Question

24. Suppose that you have a stock with an average (expected) return of 32% and a standard deviation of return of 16%. Please answer the following question (show your work in your uploaded document): What is the probability of getting a return less than zero? (Round to 4 decimals, like .0000 or 00.00%)

Answer 1

Standard deviation of return measures the dispersion of the return to its mean/average return.

Here, the average return = 32 %

and the standard deviation = 16 %

In case of normal distributed data, the probability that the number will be one standard deviation away form mean is 68.27 % (approx)

2 standard deviation away = 95.45 % (approx)

Therefore,

Probability of getting not less than 0 return and not greater than 64 % is probability that the number will be 2 standard deviation away from the mean ( ranging between 0 and 64 % return ) as mean is 32 % and 2 standard deviation from mean is between 0,64 % return.

Its probability will be 95.45 %

Hence, probability of getting less than 0 and greater than 64 % returns = 1 - probability of getting not less than 0 and greater than 64 %

= 1 - .9545

= 0.0455

= 4.55 %

So probability of getting less than 0 and greater than 64 % returns = 4.55 %.

Since the normal distribution is symmetrically distributed around its mean,hence the probability of getting less than 0 and greater than 64 % are equal, hence the probability of getting less than 0 will be half of probability of getting less than 0 and greater than 64 % returns together.

Therefore,

probability of getting less than 0 = 4.55 / 2 = 2.275 %

Hence the required probability is 2.275 % (approx)

Hope it helps!