Question

Assume that you expect to hold a $20,000 investment for one year. It is forecasted to have a year end value of $21,000 with a 30% probability; a year end value of $24,000 with a 45% probability; and a year end value of $30,000 with a 25% probability. What is the standard deviation of the holding period return for this investment?

Answer 1

$3,762.98

Explanation:

Let's compute first the expectancy E (the expected value) of the investment:

E = 30% of 21,000 + 45% of 24,000 + 25% of 30,000 =

0.3*21,000 + 0.45*24,000 + 0.25*30,000 = $24,600

The standard deviation s is

`\bf s=\sqrt{((E-21,000)^2+(E-24,000)^2+(E-30,000)^2)/(3)}`

When replacing the expectancy in this formula, we get:

`\bf s=\sqrt{((24,600-21,000)^2+(24,600-24,000)^2+(24,600-30,000)^2)/(3)}=\\=3,762.978\approx \$3,762.98`