Sharpe ratio is a very commonly used performance and risk metric that's used in the industry to measure and compare the performance of algorithmic trading strategies. Sharpe ratio is defined as the ratio of average PnL over a period of time and the PnL standard deviation over the same period. The benefit of the Sharpe ratio is that it captures the profitability of a trading strategy while also accounting for the risk by using the volatility of the returns. Let's have a look at the mathematical representation:

Here, we have the following:

• : PnL on the  trading day.
• : Number of trading days over which this Sharpe is being computed.

Another performance and risk measure similar to the Sharpe ratio is known as the Sortino ratio, which only uses observations where the trading strategy loses money and ignores the ones where the trading strategy makes money. The simple idea is that, for a trading strategy, Sharpe upside moves in PnLs are a good thing, so they should not be considered when computing the standard deviation. Another way to say the same thing would be that only downside moves or losses are actual risk observations.

Let's compute the Sharpe and Sortino ratios for our trading strategy. We will use a week as the time horizon for our trading strategy:

last_week = 0
weekly_pnls = []
weekly_losses = []
for i in range(0, num_days):
  if i - last_week >= 5:
    pnl_change = pnl[i] - pnl[last_week]
    weekly_pnls.append(pnl_change)
    if pnl_change < 0:
      weekly_losses.append(pnl_change)
    last_week = i

from statistics import stdev, mean

sharpe_ratio = mean(weekly_pnls) / stdev(weekly_pnls)
sortino_ratio = mean(weekly_pnls) / stdev(weekly_losses)

print('Sharpe ratio:', sharpe_ratio)
print('Sortino ratio:', sortino_ratio)

The preceding code will return the following output:

Sharpe ratio: 0.09494748065583607
Sortino ratio: 0.11925614548156238

Here, we can see that the Sharpe ratio and the Sortino ratio are close to each other, which is what we expect since both are risk-adjusted return metrics. The Sortino ratio is slightly higher than the Sharpe ratio, which also makes sense since, by definition, the Sortino ratio does not consider large increases in PnLs as being contributions to the drawdown/risk for the trading strategy, indicating that the Sharpe ratio was, in fact, penalizing some large +ve jumps in PnLs.