Question

Given the following information, what is the standard deviation of Stock "B"? Rate of Return if State Occurs State of Stock Probability of State of Economy Stock A Stock B Economy Boom 45% 0.20 0.45 0.32 Bust 55% -0.10 -0.35 -0.21 Asset Weights 50% 2503 25%

Answer 1

For Stock B

Expected Return of the stock = $\sum$Probability * Return

Expected Return of the stock B = (0.45 * 0.45) + (0.55 * (-0.35)) = 0.2025 - 0.1925

Expected Return of the stock B, Bbar = 0.01

Now,

Standard Deviation = Square root [ $\sum$(Bvalue - Bbar)^²  * Probability ]

Standard Deviation = Square root { [ (0.45 - 0.01)^² * 0.45] + [ (-0.35 - 0.01)^² * 0.55] }

Standard Deviation = Square root { [0.1936 * 0.45] + [0.1296 * 0.55] }

Standard Deviation = Square root (0.1584)

Standard Deviation = 0.3980 = 39.80%