Risk-Adjusted Return Calculator Formula
Understand the math behind the risk-adjusted return calculator. Each variable explained with a worked example.
Formulas Used
Sharpe Ratio
sharpe_ratio = std_deviation > 0 ? excess_return / std_deviation : 0Sortino Ratio
sortino_ratio = downside_dev > 0 ? excess_return / downside_dev : 0Excess Return
excess_ret = excess_returnReturn per Unit of Risk
return_per_unit = std_deviation > 0 ? portfolio_return / std_deviation : 0Variables
| Variable | Description | Default |
|---|---|---|
portfolio_return | Portfolio Annual Return(%) | 12 |
risk_free_rate | Risk-Free Rate(%) | 4 |
std_deviation | Standard Deviation (Volatility)(%) | 15 |
downside_dev | Downside Deviation(%) | 10 |
excess_return | Derived value= portfolio_return - risk_free_rate | calculated |
How It Works
Risk-Adjusted Performance
Raw returns do not tell the full story. A 15% return with 30% volatility may be worse than 10% with 10% volatility.
Sharpe Ratio
Sharpe = (Portfolio Return - Risk-Free Rate) / Standard Deviation
Sortino Ratio
Sortino = (Portfolio Return - Risk-Free Rate) / Downside Deviation
The Sortino ratio only penalizes downside volatility, which is more relevant since investors do not mind upside surprises.
Worked Example
12% return, 4% risk-free rate, 15% volatility, 10% downside deviation.
- 01Excess return = 12% - 4% = 8%
- 02Sharpe ratio = 8% / 15% = 0.53
- 03Sortino ratio = 8% / 10% = 0.80
- 04The Sortino is higher because downside deviation < total volatility
Frequently Asked Questions
What is a good Sharpe ratio?
A Sharpe ratio above 1.0 is considered good, above 2.0 is very good, and above 3.0 is excellent. Most diversified portfolios have Sharpe ratios between 0.4 and 1.0. The S&P 500 long-term Sharpe is about 0.4-0.5.
Which is better: Sharpe or Sortino?
The Sortino ratio is generally more informative because it only penalizes harmful volatility (downside). The Sharpe ratio treats upside and downside volatility equally, which unfairly penalizes investments with large positive moves.
Can I compare different investments with these ratios?
Yes, that is their primary purpose. When comparing two investments, the one with the higher Sharpe or Sortino ratio delivered better returns per unit of risk, regardless of absolute return levels.
Ready to run the numbers?
Open Risk-Adjusted Return Calculator