Question

Tracy is an analyst in an investment bank. She is analysing the value of Bellamy Ltd’s

share and predict the following scenarios of the return over the next year:

Scenarios

Economic recession:probability=25%, Return of BEL=-2%

Fairly stable:Probability=40%, Return of BEL=6%

Economic growth:Probability=35%, Return of BEL=10%

a.Calculate the expected return of BEL over the next year.

b.Calculate the standard deviation of return of BEL over the next year.

Answer 1

Answer A: Expected return Formula : Summation of all Probability * Return

	Probability	Return	Expected return
Recession	0.25	-2%	-0.005
Stable	0.4	6%	0.024
Growth	0.35	10%	0.035
Expected return			5.4%

Answer B: Standard Deviation Calculation

Var(X) = Σx²p − μ²

Var(X) = (-2)^2 * 0.25 + (6%)^2 *0.4 +0.35*(10%)^2 - (5.4)^2

Var(X) = 0.00504 - 0.002916

Var(X) = 0.002124

Standard Deviation = Square root of Var(X)

Standard Deviation = Square root (0.002124)

Standard Deviation = 0.046087 or 4.6%