Question

Calculating returns and standard deviation. Based on the following information, can you calculate the expected return and standard deviation for the two stocks?:

State of economy. Prob of st of econ Rate of return if state occurs

  Stock A Stock B

Recession    .25 .06 -.20    

Normal .55 .07 .13

Boom .20 . .11 .33

Answer 1

The values provided for stock A and stock B in the question are putting in the table as follows:

FOR STOCK A
STATE OF ECONOMY	PROBABILITY		RETURN	PROBABILITY * RETURN	(RETURN-EXPECTED RETURN)	SQUARED OF (RETURN -EXPECTED RETURN)	PROBABILITY * SQUARED OF (RETURN -EXPECTED RETURN)
A	B		C	D=B * C	E=C-D	F=E^2	G= B * F
Recession	0.25		6	1.5	4.5	20.25	5.0625
Normal	0.55		7	3.85	3.15	9.9225	5.457375
Boom	0.2		11	2.2	8.8	77.44	15.488
							0
TOTAL	1			EXPECTED RETURN OF STOCK A =7.55			0
							VARIANCE=26.007875
FOR STOCK B
STATE OF ECONOMY	PROBABILITY		RETURN	PROBABILITY * RETURN	(RETURN-EXPECTED RETURN)	SQUARED OF (RETURN -EXPECTED RETURN)	PROBABILITY * SQUARED OF (RETURN -EXPECTED RETURN)
A	B		C	D=B * C	E=C-D	F=E^2	G= B * F
Recession	0.25		-20	-5	-15	225	56.25
Normal	0.55		13	7.15	5.85	34.2225	18.822375
Boom	0.2		33	6.6	26.4	696.96	139.392
							0
TOTAL	1			EXPECTED RETURN OF STOCK B =8.75			0
	Variance of stock A=26.007875		Variance of stock B=214.464375 standard deviation for the stocks B = Square Root of variance of stock B=14.64%				VARIANCE=214.464375
standard deviation for the stocks	A = Square Root of variance of stock A =5.10%