Question

the following investments you and your friend has provided their expectations for the markets for next year.

State of Economy	Probability of State of Economy	Stock A	Stock B	TSX
Boom	.30	30%	-9%	18%
Normal	.40	16%	12%	10%
Recession	.30	-10%	20%	-10%

              Remember to show all of your work - make clear and understandable and CORRECT

1. Calculate the expected return for stock A.

2. Calculate the expected return for stock B.

  

3. Calculate the expected return for the TSX.

4. Calculate the risk for stock A.

Answer 1

Expected Return = P_B x R_B + P_N x R_N + P_R x R_R

Where,

P_B = Probability of Boom Economy

R_B = Expected Return in a Boom Economy

P_N = Probability of Normal Economy

R_N = Expected Return in a Normal Economy

P_R = Probability of Recession Economy

R_R = Expected Return in a Recession Economy

Using the above formula,

Expected return for Stock A = E_A = (0.3 x 30%) + (0.4 x 16%) + (0.3 x -10%) = 12.40%

Expected return for Stock B = (0.3 x -9%) + (0.4 x 12%) + (0.3 x 20%) = 8.10%

Expected return for the TSX = (0.3 x 18%) + (0.4 x 10%) + (0.3 x -10%) = 6.40%

In order to calculate the risk for Stock A, we need to find the standard deviation for Stock A which is calculated using the following formula:

Standard Deviation (Risk) = Square Root of [ P_B x (R_B - E_A)² + P_N x (R_N - E_A)² + P_R x (R_R - E_A)² ]

= Square Root of [ 0.3 x (30% - 12.4%)² + 0.4 x (16% - 12.4%)² + 0.3 x (-10% - 12.4%)² ]

So, Risk for Stock A = 15.77%