The Sortino Ratio, developed by Frank Sortino in the 1980s, refines the idea behind the Sharpe Ratio. It specifically measures the risk-adjusted return of an investment by considering only downside volatility—the risk of negative returns. Unlike the Sharpe Ratio, which treats all volatility as equally undesirable, the Sortino Ratio distinguishes between "good" volatility (positive returns) and "bad" volatility (negative returns), thus better aligning with typical investor preferences.
Imagine you're evaluating two runners based on consistency. One occasionally runs faster than expected (positive volatility) while the other frequently runs slower (negative volatility). Naturally, you'd prefer the first, as positive deviations from expectations are beneficial, while negative deviations aren't.
Similarly, investors prefer investments where deviations are positive (exceed expectations) rather than negative. The Sortino Ratio captures this investor preference by only penalizing negative deviations, thus focusing purely on downside risk.
Consider two portfolios with identical Sharpe Ratios of 1.0 and the same average return of 8%, each with a different return pattern:
Portfolio A: Frequent small positive returns with occasional large negative returns
Portfolio B: Occasional large positive returns with frequent small negative returns
While both portfolios have the same standard deviation (and thus Sharpe Ratio), Portfolio A would have a better Sortino Ratio because it has less downside deviation, making it more attractive to most investors who are particularly concerned with avoiding losses.
The Sortino Ratio is mathematically defined as:
where:
The crucial difference in the Sortino Ratio is its risk measure, downside deviation, defined as:
where:
Typically, the target is set to zero, capturing all negative returns.
Our portfolio optimization application calculates the Sortino Ratio as follows:
Calculate daily returns ()
Calculate annualized return ():
Calculate downside deviation:
Identify negative daily returns
Compute standard deviation of only these negative returns (downside deviation)
Calculate Sortino Ratio:
downside_std = port_returns[port_returns < 0].std()
sortino = 0.0
if downside_std > 1e-9:
mean_daily = port_returns.mean()
annual_ret = mean_daily * 252
sortino = (annual_ret - risk_free_rate) / (downside_std * np.sqrt(252))Emphasizes downside risk, aligning closely with typical investor preferences who are more concerned about losses than gains.
Avoids penalizing portfolios that have positive, beneficial volatility, leading to more nuanced risk assessment.
Especially useful during bear markets or volatile periods, providing a clearer risk-adjusted performance perspective when downside protection is particularly important.
Below average performance
Investment's returns don't sufficiently compensate for downside risk. The portfolio may have too many significant negative returns.
Good performance
Favorable downside risk-return trade-off. The portfolio demonstrates a good balance between returns and protection against losses.
Excellent performance
Very attractive investment with well-managed downside risk. The portfolio delivers strong returns while effectively limiting losses.
While both ratios measure risk-adjusted returns, they differ fundamentally in how they define and calculate risk:
Risk Measure: Total volatility (standard deviation of all returns)
Formula Denominator: (standard deviation of all returns)
Penalizes: Both upside and downside volatility equally
Assumption: Investors are concerned with overall volatility
Best Used When: Returns are normally distributed or when both upside and downside risks matter equally
Risk Measure: Downside deviation (standard deviation of only negative returns)
Formula Denominator: (downside deviation)
Penalizes: Only negative (harmful) volatility
Assumption: Investors are primarily concerned with losing money
Best Used When: Returns are asymmetric or when downside protection is a priority
Consider a portfolio with the following characteristics:
Annual return: 12%
Risk-free rate: 3%
Standard deviation of all returns: 15%
Standard deviation of only negative returns: 10%
Sharpe Ratio: (12% - 3%) / 15% = 0.60
Sortino Ratio: (12% - 3%) / 10% = 0.90
This portfolio looks significantly better when evaluated using the Sortino Ratio because it has proportionally less downside risk than total risk.
More closely aligns with investor concerns, emphasizing losses over volatility in general. This psychological alignment with how investors actually perceive risk makes the metric more intuitive.
Provides clearer insights during market downturns or heightened volatility. When markets become turbulent, the Sortino Ratio helps distinguish between portfolios that maintain downside protection versus those that don't.
In a year where the market has significant upswings and downswings, two portfolios might have identical Sharpe Ratios. However, the portfolio that captured more of the upswings while avoiding downswings would have a higher Sortino Ratio, correctly reflecting its superior risk management approach from an investor's perspective.
The choice of threshold (usually zero or risk-free rate) can significantly affect results. Different threshold choices can lead to different rankings of portfolios, potentially leading to inconsistent evaluations.
Requires enough negative observations to accurately estimate downside deviation. With limited data or in strong bull markets, there may be too few negative returns to reliably calculate the ratio.
Sortino, F. A., & Price, L. N. (1994). "Performance Measurement in a Downside Risk Framework." Journal of Investing, 3(3), 59-64.
Sortino, F. A., & Van Der Meer, R. (1991). "Downside Risk." Journal of Portfolio Management, 17(4), 27-31.
Sortino, F. A., & Satchell, S. (2001). Managing Downside Risk in Financial Markets. Butterworth-Heinemann.
Kaplan, P. D., & Knowles, J. A. (2004). "Kappa: A Generalized Downside Risk-Adjusted Performance Measure." Journal of Performance Measurement, 8, 42-54.