95% chance of 1.6 Standard deviation?

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I'M reading a book on portfolio management and I can't understand how the author came up with 95% chance of volatility reaching 1.6 times..here's the excerpt:
"Suppose that we were to forecast that equity volatility over the next five years(our investment horizon) would average 20 percent a year (the long-term average or close to it). An equity exposure of 60 percent in our portfolio would translate this to a 12 percent volatility (0.60 times 20 percent) from the equity risk factor. This means an approximately 5 percent chance, of a drawdown of 1.6 times the volatility, that is, a 1 in 20 chance of a drawdown of more than 19.2 percent."



From what I remember from stats,in a normal distribution,95% equates to 2 STD and not 1.6. Shouldn't the 19.2% drawdown be 24%?






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    I'M reading a book on portfolio management and I can't understand how the author came up with 95% chance of volatility reaching 1.6 times..here's the excerpt:
    "Suppose that we were to forecast that equity volatility over the next five years(our investment horizon) would average 20 percent a year (the long-term average or close to it). An equity exposure of 60 percent in our portfolio would translate this to a 12 percent volatility (0.60 times 20 percent) from the equity risk factor. This means an approximately 5 percent chance, of a drawdown of 1.6 times the volatility, that is, a 1 in 20 chance of a drawdown of more than 19.2 percent."



    From what I remember from stats,in a normal distribution,95% equates to 2 STD and not 1.6. Shouldn't the 19.2% drawdown be 24%?






    probability normal-distribution standard-deviation







    share|cite|improve this question























      up vote
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      up vote
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      down vote

      favorite











      I'M reading a book on portfolio management and I can't understand how the author came up with 95% chance of volatility reaching 1.6 times..here's the excerpt:
      "Suppose that we were to forecast that equity volatility over the next five years(our investment horizon) would average 20 percent a year (the long-term average or close to it). An equity exposure of 60 percent in our portfolio would translate this to a 12 percent volatility (0.60 times 20 percent) from the equity risk factor. This means an approximately 5 percent chance, of a drawdown of 1.6 times the volatility, that is, a 1 in 20 chance of a drawdown of more than 19.2 percent."



      From what I remember from stats,in a normal distribution,95% equates to 2 STD and not 1.6. Shouldn't the 19.2% drawdown be 24%?






      probability normal-distribution standard-deviation







      share|cite|improve this question













      I'M reading a book on portfolio management and I can't understand how the author came up with 95% chance of volatility reaching 1.6 times..here's the excerpt:
      "Suppose that we were to forecast that equity volatility over the next five years(our investment horizon) would average 20 percent a year (the long-term average or close to it). An equity exposure of 60 percent in our portfolio would translate this to a 12 percent volatility (0.60 times 20 percent) from the equity risk factor. This means an approximately 5 percent chance, of a drawdown of 1.6 times the volatility, that is, a 1 in 20 chance of a drawdown of more than 19.2 percent."



      From what I remember from stats,in a normal distribution,95% equates to 2 STD and not 1.6. Shouldn't the 19.2% drawdown be 24%?






      probability normal-distribution standard-deviation




      probability normal-distribution standard-deviation






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      asked 5 hours ago









      gaston

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          A two-sided 95% confidence interval covers roughly -2 to +2 standard deviations of a normal distribution. In the quoted passage, we are only concerned about movement in the downward direction, corresponding to a one-sided confidence interval. A one-sided 95% confidence interval covers all values greater than -1.6 standard deviations of a normal distribution.






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            A two-sided 95% confidence interval covers roughly -2 to +2 standard deviations of a normal distribution. In the quoted passage, we are only concerned about movement in the downward direction, corresponding to a one-sided confidence interval. A one-sided 95% confidence interval covers all values greater than -1.6 standard deviations of a normal distribution.






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              A two-sided 95% confidence interval covers roughly -2 to +2 standard deviations of a normal distribution. In the quoted passage, we are only concerned about movement in the downward direction, corresponding to a one-sided confidence interval. A one-sided 95% confidence interval covers all values greater than -1.6 standard deviations of a normal distribution.






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                A two-sided 95% confidence interval covers roughly -2 to +2 standard deviations of a normal distribution. In the quoted passage, we are only concerned about movement in the downward direction, corresponding to a one-sided confidence interval. A one-sided 95% confidence interval covers all values greater than -1.6 standard deviations of a normal distribution.






                share|cite|improve this answer












                A two-sided 95% confidence interval covers roughly -2 to +2 standard deviations of a normal distribution. In the quoted passage, we are only concerned about movement in the downward direction, corresponding to a one-sided confidence interval. A one-sided 95% confidence interval covers all values greater than -1.6 standard deviations of a normal distribution.







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                answered 4 hours ago









                shimao

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