File: Ch.

07, Chapter 7: Portfolio Theory

Multiple Choice Questions

1. With a continuous probability distribution,:

a. a probability is assigned to each possible outcome.

b. possible outcomes are constantly changing.
c. an infinite number of possible outcomes exist.
d. there is no variance.

Ans: c
Difficulty: Moderate
Ref: Dealing With Uncertainty

2. The expected value is the:

a. inverse of the standard deviation

b. correlation between a securitys risk and return.
c. weighted average of all possible outcomes.
d. same as the discrete probability distribution.

Ans: c
Difficulty: Easy
Ref: Dealing With Uncertainty

3. -------------------is concerned with the interrelationships between security returns

as well as the expected returns and variances of those returns.

a. random diversification.
b. correlating diversification
c. Friedman diversification
d. Markowitz diversification

Ans: d
Difficulty: Moderate
Ref: Introduction to Modern Portfolio Theory

4. Which of the following would be considered a random variable:

a. expected value.
b. correlation coefficient between two assets
c. one-period rate of return for an asset.
d. beta.

Ans: c
Difficulty: Easy
Ref: Dealing With Uncertainty

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5. Given the following probability distribution, calculate the expected return of
security XYZ.

Security XYZ's
Potential return Probability
20% 0.3
30% 0.2
-40% 0.1
50% 0.1
10% 0.3

a. 16 percent
b. 22 percent
c. 25 percent
d. 18 percent

Ans: b
Difficulty: Moderate
Solution: E(R) = Ripri = (20)(0.3)+ (30)(0.2)+(- 40)(0.1)+(50)(0.1) +(10)(0.3)= 22%.
Ref: Dealing With Uncertainty

6. Probability distributions:

a. are always discrete.

b. are always continuous.
c. can be either discrete or continuous.
d. are inverse to interest rates.

Ans: c
Difficulty: Easy
Ref: Dealing With Uncertainty

7. The bell-shaped curve, or normal distribution, is considered:

a. discrete.
b. downward sloping
c. linear
d. continuous

Ans: d
Difficulty: Easy
Ref: Dealing With Uncertainty

8. Portfolio weights are found by:

a. dividing standard deviation by expected value

b. calculating the percentage each assets value to the total portfolio value
c. calculating the return of each asset to total portfolio return

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Portfolio Theory
d. dividing expected value by the standard deviation

Ans: b
Difficulty: Moderate
Ref: Portfolio Return and Risk

9. Which of the following statements regarding expected return of a portfolio

is true?

a. It can be higher than the weighted average expected return of individual assets
b. It can be lower than the weighted average return of the individual assets
c. It can never be higher or lower than the weighted average expected return of
individual assets
d. Expected return of a portfolio is impossible to calculate

Ans: c
Difficulty: Moderate
Ref: Portfolio Return and Risk

10. In order to determine the expected return of a portfolio, all of the following must
be known, except:

a. probabilities of expected returns of individual assets

b. weight of each individual asset to total portfolio value
c. expected return of each individual asset
d. variance of return of each individual asset and correlation of returns between
assets

Ans: a
Difficulty: Difficult
Ref: Portfolio Return and Risk

11. Which of the following is true regarding the expected return of a portfolio?

a. It is a weighted average only for stock portfolios

b. It can only be positive
c. It can never be above the highest individual asset return
d. It is always below the highest individual asset return

Ans: c
Difficulty: Moderate
Ref: Portfolio Return and Risk

12. Which of the following is true regarding random diversification?

a. Investment characteristics are considered important in random diversification

b. The benefits of random diversification eventually no longer continue as more
securities are added
c. Random diversification, if done correctly, can eliminate all risk in a portfolio

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Portfolio Theory
d. Random diversification eventually removes all company specific risk from a
portfolio

Ans: b
Difficulty: Difficult
Ref: Analyzing Portfolio Risk

13. Company specific risk is also known as:

a. market risk
b. systematic risk
c. non-diversifiable risk
d. idiosyncratic risk

Ans: d
Difficulty: Moderate
Ref: Analyzing Portfolio Risk

14. The relevant risk for a well-diversified portfolio is:

a. interest rate risk

b. inflation risk
c. business risk
d. market risk

Ans: d
Difficulty: Easy
Ref: Analyzing Portfolio Risk

15. Which of the following statements regarding the correlation coefficient is

not true?

a. It is a statistical measure
b. It measure the relationship between two securities returns
c. It determines the causes of the relationship between two securities returns
d. It is greater than or equal to -1 and less than or equal to +1

Ans: c
Difficulty: Difficult
Ref: Analyzing Portfolio Risk

16. Two stocks with perfect negative correlation will have a correlation coefficient of:

a. +1.0
b. -2.0
c. 0
d. 1.0

Ans: d

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Portfolio Theory
Difficulty: Easy
Ref: Analyzing Portfolio Risk

17. Security A and Security B have a correlation coefficient of 0. If Security As

return is expected to increase by 10 percent,

a. Security Bs return should also increase by 10 percent

b. Security Bs return should decrease by 10 percent
c. Security Bs return should be zero
d. Security Bs return is impossible to determine from the above information

Ans: d
Difficulty: Moderate
Ref: Analyzing Portfolio Risk

18. Which of the following portfolios has the least reduction of risk?

a. A portfolio with securities all having positive correlation with each other
b. A portfolio with securities all having zero correlation with each other
c. A portfolio with securities all having negative correlation with each other
d. A portfolio with securities all having skewed correlation with each other

Ans: a
Difficulty: Moderate
Ref: Analyzing Portfolio Risk

19. The major difference between the correlation coefficient and the
covariance is that:

a. the correlation coefficient can be positive, negative or zero while the covariance is
always positive
b. the correlation coefficient measures relationship between securities and the
covariance measures relationships between a security and the market
c. the correlation coefficient is a relative measure showing association between
security returns and the covariance is an absolute measure showing association
between security returns
d. the correlation coefficient is a geometric measure and the covariance is a
statistical measure

Ans: c
Difficulty: Difficult
Ref: Analyzing Portfolio Risk

20. Which of the following statements regarding portfolio risk and number of stocks
is generally true?

a. Adding more stocks increases risk

b. Adding more stocks decreases risk but does not eliminate it
c. Adding more stocks has no effect on risk

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Portfolio Theory
d. Adding more stocks increases only systematic risk

Ans: b
Difficulty: Moderate
Ref: Analyzing Portfolio Risk

21. When returns are perfectly positively correlated, the risk of the portfolio is:

a. zero
b. the weighted average of the individual securities risk
c. equal to the correlation coefficient between the securities
d. infinite

Ans: b
Difficulty: Moderate
Ref: Analyzing Portfolio Risk

22. Portfolio risk is most often measured by professional investors using the:

a. expected value
b. portfolio beta
c. weighted average of individual risk
d. standard deviation

Ans: d
Difficulty: Easy
Ref: Analyzing Portfolio Risk

23. A change in the correlation coefficient of the returns of two securities in a

portfolio causes a change in

a. both the expected return and the risk of the portfolio

b. only the expected return of the portfolio
c. only the risk level of the portfolio
d. neither the expected return nor the risk level of the portfolio

Ans: c
Difficulty: Moderate
Ref: Analyzing Portfolio Risk

24. Markowitz's main contribution to portfolio theory is:

a. that risk is the same for each type of financial asset

b. that risk is a function of credit, liquidity and market
factors
c. risk is not quantifiable
d. insight about the relative importance of variance and covariance in determining
portfolio risk

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Portfolio Theory
Ans: d
Difficulty: Moderate
Ref: Analyzing Portfolio Risk

25. Owning two securities instead of one will not reduce the risk taken by an investor
if the two securities are

a. perfectly positively correlated with each other

b. perfectly independent of each other
c. perfectly negatively correlated with each other
d. of the same category, e.g. blue chips

Ans: a
Difficulty: Easy
Ref: Analyzing Portfolio Risk

26. When the covariance is positive, the correlation will be:

a. positive
b. negative
c. zero
d. impossible to determine

Ans: a
Difficulty: Easy
Ref: Analyzing Portfolio Risk

27. Calculate the risk (standard deviation) of the following two-security portfolio if
the correlation coefficient between the two securities is equal to 0.5.

Variance Weight (in the portfolio)

Security A 10 0.3
Security B 20 0.7

a. 17.0 percent
b. 5.4 percent
c. 2.0 percent
d. 3.7 percent

Solution: p = [w1212 + w2222 + 2(w1)(w2)(1,2)12]1/2

= [(0.3)2(10) + (0.7)2(20) +
= 2(0.3)(0.7)(0.5)(10)1/2(20)1/2]1/2 =
3.7%

Ans: d
Difficulty: Difficult
Ref: Analyzing Portfolio Risk

28. The major problem with the Markowitz model is its:

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Portfolio Theory
a. lack of accuracy
b. predictability flaws
c. complexity
d. inability to handle large number of inputs

Ans: c
Difficulty: Difficult
Ref: Calculating Portfolio Risk

29. With a discrete probability distribution:

a. a probability is assigned to each possible outcome

b. possible outcomes are constantly changing
c. an infinite number of possible outcomes exist
d. there is no variance

Ans: a
Difficulty: Moderate
Ref: Dealing With Uncertainty

True-False Questions

1. Standard deviations for well-diversified portfolios are reasonably steady over

time.

Ans: T
Difficulty: Moderate
Ref: Dealing With Uncertainty

2. A probability distribution shows the likely outcomes that may occur and the
probabilities associated with these likely outcomes.

Ans: T
Difficulty: Easy
Ref: Dealing With Uncertainty

3. Portfolio risk is a weighted average of the individual security risks.

Ans: F
Difficulty: Moderate
Ref: Portfolio Return and Risk

4. A negative correlation coefficient indicates that the returns of two

securities have a tendency to move in opposite directions.

Ans: T
Difficulty: Easy
Ref: The Components of Portfolio Risk

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Portfolio Theory
5. Investments in commodities such as precious metals may provide additional
diversification opportunities for portfolios consisting primarily of stocks and
bonds.

Ans: T
Difficulty: Moderate
Ref: Analyzing Portfolio Risk

6. According to the Law of Large Numbers, the larger the sample size, the more
likely it is that the sample mean will be close to the population expected value.

Ans: T
Difficulty: Moderate
Ref: Analyzing Portfolio Risk

7. Throwing a dart at the WSJ and selecting stocks on this basis would be
considered random diversification.

Ans: T
Difficulty: Easy
Ref: Analyzing Portfolio Risk

8. Portfolio risk can be reduced by reducing portfolio weights for assets with
positive correlations.

Ans: T
Difficulty: Moderate
Ref: Calculating Portfolio Risk

9. If an analyst uses ex post data to calculate the correlation coefficient and

covariance and uses them in the Markowitz model, the assumption is that
past relationships will continue in the future.

Ans: T
Difficulty: Difficult
Ref: Obtaining the Data

10. In the case of a four-security portfolio, there will be 8 covariances.

Ans: F
Difficulty: Moderate
Ref: Obtaining the Data

11. The correlation coefficient explains the cause in the relative movement in returns
between two securities.

Ans: F
Difficulty: Easy

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Portfolio Theory
 Ref: The Components of Portfolio Risk

12. In a portfolio consisting of two perfectly negatively correlated securities, the

highest attainable expected return will consist of a portfolio containing 100% of
the asset with the highest expected return.

Ans: T
Difficulty: Difficult
Ref: The Components of Portfolio Risk

Short-Answer Questions

1. Are the expected returns and standard deviation of a portfolio both weighted
averages of the individual securities expected returns and standard deviations? If
not, what other factors are required?

Answer: The expected return is a weighted average. The portfolio standard

deviation is not a weighted average but also requires correlation
coefficients among the securities.
Difficulty: Moderate

2. How is the correlation coefficient important in choosing among securities for a

portfolio?

Answer: If security returns are highly correlated (high positive correlation)

diversification does little to reduce risk of returns. The lower the
correlation coefficients among the securities, the more advantage is
gained from diversification.
Difficulty: Moderate

3. Why was the Markowitz model impractical for commercial use when it was first
introduced in 1952? What has changed by the 1990s?

Answer: The volume of calculations required for a large portfolio was

physically impractical in the 1950s. By the 1990s, the proliferation
of computers has made the volume of calculations practical.
Difficulty: Moderate

4. Provide an example of two industries that might have low correlation with one
another. Give an example that might exhibit high correlation.

Answer: Low correlation might be found between large appliances and retail
food markets in that retail food is somewhat steady through
economic ups and downs, while appliances tend to fall off during
economic slow downs. High correlation might be found between auto
manufacturers and steel manufacturers.
Difficulty: Moderate

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Portfolio Theory
 5. When constructing a portfolio, standard deviations, expected returns, and
correlation coefficients are typically calculated from historical data. Why may
that be a problem?

Answer: The problem is that historical patterns may not be repeated in the future.
We are planning a portfolio for the future and would like to have future
(ex ante) data but have only historical (ex post) data.
Difficulty: Moderate

6. A portfolio consisting of two securities with perfect negative correlation in the

proper proportions can be shown to have a standard deviation of zero. What
makes this riskless portfolio impossible to achieve in the real world?

Answer: Perfect negative correlation is not achievable in most cases since most
securities have positive correlation or low correlation. Even if it were
observed for a period of time, it could not be counted on to hold for long
in the future.
Difficulty: Difficult

Fill-in-the-blank Questions

1. Markowitz diversification, also called _____________ diversification, removes

_________________ risk from the portfolio.

Answer: efficient, idiosyncratic (also known as company specific, unsystematic, or

diversifiable)
Difficulty: Difficult

2. An efficiently diversified portfolio still has _____________________ risk.

Answer: market (also known as systematic or un-diversifiable)

Difficulty: Difficult

3. The major problem with Markowitz diversification model is that it requires a full
set of ________________________ between the returns of all securities being
considered in order to calculate portfolio variance.

Answer: covariances
Difficulty: Moderate

4. The number of covariances in the Markowitz model is ________ ; the number of

unique covariances is [n (n-1)]/2.

Answer: n(n-1)
Difficulty: Difficult

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Portfolio Theory
 Critical Thinking/Essay Questions

1. Conventional wisdom has long held that diversification of a stock portfolio

should be across industries. Does the correlation coefficient indirectly
recommend the same thing?

Answer: Correlation coefficients between securities in different industries

represent the extent to which their fortunes depend on mutual factors.
The correlation coefficients, then, simply give investors a way to measure
conventional wisdom.
Difficulty: Difficult

2. Why is more Difficult to put Markowitz diversification into effect than random
diversification?

Answer: It requires more quantitative analysis and generally the use of a

computer software program. In addition, it is Difficulter to find
securities with either negative correlation or low correlation than it is to
simply select securities in different industries and sectors as is done in
random diversification.
Difficulty: Moderate

Problems

1. Calculate the expected return and risk (standard deviation) for General Fudge for
200X, given the following information:

Probabilities 0.20 0.15 0.50 0.15

Possible Outcomes 20% 15% 11% -5%

Solution: E(Ri) = .20(.20) + .15(.15) + .50(.11) + .15(-.05)

= .04 + .0225 + .055 + (-.0075)
= .1
m
[ [ R i E( R i )] 2 pri ]1 / 2
i 1

(1) (2) (3) (4) (5) (6)

Possible
Outcome ER R-ER (PR-ER)2 Prob. (4) x (5)
.20 .11 .09 .0081 .20 .00162
.15 .11 .04 .0016 .15 .00024
.11 .11 .00 .0000 .50 .00000
-.05 .11 -.16 .0256 .15 .00384

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Portfolio Theory
 .00570

= (.00570)1/2 = 7.55 percent

Difficulty: Moderate

Chapter Seven 94
Portfolio Theory