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You observe a portfolio for five years and determine that its average annual return is 13%...

You observe a portfolio for five years and determine that its average annual return is 13% and the standard deviation of its returns is 21%. Can you be 95% confident that this portfolio will not lose more than 30% of its value next year?

Yes

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Answer #1

Average return = 13%
Standard deviation = 21%
z-score for 95% confidence interval = 1.96

Low end for 95% prediction interval = Average return - (z score x SD)
= 13% - (1.96 * 21%)
= 13% - 41.16%
= -28.16%

Low end of the prediction interval is greater than -30%.

Yes, you can be confident that the portfolio will not lose more than 30% of its value next year.

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