Question

Please show all work and formula:

Please use the information on the table below to answer this question.

Security                       Actual Return             Beta

A                                 12%                             1.2

B                                  10%                             1.0

C                                  14%                             1.4

1. Assume the risk-free interest rate is 1% and the market risk premium is 5.5%. An investor would like to invest $40,000 in Security A, $25,000 in security B and $50,000 in Security C. Find the portfolio’s expected return.
2. Find the portfolio’s actual return.
3. Based on your answers to a and b, is the portfolio’s return higher or lower than required? How should prices react?

Answer 1

Expected returns

Stock A

As per CAPM

expected return = risk-free rate + beta * (Market risk premium)

Expected return% = 1 + 1.2 * (5.5)

Expected return% = 7.6

Stock B

As per CAPM

expected return = risk-free rate + beta * (Market risk premium)

Expected return% = 1 + 1 * (5.5)

Expected return% = 6.5

Stock C

As per CAPM

expected return = risk-free rate + beta * (Market risk premium)

Expected return% = 1 + 1.4 * (5.5)

Expected return% = 8.7

Total Portfolio value = Value of Stock A + Value of Stock B + Value of Stock C

=40000+25000+50000

=115000

Weight of Stock A = Value of Stock A/Total Portfolio Value

= 40000/115000

=0.3478

Weight of Stock B = Value of Stock B/Total Portfolio Value

= 25000/115000

=0.2174

Weight of Stock C = Value of Stock C/Total Portfolio Value

= 50000/115000

=0.4348

Expected return of Portfolio = Weight of Stock A*Expected return of Stock A+Weight of Stock B*Expected return of Stock B+Weight of Stock C*Expected return of Stock C

Expected return of Portfolio = 7.6*0.3478+6.5*0.2174+8.7*0.4348

Expected return of Portfolio = 7.8391

Total Portfolio value = Value of Stock A + Value of Stock B + Value of Stock C

=40000+25000+50000

=115000

Weight of Stock A = Value of Stock A/Total Portfolio Value

= 40000/115000

=0.3478

Weight of Stock B = Value of Stock B/Total Portfolio Value

= 25000/115000

=0.2174

Weight of Stock C = Value of Stock C/Total Portfolio Value

= 50000/115000

=0.4348

Actual return of Portfolio = Weight of Stock A*Actual return of Stock A+Weight of Stock B*Actual return of Stock B+Weight of Stock C*Actual return of Stock C

Actual return of Portfolio = 12*0.3478+10*0.2174+14*0.4348

Actual return of Portfolio = 12.4348

Actual return is more than expected return prices will fall