Question

Consider the following information:

 

	Probability of State	Rate of Return if State Occurs
Economy	of Economy	Stock A	Stock B
Recession	.24	.055	–.34
Normal	.64	.135	.24
Boom	.12	.230	.47

 

a.	Calculate the expected return for the two stocks. (Do not round intermediate calculations and enter your answers as a percent rounded to 2 decimal places, e.g., 32.16.)
b.	Calculate the standard deviation for the two stocks. (Do not round intermediate calculations and enter your answers as a percent rounded to 2 decimal places, e.g., 32.16.)

  

Answer 1

Consider the following information:

		Rate of Return if State Occurs
State of	Probability of State
Economy	of Economy	Stock A	Stock B
Recession	.24	.055	–.34
Normal	.64	.135	.24
Boom	.12	.230	.47

Requirement 1= Expected Return of=

Stock A= (0.24*0.055) + (0.64*0.135) + (0.12*0.230) = 12.72%

Stock B=(0.24*-0.34) + (0.64*0.24) + (0.12*0.47) = 12.84%

Requirement 2=The Standard Deviation for the two Stocks:

Stock A=

Probability	Rate of Return	XP	X2P
P	X
0.24	0.055	0.0132	0.000726
0.64	0.135	0.0864	0.011664
0.12	0.230	0.0276	0.006348
		0.1272	0.018738

Standard Deviation = Square Root (0.018738- (0.1272)2 )

   = Square Root (0.018738-0.01617984) = Square Root (0.00255816)

= 0.0505 = 5.05 %

Stock B=

Probability	Rate of Return	XP	X2P
P	X
0.24	-0.34	-0.0816	0.027744
0.64	0.24	0.1536	0.036864
0.12	0.47	0.0564	0.026508
		0.1284	0.091116

Standard Deviation = Square Root (0.091116- (0.1284)2 )

   = Square Root (0.091116-0.01648656) = Square Root (0.07462944)

= 0.27318 = 27.32 %