Answer
At least 75% of returns will be between -13% and 44.2%
At least 88.9% of returns will be between -27.3% and 58.5%
So, it is not a surprise for an investor if he/she has a negative rate of return. This is not a very difficult occurrence.
Work Step by Step
$μ=15.8$% and $σ=14.3$%
Using the Chebyshev’s inequality with k = 2:
$1-\frac{1}{k^2}=1-\frac{1}{2^2}=0.75=75$%
At least 75% of returns will be between $μ-2σ=15.6-2\times14.3=-13$% and $μ+2σ=15.6+2\times14.3=44.2$%
And for k = 3:
$1-\frac{1}{k^2}=1-\frac{1}{3^2}=0.889=88.9$%
At least 88.9% of returns will be between $μ-3σ=15.6-3\times14.3=-27.3$% and $μ+3σ=15.6+3\times14.3=58.5$%
