Question

An investment has the following possible values in one year:

Probability	Value in one year
20%	$100
10%	$0
60%	$50
10%	$200

Calculate the expected value and the standard deviation of the future values for the investment.

	A.	E( v ) = $70; Sdv(value) = $50.99
	B.	E(v) = $70; Sdv(value) = $0.00
	C.	E(~v) = $87.50; Sdv(value) = $26.00
	D.	E(v) = $87.50; Sdv(value) = $45.93

Answer 1

Expected Value = 20% * 100 + 10% * 0 + 60% * 50 + 10%* 200 = 20 + 0 +30+20 = 70

Variance = ( Return_n - Expected Return)² * Probability_n = (100-70)² * 0.2 +  (0-70)² * 0.1 + (50 -70)² * 0.6 + ( 200 -70)² * 0.1 = 900 * 0.2 + 4900 * 0.1 + 400 * 0.6 + 16900 * 0.1 = 180 + 490 + 240 + 1690 = 2600

Standard Deviation = Variance ^0.5 = 2600 ^0.5 = 50.99

A.	E( v ) = $70; Sdv(value) = $50.99, Option a is correct

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