Sunday, January 27, 2019

Understanding and Interpreting Standard Deviations

Often I have seen that it becomes a challenge to explain how Standard Deviation is to be understood. 

Excel Formula: =STDEV.S(Select the Cells with data) 
The resultant will be 1 Standard Deviation (SD). 

1 SD covers 66% of the sample data
2 SD covers 95% of the sample data

Example: 10 yr Avg returns is 13% and the Std Dev is  1.98%. 

1SD = 11.38% to 15.38% 

Calculation
13.40+1.98  = 15.38
13.40 - 1.98 = 11.38

2SD = 9.44% to 17.36%

Calculation
13.40+(2x1.98)  = 17.36
13.40 - (2x1.98) = 9.44

Meaning: 9.44% to 17.36% is the range in which 95% of the data points are over the last 10 years.

Relevant questions:
How many working days were there?
How many data points were used to derive SD?
If there is a massive discrepancy in the above data then perhaps understanding the source of the data and the calculation methodology is important.

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