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Variance PowerPoint PPT Presentation


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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.

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Variance

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Variance l.jpg

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


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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


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How to calculate variance

  • Alternative Formula


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Calculating Standard Deviation

  • Calculate Variance

  • Take the Square Root

  • Or use spreadsheet function STDEV


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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


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Volatility

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


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Drawbacks

  • Variance does not give the whole picture

    • Skewness may be important

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


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Scenario Analysis

  • Specify hypothetical outcomes

  • Assign probability distribution

  • Example: Insurance company

  • Example: Corporate bond


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