Modern Portfolio Theory and Investment Analysis, 9th Edition Edwin J. Elton, Martin J. Gruber, Stephen J. Brown, William N. Goetzmann
Modern
portfolio theory and investment analysis 8e elton gruber goetzmann solutions
manual
Modern Portfolio Theory and Investment Analysis, 9th Editionexamines the characteristics and analysis of individual securities, as well as the theory and practice of optimally combining securities into portfolios. It stresses the economic intuition behind the subject matter while presenting advanced concepts of investment analysis and portfolio management.
The authors present material that captures the state of modern portfolio analysis, general equilibrium theory, and investment analysis in an accessible and intuitive manner.
Elton, Gruber,
Brown and Goetzmann
Modern
Portfolio Theory and Investment Analysis, 9th
Edition
Solutions to Text
Problems: Chapter 4
Chapter 4: Problem 1
A. Expected
return is the sum of each outcome times its associated probability.
Expected
return of Asset 1 = 
16% ´
0.25 + 12% ´ 0.5 + 8% ´ 0.25 = 12%
16% ´
0.25 + 12% ´ 0.5 + 8% ´ 0.25 = 12%
= 6%; 
= 14%; 
= 12%
Standard
deviation of return is the square root of the sum of the squares of each outcome
minus the mean times the associated probability.
Standard
deviation of Asset 1 =
= [(16% - 12%)2 ´
0.25 + (12% - 12%)2
´ 0.5 + (8% -
12%)2 ´ 0.25]1/2
= 81/2
=
2.83%
= 21/2 = 1.41%; 
= 181/2 = 4.24%; 
= 10.71/2 = 3.27%
B. Covariance of return between Assets 1 and 2
= 
=
=
(16 -
12) ´ (4 - 6) ´
0.25 + (12 - 12) ´ (6 -
6) ´ 0.5 + (8 - 12) ´
(8 - 6) ´ 0.25
=
- 4
The variance/covariance matrix for all
pairs of assets is:
|
|
|
1
|
2
|
3
|
4
|
|
|
1
|
8
|
-
4
|
12
|
0
|
|
|
2
|
-
4
|
2
|
-
6
|
0
|
|
|
3
|
12
|
-
6
|
18
|
0
|
|
|
4
|
0
|
0
|
0
|
10.7
|
Correlation
of return between Assets 1 and 2 = 
.
.
The correlation matrix for all pairs of
assets is:
|
|
|
1
|
2
|
3
|
4
|
|
|
1
|
1
|
-
1
|
1
|
0
|
|
|
2
|
-
1
|
1
|
-
1
|
0
|
|
|
3
|
1
|
-
1
|
1
|
0
|
|
|
4
|
0
|
0
|
0
|
1
|
C. Portfolio Expected
Return
A 1/2
´ 12% + 1/2 ´
6% = 9%
B 13%
C 12%
D 10%
E 13%
F 1/3
´ 12% + 1/3 ´
6% + 1/3 ´ 14% =
10.67%
G 10.67%
H 12.67%
I 1/4
´ 12% + 1/4 ´ 6%
+ 1/4 ´ 14% + 1/4 ´ 12% = 11%
Portfolio Variance
A (1/2)2
´ 8 + (1/2)2 ´
2 + 2 ´ 1/2 ´ 1/2 ´
(- 4) = 0.5
B 12.5
C 4.6
D 2
E 7
F (1/3)2
´ 8 + (1/3)2 ´
2 + (1/3)2 ´
18 + 2 ´ 1/3 ´ 1/3 ´
(- 4)
+ 2 ´ 1/3 ´
1/3 ´ 12 + 2 ´ 1/3 ´
1/3 ´ (- 6) = 3.6
G 2
H 6.7
I (1/4)2
´ 8 + (1/4)2 ´
2 + (1/4)2 ´
18 + (1/4)2 ´
10.7
+
2 ´ 1/4 ´ 1/4 ´
(- 4) + 2 ´
1/4 ´ 1/4 ´ 12 + 2 ´
1/4
´ 1/4 ´ 0 + 2 ´
1/4 ´ 1/4 ´ (-
6) + 2 ´ 1/4 ´ 1/4 ´
0 + 2 ´ 1/4 ´ 1/4 ´
0 = 2.7
Chapter 4: Problem 2
A. Monthly Returns
Month
Security 1 2 3 4 5 6
A 3.7% 0.4% -6.5% 1.4% 6.2% 2.1%
B 10.5% 0.5% 3.7% 1.0% 3.4% -1.4%
C 1.4% 14.9% -1.4% 10.8% 4.9% 16.9%
B. Sample Average (Mean) Monthly Returns
C. Sample Standard Deviations of
Monthly Returns
D. Sample Covariances and Correlation
Coefficients of Monthly Returns
; 
; 
E. Portfolio Returns and
Standard Deviations
Portfolio 1 (X1 =
1/2; X2= 1/2; X3= 0):
Portfolio 2 (X1 =
1/2; X2= 0; X3= 1/2):
Portfolio 3 (X1 =
0; X2= 1/2; X3= 1/2):
Portfolio 4 (X1 =
1/3; X2= 1/3; X3= 1/3):
Chapter
4: Problem 3
It is shown
in the text below Table 4.8 that a formula
for the variance of an equally weighted portfolio (where Xi = 1/N for i = 1, …, N securities) is
where 
is the average
variance across all securities, 
is the average
covariance across all pairs of securities, and N is the number of securities. Using the above formula with = 50 and = 10 we have:
is the average
variance across all securities, is the average
covariance across all pairs of securities, and N is the number of securities. Using the above formula with = 50 and = 10 we have:
Portfolio Size (N) 
5 18
10 14
20 12
50 10.8
100 10.4
Chapter
4: Problem 4
As is shown
in the text, as the number of securities (N)
approaches infinity, an equally weighted portfolio’s variance (total risk)
approaches a minimum equal to the average covariance of the pairs of securities
in the portfolio, which in Problem 3 is given as 10. Therefore, 10% above the
minimum risk level would result in the portfolio’s variance being equal to 11.
Setting the formula shown in the above
answer to Problem 3 equal to 11 and using = 50 and = 10 we have:
= 50 and = 10 we have:
Solving the above equation for N
gives N = 40 securities.
Chapter
4: Problem 5
As shown in
the text, if the portfolio contains only one security, then the portfolio’s
average variance is equal to the average
variance across all securities, . If instead an equally weighted portfolio contains a
very large number of securities, then its variance will be approximately equal
to the average covariance of the pairs of securities in the portfolio, . Therefore, the fraction of risk that of an individual
security that can be eliminated by holding a large portfolio is expressed by
the following ratio:
. If instead an equally weighted portfolio contains a
very large number of securities, then its variance will be approximately equal
to the average covariance of the pairs of securities in the portfolio, . Therefore, the fraction of risk that of an individual
security that can be eliminated by holding a large portfolio is expressed by
the following ratio:
From Table 4.9, the above ratio is equal to 0.6 (60%) for Italian
securities and 0.8 (80%) for Belgian securities. Setting the above ratio equal
to those values and solving for gives 
for Italian securities
and 
for Belgian
securities.
gives for Italian securities
and for Belgian
securities.
Thus, the ratio 
equals 
for Italian securities
and 
for Belgian
securities.
equals for Italian securities
and for Belgian
securities.
If the average variance of a single security, , in each country equals 50, then 
for Italian securities
and 
for Belgian
securities.
, in each country equals 50, then for Italian securities
and for Belgian
securities.
Using the formula shown in the preceding answer to Problem 3 with = 50 and either = 20 for Italy
or = 10 for Belgium
= 50 and either = 20 for = 10 for
Portfolio Size (N securities) Italian Belgian
Belgian
5 26 18
20 21.5 12
100 20.3 10.4
Chapter
4: Problem 6
The formula for an equally weighted portfolio's variance that appears
below Table 4.8 in the text is
where 
is the average
variance across all securities, is the average
covariance across all securities, and N
is the number of securities. The text below Table 4.8 states that the average
variance for the securities in that table was 46.619 and that the average
covariance was 7.058. Using the above equation with those two numbers, setting 
equal to 8, and
solving for N gives:
is the average
variance across all securities, is the average
covariance across all securities, and N
is the number of securities. The text below Table 4.8 states that the average
variance for the securities in that table was 46.619 and that the average
covariance was 7.058. Using the above equation with those two numbers, setting equal to 8, and
solving for N gives:
8
= 1/N (46.619 - 7.058) + 7.058
.942N = 39.561
N = 41.997.
Since the portfolio's variance decreases as N increases, holding 42 securities will provide a variance less
than 8, so 42 is the minimum number of securities that will provide a portfolio
variance less than 8.
MODERN
PORTFOLIO THEORY AND INVESTMENT ANALYSIS
9TH EDITION
ELTON, GRUBER, BROWN, & GOETZMANN
The following exam questions are organized according to the text's
sections. Within each section, questions follow the order of the text's
chapters and are organized as multiple choice, true-false with discussion,
problems, and essays. The correct answers and the corresponding chapter(s) are
indicated below each question.
PART 1: INTRODUCTION
Multiple Choice
1. Julia earns $60,000 each year for two consecutive
years. She has an option to invest in treasury funds to earn a 5% interest
today, and consume the entire amount in the second year. Alternatively, she can
choose to borrow money at 5% against the second period’s income. Assume that
the optimum decision for her is to invest money at 5%. Determine the maximum
amount she could consume in period 2.
a. $60,000
b. $0
c. $123,000
d. $117,143
Answer: c
Chapter: 1
2. Which of the following security’s value is
contingent on the performance of an underlying security?
a. Treasury Bill
b. Option
c. Corporate Bond
d. Equity
Answer: b
Chapter: 2
3. Collateralized debt obligations (CBO)are
backed by one of the following:
a. Pools of mortgages
b. Pools of commercial or personal loans
b. Low Investment-grade corporate bonds
Answer: b
Chapter: 2
4. An order which is activated only when the
price of the stock reaches or passes through a predetermined limit is called
the:
a. stop order.
b. day order.
c. limit order.
d. market order.
Answer: a
Chapter: 3
True/False
1. Dow Jones Industrial Average Index (DJIA) is consisted
of a price-weighted average of 30 large “blue chip” stocks.
Answer: True
Chapter: 2
2. Stocks are traded only in the listing exchange. For
example, the fact that IBM is listed in NYSE implies that it can only be traded
in NYSE
Answer: False
Chapter: 3
3. In a book market, orders are ranked by price and time.
That is, one the bid (buy) side of the book, a high priced limit order has
priority over a lower priced order. On the offer (ask) side of the book, a low
priced limit order has priority.
Answer: True
Chapter: 3
4. In case of government bonds, non-competitive bidders
have price uncertainty and competitive bidders face volume uncertainty.
Answer: True
Chapter: 3
Essays
1. Given a typical set of indifference curves and a budget
constraint for a 1-period (2-date) consumption model, where will the optimum
consumption pair (for date 1 and date 2) be found on the graph and why is it
optimal?
Answer:
The amount an investor consumes over the period is constrained by the
amount of income the investor has available in the period. A budget constraint
specifies the options that are available to the investor, and can be used to
determine the opportunity set. The first part of the analysis is to determine
the options open to the investor. One option available is to save nothing and
consume everything on receipt. The second option is to save all income received
on date 1. On date 2, income saved on the first date plus interest earned on it
is consumed along with the income received on date 2. The third option is to
consume everything now and not worry about tomorrow. The amount consumed would
be the amount received on date 1 and the amount that can be borrowed against
the amount to be received on date 2. This can be plotted on a graph as a
straight line to depict the investor’s opportunity set.
The economic theory of choice states that an investor chooses among the
opportunities in the opportunity set by specifying a series of curves called
utility functions or indifference curves. These curves represent the investor’s
preference for income over a period. The optimum consumption pattern for the
investor is determined by the point at which an indifference curve is tangent
to the opportunity set. The investor can
select either of the two consumption patterns indicated by the points where the
indifference curve intersects the opportunity set. This is because an investor
is better off selecting a consumption pattern lying on a higher indifference
curve. However, an investor cannot choose an indifference curve above the
opportunity set as there is no feasible investment opportunity available on
this curve. The investor will move to higher indifference curves until the
highest one that contains a feasible consumption pattern is reached. In other
words, the optimum consumption pattern is where the highest feasible
indifference curve is just tangent to the opportunity set.
Chapter: 1
2. List the factors that affect
risk.
Answer: The following are the factors that affect risk:
1.
The maturity of an instrument (usually, longer the
maturity assets are riskier)
2.
The risk characteristics and creditworthiness of the
issuer or guarantor of the investment.
3.
The nature and priority of the claims the investment has
on income and assets.
4.
The liquidity of the instrument and the type of market in
which it is being traded.
Chapter: 2
3. List and discuss the
characteristics of various types of financial securities.
Answer: A security
is a legal contract representing the right to receive future benefits under a
stated set of conditions. The various types of financial securities are:
A.
Money Market Securities
Money market securities are short-term debt instruments
sold by governments, financial institutions, and corporations. Money market
instruments have maturities of one year or less when issued and their
transaction size is typically large. The various types of money market
instruments are:
1.
Treasury Bills (T-bills): These are
the least risky and the most marketable of all money market instruments.
T-bills are sold at a discount from face value and pay no explicit interest
payments. The difference between the purchase price and the face value
constitutes the return the investor receives. These are considered to be the closest
approximations available to a riskless investment.
2.
Repurchase Agreements (Repos): These refer to an agreement between a borrower and a lender to sell and
repurchase a U.S. government security. The maturity of a repo is usually very
short (less than 14 days), with overnight repos being fairly common. Longer
repos, often labeled “term repos,” may have maturities of 30 days or more.
3.
Other Short-Term Instruments: CDs
(negotiable certificates of deposit) are time deposits with a bank. Bankers’
acceptances are contracts by a bank to pay a specific sum of money on a
particular date. Both instruments sell at rates that depend on the credit
rating of the bank that backs them. Commercial paper is a short-term debt
instrument issued by large, well-known corporations, and rates are determined
in part by the creditworthiness of the corporation.
B.
Capital Market Securities
Capital market securities include instruments with
maturities greater than one year, and those with no designated maturity at all. The types of capital market instruments are:
1.
Fixed Income Securities: These
securities have a specified payment schedule promising to pay specific amounts
at specific times. In almost all cases, failure to meet any specific payment
puts them into default, with all remaining payments (missed interest plus
principal) due immediately.
·
Treasury Notes and Bonds: The federal government issues
fixed income securities over a broad range of the maturity spectrum. Securities
with maturity of 1 to 10 years are called Treasury notes, and securities with a
maturity beyond 10 years are known as Treasury bonds. Both notes and bonds pay
interest twice a year and repay principal on the maturity date.
·
Federal Agency Securities: They are issued by various
federal agencies that have been granted the power to issue debt in order to
help certain sectors of the economy.
·
Municipal Bonds: They are debt instruments sold by
political entities such as states, counties, cities, and so forth, other than
the federal government or its agencies. In contrast to agency bonds, municipal
bonds can default and the interest on municipal bonds is exempt from federal
and usually state taxes.
·
Corporate Bonds: They promise to pay interest at periodic
intervals and to return principal at a fixed date. The major difference is that
these bonds are issued by business entities and thus have a risk of default.
2.
Not-So-Fixed Income Securities: These securities have a greater degree of variability in cash flows and
variability does not result in the holder’s right to force bankruptcy.
·
Preferred Stock: These securities promise
to pay the holder periodic payments like coupons which are known as dividends
rather than interest. Usually when a firm fails to pay dividends, these
dividends are cumulated and all unpaid preferred stock dividends must be paid
off before any common stock dividends can be paid.
·
Mortgage-Backed Securities: These instruments represent a
share in a pool of mortgages.
3.
Other Asset-Backed Securities: There are
securities issued by financial institutions and backed by a pool of other fixed
income securities usually structured so that there are several classes with
different maturities and different levels of risk.
4.
Common Stock (Equity): It represents
an ownership claim on the earnings and assets of a corporation. After debt holders’
claims are paid, the management of the company can either pay out the remaining
earnings to stockholders in the form of dividends or reinvest part or all of
the earnings in the business.
C.
Derivative Instruments: These are securities whose value is
derived from the value of an underlying security or basket of securities. The
most common derivatives are:
1.
Options: An option on a security
gives the holder the right to either buy (a call option) or sell (a put option)
a particular asset or a bundle of assets at a future date or during a
particular period of time for a specified price.
2.
Futures: They are obligations to
buy a particular security or a bundle of securities at a particular time for a
stated price.
3.
Credit default swaps (CDS): These are
insurance contracts to protect lenders against credit defaults. Essentially the
lender pays an insurance premium to the issuer of the CDS, who will purchase
the asset in the event of a default.
D.
Mutual fund
A mutual fund holds a portfolio of securities, usually in line with a
stated policy and objective. Mutual
funds have two variants: open-end funds and closed-end funds. Open-end fund
shares are purchased (and sold) directly from (and to) the mutual fund. They
are purchased (and sold) at the value of the net assets standing behind each
share. Closed-end funds sell at predetermined number of shares in the fund.
They then take the proceeds (minus costs) from the sale of fund shares, and
invest in stocks or stocks and bonds. The shares of a closed-end mutual fund
can sell at a discount or a premium to their net asset value.
Chapter: 2
4. List and discuss the
characteristics of various types of financial markets.
Answer: Financial markets can be classified in many different
ways. We will look at four such ways to classify them. First, markets can be
classified as primary or secondary. Primary markets are for new issues of
securities. Secondary markets are where securities are resold.
The second
classification divides markets into call or continuous markets. In a call
market, trading takes place at specified time intervals with the prices being
announced verbally, or with the use of a computer. To prevent a temporary order
imbalance from dramatically moving the price, some call markets have a provision
that limits the movement from the prior price. Continuous markets are markets
where trading takes place on a continuous basis. These markets execute market
orders quickly at the best available price.
The third way of classifying markets is based on
whether they are dealer or broker markets. In a broker market, a broker acts as
an agent for an investor and buys or sells shares on the investor’s behalf. In
a broker market, shareholders trade with other shareholders, albeit utilizing
an agent. In a dealer market, the dealer purchases or sells shares for the
investor utilizing his own inventory.
The fourth way to classify markets is to determine
whether the trading is executed by humans or done electronically. An advantage
of an electronic market is that the power of the computer allows complex
conditional trades to be handled.
There are some characteristics for a desirable market:
(a)
Market information should be promptly and accurately
available to investors.
(b)
Trading costs should be low.
(c)
Share prices should reflect all available information
about the shares.
(d)
The market should be liquid.
Liquidity here refers to the ability to transact a
large number of shares at prices that don’t vary substantially from past
prices, unless new information enters the market.
Chapter: 3
No comments:
Post a Comment