Question

Consider the following information: State Probability ABC, Inc. Return Boom .25 0.154 Normal .50 0.08. Slowdown .15 0.04 Recession .10 -0.034 1) 2) 3) What is the expected return?- What is the variance? What is the standard deviation?

Answer 1

Part 1) Expected return = Probability*ABC Inc return = (0.25*0.15)+(0.5*0.08)+(0.15*0.04)+(0.1*-0.03) = 0.0375+0.04+0.06-0.003 = 0.0805

Part 2)

State	Probability	Return	Expected return (Probability*Return)	Expected return-ΣExpected return	(Expected return-ΣExpected return)^2	Probability*(Expected return-ΣExpected return)^2
Boom	0.25	0.15	0.0375	-0.0430	0.00184900	0.0004622500
Normal	0.50	0.08	0.0400	-0.0405	0.00164025	0.0008201250
Slowdown	0.15	0.04	0.0060	-0.0745	0.00555025	0.0008325375
Recession	0.10	-0.03	-0.0030	-0.0835	0.00697225	0.0006972250
			0.0805		0.01601175	0.0028121375

Variance = Σ{Probability*(Expected return-ΣExpected return)^2} = 0.0028121375

Part 3)

Standard deviation = Square root of (Variance) = Square root of (0.0028121375) = 0.0530295908 or 5.3%