Portfolio Selection and Risk Management Coursera Quiz Answers

All WeeKS Portfolio Selection and Risk Management Coursera Quiz Answers

Week 1 Quiz Answers

Quiz 1: Risk and return: Measuring returns

Q1. Consider the following distribution of returns of a stock:

Year	Return (r)
1	-10%
2	20%
3	30%

What is the geometric mean return of the stock over 3 years? Round off your final answer to two digits after the decimal point. State your answer as a percentage rate, i.e ‘13.55’.

Enter your Answer

Q2. Consider the following distribution of returns of a stock:

Year	Return (r)
1	-10%
2	20%
3	30%

What is the arithmetic mean return of the stock over 3 years? Round off your final answer to two digits after the decimal point. State your answer as a percentage rate, i.e ‘10.55’

Enter your Answer

Q3. Which of the following measures is most informative about the average past return of an investment?

• The arithmetic average return over the period of interest
• The geometric average return over the period of interest
• Both arithmetic and geometric average returns over the period of interest
• The standard deviation of the returns over the period of interest

Q4. In which of the following cases you should take into account compounding?

• When you calculate the arithmetic average return, you are computing the compounded average return.
• You are using compounded returns when you compute volatility.
• Calculating the arithmetic average or the geometric return always gives the same answer.
• When you calculate the geometric average return, you are computing the compounded average return.

Q5. If you want to have an indication of the expected rate of return for an investment, you would prefer to look at:

• The arithmetic average return over the period of interest
• The geometric average return over the period of interest
• Both arithmetic and geometric average returns over the period of interest
• The standard deviation of the returns over the period of interest

Quiz 2: Risk & Return: Measuring risk

Q1. Which of the following is a common measure of risk for returns?

• Expected return
• Standard deviation
• Inflation
• Geometric mean of returns

Q2. Based on the following distribution of returns for stock A, compute the standard deviation for stock A. Round off our final answer to two digits after the decimal point. State your answer as a percentage rate (such as 5.55) Probability
Return on A

• 30%

• 10%
• 40%
• 5%
• 30%
• 30%

Enter answer here

Q3. In the following graph we observe the probability distributions of assets A and B. Which of the following statements is correct?

• E(RA)
  = E(RB) and σA < σB
• E(RA)
  < E(RB) and σA = σB
• E(RA)
  < E(RB) and σA > σB
• E(RA)
  = E(RB) and σA > σB

Q4. When a distribution is skewed to the right:

• a. The
  extreme positive values dominate and the measure is positive
• b. The
  extreme negative values dominate and the measure is negative
• c. The
  standard deviation will underestimate risk
• d. both a
  and c are correct

Q5. Kurtosis measure the degree of fat tails of a distribution. Which of the following answers is or are true? (More than one answer can be correct)

• The presence of fat tails implies that there is greater probability mass in extreme events in the
  tails
• Normal
  distribution has a kurtosis equal to 3
• Normal
  distribution has a kurtosis equal to 0
• The presence of fat
  tails implies that there is lower probability mass in extreme events in the

Quiz 3: Module 1: Risk & Return

Q1. If your holding
period return on a $100 investment was 12% at the end of the first year, -10%
at the end of the second year and 5% at the end of the third year, what
was your three-year holding period return?

• 4.45%
• 4.8%
• 5.84%
• 6%
• 7%

Q2. Suppose the probabilities of a recession, a boom and no change
in the current economic environment are 40%, 30%, and 30% respectively.
Also suppose you will have an annual return on your investments of 10% in
a recession, 40% in a boom and 20 % if there is no change. What is your
expected annual return on your investment?

• 19%
• 20%
• 21%
• 22%
• 23%

Q3. You bought a stock of company
Alpha and held it over a five-year period. The annual returns of the stock
are given by the following table. Based on the annual returns, we calculated the
gross yearly returns. Are the calculations correct or are they false?

Year	Return = r	Gross return
1	– 10%	0.9
2	– 20%	0.8
3	30%	1.3
4	20%	1.2
5	15%	1.15

• The calculations are correct.
• The calculations are false.

Q4. What is the geometric mean return of the stock over 5 years?

Year	Return = r	Gross return
1	– 10%	0.9
2	– 20%	0.8
3	30%	1.3
4	20%	1.2
5	15%	1.15

• 4.23%
• 5.25%
• 30%
• 35%

Q5. What is the arithmetic mean return of the stock over five years?

Year	Return = r	Gross return
1	– 10%	0.9
2	– 20%	0.8
3	30%	1.3
4	20%	1.2
5	15%	1.15

• 7%
• 5.24%
• 7.5%
• 9%
• 35%

Q6. Suppose the probabilities of a recession, a boom and no change
in the current economic environment are 40%, 30 %, and 30 % respectively.
Also suppose you will have an annual return on your investments of 10% in
a recession, 40% in a boom and 20 % if there is no change. What is the
standard deviation of your annual return on your investment?

• 6.48
• 9.50
• 12.49
• 13.50
• 14.28

Q7. An analyst’s forecast for the end-of-year prices and dividend payments for company XYZ under various states of the economy are as follows:

State of the economy	Probability	Year-end price	Cash dividends
Crash	0.25	160	5
Poor	0.40	150	10
Good	0.30	160	20
Excellent	0.05	200	30

Suppose you bought one share of stock for $160. What’s the second highest rate of return you might get? Round off to one decimal. (i.e. “x.x”)

Enter answer here

Q8. Again, assuming that you bought one share of stock for $160, what is the expected annual return for this stock?

• -3.16%
• 0%
• 3.16%
• 6.72%
• 20%

Q9. A volatility strategy is:

• An investment strategy that collects a premium during stable periods, but has large losses during volatile times
• An investment strategy that consists in diversifying a securities portfolio.
• None of the above.

Q10. Suppose you have $100,000 to invest. Investing in equities will generate a gain of $50,000 with a probability of 60%, or a loss of $30,000 with a probability of 40%. Investing in the risk-free U.S. Treasury bills on the other hand will generate a sure gain of $5000. Based on this data, what is the expected risk premium associated with investing in risky equities versus risk-free T-bills?

• 18%
• 13%
• 5%
• 12%

Week 2

Quiz 1: Measuring expected portfolio return

Q1. Consider the following distribution of returns:

Probability	Return on A	Return on B	Return on C
30%	-20%	-5%	5%
40%	5%	10%	3%
30%	40%	15%	2%

What is the expected return of security A? Round off your answer to two digits after the decimal point. State your answer as a percentage rate (such as 5.55)

Q2. Consider the following distribution of returns:

Probability	Return on A	Return on B	Return on C
30%	-20%	-5%	5%
40%	5%	10%	3%
30%	40%	15%	2%

What is the expected return of security B? Round off your answer to two digits after the decimal point. State your answer as a percentage rate (such as 5.55)

Q3. Consider the following distribution of returns:

Probability	Return on A	Return in B	Return on C
30%	-20%	-5%	5%
40%	5%	10%	3%
30%	40%	15%	2%

What is the expected return of security C? Round off your answer to two digit after the decimal point. State your answer as a percentage rate (such as 5.55).

Q4. Consider the following distribution of returns:

Probability	Return on A	Return on B	Return on C
30%	-20%	-5%	5%
40%	5%	10%	3%
30%	40%	15%	2%

Using your answers for questions 1-3, now compute the expected return of a portfolio with 40% in A, 40% in B, and 20% in C. Round off your answer to two-digits after the decimal point. State your answer as a percentages rate (such as 5.55)

Q5. Consider the following distribution of returns:

Probability	Return on A	Return on B	Return on C
30%	-20%	-5%	5%
40%	5%	10%	3%
30%	40%	15%	2%

Using your answers for questions 1-3, what is the expected return of an equally weighted portfolio? Round off your final answer to two digits after the decimal point. State your answer as a percentage rate (such as 5.55)

Q6. An investor has total wealth of $50,000 and wants to invest in a portfolio with 3 securities A, B, and C with expected returns E(R_A) = 20%, E(R_B) = 15% and E(R_C) =17% respectively. If he chooses to invest $25,000 in security A, $12,500 in security B, and $12,500 in security C, what will be the expected return of this portfolio? State your answer as a percentage rate (such as 5.55)

Q.7 An investor has total wealth of $50,000 and wants to invest in a portfolio with 3 securities A, B, and C with expected returns E(R_A)=20%, E(R_B)=15% and E(R_C)=17% respectively. If he chooses to invest $20,000 in security A, $10,000 in security B and $20,000 in security C, what will be the expected return of this portfolio? Round off your answer to digits after the decimal point. State your answer as a percentage rate (such as 5.55)

Q8. Suppose your investment budget is $300,000. In addition, you borrow an additional $120,000 investing the total available funds in equities. If the expected rate of return in equities is 8%, and you borrow at 5%, what is your expected portfolio return?

• 18.2%
• 1.4%
• 9.2%
• 3%

Quiz 2: Measuring portfolio volatility

Q1. Consider the following distribution of returns:

Probability	Return on A	Return on B	Return on C
30%	-20%	-5%	5%
40%	5%	10%	3%
30%	40%	15%	2%

What is the standard deviation of security A? Round off your answer to two digits after the decimal point (such as 5.55).

Q2. Consider the following distribution of returns:

Probability	Return on A	Return on B	Return on C
30%	-20%	-5%	5%
40%	5%	10%	3%
30%	40%	15%	2%

What is the standard deviation of security B? Round off your answer to two digits after the decimal point (such as 5.55).

Q3. Consider the following distribution of returns:

Probability	Return on A	Return on B	Return C
30%	-20%	-5%	5%
40%	5%	10%	3%
30%	40%	15%	2%

What is the standard deviation of security C? Round off your answer to two digits after the decimal point (such as 5.55).

Q4. Consider the following distribution of returns:

Probability	Return on A	Return on B	Return on C
30%	-20%	-5%	5%
40%	5%	10%	3%
30%	40%	15%	2%

What is the expected return of a portfolio with 40% in A, 20% in B and 40% in C? Round off your final answer to two digits after the decimal point. State your answer as a percentage rate (such as 5.55).

Q5. Consider the following distribution of returns:

Probability	Return on A	Return on B	Return on C
30%	-20%	-5%	5%
40%	5%	10%	3%
30%	40%	15%	2%

Which of the following pairwise covariance measures are correct?

• σ_AB = 174
• σ_AC = – 26.4
• σ_BC = 26.4
• σ_BC = -9.60

Q6. Consider the following distribution of returns:

Probability	Return on A	Return on B	Return on C
30%	-20%	-5%	5%
40%	5%	10%	3%
30%	40%	15%	2%

Which of the following pairwise correlation coefficients are correct? (Hint: Your answers to the previous questions may be useful.)

• ρ_AC = −0.95
• ρ_AC = 0.95
• ρ_CB = −0.99
• ρ_CB = 0.99
• ρ_AB = -0.92
• ρ_AB= 0.92

Q6. Consider the following distribution of returns:

Probability	Return on A	Return on B	Return on C
30%	-20%	-5%	5%
40%	5%	10%	3%
30%	40%	15%	2%

Find the expected return of a portfolio that is equally weighted between securities A and C. Round off your final answer to two digits after the decimal point. State your answer as a percentage rate (such as 5.55) (Hint: Your answers to previous questions may be useful)

Q8. Consider the following distribution of returns:

Probability	Return on A	Return on B	Return on C
30%	-20%	-5%	5%
40%	5%	10%	3%
30%	40%	15%	2%

Compute the volatility of a portfolio that is equally invested in A and C. Round off your final answer to two digits after the decimal point (such as 5.55) (Hint: Your answers to previous questions may be useful.)

Q9. Consider the following distribution of returns:

Probability	Return on A	Return on B	Return on C
30%	-20%	-5%	5%
40%	5%	10%	3%
30%	40%	15%	2%

Find the expected return of a portfolio with 60% in A and 40% in B. Round off your final answer to two digits after the decimal point. State your answer as a percentage rate (such as 5.55) (Hint: Your answers to previous questions may be useful.)

Q10. Consider the following distribution of returns:

Probability	Return on A	Return on B	Return on C
30%	-20%	-5%	5%
40%	5%	10%	3%
30%	40%	15%	2%

Compute the volatility of a portfolio that is 60% invested in A and 40% invested in B. Round off your final answer to two digits after the decimal point. State your answer as a percentage rate (such as 5.55) (Hint: Your answers to previous questions may be useful.)

Quiz 3: Diversification and portfolio risk

Q1. The volatility of a portfolio’s return is always equal to the weighted average of the standard deviations of the assets in the portfolio. True or false?

• True
• False.

Q2. Which of the following statements is correct?

• A well-diversified portfolio eliminates market risk.
• A well-diversified portfolio eliminates unique risk.
• Unique risk and market risk can both be eliminated through diversification.
• Increased insurance costs is an example of pure systematic risk for a corporation.

Q3. The measure of risk for an asset that is held in a diversified portfolio is:

• Specific risk
• Volatility
• Liquidity risk
• Covariance

Q4. Consider the following distribution of returns:

Probability	Return on A	Return on B
30%	-10%	10%
40%	5%	20%
30%	30%	30%

Compute the covariance between A and B. Round off your final answer to two digits after the decimal point (such as 5.55).

Enter answer here

Q5. Consider the following distribution of returns:

Compute the correlation coefficient between A and B. Round off your final answer to two digits after the decimal point (such as 5.55)

Enter answer here

Q6. A portfolio consists of 120 shares of Jones stock, which sells
for $50 per share, and 150 shares of Rice stock, which sells for $20 per
share. What are the weights of the
two stocks in this portfolio?

• For the Jones stock: wJ=66.67% and for the
  Rice stock: wR=33.33%
• For the Jones stock: wJ=50% and for the Rice
  stock: wR=50%
• For the Jones stock: wJ=70% and for the Rice
  stock: wR=30%
• For the Jones stock: wJ=33.33% and for the
  Rice stock: wR=33.33%

Q7. Jones stock has an expected return of 12 percent, and a
standard deviation of 9 percent per year.
Rice stock has an expected return of 18 percent, and a standard
deviation of 25 percent per year.
What is the expected return on a portfolio that consists of 30
percent Jones and 70 percent Rice? Round off your final answer to two digits after the decimal point. State your answer as a percentage rate (such as 5.55)

Enter answer here

Q8. If the correlation between the returns of Jones and Rice is
0.2, what is the return volatility of a portfolio described in the previous question? Round off your final answer to two digits after the decimal point (such as 5.55)

Enter answer here

Q9. Which of the following are examples of sources of market
risk?

• Microsoft’s CEO is resigned.
• ExxonMobil decides to invest more heavily on R&D.
• The majority of British people votes at the
  referendum that Great Britain should leave the European Union
• Oil prices rise.

Q10. Assume there are N securities in the market. The expected
return on every security is 10 percent. All securities have the same
variance of 0.0025. The covariance between any pair of securities is
0.0064. What will happen to the variance of an equally weighted portfolio
containing all N securities as N approaches infinity? Note: the weight of
each security in the portfolio is 1/N.

• It will approach infinity
• It will approach zero
• It will approach the value 0.0064
• It will approach the value 0.0025

Q11. Which of the following statements is false about the mean-variance frontier?

• The bottom half of the mean-variance frontier is efficient.
• For two assets, it consists simply of all possible portfolio combinations of the two assets.
• The mean variance frontier expands as we add more assets to the mix.
• Mean-variance frontier is the locus of the portfolios in expected return-standard deviation space that have the minimum variance for each expected return.

Q12. Which of the following statements are true? Choose all that apply.

• The left-most point on the minimum variance frontier is called the minimum variance portfolio.
• Optimal portfolios are all the portfolios that lie on the minimum-variance frontier from the minimum-variance portfolio and upwards.
• Optimal portfolios can be obtained without diversification.
• Diversification removes idiosyncratic risk but does not influence the overall risk of the portfolio.

Q13. Suppose you are considering to add real estate to your portfolio that currently includes only stocks, bonds, and cash. Which return characteristic of real estate would affect your portfolio risk?

• Standard deviation of real estate returns
• Expected return on real estate
• Age of the real estate properties
• Correlation with returns of the other asset classes

Q14. All individual assets lie inside the efficient frontier in the expected return-volatility space. True or false?

• True.
• False.

Q15. Which of the following statements is correct?

• Portfolio theory is about elimination of systematic risk
• Portfolio theory is concerned with the effect of diversification on portfolio risk.
• Portfolio theory is about how active portfolio management can enhance returns.
• Portfolio theory is concerned with maximizing unsystematic risk to enhance returns.

Quiz 4: Portfolio construction and diversification

Q1. The term ‘efficient frontier’ refers to the portfolios that:

(Choose all that apply.)

• a. Yield the greatest return for a given level of risk
• b. Involve the least risk for a given level of expected return
• c. Yield the greatest return for maximum risk
• d. None of the above.

Q2. An investor has total
wealth of $100,000 and wants to invest in a portfolio with 3 securities A,
B and C. If he chooses to invest $50,000 in security A, $25,000 in security B and $25,000 in security C, what will be the expected return of
this portfolio? Round off your final answer to two digits after the decimal point. State your answer as a percentage rate (such as 5.55)

Enter answer here

Q3. Consider the following distribution of returns:

Which of the following statements are correct?

• E(RA) = 15.5% and σB = 13.31%
• E(RB) = 12.5% and σA = 5.22%
• E(RC) = 4.6% and E(RB)
  = 14.5%
• σA = 5.22% and σC = 6.25%

Q4. Consider the following distribution of returns:

Based on the distribution above compute the covariance between A and B. Round off your final answer to two digits after the decimal point (such as 5.55). (Hint: Your answers to previous questions may be useful.)

Enter answer here

Q5. Consider the
following distribution of returns:

Expansion Calculate the correlation coefficient between A and B. Round off your final answer to two digits after the decimal point (such as 5.55). (Hint: Your answers to previous questions may be useful.)

Enter answer here

Q6. Consider the following distribution of returns:

What would be the expected return and standard
deviation of a portfolio with 60% in A and 40% in B?

E(RP) = 15.10% and σP = 8.19%

E(RP) = 16.23% and σP = 5.25%

E(RP) = 10.13% and σP = 7.50%


E(RP) = 20.20% and σP = 3.00%

Q7. What characteristics
of a security are most important in the determination of the variance of a
well-diversified portfolio?

• The
  expected return of a portfolio
• The
  selection of an equally weighted portfolio
• The
  correlation between the securities of a portfolio
• The
  number of the securities that form the portfolio

Q8. Which of the following options can be classified as a case of unique risk?

• A sudden change at the exchange rate between US dollar and euro.
• Kraft Foods buys Cadbury.
• Federal Reserve Bank tightens monetary policy.
• Oil
  prices fall.

Q9. Which of the following statements are true about the mean-variance frontier? Choose all that apply.

• Mean-variance
  frontier is the locus of the portfolios in expected return-volatility space that have the maximum variance for a given level of expected return.
• When there are only two assets, mean-variance frontier consists simply of all possible portfolio combinations of these two assets.
• The
  left-most point on the minimum variance frontier is called the minimum variance
  portfolio.
• The
  mean variance frontier shifts to the right in mean-variance space as we add more assets to the mix.

Q10. Consider a portfolio of risky equities and Treasury bills. Suppose the expected return on equities is 12% per year with a volatility of 18%. Let’s also suppose that T-bills offer a risk-free 7% rate of return. What would be the volatility of your portfolio if you have 60% in equities and 40% in Treasuries?

• 10.0%
• 13.6%
• 1.94%
• 10.8%

Week 3

Quiz 1: Utility and risk aversion

Q1. One way to measure investors’ risk aversion is by comparing their certainty equivalent. Economists define the certainty equivalent return rCE of a risky portfolio as the sure return that an investor would be wiling to accept instead of the risky portfolio. If you are more risk averse, what do you expect your rCE to be smaller or larger?

• If the investor is more risk averse, rCE will be larger
• If the investor is more risk averse, rCE will be smaller
• The value of rCE will be indifferent of how risk averse the investor is.
• The value of rCE will be equal to zero and indifferent of how risk averse the investor is.

Q2. Suppose that we have the following utility function. What can you conclude about this investor’s attitude towards risk based on her utility function?

• A risk neutral investor
• A risk-loving investor
• A risk averse investor
• None of the above

Q3. Which of the following statements are correct? (Select all that apply.)

• Most individuals have risk aversion levels between 1 and 10.
• The concavity of the utility function measures the degree of risk aversion.
• The level of risk aversion is different for each individual.
• Utility functions typically decrease with wealth.

Q4. Which of the following statements is true about a risk-neutral investor?

• A risk-neutral investor considers only the expected return in judging a risky portfolio.
• For a risk-neutral investor, the certainty equivalent is greater than the expected rate of return on a risky prospect.
• A risk-neutral investor is characterized by an infinite risk aversion coefficient.
• A risk-neutral investor penalizes the expected rate of return from a risky portfolio to account for the risk involved.

Q5. The concavity of the utility function implies that going from $1 to $2 is more valuable for investors than going from $100,000 to $100,001.

• True
• False

Quiz 2: Portfolio choice with mean-variance preferences

Q1. Consider the following three investment options:

Which investment would you choose if your preferences are represented by mean-variance utility and your risk aversion coefficient is equal to 3?

• Investment A
• Investment B
• Investment C

Q2. Suppose you have the following utility function.
You have an investment opportunity that will give you a future wealth of either
$4,000 or $6,000 with equal probability. Which of the following statements is
correct?

• For a certain wealth of $5,000, the utility you
  will get will be equal to 2.23.
• For a certain wealth of $5,000, the utility you
  will get will be lower than 2.23.
• For a certain wealth of $5,000, the utility you
  will get will be higher than 2.23.
• For a certain wealth of $5,000, the utility you
  will get will be higher than 2.50.

Q3. Compare S&P 500 and volatility strategies (Ang (2014)):
Below is a graph that compares the cumulative wealth obtained from
investing $1 in March 1989 from two strategies: investing in the S&P
500 equity index and volatility strategy. Volatility strategy is an
investment strategy that earns premiums during stables times (essentially
equivalent to selling volatility insurance), but has large losses during
volatile times such as the financial crisis of 2008-09.

Which one of the following is a limitation of using mean-variance preferences in comparing these two strategies?

• It does not account for tail events.
• It does not account for risk aversion.
• It takes into account only expected returns of each strategy
• It takes into account only the volatility of each strategy

Q4. Consider the three following investment opportunities:

Which investment would you choose if your preferences are represented by mean-variance utility function and you are risk-neutral?

• Investment A
• Investment B
• Investment C

Q5. Which of the following statements is correct?

• In the mean-variance space, the indifference curve of a less risk-averse investor will be steeper compared to that of a more risk-averse investor.
• Indifference curves are graphical representations of choices or combinations that give individuals the same level of utility.
• Moving northwest in mean-variance space, indifference curves are associated with lower levels of utility
• The risk aversion of an investor is irrelevant to indifference curves.

Q6. Your financial advisor offers you a portfolio of equities with an expected return of 20% and standard deviation of 30%. Suppose at the time of this offer, U.S. Treasuries offer a safe return of 5%. Suppose your preferences can be described by mean-variance preferences, and you know your risk aversion parameter A to be equal to 2. Which would you prefer?

• Equities
• U.S. Treasuries

Q7. Suppose you have two investment opportunities: A gives you a future wealth of either $150,000 or $50,000 with equal probability. B gives you a future wealth of 125,000 with probability 2/3 and 55,000 with probability of 1/3. Suppose, also, that your preferences can be described by a log utility function. In other words, U(W)=ln(W). If you are maximizing your expected utility, which investment would you choose?

• Investment A
• Investment B

Q8. Maximizing utility in mean-variance space graphically corresponds to

• Choosing the steepest indifference curve you can attain
• Choosing the flattest indifference curve you can attain
• Choosing the highest indifference curve moving northwest
• Choosing the lowest indifference curve moving southeast

Quiz 3:  Mean-variance preferences

Q1. True or False.

A fair game is a risky prospect that has a zero risk premium. It will not be undertaken by a risk-neutral investor.

• True
• False

Q2. Which of the following statements is false?

• Indifference curves in mean-variance space show the risk and return combinations that give us the same level of utility.
• The degree of risk aversion of an investor characterizes the slope of the indifference curve.
• More risk-averse investors have less steep indifference curves.
• The level of utility increases as one moves in northwest direction to higher indifference curves in the mean-variance space.

Q3. Consider the following data:

Which investment would you select if your preferences are represented by mean-variance utility function, and your risk aversion coefficient is equal to 4?

• Investment A
• Investment B
• Investment C

Q4. Which of the following is/are true about mean-variance preferences? (Select all that apply.)

• The utility score of a risky portfolio can be interpreted as the certainty equivalent rate of return.
• The certainty equivalent rate is the maximum rate that a risky portfolio would need to provide.
• The certainty equivalent rate is the minimum rate that a risky portfolio would have to provide.
• Certainty equivalent rate is the rate that if earned with certainty would provide the same utility as that of the risky portfolio under consideration.

Q5. What does the coefficient A in the mean-variance utility function (below) represent?

U = E(r) – ½ A σ2

• Investor’s required return
• The certainty equivalent rate
• Risk premium required by the investor
• Investor’s degree of risk aversion

Q6. What is the value of the risk aversion coefficient for the mean-variance utility function shown in the graph below? Answer in whole numbers.

Enter answer here

Week 4

Quiz 1: Mean-variance optimization

Q1. Which of these is not correct about the Capital Allocation Line (CAL)?

• The slope of the CAL is called reward to return ratio.
• The CAL provides us with all the possible combinations of the optimal risky portfolio with the risk-free asset.
• The slope of the CAL is called Sharpe ratio.
• The CAL goes from the risk-free rate and through the optimal risky portfolio.

Q2. Which of the following statements is not true?

• Other things equal, investors would prefer a steeper-sloping CAL.
• The optimal capital allocation in the risky portfolio for an investor is proportional to the risk premium.
• Sharpe ratio is the ratio of the return of the risky asset to the return of the risk-free asset.
• The solution to the optimal capital allocation decision for an investor is found graphically by finding the tangency portfolio between the investor’s indifference curve and the CAL.

Q3. Suppose you hold a
portfolio of risky assets with an expected return of 10% and volatility of
17%. The risk-free asset has a return of 1.5%. What is the Sharpe ratio of
the risky portfolio?

• 0.70
• 0.50
• 0.45
• 1.10

Q4. Suppose you would
like to have a portfolio with a volatility of 30%. If a passive portfolio
that mimics the S&P 500 stock index yields an expected rate of return
of 13% and a standard deviation of 25%, and the current Treasury bill rate
is 5%, what would your capital allocation between these two assets have to
be?

• Invest 43.3% in the index fund and 56.67% in Treasuries
• Borrow 20% of your wealth and invest 120% of your wealth in the index fund
• Invest 20% in Treasuries and 80% in the index fund
• Invest 100% of your wealth in the index fund

Q5. Suppose you expect
the U.S. equities market portfolio to have an annual return of 10% and
volatility of 15% going forward. Suppose also that the current Treasury
bill rate is 5%. What would you advise a client with a risk aversion
coefficient of 3 to allocate to the risk-free asset, if she were looking
to maximize her mean-variance utility? Round off your final answer to two
digits after the decimal point. (i.e “5.55”)

Enter answer here

Quiz 2: Optimal capital allocation and portfolio choice

Q1. The variance of the minimum variance portfolio of all risky securities must be lower than those of all other securities or portfolios. True or false?

• True.
• False.

Q2. The minimum variance portfolio is the optimal risky portfolio on the frontier. True or false?

• True
• False

Q3. Suppose you have $100,000 and the following two assets to construct a portfolio: a risk-free asset with a rate of return of 6% per year and a risky asset with an expected return of 15% per year, and a standard deviation of 25%. If you construct a portfolio with a standard deviation of 20%, what is your expected rate of return? Please round off your final answer to one digit after the decimal point. State your answer as a percentage rate.

Enter answer here

Q4. The standard deviation of the portfolio is always equal to the weighted average of the standard deviation of the assets in the portfolio. True or false?

• True
• False

Q5. Suppose you have $600,000 invested in a diversified portfolio. You then inherit from a family member $100,000 worth of Felix Company stock. Your financial advisor provides you with the following information:

The correlation coefficient between your diversified portfolio and Felix stock is 0.40.

Calculate your expected return of your new portfolio which includes Felix stock. State your answer as a percentage rate.

Enter answer here

Q6. Continuing with the previous question, what would be volatility of your new portfolio?

• 32.1%
• 26.4%
• 19.3%
• 22.2%

Q7. Continuing with the previous questions, suppose you decide to sell off your position in Felix stock and invest in government securities that yield 5% per year. What would be your expected return on the new portfolio that includes the government securities? State your answer as a percentage rate. Round off to three digits after the decimal point. (i.e. if your final answer is 0.01234, you would input 1.234)

Enter answer here

Q8. Continuing with the previous questions, what would be the volatility of this new portfolio including the government securities?

• 14%
• 28%
• 32%
• 24%

Q9. Finally, your friend who has not taken this course argues that it would not matter if you replaced Felix stock with the Tirex stock which has the same expected return and standard deviation of Felix. She says “It doesn’t matter at all whether you keep all of Felix or replace it with Tirex”. Which of the following would be an incorrect response to her?

• You agree with her wholeheartedly that it does not matter.
• You tell her she is wrong.
• You tell her that she does not know much about how combining assets affect portfolio risk and advise her to take this course.
• You explain that no it would matter because Tirex might have a different covariance with the rest of your portfolio.

Week 5

Quiz 1: Equilibrium asset pricing models: Capital Asset Pricing Model

Q1. Which of the following is true about the market portfolio in CAPM?

• The market portfolio in CAPM defines “the domestic market”.
• CAPM defines the market portfolio as the stock market.
• The true market portfolio holds all the world’s assets – stocks, bonds, real estate, commodities as well as labor income – weighted in proportion to their market value.
• Holding the market portfolio is not optimal.

Q2. Which of the following in not true about the Capital Market Line?

• The capital allocation line that goes through the risk-free asset and the market portfolio is called the Capital Market Line.
• The Capital Market Line maximizes the Sharpe ratio.
• The Capital Market Line is tangent to the efficient frontier.
• The Capital Market Line minimizes the Sharpe ratio.

Q3. Which of the following is not true about passive investing?

• Passive investing is buying a well-diversified portfolio to represent a broad-based market index without attempting to search out mispriced securities.
• Holding the market portfolio is efficient, so passive investing is efficient as well.
• Passive investing cannot be efficient because it involves passive investors.
• The amount of diversifiable risk in an index fund is near zero.

Q4. Your investment
portfolio consists of $150,000 invested in only one stock – Pocemon. Suppose the risk free rate is 3%. The
Pocemon stock has an expected return of 12%, and a volatility of 40%, and
the market portfolio has an expected return of 10% and volatility of
18%. Under the CAPM assumptions, what
is the volatility of a better alternative portfolio that has the same
expected return as Pocemon?

• σ = 15.52%
• σ = 23.14%
• σ = 30.25%
• σ = 35.13%

Q5. Your investment
portfolio consists of $150,000 invested in only one stock – Pocemon. Suppose the risk free rate is 3%. The
Pocemon stock has an expected return of 12%, and a volatility of 40%, and
the market portfolio has an expected return of 10% and volatility of
18%. Now what if you had the
stomach for the kind of volatility Pocemon has. Under the CAPM assumptions,
what would be the expected return you should then earn?

• E(r) = 13.65%
• E(r) = 15.30%
• E(r) = 18.56%
• E(r) = 20.38%

Q6. Suppose you have invested $30,000 in the following four stocks:

The risk free rate is 2%,
and the expected return on the market portfolio is 8%. Based on the CAPM, what is the beta of the
portfolio?

• βP = 0.95
• βP = 1.19
• βP = 1.29
• βP = 1.62

Q7. Security

Based on the data
provided in question 6 (table shown above) and based on the CAPM, what is the expected return of
the portfolio?

• E(rP) = 9.74%
• E(rP) = 10.55%
• E(rP) = 13.00%
• E(rP) = 15.23%

Q8. There are two stocks
in the market, stock A and stock B.
The price of stock A today is $50.
The price of stock A next year will be $40 if the economy is in a
recession, $55 if the economy is normal, and $60 if the economy is
expanding. The probabilities of
recession, normal times, and expansion are 0.1, 0.8, and 0.1
respectively. Stock A pays no
dividend. Assume CAPM is true. The volatility of the return on the
market portfolio (σM) is 10%.
The expected return of stock B is 7% and the volatility of the
return of stock B is 12%.
Furthermore, the correlation between the return on stock A and the
market portfolio return is 0.8, the correlation between the return on
stock B and the market portfolio return is 0.5, and the correlation
between the returns of the two stocks is 0.6. What is the beta of stock A?

• βA = 0.66
• βA = 0.78
• βA = 0.95
• βA = 1.30

Q9. There are two stocks
in the market, stock A and stock B.
The price of stock A today is $50.
The price of stock A next year will be $40 if the economy is in a
recession, $55 if the economy is normal, and $60 if the economy is
expanding. The probabilities of
recession, normal times, and expansion are 0.1, 0.8, and 0.1
respectively. Stock A pays no
dividend. Assume CAPM is true. The volatility of the return on the
market portfolio (σM) is 10%.
The expected return of stock B is 7% and the volatility of the
return of stock B is 12%.
Furthermore, the correlation between the return on stock A and the
market portfolio return is 0.8, the correlation between the return on
stock B and the market portfolio return is 0.54, and the correlation
between the returns of the two stocks is 0.6. What is the beta of stock B?

• βB = 0.65
• βB = 0.87
• βB = 0.96
• βB = 1.25

Q10. You invest in a stock
with beta equal to 0.80. The risk free rate is 2% and the expected return
on the market portfolio is 8%.
Based on the CAPM, what is the expected return of the stock?

• E(r) = 6.80%
• E(r) = 5.35%
• E(r) = 10.25%
• E(r) = 13.70%

Q11. Based on the
following plot of the Security Market Line, which of the following
statements is correct?

• The risk-free rate is equal to 3%
• The expected return of the market portfolio is equal to 8%.
• The expected return of the market portfolio is equal to 2%.
• The risk-free rate is equal to 8%

Q12. Suppose you find an
asset that, based on its price today, has a lower expected return than
what is suggested by the SML. If the Capital Asset Pricing Model holds,
which of the following statements is/are correct? (Select all that apply.)

• If the asset has a lower expected return than the one
  suggested by the SML, that means that the price is too low.
• If the asset has a lower expected return than the one
  suggested by the SML, that means that the price is too high.
• The asset would plot below the SML.
• The asset would plot above the SML.

Quiz 2: Equilibrium asset pricing models

Q1. TRUE OR FALSE. You can construct a
portfolio with a beta of 0.7 by investing 70% of your investment budget in
Treasury bills and the remainder in the market portfolio.

• True
• False

Q2. Suppose you are the
portfolio manager for a bank trust department. You meet with Ms. X to
review her investment objectives. Ms. X currently holds a diversified
portfolio of risky assets. She says he would like to increase the expected
return of her portfolio. Which of the following do you advise her?

• You tell her that is not possible.
• You suggest to re-design a portfolio with a lower beta.
• You tell her to get out of the risky assets completely and just hold cash.
• You explain that she can level up by borrowing and investing more in risky assets.

Q3. Consider the following distribution of returns:

Assume that CAPM holds. The volatility of the return on the market portfolio (σm) is 10%. The correlation between the return on stock A and the market portfolio return is 0.9. What is the beta of stock A?

• βA = 0.25
• βA = 0.47
• βA = 0.55
• βA = 1.15

Q4. Consider the following distribution of returns:

Assume that CAPM holds. The
volatility of the return on the market portfolio (σm) is 10%. The expected return of another stock, B, is 12% and the
volatility of the return of stock B is 11%.
Also, the correlation between the return on stock A and the market
portfolio return is 0.9, the correlation between the return on stock B and the
market portfolio return is 0.26, and the correlation between the returns of the
two stocks is 0.5. What would be the beta of a portfolio consisting 50% of
stock A and 50% of stock B?

• βP = 0.25
• βP = 0.38
• βP = 0.75
• βP = 0.95

Q5. Which of the following is not true:

• The size factor is captured by the return on a zero-net-investment portfolio that is constructed by going short the small-cap and going long large-cap stocks.
• The size effect has dissipated significantly since its discovery.
• The size effect refers to the fact historical average returns on stocks with small capitalization are higher than predicted by the Capital Asset Pricing Model.
• The size factor is captured by the return on a zero-net-investment portfolio that is constructed by going long the small-cap and going short large-cap stocks.

Q6. Consider the
following plot of the security market line. Which of the following labels for
(a), (b) and (c) are correct?

• (a)=beta (β),
  • (b)=E(r) and
  • (c)=risk-free rate (rf)
• (a)=volatility (β),
  • (b)=E(r) and
  • (c)=risk-free rate (rf)
• (a)=volatility (β),
  • (b)= beta and
  • (c)=expected return of the market portfolio
• (a)=beta (β),
  • (b)=E(r) and
  • (c)= expected return of the market portfolio

Q7. TRUE OR FALSE. CAPM implies that
investors require a high rate of return to hold securities with high
volatility.

• True
• False

Q8. Which of the following is not a factor in the three-factor Fama-French model?

• Liquidity
• Market
• Book-to-market
• Size

Q9. Here are data on twocompanies. Assume that the risk-free rate is 4% and the market riskpremium is 6%.

According to the CAPM, characterize Wallet Mart.

• Overpriced
• Underpriced
• Properly priced
• Not enough information

Q10. Here are data on two companies. Assume that the risk-free rate is 4% and the market risk premium is 6%.

According to the CAPM, characterize Target Mart.

• Overpriced
• Underpriced
• Properly priced
• Not enough information

Q11. Which of the following statements is not correct?

• High book-to-market stocks are called value assets because, for the large part, their market values derive from assets in place – the book value of the assets are high relative to their market value.
• The HML factor in the Fama-French three-factor model is constructed by going long in low book-to-market stocks and going short in high book-to-market stocks.
• Low book-to-market stocks are called growth assets because the market value of their assets is high relative to their value, indicating that the value is coming from expected growth in future cash flows – that is, one anticipates growth to justify the current market value of the assets.
• The HML factor in the Fama-French three-factor model is constructed by going long in high book-to-market stocks and going short in low book-to-market stocks.

Q12. According to CAPM, what is the expected return on a zero-beta asset?

• The market rate of return
• Depends on the market conditions
• A zero-rate of return
• Risk-free rate of return

Q13. Capital Asset Pricing Model says that portfolio returns are determined by:

• Economic factors
• Systematic risk
• Idiosyncratic risk
• Rain fall

Q14. A mutual fund with a
beta of 0.8 has an expected rate of return of 16%. If the risk-free rate
is 4% and you expect the rate of return on the market portfolio to be 13%,
should you invest in this fund?

• Yes

No

Q15. When a company has a high equity beta, this means that:

• We expect its stock to co-move strongly with the rest of the market.
• We expect its stock to show little co-movement with the rest of the market.
• We need more information in order to decide whether the co-movement with the rest of the market is strong or weak.
• The non-systematic risk is high.

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