Question

If the mean annual return for a stock is 14%, what is the risk (standard deviation) you would take for a probability of 32% of a return being at least 19%?

a) 8%
b) 6%
c) 14%
d) 21%
e) 11%
f) 17%

Answer 1

To find the risk or standard deviation for a probability of 32% of a return being at least 19%, we can use the z-score formula. The risk or standard deviation is approximately 15.63%.

Step-by-step explanation:

To find the risk or standard deviation for a probability of 32% of a return being at least 19%, we can use the z-score formula. The z-score is calculated using the formula: z = (x - mean) / standard deviation. In this case, we know that the mean annual return is 14% and we need to find the standard deviation.

Let's assume the standard deviation is denoted by 's'. We can rearrange the formula to solve for 's' as follows: s = (x - mean) / z.

Given that the return we're interested in is 19%, the z-score can be calculated as follows: z = (19 - 14) / s = 0.32.

Now we can solve for 's':

s = (19 - 14) / 0.32

s = 5 / 0.32

s ≈ 15.63%

Therefore, the risk or standard deviation we would take for a probability of 32% of a return being at least 19% is approximately 15.63%.