Question

State of Economy Probability of State of the Economy Security Return if State Occurs

Recession .30 -8%

Normal .40 13%

Boom .30 23%

Find the standard deviation  of the portfolio

Answer 1

Expected Return = 0.30 * (8)% + 0.40 * 13% + 0.30 * 23%  

= 9.7%

Given Return (X)	Expected Return (X1)	(X-X1)^2	prob	(X-X1)^2 * prob
-0.08	0.097	0.031329	0.30	0.0093987
0.13	0.097	0.001089	0.40	0.0004356
0.23	0.097	0.017689	0.30	0.0053067
		Total		0.015141

Standard Deviation =

=

= 0.1230 OR 12.30%

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