Question

An investor buys an asset at an initial cost of $400,000. The investor believes that one
year from now, the asset could have four possible values. These values are $225,000,
$300,000, $400,000 and $1,000,000 with respective probabilities of 15%, 35%, 45% and
5%.

a) What is the expected outcome of the asset’s value?

b) What is the expected return on the asset?

c) What is the standard deviation on the asset’s value?

Answer 1

a)

Expected outcome = sum of (probability of state * value of state)

= 0.15 * 225000 + 0.35 * 300000 + 0.45 * 400000 + 0.05 * 1000000

= 368750

b)

expected return = (368750 - 400000)/400000

= -7.81%

E(X^2) =  sum of (probability of state * return of state^2)

= 0.15 * 225000^2 + 0.35 * 300000^2 + 0.45 * 400000^2 + 0.05 * 1000000^2

= 161093750000

variance = E(X^2) - (E(X))^2

= 161093750000 - 368750^2

= 25117187500

Standard deviation = sqrt(variance)

= sqrt(25117187500)

= 158484.03