finance calculator

Risk-Adjusted Return Calculator

Calculate Sharpe, Sortino, Treynor, Jensen's Alpha, and Information ratios to evaluate portfolio performance.

Formula Verified by Dr. Elizabeth Vance, PhD

Quick actions: Save inputs, view saved runs, print, share, or export results

Saved Runs

Inputs

Portfolio Returns

Portfolio Return (%)%

Risk-Free Rate (%)%

Portfolio Beta

Risk & Benchmark Metrics

Standard Deviation (Vol %)%

Downside Deviation (%)%

Benchmark Return (%)%

Tracking Error (%)%

Results

Sharpe Ratio

0.567

Sortino Ratio

0.850

Treynor Ratio7.727

Jensen's Alpha190.00%

Information Ratio0.714

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Portfolio returns are only half the story. Save this page to verify if your investment returns justify their risk profile when volatility or rates adjust.

Formula

Sharpe Ratio formula

\text{Sharpe} = \frac{R_p - R_f}{\sigma_p}

Standardizes excess returns using total portfolio volatility.

Step by step

How the calculation works

1Enter annual portfolio return and risk-free interest rate.
2Input standard deviation (total risk) and downside deviation.
3Define the portfolio Beta and the benchmark returns.
4Review Sharpe, Sortino, Treynor, Jensen's Alpha, and Information ratios.

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Learn more about this calculation

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ROI Calculation: Formula, Annualized Return, and Examples

Calculate ROI and annualized return with total costs included, compare opportunities consistently, and understand what a simple ROI result leaves out.

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Understanding Calculator Formulas: How DTC Turns Inputs into Results

Understand how Do The Calculation formulas are presented, what the explanation blocks mean, and how to verify calculator logic before using a result in a real decision.

How to understand and use this calculator

Why Risk-Adjusted Return Matters

Evaluating investment performance solely by raw percentage return is incomplete. A portfolio that gains 15% with massive volatility and drawdown exposure may be less efficient than a portfolio that gains 12% with steady, low-risk growth.

Risk-adjusted return metrics standardize investment returns by factoring in risk (either total volatility, downside volatility, or systematic market risk), allowing analysts to compare different portfolios or asset managers fairly.

Total Volatility Metrics: Sharpe and Sortino Ratios

The Sharpe and Sortino ratios measure excess return per unit of portfolio volatility.

Sharpe Ratio: Standardizes excess return by the portfolio's total risk (standard deviation):

$$\text{Sharpe Ratio} = \frac{R_p - R_f}{\sigma_p}$$

Where $R_p$ is the portfolio return, $R_f$ is the risk-free rate, and $\sigma_p$ is the standard deviation of portfolio returns.

Sortino Ratio: Standardizes excess return by downside deviation (ignoring positive volatility since investors only fear losses):

$$\text{Sortino Ratio} = \frac{R_p - R_f}{\sigma_{d}}$$

Where $\sigma_d$ is the downside standard deviation (semi-standard deviation of negative excess returns).

Systematic Risk and Alpha: Treynor and Jensen's Alpha

These metrics relate portfolio performance to systematic market risk (Beta).

Treynor Ratio: Measures excess return per unit of systematic risk:

$$\text{Treynor Ratio} = \frac{R_p - R_f}{\beta_p}$$

Where $\beta_p$ is the portfolio Beta, representing its sensitivity to market movements.

Jensen's Alpha ($\alpha$): Measures the portfolio's excess return above what is predicted by the Capital Asset Pricing Model (CAPM):

$$\alpha = R_p - [R_f + \beta_p (R_m - R_f)]$$

Where $R_m$ is the benchmark market return. A positive Alpha indicates the portfolio manager has generated excess return through active selection.

Active Performance: Information Ratio

The Information Ratio measures active return relative to a benchmark per unit of active risk (tracking error):

$$\text{Information Ratio} = \frac{R_p - R_b}{\text{Tracking Error}}$$

Where $R_b$ is the benchmark return, and tracking error is the standard deviation of the differences between portfolio and benchmark returns.

Related concepts

Sharpe Ratio

Excess return divided by total portfolio return volatility.

Sortino Ratio

Excess return divided by downside portfolio return volatility.

Jensen's Alpha

The active outperformance of a portfolio relative to CAPM expectations.

Frequently Asked Questions

What is a good Sharpe Ratio?+

A Sharpe ratio above 1.0 is considered good, as it indicates the portfolio generates excess return relative to its volatility. A ratio above 2.0 is very good, and above 3.0 is excellent.

Why is the Sortino ratio preferred for asymmetric returns?+

The Sortino ratio only penalizes downside volatility. If a portfolio has large positive spikes (which increases standard deviation but benefits the investor), the Sharpe ratio falls, while the Sortino ratio remains high.

What is Beta in finance?+

Beta measures a portfolio's sensitivity to market movements. A Beta of 1.0 means the portfolio moves in sync with the market. A Beta of 1.5 means it is 50% more volatile than the market.

How is Jensen's Alpha interpreted?+

A positive Alpha (e.g., +2.0%) means the portfolio outperformed its risk-adjusted benchmark by 2.0%. A negative Alpha means it underperformed relative to the risk assumed.

What is risk-free rate?+

The risk-free rate is the rate of return on an investment with no risk of default, standardly represented by US Treasury bill yields.

What is standard deviation in portfolio returns?+

Standard deviation measures the dispersion of returns from the mean. A higher standard deviation indicates greater historic price volatility.

What is tracking error?+

Tracking error measures the volatility of the excess returns of a portfolio relative to its benchmark, indicating how closely the portfolio mirrors the index.

How does risk-adjusted return help in diversification?+

It helps identify assets that add return without increasing total portfolio risk, improving the portfolio's overall efficiency (moving it toward the efficient frontier).

What is downside deviation?+

Downside deviation is a variation of standard deviation that only measures the volatility of returns that fall below a minimum acceptable return or risk-free rate.

What is the Information Ratio used for?+

The Information Ratio is used to evaluate active fund managers, measuring their ability to consistently beat a benchmark relative to the active risk they take.

How to understand and use this calculator

Why Risk-Adjusted Return Matters

Total Volatility Metrics: Sharpe and Sortino Ratios

The Sharpe and Sortino ratios measure excess return per unit of portfolio volatility.

Sharpe Ratio: Standardizes excess return by the portfolio's total risk (standard deviation):

$$\text{Sharpe Ratio} = \frac{R_p - R_f}{\sigma_p}$$

Where $R_p$ is the portfolio return, $R_f$ is the risk-free rate, and $\sigma_p$ is the standard deviation of portfolio returns.

Sortino Ratio: Standardizes excess return by downside deviation (ignoring positive volatility since investors only fear losses):

$$\text{Sortino Ratio} = \frac{R_p - R_f}{\sigma_{d}}$$

Where $\sigma_d$ is the downside standard deviation (semi-standard deviation of negative excess returns).

Systematic Risk and Alpha: Treynor and Jensen's Alpha

These metrics relate portfolio performance to systematic market risk (Beta).

Treynor Ratio: Measures excess return per unit of systematic risk:

$$\text{Treynor Ratio} = \frac{R_p - R_f}{\beta_p}$$

Where $\beta_p$ is the portfolio Beta, representing its sensitivity to market movements.

Jensen's Alpha ($\alpha$): Measures the portfolio's excess return above what is predicted by the Capital Asset Pricing Model (CAPM):

$$\alpha = R_p - [R_f + \beta_p (R_m - R_f)]$$

Where $R_m$ is the benchmark market return. A positive Alpha indicates the portfolio manager has generated excess return through active selection.

Active Performance: Information Ratio

The Information Ratio measures active return relative to a benchmark per unit of active risk (tracking error):

$$\text{Information Ratio} = \frac{R_p - R_b}{\text{Tracking Error}}$$

Where $R_b$ is the benchmark return, and tracking error is the standard deviation of the differences between portfolio and benchmark returns.

Related concepts

Sharpe Ratio

Excess return divided by total portfolio return volatility.

Sortino Ratio

Excess return divided by downside portfolio return volatility.

Jensen's Alpha

The active outperformance of a portfolio relative to CAPM expectations.

Frequently Asked Questions

What is a good Sharpe Ratio?+

A Sharpe ratio above 1.0 is considered good, as it indicates the portfolio generates excess return relative to its volatility. A ratio above 2.0 is very good, and above 3.0 is excellent.

Why is the Sortino ratio preferred for asymmetric returns?+

What is Beta in finance?+

Beta measures a portfolio's sensitivity to market movements. A Beta of 1.0 means the portfolio moves in sync with the market. A Beta of 1.5 means it is 50% more volatile than the market.

How is Jensen's Alpha interpreted?+

A positive Alpha (e.g., +2.0%) means the portfolio outperformed its risk-adjusted benchmark by 2.0%. A negative Alpha means it underperformed relative to the risk assumed.

What is risk-free rate?+

The risk-free rate is the rate of return on an investment with no risk of default, standardly represented by US Treasury bill yields.

What is standard deviation in portfolio returns?+

Standard deviation measures the dispersion of returns from the mean. A higher standard deviation indicates greater historic price volatility.

What is tracking error?+

Tracking error measures the volatility of the excess returns of a portfolio relative to its benchmark, indicating how closely the portfolio mirrors the index.

How does risk-adjusted return help in diversification?+

It helps identify assets that add return without increasing total portfolio risk, improving the portfolio's overall efficiency (moving it toward the efficient frontier).

What is downside deviation?+

Downside deviation is a variation of standard deviation that only measures the volatility of returns that fall below a minimum acceptable return or risk-free rate.

What is the Information Ratio used for?+

The Information Ratio is used to evaluate active fund managers, measuring their ability to consistently beat a benchmark relative to the active risk they take.

Risk-Adjusted Return Calculator

Inputs

Portfolio Returns

Risk & Benchmark Metrics

Results

Bookmark this Risk-Adjusted Tool

Sharpe Ratio formula

How the calculation works

Learn more about this calculation

ROI Calculation: Formula, Annualized Return, and Examples

Understanding Calculator Formulas: How DTC Turns Inputs into Results

Risk-Adjusted Return Calculator

Inputs

Portfolio Returns

Risk & Benchmark Metrics

Results

Bookmark this Risk-Adjusted Tool

Key output metrics

Ratios Comparison

How to understand and use this calculator

Why Risk-Adjusted Return Matters

Total Volatility Metrics: Sharpe and Sortino Ratios

Systematic Risk and Alpha: Treynor and Jensen's Alpha

Active Performance: Information Ratio

Related concepts

Frequently Asked Questions

Sharpe Ratio formula

How the calculation works

Learn more about this calculation

ROI Calculation: Formula, Annualized Return, and Examples

Understanding Calculator Formulas: How DTC Turns Inputs into Results

Key output metrics

Ratios Comparison

How to understand and use this calculator

Why Risk-Adjusted Return Matters

Total Volatility Metrics: Sharpe and Sortino Ratios

Systematic Risk and Alpha: Treynor and Jensen's Alpha

Active Performance: Information Ratio

Related concepts

Frequently Asked Questions