Risk Adjusted Returns: Complete Guide to Formulas, Calculations & Performance Measures

What is risk adjusted return? Risk adjusted return is a measure that evaluates investment performance by accounting for the amount of risk taken to achieve those returns. Unlike simple returns that only show gains or losses, risk adjusted returns help investors understand if they're being adequately compensated for the risks they're taking.

In this comprehensive guide, you'll learn:

• The risk adjusted return formula and how to calculate it
• Key risk adjusted performance measures (Sharpe, Sortino, Treynor)
• How to calculate risk adjusted return on capital (RAROC)
• Practical examples with step-by-step calculations

What Is Risk Adjusted Return and Why Does It Matter?

Last month, I was reviewing a client's portfolio that had achieved a 15% annual return. On the surface, this seemed impressive—until we compared it to a benchmark that delivered 17% with less volatility. This real-world example illustrates why looking at returns in isolation can be misleading.

Risk-adjusted performance measures help investors:

• Compare investments with different risk profiles
• Identify investments that deliver the most return per unit of risk
• Make more informed decisions about portfolio construction
• Evaluate investment managers more effectively

Risk Adjusted Performance Measures: Key Metrics Explained

There are several risk adjusted performance measures used by professional investors. Here are the most important ones:

The Sharpe Ratio: The Risk Adjusted Return Formula

The Sharpe ratio, developed by Nobel laureate William Sharpe, is the most widely used risk adjusted return formula. It measures excess return per unit of total risk.

Risk Adjusted Return Formula (Sharpe Ratio):

Sharpe Ratio = (Investment Return - Risk-Free Rate) / Standard Deviation

Component	Description	Example
Investment Return	Total return of the investment	12%
Risk-Free Rate	Treasury bill yield	2%
Standard Deviation	Volatility of returns	10%
Sharpe Ratio	Risk adjusted return	1.0

How to interpret the Sharpe ratio:

• Sharpe ratio < 1.0: Suboptimal risk adjusted return
• Sharpe ratio 1.0-2.0: Good risk adjusted performance
• Sharpe ratio > 2.0: Excellent risk adjusted yield

Risk Adjusted Return Calculation Example

Let's walk through a risk adjusted return calculation comparing two mutual funds:

Fund	Return	Std Dev	Risk-Free Rate	Sharpe Ratio
Fund A	12%	10%	2%	(12-2)/10 = 1.0
Fund B	10%	7%	2%	(10-2)/7 = 1.14

Result: Fund B has better risk adjusted returns despite lower absolute returns.

The Sortino Ratio: Focusing on Downside Risk

While the Sharpe ratio treats all volatility equally, the Sortino ratio focuses only on downside volatility—the harmful kind that represents actual risk to investors.

Sortino Ratio = (Investment Return - Risk-Free Rate) / Downside Deviation

The Sortino ratio is particularly useful for:

• Evaluating investments with asymmetric return distributions
• Portfolios designed to capture upside volatility while minimizing downside risk
• Strategies that don't follow a normal distribution pattern

The Treynor Ratio: Measuring Systematic Risk

The Treynor ratio evaluates excess return relative to systematic risk (beta) rather than total risk.

Treynor Ratio = (Investment Return - Risk-Free Rate) / Beta

This metric is especially valuable when:

• Evaluating well-diversified portfolios where systematic risk dominates
• Comparing investments within the same asset class
• Assessing how well managers are compensated for taking market risk

Practical Implementation in Your Portfolio

Step 1: Gather the Necessary Data

To calculate risk-adjusted returns, you'll need:

• Historical returns for your investments (preferably monthly data over 3-5 years)
• The current risk-free rate (typically the yield on 3-month Treasury bills)
• Benchmark returns for the same period
• Software or spreadsheets capable of calculating standard deviation and beta

Step 2: Calculate and Interpret the Metrics

Let's walk through a practical example using a portfolio I recently analyzed:

Investment	Annual Return	Standard Deviation	Downside Deviation	Beta	Sharpe Ratio	Sortino Ratio	Treynor Ratio
Portfolio A	14.5%	12.0%	8.5%	0.95	1.04	1.47	13.16
S&P 500	13.0%	15.0%	10.2%	1.00	0.73	1.08	11.00

In this case, Portfolio A outperformed the S&P 500 on all risk-adjusted metrics, indicating superior risk management relative to returns.

Step 3: Make Informed Decisions

Based on risk-adjusted performance metrics, you can:

• Reallocate assets toward investments with higher risk-adjusted returns
• Evaluate whether active managers are truly adding value
• Determine if you're being adequately compensated for the risks you're taking
• Identify which investment strategies are most efficient at generating returns

Common Pitfalls to Avoid

1. Short-term focus: Risk-adjusted metrics are most meaningful over longer time periods (3+ years).
2. Ignoring changing market conditions: Metrics calculated during bull markets may not reflect performance during downturns.
3. Overlooking other factors: Risk-adjusted returns are important but shouldn't be the only consideration in investment decisions.
4. Using inappropriate benchmarks: Always compare investments to relevant benchmarks with similar risk characteristics.

Risk Adjusted Return on Capital (RAROC)

Risk adjusted return on capital (RAROC) is a metric commonly used by banks and financial institutions to measure profitability relative to the risk taken. It's essential for capital allocation decisions.

RAROC Formula

RAROC = (Revenue - Costs - Expected Losses) / Economic Capital

Component	Description
Revenue	Total income generated
Costs	Operating expenses
Expected Losses	Anticipated credit losses
Economic Capital	Capital required to cover unexpected losses

Example RAROC Calculation:

• Revenue: $10 million
• Costs: $3 million
• Expected Losses: $1 million
• Economic Capital: $50 million
• RAROC = (10 - 3 - 1) / 50 = 12%

A RAROC above the cost of capital indicates the activity is creating value.

Advanced Risk Adjusted Performance Measures

For those looking to deepen their understanding, consider these advanced risk adjusted performance measures:

Information Ratio

The Information Ratio measures active return divided by active risk (tracking error), showing how consistently a manager outperforms a benchmark.

Information Ratio = (Portfolio Return - Benchmark Return) / Tracking Error

Calmar Ratio

Particularly useful for evaluating investments with significant drawdown risk, such as hedge funds:

Calmar Ratio = Average Annual Rate of Return / Maximum Drawdown

Jensen's Alpha

This measures the excess return of a portfolio over what would be predicted by the Capital Asset Pricing Model (CAPM):

Alpha = Portfolio Return - [Risk-Free Rate + Beta × (Market Return - Risk-Free Rate)]

Implementing Risk-Adjusted Thinking in Your Investment Process

To truly benefit from risk-adjusted performance analysis:

1. Establish a consistent evaluation framework that includes multiple risk-adjusted metrics
2. Set appropriate expectations for different asset classes and investment strategies
3. Regularly review performance using both absolute and risk-adjusted measures
4. Make incremental adjustments rather than wholesale changes based on metrics
5. Consider the economic environment and how it might affect risk-adjusted performance

How to Calculate Risk Adjusted Return in Excel

You can easily calculate risk adjusted returns in Excel using these steps:

Step 1: Calculate Average Return

=AVERAGE(B2:B13)  // Monthly returns in column B

Step 2: Calculate Standard Deviation

=STDEV(B2:B13)  // Standard deviation of returns

Step 3: Calculate Sharpe Ratio (Risk Adjusted Return)

=(AVERAGE(B2:B13) - C1) / STDEV(B2:B13)  // C1 = risk-free rate

Pro Tip: Annualize monthly data by multiplying the average by 12 and standard deviation by √12.

Frequently Asked Questions About Risk Adjusted Returns

What is risk adjusted return in simple terms?

Risk adjusted return measures how much return an investment generates relative to the risk taken. A higher risk adjusted return means better performance per unit of risk.

What is a good risk adjusted return?

A Sharpe ratio above 1.0 is considered good, above 2.0 is excellent. For RAROC, any value above your cost of capital indicates value creation.

How do you calculate risk adjusted return?

The most common formula is the Sharpe ratio: (Investment Return - Risk-Free Rate) / Standard Deviation. This gives you the excess return per unit of volatility.

What's the difference between return and risk adjusted return?

Regular return only shows gains/losses. Risk adjusted return accounts for the volatility or risk taken to achieve those returns, giving a more complete picture of performance.

Conclusion: Mastering Risk Adjusted Returns

Understanding and applying risk adjusted return metrics transforms you from a return-chaser to a sophisticated investor who recognizes the crucial relationship between risk and reward. The key risk adjusted performance measures—Sharpe ratio, Sortino ratio, Treynor ratio, and RAROC—each provide unique insights into investment efficiency.

Remember: investing isn't about achieving the highest possible returns—it's about achieving the best risk adjusted returns for your risk tolerance. By mastering these risk adjusted return formulas and calculations, you gain powerful tools to navigate investing with greater confidence.

This article is for informational purposes only and does not constitute investment advice. Always conduct your own research or consult with a qualified financial advisor before making investment decisions.