Question

A portfolio has an average return of 14.2 percent and a standard deviation of 12.85 percent. Given this, you should expect to lose at least _____ percent on an annual basis once every century.

Probability of loss "z" value
1.0 % 2.326
2.5 1.960
5.0 1.645

Answer 1

15.69%

Explanation:

The probability that a particular loss will occur once in a century is 1% (one year in 100 years). The z-value of that is given in the table as -2.326, so the corresponding x-value is ...

x = µ +zσ = 14.2 -2.326·12.85 = -15.69

We expect an annual loss of at least 15.7% once in a century.