Sharpe ratio and Sortino ratio: formulas, examples and interview questions

The Sharpe ratio

Sharpe ratio = (R_p − R_f) / σ_p

Where R_p is the portfolio return, R_f is the risk-free rate, and σ_p is the standard deviation of portfolio returns over the same period. The measure was introduced by William F. Sharpe.

The Sortino ratio

Sortino ratio = (R_p − T) / σ_d

Where T is a target or minimum acceptable return (often zero or the risk-free rate), and σ_d is downside deviation: the standard deviation calculated using only returns below the target.

Worked example

A strategy returns 12% a year with 16% annual volatility. The risk-free rate is 4%, and the downside deviation below a 4% target is 10%.

The Sortino ratio is higher because much of the strategy's volatility comes from upside moves, which Sortino does not penalise.

Annualising

If you calculate Sharpe on daily returns, multiply by the square root of the number of trading days, commonly about 252. For monthly data, multiply by the square root of 12. This scaling assumes returns are independent from period to period; autocorrelated returns make it inaccurate.

When each ratio misleads

Skewed returns. Strategies that earn small, steady gains and occasionally lose heavily, such as selling options, can show a high Sharpe until the loss arrives.

Short samples. Sharpe estimates are noisy. Under simplifying assumptions, the standard error of an annualised Sharpe estimate shrinks only with the square root of the number of years observed, so a few years of data leave wide uncertainty.

Overfitting. Testing many strategy variants and reporting the best one inflates Sharpe. Out-of-sample testing and adjustments for multiple testing matter.

Capacity. High-frequency strategies can show very high Sharpe ratios on small capital that do not survive scaling.

Downside deviation choices. Sortino results change with the target return and calculation method, so comparisons require the same definition.

Sharpe versus Sortino

Questions quant interviewers ask

1. How would you annualise a Sharpe ratio calculated on daily returns, and what assumption does that rely on?
2. A backtest shows a Sharpe of 4. What would you check before believing it?
3. Why might a short-volatility strategy have a high Sharpe but be dangerous?
4. When would you prefer Sortino over Sharpe?
5. How does leverage affect the Sharpe ratio, ignoring financing costs?
6. How confident are you in a Sharpe of 1.5 estimated from two years of monthly data?

A useful answer to question 5: scaling returns and volatility by the same leverage factor leaves Sharpe unchanged before costs, which is why it is used to compare strategies of different sizes.

Why this matters for quant careers

Risk-adjusted return is part of everyday language in quant research and portfolio management. Interviewers use these ratios to test whether candidates understand estimation error and overfitting, not just formulas. See the skills firms assess in the HFT skills matrix.

Calculating Sharpe from daily returns, step by step

1. Collect daily returns for the strategy over the period.
2. Subtract the daily risk-free rate from each return to get excess returns.
3. Calculate the mean and standard deviation of the excess returns.
4. Divide the mean by the standard deviation to get the daily Sharpe ratio.
5. Multiply by the square root of 252 to annualise.

If average daily excess return is 0.05% and daily standard deviation is 1%, the daily Sharpe is 0.05. Annualised, that is about 0.05 × 15.87, or roughly 0.79.

```python import numpy as np

def sharpe(returns, rf_daily=0.0, periods=252): excess = np.asarray(returns) - rf_daily return excess.mean() / excess.std(ddof=1) * np.sqrt(periods)

def sortino(returns, target_daily=0.0, periods=252): r = np.asarray(returns) downside = np.minimum(r - target_daily, 0) dd = np.sqrt((downside ** 2).mean()) return (r.mean() - target_daily) / dd * np.sqrt(periods) ```

The Sortino function above uses one common definition of downside deviation: the root mean square of shortfalls below the target, calculated across all periods. Other definitions exist, so always state which one you use.

Related risk-adjusted measures

The deflated Sharpe ratio, introduced by David Bailey and Marcos López de Prado, is especially relevant to quant research because it penalises the selection bias that comes from testing many variants.

How practitioners use these ratios

Researchers use Sharpe to compare signals, but combine it with turnover, capacity and costs. A signal with a lower Sharpe but much higher capacity may be more valuable.

Portfolio managers watch rolling Sharpe and drawdowns to detect when a strategy stops working, and to size positions.

Allocators and CIOs compare managers on Sharpe, Sortino and drawdown together, and ask how results were produced before trusting them. See how this shapes investment leadership hiring.

Model answers to common interview questions

How confident are you in a Sharpe of 1.5 from two years of monthly data? Not very. With 24 observations the estimate has wide uncertainty, and under simple independence assumptions the standard error of an annualised Sharpe estimate is roughly the square root of one divided by the number of years, which is about 0.7 here. The true Sharpe could plausibly be far lower.

A backtest shows a Sharpe of 4. What do you check? Look-ahead bias, survivorship bias in the data, realistic transaction costs and slippage, capacity, the number of variants tested, out-of-sample and live results, and whether returns are autocorrelated or dependent on a single period.

Why can a short-volatility strategy show a high Sharpe? Its returns are negatively skewed: frequent small gains and rare large losses. Standard deviation over a calm sample understates tail risk until a large loss occurs.