Sharpe vs Sortino vs Modified Sharpe: When to Use Each

Use the Sharpe ratio when returns are roughly normal, the Sortino ratio when the investor cares about losses, and Modified Sharpe when a strategy has real skew or fat tails. Sharpe is the most cited risk-adjusted return measure in finance and works well for diversified long-only portfolios. For hedge funds, private equity, structured products and anything else with skewed or fat-tailed returns, it overstates performance, sometimes by a lot.

The CAIA® Level I curriculum covers Sharpe and Sortino, and questions keep asking which one to apply and why. Modified Sharpe, the Cornish-Fisher version, isn't in either CAIA level's curriculum, but it's the one to reach for when a strategy's returns are skewed or fat-tailed.

The three ratios

Sharpe

William Sharpe introduced the ratio in 1966:

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

$R_p$ is the portfolio's return, $R_f$ is the risk-free rate, and $\sigma_p$ is the standard deviation of portfolio returns. It's excess return per unit of total volatility, and higher is better. A long-only equity fund with a Sharpe of 0.6 is fairly average, and a diversified multi-strategy hedge fund claiming 2.0 deserves a closer look.

Sharpe is exactly right when returns are normal (no skew, no fat tails), when the investor minds upside surprises as much as downside ones, and when the risk-free rate is meaningful, as in most developed markets. When those don't hold, it's misleading. Hedge fund marketing decks often quote a Sharpe of 1.5 or higher, so check the skew and kurtosis first: short-volatility, illiquid and credit-spread strategies produce smooth-looking returns that hide tail risk, and their Sharpe is high because the volatility looks low until the tail event arrives.

Sortino

Frank Sortino's version, proposed in the 1980s, swaps total volatility for downside deviation:

$$\text{Sortino} = \frac{R_p - R_T}{\sigma_D}$$

$R_T$ is a target return (often the risk-free rate, sometimes zero, sometimes a minimum acceptable return), and $\sigma_D$ is the downside deviation:

$$\sigma_D = \sqrt{\frac{1}{n} \sum_{t=1}^{n} \min(R_t - R_T, 0)^2}$$

Returns above the target add zero to the denominator, and returns below it are squared and averaged, so a fund with occasional 8% monthly gains takes no penalty for them. Most investors don't treat upside volatility as risk, and most retail and institutional mandates are written around limiting losses rather than volatility. For strategies built to limit the downside (protective puts, collared equity, some absolute-return programs), Sortino can be twice as high as Sharpe and still be the more accurate number.

Sortino has weak spots. The result depends heavily on the target, so Sortino with $R_T = R_f$ is a different number from Sortino with $R_T = 0$. With few observations the downside deviation is noisy, and a strategy that hasn't had a big drawdown yet looks better than it should. And it can't adjust for tail risk the historical sample doesn't contain.

Modified Sharpe

For strategies with material skew and kurtosis, even Sortino can mislead. Modified Sharpe uses the Cornish-Fisher expansion to adjust the normal z-score and puts the adjusted score into a Value-at-Risk denominator:

$$z'_\alpha = z_\alpha + (z_\alpha^2 - 1)\frac{S}{6} + (z_\alpha^3 - 3z_\alpha)\frac{K}{24} - (2z_\alpha^3 - 5z_\alpha)\frac{S^2}{36}$$

$$\text{mVaR}_\alpha = -(\mu + z'_\alpha \cdot \sigma)$$

$$\text{Modified Sharpe} = \frac{R_p - R_f}{\text{mVaR}_\alpha}$$

$z_\alpha$ is the normal z-score at confidence level $\alpha$, $S$ is the skewness of returns, and $K$ is the excess kurtosis (kurtosis minus 3). The correction penalizes negative skew (a longer left tail than the normal would imply) and high excess kurtosis (fatter tails). It's the right tool for hedge funds, structured products, options-writing strategies and credit-spread trades, where a smooth premium most of the time and an occasional big loss break both Sharpe and Sortino.

Comparing them on the same strategies

Take three strategies, each with an 8% mean return, 10% volatility and a 2% risk-free rate, and compute Modified Sharpe at 99% with the formulas above:

All three look identical on Sharpe, and Modified Sharpe cuts the short-volatility book to about half the others. Modified Sharpe divides by a 99% VaR rather than one standard deviation, so compare it across strategies rather than with Sharpe. Sortino isn't in the table because it needs the full return history, not just four moments. With the same mean and volatility, a negatively skewed book usually has more of its variance below the target, so its Sortino comes out lower too. Sortino mainly flatters a short-volatility strategy when the sample hasn't caught its bad months yet. For a non-normal strategy, pair Sharpe with at least one of the others, and ideally both.

Real fund data distorts all three. Private equity, real estate and some credit hedge funds mark positions quarterly from models, which smooths reported returns, understates volatility and inflates Sharpe and Sortino. Modified Sharpe doesn't repair that on its own, because its skew and kurtosis come from the same smoothed returns. Unsmoothing has to be estimated fund by fund: Getmansky, Lo and Makarov (2004) fit a smoothing model to hedge fund returns and found the amount of smoothing varies a lot by strategy. Two database problems sit on top of that. If a database drops dead funds, the survivors show higher means and lower volatility than the strategy delivered, so check whether yours keeps the defunct funds. And funds often start reporting after a good run and backfill that history, so check whether the database flags backfilled returns and drop those, rather than cutting a fixed number of months from every fund. If you want to see how sensitive a ratio is to survivorship, shade the mean down and the volatility up by amounts you choose, and label them as assumptions, not corrections. And a strategy that's uncorrelated with equities in normal times often turns highly correlated in a crisis, which none of the three captures, so pair them with conditional VaR or stress tests.

What the CAIA® exams test

Level I covers Sharpe and Sortino, alongside Treynor, the information ratio and return on VaR, in the risk and performance readings of the Introduction to Alternative Investments topic. Level I also covers non-normal returns directly, including skewness, kurtosis and testing for normality, and Level II adds ways to handle skewness and kurtosis in mean-variance optimization. Modified Sharpe isn't tested at either level. Based on the Level I learning objectives, be ready for:

• A direct Sharpe calculation from mean return, risk-free rate and standard deviation.
• A scenario asking which ratio fits a described strategy.
• A trap where Sharpe looks high but the skew or kurtosis calls for a different ratio.
• A Sortino calculation with a non-zero target return, a common slip.

Before you compute any ratio, ask what the return distribution looks like and whether Sharpe suits it or Sortino fits better. You'll need the same habit at Level II, where skewness and kurtosis come back in mean-variance optimization. The CAIA Level I formula sheet has the Sharpe and Sortino definitions side by side, and the free CAIA Level I question bank has hundreds of risk-metric questions tagged by topic, with solutions that cover both the math and the choice of measure.