There are 20 multiple choice questions and two short answer questions. The percentage or marks indicated shows the proportion of time you may wish to spend on that part.

Question 1 (4 points)

Which of the following statements is correct?

A.   A well-diversified portfolio diversifies essentially all market risk of a stock.

B.   A well-diversified portfolio diversifies essentially all risk of a stock.

C.   A well-diversified portfolio diversifies essentially all idiosyncratic risk of a stock.

D.   A well-diversified portfolio diversifies essentially all systematic risk of a stock.

E.    A well-diversified portfolio maximizes the ratio of firm-specific risk to market risk.

Solution: C

A well-diversified portfolio eliminates idiosyncratic (= unsystematic = diversifiable = firm-specific) risk and not reduces market (= systematic = undiversifiable).

Question 2 (4 points)

Which of the following statements about the correlation coefficient is correct?

A.   Positive correlation coefficients imply that the returns on Security A tend to move in the opposite direction as those on security B.

B.    Negative correlation coefficients imply that the returns on Security A tend to move in the same direction to those on security B.

C.   The closer the absolute value of the correlation coefficient is to one, the stronger the relationship between the returns on the two securities.

D.   All of these statements.

E.    None of these statements.

Solution: C

The correlation coefficient represents the relationship between the two dataset and its max/min value is 1/-1.

Question 3 (4 points)

If weights of securities in a portfolio are positive: 1) can the return on a portfolio ever be less than  the smallest return on an individual security in the portfolio? 2) can the variance of a portfolio ever less than the smallest variance of an individual security in the portfolio?

A.   yes; 2) yes

B.   yes; 2) no

C.   no; 2) yes

D.   no; 2) no

E.    maybe; 2) yes

Solution: C

1)   If there is two assets A and B,

E(RP ) = wA RA  + wB RB, if wA>0 and wB >0, wA + wB  =1, and RA<RB, then the min value of E(RP ) = wA RA .

2)   Yes, if corr(A,B) is small enough, it can go smaller than the smallest variance of an individual security due to the diversification effect.

Question 4 (4 points)

The return on stock A has a covariance of 0.1 with the return on S&P500 whereas the return on     stock B has covariance of 0.3 with S&P500 return. The return on which stock correlated more with the return on S&P500?

A.   Stock A.

B.   Stock B.

C.    Insufficient information: we would also need the variance of S&P500 returns.

D.    Insufficient information: we would also need the standard deviation of both A and B.

E.    Insufficient information: we would also need the covariance of both A and B.

Solution: D

The correlation between an asset i and a market is ρ i,m  = Cov (i,m) / σ i ∙σm

Thus, to compare the correlations ρA,m and ρ B,m, we need σA and σ B .

Question 5 (4 points)

You have the following information on two stocks:

Probability	Stock A Return	Stock B Return
0.1	-20%	10%
0.8	20%	15%
0.1	40%	20%

The expected return for stock A is 18%, the expected return for stock B is 15% and the correlation between returns for the two stocks is 0.96. If you form an equally weighted portfolio of the two    stocks, what is the portfolio's expected return?

A.   8.1%

B.    10.5%

C.    13.4%

D.    16.5%

E.    20.0%

Solution: D

See the excel spreadsheet.

Question 6 (4 points)

Which of the following statements about risk-averse investors is most accurate? A risk-averse investor:

A.   seeks out the investment with minimum risk, while return is not a major consideration.

B.   will take additional investment risk if sufficiently compensated for this risk.

C.   avoids participating in global equity markets.

D.   rejects speculative prospects with positive risk premiums.

Solution: B

Please refer textbook (Investments (12th  Edition) by Bodie, Kane, Marcus, p. 160)

Question 7 (4 points)

Which of the following statements about covariance and correlation is least accurate?

A.   A zero covariance implies there is no linear relationship between the returns on two assets.

B.    If two assets have perfect negative correlation, the variance of returns for a portfolio that consists of these two assets will equal zero.

C.   The covariance of a 2-stock portfolio is equal to the correlation coefficient times the         standard deviation of one stock's return times the standard deviation of the other stock's return.

D.   The diversification effect is maximum when the correlation coefficient is -1.

E.    None of these choices.

Solution: B

VARP  = wA2σA2 + wB2σ B2+2∙wA ∙wB  ∙σA  ∙σ B ∙ ρA, B . If ρA, B = -1, VARP  = wA2σA2 + wB2σ B2-2 ∙wA ∙wB  ∙σA  ∙σ B, and it is non-zero value except for the following three cases.

1.   wA=0 and σ B=0

2.   wB=0 and σA=0

3.    σA=0 and σ B=0

Question 8 (4 points)

The standard deviation of returns is 0.30 for Stock A and 0.20 for Stock B. The covariance between the returns of A and B is 0.006. The correlation of returns between A and B is:

A.   0

B.    0.10

C.   0.20

D.   0.30

E.    0.40

Solution: B

ρA, B  = Cov (A,B) / σA ∙σ B = 0.006 / 0.30*0.20 = 0.10

Question 9 (4 points)

Which of the following statements about correlation is least accurate?

A.   Diversification reduces risk when correlation is less than +1.

B.    If the correlation coefficient is 0, a zero variance portfolio can be constructed.

C.   The lower the correlation coefficient, the greater the potential benefits from diversification.

D.   The less correlated the assets, the better the risk return trade off obtained within a portfolio.

E.    None of these choices.

Solution: B

Same to Q7.

VARP  = wA2σA2 + wB2σ B2+2∙wA ∙wB  ∙σA  ∙σ B ∙ ρA, B . If ρA, B = -1, VARP  = wA2σA2 + wB2σ B2-2 ∙wA ∙wB  ∙σA  ∙σ B, and it is non-zero value except for the following three cases.

1.   wA=0 and σ B=0

2.   wB=0 and σA=0

3.    σA=0 and σ B=0

Question 10 (4 points)

A measure of how the returns of two risky assets move in relation to each other is the:

A.   range

B.   covariance

C.   standard deviation

D.   alpha

E.    none of these choices.

Solution: B

Covariance measures the relation of two dataset.

Question 11 (4 points)

In a 5-year period, the annual returns on an investment are 7%, -4%, 2%, -3%, and 6%. The standard deviation of annual returns on this investment is closest to: (Hint: Use Arithmetic Mean)

A.   4.55.%

B.    5.03%

C.    25.30%

D.   10.35%

E.    4.50%

Solution: B

Mean annual return = (7%-4%+2%-3%+6%)/5 = 1.6%

Squared deviations from the mean:

7%-1.6% = 5.4% -> 5.4 = 29.16

-4%-1.6% = -5.6% -> -5.6 = 31.36

2%-1.6% = 0.4% -> 0.4 = 0.16

-3%-1.6% = -4.6% -> -4.6 = 21.16

6%-1.6% = 4.4% -> 4.4 = 19.36

Sum of squared deviations = 101.2

Sample variance = sum of squared deviation / (n-1) = 101.2 / (5-1) = 25.3

Sample standard deviation = 25.30.5  = 5.02991053… = 5.03%

Question 12 (4 points)

Which of the following characteristics of a return distribution would most likely be associated with a low frequency of downside deviations from the mean?

A.   Kurtosis

B.    Fat tails

C.    Positive skew

D.   Negative skew

E.    None of these choices

Solution: C

See P.57 Lecture Note 1.

Question 13 (4 points)

Match the following investment products with their correct explanations.

Pair 1

Prompt: Assets Owned by the Individual, Considers Tax Needs, Large Minimum Investment Answer: Separately Managed Account (SMA)

Pair 2

Prompt: Restricted Liquidity, High Management Fees, Large Minimum Investment Answer: Hedge Funds

Pair 3

Prompt: Have prices that track net asset value, pay dividends out to investors, trade like closed-end funds

Answer: Exchange-Traded Funds

Pair 4

Prompt: Minimum investment requirement, fees for funds under management and performance, short-term & private investment

Answer: Buyout and Venture Capital Funds

See P.63-82 Lecture Note 2.

Question 14 (4 points)

Which of the following is a FALSE statement of separately managed account (SMA)?

A.   Commonly referred to as a “managed account,” “wrap account,” or “individually managed account,”

B.    Investment portfolio managed exclusively for the benefit of an individual or institution.

C.   Allows for individual shares to be held directly by the investor, and in return for annual fees, an individual can receive personalized investment advice.

D.    It usually does not require a large minimum investment.

Solution: D

See P.76-77 Lecture Note 2.

Question 15 (4 points)

Standard deviation measures the (1)_______ risk and beta measures the (2)_______ risk of a portfolio.

A.   Unsystematic; (2) systematic

B.   Systematic; (2) unsystematic

C.    Unsystematic; (2) total

D.   Total; (2) unsystematic

E.   Total; (2) systematic

Solution: E

Total risk (standard deviation) = systematic risk (beta) + unsystematic risk.

Question 16 (4 points)

You have observed the following information about the two stocks you hold in your portfolio:

	ABC	DEF	GHI
Expected return	15%	9%	11%
Standard deviation of returns	8%	5%	6%
Value	E30,000	E50,000	E20,000

The correlation coefficients are given as:  ρABC, DEF  = -0.40 (negative 0.40), ρ DEF,GHI  =  0.10, and ρABC,GHI  = 0.50. The standard deviation of your portfolio is closest to:

A.   0.0865%

B.    2.94%

C.   5.18%

D.   8.65%

E.    11.20%

Solution: B

See the excel file for the calculation. (Full credit is give to all students due to a calculation error)

Question 17 (4 points)

If you invested $500 in asset 1 and $750 in asset 2; then which of the following statements are true:

I. the return on the portfolio can never be less than the smallest return on the two assets

II. the return on the portfolio might be less than the smallest return on the two assets

III. the variance of the portfolio can never be less than the smallest variance on the two assets

IV. the variance of the portfolio might be less than the smallest variance on the two assets

A.   I. and III.

B.    I. and IV.

C.    II. and IV.

D.   II. and III.

E.    None of these statements.

Solution: B

E(Rp)={500/(500+750)}*Ra+{750/(500+750)}*Rb

If Ra>Rb, then we can say Rb+x=Ra and x>0.

{500/(500+750)}*Ra+{750/(500+750)}*Rb

= {500/(500+750)}*(Rb+x)+{750/(500+750)}*Rb

= {500/(500+750)}*x + Rb > Rb

If Ra<Rb, then we can say Ra+y=Rb and y>0.

{500/(500+750)}*Ra+{750/(500+750)}*Rb

= {500/(500+750)}*Ra+{750/(500+750)}*(Rb+y)

= {750/(500+750)}*y + Ra > Ra

Thus, E(Rp) cannot be less than the smallest return on the two assets.

The portfolio variance can be small due to the diversification effect (when correlation coefficient is less than 1)

Question 18 (4 points)

You have observed the following information about the two stocks you hold in your portfolio:

	XXS	YYK
Expected return	10%	5%
Standard deviation of returns	8%	2%
Value	E15,000	E25,000

The covariance between XXS and YYK is 0.01. The expected return and standard deviation of your portfolio are closest to:

A.   expected return = 6.88%; standard deviation = 3.26%

B.   expected return = 6.88%; standard deviation = 7.58%

C.   expected return = 8.13%; standard deviation = 3.26%

D.   expected return = 8.13%; standard deviation = 5.38%

Solution: B

See the excel file for the calculation

Question 19 (4 points)

Which of the following is a FALSE statement of the correlation coefficient?

A.   It measures how security returns move in relation to one another.

B.    Positive correlation coefficients imply that the returns on Security A tend to move in the same direction as those on security B.

C.   The closer the absolute value of the correlation coefficient is to one, the weaker the relationship between the returns on the two securities.

D.   Negative correlation coefficients imply that the returns on Security A tend to move in the opposite direction to those on security B.

E.    All of the statements are correct.

F.    None of the statements are correct.

Solution: C

The closer the value of the correlation coefficient is to -1, the weaker relationship between the returns of two securities.

Question 20 (4 points)

You have observed the following annual returns for SonDisplay, Inc: 25%, 15%, -20%, 30%, and -15%. What are the variance and standard deviation of returns? (Hint: Use Arithmetic Mean)

A.   Variance = 0.04260; standard deviation = 0.20640

B.   Variance = 0.05030; standard deviation = 0.20640

C.   Variance = 0.05325; standard deviation = 0.23076

D.   Variance = 0.23076; standard deviation = 0.05325

Solution: C

See the excel spreadsheet.

Question 21 (10 points)

We routinely assume that investors are risk-averse return-seekers; i.e., they like returns and dislike risk. If so, why do we contend that only systematic risk is important? (Alternatively, why is total risk not important to investors, in and of itself?)

Solution:

Students should state followings discussions in the lectures, tutorials, and textbooks: