Question

Suppose your expectations regarding the stock market are in the chart below. What is the standard deviation of the HPRs on stocks? convert to percentages and round your answer to two decimal places State of the Economy Probability HPR Boom 10% 35% Normal Growth 40% 8% Recession 50% -20

Answer 1

Calculation of Standard Deviation of Holding Period Return :

Mean = Sum of (HPR * Probabilities)

= (35% * 0.10) + (8% * 0.40) + (-20% * 0.50)

= 3.5% + 3.2% - 10%

= -3.3%

Calculation of Standard Deviation

Standard Deviation = (Sum of Square of Variation from Mean )^(1/2)

Below is the table showing Calculation of Standard Deviation

Possible Outcomes	HPR	Probabilities	(d=HPR - Mean)	d^2	p*(d^2)
Boom	35%	0.10	38.3 (35+3.3)	1466.89	146.689 (1466.89 * 0.10)
Normal	8%	0.40	11.3(8 +3.3)	127.69	51.076 (127.69 * 0.40)
Recession	-20%	0.50	16.7 (-20 +3.3)	278.89	139.445 (278.89 * 0.50)
				Total	337.21

Standard Deviation = [Sum of (p * d^2 ]^(1/2)

= (337.21)^(1/2)

= 18.36%