We need to measure how much the PnLs can vary from day to day or even week to week. This is an important measure of risk because if a trading strategy has large swings in PnLs, the account value is very volatile and it is hard to run a trading strategy with such a profile. Often, we compute the Standard Deviation of returns over different days or weeks or whatever timeframe we choose to use as our investment time horizon. Most optimization methods try to find optimal trading performance as a balance between PnLs and the Standard Deviation of returns.

Computing the standard deviation of returns is easy. Let's compute the standard deviation of weekly returns, as shown in the following code:

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

from statistics import stdev
print('Weekly PnL Standard Deviation:', stdev(weekly_pnls))

plt.hist(weekly_pnls, 50)
plt.gca().set(title='Weekly PnL Distribution', xlabel='$', ylabel='Frequency')
plt.show()

The preceding code will return the following output:

Weekly PnL Standard Deviation: 1995.1834727008127

The following plot shows the weekly PnL distribution that was created from the preceding code:

We can see that the weekly PnLs are close to being normally distributed around a mean of $0, which intuitively makes sense. The distribution is right skewed, which yields the positive cumulative PnLs for this trading strategy. There are some very large profits and losses for some weeks, but they are very rare, which is also within the expectations of what the distribution should look like.