FRM Part I · FRM Exam Part I · Hypothesis Testing
A portfolio's return distribution is unknown, with mean 0 and standard deviation 4%. Using Chebyshev's inequality, what is the minimum probability that a return lies within the interval -10% to +10%?
At least 84%. The interval of plus or minus 10% equals 2.5 standard deviations, so Chebyshev limits the chance of falling outside to 1 over 2.5 squared, or 16%. The probability of being inside is therefore at least 84%.
- AAt least 84%Correct
- BAt least 96%
- CAt least 75%
- DAt least 60%
Explanation
The interval is 10%/4% = 2.5 standard deviations from the mean. Chebyshev gives P(outside) <= 1/2.5^2 = 0.16, so P(inside) >= 1 - 0.16 = 0.84. The 96% option wrongly uses 1/k^2 with k = 5, and the 75% option uses k = 2.
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