Question

XYZ Investment Corporation is considering a portfolio with 70% weighing in a cyclical stock and 30% weighing in a countercyclical stock. It is expected that there will be three economic states; Good, Average, and Bad, each with equal probabilities of occurrence. The cyclical stock is expected to have returns of 25%, 5%, and 1% in Good, Average, and Bad economics respectively.  The countercyclical stock is expected to have returns of -8%, 2%, and 14% in Good, Average, and Bad economies respectively. Given this information, calculate the portfolio return.

a) 6.5%

b) 8.03%

c) 5.0%

Answer 1

Solution :

As per the information given in the question, it is expected that there will be three economic states; Good, Average, and Bad, each with equal probabilities of occurrence. Thus the probability of each state = 1 / 3

Calculation of Expected Return of Cyclical Stock :

The cyclical stock is expected to have returns of 25%, 5%, and 1% in Good, Average, and Bad economics respectively.

Thus the Expected Return of Cyclical Stock based on the probability = ( 25 % + 5 % + 1 % ) / 3

= 31 % / 3 = 10.3333 %

Calculation of Expected Return of Countercyclical Stock :

The Counter cyclical stock is expected to have returns of – 8 %, 2 %, and 14 % in Good, Average, and Bad economics respectively.

Thus the Expected Return of Countercyclical Stock based on the probability = ( - 8 % + 2 % + 14 % ) / 3

= 8 % / 3 = 2.6667 %

Calculation of Portfolio Return :

The formula for calculation of portfolio Return is

ER = ( R_A * W_A ) + ( R_B * W_B )

Where

E(R_P) = Portfolio Return

R_A = Expected Return of Cyclical stock ;    W_A = Weight of Investment in Cyclical Stock

R_B = Expected Return of Countercyclical stock ;    W_B = Weight of Investment in Countercyclical Stock

As per the information available we have

R_A = 10.3333 %   ; W_A = 70 % = 0.70    ;    R_B = 2.6667 %    ;    W_B = 30 % = 0.30    ;

Applying the values in the formula we have

= ( 10.3333 % * 0.70 ) + ( 2.6667 % * 0.30 )

= 7.2333 % + 0.8000 % = 8.0333 %

Thus the Portfolio return = 8.03 % ( when rounded off to two decimal places )

The solution is Option b) 8.03 %