# Portfolio Selection and Risk Management Quiz

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## Week- 1

### Module 1: Risk & Return

1.
Question 1

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?

1 point

• 4.45%
• 4.8%
• 5.84%
• 6%
• 7%

2.
Question 2

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?

1 point

• 19%
• 20%
• 21%
• 22%
• 23%

3.
Question 3

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
1 point

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

4.
Question 4
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
1 point

• 4.23%
• 5.25%
• 30%
• 35%

5.
Question 5
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
1 point

• 7%
• 5.24%
• 7.5%
• 9%
• 35%

6.
Question 6

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

1 point

• 6.48
• 9.50
• 12.49
• 13.50
• 14.28

7.
Question 7

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”)

1 point

 1.1

8.
Question 8
Again, assuming that you bought one share of stock for \$160, what is the expected annual return for this stock?

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
1 point

• -3.16%
• 0%
• 3.16%
• 6.72%
• 20%

9.
Question 9

A volatility strategy is:

1 point

• 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.

10.
Question 10
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?

1 point

• 18%
• 13%
• 5%

## Week- 2

### Peer-graded Assignment: Measuring portfolio returns and volatility

Week 2 Assignment 1 :

### Peer-graded Assignment: Constructing mean-variance frontier for two risky assets

Week 2 Assignment 2 :

### Module 2: Portfolio construction and diversification

1.
Question 1
The term ‘efficient frontier’ refers to the portfolios that:

(Choose all that apply.)

1 point

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.

2.
Question 2

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)

E(r)
Security A 15.5%
Security B 14.5%
Security C 4.6%
1 point

 12.53

3.
Question 3
Consider the following distribution of returns:

State of the economy Prob. Return on A Return on B Return on C
Depression 30% 10% -5% -3%
Normal 50% 15% 20% 5%
Expansion 20% 25% 30% 15%
Which of the following statements are correct?

1 point

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%

4.
Question 4

Consider the
following distribution of returns:

State of the economy Prob. Return on A Return on B
Depression 30% 10% -5%
Normal 50% 15% 20%
Expansion 20% 25% 30%
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.)

1 point

 60.25

5.
Question 5

Consider the
following distribution of returns:

State of the economy Prob. Return on A Return on B
Depression 30% 10% -5%
Normal 50% 15% 20%
Expansion 20% 25% 30%

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.)

1 point

 0.87

6.
Question 6

Consider the
following distribution of returns:

State of the economy Prob. Return on A Return on B
Depression 30% 10% -5%
Normal 50% 15% 20%
Expansion 20% 25% 30%
What would be the expected return and standard
deviation of a portfolio with 60% in A and 40% in B?

1 point

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%

7.
Question 7

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

1 point

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

8.
Question 8

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

1 point

A sudden change at the exchange rate between US dollar and euro.

Federal Reserve Bank tightens monetary policy.

Oil prices fall.

9.
Question 9

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

1 point

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.

10.
Question 10
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?

1 point

10.0%

13.6%

1.94%

10.8%

## Week- 3

### Module 3: Mean-variance preferences

1.
Question 1
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.

1 point

True

False

2.
Question 2

Which of the
following statements is false?

1 point

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.

3.
Question 3

Consider the
following data:

Investment Expected return Standard deviation
A 15% 25%
B 20% 30%
C 25% 45%
Which investment would you select if your preferences are represented by mean-variance utility function, and your risk aversion coefficient is equal to 4?

1 point

Investment A

Investment B

Investment C

4.
Question 4

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

1 point

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.

5.
Question 5
What does the coefficient A in the mean-variance utility function (below) represent?

U = E(r) – ½ A σ2

1 point

Investor’s required return

The certainty equivalent rate

Risk premium required by the investor

Investor’s degree of risk aversion

6.
Question 6

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

## Week- 4

### Peer-graded Assignment: Optimal asset allocation and portfolio choice

Week 4 Assignment :

### Optimal capital allocation and portfolio choice

1.
Question 1
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?

1 point

True.

False.

2.
Question 2
The minimum variance portfolio is the optimal risky portfolio on the frontier. True or false?

1 point

True

False

3.
Question 3
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.

1 point

4.
Question 4
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?

1 point

True

False

5.
Question 5
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:

Expected return Standard Deviation
Felix Company 15% 35%
The correlation coefficient between your diversified portfolio and Felix stock is 0.40.

1 point
6.
Question 6
Continuing with the previous question, what would be volatility of your new portfolio?

1 point

32.1%

26.4%

19.3%

22.2%

7.
Question 7
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)

1 point

8.
Question 8
Continuing with the previous questions, what would be the volatility of this new portfolio including the government securities?

1 point

14%

28%

32%

24%

9.
Question 9
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?

1 point

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

### Module 5 Quiz: Equilibrium asset pricing models

1.
Question 1

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.

1 point

True

False

2.
Question 2

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?

1 point

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.

3.
Question 3

Consider the
following distribution of returns:

State of the economy Probability R_A
Depression 30% 10%
Normal 50% 15%
Expansion 20% 25%
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?

1 point

βA = 0.25

βA = 0.47

βA = 0.55

βA = 1.15

4.
Question 4

Consider the
following distribution of returns:

State of the economy Probability R_A
Depression 30% 10%
Normal 50% 15%
Expansion 20% 25%

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?

1 point

βP = 0.25

βP = 0.38

βP = 0.75

βP = 0.95

5.
Question 5

Which of the
following is not true:

1 point

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.

6.
Question 6

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

1 point

(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

7.
Question 7

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

1 point

True

False

8.
Question 8

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

1 point

Liquidity

Market

Book-to-market

Size

9.
Question 9

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

Wallet Mart Target Mart
Forecasted return 6% 11%
Standard deviation of returns 8% 10%
Beta 1.5 1.0

According to the CAPM, characterize Wallet
Mart.

1 point

Overpriced

Underpriced

Properly priced

Not enough information

10.
Question 10

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

Wallet Mart Target Mart
Forecasted return 6% 11%
Standard deviation of returns 8% 10%
Beta 1.5 1.0
According to the CAPM, characterize Target
Mart.
1 point

Overpriced

Underpriced

Properly priced

Not enough information

11.
Question 11

Which of the
following statements is not correct?

1 point

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.

12.
Question 12

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

1 point

The market rate of return

Depends on the market conditions

A zero-rate of return

Risk-free rate of return

13.
Question 13

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

1 point

Economic factors

Systematic risk

Idiosyncratic risk

Rain fall

14.
Question 14

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?

1 point

Yes

No

15.
Question 15

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

1 point

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.