Question

Ex-Ante Standard Deviation An analyst estimates a 20% probability of a recession next year, a 44% probability of normal economic growth and a 36% probability of a strong recovery. If a recession occurs a stock is projected to have a -15.5% return. With normal growth the stock will generate a 10.5% return and if the strong recovery occurs the stock will have a 25.5% rate of return. This stock's standard deviation is _______. 11.65% 10.70% 14.70% 11.92%

Answer 1

Ans 14.70%

State of Economy	Probability (P)	Return (Y)	(P * Y )	P * (Y -Average Return of Y)^2
Recession	20%	-15.5	-3.10	137.29
Normal	44%	10.5	4.62	0.02
Strong	36%	25.5	9.18	78.85
		TOTAL	10.70	216.16
Expected Return =		(P * Y)
		10.70%
VARIANCE =		P * (Y -Average Return of Y)^2
		216.1600
Standard Deviation =		Square root of (P * (Y -Average Return of Y)^2)
		Square root of 216.16
		14.70