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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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Presentation Transcript
variance
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
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 variance3
How to calculate variance
  • Alternative Formula
calculating standard deviation
Calculating Standard Deviation
  • Calculate Variance
  • Take the Square Root
  • Or use spreadsheet function STDEV
annualize
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
Volatility
  • The annualized standard deviation of returns is sometimes called “Volatility”
drawbacks
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
Scenario Analysis
  • Specify hypothetical outcomes
  • Assign probability distribution
  • Example: Insurance company
  • Example: Corporate bond