Question

Consider the following returns and states of the economy for TZ.Com.:

Economy
Probability
Return
Weak
25%
2%
Normal
50%
8%
Strong
25%
15%

What is the standard deviation of TZ's returns?

Answer 1

Answer: To calculate the standard deviation of TZ's returns, we need to first find the expected return and variance.

The expected return is:

(0.25 x 0.02) + (0.50 x 0.08) + (0.25 x 0.15) = 0.0875 or 8.75%

The variance is:

[(0.02 - 0.0875)^2 x 0.25] + [(0.08 - 0.0875)^2 x 0.50] + [(0.15 - 0.0875)^2 x 0.25] = 0.006109375

Finally, the standard deviation is the square root of the variance:

sqrt(0.006109375) = 0.0781 or 7.81%

Therefore, the standard deviation of TZ's returns is approximately 7.81%.

Step-by-step explanation: