Systematic versus Unsystematic Risk [LO3] Consider the following information about Stocks I and II: The market risk premium is 7 percent, and the risk-free rate is 4 percent. Which stock has the most systematic risk? Which one has the most unsystematic risk? Which stock is “riskier”? Explain.

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Answer 1

Textbook Question

Chapter 13, Problem 26QP

Systematic versus Unsystematic Risk [LO3] Consider the following information about Stocks I and II:

Chapter 13, Problem 26QP, Systematic versus Unsystematic Risk [LO3] Consider the following information about Stocks I and II:

The market risk premium is 7 percent, and the risk-free rate is 4 percent. Which stock has the most systematic risk? Which one has the most unsystematic risk? Which stock is “riskier”? Explain.

Expert Solution & Answer

Summary Introduction

To determine: The stock that has the most systematic risk and most unsystematic risk.

Introduction:

Systematic risk refers to the market-specific risk that affects all the stocks in the market. Unsystematic risk refers to the company-specific risk that affects only the individual company.

Answer to Problem 26QP

The expected return on Stock I is 15.90 percent, the beta is 1.70, and the standard deviation is 7.87%. The expected return on Stock II is 9.15 percent, the beta is 0.74, and the standard deviation is 18.90%.

The beta refers to the systematic risk of the stock. Stock I has higher beta than Stock II. Hence, the systematic risk of Stock I is higher. The standard deviation indicates the total risk of the stock. The standard deviation is high for Stock II despite having a low beta. Hence, a major portion of the standard deviation of Stock II is the unsystematic risk.

Stock II has higher unsystematic risk than Stock I. The formation of a portfolio helps in diversifying the unsystematic risk. Although Stock II has a higher unsystematic risk, it can be diversified completely. However, the beta cannot be eliminated. Hence, Stock I is riskier than Stock II.

The expected return and the market risk premium depends on the beta of the stock. As Stock I has a higher beta, the expected return and market risk premium of the stock will be higher than Stock II.

Explanation of Solution

Given information:

The probability of having a recession, normal economy, and irrational exuberance is 0.15, 0.70, and 0.15 respectively. Stock I will yield 2%, 21%, and 6% when there is a recession, normal economy, and irrational exuberance respectively.

Stock II will yield (25%), 9%, and 44% when there is a recession, normal economy, and irrational exuberance respectively. The market risk premium is 7% and the risk-free rate is 4%.

The formula to calculate the expected return on the stock:

$Expected returns[E(R)]=[(Possible returns(R1)×Probability(P1))+…+(Possible returns(Rn)×Probability(Pn))]$

The formula to calculate the beta of the stock:

$E(Ri)=Rf+[E(RM)−Rf]×βi$

Where,

“E (R_i)” refers to the expected return on a risky asset

“R_f” refers to the risk-free rate

“E (R_M)” refers to the expected return on the market portfolio

“β_i” refers to the beta coefficient of the risky asset relative to the market portfolio

The formula to calculate the standard deviation:

$Standarddeviation}=([(Possible returns(R1)−Expected returnsE(R))2×Probability(P1)]+…+[(Possible returns(Rn)−Expected returnsE(R))2×Probability(Pn)])$

Compute the expected return on Stock I:

“R₁” is the returns during the recession. The probability of having a recession is “P₁”. Similarly, “R₂” is the returns in a normal economy. The probability of having a normal is “P₂”. “R₃” is the returns in irrational exuberance. The probability of having an irrational exuberance is “P₃”.

$Expected returns[E(R)]=[(Possible returns(R1)×Probability(P1))+(Possible returns(R2)×Probability(P2))+(Possible returns(R2)×Probability(P2))]=((0.15)×0.02)+(0.70×0.21)+(0.15×0.06)=0.1590 or 15.90%$

Hence, the expected return on Stock I is 15.90 percent.

Compute the beta of Stock I:

$E(RI)=Rf+[E(RM)−Rf]×βI0.1590=0.04+[0.07]×βIβI=1.70$

Hence, the beta of Stock I is 1.70.

Compute the standard deviation of Stock I:

“R₁” is the returns during the recession. The probability of having a recession is “P₁”. Similarly, “R₂” is the returns in a normal economy. The probability of having a normal is “P₂”. “R₃” is the returns in irrational exuberance. The probability of having an irrational exuberance is “P₃”.

$Standarddeviation}=([(Possible returns(R1)−Expected returnsE(R))2×Probability(P1)]+…+[(Possible returns(Rn)−Expected returnsE(R))2×Probability(Pn)])=[[(0.02−0.1590)2×0.15]+[(0.21−0.1590)2×0.70]+[((0.06)−0.1590)2×0.15]]=0.00619=0.0787 or 7.87%$

Hence, the standard deviation of Stock I is 7.87%.

Compute the expected return on Stock II:

“R₁” is the returns during the recession. The probability of having a recession is “P₁”. Similarly, “R₂” is the returns in a normal economy. The probability of having a normal is “P₂”. “R₃” is the returns in irrational exuberance. The probability of having an irrational exuberance is “P₃”.

$Expected returns[E(R)]=[(Possible returns(R1)×Probability(P1))+(Possible returns(R2)×Probability(P2))+(Possible returns(R2)×Probability(P2))]=((0.15)×(0.25))+(0.70×0.09)+(0.15×0.44)=0.0915 or 9.15%$

Hence, the expected return on Stock II is 9.15 percent.

Compute the beta of Stock II:

$E(RII)=Rf+[E(RM)−Rf]×βII0.0915=0.04+[0.07]×βIIβII=0.74$

Hence, the beta of Stock II is 0.74.

Compute the standard deviation of Stock II:

“R₁” is the returns during the recession. The probability of having a recession is “P₁”. Similarly, “R₂” is the returns in a normal economy. The probability of having a normal is “P₂”. “R₃” is the returns in irrational exuberance. The probability of having an irrational exuberance is “P₃”.

$Standarddeviation}=([(Possible returns(R1)−Expected returnsE(R))2×Probability(P1)]+…+[(Possible returns(Rn)−Expected returnsE(R))2×Probability(Pn)])=[[((0.25)−0.0915)2×0.15]+[(0.09−0.0915)2×0.70]+[((0.44)−0.0915)2×0.15]]=0.03571=0.1890 or 18.90%$

Hence, the standard deviation of Stock II is 18.90%.

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Answer 2

Textbook Question

Chapter 13, Problem 26QP

Systematic versus Unsystematic Risk [LO3] Consider the following information about Stocks I and II:

Chapter 13, Problem 26QP, Systematic versus Unsystematic Risk [LO3] Consider the following information about Stocks I and II:

The market risk premium is 7 percent, and the risk-free rate is 4 percent. Which stock has the most systematic risk? Which one has the most unsystematic risk? Which stock is “riskier”? Explain.

Expert Solution & Answer

Summary Introduction

To determine: The stock that has the most systematic risk and most unsystematic risk.

Introduction:

Systematic risk refers to the market-specific risk that affects all the stocks in the market. Unsystematic risk refers to the company-specific risk that affects only the individual company.

Answer to Problem 26QP

The expected return on Stock I is 15.90 percent, the beta is 1.70, and the standard deviation is 7.87%. The expected return on Stock II is 9.15 percent, the beta is 0.74, and the standard deviation is 18.90%.

The beta refers to the systematic risk of the stock. Stock I has higher beta than Stock II. Hence, the systematic risk of Stock I is higher. The standard deviation indicates the total risk of the stock. The standard deviation is high for Stock II despite having a low beta. Hence, a major portion of the standard deviation of Stock II is the unsystematic risk.

Stock II has higher unsystematic risk than Stock I. The formation of a portfolio helps in diversifying the unsystematic risk. Although Stock II has a higher unsystematic risk, it can be diversified completely. However, the beta cannot be eliminated. Hence, Stock I is riskier than Stock II.

The expected return and the market risk premium depends on the beta of the stock. As Stock I has a higher beta, the expected return and market risk premium of the stock will be higher than Stock II.

Explanation of Solution

Given information:

The probability of having a recession, normal economy, and irrational exuberance is 0.15, 0.70, and 0.15 respectively. Stock I will yield 2%, 21%, and 6% when there is a recession, normal economy, and irrational exuberance respectively.

Stock II will yield (25%), 9%, and 44% when there is a recession, normal economy, and irrational exuberance respectively. The market risk premium is 7% and the risk-free rate is 4%.

The formula to calculate the expected return on the stock:

$Expected returns[E(R)]=[(Possible returns(R1)×Probability(P1))+…+(Possible returns(Rn)×Probability(Pn))]$

The formula to calculate the beta of the stock:

$E(Ri)=Rf+[E(RM)−Rf]×βi$

Where,

“E (R_i)” refers to the expected return on a risky asset

“R_f” refers to the risk-free rate

“E (R_M)” refers to the expected return on the market portfolio

“β_i” refers to the beta coefficient of the risky asset relative to the market portfolio

The formula to calculate the standard deviation:

$Standarddeviation}=([(Possible returns(R1)−Expected returnsE(R))2×Probability(P1)]+…+[(Possible returns(Rn)−Expected returnsE(R))2×Probability(Pn)])$

Compute the expected return on Stock I:

“R₁” is the returns during the recession. The probability of having a recession is “P₁”. Similarly, “R₂” is the returns in a normal economy. The probability of having a normal is “P₂”. “R₃” is the returns in irrational exuberance. The probability of having an irrational exuberance is “P₃”.

$Expected returns[E(R)]=[(Possible returns(R1)×Probability(P1))+(Possible returns(R2)×Probability(P2))+(Possible returns(R2)×Probability(P2))]=((0.15)×0.02)+(0.70×0.21)+(0.15×0.06)=0.1590 or 15.90%$

Hence, the expected return on Stock I is 15.90 percent.

Compute the beta of Stock I:

$E(RI)=Rf+[E(RM)−Rf]×βI0.1590=0.04+[0.07]×βIβI=1.70$

Hence, the beta of Stock I is 1.70.

Compute the standard deviation of Stock I:

“R₁” is the returns during the recession. The probability of having a recession is “P₁”. Similarly, “R₂” is the returns in a normal economy. The probability of having a normal is “P₂”. “R₃” is the returns in irrational exuberance. The probability of having an irrational exuberance is “P₃”.

$Standarddeviation}=([(Possible returns(R1)−Expected returnsE(R))2×Probability(P1)]+…+[(Possible returns(Rn)−Expected returnsE(R))2×Probability(Pn)])=[[(0.02−0.1590)2×0.15]+[(0.21−0.1590)2×0.70]+[((0.06)−0.1590)2×0.15]]=0.00619=0.0787 or 7.87%$

Hence, the standard deviation of Stock I is 7.87%.

Compute the expected return on Stock II:

“R₁” is the returns during the recession. The probability of having a recession is “P₁”. Similarly, “R₂” is the returns in a normal economy. The probability of having a normal is “P₂”. “R₃” is the returns in irrational exuberance. The probability of having an irrational exuberance is “P₃”.

$Expected returns[E(R)]=[(Possible returns(R1)×Probability(P1))+(Possible returns(R2)×Probability(P2))+(Possible returns(R2)×Probability(P2))]=((0.15)×(0.25))+(0.70×0.09)+(0.15×0.44)=0.0915 or 9.15%$

Hence, the expected return on Stock II is 9.15 percent.

Compute the beta of Stock II:

$E(RII)=Rf+[E(RM)−Rf]×βII0.0915=0.04+[0.07]×βIIβII=0.74$

Hence, the beta of Stock II is 0.74.

Compute the standard deviation of Stock II:

“R₁” is the returns during the recession. The probability of having a recession is “P₁”. Similarly, “R₂” is the returns in a normal economy. The probability of having a normal is “P₂”. “R₃” is the returns in irrational exuberance. The probability of having an irrational exuberance is “P₃”.

$Standarddeviation}=([(Possible returns(R1)−Expected returnsE(R))2×Probability(P1)]+…+[(Possible returns(Rn)−Expected returnsE(R))2×Probability(Pn)])=[[((0.25)−0.0915)2×0.15]+[(0.09−0.0915)2×0.70]+[((0.44)−0.0915)2×0.15]]=0.03571=0.1890 or 18.90%$

Hence, the standard deviation of Stock II is 18.90%.

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Answer 3

Textbook Question

Chapter 13, Problem 26QP

Systematic versus Unsystematic Risk [LO3] Consider the following information about Stocks I and II:

Chapter 13, Problem 26QP, Systematic versus Unsystematic Risk [LO3] Consider the following information about Stocks I and II:

The market risk premium is 7 percent, and the risk-free rate is 4 percent. Which stock has the most systematic risk? Which one has the most unsystematic risk? Which stock is “riskier”? Explain.

Expert Solution & Answer

Summary Introduction

To determine: The stock that has the most systematic risk and most unsystematic risk.

Introduction:

Systematic risk refers to the market-specific risk that affects all the stocks in the market. Unsystematic risk refers to the company-specific risk that affects only the individual company.

Answer to Problem 26QP

The expected return on Stock I is 15.90 percent, the beta is 1.70, and the standard deviation is 7.87%. The expected return on Stock II is 9.15 percent, the beta is 0.74, and the standard deviation is 18.90%.

The beta refers to the systematic risk of the stock. Stock I has higher beta than Stock II. Hence, the systematic risk of Stock I is higher. The standard deviation indicates the total risk of the stock. The standard deviation is high for Stock II despite having a low beta. Hence, a major portion of the standard deviation of Stock II is the unsystematic risk.

Stock II has higher unsystematic risk than Stock I. The formation of a portfolio helps in diversifying the unsystematic risk. Although Stock II has a higher unsystematic risk, it can be diversified completely. However, the beta cannot be eliminated. Hence, Stock I is riskier than Stock II.

The expected return and the market risk premium depends on the beta of the stock. As Stock I has a higher beta, the expected return and market risk premium of the stock will be higher than Stock II.

Explanation of Solution

Given information:

The probability of having a recession, normal economy, and irrational exuberance is 0.15, 0.70, and 0.15 respectively. Stock I will yield 2%, 21%, and 6% when there is a recession, normal economy, and irrational exuberance respectively.

Stock II will yield (25%), 9%, and 44% when there is a recession, normal economy, and irrational exuberance respectively. The market risk premium is 7% and the risk-free rate is 4%.

The formula to calculate the expected return on the stock:

$Expected returns[E(R)]=[(Possible returns(R1)×Probability(P1))+…+(Possible returns(Rn)×Probability(Pn))]$

The formula to calculate the beta of the stock:

$E(Ri)=Rf+[E(RM)−Rf]×βi$

Where,

“E (R_i)” refers to the expected return on a risky asset

“R_f” refers to the risk-free rate

“E (R_M)” refers to the expected return on the market portfolio

“β_i” refers to the beta coefficient of the risky asset relative to the market portfolio

The formula to calculate the standard deviation:

$Standarddeviation}=([(Possible returns(R1)−Expected returnsE(R))2×Probability(P1)]+…+[(Possible returns(Rn)−Expected returnsE(R))2×Probability(Pn)])$

Compute the expected return on Stock I:

“R₁” is the returns during the recession. The probability of having a recession is “P₁”. Similarly, “R₂” is the returns in a normal economy. The probability of having a normal is “P₂”. “R₃” is the returns in irrational exuberance. The probability of having an irrational exuberance is “P₃”.

$Expected returns[E(R)]=[(Possible returns(R1)×Probability(P1))+(Possible returns(R2)×Probability(P2))+(Possible returns(R2)×Probability(P2))]=((0.15)×0.02)+(0.70×0.21)+(0.15×0.06)=0.1590 or 15.90%$

Hence, the expected return on Stock I is 15.90 percent.

Compute the beta of Stock I:

$E(RI)=Rf+[E(RM)−Rf]×βI0.1590=0.04+[0.07]×βIβI=1.70$

Hence, the beta of Stock I is 1.70.

Compute the standard deviation of Stock I:

“R₁” is the returns during the recession. The probability of having a recession is “P₁”. Similarly, “R₂” is the returns in a normal economy. The probability of having a normal is “P₂”. “R₃” is the returns in irrational exuberance. The probability of having an irrational exuberance is “P₃”.

$Standarddeviation}=([(Possible returns(R1)−Expected returnsE(R))2×Probability(P1)]+…+[(Possible returns(Rn)−Expected returnsE(R))2×Probability(Pn)])=[[(0.02−0.1590)2×0.15]+[(0.21−0.1590)2×0.70]+[((0.06)−0.1590)2×0.15]]=0.00619=0.0787 or 7.87%$

Hence, the standard deviation of Stock I is 7.87%.

Compute the expected return on Stock II:

“R₁” is the returns during the recession. The probability of having a recession is “P₁”. Similarly, “R₂” is the returns in a normal economy. The probability of having a normal is “P₂”. “R₃” is the returns in irrational exuberance. The probability of having an irrational exuberance is “P₃”.

$Expected returns[E(R)]=[(Possible returns(R1)×Probability(P1))+(Possible returns(R2)×Probability(P2))+(Possible returns(R2)×Probability(P2))]=((0.15)×(0.25))+(0.70×0.09)+(0.15×0.44)=0.0915 or 9.15%$

Hence, the expected return on Stock II is 9.15 percent.

Compute the beta of Stock II:

$E(RII)=Rf+[E(RM)−Rf]×βII0.0915=0.04+[0.07]×βIIβII=0.74$

Hence, the beta of Stock II is 0.74.

Compute the standard deviation of Stock II:

“R₁” is the returns during the recession. The probability of having a recession is “P₁”. Similarly, “R₂” is the returns in a normal economy. The probability of having a normal is “P₂”. “R₃” is the returns in irrational exuberance. The probability of having an irrational exuberance is “P₃”.

$Standarddeviation}=([(Possible returns(R1)−Expected returnsE(R))2×Probability(P1)]+…+[(Possible returns(Rn)−Expected returnsE(R))2×Probability(Pn)])=[[((0.25)−0.0915)2×0.15]+[(0.09−0.0915)2×0.70]+[((0.44)−0.0915)2×0.15]]=0.03571=0.1890 or 18.90%$

Hence, the standard deviation of Stock II is 18.90%.

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Answer 4

Textbook Question

Chapter 13, Problem 26QP

Systematic versus Unsystematic Risk [LO3] Consider the following information about Stocks I and II:

Chapter 13, Problem 26QP, Systematic versus Unsystematic Risk [LO3] Consider the following information about Stocks I and II:

The market risk premium is 7 percent, and the risk-free rate is 4 percent. Which stock has the most systematic risk? Which one has the most unsystematic risk? Which stock is “riskier”? Explain.

Expert Solution & Answer

Summary Introduction

To determine: The stock that has the most systematic risk and most unsystematic risk.

Introduction:

Systematic risk refers to the market-specific risk that affects all the stocks in the market. Unsystematic risk refers to the company-specific risk that affects only the individual company.

Answer to Problem 26QP

The expected return on Stock I is 15.90 percent, the beta is 1.70, and the standard deviation is 7.87%. The expected return on Stock II is 9.15 percent, the beta is 0.74, and the standard deviation is 18.90%.

The beta refers to the systematic risk of the stock. Stock I has higher beta than Stock II. Hence, the systematic risk of Stock I is higher. The standard deviation indicates the total risk of the stock. The standard deviation is high for Stock II despite having a low beta. Hence, a major portion of the standard deviation of Stock II is the unsystematic risk.

Stock II has higher unsystematic risk than Stock I. The formation of a portfolio helps in diversifying the unsystematic risk. Although Stock II has a higher unsystematic risk, it can be diversified completely. However, the beta cannot be eliminated. Hence, Stock I is riskier than Stock II.

The expected return and the market risk premium depends on the beta of the stock. As Stock I has a higher beta, the expected return and market risk premium of the stock will be higher than Stock II.

Explanation of Solution

Given information:

The probability of having a recession, normal economy, and irrational exuberance is 0.15, 0.70, and 0.15 respectively. Stock I will yield 2%, 21%, and 6% when there is a recession, normal economy, and irrational exuberance respectively.

Stock II will yield (25%), 9%, and 44% when there is a recession, normal economy, and irrational exuberance respectively. The market risk premium is 7% and the risk-free rate is 4%.

The formula to calculate the expected return on the stock:

$Expected returns[E(R)]=[(Possible returns(R1)×Probability(P1))+…+(Possible returns(Rn)×Probability(Pn))]$

The formula to calculate the beta of the stock:

$E(Ri)=Rf+[E(RM)−Rf]×βi$

Where,

“E (R_i)” refers to the expected return on a risky asset

“R_f” refers to the risk-free rate

“E (R_M)” refers to the expected return on the market portfolio

“β_i” refers to the beta coefficient of the risky asset relative to the market portfolio

The formula to calculate the standard deviation:

$Standarddeviation}=([(Possible returns(R1)−Expected returnsE(R))2×Probability(P1)]+…+[(Possible returns(Rn)−Expected returnsE(R))2×Probability(Pn)])$

Compute the expected return on Stock I:

“R₁” is the returns during the recession. The probability of having a recession is “P₁”. Similarly, “R₂” is the returns in a normal economy. The probability of having a normal is “P₂”. “R₃” is the returns in irrational exuberance. The probability of having an irrational exuberance is “P₃”.

$Expected returns[E(R)]=[(Possible returns(R1)×Probability(P1))+(Possible returns(R2)×Probability(P2))+(Possible returns(R2)×Probability(P2))]=((0.15)×0.02)+(0.70×0.21)+(0.15×0.06)=0.1590 or 15.90%$

Hence, the expected return on Stock I is 15.90 percent.

Compute the beta of Stock I:

$E(RI)=Rf+[E(RM)−Rf]×βI0.1590=0.04+[0.07]×βIβI=1.70$

Hence, the beta of Stock I is 1.70.

Compute the standard deviation of Stock I:

“R₁” is the returns during the recession. The probability of having a recession is “P₁”. Similarly, “R₂” is the returns in a normal economy. The probability of having a normal is “P₂”. “R₃” is the returns in irrational exuberance. The probability of having an irrational exuberance is “P₃”.

$Standarddeviation}=([(Possible returns(R1)−Expected returnsE(R))2×Probability(P1)]+…+[(Possible returns(Rn)−Expected returnsE(R))2×Probability(Pn)])=[[(0.02−0.1590)2×0.15]+[(0.21−0.1590)2×0.70]+[((0.06)−0.1590)2×0.15]]=0.00619=0.0787 or 7.87%$

Hence, the standard deviation of Stock I is 7.87%.

Compute the expected return on Stock II:

“R₁” is the returns during the recession. The probability of having a recession is “P₁”. Similarly, “R₂” is the returns in a normal economy. The probability of having a normal is “P₂”. “R₃” is the returns in irrational exuberance. The probability of having an irrational exuberance is “P₃”.

$Expected returns[E(R)]=[(Possible returns(R1)×Probability(P1))+(Possible returns(R2)×Probability(P2))+(Possible returns(R2)×Probability(P2))]=((0.15)×(0.25))+(0.70×0.09)+(0.15×0.44)=0.0915 or 9.15%$

Hence, the expected return on Stock II is 9.15 percent.

Compute the beta of Stock II:

$E(RII)=Rf+[E(RM)−Rf]×βII0.0915=0.04+[0.07]×βIIβII=0.74$

Hence, the beta of Stock II is 0.74.

Compute the standard deviation of Stock II:

“R₁” is the returns during the recession. The probability of having a recession is “P₁”. Similarly, “R₂” is the returns in a normal economy. The probability of having a normal is “P₂”. “R₃” is the returns in irrational exuberance. The probability of having an irrational exuberance is “P₃”.

$Standarddeviation}=([(Possible returns(R1)−Expected returnsE(R))2×Probability(P1)]+…+[(Possible returns(Rn)−Expected returnsE(R))2×Probability(Pn)])=[[((0.25)−0.0915)2×0.15]+[(0.09−0.0915)2×0.70]+[((0.44)−0.0915)2×0.15]]=0.03571=0.1890 or 18.90%$

Hence, the standard deviation of Stock II is 18.90%.

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Answer 5

Textbook Question

Answer 6

Textbook Question

Answer 7

Expert Solution & Answer

Summary Introduction

To determine: The stock that has the most systematic risk and most unsystematic risk.

Introduction:

Systematic risk refers to the market-specific risk that affects all the stocks in the market. Unsystematic risk refers to the company-specific risk that affects only the individual company.

Answer to Problem 26QP

The expected return on Stock I is 15.90 percent, the beta is 1.70, and the standard deviation is 7.87%. The expected return on Stock II is 9.15 percent, the beta is 0.74, and the standard deviation is 18.90%.

The beta refers to the systematic risk of the stock. Stock I has higher beta than Stock II. Hence, the systematic risk of Stock I is higher. The standard deviation indicates the total risk of the stock. The standard deviation is high for Stock II despite having a low beta. Hence, a major portion of the standard deviation of Stock II is the unsystematic risk.

Stock II has higher unsystematic risk than Stock I. The formation of a portfolio helps in diversifying the unsystematic risk. Although Stock II has a higher unsystematic risk, it can be diversified completely. However, the beta cannot be eliminated. Hence, Stock I is riskier than Stock II.

The expected return and the market risk premium depends on the beta of the stock. As Stock I has a higher beta, the expected return and market risk premium of the stock will be higher than Stock II.

Explanation of Solution

Given information:

The probability of having a recession, normal economy, and irrational exuberance is 0.15, 0.70, and 0.15 respectively. Stock I will yield 2%, 21%, and 6% when there is a recession, normal economy, and irrational exuberance respectively.

Stock II will yield (25%), 9%, and 44% when there is a recession, normal economy, and irrational exuberance respectively. The market risk premium is 7% and the risk-free rate is 4%.

The formula to calculate the expected return on the stock:

$Expected returns[E(R)]=[(Possible returns(R1)×Probability(P1))+…+(Possible returns(Rn)×Probability(Pn))]$

The formula to calculate the beta of the stock:

$E(Ri)=Rf+[E(RM)−Rf]×βi$

Where,

“E (R_i)” refers to the expected return on a risky asset

“R_f” refers to the risk-free rate

“E (R_M)” refers to the expected return on the market portfolio

“β_i” refers to the beta coefficient of the risky asset relative to the market portfolio

The formula to calculate the standard deviation:

$Standarddeviation}=([(Possible returns(R1)−Expected returnsE(R))2×Probability(P1)]+…+[(Possible returns(Rn)−Expected returnsE(R))2×Probability(Pn)])$

Compute the expected return on Stock I:

“R₁” is the returns during the recession. The probability of having a recession is “P₁”. Similarly, “R₂” is the returns in a normal economy. The probability of having a normal is “P₂”. “R₃” is the returns in irrational exuberance. The probability of having an irrational exuberance is “P₃”.

$Expected returns[E(R)]=[(Possible returns(R1)×Probability(P1))+(Possible returns(R2)×Probability(P2))+(Possible returns(R2)×Probability(P2))]=((0.15)×0.02)+(0.70×0.21)+(0.15×0.06)=0.1590 or 15.90%$

Hence, the expected return on Stock I is 15.90 percent.

Compute the beta of Stock I:

$E(RI)=Rf+[E(RM)−Rf]×βI0.1590=0.04+[0.07]×βIβI=1.70$

Hence, the beta of Stock I is 1.70.

Compute the standard deviation of Stock I:

“R₁” is the returns during the recession. The probability of having a recession is “P₁”. Similarly, “R₂” is the returns in a normal economy. The probability of having a normal is “P₂”. “R₃” is the returns in irrational exuberance. The probability of having an irrational exuberance is “P₃”.

$Standarddeviation}=([(Possible returns(R1)−Expected returnsE(R))2×Probability(P1)]+…+[(Possible returns(Rn)−Expected returnsE(R))2×Probability(Pn)])=[[(0.02−0.1590)2×0.15]+[(0.21−0.1590)2×0.70]+[((0.06)−0.1590)2×0.15]]=0.00619=0.0787 or 7.87%$

Hence, the standard deviation of Stock I is 7.87%.

Compute the expected return on Stock II:

“R₁” is the returns during the recession. The probability of having a recession is “P₁”. Similarly, “R₂” is the returns in a normal economy. The probability of having a normal is “P₂”. “R₃” is the returns in irrational exuberance. The probability of having an irrational exuberance is “P₃”.

$Expected returns[E(R)]=[(Possible returns(R1)×Probability(P1))+(Possible returns(R2)×Probability(P2))+(Possible returns(R2)×Probability(P2))]=((0.15)×(0.25))+(0.70×0.09)+(0.15×0.44)=0.0915 or 9.15%$

Hence, the expected return on Stock II is 9.15 percent.

Compute the beta of Stock II:

$E(RII)=Rf+[E(RM)−Rf]×βII0.0915=0.04+[0.07]×βIIβII=0.74$

Hence, the beta of Stock II is 0.74.

Compute the standard deviation of Stock II:

“R₁” is the returns during the recession. The probability of having a recession is “P₁”. Similarly, “R₂” is the returns in a normal economy. The probability of having a normal is “P₂”. “R₃” is the returns in irrational exuberance. The probability of having an irrational exuberance is “P₃”.

$Standarddeviation}=([(Possible returns(R1)−Expected returnsE(R))2×Probability(P1)]+…+[(Possible returns(Rn)−Expected returnsE(R))2×Probability(Pn)])=[[((0.25)−0.0915)2×0.15]+[(0.09−0.0915)2×0.70]+[((0.44)−0.0915)2×0.15]]=0.03571=0.1890 or 18.90%$

Hence, the standard deviation of Stock II is 18.90%.

Answer 8

Expert Solution & Answer

Summary Introduction

To determine: The stock that has the most systematic risk and most unsystematic risk.

Introduction:

Systematic risk refers to the market-specific risk that affects all the stocks in the market. Unsystematic risk refers to the company-specific risk that affects only the individual company.

Answer to Problem 26QP

The expected return on Stock I is 15.90 percent, the beta is 1.70, and the standard deviation is 7.87%. The expected return on Stock II is 9.15 percent, the beta is 0.74, and the standard deviation is 18.90%.

The beta refers to the systematic risk of the stock. Stock I has higher beta than Stock II. Hence, the systematic risk of Stock I is higher. The standard deviation indicates the total risk of the stock. The standard deviation is high for Stock II despite having a low beta. Hence, a major portion of the standard deviation of Stock II is the unsystematic risk.

Stock II has higher unsystematic risk than Stock I. The formation of a portfolio helps in diversifying the unsystematic risk. Although Stock II has a higher unsystematic risk, it can be diversified completely. However, the beta cannot be eliminated. Hence, Stock I is riskier than Stock II.

The expected return and the market risk premium depends on the beta of the stock. As Stock I has a higher beta, the expected return and market risk premium of the stock will be higher than Stock II.

Explanation of Solution

Given information:

The probability of having a recession, normal economy, and irrational exuberance is 0.15, 0.70, and 0.15 respectively. Stock I will yield 2%, 21%, and 6% when there is a recession, normal economy, and irrational exuberance respectively.

Stock II will yield (25%), 9%, and 44% when there is a recession, normal economy, and irrational exuberance respectively. The market risk premium is 7% and the risk-free rate is 4%.

The formula to calculate the expected return on the stock:

$Expected returns[E(R)]=[(Possible returns(R1)×Probability(P1))+…+(Possible returns(Rn)×Probability(Pn))]$

The formula to calculate the beta of the stock:

$E(Ri)=Rf+[E(RM)−Rf]×βi$

Where,

“E (R_i)” refers to the expected return on a risky asset

“R_f” refers to the risk-free rate

“E (R_M)” refers to the expected return on the market portfolio

“β_i” refers to the beta coefficient of the risky asset relative to the market portfolio

The formula to calculate the standard deviation:

$Standarddeviation}=([(Possible returns(R1)−Expected returnsE(R))2×Probability(P1)]+…+[(Possible returns(Rn)−Expected returnsE(R))2×Probability(Pn)])$

Compute the expected return on Stock I:

“R₁” is the returns during the recession. The probability of having a recession is “P₁”. Similarly, “R₂” is the returns in a normal economy. The probability of having a normal is “P₂”. “R₃” is the returns in irrational exuberance. The probability of having an irrational exuberance is “P₃”.

$Expected returns[E(R)]=[(Possible returns(R1)×Probability(P1))+(Possible returns(R2)×Probability(P2))+(Possible returns(R2)×Probability(P2))]=((0.15)×0.02)+(0.70×0.21)+(0.15×0.06)=0.1590 or 15.90%$

Hence, the expected return on Stock I is 15.90 percent.

Compute the beta of Stock I:

$E(RI)=Rf+[E(RM)−Rf]×βI0.1590=0.04+[0.07]×βIβI=1.70$

Hence, the beta of Stock I is 1.70.

Compute the standard deviation of Stock I:

“R₁” is the returns during the recession. The probability of having a recession is “P₁”. Similarly, “R₂” is the returns in a normal economy. The probability of having a normal is “P₂”. “R₃” is the returns in irrational exuberance. The probability of having an irrational exuberance is “P₃”.

$Standarddeviation}=([(Possible returns(R1)−Expected returnsE(R))2×Probability(P1)]+…+[(Possible returns(Rn)−Expected returnsE(R))2×Probability(Pn)])=[[(0.02−0.1590)2×0.15]+[(0.21−0.1590)2×0.70]+[((0.06)−0.1590)2×0.15]]=0.00619=0.0787 or 7.87%$

Hence, the standard deviation of Stock I is 7.87%.

Compute the expected return on Stock II:

“R₁” is the returns during the recession. The probability of having a recession is “P₁”. Similarly, “R₂” is the returns in a normal economy. The probability of having a normal is “P₂”. “R₃” is the returns in irrational exuberance. The probability of having an irrational exuberance is “P₃”.

$Expected returns[E(R)]=[(Possible returns(R1)×Probability(P1))+(Possible returns(R2)×Probability(P2))+(Possible returns(R2)×Probability(P2))]=((0.15)×(0.25))+(0.70×0.09)+(0.15×0.44)=0.0915 or 9.15%$

Hence, the expected return on Stock II is 9.15 percent.

Compute the beta of Stock II:

$E(RII)=Rf+[E(RM)−Rf]×βII0.0915=0.04+[0.07]×βIIβII=0.74$

Hence, the beta of Stock II is 0.74.

Compute the standard deviation of Stock II:

“R₁” is the returns during the recession. The probability of having a recession is “P₁”. Similarly, “R₂” is the returns in a normal economy. The probability of having a normal is “P₂”. “R₃” is the returns in irrational exuberance. The probability of having an irrational exuberance is “P₃”.

$Standarddeviation}=([(Possible returns(R1)−Expected returnsE(R))2×Probability(P1)]+…+[(Possible returns(Rn)−Expected returnsE(R))2×Probability(Pn)])=[[((0.25)−0.0915)2×0.15]+[(0.09−0.0915)2×0.70]+[((0.44)−0.0915)2×0.15]]=0.03571=0.1890 or 18.90%$

Hence, the standard deviation of Stock II is 18.90%.

Answer 9

Expert Solution & Answer

Answer 10

Expert Solution & Answer

Answer 11

Summary Introduction

To determine: The stock that has the most systematic risk and most unsystematic risk.

Introduction:

Systematic risk refers to the market-specific risk that affects all the stocks in the market. Unsystematic risk refers to the company-specific risk that affects only the individual company.

Answer 12

Answer to Problem 26QP

The expected return on Stock I is 15.90 percent, the beta is 1.70, and the standard deviation is 7.87%. The expected return on Stock II is 9.15 percent, the beta is 0.74, and the standard deviation is 18.90%.

The beta refers to the systematic risk of the stock. Stock I has higher beta than Stock II. Hence, the systematic risk of Stock I is higher. The standard deviation indicates the total risk of the stock. The standard deviation is high for Stock II despite having a low beta. Hence, a major portion of the standard deviation of Stock II is the unsystematic risk.

Stock II has higher unsystematic risk than Stock I. The formation of a portfolio helps in diversifying the unsystematic risk. Although Stock II has a higher unsystematic risk, it can be diversified completely. However, the beta cannot be eliminated. Hence, Stock I is riskier than Stock II.

The expected return and the market risk premium depends on the beta of the stock. As Stock I has a higher beta, the expected return and market risk premium of the stock will be higher than Stock II.

Answer 13

Explanation of Solution

Given information:

The probability of having a recession, normal economy, and irrational exuberance is 0.15, 0.70, and 0.15 respectively. Stock I will yield 2%, 21%, and 6% when there is a recession, normal economy, and irrational exuberance respectively.

Stock II will yield (25%), 9%, and 44% when there is a recession, normal economy, and irrational exuberance respectively. The market risk premium is 7% and the risk-free rate is 4%.

The formula to calculate the expected return on the stock:

$Expected returns[E(R)]=[(Possible returns(R1)×Probability(P1))+…+(Possible returns(Rn)×Probability(Pn))]$

The formula to calculate the beta of the stock:

$E(Ri)=Rf+[E(RM)−Rf]×βi$

Where,

“E (R_i)” refers to the expected return on a risky asset

“R_f” refers to the risk-free rate

“E (R_M)” refers to the expected return on the market portfolio

“β_i” refers to the beta coefficient of the risky asset relative to the market portfolio

The formula to calculate the standard deviation:

$Standarddeviation}=([(Possible returns(R1)−Expected returnsE(R))2×Probability(P1)]+…+[(Possible returns(Rn)−Expected returnsE(R))2×Probability(Pn)])$

Compute the expected return on Stock I:

“R₁” is the returns during the recession. The probability of having a recession is “P₁”. Similarly, “R₂” is the returns in a normal economy. The probability of having a normal is “P₂”. “R₃” is the returns in irrational exuberance. The probability of having an irrational exuberance is “P₃”.

$Expected returns[E(R)]=[(Possible returns(R1)×Probability(P1))+(Possible returns(R2)×Probability(P2))+(Possible returns(R2)×Probability(P2))]=((0.15)×0.02)+(0.70×0.21)+(0.15×0.06)=0.1590 or 15.90%$

Hence, the expected return on Stock I is 15.90 percent.

Compute the beta of Stock I:

$E(RI)=Rf+[E(RM)−Rf]×βI0.1590=0.04+[0.07]×βIβI=1.70$

Hence, the beta of Stock I is 1.70.

Compute the standard deviation of Stock I:

“R₁” is the returns during the recession. The probability of having a recession is “P₁”. Similarly, “R₂” is the returns in a normal economy. The probability of having a normal is “P₂”. “R₃” is the returns in irrational exuberance. The probability of having an irrational exuberance is “P₃”.

$Standarddeviation}=([(Possible returns(R1)−Expected returnsE(R))2×Probability(P1)]+…+[(Possible returns(Rn)−Expected returnsE(R))2×Probability(Pn)])=[[(0.02−0.1590)2×0.15]+[(0.21−0.1590)2×0.70]+[((0.06)−0.1590)2×0.15]]=0.00619=0.0787 or 7.87%$

Hence, the standard deviation of Stock I is 7.87%.

Compute the expected return on Stock II:

“R₁” is the returns during the recession. The probability of having a recession is “P₁”. Similarly, “R₂” is the returns in a normal economy. The probability of having a normal is “P₂”. “R₃” is the returns in irrational exuberance. The probability of having an irrational exuberance is “P₃”.

$Expected returns[E(R)]=[(Possible returns(R1)×Probability(P1))+(Possible returns(R2)×Probability(P2))+(Possible returns(R2)×Probability(P2))]=((0.15)×(0.25))+(0.70×0.09)+(0.15×0.44)=0.0915 or 9.15%$

Hence, the expected return on Stock II is 9.15 percent.

Compute the beta of Stock II:

$E(RII)=Rf+[E(RM)−Rf]×βII0.0915=0.04+[0.07]×βIIβII=0.74$

Hence, the beta of Stock II is 0.74.

Compute the standard deviation of Stock II:

“R₁” is the returns during the recession. The probability of having a recession is “P₁”. Similarly, “R₂” is the returns in a normal economy. The probability of having a normal is “P₂”. “R₃” is the returns in irrational exuberance. The probability of having an irrational exuberance is “P₃”.

$Standarddeviation}=([(Possible returns(R1)−Expected returnsE(R))2×Probability(P1)]+…+[(Possible returns(Rn)−Expected returnsE(R))2×Probability(Pn)])=[[((0.25)−0.0915)2×0.15]+[(0.09−0.0915)2×0.70]+[((0.44)−0.0915)2×0.15]]=0.03571=0.1890 or 18.90%$

Hence, the standard deviation of Stock II is 18.90%.

Answer 14

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Systematic versus Unsystematic Risk [LO3] Consider the following information about Stocks I and II: The market risk premium is 7 percent, and the risk-free rate is 4 percent. Which stock has the most systematic risk? Which one has the most unsystematic risk? Which stock is “riskier”? Explain.

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Answer to Problem 26QP

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