Ratio is particularly informative in a diversified portfolio context, as it focuses on systemic risk.

It is most appropriate for portfolios that are well-diversified.

We also used the Treynor Ratio when looking at the following portfolio approaches:

## Information Ratio

The Information Ratio assesses the active return of a portfolio to its active risk.

Active return is the difference between the portfolio returns and the benchmark returns, and active risk is the standard deviation of this difference.

### Significance

This ratio is used for evaluating the skill of portfolio managers in generating excess returns relative to a benchmark, adjusting for the volatility of those excess returns.

## Omega Ratio

The Omega Ratio is a risk-return performance measure of an investment asset, portfolio, or strategy.

It’s calculated by dividing the probability-weighted gain above a minimum acceptable return by the probability-weighted loss below that threshold.

### Significance

The Omega Ratio is a more comprehensive measure as it accounts for the entire distribution of returns rather than just focusing on the mean and variance.

## Bias Ratio

The Bias Ratio is a financial metric used to detect valuation biases or price manipulation in investment portfolios.

It’s more popularly used by hedge fund managers, by analyzing the distribution of returns and identifying abnormalities that suggest biased pricing.

It is particularly effective in revealing the smoothing of returns through subjective pricing of illiquid assets.

Values deviating from 1 indicate the presence of such biases.

### Significance

This ratio helps in understanding whether reported returns are being manipulated.

## Active Return

Active Return refers to the difference in returns between a portfolio and its benchmark.

It represents the value added (or subtracted) by a portfolio manager’s trading/investment decisions.

### Significance

Active Return is a direct measure of a portfolio manager’s skill and effectiveness in generating returns that outperform the market benchmark.

Most common in mutual funds.

## Active Risk

Active Risk, also known as tracking error, is the standard deviation of the active returns.

It measures the volatility of a portfolio’s returns relative to its benchmark.

### Significance

Active Risk is used to gauge the consistency of a portfolio manager’s ability to achieve returns above or below the benchmark.

It reflects the degree of deviation from the benchmark performance.