Question

Portfolio Beta and Expected Return   

Assume that CAPM holds and that both Apple and Yahoo plot on the SML. Apple has a beta of 2.6 and Yahoo has a beta of 0.9. The expected return on the market portfolio is 9.25% and the risk-free rate is 1.0%.

1. Based on the above data, what is the expected return for Apple? (Express your answer in percentage, rounded to 2 decimal places.)

The expected return for Apple (in %):  

Show the formula and calculations here:

2. Based o n the above data, what is the expected return for Yahoo? (Express your answer in percentage, rounded to 2 decimal places.)

Expected return for Yahoo (in %):

Show the formula and calculations here:

3. Suppose that you wish to hold a portfolio consisting of only Apple and Yahoo and have your portfolio beta equal to 1.2.

1. What proportion of your portfolio must be in Apple? (Express your answers in percentage, rounded to 2 decimal places.)

[Hint: Review: βp=i=1nwi×βi    The sum of investment proportions (weights, wi ) must equal to one.]

Proportion of investment in Apple (in %):  

Show your calculations here:

2. What proportion of your portfolio must be in Yahoo? (Express your answer in percentage, rounded to 2 decimal places.)

Proportion of investment in Yahoo (in %):

Show your calculations here: [Type here]

4. Based on the above figures, what is the expected return on your portfolio? (Express the final answer in percentage, rounded to 2 decimal places.)

Expected return for your portfolio (in %):  

Show the formula and calculations here:

Compare and comment on your portfolio expected return with the expected return of each of the individual stock. Is the expected return of your portfolio closer to that of Apple or Yahoo? Explain your answer. Include the investment weights (proportions calculated above) for each stock and relevant figures in your explanations. [Word limit: 120 words]

Answer 1

a. Expected Return of Apple using CAPM formula =Risk free Rate+Beta*(Market Return-Risk free rate)
=1%+2.6*(9.25%-1%) =22.45%
b. Expected Return of Yahoo using CAPM formula =Risk free Rate+Beta*(Market Return-Risk free rate)
=1%+0.9*(9.25%-1%) =8.425%

c. i) Weight of Apple +Weight of Yahoo =1
Weight of Apple*Beta of Apple+(1-Weight of Apple)*Beta of Yahoo =1.2
Wa*2.6+(1-Wa)*0.9 =1.2
Wa =(1.2-0.9)/(2.6-0.9) =17.65%
Proportion of portfolio in Apple =16.65%

ii) Proportion of portfolio in Yahoo =1-16.65% =82.35%

d)Expected return of Portfolio =Risk free Rate+Beta Portfolio*(Market Return-Risk free rate)
=1%+1.2*(9.25%-1%) =10.90%

Expected return of Apple is greater than return of yahoo because beta of Apple is higher. The expected return of Yahoo is closer to expected return of portfolio because beta of yahoo is closer to beta of portfolio. The weight of investment in Yahoo of 82.35% is lot higher than weight of investment in Apple. Hence portfolio expected return of portfolio and beta of portfolio is closer to that of Yahoo.