Question

3) You have been provided the following information related to Stock A (Canadian Stock) and Stock B (American stock) Stock A: Canadian Stock | State of Economy | Probability of State of Economy Rate of Return if State Occurs | Boom 18% 22% Good 50% 20% Poor 8% | Bust 6 % -15% + Stock B: American Stock | State of Economy Probability of State of Economy Rate of Return if State Occurs Boom 0.30 0.25 Good 0.50 0.16 Poor 0.14 0.06 Bust 0.06 -0.10 Based on the given information, what is the standard deviation of the returns on i) Stock A (Canadian Stock) and ii) Stock B (American stock)? Which stock has higher standard deviation? Why? Please provide your reasoning. Please show all the calculations by which you came up with the final answer. (8 Points)

Answer 1

Stock A

State of Economy	Probability of state of Economy	Rate of return if state occurs
Boom	18%	22%
Good	50%	20%
Poor	26%	8%
Bust	6%	-15%

p1 = 18%, p2 = 50%, p3 = 26%, p4 = 6%

R1 = 22%, R2 = 20%, R3 = 8%, R4 = -15%

Expected return of stock A = E[RA] = p1*R1 + p2*R2 + p3*R3 + p4*R4 = 18%*22% + 50%*20% + 26%*8% + 6%*(-15%) = 3.96% + 10% + 2.08% + (-0.9%) = 15.14%

Variance of stock A = σA2 = p1*(R1 - E[RA])2 + p2*(R2 - E[RA])2 + p3*(R3 - E[RA])2 + p4*(R4 - E[RA])2 = 18%*(22%-15.14%)2 + 50%*(20%-15.14%)2 + 26%*(8%-15.14%)2 + 6%*(-15%-15.14%)2 = 0.0008470728+0.00118098+0.0013254696+0.0054505176 = 0.00880404

Standard deviation is square root of variance

Standard deviation of stock A = σA = (0.00880404)1/2 = 9.38298459979553% ~ 9.38% (Rounded to two decimals)

Stock B

State of Economy	Probability of state of Economy	Rate of return if state occurs
Boom	0.30	0.25
Good	0.50	0.16
Poor	0.14	0.06
Bust	0.06	-0.10

p1 = 0.30, p2 = 0.50, p3 =0.14, p4 = 0.06

R1 = 0.25, R2 = 0.16, R3 = 0.06, R4 = -0.10

Expected return of stock B = E[RB] = p1*R1 + p2*R2 + p3*R3 + p4*R4 = 0.30*0.25 + 0.50*0.16 + 0.14*0.06 + 0.06*(-0.10) = 7.5% + 8% + 0.84% + (-0.6%) = 0.1574

Variance of stock B = σB2 = p1*(R1 - E[RB])2 + p2*(R2 - E[RB])2 + p3*(R3 - E[RB])2 + p4*(R4 - E[RB])2 = 0.3*(0.25-0.1574)2 + 0.5*(0.16-0.1574)2 + 0.14*(0.06-0.1574)2 + 0.06*(-0.1-0.1574)2 = 0.002572428+0.00000338+0.0013281464+0.0039752856 = 0.00787924

Standard deviation is square root of variance

Standard deviation of stock B = σB = (0.00787924)1/2 = 8.87650832253314% ~ 8.88% (Rounded to two decimals)

i) Standard deviation of stock A = σA = 9.38%

ii) Standard deviation of stock B = σB = 8.88%

Stock A has a higher standard deviation (9.38%) than stock B (8.88%) as volatility in returns is higher in case of stock A