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Variance

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- Expected squared deviation from the mean
- Standard Deviation:
- Square root of variance
Most widely used measures of risk

- Square root of variance
- Can calculate from historical data
- Very easy to calculate in a spreadsheet
- Often expressed as annualized number

- Calculate returns each period
- Daily, Weekly, or Monthly

- Find the average return
- Sample mean, CAPM expected return, or Zero

- For each period, calculate difference between realized return and expected return
- Square them, sum, and divide by N-1
- Or, just use spreadsheet function VAR

- Alternative Formula

- Calculate Variance
- Take the Square Root
- Or use spreadsheet function STDEV

- To annualize variance:
- For monthly data, multiply by 12
- For weekly data, multiply by 52
- For daily data, multiply by 252

- To annualize standard deviation
- Multiply by square root of 12, 52 or 252

- The annualized standard deviation of returns is sometimes called “Volatility”

- Variance does not give the whole picture
- Skewness may be important
- Variance treats large negative events the same as large positive ones

- Specify hypothetical outcomes
- Assign probability distribution
- Example: Insurance company
- Example: Corporate bond