Question

Consider the following information on returns and probabilities:

Invest 0 of your money in Asset A and 100%in Asset B.

State      Probability           A             B                           

Boom         .25                   12%       4%         

Bust            .75                   6%         18%      

What is the expected return for the portfolio?

		a. 1.7
		b. 2.9
		c. 3.9
		d. 14.5
		e. 15.5
		f. 16.9
		g. 7.5
		h. 9.0
		i. 8.2
		j. 11                    %

Answer 1

Solution :

Calculation of the expected return of Asset A :

The expected return of an Asset can be calculated using the formula

Expected Return = ( P1 * R1 ) + ( P2 * R2 )

Where

P1 = Probability that the economy will boom ; R1 : Expected Return if the economy Booms

P2 = Probability that the economy will bust   ; R2 : Expected Return if the economy busts

As per the information given in the question with respect to Asset A we have:

P1 = 0.25 ; R1 = 12 %   ;   P2 = 0.75    ;   R2 = 6 %

Applying the above values in the formula we have Expected return of Asset A as

= ( 0.25 * 12 % ) + ( 0.75 * 6 % )

= 3 % + 4.5 % = 7.5 %

Thus the Expected Return of Asset A = 7.5 %

Calculation of the expected return of Asset B :

The expected return of an Asset can be calculated using the formula

Expected Return = ( P1 * R1 ) + ( P2 * R2 )

Where

P1 = Probability that the economy will boom ; R1 : Expected Return if the economy Booms

P2 = Probability that the economy will bust   ; R2 : Expected Return if the economy busts

As per the information given in the question with respect to Asset B we have:

P1 = 0.25 ; R1 = 4 %   ;   P2 = 0.75    ;   R2 = 18 %

Applying the above values in the formula we have Expected return of Asset B as

= ( 0.25 * 4 % ) + ( 0.75 * 18 % )

= 1 % + 13.5 % = 14.5 %

Thus the Expected Return of Asset B = 14.5 %

Calculation of expected return of a portfolio :

The formula for calculating the expected return of a portfolio is

RP = ( RE * WE ) + ( RF * WF )

where

RA = Expected Return of Asset A   ;     WA = Weight of Asset A

RB = Expected Return of Asset B   ;     WB = Weight of Asset B

As per the information given we have

RA = 7.5   %    ;    WA = 0 % = 0.00        ; RB = 14.5 %       ;     WB = 100 % = 1

Applying the above values in the formula we have

= ( 7.5 % * 0 % ) + ( 14.5 % * 100 % )

= 14.5 %

The expected return for the portfolio is = 14.5 %

The solution is Option d. 14.5