Question

Consider the following information:

  

		Rate of Return if State Occurs
State of Economy	Probability of State of Economy	Stock A	Stock B
Recession	.10	.06	–.21
Normal	.70	.08	.16
Boom	.20	.16	.34

  

Calculate the expected return for Stock A.

  

Calculate the expected return for Stock B.

  

Calculate the standard deviation for Stock A.

  

Calculate the standard deviation for Stock B.

Answer 1

Total expected return of A = 6 *.10 + 8*.70 +16*.20 = .6 + 5.6 + 3.2 =9.4%

Calculation of standard deviation

Recession	(6 - 9.4)2*.10	1.156
Normal	(8 - 9.4)2*.70	1.372
Boom	(16 - 9.4)2*.20	8.712
	TOTAL	11.24

so standard deviation is equalto square root of 11.24 = 3.35

Total expected return of B = -21 *.10 + 16*.70 +34*.20 = -2.1 + 11.2 + 6.8 =15.9%

Calculation of standard deviation

Recession	(-21-15.9)2*.10	136.161
Normal	(16 - 15.9)2*.70	.007
Boom	(34 - 15.9)2*.20	65.522
	TOTAL	201.69

so standard deviation is equalto square root of 201.69 = 14.20