Question

Suppose you have a project that has a 0.5 chance of tripling your investment in a year and a 0.5 chance of doubling your investment in a year. What is the standard deviation of the rate of return on this investment?

Answer 1

Answer:

50%

Explanation:

Suppose the return form tripling = 300%

Suppose the return form doubling = 200%

Probability   Return           Calculation           Expected return

0.50             300%       150% (0.50*300%)          150%

0.50              200%      100% (0.50*200%)          100%

                                      Expected return             250%

Standard deviation = $\sqrt{P1*(Rt - E(R))^2 + Pd*(Rd - E(R))^2}$

Standard deviation = $\sqrt{0.50 * (300% - 250%)^2 + 0.50*(200% - 250%)^2}$

Standard deviation = $\sqrt{1250% + 1250%}$

Standard deviation = $\sqrt{2500%}$

Standard deviation = 50%

Hence, the Standard deviation is 50%