Question

A project has a 0.7 chance of doubling your investment in a year and a 0.3 chance of halving your investment in year. What is the standard deviation of the rate of return on this investment? (Do not round intermediate calculations. Round your answer to 2 decimal places.) Standard deviation

Answer 1

To find the standard deviation first we need to find expected return and variance:

Expected return = E(r) = (0.70 x 100%)+(0.30 x -50%)

= 0.70+(-0.15)

=0.55

=55%

Variance =

$\fn_jvn \sigma$²= 0.70 x [1-E(r)]² + 0.30 x [-0.50-E(r)]²

= 0.70 x [1- 0.55]² + 0.30 x [-0.50-0.55]²

= 14.175% + 33.075%

$\fn_jvn \sigma$²=47.25%

Standard Deviation = $\fn_jvn \sqrt{\sigma ^2}$

$\fn_jvn \sigma$ = $\fn_jvn \sqrt{0.4725}$

= 0.6874

=68.74%