Question

A project has a 60% chance of doubling your investment in 1 year and a 40% chance of losing half your money. What is the standard deviation of this investment?

Answer 1

Answer:

The standard deviation is 0.73 times the value of your investment

Explanation:

Standard deviation is the measure of dispersion from the mean of the group as a whole.

It is a group statistic, so it is necessary to see the project's result as a group result.

Let P be the value of your investment.

If you can invest 100 times in the project then after 1 year you will receive 2P for 60 times and 0.5P for 40 times. The 40% ad 60% information is not conditioned on a sample so the case should be considered a measurement on population.

Mean = $\frac{\sum x_{i}}{n}$ = $\frac{60 \times 2P + 40 \times 0.5P}{100}$

Variance = $\frac{\sum {(x_{i} - Mean)^{2}}}{n}$

= $\frac{(2P - 1.4P)^2 \times 60 + (0.5P - 1.4P)^2 \times 40} {100} =0.54P^{2}$

Standard Deviation = $\sqrt{Variance}$ = $\sqrt{0.54P^{2}}$ = 0.73P