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Consider the following information: Rate of Return If State Occurs State of Probability of Economy State of Economy Stock A Stock B Stock C Boom .55 .15 .22 .42 Bust .45 .14 .04 −.05 a. What is the expected return on an equally weighted portfolio of these three stocks? (Do not round intermediate calculations. Enter your answer as a percent rounded to 2 decimal places, e.g., 32.16.) Expected return % b. What is the variance of a portfolio invested 24 percent each in A and B and 52 percent in C? (Do not round intermediate calculations and round your answer to 6 decimal places, e.g., 32.161616.) Variance

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Answer:

Explanation:

The variance is 0.02081475

State Return

Boom =(24%*0.15+24%*0.22+52%*0.42)=0.3072

Bust =(24%*0.14+24%*0.04-52%*0.05)=0.0172

Variance=0.55*(0.3072-(0.55*0.3072+0.45*0.0172))^2+0.45*(0.0172-(0.55*0.3072+0.45*0.0172))^2=0.02081475

Answer:

a. The Expected Returns are as follows:

For Boom, it is 0.3072

For Bust, it is 0.0172

b. The variance for the entire portfolio is 0.02081475

Explanation:

a. The Expected Return on the Equally weighted portfolio is computed as follows:

Computation for Boom:

Given,

Probability of Stock A-0.15

Probability of Stock B- 0.22

Probability of Stock C-0.42

Percentage of investment in stock A-24%

Percentage of investment in stock B-24%

Percentage of investment in stock C-52%

[tex]\begin{aligned}\text{Expected Return}&=[\text{Probability of Stock A}\times\text{Percentage of investment in stock A}\\&=+\text{Probability of Stock B}\times\text{Percentage of investment in stock B}\\&=+\text{Probability of Stock C}\times\text{Percentage of investment in stock C}]\\&=[(0.15\times24\%)+(0.22\times24\%)+(0.42\times52\%)]\\&=0.036+0.0528+0.2184\\&=0.3072\end{aligned}[/tex]

Computation for Bust:

Probability of Stock A-0.14

Probability of Stock B- 0.04

Probability of Stock C--0.05

Percentage of investment in stock A-24%

Percentage of investment in stock B-24%

Percentage of investment in stock C-52%

[tex]\begin{aligned}\text{Expected Return}&=[\text{Probability of Stock A}\times\text{Percentage of investment in stock A}\\&=+\text{Probability of Stock B}\times\text{Percentage of investment in stock B}\\&=+\text{Probability of Stock C}\times\text{Percentage of investment in stock C}]\\&=[(0.14\times24\%)+(0.04\times24\%)-(0.05\times52\%)]\\&=0.0336+0.0096-0.026\\&=0.0172\end{aligned}[/tex]

b. The variance of the entire portfolio is computed as follows:

   [tex]\begin{aligned}\text{Variance}&=\sqrt{0.55\times(0.3072-(0.55\times0.3072+0.45\times0.0172))}\\&+\sqrt{0.45\times(0.0172-(0.55\times0.3072+0.45\times0.0172))}\\&=0.02081475 \end{aligned}[/tex]

For more information, please refer to the link:

https://brainly.com/question/24173787

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