Systematic versus Unsystematic Risk. Consider the following information on 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 11, Problem 30QP

Systematic versus Unsystematic Risk. Consider the following information on Stocks I and II:

Chapter 11, Problem 30QP, Systematic versus Unsystematic Risk. Consider the following information on Stocks I and II: The

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

Summary Introduction

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

Explanation of Solution

Given information:

The probability of having a recession, normal economy, and irrational exuberance is 0.25, 0.60, and 0.15 respectively. Stock I will yield 2%, 32%, and 18% when there is a recession, normal economy, and irrational exuberance respectively.

Stock II will yield −20%, 12%, and 40% 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:

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

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.

$Expected returns=[(Possible returns(R1)×Probability(P1))+(Possible returns(R2)×Probability(P2))+(Possible returns(R2)×Probability(P2))]=((0.25)×0.02)+(0.60×0.32)+(0.15×0.18)=(0.005+0.192+0.027)=0.2240$

Hence, the expected return on Stock I is 0.2240 or 22.40 percent.

Compute the beta of Stock I:

$E(RI)=Rf+[E(RM)−Rf]×βI0.2240=0.04+[0.07]×βI(0.2240−0.04)=0.07βI0.1840.07=βI2.63=βI$

Hence, the beta of Stock I is 2.63.

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.

$Standarddeviation}=([(Possible returns(R1)−Expected returnsE(R))2× Probability(P1)]+[(Possible returns(R2)−Expected returnsE(R))2× Probability(P2)]+[(Possible returns(R3)−Expected returnsE(R))2× Probability(P3)])=[[(0.02−0.2240)2×0.25]+[(0.32−0.2240)2×0.60]+[(0.18−0.2240)2×0.15]]=((−0.204)2×0.25)+((0.096)2×0.60)+((−0.044)2×0.15)=(0.041616×0.25)+(0.009216×0.60)+(0.001936×0.15)$

$=0.010404+0.0055296+0.0002904=0.016224=0.1274$

Hence, the standard deviation of Stock I is 0.1274 or 12.74%.

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.

$Expected returns=[(Possible returns(R1)×Probability(P1))+(Possible returns(R2)×Probability(P2))+(Possible returns(R2)×Probability(P2))]=((−0.20)×(0.25))+(0.12×0.60)+(0.40×0.15)=(−0.05+0.072+0.06)=0.0820$

Hence, the expected return on Stock II is 0.0820 or 8.20 percent.

Compute the beta of Stock II:

$E(RII)=Rf+[E(RM)−Rf]×βII0.0820=0.04+[0.07]×βII(0.0820−0.04)=0.07βII0.0420.07=βII0.6=βII$

Hence, the beta of Stock II is 0.6.

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.

$Standarddeviation}=([(Possible returns(R1)−Expected returnsE(R))2× Probability(P1)]+[(Possible returns(R2)−Expected returnsE(R))2× Probability(P2)]+[(Possible returns(R3)−Expected returnsE(R))2× Probability(P3)])=[[((−0.20)−0.0820)2×0.25]+[(0.12−0.0820)2×0.60]+[(0.40−0.0820)2×0.15]]=((−0.282)2×0.25)+((0.038)2×0.60)+((0.318)2×0.15)=(0.079524×0.25)+(0.001444×0.60)+(0.101124×0.15)$

$=(0.019881+0.0008664+0.0151686)=0.035916=0.1895$

Hence, the standard deviation of Stock II is 0.1895 or 18.95%.

Interpretation:

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. Therefore, Stock II has higher unsystematic risk than Stock I.

Expert Solution

Summary Introduction

To discuss: The riskier Stock among Stock I and Stock II.

Introduction:

Risk refers to the movement or fluctuation in the value of an investment. The movement can be positive or negative. A positive fluctuation in the price benefits the investor. The investor will lose money if the price movement is negative.

Explanation of Solution

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

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Answer 2

Textbook Question

Chapter 11, Problem 30QP

Systematic versus Unsystematic Risk. Consider the following information on Stocks I and II:

Chapter 11, Problem 30QP, Systematic versus Unsystematic Risk. Consider the following information on Stocks I and II: The

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

Summary Introduction

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

Explanation of Solution

Given information:

The probability of having a recession, normal economy, and irrational exuberance is 0.25, 0.60, and 0.15 respectively. Stock I will yield 2%, 32%, and 18% when there is a recession, normal economy, and irrational exuberance respectively.

Stock II will yield −20%, 12%, and 40% 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:

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

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.

$Expected returns=[(Possible returns(R1)×Probability(P1))+(Possible returns(R2)×Probability(P2))+(Possible returns(R2)×Probability(P2))]=((0.25)×0.02)+(0.60×0.32)+(0.15×0.18)=(0.005+0.192+0.027)=0.2240$

Hence, the expected return on Stock I is 0.2240 or 22.40 percent.

Compute the beta of Stock I:

$E(RI)=Rf+[E(RM)−Rf]×βI0.2240=0.04+[0.07]×βI(0.2240−0.04)=0.07βI0.1840.07=βI2.63=βI$

Hence, the beta of Stock I is 2.63.

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.

$Standarddeviation}=([(Possible returns(R1)−Expected returnsE(R))2× Probability(P1)]+[(Possible returns(R2)−Expected returnsE(R))2× Probability(P2)]+[(Possible returns(R3)−Expected returnsE(R))2× Probability(P3)])=[[(0.02−0.2240)2×0.25]+[(0.32−0.2240)2×0.60]+[(0.18−0.2240)2×0.15]]=((−0.204)2×0.25)+((0.096)2×0.60)+((−0.044)2×0.15)=(0.041616×0.25)+(0.009216×0.60)+(0.001936×0.15)$

$=0.010404+0.0055296+0.0002904=0.016224=0.1274$

Hence, the standard deviation of Stock I is 0.1274 or 12.74%.

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.

$Expected returns=[(Possible returns(R1)×Probability(P1))+(Possible returns(R2)×Probability(P2))+(Possible returns(R2)×Probability(P2))]=((−0.20)×(0.25))+(0.12×0.60)+(0.40×0.15)=(−0.05+0.072+0.06)=0.0820$

Hence, the expected return on Stock II is 0.0820 or 8.20 percent.

Compute the beta of Stock II:

$E(RII)=Rf+[E(RM)−Rf]×βII0.0820=0.04+[0.07]×βII(0.0820−0.04)=0.07βII0.0420.07=βII0.6=βII$

Hence, the beta of Stock II is 0.6.

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.

$Standarddeviation}=([(Possible returns(R1)−Expected returnsE(R))2× Probability(P1)]+[(Possible returns(R2)−Expected returnsE(R))2× Probability(P2)]+[(Possible returns(R3)−Expected returnsE(R))2× Probability(P3)])=[[((−0.20)−0.0820)2×0.25]+[(0.12−0.0820)2×0.60]+[(0.40−0.0820)2×0.15]]=((−0.282)2×0.25)+((0.038)2×0.60)+((0.318)2×0.15)=(0.079524×0.25)+(0.001444×0.60)+(0.101124×0.15)$

$=(0.019881+0.0008664+0.0151686)=0.035916=0.1895$

Hence, the standard deviation of Stock II is 0.1895 or 18.95%.

Interpretation:

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. Therefore, Stock II has higher unsystematic risk than Stock I.

Expert Solution

Summary Introduction

To discuss: The riskier Stock among Stock I and Stock II.

Introduction:

Risk refers to the movement or fluctuation in the value of an investment. The movement can be positive or negative. A positive fluctuation in the price benefits the investor. The investor will lose money if the price movement is negative.

Explanation of Solution

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

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Answer 3

Textbook Question

Chapter 11, Problem 30QP

Systematic versus Unsystematic Risk. Consider the following information on Stocks I and II:

Chapter 11, Problem 30QP, Systematic versus Unsystematic Risk. Consider the following information on Stocks I and II: The

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

Summary Introduction

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

Explanation of Solution

Given information:

The probability of having a recession, normal economy, and irrational exuberance is 0.25, 0.60, and 0.15 respectively. Stock I will yield 2%, 32%, and 18% when there is a recession, normal economy, and irrational exuberance respectively.

Stock II will yield −20%, 12%, and 40% 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:

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

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.

$Expected returns=[(Possible returns(R1)×Probability(P1))+(Possible returns(R2)×Probability(P2))+(Possible returns(R2)×Probability(P2))]=((0.25)×0.02)+(0.60×0.32)+(0.15×0.18)=(0.005+0.192+0.027)=0.2240$

Hence, the expected return on Stock I is 0.2240 or 22.40 percent.

Compute the beta of Stock I:

$E(RI)=Rf+[E(RM)−Rf]×βI0.2240=0.04+[0.07]×βI(0.2240−0.04)=0.07βI0.1840.07=βI2.63=βI$

Hence, the beta of Stock I is 2.63.

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.

$Standarddeviation}=([(Possible returns(R1)−Expected returnsE(R))2× Probability(P1)]+[(Possible returns(R2)−Expected returnsE(R))2× Probability(P2)]+[(Possible returns(R3)−Expected returnsE(R))2× Probability(P3)])=[[(0.02−0.2240)2×0.25]+[(0.32−0.2240)2×0.60]+[(0.18−0.2240)2×0.15]]=((−0.204)2×0.25)+((0.096)2×0.60)+((−0.044)2×0.15)=(0.041616×0.25)+(0.009216×0.60)+(0.001936×0.15)$

$=0.010404+0.0055296+0.0002904=0.016224=0.1274$

Hence, the standard deviation of Stock I is 0.1274 or 12.74%.

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.

$Expected returns=[(Possible returns(R1)×Probability(P1))+(Possible returns(R2)×Probability(P2))+(Possible returns(R2)×Probability(P2))]=((−0.20)×(0.25))+(0.12×0.60)+(0.40×0.15)=(−0.05+0.072+0.06)=0.0820$

Hence, the expected return on Stock II is 0.0820 or 8.20 percent.

Compute the beta of Stock II:

$E(RII)=Rf+[E(RM)−Rf]×βII0.0820=0.04+[0.07]×βII(0.0820−0.04)=0.07βII0.0420.07=βII0.6=βII$

Hence, the beta of Stock II is 0.6.

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.

$Standarddeviation}=([(Possible returns(R1)−Expected returnsE(R))2× Probability(P1)]+[(Possible returns(R2)−Expected returnsE(R))2× Probability(P2)]+[(Possible returns(R3)−Expected returnsE(R))2× Probability(P3)])=[[((−0.20)−0.0820)2×0.25]+[(0.12−0.0820)2×0.60]+[(0.40−0.0820)2×0.15]]=((−0.282)2×0.25)+((0.038)2×0.60)+((0.318)2×0.15)=(0.079524×0.25)+(0.001444×0.60)+(0.101124×0.15)$

$=(0.019881+0.0008664+0.0151686)=0.035916=0.1895$

Hence, the standard deviation of Stock II is 0.1895 or 18.95%.

Interpretation:

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. Therefore, Stock II has higher unsystematic risk than Stock I.

Expert Solution

Summary Introduction

To discuss: The riskier Stock among Stock I and Stock II.

Introduction:

Risk refers to the movement or fluctuation in the value of an investment. The movement can be positive or negative. A positive fluctuation in the price benefits the investor. The investor will lose money if the price movement is negative.

Explanation of Solution

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

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Answer 4

Textbook Question

Chapter 11, Problem 30QP

Systematic versus Unsystematic Risk. Consider the following information on Stocks I and II:

Chapter 11, Problem 30QP, Systematic versus Unsystematic Risk. Consider the following information on Stocks I and II: The

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

Summary Introduction

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

Explanation of Solution

Given information:

The probability of having a recession, normal economy, and irrational exuberance is 0.25, 0.60, and 0.15 respectively. Stock I will yield 2%, 32%, and 18% when there is a recession, normal economy, and irrational exuberance respectively.

Stock II will yield −20%, 12%, and 40% 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:

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

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.

$Expected returns=[(Possible returns(R1)×Probability(P1))+(Possible returns(R2)×Probability(P2))+(Possible returns(R2)×Probability(P2))]=((0.25)×0.02)+(0.60×0.32)+(0.15×0.18)=(0.005+0.192+0.027)=0.2240$

Hence, the expected return on Stock I is 0.2240 or 22.40 percent.

Compute the beta of Stock I:

$E(RI)=Rf+[E(RM)−Rf]×βI0.2240=0.04+[0.07]×βI(0.2240−0.04)=0.07βI0.1840.07=βI2.63=βI$

Hence, the beta of Stock I is 2.63.

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.

$Standarddeviation}=([(Possible returns(R1)−Expected returnsE(R))2× Probability(P1)]+[(Possible returns(R2)−Expected returnsE(R))2× Probability(P2)]+[(Possible returns(R3)−Expected returnsE(R))2× Probability(P3)])=[[(0.02−0.2240)2×0.25]+[(0.32−0.2240)2×0.60]+[(0.18−0.2240)2×0.15]]=((−0.204)2×0.25)+((0.096)2×0.60)+((−0.044)2×0.15)=(0.041616×0.25)+(0.009216×0.60)+(0.001936×0.15)$

$=0.010404+0.0055296+0.0002904=0.016224=0.1274$

Hence, the standard deviation of Stock I is 0.1274 or 12.74%.

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.

$Expected returns=[(Possible returns(R1)×Probability(P1))+(Possible returns(R2)×Probability(P2))+(Possible returns(R2)×Probability(P2))]=((−0.20)×(0.25))+(0.12×0.60)+(0.40×0.15)=(−0.05+0.072+0.06)=0.0820$

Hence, the expected return on Stock II is 0.0820 or 8.20 percent.

Compute the beta of Stock II:

$E(RII)=Rf+[E(RM)−Rf]×βII0.0820=0.04+[0.07]×βII(0.0820−0.04)=0.07βII0.0420.07=βII0.6=βII$

Hence, the beta of Stock II is 0.6.

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.

$Standarddeviation}=([(Possible returns(R1)−Expected returnsE(R))2× Probability(P1)]+[(Possible returns(R2)−Expected returnsE(R))2× Probability(P2)]+[(Possible returns(R3)−Expected returnsE(R))2× Probability(P3)])=[[((−0.20)−0.0820)2×0.25]+[(0.12−0.0820)2×0.60]+[(0.40−0.0820)2×0.15]]=((−0.282)2×0.25)+((0.038)2×0.60)+((0.318)2×0.15)=(0.079524×0.25)+(0.001444×0.60)+(0.101124×0.15)$

$=(0.019881+0.0008664+0.0151686)=0.035916=0.1895$

Hence, the standard deviation of Stock II is 0.1895 or 18.95%.

Interpretation:

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. Therefore, Stock II has higher unsystematic risk than Stock I.

Expert Solution

Summary Introduction

To discuss: The riskier Stock among Stock I and Stock II.

Introduction:

Risk refers to the movement or fluctuation in the value of an investment. The movement can be positive or negative. A positive fluctuation in the price benefits the investor. The investor will lose money if the price movement is negative.

Explanation of Solution

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

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Answer 5

Textbook Question

Answer 6

Textbook Question

Answer 7

Expert Solution

Summary Introduction

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

Explanation of Solution

Given information:

The probability of having a recession, normal economy, and irrational exuberance is 0.25, 0.60, and 0.15 respectively. Stock I will yield 2%, 32%, and 18% when there is a recession, normal economy, and irrational exuberance respectively.

Stock II will yield −20%, 12%, and 40% 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:

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

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.

$Expected returns=[(Possible returns(R1)×Probability(P1))+(Possible returns(R2)×Probability(P2))+(Possible returns(R2)×Probability(P2))]=((0.25)×0.02)+(0.60×0.32)+(0.15×0.18)=(0.005+0.192+0.027)=0.2240$

Hence, the expected return on Stock I is 0.2240 or 22.40 percent.

Compute the beta of Stock I:

$E(RI)=Rf+[E(RM)−Rf]×βI0.2240=0.04+[0.07]×βI(0.2240−0.04)=0.07βI0.1840.07=βI2.63=βI$

Hence, the beta of Stock I is 2.63.

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.

$Standarddeviation}=([(Possible returns(R1)−Expected returnsE(R))2× Probability(P1)]+[(Possible returns(R2)−Expected returnsE(R))2× Probability(P2)]+[(Possible returns(R3)−Expected returnsE(R))2× Probability(P3)])=[[(0.02−0.2240)2×0.25]+[(0.32−0.2240)2×0.60]+[(0.18−0.2240)2×0.15]]=((−0.204)2×0.25)+((0.096)2×0.60)+((−0.044)2×0.15)=(0.041616×0.25)+(0.009216×0.60)+(0.001936×0.15)$

$=0.010404+0.0055296+0.0002904=0.016224=0.1274$

Hence, the standard deviation of Stock I is 0.1274 or 12.74%.

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.

$Expected returns=[(Possible returns(R1)×Probability(P1))+(Possible returns(R2)×Probability(P2))+(Possible returns(R2)×Probability(P2))]=((−0.20)×(0.25))+(0.12×0.60)+(0.40×0.15)=(−0.05+0.072+0.06)=0.0820$

Hence, the expected return on Stock II is 0.0820 or 8.20 percent.

Compute the beta of Stock II:

$E(RII)=Rf+[E(RM)−Rf]×βII0.0820=0.04+[0.07]×βII(0.0820−0.04)=0.07βII0.0420.07=βII0.6=βII$

Hence, the beta of Stock II is 0.6.

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.

$Standarddeviation}=([(Possible returns(R1)−Expected returnsE(R))2× Probability(P1)]+[(Possible returns(R2)−Expected returnsE(R))2× Probability(P2)]+[(Possible returns(R3)−Expected returnsE(R))2× Probability(P3)])=[[((−0.20)−0.0820)2×0.25]+[(0.12−0.0820)2×0.60]+[(0.40−0.0820)2×0.15]]=((−0.282)2×0.25)+((0.038)2×0.60)+((0.318)2×0.15)=(0.079524×0.25)+(0.001444×0.60)+(0.101124×0.15)$

$=(0.019881+0.0008664+0.0151686)=0.035916=0.1895$

Hence, the standard deviation of Stock II is 0.1895 or 18.95%.

Interpretation:

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. Therefore, Stock II has higher unsystematic risk than Stock I.

Expert Solution

Summary Introduction

To discuss: The riskier Stock among Stock I and Stock II.

Introduction:

Risk refers to the movement or fluctuation in the value of an investment. The movement can be positive or negative. A positive fluctuation in the price benefits the investor. The investor will lose money if the price movement is negative.

Explanation of Solution

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

Answer 8

Expert Solution

Summary Introduction

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

Explanation of Solution

Given information:

The probability of having a recession, normal economy, and irrational exuberance is 0.25, 0.60, and 0.15 respectively. Stock I will yield 2%, 32%, and 18% when there is a recession, normal economy, and irrational exuberance respectively.

Stock II will yield −20%, 12%, and 40% 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:

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

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.

$Expected returns=[(Possible returns(R1)×Probability(P1))+(Possible returns(R2)×Probability(P2))+(Possible returns(R2)×Probability(P2))]=((0.25)×0.02)+(0.60×0.32)+(0.15×0.18)=(0.005+0.192+0.027)=0.2240$

Hence, the expected return on Stock I is 0.2240 or 22.40 percent.

Compute the beta of Stock I:

$E(RI)=Rf+[E(RM)−Rf]×βI0.2240=0.04+[0.07]×βI(0.2240−0.04)=0.07βI0.1840.07=βI2.63=βI$

Hence, the beta of Stock I is 2.63.

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.

$Standarddeviation}=([(Possible returns(R1)−Expected returnsE(R))2× Probability(P1)]+[(Possible returns(R2)−Expected returnsE(R))2× Probability(P2)]+[(Possible returns(R3)−Expected returnsE(R))2× Probability(P3)])=[[(0.02−0.2240)2×0.25]+[(0.32−0.2240)2×0.60]+[(0.18−0.2240)2×0.15]]=((−0.204)2×0.25)+((0.096)2×0.60)+((−0.044)2×0.15)=(0.041616×0.25)+(0.009216×0.60)+(0.001936×0.15)$

$=0.010404+0.0055296+0.0002904=0.016224=0.1274$

Hence, the standard deviation of Stock I is 0.1274 or 12.74%.

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.

$Expected returns=[(Possible returns(R1)×Probability(P1))+(Possible returns(R2)×Probability(P2))+(Possible returns(R2)×Probability(P2))]=((−0.20)×(0.25))+(0.12×0.60)+(0.40×0.15)=(−0.05+0.072+0.06)=0.0820$

Hence, the expected return on Stock II is 0.0820 or 8.20 percent.

Compute the beta of Stock II:

$E(RII)=Rf+[E(RM)−Rf]×βII0.0820=0.04+[0.07]×βII(0.0820−0.04)=0.07βII0.0420.07=βII0.6=βII$

Hence, the beta of Stock II is 0.6.

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.

$Standarddeviation}=([(Possible returns(R1)−Expected returnsE(R))2× Probability(P1)]+[(Possible returns(R2)−Expected returnsE(R))2× Probability(P2)]+[(Possible returns(R3)−Expected returnsE(R))2× Probability(P3)])=[[((−0.20)−0.0820)2×0.25]+[(0.12−0.0820)2×0.60]+[(0.40−0.0820)2×0.15]]=((−0.282)2×0.25)+((0.038)2×0.60)+((0.318)2×0.15)=(0.079524×0.25)+(0.001444×0.60)+(0.101124×0.15)$

$=(0.019881+0.0008664+0.0151686)=0.035916=0.1895$

Hence, the standard deviation of Stock II is 0.1895 or 18.95%.

Interpretation:

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. Therefore, Stock II has higher unsystematic risk than Stock I.

Answer 9

Expert Solution

Answer 10

Expert Solution

Answer 11

Expert Solution

Answer 12

Summary Introduction

To determine: The stock that has the most systematic risk and the 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 13

Explanation of Solution

Given information:

The probability of having a recession, normal economy, and irrational exuberance is 0.25, 0.60, and 0.15 respectively. Stock I will yield 2%, 32%, and 18% when there is a recession, normal economy, and irrational exuberance respectively.

Stock II will yield −20%, 12%, and 40% 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:

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

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.

$Expected returns=[(Possible returns(R1)×Probability(P1))+(Possible returns(R2)×Probability(P2))+(Possible returns(R2)×Probability(P2))]=((0.25)×0.02)+(0.60×0.32)+(0.15×0.18)=(0.005+0.192+0.027)=0.2240$

Hence, the expected return on Stock I is 0.2240 or 22.40 percent.

Compute the beta of Stock I:

$E(RI)=Rf+[E(RM)−Rf]×βI0.2240=0.04+[0.07]×βI(0.2240−0.04)=0.07βI0.1840.07=βI2.63=βI$

Hence, the beta of Stock I is 2.63.

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.

$Standarddeviation}=([(Possible returns(R1)−Expected returnsE(R))2× Probability(P1)]+[(Possible returns(R2)−Expected returnsE(R))2× Probability(P2)]+[(Possible returns(R3)−Expected returnsE(R))2× Probability(P3)])=[[(0.02−0.2240)2×0.25]+[(0.32−0.2240)2×0.60]+[(0.18−0.2240)2×0.15]]=((−0.204)2×0.25)+((0.096)2×0.60)+((−0.044)2×0.15)=(0.041616×0.25)+(0.009216×0.60)+(0.001936×0.15)$

$=0.010404+0.0055296+0.0002904=0.016224=0.1274$

Hence, the standard deviation of Stock I is 0.1274 or 12.74%.

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.

$Expected returns=[(Possible returns(R1)×Probability(P1))+(Possible returns(R2)×Probability(P2))+(Possible returns(R2)×Probability(P2))]=((−0.20)×(0.25))+(0.12×0.60)+(0.40×0.15)=(−0.05+0.072+0.06)=0.0820$

Hence, the expected return on Stock II is 0.0820 or 8.20 percent.

Compute the beta of Stock II:

$E(RII)=Rf+[E(RM)−Rf]×βII0.0820=0.04+[0.07]×βII(0.0820−0.04)=0.07βII0.0420.07=βII0.6=βII$

Hence, the beta of Stock II is 0.6.

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.

$Standarddeviation}=([(Possible returns(R1)−Expected returnsE(R))2× Probability(P1)]+[(Possible returns(R2)−Expected returnsE(R))2× Probability(P2)]+[(Possible returns(R3)−Expected returnsE(R))2× Probability(P3)])=[[((−0.20)−0.0820)2×0.25]+[(0.12−0.0820)2×0.60]+[(0.40−0.0820)2×0.15]]=((−0.282)2×0.25)+((0.038)2×0.60)+((0.318)2×0.15)=(0.079524×0.25)+(0.001444×0.60)+(0.101124×0.15)$

$=(0.019881+0.0008664+0.0151686)=0.035916=0.1895$

Hence, the standard deviation of Stock II is 0.1895 or 18.95%.

Interpretation:

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. Therefore, Stock II has higher unsystematic risk than Stock I.

Answer 14

Expert Solution

Summary Introduction

To discuss: The riskier Stock among Stock I and Stock II.

Introduction:

Risk refers to the movement or fluctuation in the value of an investment. The movement can be positive or negative. A positive fluctuation in the price benefits the investor. The investor will lose money if the price movement is negative.

Explanation of Solution

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

Answer 15

Expert Solution

Answer 16

Expert Solution

Answer 17

Expert Solution

Answer 18

Summary Introduction

To discuss: The riskier Stock among Stock I and Stock II.

Introduction:

Risk refers to the movement or fluctuation in the value of an investment. The movement can be positive or negative. A positive fluctuation in the price benefits the investor. The investor will lose money if the price movement is negative.

Answer 19

Explanation of Solution

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

Answer 20

Ch. 11.1 - How do we calculate the expected return on a...Ch. 11.1 - Prob. 11.1BCQ Ch. 11.2 - What is a portfolio weight?Ch. 11.2 - How do we calculate the expected return on a...Ch. 11.2 - Is there a simple relationship between the...Ch. 11.3 - Prob. 11.3ACQ Ch. 11.3 - Prob. 11.3BCQ Ch. 11.4 - Prob. 11.4ACQ Ch. 11.4 - Prob. 11.4BCQ Ch. 11.5 - Prob. 11.5ACQ

Systematic versus Unsystematic Risk. Consider the following information on 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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