Question

Suppose we have the following projections for three stocks. What is the expected return on stock B? What is the standard deviation of returns on stock B?

State of Economy	Probability of State of Economy	Returns if State Occurs
		Stock A	Stock B	Stock C
Boom	0.4	10%	15%	20%
Bust	0.6	8%	5%	0%

Answer 1

> Formula

• Expected Return = Sum of PX

                       where P = Probablity of returns

          X = Returns

• Standard Deviation = [ Sum of { P * ( X - Mean X )2 } ]1/2

> Calculation

State	Probablity	X	PX	( X - Mean X )2	P* ( X - Mean X )2
Boom	0.4	15	6	36	14.4
Bust	0.6	5	3	16	9.6
			9		24

• Mean X = PX

           As per table, PX = 9 %      

• Expected Return on Stock B = PX

Thus PX = 9%

Hence Expected Returns on Stock B is 9%.

• Standard Deviation = [ Sum of { P * ( X - Mean X )2 } ]1/2

                                            = [ 24 ] 1/2

                                            = 4.899 %

> Answer

• Expected returns = 9%
• Standard Deviation = 4.899%

Hope you understand the solution.