Volatility describes the fluctuation you should expect for an investment/portfolio within a given time frame

Volatility mathematically, is the Standard Deviation of your daily returns.

Standard Deviation

Standard deviation measures the amount of variation in a set of values. In volatility these values are your daily return rates.

Standard Deviation will take all of your daily return rates as inputs, and start by calculating the average (known as the mean). From this starting points it will determine 3 buckets of variation. Each variation bucket is known as a standard deviation. Standard Deviation is notated with the symbol "sigma" : σ. 

Each bucket is named 1σ, 2σ, 3σ. On the spectrum, the middle is your mean (average), and each bucket goes above and below this middle.  

The curve fits all your data points under it, and uses σ to notate its abnormality. +/- 1σ encompass 68.2% of the data points, +/-2σ covers 27.2% data points, +/- 3σ cover 4.1% of the data points, and anything greater than 3σ is 0.2% of data points.  

σ is one number, the larger the number the more variability in your returns. Sharpe Ratio says: if you have large variability, then you need large returns to compensate. 

Example: If σ = 1.5% , and the mean (average) is = 0.5% ;
+1σ = 2% and -1σ = -1%. This means approximately 68.2% of the time your daily returns are between -1% and +2%.  

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