Sortino ratio on short time series -> divition by zero

[emiliobasualdo]

Hi guys. I don't want to place an issue because I might not understand well the Sortino Ratio.
Basically, I was optimizing with bt.optimize and set the logger toroot.setLevel(logging.INFO) and a warning appeared:

.venv/lib/python3.8/site-packages/backtesting/backtesting.py:1584: RuntimeWarning: divide by zero encountered in double_scalars
  s.loc['Sortino Ratio'] = np.clip(annualized_return / (np.sqrt(np.mean(day_returns.clip(-np.inf, 0)**2)) * np.sqrt(annual_trading_days)), 0, np.inf)  # noqa: E501

I'm optimizing with a time series that has minute candles and lasts almost 4 days.

I can confirm with the debugger that:
(np.sqrt(np.mean(day_returns.clip(-np.inf, 0)**2)) * np.sqrt(annual_trading_days)) = 0
and that

day_returns=
(Timestamp('2021-03-16 00:00:00', freq='D'), nan) 
(Timestamp('2021-03-17 00:00:00', freq='D'), 0.0209088078795423) 
(Timestamp('2021-03-18 00:00:00', freq='D'), 0.0032580727254232222) 
(Timestamp('2021-03-19 00:00:00', freq='D'), 0.00014225292238778664)

and that

day_returns.clip(-np.inf, 0)=
(Timestamp('2021-03-16 00:00:00', freq='D'), nan) 
(Timestamp('2021-03-17 00:00:00', freq='D'), 0.0) 
(Timestamp('2021-03-18 00:00:00', freq='D'), 0.0) 
(Timestamp('2021-03-19 00:00:00', freq='D'), 0.0)

My questions are:
I this a normal expected outcome?
Does it make sense to study the Sortino Ratio over this series?

Thank you for your help.
Regards!

[kernc]

I'm optimizing with a time series that has minute candles and lasts almost 4 days.

Well, you only have 4 days and none of those days' returns are negative. Since this is the same as in Quantopian empyrical:
https://github.com/quantopian/empyrical/blob/b026b4e08b7147ee7e71ff5622f13913cdcaa99d/empyrical/stats.py#L870-L877
I think we're in clear, and Sortino is indeed just not suited to your sample of data.

[emiliobasualdo]

Thanks!