Variance Calculator Function - why mean of SMA-1 is taken?

Options & Futures
1

Course Name: Trading using Options Sentiment Indicators, Section No: 2, Unit No: 9, Unit type: WaterMarkVideo

def variance_calculator(series,series_average,win_len):
sma = win_len
temp = series.subtract(series_average) # a-b
temp2 = temp.apply(lambda x: x**2) #(a-b)^2
temp3 = temp2.rolling(sma-1).mean() # summation[(a-b)^2 ]/ (sma -1)
sigma = temp3.apply(lambda x : math.sqrt(x)) #sigma is the standard deviation
return sigma =========================================================== I want to intention behind using temp2.rolling(sma-1).mean() as this is not equivalent of what is in the comment against this line of code # summation[(a-b)^2 ]/ (sma -1). 'temp2.rolling(sma-1).mean() ’ will not calculate sample Standard deviation and is not equivalent of summation[(a-b)^2 ]/ (sma -1), if intention was to calculate sample standard deviation - this can be be done - sigma = series.rolling(win_len).std(ddof=1) ? Can you please advise , if I am thinking along on correct lines ?

2

or keeping with same code structure we can probably do following -

# Compute rolling sum over full window (sma)
temp3 = temp2.rolling(win_len).sum()

# Apply proper Bessel’s correction: divide by (win_len-1)
temp3 = temp3 / (win_len - 1)

# Take the square root to get standard deviation
sigma = temp3.apply(lambda x: math.sqrt(x))
3

Hi Rohan,

Thanks for pointing this out. You may have a valid point, and we are currently evaluating it.
If you have any other concerns, feel free to reach out us via the community.

Best,
Ajay

4

Thanks so much for your response. Please update me once you guys have reviewed. Thanks.

5

Hi Rohan,

Thank you for your input.
The intention is to calculate the sample standard deviation, which can be achieved through the following methods:

  • temp3 = temp2.rolling(sma).mean() / (sma - 1) [implemented].
  • sigma = series.rolling(win_len).std(ddof=1)

I’ve updated the content accordingly.
If you have any further concerns, feel free to reach out via the community.

Regards,
Ajay

6

Thanks Ajay for udpate.