question archive An analyst expects that the economy will be in one of three states: boom, normal or bust
An analyst expects that the economy will be in one of three states: boom, normal or bust
Subject:FinancePrice:4.89 Bought3
An analyst expects that the economy will be in one of three states: boom, normal or bust. The table below provides the analysts' expectations about the probability of each of these three states and the returns she expects Garmium Ltd's shares will be in each state:
State
Probability
Return
Bust
10%
-15%
Normal
70%
8%
Boom
20%
12%
Calculate the standard deviation of returns for Garmium Ltd's shares. Express your answer as a decimal to four decimal places. For example, if the standard deviation is 5.92% then write 0.0592.
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Probability(a) x Return(b) = Expected Return
BUST 10% x -15% = -1.50%
NORMAL 70% x 8% = 5.60%
BOOM 20% x 12% = 2.40%
EXPECTED VALUE 6.50%
[(b - 6.5% ) x (b - 6.5% )] x a
BUST = [(-15% - 6.5% ) x (-15% - 6.5% )] x 10% = 0.004623
NORMAL = [(8% - 6.5% ) x (8% - 6.5% )] x 70% = 0.000158
BOOM = [(12% - 6.5% ) x (12% - 6.5% )] x 20% = 0.000605
Variance 0.005385
STANDARD DEVIATION = SQUARE ROOT OF VARIANCE = SQUARE ROOT OF 0.005385 = 0.0734
