Question

Consider the following for returns of Stock A and B

State of economy Recession Probability 0.20 Stock A -0.020 Stock B. 0.034

Normal Probability 0.50 Stock A 0.138 Stock B. 0.062

Boom Probability 0.30 Stock A 0.218 Stock B 0.092

The market return is 12% the risk free rate is 5% assuming CAPM holds the market is in equilibrium the forecast E(r)= required E(R)

Which stock has more total risk which stock has more systametic risk explain your answers

Answer 1

Stock A:

Expected Return = 0.20 * (-0.020) + 0.50 * 0.138 + 0.30 * 0.218
Expected Return = 0.1304 or 13.04%

Expected Return = Risk-free Rate + Beta * (Market Return - Risk-free Rate)
0.1304 = 0.05 + Beta * (0.12 - 0.05)
0.0804 = Beta * 0.07
Beta = 1.15

Variance = 0.20 * (-0.020 - 0.1304)^2 + 0.50 * (0.138 - 0.1304)^2 + 0.30 * (0.218 - 0.1304)^2
Variance = 0.00685504

Standard Deviation = (0.00685504)^(1/2)
Standard Deviation = 0.0828 or 8.28%

Stock B:

Expected Return = 0.20 * 0.034 + 0.50 * 0.062 + 0.30 * 0.092
Expected Return = 0.0654 or 6.54%

Expected Return = Risk-free Rate + Beta * (Market Return - Risk-free Rate)
0.0654 = 0.05 + Beta * (0.12 - 0.05)
0.0154 = Beta * 0.07
Beta = 0.22

Variance = 0.20 * (0.034 - 0.0654)^2 + 0.50 * (0.062 - 0.0654)^2 + 0.30 * (0.092 - 0.0654)^2
Variance = 0.00041524

Standard Deviation = (0.00041524)^(1/2)
Standard Deviation = 0.0204 or 2.04%

Total risk is measured by standard deviation. Stock A has higher standard deviation and hence higher total risk.
Systematic risk is measured by beta. Stock A has higher beta and hence higher systematic risk.