CIPM Level I 2025: Risk Metrics—Sortino vs. Sharpe Ratio

Kateryna Myrko
Jul 30
3 min read

In performance measurement, understanding when to use the Sharpe ratio versus the Sortino ratio is essential. Both metrics relate excess return to risk, but they differ in their definition of “risk.” This article outlines their theoretical foundations, assumptions, strengths, weaknesses, and practical guidance on selecting the appropriate metric in various investment contexts.

1. Defining the Metrics CIPM Level I 2025 , Sortino vs. Sharpe Ratio

1.1 Sharpe Ratio

The Sharpe ratio measures excess return per unit of total volatility (standard deviation), treating both upside and downside swings equally. It is defined as:

E(Rₚ): expected portfolio return CIPM Level I 2025 , Sortino vs. Sharpe Ratio
R_f: risk-free rate CIPM Level I 2025 , Sortino vs. Sharpe Ratio
σₚ: standard deviation of portfolio returns

Key Assumptions

Returns are symmetrically distributed (e.g., normal).
Both positive and negative deviations from the mean are equally “risky.”
Investors are risk-averse but indifferent between upside and downside volatility.

1.2 Sortino Ratio

The Sortino ratio refines the Sharpe by penalizing only downside volatility—the variation of returns below a specified target T (often the risk-free rate). It’s defined as:

T: target or minimum acceptable return (e.g., R_f) CIPM Level I 2025 , Sortino vs. Sharpe Ratio
σ_D(T): downside deviation relative to T (i.e., semideviation)

Key Assumptions

Investors care only about returns below T; upside variance is not penalized.
Loss-aversion preference: negative returns hurt more than positive returns help.

2. Computing Downside Deviation

Downside deviation, σ_D(T), is calculated as the square root of average squared shortfalls below T:

Only returns Rᵢ < T contribute
When T = R_f, Sortino and an “adjusted Sharpe” share the same benchmark but differ in denominator

3. Strengths & Weaknesses

Aspect	Sharpe Ratio	Sortino Ratio
Risk Definition	Total volatility (σₚ)	Downside deviation (σ_D)
Symmetry	Penalizes upside and downside equally	Penalizes only downside
Assumptions	Normal returns, symmetric utility	Loss-aversion, focus on shortfalls
Use Cases	Balanced funds, mean-variance optimization	Strategies aiming strictly to avoid losses
Limitations	Misleading when return distribution is skewed or kurtotic; rewards negative skew	Can overstate performance if upside volatility is high; ignores upside risk

4. When to Use Sharpe vs. Sortino

Scenario	Preferred Metric
Broad portfolio comparison (equity, balanced, multi-asset)	Sharpe
Mean-variance optimization	Sharpe
Strategies with significant upside volatility	Sharpe
Loss-averse investors	Sortino
Hedge funds with non-normal return profiles	Sortino
Performance fee structures (high-water marks, drawdown limits)	Sortino
When benchmarking to a positive target/hurdle	Sortino
Evaluating worst-case vs. best-case balance	Sortino

Sharpe is appropriate when overall volatility reflects true risk and upside and downside swings are equally undesirable (e.g., broad mutual funds).
Sortino excels when the investment mandate prioritizes capital preservation or has contractual drawdown constraints.

5. Practical Considerations

Choice of Target (T)
- Often set to the risk-free rate (R_f), but can be a hurdle rate reflecting investor goals.
- A higher T increases downside deviation and lowers the Sortino ratio.
Data Frequency
- Ensure consistency: use daily returns for daily volatility, monthly for monthly.
Sample Size & Period
- Longer histories stabilize both σₚ and σ_D estimates.
- For non-stationary strategies, rolling windows can capture evolving risk.
Return Distribution
- If returns are skewed or exhibit fat tails, Sharpe may mislead; Sortino better reflects downside risk.
- However, extreme positive skew can inflate Sortino, so supplement with other tail‐risk measures (e.g., Value-at-Risk, skewness).
Comparability
- Only compare metrics calculated over the same period, frequency, and target (for Sortino).

Formula Snippets

Sharpe ratio uses total volatility; best for symmetric-risk contexts and mean-variance frameworks.
Sortino ratio uses downside deviation; ideal for loss-averse mandates, drawdown-sensitive structures, and non-normal return profiles.
Selection depends on investment objectives, return distribution, and risk tolerance.

Mastery of both ratios allows CIPM Level I candidates to evaluate performance metrics accurately and choose the appropriate measure for any given investment strategy.

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