Quiz 12 Solutions Spring 2023
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Feb 20, 2024
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Quiz 11 Solutions
Conceptual: Portfolio ER = weighted average and port SD < weighted average 1. Some of a portfolio consists of stock A, which has an expected return of 18.4% and a standard deviation of returns of 28.9%, and the rest of the portfolio consists of stock B, which has an expected return of 18.4% and a standard deviation of returns of 28.9%. If the returns of stock A and stock B do not move perfectly together in the same direction by the same relative amount, then which one of the following assertions is true? Assume that the portfolio has at least some stock A and some stock B.
A. The expected return of the portfolio is 18.4% and the standard deviation of the portfolio is 28.9%
B. The expected return of the portfolio is 18.4% and the standard deviation of the portfolio is not 28.9%
C. The expected return of the portfolio is not 18.4% and the standard deviation of the portfolio is 28.9%
D. The expected return of the portfolio is not 18.4% and the standard deviation of the portfolio is not 28.9%
E. The question can not be answered without more specific information on how much of the portfolio consists of stock A and how much consists of stock B
Answer: B. The expected return of the portfolio is 18.4% and the standard deviation of the portfolio is not 28.9%
The expected return of the portfolio is equal to 18.4%
The expected return for a portfolio over a period equals the value-weighted average of the expected returns of the assets in the portfolio such that E(R
p
) = [x
A
× E(R
A
)] + [x
B
× E(R
B
)]
In this case, E(R
p
) = [x
A
× 0.18.4] + [(1 – x
A
) × 0.18.4] = 0.18.4 = 18.4% for any weight x
A
Because of the benefits of diversification, the standard deviation of the portfolio is less than 28.9%
If the returns of all the assets in a portfolio do not move perfectly together in the same direction by the same relative amount, then there are “diversification benefits” whereby the standard deviation of portfolio returns is less than the weighted average of the standard deviation of the returns of the assets in the portfolio. In this case, SD(R
p
) would be less than [x
A
× SD(R
A
)] + [x
B
× SD(R
B
)]
So SD(R
p
) < [x
A
× 0.28.9] + [(1 – x
A
) × 0.28.9] = 0.28.9 = 28.9% for any weight x
A
SD(R
p
) < 28.9%
1. Some of a portfolio consists of stock A, which has an expected return of 18.9% and a standard deviation of returns of 28.4%, and the rest of the portfolio consists of stock B, which has an expected return of 18.9% and a standard deviation of returns of 28.4%. If the returns of stock A and stock B do not move perfectly together in the same direction by the same relative amount, then which one of the following assertions is true? Assume that the portfolio has at least some stock A and some stock B.
A. The expected return of the portfolio is not 18.9% and the standard deviation of the portfolio is not 28.4%
B. The expected return of the portfolio is not 18.9% and the standard deviation of the portfolio is 28.4%
C. The expected return of the portfolio is 18.9% and the standard deviation of the portfolio is not 28.4%
D. The expected return of the portfolio is 18.9% and the standard deviation of the portfolio is 28.4%
E. The question can not be answered without more specific information on how much of the portfolio consists of stock A and how much consists of stock B
Answer: C. The expected return of the portfolio is 18.9% and the standard deviation of the portfolio is not 28.4%
The expected return of the portfolio is equal to 18.9%
The expected return for a portfolio over a period equals the value-weighted average of the expected returns of the assets in the portfolio such that E(R
p
) = [x
A
× E(R
A
)] + [x
B
× E(R
B
)]
In this case, E(R
p
) = [x
A
× 0.18.9] + [(1 – x
A
) × 0.18.9] = 0.18.9 = 18.9% for any weight x
A
Because of the benefits of diversification, the standard deviation of the portfolio is less than 28.4%
If the returns of all the assets in a portfolio do not move perfectly together in the same direction by the same relative amount, then there are “diversification benefits” whereby the standard deviation of portfolio returns is less than the weighted average of the standard deviation of the returns of the assets in the portfolio. In this case, SD(R
p
) would be less than [x
A
× SD(R
A
)] + [x
B
× SD(R
B
)]
So SD(R
p
) < [x
A
× 0.28.4] + [(1 – x
A
) × 0.28.4] = 0.28.4 = 28.4% for any weight x
A
SD(R
p
) < 28.4%
1. Some of a portfolio consists of stock A, which has an expected return of 13.7% and a standard deviation of returns of 24.6%, and the rest of the portfolio consists of stock B, which has an expected return of 13.7% and a standard deviation of returns of 24.6%. If the returns of stock A and stock B do not move perfectly together in the same direction by the same relative amount, then which one of the following assertions is true? Assume that the portfolio has at least some stock A and some stock B.
A. The question can not be answered without more specific information on how much of the portfolio consists of stock A and how much consists of stock B
B. The expected return of the portfolio is 13.7% and the standard deviation of the portfolio is 24.6%
C. The expected return of the portfolio is 13.7% and the standard deviation of the portfolio is not 24.6%
D. The expected return of the portfolio is not 13.7% and the standard deviation of the portfolio is 24.6%
E. The expected return of the portfolio is not 13.7% and the standard deviation of the portfolio is not 24.6%
Answer: C. The expected return of the portfolio is 13.7% and the standard deviation of the portfolio is not 24.6%
The expected return of the portfolio is equal to 13.7%
The expected return for a portfolio over a period equals the value-weighted average of the expected returns of the assets in the portfolio such that E(R
p
) = [x
A
× E(R
A
)] + [x
B
× E(R
B
)]
In this case, E(R
p
) = [x
A
× 0.13.7] + [(1 – x
A
) × 0.13.7] = 0.13.7 = 13.7% for any weight x
A
Because of the benefits of diversification, the standard deviation of the portfolio is less than 24.6%
If the returns of all the assets in a portfolio do not move perfectly together in the same direction by the same relative amount, then there are “diversification benefits” whereby the standard deviation of portfolio returns is less than the weighted average of the standard deviation of the returns of the assets in the portfolio. In this case, SD(R
p
) would be less than [x
A
× SD(R
A
)] + [x
B
× SD(R
B
)]
So SD(R
p
) < [x
A
× 0.24.6] + [(1 – x
A
) × 0.24.6] = 0.24.6 = 24.6% for any weight x
A
SD(R
p
) < 24.6%
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1. Some of a portfolio consists of stock A, which has an expected return of 14.6% and a standard deviation of returns of 23.7%, and the rest of the portfolio consists of stock B, which has an expected return of 14.6% and a standard deviation of returns of 23.7%. If the returns of stock A and stock B do not move perfectly together in the same direction by the same relative amount, then which one of the following assertions is true? Assume that the portfolio has at least some stock A and some stock B.
A. The question can not be answered without more specific information on how much of the portfolio consists of stock A and how much consists of stock B
B. The expected return of the portfolio is not 14.6% and the standard deviation of the portfolio is not 23.7%
C. The expected return of the portfolio is not 14.6% and the standard deviation of the portfolio is 23.7%
D. The expected return of the portfolio is 14.6% and the standard deviation of the portfolio is not 23.7%
E. The expected return of the portfolio is 14.6% and the standard deviation of the portfolio is 23.7%
Answer: D. The expected return of the portfolio is 14.6% and the standard deviation of the portfolio is not 23.7%
The expected return of the portfolio is equal to 14.6%
The expected return for a portfolio over a period equals the value-weighted average of the expected returns of the assets in the portfolio such that E(R
p
) = [x
A
× E(R
A
)] + [x
B
× E(R
B
)]
In this case, E(R
p
) = [x
A
× 0.14.6] + [(1 – x
A
) × 0.14.6] = 0.14.6 = 14.6% for any weight x
A
Because of the benefits of diversification, the standard deviation of the portfolio is less than 23.7%
If the returns of all the assets in a portfolio do not move perfectly together in the same direction by the same relative amount, then there are “diversification benefits” whereby the standard deviation of portfolio returns is less than the weighted average of the standard deviation of the returns of the assets in the portfolio. In this case, SD(R
p
) would be less than [x
A
× SD(R
A
)] + [x
B
× SD(R
B
)]
So SD(R
p
) < [x
A
× 0.23.7] + [(1 – x
A
) × 0.23.7] = 0.23.7 = 23.7% for any weight x
A
SD(R
p
) < 23.7%
Find real return of stock from P0, P1, D1, inflation, and Rf
2. What was the real rate of return over the past year (from one year ago to today) for a stock if the inflation rate over the past year was 4.20%, the risk-free return over the past year was 2.40%, the stock is currently priced at $41.37, the stock was priced at $39.29 1 year ago, and the stock just paid a dividend of $1.46?
A. 4.62% (plus or minus 0.03 percentage points)
B. 6.61% (plus or minus 0.03 percentage points)
C. 1.05% (plus or minus 0.03 percentage points)
D. 13.59% (plus or minus 0.03 percentage points)
E. None of the above is within 0.03 percentage points of the correct answer
To solve:
1) Find the nominal return over the past year for the stock
2) Find the real rate of return
1) Find the nominal return over the past year for the stock
The nominal return over the past year is the percentage return over the past year
Percentage return over past year
= (dividends paid in period + ending value – initial value) / initial value
= (dividends paid during year + stock price today – stock price 1 year ago) / stock price 1 year ago
= (1.46 + 41.37 – 39.29) / 39.29
= (1.46 + 2.08) / 39.29
= 3.54 / 39.29
= .0901 = 9.01%
2) Find the real rate of return
(1+real rate) = (1+nominal rate) ÷ (1+inflation rate)
Real rate = [(1+nominal rate) ÷ (1+inflation rate)] – 1
= [(1 + .0901) ÷ (1 + .0420)] – 1
= [1.0901 / 1.0420] – 1
= .0462 = 4.62%
Answers may differ slightly due to rounding
2. What was the real rate of return over the past year (from one year ago to today) for a stock if the inflation rate over the past year was 2.40%, the risk-free return over the past year was 4.20%, the stock is currently priced at $41.37, the stock was priced at $39.29 1 year ago, and the stock just paid a dividend of $1.46?
A. 6.46% (plus or minus 0.03 percentage points)
B. 4.81% (plus or minus 0.03 percentage points)
C. 2.83% (plus or minus 0.03 percentage points)
D. 11.63% (plus or minus 0.03 percentage points)
E. None of the above is within 0.03 percentage points of the correct answer
To solve:
1) Find the nominal return over the past year for the stock
2) Find the real rate of return
1) Find the nominal return over the past year for the stock
The nominal return over the past year is the percentage return over the past year
Percentage return over past year
= (dividends paid in period + ending value – initial value) / initial value
= (dividends paid during year + stock price today – stock price 1 year ago) / stock price 1 year ago
= (1.46 + 41.37 – 39.29) / 39.29
= (1.46 + 2.08) / 39.29
= 3.54 / 39.29
= .0901 = 9.01%
2) Find the real rate of return
(1+real rate) = (1+nominal rate) ÷ (1+inflation rate)
Real rate = [(1+nominal rate) ÷ (1+inflation rate)] – 1
= [(1 + .0901) ÷ (1 + .0240)] – 1
= [1.0901 / 1.0240] – 1
= .0646 = 6.46%
Answers may differ slightly due to rounding
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2. What was the real rate of return over the past year (from one year ago to today) for a stock if the inflation rate over the past year was 4.20%, the risk-free return over the past year was 2.40%, the stock is currently priced at $31.56, the stock was priced at $29.39 1 year ago, and the stock just paid a dividend of $1.26?
A. 7.17% (plus or minus 0.03 percentage points)
B. 9.27% (plus or minus 0.03 percentage points)
C. 3.06% (plus or minus 0.03 percentage points)
D. 16.36% (plus or minus 0.03 percentage points)
E. None of the above is within 0.03 percentage points of the correct answer
To solve:
1) Find the nominal return over the past year for the stock
2) Find the real rate of return
1) Find the nominal return over the past year for the stock
The nominal return over the past year is the percentage return over the past year
Percentage return over past year
= (dividends paid in period + ending value – initial value) / initial value
= (dividends paid during year + stock price today – stock price 1 year ago) / stock price 1 year ago
= (1.26 + 31.56 – 29.39) / 29.39
= (1.26 + 2.17) / 29.39
= 3.43 / 29.39
= .1167 = 11.67%
2) Find the real rate of return
(1+real rate) = (1+nominal rate) ÷ (1+inflation rate)
Real rate = [(1+nominal rate) ÷ (1+inflation rate)] – 1
= [(1 + .1167) ÷ (1 + .0420)] – 1
= [1.1167 / 1.0420] – 1
= .0717 = 7.17%
Answers may differ slightly due to rounding
2. What was the real rate of return over the past year (from one year ago to today) for a stock if the inflation rate over the past year was 2.40%, the risk-free return over the past year was 4.20%, the stock is currently priced at $31.56, the stock was priced at $29.39 1 year ago, and the stock just paid a dividend of $1.26?
A. 9.05% (plus or minus 0.03 percentage points)
B. 7.47% (plus or minus 0.03 percentage points)
C. 4.87% (plus or minus 0.03 percentage points)
D. 14.35% (plus or minus 0.03 percentage points)
E. None of the above is within 0.03 percentage points of the correct answer
To solve:
1) Find the nominal return over the past year for the stock
2) Find the real rate of return
1) Find the nominal return over the past year for the stock
The nominal return over the past year is the percentage return over the past year
Percentage return over past year
= (dividends paid in period + ending value – initial value) / initial value
= (dividends paid during year + stock price today – stock price 1 year ago) / stock price 1 year ago
= (1.26 + 31.56 – 29.39) / 29.39
= (1.26 + 2.17) / 29.39
= 3.43 / 29.39
= .1167 = 11.67%
2) Find the real rate of return
(1+real rate) = (1+nominal rate) ÷ (1+inflation rate)
Real rate = [(1+nominal rate) ÷ (1+inflation rate)] – 1
= [(1 + .1167) ÷ (1 + .0240)] – 1
= [1.1167 / 1.0240] – 1
= .0905 = 9.05%
Answers may differ slightly due to rounding
Risk prem of port from 2 assets’ shares, prices, & ER, & RF/inflation
3. You own a portfolio that has 6,000 shares of stock A, which is priced at $9.50 per share and has an expected return of 16.96%, and 16,000 shares of stock B, which is priced at $2.25 per share and has an expected return of 8.29%. The risk-free return is 5.92% and inflation is expected to be 2.38%. What is the risk premium for your portfolio?
A. 7.68% (plus or minus 0.05 percentage points)
B. 11.22% (plus or minus 0.05 percentage points)
C. 10.96% (plus or minus 0.05 percentage points)
D. 4.73% (plus or minus 0.05 percentage points)
E. None of the above is within 0.05 percentage points of the correct answer
Solve in 2 steps:
1. Find your portfolio’s expected return
2. Find your portfolio’s risk premium
1. Find your portfolio’s expected return
E(R
p
) = [x
A
× E(R
A
)] + [x
B
× E(R
B
)]
E(R
A
) = 0.1696
E(R
B
) = 0.0829
x
A
= weight for A = value of A / value of portfolio
x
B
= weight for B = value of B / value of portfolio
Value of A = 6,000 × $9.50 = $57,000
Value of B = 16,000 × $2.25 = $36,000
Total portfolio value = $57,000 + $36,000 = $93,000
x
A
= weight for A = 57,000 / 93,000
x
B
= weight for B = 36,000 / 93,000
E(R
p
) = [(57,000/93,000) × .1696] + [(36,000/93,000) × .0829]
= .1039 + .0321
= .1360 = 13.60%
2. Find your portfolio’s risk premium
Risk premium for your portfolio = expected return on your portfolio – risk-free return
= .1360 – .0592 = .0768 = 7.68%
Answers may differ slightly due to rounding
Note that the inflation rate is irrelevant
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3. You own a portfolio that has 6,000 shares of stock A, which is priced at $9.50 per share and has an expected return of 16.96%, and 16,000 shares of stock B, which is priced at $2.25 per share and has an expected return of 8.29%. The risk-free return is 6.89% and inflation is expected to be 3.82%. What is the risk premium for your portfolio?
A. 6.71% (plus or minus 0.05 percentage points)
B. 9.78% (plus or minus 0.05 percentage points)
C. 9.42% (plus or minus 0.05 percentage points)
D. 3.76% (plus or minus 0.05 percentage points)
E. None of the above is within 0.05 percentage points of the correct answer
Solve in 2 steps:
1. Find your portfolio’s expected return
2. Find your portfolio’s risk premium
1. Find your portfolio’s expected return
E(R
p
) = [x
A
× E(R
A
)] + [x
B
× E(R
B
)]
E(R
A
) = 0.1696
E(R
B
) = 0.0829
x
A
= weight for A = value of A / value of portfolio
x
B
= weight for B = value of B / value of portfolio
Value of A = 6,000 × $9.50 = $57,000
Value of B = 16,000 × $2.25 = $36,000
Total portfolio value = $57,000 + $36,000 = $93,000
x
A
= weight for A = 57,000 / 93,000
x
B
= weight for B = 36,000 / 93,000
E(R
p
) = [(57,000/93,000) × .1696] + [(36,000/93,000) × .0829]
= .1039 + .0321
= .1360 = 13.60%
2. Find your portfolio’s risk premium
Risk premium for your portfolio = expected return on your portfolio – risk-free return
= .1360 – .0689 = .0671 = 6.71%
Answers may differ slightly due to rounding
Note that the inflation rate is irrelevant
3. You own a portfolio that has 6,000 shares of stock A, which is priced at $9.50 per share and has an expected return of 8.29%, and 16,000 shares of stock B, which is priced at $2.25 per share
and has an expected return of 16.96%. The risk-free return is 5.92% and inflation is expected to be 2.38%. What is the risk premium for your portfolio?
A. 5.73% (plus or minus 0.05 percentage points)
B. 9.27% (plus or minus 0.05 percentage points)
C. 9.05% (plus or minus 0.05 percentage points)
D. 8.68% (plus or minus 0.05 percentage points)
E. None of the above is within 0.05 percentage points of the correct answer
Solve in 2 steps:
1. Find your portfolio’s expected return
2. Find your portfolio’s risk premium
1. Find your portfolio’s expected return
E(R
p
) = [x
A
× E(R
A
)] + [x
B
× E(R
B
)]
E(R
A
) = 0.0829
E(R
B
) = 0.1696
x
A
= weight for A = value of A / value of portfolio
x
B
= weight for B = value of B / value of portfolio
Value of A = 6,000 × $9.50 = $57,000
Value of B = 16,000 × $2.25 = $36,000
Total portfolio value = $57,000 + $36,000 = $93,000
x
A
= weight for A = 57,000 / 93,000
x
B
= weight for B = 36,000 / 93,000
E(R
p
) = [(57,000/93,000) × .0829] + [(36,000/93,000) × .1696]
= .0508 + .0657
= .1165 = 11.65%
2. Find your portfolio’s risk premium
Risk premium for your portfolio = expected return on your portfolio – risk-free return
= .1165 – .0592 = .0573 = 5.73%
Answers may differ slightly due to rounding
Note that the inflation rate is irrelevant
3. You own a portfolio that has 6,000 shares of stock A, which is priced at $9.50 per share and has an expected return of 8.29%, and 16,000 shares of stock B, which is priced at $2.25 per share
and has an expected return of 16.96%. The risk-free return is 6.89% and inflation is expected to be 3.82%. What is the risk premium for your portfolio?
A. 4.76% (plus or minus 0.05 percentage points)
B. 7.83% (plus or minus 0.05 percentage points)
C. 7.54% (plus or minus 0.05 percentage points)
D. 7.71% (plus or minus 0.05 percentage points)
E. None of the above is within 0.05 percentage points of the correct answer
Solve in 2 steps:
1. Find your portfolio’s expected return
2. Find your portfolio’s risk premium
1. Find your portfolio’s expected return
E(R
p
) = [x
A
× E(R
A
)] + [x
B
× E(R
B
)]
E(R
A
) = 0.0829
E(R
B
) = 0.1696
x
A
= weight for A = value of A / value of portfolio
x
B
= weight for B = value of B / value of portfolio
Value of A = 6,000 × $9.50 = $57,000
Value of B = 16,000 × $2.25 = $36,000
Total portfolio value = $57,000 + $36,000 = $93,000
x
A
= weight for A = 57,000 / 93,000
x
B
= weight for B = 36,000 / 93,000
E(R
p
) = [(57,000/93,000) × .0829] + [(36,000/93,000) × .1696]
= .0508 + .0657
= .1165 = 11.65%
2. Find your portfolio’s risk premium
Risk premium for your portfolio = expected return on your portfolio – risk-free return
= .1165 – .0689 = .0476 = 4.76%
Answers may differ slightly due to rounding
Note that the inflation rate is irrelevant
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Find 2-stock portfolio beta and compare systematic & unsystematic risk to well-diversified, average systematic risk portfolio 4. Portfolio A is a well-diversified portfolio that is equally-weighted among 12,000 different and diverse stocks. Portfolio A has an average amount of systematic risk, so it has exactly the same amount of systematic risk as the market portfolio. Portfolio B consists of 2 stocks that operate in the active leisure industry: 3,000 shares of Treetop Entertainment stock, which has a price of $14.00
per share and a beta of 1.23; and 2,000 shares of Garfield Recreational stock, which has a price of $6.00 per share and a beta of 0.32. All stocks have some unsystematic risk and all stocks have the same level of unsystematic risk. Which one of the following assertions is most likely to be true?
A. Portfolio B has more systematic risk than portfolio A, and portfolio A has more unsystematic risk than portfolio B B. Portfolio B has more systematic risk than portfolio A, and portfolio B has more unsystematic risk than portfolio A
C. Portfolio A has more systematic risk than portfolio B, and portfolio A more unsystematic risk than
portfolio B D. Portfolio A has more systematic risk than portfolio B, and portfolio B has more unsystematic risk than portfolio A E. Portfolio A either has the same amount of systematic risk as portfolio B or portfolio A has the same amount of unsystematic risk as portfolio B, or portfolio A has the same amount of systematic risk and unsystematic risk as portfolio B Answer: B. Portfolio B has more systematic risk than portfolio A, and portfolio B has more unsystematic risk than portfolio A Systematic risk: compare betas
For portfolio A: β
p
= 1, since the market portfolio has a beta of 1
For portfolio B: β
p
= x
1
β
1
+ x
2
β
2
= x
TE
β
TE
+ x
GR
β
GR
Value of Treetop Entertainment stock = number of shares × price per share = 3,000 × $14.00 = $42,000
Value of Garfield Recreational stock = number of shares × price per share = 2,000 × $6.00 = $12,000
Total value of portfolio = $42,000 + $12,000 = $54,000
Weight for Treetop Entertainment stock = x
TE
= $42,000 / $54,000 Weight for Garfield Recreational stock = x
GR
= $12,000 / $54,000
β
TE
= 1.23
β
GR
= 0.32
For portfolio B: β
p
= [(42,000/54,000) × 1.23] + [(12,000/54,000) × 0.32] = 0.9567 + .0711 = 1.0278 ≈ 1.03
β
B
= 1.03 > β
A
= 1.00, so portfolio B has more systematic risk than portfolio A
Unsystematic risk:
Portfolio A is well-diversified with 12,000 stocks, so it has no unsystematic risk, as it is diversified away.
Portfolio B only has 2 stocks, which are both active leisure stocks, so it is not very well-diversified. Therefore, portfolio B is likely to have unsystematic risk, so portfolio B has more unsystematic risk than portfolio A
4. Portfolio A is a well-diversified portfolio that is equally-weighted among 12,000 different and diverse stocks. Portfolio A has an average amount of systematic risk, so it has exactly the same amount of systematic risk as the market portfolio. Portfolio B consists of 2 stocks that operate in the active leisure industry: 3,000 shares of Treetop Entertainment stock, which has a price of $14.00
per share and a beta of 0.73; and 2,000 shares of Garfield Recreational stock, which has a price of $6.00 per share and a beta of 1.73. All stocks have some unsystematic risk and all stocks have the same level of unsystematic risk. Which one of the following assertions is most likely to be true?
A. Portfolio B has more systematic risk than portfolio A, and portfolio A has more unsystematic risk than portfolio B B. Portfolio B has more systematic risk than portfolio A, and portfolio B has more unsystematic risk than portfolio A C. Portfolio A has more systematic risk than portfolio B, and portfolio A more unsystematic risk than
portfolio B D. Portfolio A has more systematic risk than portfolio B, and portfolio B has more unsystematic risk than portfolio A
E. Portfolio A either has the same amount of systematic risk as portfolio B or portfolio A has the same amount of unsystematic risk as portfolio B, or portfolio A has the same amount of systematic risk and unsystematic risk as portfolio B D. Portfolio A has more systematic risk than portfolio B, and portfolio B has more unsystematic risk than portfolio A
Systematic risk: compare betas
For portfolio A: β
p
= 1, since the market portfolio has a beta of 1
For portfolio B: β
p
= x
1
β
1
+ x
2
β
2
= x
TE
β
TE
+ x
GR
β
GR
Value of Treetop Entertainment stock = number of shares × price per share = 3,000 × $14.00 = $42,000
Value of Garfield Recreational stock = number of shares × price per share = 2,000 × $6.00 = $12,000
Total value of portfolio = $42,000 + $12,000 = $54,000
Weight for Treetop Entertainment stock = x
TE
= $42,000 / $54,000 Weight for Garfield Recreational stock = x
GR
= $12,000 / $54,000
β
TE
= 0.73
β
GR
= 1.73
For portfolio B: β
p
= [(42,000/54,000) × 0.73] + [(12,000/54,000) × 1.73] = 0.5678 + .3844 = 0.9522 ≈ 0.95
β
B
= 0.95 < β
A
= 1.00, so portfolio A has more systematic risk than portfolio B
Unsystematic risk:
Portfolio A is well-diversified with 12,000 stocks, so it has no unsystematic risk, as it is diversified away.
Portfolio B only has 2 stocks, which are both active leisure stocks, so it is not very well-diversified. Therefore, portfolio B is likely to have unsystematic risk, so portfolio B has more unsystematic risk than portfolio A
4. Portfolio A is a well-diversified portfolio that is equally-weighted among 12,000 different and diverse stocks. Portfolio A has an average amount of systematic risk, so it has exactly the same amount of systematic risk as the market portfolio. Portfolio B consists of 2 stocks that operate in the active leisure industry: 3,000 shares of Treetop Entertainment stock, which has a price of $14.00
per share and a beta of 1.27; and 2,000 shares of Garfield Recreational stock, which has a price of $6.00 per share and a beta of 0.29. All stocks have some unsystematic risk and all stocks have the same level of unsystematic risk. Which one of the following assertions is most likely to be true?
A. Portfolio A has more systematic risk than portfolio B, and portfolio B has more unsystematic risk than portfolio A B. Portfolio A has more systematic risk than portfolio B, and portfolio A more unsystematic risk than
portfolio B C. Portfolio B has more systematic risk than portfolio A, and portfolio B has more unsystematic risk than portfolio A
D. Portfolio B has more systematic risk than portfolio A, and portfolio A has more unsystematic risk than portfolio B E. Portfolio A either has the same amount of systematic risk as portfolio B or portfolio A has the same amount of unsystematic risk as portfolio B, or portfolio A has the same amount of systematic risk and unsystematic risk as portfolio B
C. Portfolio B has more systematic risk than portfolio A, and portfolio B has more unsystematic risk than portfolio A
Systematic risk: compare betas
For portfolio A: β
p
= 1, since the market portfolio has a beta of 1
For portfolio B: β
p
= x
1
β
1
+ x
2
β
2
= x
TE
β
TE
+ x
GR
β
GR
Value of Treetop Entertainment stock = number of shares × price per share = 3,000 × $14.00 = $42,000
Value of Garfield Recreational stock = number of shares × price per share = 2,000 × $6.00 = $12,000
Total value of portfolio = $42,000 + $12,000 = $54,000
Weight for Treetop Entertainment stock = x
TE
= $42,000 / $54,000 Weight for Garfield Recreational stock = x
GR
= $12,000 / $54,000
β
TE
= 1.27
β
GR
= 0.29
For portfolio B: β
p
= [(42,000/54,000) × 1.27] + [(12,000/54,000) × 0.29] = 0.9878 + .0644 = 1.0522 ≈ 1.05
β
B
= 1.05 > β
A
= 1.00, so portfolio B has more systematic risk than portfolio A
Unsystematic risk:
Portfolio A is well-diversified with 12,000 stocks, so it has no unsystematic risk, as it is diversified away.
Portfolio B only has 2 stocks, which are both active leisure stocks, so it is not very well-diversified. Therefore, portfolio B is likely to have unsystematic risk, so portfolio B has more unsystematic risk than portfolio A
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4. Portfolio A is a well-diversified portfolio that is equally-weighted among 12,000 different and diverse stocks. Portfolio A has an average amount of systematic risk, so it has exactly the same amount of systematic risk as the market portfolio. Portfolio B consists of 2 stocks that operate in the active leisure industry: 3,000 shares of Treetop Entertainment stock, which has a price of $14.00
per share and a beta of 0.68; and 2,000 shares of Garfield Recreational stock, which has a price of $6.00 per share and a beta of 1.86. All stocks have some unsystematic risk and all stocks have the same level of unsystematic risk. Which one of the following assertions is most likely to be true?
A. Portfolio A has more systematic risk than portfolio B, and portfolio B has more unsystematic risk than portfolio A
B. Portfolio A has more systematic risk than portfolio B, and portfolio A more unsystematic risk than
portfolio B C. Portfolio B has more systematic risk than portfolio A, and portfolio B has more unsystematic risk than portfolio A D. Portfolio B has more systematic risk than portfolio A, and portfolio A has more unsystematic risk than portfolio B E. Portfolio A either has the same amount of systematic risk as portfolio B or portfolio A has the same amount of unsystematic risk as portfolio B, or portfolio A has the same amount of systematic risk and unsystematic risk as portfolio B A. Portfolio A has more systematic risk than portfolio B, and portfolio B has more unsystematic risk than portfolio A
Systematic risk: compare betas
For portfolio A: β
p
= 1, since the market portfolio has a beta of 1
For portfolio B: β
p
= x
1
β
1
+ x
2
β
2
= x
TE
β
TE
+ x
GR
β
GR
Value of Treetop Entertainment stock = number of shares × price per share = 3,000 × $14.00 = $42,000
Value of Garfield Recreational stock = number of shares × price per share = 2,000 × $6.00 = $12,000
Total value of portfolio = $42,000 + $12,000 = $54,000
Weight for Treetop Entertainment stock = x
TE
= $42,000 / $54,000 Weight for Garfield Recreational stock = x
GR
= $12,000 / $54,000
β
TE
= 0.68
β
GR
= 1.86
For portfolio B: β
p
= [(42,000/54,000) × 0.68] + [(12,000/54,000) × 1.86] = 0.5289 + .4133 = 0.9422 ≈ 0.94
β
B
= 0.94 < β
A
= 1.00, so portfolio A has more systematic risk than portfolio B
Unsystematic risk:
Portfolio A is well-diversified with 12,000 stocks, so it has no unsystematic risk, as it is diversified away.
Portfolio B only has 2 stocks, which are both active leisure stocks, so it is not very well-diversified. Therefore, portfolio B is likely to have unsystematic risk, so portfolio B has more unsystematic risk than portfolio A
Effectiveness of fundamental/technical analysis in markets of varying levels of efficiency
5. How many of the following statements are true if K’s analysis involves drawing charts of stock
returns and attempting to identify patterns that indicate that the price of the stock is going to increase substantially? Statement 1: There could be predictable benefits from K’s analysis in markets that are not efficient. Statement 2: There could be predictable benefits from K’s analysis in markets that are weak form efficient. Statement 3: There could be predictable benefits from K’s analysis in markets that are semi-
strong form efficient. Statement 4: There could be predictable benefits from K’s analysis in markets that are strong form efficient.
A. 0
B. 1
C. 2
D. 3
E. 4
Answer: 1
K is conducting technical analysis. This type of analysis involves forecasting the future price of a security by evaluating public trading information. The goal is to identify securities that are currently underpriced and are going to increase in price substantially in the future (producing very large returns) based on past patterns in prices, volumes, returns, etc.
Statement 1 is true
In markets that are not efficient, prices do not reflect all past trading information, so there is an opportunity to evaluate past trading information, which is technical analysis, and earn predictable benefits.
Statements 2, 3, and 4 are false
There is no predictable benefit from technical analysis in markets that are either weak, semi-
strong, or strong form efficient, as all 3 forms of efficiency involve asset prices that reflect all past trading information and technical analysis involves evaluating past trading information.
5. How many of the following statements are true if K’s analysis involves analyzing publicly available company financial statements, government data, and industry reports and attempting to identify stocks of firms that are undervalued?
Statement 1: There could be predictable benefits from K’s analysis in markets that are not efficient. Statement 2: There could be predictable benefits from K’s analysis in markets that are weak form efficient. Statement 3: There could be predictable benefits from K’s analysis in markets that are semi-
strong form efficient. Statement 4: There could be predictable benefits from K’s analysis in markets that are strong form efficient.
A. 0
B. 1
C. 2
D. 3
E. 4
Answer: 2
K is conducting fundamental analysis. This type of analysis involves estimating the “true” value of a security by evaluating public non-trading information. The goal is to find assets that have market prices that are lower than their true value and that will experience substantial returns when this fact becomes clear to other investors in time.
Statement 1 is true
In markets that are not efficient, prices do not reflect all public information. They don’t even reflect past trading information, so there is certainly an opportunity to evaluate public non-
trading information and earn predictable benefits.
Statement 2 is true
In markets that are weak form efficient, prices do not reflect all public information. They only
reflect past trading information, so there is an opportunity to evaluate public non-trading information and earn predictable benefits.
Statements 3 and 4 are false
There is no predictable benefit from fundamental analysis in markets that are either semi-
strong or strong form efficient, as both forms of efficiency involve asset prices that reflect all public information and fundamental analysis involves evaluating public non-trading information.
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5. How many of the following statements are true if K’s analysis involves drawing charts of stock
returns and attempting to identify patterns that indicate that the price of the stock is going to increase substantially? Statement 1: There could be predictable benefits from K’s analysis in markets that are not efficient. Statement 2: There could be predictable benefits from K’s analysis in markets that are weak form efficient. Statement 3: There could be predictable benefits from K’s analysis in markets that are semi-
strong form efficient. Statement 4: There could be predictable benefits from K’s analysis in markets that are strong form efficient.
A. 4
B. 3
C. 2
D. 1
E. 0
Answer: 1
K is conducting technical analysis. This type of analysis involves forecasting the future price of a security by evaluating public trading information. The goal is to identify securities that are currently underpriced and are going to increase in price substantially in the future (producing very large returns) based on past patterns in prices, volumes, returns, etc.
Statement 1 is true
In markets that are not efficient, prices do not reflect all past trading information, so there is an opportunity to evaluate past trading information, which is technical analysis, and earn predictable benefits.
Statements 2, 3, and 4 are false
There is no predictable benefit from technical analysis in markets that are either weak, semi-
strong, or strong form efficient, as all 3 forms of efficiency involve asset prices that reflect all past trading information and technical analysis involves evaluating past trading information.
5. How many of the following statements are true if K’s analysis involves analyzing publicly available company financial statements, government data, and industry reports and attempting to identify stocks of firms that are undervalued?
Statement 1: There could be predictable benefits from K’s analysis in markets that are not efficient. Statement 2: There could be predictable benefits from K’s analysis in markets that are weak form efficient. Statement 3: There could be predictable benefits from K’s analysis in markets that are semi-
strong form efficient. Statement 4: There could be predictable benefits from K’s analysis in markets that are strong form efficient.
A. 4
B. 3
C. 2
D. 1
E. 0
Answer: 2
K is conducting fundamental analysis. This type of analysis involves estimating the “true” value of a security by evaluating public non-trading information. The goal is to find assets that have market prices that are lower than their true value and that will experience substantial returns when this fact becomes clear to other investors in time.
Statement 1 is true
In markets that are not efficient, prices do not reflect all public information. They don’t even reflect past trading information, so there is certainly an opportunity to evaluate public non-
trading information and earn predictable benefits.
Statement 2 is true
In markets that are weak form efficient, prices do not reflect all public information. They only
reflect past trading information, so there is an opportunity to evaluate public non-trading information and earn predictable benefits.
Statements 3 and 4 are false
There is no predictable benefit from fundamental analysis in markets that are either semi-
strong or strong form efficient, as both forms of efficiency involve asset prices that reflect all public information and fundamental analysis involves evaluating public non-trading information.
Find risk premium from real, inflation, and inflation
6. What is risk premium for T&S Footwear stock if its expected real return is 10.23%, the expected inflation rate is 3.24%, and the risk-free return is 4.67%?
A. 9.13% (plus or minus 0.05 percentage points)
B. 2.10% (plus or minus 0.05 percentage points)
C. 5.56% (plus or minus 0.05 percentage points)
D. 6.99% (plus or minus 0.05 percentage points)
E. None of the above is within 0.05 percentage points of the correct answer
The risk premium T&S Footwear stock = expected return for T&S Footwear stock – return on the risk-free asset = expected return for T&S Footwear stock – .0467
We need to find the expected return for T&S Footwear stock, which is another way of referring to the expected nominal rate of return for T&S Footwear stock
Find the expected nominal rate of return
(1 + nominal rate) = (1 + real rate) × (1 + inflation rate)
(1+nominal rate) = (1.1023) × (1.0324) = 1.1380
Nominal rate = .1380 = 13.80%
Find the risk premium
Risk premium T&S Footwear stock = expected return for T&S Footwear stock – return on risk-free asset = 13.80% – 4.67% = 9.13%
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6
. What is risk premium for T&S Footwear stock if its expected real return is 10.23%, the expected inflation rate is 3.17%, and the risk-free return is 4.98%?
A. 8.74% (plus or minus 0.05 percentage points)
B. 1.86% (plus or minus 0.05 percentage points)
C. 5.25% (plus or minus 0.05 percentage points)
D. 7.06% (plus or minus 0.05 percentage points)
E. None of the above is within 0.05 percentage points of the correct answer
The risk premium T&S Footwear stock = expected return for T&S Footwear stock – return on the risk-free asset = expected return for T&S Footwear stock – .0498
We need to find the expected return for T&S Footwear stock, which is another way of referring to the expected nominal rate of return for T&S Footwear stock
Find the expected nominal rate of return
(1 + nominal rate) = (1 + real rate) × (1 + inflation rate)
(1+nominal rate) = (1.1023) × (1.0317) = 1.1372
Nominal rate = .1372= 13.72%
Find the risk premium
Risk premium T&S Footwear stock = expected return for T&S Footwear stock – return on risk-free asset = 13.72% – 4.98% = 8.74%
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6. What is risk premium for T&S Footwear stock if its expected real return is 11.29%, the expected inflation rate is 3.24%, and the risk-free return is 4.67%?
A. 10.23% (plus or minus 0.05 percentage points)
B. 3.13% (plus or minus 0.05 percentage points)
C. 6.62% (plus or minus 0.05 percentage points)
D. 8.05% (plus or minus 0.05 percentage points)
E. None of the above is within 0.05 percentage points of the correct answer
The risk premium T&S Footwear stock = expected return for T&S Footwear stock – return on the risk-free asset = expected return for T&S Footwear stock – .0467
We need to find the expected return for T&S Footwear stock, which is another way of referring to the expected nominal rate of return for T&S Footwear stock
Find the expected nominal rate of return
(1 + nominal rate) = (1 + real rate) × (1 + inflation rate)
(1+nominal rate) = (1.1129) × (1.0324) = 1.1490
Nominal rate = .1490 = 14.90%
Find the risk premium
Risk premium T&S Footwear stock = expected return for T&S Footwear stock – return on risk-free asset = 14.90% – 4.67% = 10.23%
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6. What is risk premium for T&S Footwear stock if its expected real return is 11.29%, the expected inflation rate is 3.17%, and the risk-free return is 4.98%?
A. 9.84% (plus or minus 0.05 percentage points)
B. 2.89% (plus or minus 0.05 percentage points)
C. 6.31% (plus or minus 0.05 percentage points)
D. 8.12% (plus or minus 0.05 percentage points)
E. None of the above is within 0.05 percentage points of the correct answer
The risk premium T&S Footwear stock = expected return for T&S Footwear stock – return on the risk-free asset = expected return for T&S Footwear stock – .0498
We need to find the expected return for T&S Footwear stock, which is another way of referring to the expected nominal rate of return for T&S Footwear stock
Find the expected nominal rate of return
(1 + nominal rate) = (1 + real rate) × (1 + inflation rate)
(1+nominal rate) = (1.1129) × (1.0317) = 1.1482
Nominal rate = .1482= 14.82%
Find the risk premium
Risk premium T&S Footwear stock = expected return for T&S Footwear stock – return on risk-free asset = 14.82% – 4.98% = 9.84%
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Stock exp ret from mkt return, inflation, risk-free rate, & stock beta
7. If the expected return on the market is 17.28 percent, the inflation rate is 2.34 percent, the risk-
free rate is 4.86 percent, and West Side Burger common stock has a beta of 0.84, then what is the
expected return for West Side Burger stock?
A. 15.29% (plus or minus .05 percentage points)
B. 14.89% (plus or minus .05 percentage points)
C. 17.41% (plus or minus .05 percentage points)
D. 14.52% (plus or minus .05 percentage points)
E. None of the above is within .05 percentage points of the correct answer
E(R
i
) = R
f
+ (β
i
× [E(R
M
) – R
f
])
The expected return on the market is 17.28 percent, so E(R
M
) = .1728
R
f
= .0486
β
i
= 0.84
E(R
i
) = .0486 + (0.84 × [.1728 – .0486])
= .0486 + (0.84 × .1242)
= .0486 + .1043
= .1529 = 15.29%
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Note that inflation is not relevant for solving the problem
7. If the expected return on the market is 17.28 percent, the inflation rate is 2.34 percent, the risk-
free rate is 4.86 percent, and West Side Burger common stock has a beta of 0.76, then what is the
expected return for West Side Burger stock?
A. 14.30% (plus or minus .05 percentage points)
B. 11.35% (plus or minus .05 percentage points)
C. 16.21% (plus or minus .05 percentage points)
D. 13.13% (plus or minus .05 percentage points)
E. None of the above is within .05 percentage points of the correct answer
E(R
i
) = R
f
+ (β
i
× [E(R
M
) – R
f
])
The expected return on the market is 17.28 percent, so E(R
M
) = .1728
R
f
= .0486
β
i
= 0.76
E(R
i
) = .0486 + (0.76 × [.1728 – .0486])
= .0486 + (0.76 × .1242)
= .0486 + .0944
= .1430 = 14.30%
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Note that inflation is not relevant for solving the problem
7. If the expected return on the market is 15.28 percent, the inflation rate is 2.34 percent, the risk-
free rate is 4.86 percent, and West Side Burger common stock has a beta of 0.84, then what is the
expected return for West Side Burger stock?
A. 13.61% (plus or minus .05 percentage points)
B. 10.87% (plus or minus .05 percentage points)
C. 15.73% (plus or minus .05 percentage points)
D. 12.84% (plus or minus .05 percentage points)
E. None of the above is within .05 percentage points of the correct answer
E(R
i
) = R
f
+ (β
i
× [E(R
M
) – R
f
])
The expected return on the market is 15.28 percent, so E(R
M
) = .1528
R
f
= .0486
β
i
= 0.84
E(R
i
) = .0486 + (0.84 × [.1528 – .0486])
= .0486 + (0.84 × .1042)
= .0486 + .0875
= .1361 = 13.61%
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Note that inflation is not relevant for solving the problem
7. If the expected return on the market is 15.28 percent, the inflation rate is 2.34 percent, the risk-
free rate is 4.86 percent, and West Side Burger common stock has a beta of 0.76, then what is the
expected return for West Side Burger stock?
A. 12.78% (plus or minus .05 percentage points)
B. 9.83% (plus or minus .05 percentage points)
C. 14.69% (plus or minus .05 percentage points)
D. 11.61% (plus or minus .05 percentage points)
E. None of the above is within .05 percentage points of the correct answer
E(R
i
) = R
f
+ (β
i
× [E(R
M
) – R
f
])
The expected return on the market is 15.28 percent, so E(R
M
) = .1528
R
f
= .0486
β
i
= 0.76
E(R
i
) = .0486 + (0.76 × [.1528 – .0486])
= .0486 + (0.76 × .1042)
= .0486 + .0792
= .1278 = 12.78%
Note that inflation is not relevant for solving the problem
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Related Documents
Related Questions
Question 7
The following figures show the optimal portfolio choice for two investors with different levels of risk-aversion graphically. Which statement
is correct?
E[R]
0.3
0.25
0.2
0.15
0.1
0.05
0
0
0.05 0.1
0.15
Figure 1
0.2 0.25 0.3 0.35 0.4 0.45
o(R)
[a]H
0.3
0.25
0.2
0.15
0.1
0.05
0
0
Figure (2) shows an investor that borrows in risk-free rate and invests in the risky asset.
Figure (1) shows an investor with a conservative investment behavior.
0.05
0.1 0.15
In the optimal point of both figures, the highest indifference curve is tangent to the efficient frontier.
In Figure (1), more aggressive investment decision led to a higher Sharpe ratio.
Figure 2
0.2 0.25
o (R)
0.3
0.35 0.4 0.45
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Portfolio theory with two assets
E(R1)=0.15 E(01)= 0.10 W1=0.5
E(R2)=0.20 E(02) = 0.20 W2=0.5
Calculate the expected return and the standard deviation of the two portfolios if r1,2 = 0.4 and -0.60
respectively.
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Consider following information on a risky portfolio, risk-free asset and the market index.
What is the T2 of the risky portfolio?
Risky portfolio
Risk-free asset
Market index
Average return
8.2%
2%
6%
Std. Dev.
26%
20%
Residual std. dev.
10%
Alpha
1.4%
Beta
1.2
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Baghiben
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D6)
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You are given the following information concerning three portfolios, the market portfolio, and the risk-free asset:
Portfolio
X
Y
Z
Market
Risk-free
Rp
11.0%
ор
33.00%
10.0
28.00
8.1
10.4
5.2
18.00
23.00
Ө
вр
1.45
1.20
0.75
1.00
Ө
Assume that the correlation of returns on Portfolio Y to returns on the market is 0.66. What percentage of Portfolio Y's return is driven
by the market?
Note: Enter your answer as a decimal not a percentage. Round your answer to 4 decimal places.
R-squared
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Problem 2: You have access to three risky assets (Stocks A, B, and C) and ariskless asset:Expected Return, Standard DeviationStock A 8% , 35%Stock B 12% , 50%Stock C 15% , 75%
Riskless Asset expected return 5%Correlation(A,B) 0.2Correlation(A,C) 0.2Correlation(B,C) -0.2
a) What are the portfolio weights of the tangency portfolio?b) What is the Sharpe ratio of the tangency portfolio?
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9.2- Use the diagrams to answer the question
q1- This question relates to Diagrams 1 - 4 from the 9.2 diagrams, each of which shows a set of portfolios plotted on a set of risk/return axes.
Which diagram shows (in red) the set of feasible portfolios?
Select one:
a.
Diagram 1
b.
Diagram 2
c.
Diagram 3
d.
Diagram 4
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Give typing answer with explanation and conclusion
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H3.
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None
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Consider following information on a risky portfolio, risk-free asset and the market index.
What is the Sharpe ratio of the market index?
Risky portfolio
Risk-free asset
Market index
Average return
8.2%
2%
6%
Std. Dev.
26%
20%
Residual std. dev.
10%
Alpha
1.4%
Beta
1.2
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QUESTIONS AND PROBLEMS
1. Assume that the following two-index model describes returns:
R=a+b+b212 +e;
Assume that the following three portfolios are observed.
Portfolio
ABC
Expected Return
12.0
13.4
12.0
bil
b₁₂
0.5
1
0.2
3
-0.5
3
Find the equation of the plane that must describe equilibrium returns.
111 illustrate the arbitrage opportunities that
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None
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Problem 1
You are given the following information about stock X and the market portfolio, M:
Riskless Asset (f)
Stock X
Market Portfolio (M)
E(r)
0.04 (4%)
?
0.10
σ
0.00
0.30
0.20
You are not given the expected return of stock X. The correlation of the returns on the stock X and
the market portfolio is equal to 0.4.
a) What is the beta (6) of stock X?
b) Assuming the CAPM holds, what is the expected return on stock X?
c) You have $1,000 to invest in some combination of the risk-free asset, stock X, and the market
portfolio. You are thinking of investing $300 in the risk free asset, $400 in stock X, and $300
in the market portfolio. What is the overall expected return, standard deviation and beta of
this portfolio?
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sa.3
answer must be correct or i will give down vote
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Vijay
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What is the expected return of a portfolio of two risky assets if the expected return
E(Ri), standard deviation (SDi), covariance (COVij), and asset weight (Wi) are as
shown below?
Asset (A)
E(R₂) = 10%
SDA = 8%
WA = 0.25
COVAB = 0.006
Select one:
A.
13.75%
B.
7.72%
C.
12.5%
D.
8.79%
Asset (B)
E(RB) = 15%
SDB = 9.5%
WB = 0.75
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PLS HELP ASAP
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son.3
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