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# Variance PowerPoint PPT Presentation

Variance. Expected squared deviation from the mean Standard Deviation: Square root of variance Most widely used measures of risk Can calculate from historical data Very easy to calculate in a spreadsheet Often expressed as annualized number. How to calculate variance.

Variance

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### Variance

• Expected squared deviation from the mean

• Standard Deviation:

• Square root of variance

Most widely used measures of risk

• Can calculate from historical data

• Very easy to calculate in a spreadsheet

• Often expressed as annualized number

### How to calculate variance

• 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

### How to calculate variance

• Alternative Formula

### Calculating Standard Deviation

• Calculate Variance

• Take the Square Root

• Or use spreadsheet function STDEV

### Annualize

• 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

### Volatility

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

### Drawbacks

• Variance does not give the whole picture

• Skewness may be important

• Variance treats large negative events the same as large positive ones

### Scenario Analysis

• Specify hypothetical outcomes

• Assign probability distribution

• Example: Insurance company

• Example: Corporate bond