Question

A portfolio consists of 50% invested in Stock X and 50% invested in Stock Y. We expect two probable states to occur in the future: boom or normal. The probability of each state and the return of each stock in each state are presented in the table below. State Probability of state Return on Stock X Return on Stock Y Boom 20% 25% 35% Normal 80% 10% 5% What are the expected portfolio return and standard deviation?

Select one: a. 12% and 8.1% b. 12% and 9% c. 14.25% and 10.31% d. 14.25% and 9% e. 18.75% and 12.12%

Answer 1

Table 01 Details :

• Portfolio Return in Each State = Weight of Stock X * Return on Stock X + Weight of Stock Y * Return on Stock Y = 0.5 * Return on Stock X + 0.5 * Return on Stock Y
• cumulative portfolio return = Portfolio Return in Each State* Probability of state
• Expected Return = Sum of cumulative portfolio return in each State

Table 02 Details :

• Squared Deviation from Expected Return (4) = ( Expected Return - Portfolio Return (3) ) 2   
• Weighted Squared Deviation from Expected Return =   Squared Deviation from Expected Return (4) * Probability of state (2)
• Variance = Sum of Weighted Squared Deviation from Expected Return in Each State
• Standard Deviation = Square Root of ( Variance )

Ans :

Expected Return 12.00%
Standard Deviation 9.00%