CHAPTER 1
THE INVESTMENT SETTING
TRUE/FALSE QUESTIONS
(t)
1
The rate of exchange between certain future dollars and certain current
dollars is known as the pure rate of interest.
(t)
2
An investment is the current commitment of dollars over time to derive
future payments to compensate the investor for the time funds are
committed, the expected rate of inflation and the uncertainty of future
payments.
(f)
3
A dollar received to day is worth less than the same dollar received in the
future.
(f)
4
Expected Return = (1 + nominal risk-free rate)(1 + inflation rate)(1 + risk
premium) - 1
(f)
5
The three components of the required rate of return are the nominal interest
rate, an inflation premium, and a risk premium.
(t)
6
Risk is the uncertainty that an investment will earn its expected rate of
return.
(f)
7
A manager with a passive asset allocation strategy will try to increase
allocation of assets that he believes will outperform other classes in the next
period.
(t)
8
People invest with one or more of the following three basic needs in mind:
income, capital preservation, capital appreciation.
(t)
9
As the level of risk increases an investor will require an expected return that
will compensate for this additional risk.
(f)
10
An internally efficient market is one where stocks trade at low prices.
(t)
11
The required rate of return is the minimum rate of return that will induce an
investor to invest.
(t)
12
Participants in primary capital markets that gather funds and channel them
to borrowers are called financial intermediaries.
(t)
13
A manager with an active security selection philosophy will try to identify
securities that will do well over the coming period.
305
MULTIPLE CHOICE QUESTIONS
(d)
1
An investment is the current commitment of resources for a period of time
in the expectation that an investor will receive in the future a compensation
for
a) the time for which the resources are committed
b) the expected rate of inflation
c) the time for which the resources are committed and the expected rate of
inflation
d) the expected rate of inflation, the time for which the resources are
committed, and the uncertainty of future payments.
e) a) and b)
(b)
2
The following is not a reason for investing
a)
b)
c)
d)
e)
(a)
3
to provide for retirement.
to fund higher levels of current consumption.
to fund higher levels of future consumption.
to fund children’s education needs.
to save up for a down payment on a house.
The statement – ‘risk drives expected returns’ refers to the notion that
a) an investor will require a higher rate of return the higher the perceived
riskiness of an asset.
b) an investor will require a lower rate of return the higher the perceived
riskiness of an asset.
c) markets over-react to news.
d) markets under-react to news.
e) none of the above.
(a)
4
The basic trade-offs in the investment process are
a) between the anticipated rate of return for a given investment
instrumentand its degree of risk.
b) between understanding the nature of a particular investment and
havingthe opportunity to purchase it.
c) between high returns available on single instruments and the
d) diversification of instruments into a portfolio.
e) between the desired level of investment and possessing the resources
necessary to carry it out.
(e)
5
The expected return is a function of
a) The real risk-free rate plus the investment's variance.
b) The prime rate and the rate of inflation.
306
c) The risk premium plus the inflation rate.
d) The nominal risk free rate minus the rate of inflation.
e) The nominal risk-free rate and the risk premium.
(c)
6
An externally efficient market is one where
a)
b)
c)
d)
e)
(d)
7
An investor should diversify investment holdings across
a)
b)
c)
d)
e)
(a)
8
9
10
11
In cash, stocks and bonds
Indirectly, in real assets and financial assets.
In options, futures and through derivatives.
Directly, indirectly and through derivatives.
In stocks, directly and through derivatives.
A direct investment occurs when an investor
a)
b)
c)
d)
e)
(d)
Transaction costs of trading are low.
Stocks of highly efficient companies trade.
New information is quickly reflected into assets prices.
There is no overreaction to news.
Stock prices are low.
An investor can invest in financial assets by investing:
a)
b)
c)
d)
e)
(a)
Different asset classes.
Different industries.
Different countries.
All of the above.
None of the above.
An internally efficient market is one where
a)
b)
c)
d)
e)
(d)
Transaction costs of trading are low.
Stocks of highly efficient companies trade.
New information is quickly reflected into assets prices.
There is no overreaction to news.
None of the above.
Buys shares of stocks or bonds.
Buys shares of stocks or options and futures.
Buys shares of stocks, bonds or mutual funds
Deposits funds in a bank or buys mutual funds
Deposits funds in a bank or buys derivatives.
An indirect investment occurs when an investor
a)
b)
c)
d)
Buys shares of stocks or bonds.
Buys shares of stocks or options and futures.
Buys shares of stocks, bonds or mutual funds
Deposits funds in a bank or buys mutual funds
307
e) Deposits funds in a bank or buys derivatives.
(c)
12
A portfolio manager with an active asset allocation decision philosophy will
manage a portfolio by
a)
b)
c)
d)
e)
(b)
13
A portfolio manager with an active security selection decision philosophy
will manage a portfolio by
a)
b)
c)
d)
e)
(d)
14
15
Tracking a well known market index
Stock picking using a top-down or bottom-up approach
Using market timing
Maintaining predetermined allocation with periodic rebalancing
None of the above
A portfolio manager with a passive security selection decision philosophy
will manage a portfolio by
a)
b)
c)
d)
e)
308
Tracking a well known market index
Stock picking using a top-down or bottom-up approach
Using market timing
Maintaining predetermined allocation with periodic rebalancing
None of the above
A portfolio manager with a passive asset allocation decision philosophy will
manage a portfolio by
a)
b)
c)
d)
e)
(a)
Tracking a well known market index
Stock picking using a top-down or bottom-up approach
Using market timing
Maintaining predetermined allocation with periodic rebalancing
None of the above
Tracking a well known market index
Stock picking using a top-down or bottom-up approach
Using market timing
Maintaining predetermined allocation with periodic rebalancing
None of the above
MULTIPLE CHOICE PROBLEMS
(d)
1
If the nominal risk rate is 5% per year, the risk premium is 6% per year and
the expected rate of inflation over the next year is 3%, an investment of
$1000 today worth_____ one year from today.
a)
b)
c)
d)
e)
(c)
2
If the nominal risk free rate is 8%, the expected rate of inflation is 2.5%,
and the risk premium is 5%, the required rate of return is
a)
b)
c)
d)
e)
(a)
3
$1000
$1081.50
$1091.80
$1113
$1146.39
10.5%
7.5%
13.4%
16.24%
10.7%
Assume that nominal risk free interest rate is 6%, the expected rate of
inflation is 2%, the risk premium is 3% and the required rate of return is
9.18%. What would be the value at the end of 25 years of $100 invested
today at the required rate of return?
a)
b)
c)
d)
e)
$898.62
$343.51
$1474.28
$704.13
$918
USE THE FOLLOWING INFORMATION FOR THE NEXT THREE PROBLEMS
Consider the following information. The average annual return on a tax-deferred
account over a 10-year period is 9%. The average annual return on a taxable account
over the same 10-year period is 13%. The tax rate is 35%, and the amount invested at
the beginning of the 10-year period is $2500.
(b)
4
The before tax value of the tax deferred investment, assuming all savings
are removed at the end of 10 years is
a)
b)
c)
d)
e)
$4414.17
$5918.41
$2943.42
$8663.71
$4987.26
309
(c)
5
The after tax value of the tax deferred investment, assuming all savings are
removed at the end of 10 years is
a)
b)
c)
d)
e)
(e)
6
The value of the taxable investment, assuming all savings are removed at
the end of 10 years is
a)
b)
c)
d)
e)
(c)
7
$4987.26
$5918.41
$3846.97
$2943.42
None of the above
$8663.71
$6943.42
$3846.97
$5918.41
$5626.46
Consider an investment portfolio consisting of three asset classes. The
allocations and returns for each asset class are as follows
Asset Class
1
2
3
Allocation Percentage Annual Return
10%
-10%
35%
35%
55%
-5%
The annual portfolio return is
a)
b)
c)
d)
e)
(d)
8
15.5%
-10.0%
8.5%
-7.75%
7.75%
Consider an investment portfolio consisting of four asset classes. The
allocations and returns for each asset class are as follows
Asset Class
1
2
3
4
Allocation Percentage Annual Return
10%
-10%
25%
15%
35%
10%
30%
5%
The annual portfolio return is
a) 15.5%
b) 10.0%
310
c) 5.0%
d) 7.75%
e) None of the above
CHAPTER 1
ANSWERS TO PROBLEMS
1
1000(1.05)(1.06) = 1113
2
(1.08)(1.05) – 1 = 11.34%
3
1.091825(100) = 898.62
4
1.0910(2500) = 5918.41
5
5918.41(1 – 0.35) = 3846.97
6
0.13(1 – 0.35) = 0.0845
1.084510(2500) = 5626.46
7
(0.1)(-0.1) + (0.35)(0.35) + (0.55)(-0.05)] = 0.085
8
[(0.1)(-0.1) + (0.25)(0.15) + (0.35)(0.10) + (0.30)(0.05)] = 0.0775
311
CHAPTER 2
RETURN AND RISK BASICS
TRUE/FALSE QUESTIONS
(f)
1
An investor should expect to receive higher returns from taking on lower
risks
(f)
2
The sources of investment returns are dividends and interest.
(f)
3
The holding period return (HPR) is equal to the return relative stated as a
percentage.
(t)
4
The geometric mean is the nth root of the product of the annual holding
period returns for N years minus one.
(f)
5
The geometric mean of a series of returns is always larger than the
arithmetic mean and the difference increases with the volatility of the series.
(t)
6
When rates of return are the same for all years,
the geometric mean and the arithmetic mean will be the same.
(f)
7
The coefficient of variation is the expected return divided by the standard
deviation of the return.
(f)
8
Historically return relatives are used to measure the risk for a series of
historical rates of return.
(t)
9
Widening interest rate spreads indicate a flight to quality.
(f)
10
The risk premium is a function of sales volatility, financial leverage, and
inflation.
MULTIPLE CHOICE QUESTIONS
(b)
1
The return relative is calculated as
a)
b)
c)
d)
e)
(b)
2
(1 – HPR)
(1 + HPR)
(1 – HPR)n
(1 + HPR)n
(1 – (Income + Price Change))
When rates of return on a security have a high standard deviation then
a) Arithmetic mean will equal geometric mean
312
b) The difference between arithmetic mean and geometric mean will be
large.
c) The difference between arithmetic mean and geometric mean will be
small.
d) Geometric mean will exceed arithmetic mean.
e) None of the above.
(d)
3
The coefficient of variation is a measure of
a)
b)
c)
d)
e)
(c)
4
The real risk free rate is influenced by the following factors:
a)
b)
c)
d)
e)
(c)
5
6
7
A downturn in the economy.
A static economy.
A change in the expected rate of inflation.
A change in the real rate of interest.
A change in risk aversion.
The nominal risk free rate is influenced by the following factors:
a)
b)
c)
d)
e)
(a)
Inflationary expectations and capital market conditions.
Business risk and financial risk.
Investment opportunities and time preference for consumption.
All of the above.
None of the above.
If a significant change is noted in the yield of a T-bill, the change is most
likely attributable to:
a)
b)
c)
d)
e)
(a)
Central tendency.
Absolute variability.
Absolute dispersion.
Relative variability.
Relative return.
Inflationary expectations and capital market conditions.
Business risk and financial risk.
Investment opportunities and time preference for consumption.
All of the above.
None of the above.
The following would be an example of systematic risk:
a) Changes in interest rates.
b) Management decisions.
313
c) Stability of sales.
d) The amount of debt financing.
e) Liquidity.
(b)
8
If U.S. firms increase their debt/total capital ratios, it will very likely cause
required returns to
a) Increase and change the slope of the capital market line (CML).
b) Increase and cause a movement up along the capital market line (CML).
c) Remain unchanged and cause a parallel shift of the capital market line
(CML).
d) Decrease and change the slope of the capital market line (CML).
e) Decrease and cause a movement down along the capital market line
(CML).
(d)
9
An increase in the slope of the Capital Market Line (CML) is caused by
a)
b)
c)
d)
e)
(d)
10
Changes in business risk.
Changes in financial risk.
Changes in liquidity risk.
Changes in systematic risk.
Changes in unsystematic risk.
A parallel shift in the capital market line (CML) is caused by changes in the
following factors:
a)
b)
c)
d)
e)
Expected real growth in the economy.
Capital market conditions.
Expected rate of inflation.
All of the above.
None of the above.
MULTIPLE CHOICE PROBLEMS
(a)
1
The HPR on a security is 6.5%. If the holding period is 1 month, the
annualized HPR is
a)
b)
c)
d)
e)
(c)
314
2
113%
78%
65%
6.5%
1.129%
The HPR on a security is 3%. If the holding period is 4 weeks month, the
annualized HPR is
a)
b)
c)
d)
e)
(d)
3
At the beginning of the year an investor purchased 100 shares of common
stock from ABC Corporation at $10 per share. During the year, the firm
paid dividends of $1 per share. At the end of the year, the investor sold the
100 shares at $11 per share. What is the HPR?
a)
b)
c)
d)
e)
(d)
4
5
1.20%
5.50%
12.00%
20.00%
30.00%
Assume that you invest $1000 for 15 years in an account that pays an
interest rate of 7% per year with annual compounding. Calculate the
proportion of the total value of the account that can be attributed to intereston-interest, at the end of 15 years.
a)
b)
c)
d)
e)
(b)
39.15%
78.87%
46.87%
158.25%
52.25%
100%
38.06%
36.24%
25.70%
0%
Given the following returns and return relatives over the past four years,
compute the arithmetic mean (AM) and geometric mean (GM) rates of
return.
Period
t1
t2
t3
t4
a)
b)
c)
d)
e)
Returns
0.05
-0.10
0.11
-0.02
Return Relative
1.05
0.90
1.11
0.98
AM = 4.000%, GM = 1.010%
AM = 1.000%, GM = 0.692%
AM = 0.692%, GM = 4.000%
AM = 1.000%, GM = 1.0692%
AM = 4.000%, GM = 0.0692%
315
USE THE FOLLOWING INFORMATION FOR THE NEXT THREE PROBLEMS
Assume that you invest $5000 for 30 years in an account that pays an interest rate of
8.5% per year with annual compounding.
(c)
6
The total value of your investment at the end of 30 years is?
a)
b)
c)
d)
e)
(b)
7
The amount of simple interest earned is?
a)
b)
c)
d)
e)
(d)
8
9
$67,750
$52,791
$57,791
$40,041
$60,000
Consider a stock that has an expected return of 10% and standard deviation
of 14%. Assuming that future returns will resemble past returns, an investor
can expect 95% of actual future returns to lie between
a)
b)
c)
d)
e)
316
$67,750
$52,791
$57,791
$40,041
$60,000
The amount of interest-on-interest earned is?
a)
b)
c)
d)
e)
(e)
$67,750
$52,791
$57,791
$40,041
$60,000
-10% and 24%
10% and 14%
-32% and 52%
-4% and 24%
-18% and 38%
CHAPTER 2
ANSWERS TO PROBLEMS
1
(1 + 0.065)1/(1/12) = 2.129. The HPR = 2.129 – 1 = 1.129
or 113%
2
(1 + 0.03)1/(4/52) = 1.4687. The HPR = 1.4687 – 1 = 0.4687
or 46.87%
3
HPR =
4
1000(1.07)15 = 2759.03
100  100 200

 0.20 or 20%
1000
1000
Original principal
Cumulative simple interest
Cumulative interest-on-interest
= 1000
= 1050
= 709.03
709.03/2759.03 = 0.257 or 25.7%
5
AM = [(.05) + (-.10) + (.11) + (-.02)]/4 =.04/4 = .01 = 1%
GM = [(1.05)(.90)(1.11)(.98)]1/4 - 1 = 1.00692 - 1 = .00692
= 0.692%
6
Value of account at the end of 30 years = 5000(1.085)30 = $57,791.26
7
Original principal
Cumulative simple interest
Total interest
Cumulative interest-on-interest
= 5000
= 30 x 0.085 x 5000 = $12,750.00
= 57,791.26 – 5000 = $52,791.26
= 52,791.26 – 12,750 = $40,041.26
8
Total interest
Cumulative interest-on-interest
= 57,791.26 – 5000 = $52,791.26
= 52,791.26 – 12,750 = $40,041.26
9
95% of returns will lie between 10% +/- 2 x 14.
That is between –18% and 38%
317
CHAPTER 3
SELECTING INVESTMENTS IN A GLOBAL MARKET
TRUE/FALSE QUESTIONS
(f)
1
The U.S. equity and bond markets have grown in terms of their relative size
of the world equity and bond market.
(t)
2
Diversification with foreign securities can help reduce portfolio risk.
(f)
3
The total domestic return on German bonds is the return that would be
experienced by a U.S. investor who owned German bonds.
(t)
4
If the exchange rate effect for Japanese bonds is negative, it means that the
domestic rate of return will be greater than the U.S. dollar return.
(t)
5
Investors who limit themselves to the U.S. equity market experienced rates
of return below those in many other countries.
(f)
6
It is very important when diversifying that the correlation between rates of
return for various countries be high and very stable over time.
(t)
7
Municipal bonds are tax-exempt.
(f)
8
A Eurobond is an international bond denominated in a currency other than
that of the United States.
(f)
9
Yields on money market funds are often lower than yields available to
individuals investing in CD's because of the fees involved.
(f)
10
Income bonds are considered as safe as debentures because they pay higher
rates of interest.
(t)
11
Warrants are options issued in connection with the sale of fixed income
securities.
(f)
12
A call option is issued by a firm in conjunction with a convertible bond.
(f)
13
For a U.K. based investor with stock investments in the U.S. a weakening
dollar will enhance returns in terms of pounds.
(t)
14
For a U.S. based investor with stock investments in the U.K. a weakening
dollar will enhance returns in dollar terms.
318
MULTIPLE CHOICE QUESTIONS
(d)
1
If you are considering investing in German stocks as a means to reduce the
risk of your portfolio, the initial factor that you should examine is:
a)
b)
c)
d)
e)
(c)
2
Correlations of returns between U.S. bonds and those of foreign countries
differ because of differences in
a)
b)
c)
d)
e)
(c)
3
4
5
A debenture.
A warrant.
An indenture.
A rights certificate.
A trustee deed.
The correlation between U.S. equities and U.S. government bonds has been
a)
b)
c)
d)
e)
(c)
Culture.
Political systems.
International trade patterns.
Language.
None of the above.
The legal document setting forth the obligations of a bond's issuer is called
a)
b)
c)
d)
e)
(b)
The average rate of return of the portfolio when you combine U.S.
and German stocks.
The standard deviation of the German stocks.
The standard deviation of the German stocks compared to the
standard deviation of U.S. stocks.
The correlation between the rates of return for German stocks and
U.S. stocks.
The coefficient of variation (CV) of rates of return for German stocks
versus the CV of rates of return for U.S. stocks.
Strongly positive.
Weakly positive.
Strong negative.
Weakly negative.
Indeterminate.
U.S. investors should consider constructing global investment portfolios
because
a)
b)
c)
d)
Overseas markets usually outperform U.S. markets.
Overseas markets are less risky.
Overseas markets offer risk reduction via diversification.
Investors will benefit from a stronger dollar
319
e)
(d)
6
In order to diversify risk an investor must have investments that that have
correlations with other investments in the portfolio that are
a)
b)
c)
d)
e)
(a)
7
b)
c)
d)
e)
8
9
diversifying across countries.
diversifying across industries.
diversifying across industries and countries.
diversifying across U.S. industries.
diversifying across U.S. asset classes.
Collateralized mortgage obligations (CMOs) offset some of the problems
associated with traditional mortgage pass-throughs because
a)
b)
c)
d)
e)
320
Countries are developing closer trade and
economic links.
Countries are becoming more segmented.
There are fewer barriers to travel.
U.S. investors are purchasing more foreign securities.
Correlations between bond markets of different countries have been
rising.
Global portfolio managers can diversify more risk by
a)
b)
c)
d)
e)
(a)
low positive
zero
negative
any of the above
none of the above
Correlations between stock markets in different countries have been rising
over time because
a)
(c)
None of the above.
They are overcolleralized.
They have variable rates.
Collateralized by auto-loans.
They are deep discount instruments.
Collateralized by credit card debt.
MULTIPLE CHOICE PROBLEMS
USE THE FOLLOWING INFORMATION FOR THE NEXT FIVE PROBLEMS
Security
U.S. government T-bills
Long-term government bonds
Long-term corporate bonds
Common Stock
Small capitalization common stocks
(c)
1
What is the maturity premium?
a)
b)
c)
d)
e)
(b)
2
3
4
5
1.66%
12.56%
4.92%
8.80%
10.46%
What is the small firm stock risk premium?
a)
b)
c)
d)
e)
(c)
3.76%
1.05%
2.71%
3.25%
4.71%
What is the common stock risk premium?
a)
b)
c)
d)
e)
(b)
3.76%
1.05%
2.71%
3.25%
4.70%
What is the default premium?
a)
b)
c)
d)
e)
(e)
Annual Percentage Return
2.04%
4.75%
5.8%
12.50%
14.60%
1.32%
2.10%
2.50%
3.50%
4.90%
If the annual rate of inflation during the period was 4 percent, what was the
real rate of return on long-term corporate bonds?
321
a)
b)
c)
d)
e)
(d)
6
1.16%
1.85%
1.73%
3.50%
4.90%
You are trying to decide between a par value corporate bond carrying a
coupon rate of 6.25% per year and a par value municipal bond that pays an
annual coupon rate of 4.75%. Assuming all other factors are the same and
you are in the 28% tax bracket, which bond should you choose and why?
a)
b)
c)
d)
e)
Corporate bond because the after tax yield is 6.25%.
Corporate bond because the after tax yield is 4.5%.
Municipal bond because the equivalent taxable yield is 6.3%.
Municipal bond because the equivalent taxable yield is 6.6%.
You will be indifferent between the two because the after tax yields are
the same.
USE THE FOLLOWING INFORMATION TO ANSWER THE NEXT FIVE PROBLEMS
Company
Ticker
Coupon
Gen Elec
GE
4.75
(b)
7
8
9
UST
99.544
4.808
62
10
$4.75
$47.50
$4.808
$48.08
$62
$62
$9.954
$48.08
$99.544
$995.44
What is the estimated yield on Treasury securities?
a) 4.188%
b) 5.428%
322
EST
Spread
What price would you pay in dollars to purchase this bond?
a)
b)
c)
d)
e)
(a)
Last
Yield
What annual dollar coupon amount will investors receive?
a)
b)
c)
d)
e)
(e)
Maturity
9/15/201
4
Last
Price
Est $
Vol
(000's)
158736
c) 5.371%
d) 4.132%
e) 4.753%
(c)
10
What is the current yield for this bond?
a)
b)
c)
d)
e)
(c)
11
What is the capital gains/loss yield on this bond?
a)
b)
c)
d)
e)
(d)
12
13
14
10.83%
-28.33%
5.71%
-5.71%
10.0%
Consider a Germany based investor who purchases U.S. stocks on January
1, 2002. One year later, on January 1, 2003 he sells the German stocks. The
total return in local currency is -5%. The exchange rate on January 1, 2002
is $1.05/euro. The exchange rate on January 1, 2003 is $0.90/euro.
Calculate the return in euro terms.
a)
b)
c)
d)
e)
(b)
-0.038%
0.456%
0.038%
-0.456%
None of the above
Consider a U.S. based investor who purchases German stocks on January 1,
2002. One year later, on January 1, 2003 he sells the German stocks. The
total return in local currency is 10%. The exchange rate on January 1, 2002
is $1.05/euro. The exchange rate on January 1, 2003 is $0.90/euro.
Calculate the return in dollar terms.
a)
b)
c)
d)
e)
(a)
4.18%
5.88%
4.77%
8.125%
4.063%
10.83%
-28.33%
5.71%
-5.71%
5.0%
An investor based in the U.S. has security investments in the U.K. The
323
exchange over a one year period has gone from $1.85 per pound to $2 per
pound. During this same period the investor’s return in dollar terms is
calculated to be 10%. Calculate the local currency returns for the U.K.
securities ( i.e. in pound terms).
a)
b)
c)
d)
e)
(c)
15
8.11%
1.75%
-1.35%
-7.5%
10.81%
Assume the exchange rate is $1.85 per pound at the beginning of the year
and $2 per pound at the end of the year. For an investor based in the U.K.
with security investments in the U.S. the exchange rate change is
a)
b)
c)
d)
e)
8.11%
15%
-7.5%
-8.11%
-15%
THE FOLLOWING INFORMATION APPLIES TO THE NEXT TWO PROBLEMS
Treasury Bills
Maturity Days to Mat
May 12 05
181
(c)
16
17
Chg
-
Ask Yld
?
$9997.75
$9997.76
$9887.37
$10002.25
$10002.24
Use the information provided to calculate the ask yield (also known as the
investment rate or the bond equivalent rate.
a)
b)
c)
d)
e)
324
Asked
2.24
Use the information provided above to calculate the ask price for this
Treasury bill.
a)
b)
c)
d)
e)
(a)
Bid
2.25
2.30%
2.25%
2.24%
3.75%
4.49%
CHAPTER 3
ANSWERS TO PROBLEMS
1
Maturity premium = 4.75 – 2.04 = 2.71%
2
Default premium = 5.8 – 4.75 = 1.05%
3
Common stock premium = 12.50 – 2.04 = 10.46%.
4
Small firm premium = 14.60 - 12.50 = 2.10%.
5
Real L-T corporate bond return = (1 + 0.058)/(1 + 0.04) – 1 = 0.0173 or 1.73%.
6
The municipal bond has an equivalent taxable yield of 0.475/(1 – 0.28)= 0.066. This is
higher than the bond yield of 0.0625.
7
Annual dollar coupon amount = (1000)(0.0475) = $47.50.
8
Price = $995.44. Or 99.544% of face value of $1000.
9
Estimated yield on 10 year Treasury = 4.808% - 0.62% = 4.188%.
10
Current yield = 47.50/995.44 = 0.0477 or 4.77%.
11
Capital gains yield = 4.808% - 4.77% = 0.038%.
12
Dollar returns = (1 + 0.10)(0.90/1.05) – 1 = -0.0571 or -5.71%
13
Euro returns = (1 - 0.05)(1.1111/0.9524) – 1 = 0.1083 or 10.83%%.
14
Exchange rate change = (2/1.85) -1 = 0.08108 or 8.11%
Local currency return = (1 + 0.10)/(1 + 0.08108) – 1 = 0.0175 or 1.75%
15
First restate exchange rates as 1/1.85 = pounds 0.5405 per $ and 1/2.0 = pounds 0.50
per dollar.
Exchange rate change = (0.50/0.5405) – 1 = -0.075 or -7.5%
16
Ask price = 10,000 – (0.0224 x 10,000 x 181)/360 = $9887.37
17
Ask yield = ((10000 – 9887.37)/9887.37) x (365/181) = 0.02296 or 2.3%
325
CHAPTER 5
THE ASSET ALLOCATION DECISION
TRUE/FALSE QUESTIONS
(t)
1
Experts suggest life insurance coverage should be seven to ten times an
individual's annual salary.
(t)
2
The gifting phase is similar to, and may be concurrent with, the spending phase.
(t)
3
Long-term, high-priority goals include some form of financial independence.
(f)
4
The investment performance of a portfolio manager of a small Capitalization
equity fund should be compared to the performance of the S&P 500 stock index.
(f)
5
Risk tolerance is exclusively a function of an individual's psychological makeup.
(f)
6
An appropriate investment objective for a typical 25-year-old investor is a lowrisk strategy, such as capital preservation or current income.
(f)
7
Marginal tax rate is defined as a person's total tax payment divided by their total
income.
(t)
8
Investment returns of an IRA investment, including any income, are deferred
until
the funds are withdrawn from the account.
(f)
9
Liquidity needs, time horizon, tax concerns and risk tolerance are all investment
constraints.
(t)
10
Average tax rate is defined as a person's total tax payment divided by their total
income.
MULTIPLE CHOICE QUESTIONS
(a)
1
Asset allocation is defined as the process of deciding how to allocate an investor’s
wealth among
a)
b)
c)
d)
e)
326
Asset classes, sectors, and countries.
Asset classes, sectors and real estate.
Asset classes, sectors and derivatives.
Asset classes.
Sectors.
(a)
2
Which of the following is not a life cycle phase?
a)
b)
c)
d)
e)
(e)
3
Which of the following is not a step in the portfolio management process?
a)
b)
c)
d)
e)
(e)
4
5
Develop a policy statement
Study current financial and economic conditions
Construct the portfolio
Monitor investor's needs and market conditions
Sell all assets and reinvest the proceeds at least once a year
An example of a risk management strategy that involves ‘risk transfer’ is
a)
b)
c)
d)
e)
(c)
Discovery phase
Accumulation phase
Consolidation phase
Spending phase
Gifting phase
Maintaining large cash reserves.
Purchasing commodities.
Investing largely in bonds.
Investing largely in stocks.
Purchasing derivative securities.
An individual in the consolidation phase of the investment life cycle would
a) Have retired and would seek to preserve the real value of their investments.
b) Have enough income to cover expenses and excess assets would be used to
benefit charities and family.
c) Be past the midpoint of their careers and have excess earnings that can be
invested in moderately risky investments.
d) Be in the early to middle stage of their career, have a small net worth and long
investment time horizon.
e) None of the above.
(d)
6
Which of the following statements is true?
a)
b)
c)
d)
Stocks are inappropriate investments in a tax deferred account.
The only way to maintain purchasing power over time is to invest in bonds.
After adjusting for taxes, long-term bonds consistently outperform stocks.
Investment in common stocks enables an investor to maintain real value over
time.
e) None of the above
327
(c)
7
In the U.K. equity allocation in pension fund portfolios stands around 78%. This
high level of allocation to equities can be explained by
a)
b)
c)
d)
e)
(e)
8
Research has shown that the asset allocation
variation in fund returns across all funds, and
particular fund over time.
a)
b)
c)
d)
e)
(a)
9
10
11
90 and 100.
100 and 40.
90 and 40.
40 and 100.
40 and 90.
risk and return
risk
return
time horizon
liquidity needs
Investors can manage risk confronting their wealth using the following
a)
b)
c)
d)
e)
(d)
decision explains % of the
% of the variation in returns for a
In an investment policy statement the objectives of an investor are expressed in
terms of
a)
b)
c)
d)
e)
(d)
The generous state pensions.
The high average age of the population.
The historically high inflation.
An illiquid stock market.
Government regulations.
risk avoidance
risk anticipation
risk transfer
all of the above
none of the above
An individual in the accumulation phase of the investment life cycle would
a) Have retired and would seek to preserve the real value of their investments.
b) Have enough income to cover expenses and excess assets would be used to
benefit charities and family.
c) Be past the midpoint of their careers and have excess earnings that can be
invested in moderately risky investments.
d) Be in the early to middle stage of their career, have a small net worth and long
investment time horizon.
328
e) None of the above.
329
MULTIPLE CHOICE PROBLEMS
(d)
1
The nominal rate of return for a security is 12.5% per year. If the relevant tax rate
is 35% and the rate of inflation is 3.75% per year, calculate the after tax real rate
of return for the security.
a)
b)
c)
d)
e)
8.75%
5.69%
8.43%
3.06%
2.95%
USE THE FOLLOWING INFORMATION FOR THE NEXT 4 PROBLEMS
As part of a retirement planning exercise, you are comparing a regular IRA with a
Roth IRA. The regular IRA contribution is tax deductible. In both cases the
contribution amount is $2000. Your time horizon is 25 years and you expect to
earn 9.5% percent per year on both types of IRA accounts. Your current tax rate
is
20% but you expect you tax rate at retirement to be 15%.
(b)
2
Calculate the tax savings generated by the regular IRA at the time of investment.
a)
b)
c)
d)
e)
(c)
3
Calculate the future value, at the end of 25 years, of the tax savings.
a)
b)
c)
d)
e)
(c)
4
$2,900.51
$3,867.35
$2,496.70
$1,248.35
$4,369.23
Calculate the total after tax future value, at the end of 25 years, of the regular IRA
contribution and the tax savings.
a)
b)
c)
d)
e)
330
$300
$400
$700
$100
$200
$19,336.73
$21,833.43
$18,932.92
$16,840.03
$16,436.23
(a)
5
Calculate the total after tax future value, at the end of 25 years, of the Roth IRA
contribution.
a)
b)
c)
d)
e)
(e)
6
Your portfolio currently has an asset allocation that is 15% cash, 35% bonds, and
50% stocks. The returns over the past years for cash was 3.5%, bonds
5.75%, and stocks –8.5%. The return on your portfolio for the past year was
a)
b)
c)
d)
e)
(a)
7
8
9
$233,976
$220,515
$250,515
$500,673
$213,321
Assume that you invest $1000 at the end of each quarter for the next 15 years in a
mutual fund. The annual rate of interest that you expect to earn in
the this account is 8.75%. The amount in the account at the end of 15 years
a)
b)
c)
d)
e)
(d)
-5.04%
5.47%
0.25%
5.91%
-1.71%
The future value of $25,000 invested today, at the end of 20 years assuming an
interest rate of 11.5% per year, with semiannual compounding, is
a)
b)
c)
d)
e)
(b)
$19,336.73
$21,833.43
$18,932.92
$16,840.03
$16,436.23
$28,790
$121,749
$60,000
$315,000
$115,637
Assuming the investor's marginal tax rate is 28% and he is considering
investing in a municipal bond yielding 7%. What is the equivalent taxable
yield?
a) 5.04%
b) 5.47%
c) 8.96%
331
d) 9.72%
e) 9.80%
USE THE FOLLOWING INFORMATION FOR THE NEXT TWO PROBLEMS
Assume that you have just retired with $1,000,000 in savings in an investment
account. You expect to earn 10% per year on your investments. You plan to
withdraw 25% annually at the beginning of each year with interest credited on the
remaining balance at the end of the year.
(d)
10
Calculate the amount withdrawn at the beginning of the second year.
a)
b)
c)
d)
e)
(d)
11
Calculate the balance in the investment account at the end of the second year
(prior to any withdrawals)
a)
b)
c)
d)
e)
(b)
12
13
$750,000
$618,750
$825,000
$680,625
$510,468
Someone in the 15 percent tax bracket can earn 8% on his investments in a taxexempt IRA account. What will be the value of a $10,000 investment after 5
years (assuming annual compounding)?
a)
b)
c)
d)
e)
(c)
$148,739
$250,000
$170,156
$206,250
$186,320
$ 6,805
$14,693
$15,528
$20,114
$50,000
Suppose you invest money in a taxable account earning 8% per year. What will be
the after-tax value of a $10,000 investment after 5 years if you are in the 15% tax
bracket (assuming annual compounding)?
a) $10,680
b) $11,765
332
c) $13,895
d) $14,693
e) $15,528
CHAPTER 5
ANSWERS TO MULTIPLE CHOICE PROBLEMS
1.
After tax real rate = ([(1 + 0.125)/(1 + 0.0375)]-1)(1-.35)
= 0.0548 or 5.48%
2.
Tax savings on regular IRA = (2000)(0.2) = 400.
3.
FV of tax savings = 400(1 + 0.076)25 = $2496.70
0.095(1 – 0.2) = 0.076
4.
Pre tax FV of regular IRA contribution = 2000(1 + 0.095)25 = $19,336.73
After tax FV of regular IRA = $19,336.73(1 – 0.15) = $16,436.22
FV of tax savings = 400(1 + 0.076)25 = $2496.70
Total after tax = $18,932.92
5.
After tax FV of Roth IRA contribution = 2000(1 + 0.095)25 = $19,336.73
6.
Portfolio return = (.15)(.035)+(.35)(.0575)+(.5)(-.085)
= -0.0171 or –1.71%
7.
FV = 25,000(1 + .057540) = $233,976
8.
 (1  .021875 60 )  1 
 =$121,749
FV = 1000
.021875


9.
Equivalent taxable yield = .07/(1 - .28) = .07/.72 = 9.72%
333
10.
Interest rate
Withdrawal rate
Year
Principal
10%
25%
outflow
Balance
0
$1,000,000.00
$250,000.00
$750,000.00
1
$ 825,000.00
$206,250.00
$618,750.00
2
$ 680,625.00
$170,156.25
$510,468.75
The initial withdrawal is $1,000,000(0.25) = $250,000
The remaining balance of $750,000 earns interest of 10%.
At the end of the year it is worth 750,000(1.1) = $825,000
The withdrawal at the beginning of the second year is = 825,000(0.25) = $206,250
11.
The remaining balance at the end of the first year = 825,000 – 206,250 = $618,750
This earns interest of 10% and at the end of year 2 is worth = 618,750(1.1) = $680,625
12.
$10,000(1 + 0.08)5 = $14,693
13.
After-tax yield = Before-tax yield (1 - Tax rate) = 0.08(1 - 0.15) = 0.068 or 6.8%
$10,000(1 + 0.068)5 = $13,895
334
CHAPTER 5 APPENDIX
MULTIPLE CHOICE QUESTIONS
(a)
1
Many endowments are tax-exempt.
a) True
b) False
(b)
2
Cash flows for nonlife insurance companies, such as property and casualty, are
similar to cash flows of life insurance companies.
a) True
b) False
(b)
3
The portfolio mixes of institutional investors around the world are approximately
the same.
a) True
b) False
(e)
4
In a defined contribution pension plan,
a) the plan does not promise to pay the retiree a specific income stream after
retirement.
b) the plan does promise to pay the retiree a specific income stream after
retirement.
c) the employee's retirement income is not an obligation of the firm.
d) the company carries the risk of paying future pension benefits to retirees.
e) Choices a and c
(d)
5
Banks typically have short-term investment horizons because
a)
b)
c)
d)
e)
they have a strong need for liquidity.
they offer short-term deposit accounts.
they are required to by federal and state laws.
Choices a and b
All of the above
335
CHAPTER 6
ORGANIZATION AND FUNCTIONING OF SECURITIES MARKETS
TRUE/FALSE QUESTIONS
(t)
1
A continuous market that has price continuity requires depth of buyers and
sellers.
(f)
2
A market where prices adjust rapidly to new information is considered to be
internally efficient.
(f)
3
Informational efficiency is where the cost of acquiring information is very
cheap.
(f)
4
The primary market is where existing issues are traded between current and
potential owners.
(t)
5
A general obligation (GO) bond is backed by the full taxing power of the
municipality.
(t)
6
Negotiated, competitive bids, and best efforts are three forms of
underwriting arrangements.
(t)
7
Secondary markets are important because they provide liquidity to
individuals who have purchased issues in the primary market.
(f)
8
In a call market, trades occur at any time while the market is open.
(t)
9
The U.S. over-the-counter market is the largest segment of the U.S.
secondary market in terms of number of issues traded.
(f)
10
The third market describes direct trading of securities between parties with
no broker intermediary.
(f)
11
The fourth market is mainly used by individual investors because it is much
cheaper than using a broker.
(t)
12
A short seller can only trade on an uptick (or zero uptick) and must pay any
dividends to the lender of the stock.
(t)
13
The increase in institutional development has caused an increase in the
number and size of block trades.
(t)
14
Super DOT is an electronic order-routing system through which member
firms can transmit market and limit orders directly to the posts where the
securities are traded.
(t)
15
In the United States commons stocks are quoted in decimals not fractions.
336
(f)
16
Decimalization has increased spread size and caused an increase in
transaction costs.
MULTIPLE CHOICE QUESTIONS
(b)
1
A central limit order book (CLOB) refers to a system where
a)
b)
c)
d)
e)
(b)
2
In a call market, trading for individual stocks
a)
b)
c)
d)
e)
(e)
3
All limit orders are electronically matched.
All limit orders are visible to the specialist only.
All limit orders are visible to markets makers and specialists.
Orders are routed through Super Dot.
None of the above.
Occurs anytime the market is open.
Takes place at specific times.
Takes place at the open and close of the trading day.
All of the above.
None of the above.
A pure auction market is one in which
a) Dealers provide liquidity by buying and selling shares of stock for
themselves.
b) Dealers compete against each other to provide the highest bid and
lowest asking prices.
c) Buyers submit bid prices to sellers.
d) Sellers submit ask prices to buyers.
e) Buyers and sellers submit bid and ask prices to a central location to be
matched.
(a)
4
In a negotiated bid, the underwriter carries out the following service(s)
a)
b)
c)
d)
e)
(d)
5
Origination, risk-bearing, and distribution.
Origination and risk-bearing.
Risk-bearing and distribution.
Origination and distribution.
Risk-bearing and distribution.
Municipal bonds are sold using the following method or methods
a) Competitive bid
337
b)
c)
d)
e)
(d)
6
When a market externally efficient, it means that
a)
b)
c)
d)
e)
(b)
7
8
Timely and accurate information is available
The market is liquid
Transaction costs are low
Prices adjust rapidly to new information
The number of buyers and sellers are the same
When a market is internally efficient, it means that
a)
b)
c)
d)
e)
(b)
Negotiated sale
Private placement
All of the above
None of the above
The market has price continuity.
The market has minimal transactions costs
The market has good depth
The market has more buyers than sellers
The market has more sellers than buyers
The impact of changing the system for quoting share prices from fractions
to decimals has been to
a) Increase spread size, increase transaction costs, and increase the number
of transactions.
b) Decrease spread size, decrease transaction costs, and increase the
number of transactions.
c) Decrease spread size, decrease transaction costs, and decrease the
number of transactions.
d) Decrease spread size, increase transaction costs, and increase the
number of transactions.
e) Decrease spread size, decrease transaction costs and decrease the
number of transactions..
(d)
9
Which of the following is not a characteristic of a "good" market?
a)
b)
c)
d)
e)
(b)
338
10
Marketability
Price continuity
Low transaction costs
Few buyers and sellers
Informational efficiency
A "good" market is one
a) In which there is a strong likelihood of insider trading.
b) Where prices reflect new information regarding supply and demand
factors.
c) Where accurate information on cost and volume for past transactions is
difficult to obtain.
d) Which is illiquid and has high transaction costs.
e) All of the above.
(e)
11
Which of the following is(are) an underwriting function?
a)
b)
c)
d)
e)
(d)
12
With a best-efforts offering, the investment banker performs all of the
following roles:
a)
b)
c)
d)
e)
(c)
13
Origination.
Risk-bearing and origination.
Distribution and origination.
Risk bearing and distribution.
Origination, risk bearing and distribution.
Designs and plans the security issue.
Acquires the total issue through a competitive bid.
Accepts the responsibility for reselling the issue.
Acts as a broker to sell as many securities it can at a stipulated price.
All of the above are true.
The basic distinction between a primary and a secondary market is
a) Proceeds from sales in the primary market go to the current owner of a
security; proceeds in secondary market go to the original owner.
b) Primary markets involve direct dealings within regional exchanges.
c) Only new securities are sold in the primary market; only outstanding
securities are brought and sold in the secondary market.
d) Primary markets deal exclusively in bonds; secondary markets deal
primarily in common stock.
e) There is no difference between a primary and secondary market
(a)
14
The underwriting function of ‘origination’ involves
a)
b)
c)
d)
e)
(c)
15
The design and planning of the security issue.
Acquiring the total issue through a competitive bid.
Accepting the responsibility for reselling the issue.
Acting as a broker to sell as many securities it can at a stipulated price.
All of the above are true.
The underwriting function of ‘risk-bearing’ involves
339
a)
b)
c)
d)
e)
(a)
16
The design and planning of the security issue.
Selling the security issue through a selling syndicate.
Accepting the responsibility for reselling the issue.
Acting as a broker to sell as many securities it can at a stipulated
price.
All of the above are true.
A dealer market is one in which
a) Dealers compete and provide liquidity by buying and selling shares of a
security for themselves.
b) One dealer sets bid and ask prices at which securities will trade.
c) Buyers submit bid prices to sellers.
d) Sellers submit ask prices to buyers.
e) Buyers and sellers submit bid and ask prices to a central location to be
matched.
(e)
17
The term ‘third market’ describes the market where dealers and brokers:
a)
b)
c)
d)
e)
(e)
18
The vast majority of trading on regional stock exchanges is in
a)
b)
c)
d)
e)
(e)
19
20
Stocks listed on the NYSE.
Stocks listed on the Nasdaq.
Dual listed stocks.
Stocks with unlisted trading privileges (UTP).
Dual listed and UTP stocks.
The member of the New York Stock Exchange who acts as a dealer on
assigned stocks is known as a
a)
b)
c)
d)
e)
(c)
Trade in stocks listed on regional stock exchanges.
Trade in stocks through electronic communication networks.
Trade in stocks listed on the London Stock Exchange.
Trade in stocks through electronic crossing systems.
Trade in exchange listed stocks away from the exchanges.
Registered trader.
Commission broker.
Registered dealer.
Floor dealer.
Specialist.
Floor brokers on the NYSE
a) Use their membership to buy and sell for their own account.
340
b) Are employees of a member firm and buy and sell for customers of the
firm.
c) Act as brokers for other members.
d) Handle limit and other special orders placed by other brokers on the
floor.
e) Maintain a fair and orderly market.
(a)
21
An order placed specifying the buy or sell price is a
a)
b)
c)
d)
e)
(c)
22
When an investor borrows part of the investment cost it is known as
a)
b)
c)
d)
e)
(e)
23
Limit order.
Short sale.
Market order.
Priced order.
Stop loss.
A short sale.
A fill or kill order.
A margin transaction.
A limit order.
A credit order.
Which of the following is not a function of the specialist?
a) Acting as a broker who handles the limit orders or special orders placed
with member brokers
b) Buying and selling securities in order to stabilize the market
c) Acting as a dealer in assigned stocks to maintain a fair and orderly
market
d) Maintain a minimum of $1 million or the value of 15,000 shares of each
stock assigned, whichever is greater
e) Speculating only for themselves, they do not execute traders for the
public nor for other brokers
(c)
24
If your broker required a maintenance margin of 25%, it means that
a) You may borrow up to 25% of a stock purchase.
b) You may borrow up to 75% of a stock purchase.
c) The ratio of your equity value to the total value of the position may not
fall below 25%.
d) The ratio of your equity value to the total value of the position may not
fall below 75%.
e) None of the above.
341
342
MULTIPLE CHOICE PROBLEMS
USE THE FOLLOWING INFORMATION FOR THE NEXT THREE PROBLEMS
Assume you deposit $100,000 in a margin account. The margin requirement is 50 percent and
commissions are ignored. Shares in Sisco Corp currently sell for $80 per share:
(b)
1
What is the value of stock that you can acquire?
a)
b)
c)
d)
e)
(c)
2
What is your profit if the price of Sisco Corp rises to $90?
a)
b)
c)
d)
e)
(c)
3
4
5
$51.25
$43.25
$53.33
$45.33
$83.33
Calculate your percentage rate of return if the shares of Sisco Corp falls to
$65.
a)
b)
c)
d)
e)
(b)
$50,000
$12,500
$25,000
$100,000
$120,000
If the maintenance margin is 25 percent, to what price can Sisco Corp fall
before you receive a margin call?
a)
b)
c)
d)
e)
(d)
$100,000
$200,000
$175,000
$150,000
$300,000
-15.00%
-25.00%
-23.07%
-37.50%
-30.50%
Suppose you buy a round lot of a stock on 55 percent margin when it is
selling at $35 a share. The broker charges a 10 percent annual interest rate
and commissions are 3 percent of the total stock value on both the purchase
and the sale. If at year end you receive a $0.90 per share dividend and sell
the stock for 32, what is your rate of return on the investment?
343
a)
b)
c)
d)
e)
-29.38%
-28.00%
-26.23%
-25.00%
-35.00%
USE THE FOLLOWING INFORMATION FOR THE NEXT TWO PROBLEMS
You decide to sell 100 shares of a stock short when it is selling at its yearly high of $22.25.
Your broker tells you that your margin requirement is 55% and that the commission on the sale
is $55. While you are short, the stock, Tuna Boat pays a $0.75 per share dividend. At the end of
one year you buy shares of the stock to cover your short sale at $18.38 and are charged a
commission of $45 and a 9% interest rate on the funds you borrowed.
(a)
6
What is your dollar return on the investment?
a)
b)
c)
d)
e)
(d)
7
$121.89
$315.05
$425.50
$637.73
$950.45
What is your rate of return on the investment?
a)
b)
c)
d)
e)
0.87%
3.87%
5.08%
9.53%
11.87%
USE THE FOLLOWING INFORMATION FOR THE NEXT FIVE PROBLEMS
You decide to sell short 200 shares of XCorp stock at a price of $75. Your margin deposit is
65%. Commission on the sale is 1.25%. During the year the stock pays a $1.75 per share
dividend. Interest on margin debt is 5.25% per year.
(d)
8
Calculate your initial investment
a)
b)
c)
d)
e)
344
$15,000
$5,250.75
$9,750.25
$9,937.50
$15,187.50
(a)
9
At the end of one year you close out your short position by purchasing
shares of XCorp at $45 per share. The commission is 1.25%. Calculate your
dollar profit.
a)
b)
c)
d)
e)
(c)
10
If at the end of one year you close out your short position by purchasing
share of XCorp at $45 per share with commission of 1.25%, what is your
rate of return on the investment?
a)
b)
c)
d)
e)
(b)
11
12
-55.92%
10.31%
51.06%
23.1%
-33.05%
Suppose at the end of one year XCorp is selling at $90 per share and you
cover your short position at this price. What is your dollar profit on the
investment? (Assume a 1.25% commission on the purchase)
a)
b)
c)
d)
e)
(a)
$5,074.38
-$4,038.13
$5250.00
-$5074.38
$4,038.13
$5,074.38
-$4,038.13
$5250.00
-$5074.38
$4,038.13
If you cover your short position at $90 per share. What is your rate of return
on the investment? (Assume a 1.25% commission on the purchase)
a)
b)
c)
d)
e)
-40.64%
-25.53%
5.21%
72.7%
–71.2%
USE THE FOLLOWING INFORMATION FOR THE NEXT FIVE PROBLEMS
Shares of RossCorp stock are selling for $45 per share. Brokerage commissions are 2% for
purchases and 2% for sales. The interest rate on margin debt is 6.25% per year. The
maintenance margin is 30%.
(e)
13
At the end of one year shares of RossCorp stock are selling for $55 per
share and the company paid dividends of $0.85 per share. Assuming that
345
you paid the full cost of the purchase, what is your rate of return if you sell
RossCorp stock?
a)
b)
c)
d)
e)
(b)
14
At the end of one year shares of RossCorp stock are selling for $35 per
share and the company paid dividends of $0.85 per share. Assuming that
you paid the full cost of the purchase, what is your rate of return if you sell
RossCorp stock?
a)
b)
c)
d)
e)
(c)
15
16
17
33.05%
-33.05%
-23.51%
-25.35%
–40.64%
Assume that you purchase 150 shares of RossCorp stock by making a
margin deposit of 75%. At what price would you receive a margin call?
a)
b)
c)
d)
346
-23.51%
29.35%
23.51%
5.21%
10.06%
At the end of one year shares of RossCorp stock are selling for $35 per
share and the company paid dividends of $0.85 per share. Assuming that
you borrowed 25% of cost of the purchase, what is your rate of return?
a)
b)
c)
d)
e)
(d)
-33.05%
-23.42%
23.42%
33.05%
–25.35%
At the end of one year shares of RossCorp stock are selling for $55 per
share and the company paid dividends of $0.85 per share. Assuming that
you borrowed 25% of cost of the purchase, what is your rate of return?
a)
b)
c)
d)
e)
(b)
18.08%
23.51%
22.32%
14.96%
19.28%
$29.39
$26.48
$50.39
$16.07
e) $50.10
CHAPTER 6
ANSWERS TO MULTIPLE CHOICE PROBLEMS
1.
If X is the total investment your share will represent 50 percent.
Thus .50x = $100,000 and X = $100,000/.50 = $200,000.
Since the shares are $80 each, you can purchase
($200,000)/$80 = 2500 shares
2.
Profit = (90 - 80)(2500) = $25,000
3.
Margin = (Market Value - Debit Balance)/ Market Value
where Market Value = Price x Number of Shares = Price x 2500
Debit Balance = Initial Loan Value = (0.5)($80)(2500) = $100,000
0.25 = ((Price x 2500) - $100,000)/(Price x 2500)
Price = $53.33
4.
Return = (65 – 80)/(0.5 x 80) = -0.375 or -37.5%
5.
Initial investment= (.55 x $3,500) + (.03 x $3500) = $2030
Beginning Value of Stock = $3500
Profit = Ending Wealth - Beginning Value of Stock - Transaction Costs - Interest
Ending Wealth = Ending Market Value + Dividend= $3200 + $90 = $3290
Transaction Costs = .03 x 3500 + .03 x 3200 = $105.00 + 96 = $201
Interest = .10 x (.45 x $3500) = $157.50
Profit = $3290 - $3500.00 - $201 - $157.50 = - $568.50
Rate of Return = Profit/Initial Investment
= -$568.50/$2030
= -28%
347
For problems 6 and 7
Initial investment = (.55 x $2225) + 55 = $1278.75
Cost = $18.38 x 100 = $1838 (without transaction costs)
Profit = Total Return - Cost - Transaction Costs - Interest
Total Return = Beginning Market Value - Dividend = $2225 - $75 = $2150
Transaction Costs = $55 + $45 = $100.00
Interest = .09 x (.45 x $2225) = $90.11
6.
Profit = $2150 - $1838 - $100 - $90.11 = $121.89
7.
Rate of Return = $121.89/$1278.75 = 9.53%
8.
Initial investment = (0.65)(200)(75) + (0.0125)(200)(75) = $9937.50
9.
10.
11.
Dollar profit = 200(75 – 45 – 1.75) – (200)(75)(0.0125) –
(200)(45)(0.0125) – (200)(75)(0.35)(0.0525) = $5074.38
Rate of return = 5074.38/9937.50 = 0.5106 or 51.06%
Dollar profit = 200(75 – 90 – 1.75) – (200)(75)(0.0125) – (200)(90)(0.0125) –
(200)(0.35)(75)(0.0525) = -$4038.13
12.
Rate of return = -4038.13/9937.50 = -0.4063 or -40.63%
13.
Rate of return = [55- 45 + 0.85 - 1.10 - 0.90]/[45 + 0.90] = 19.28%
14.
Rate of return = [35 – 45 + 0.85 -0.70 -0.90]/[45 + 0.90] = -23.42%
348
15.
Rate of return = [55-45 + 0.85 -1.10-0.90-(1-.75)(45)(.0625)]/[(0.75)(45) + 0.90]
= 23.51%
16.
Rate of return = [35-45+0.85-0.70-0.90- (1-.75)(45)(.0625)]/[(0.75)(45)+0.90]
= -33.05%
17.
0.30 = [(150)(P) – (0.25)(150)(45)]/[(150)(P)]
P = $16.07
CHAPTER 7
349
SECURITY-MARKET INDICATOR SERIES
TRUE/FALSE QUESTIONS
(t)
1
An aggregate market index can be used as a benchmark to judge the
performance of professional money managers.
(f)
2
A price-weighted index is the geometric average of the current prices of the
sampled securities.
(f)
3
The Dow-Jones Industrial Average (DJIA) is a value- weighted average.
(f)
4
The DJIA has been criticized because when a stock in the index splits there
are more shares outstanding and the importance of the stock in the
index increases.
(t)
5
Security market indexes have been used to create index funds and exchange
traded funds.
(f)
6
In a value-weighted index the highest priced stock carries the greatest
weight.
(t)
7
A value-weighted index contains an automatic adjustment for stock splits.
(f)
8
The S&P 500 stock index is an example of an equally-weighted index.
(t)
9
An index constructed using small-cap growth stocks would be referred to as
a style index .
(t)
10
The low correlations between the U.S. and the U.K., and the U.S. and
Japan, confirm the benefit of global diversification.
(t)
11
The correlations among the U.S. investment-grade-bond series were very
high because all rates of return for investment-grade bonds over time are
impacted by common macroeconomic variables.
350
MULTIPLE CHOICE QUESTIONS
(c)
1
Which of the following is not a use of security market indicator series?
a)
b)
c)
d)
e)
(c)
2
A properly selected sample for use in constructing a market indicator series
will consider the sample's source, size and
a)
b)
c)
d)
e)
(a)
3
4
5
Divisor will increase/decrease, index remains the same.
Index will increase/decrease, divisor remains the same.
Index and divisor will remain the same.
Index and divisor will both reflect the changes (immediately).
Not enough information provided.
An example of a value-weighted stock market indicator series is the
a)
b)
c)
d)
e)
(d)
Value.
Average beta.
Breadth.
Variability.
Dividend record.
What effect does a stock substitution or stock split have on a price-weighted
series, such as DJIA?
a)
b)
c)
d)
e)
(d)
To use as a benchmark of individual portfolio performance
To develop an index portfolio
To determine unsystematic risk
To determine factors influencing aggregate security price movements
To determine systematic risk
Dow Jones Industrial Average.
Nikkei-Dow Jones Average.
Value Line Index.
American Stock Exchange Index.
Lehman Brothers Index.
Which of the following indexes includes the most comprehensive list of
stocks?
a)
b)
c)
d)
e)
New York Stock Exchange Composite Index
Standard and Poor's 500 Composite Index
American Stock Exchange Market Value Index
Nasdaq Composite
Dow Jones Industrial Average
351
(c)
6
The Value Line Composite Average is based on percent price changes
which has been computed using
a)
b)
c)
d)
e)
(e)
7
An arithmetic mean.
A harmonic average.
A geometric mean.
An expected average.
A logarithmic average.
Which of the following are factors that make it difficult to create and
maintain a bond index?
a) The universe of bonds is broader than stocks.
b) The universe of bonds is constantly changing due to new issues, bond
maturities, calls, and bond sinking funds.
c) There can be difficulties in correctly pricing bond issues.
d) Choices a and c.
e) Choices a, b and c.
(a)
8
Low correlations between the S&P 500 stock index and the MSCI EAFE
suggest
a)
b)
c)
d)
e)
(d)
9
That investors should diversify investment portfolios.
That investors should invest only in U.S. stocks.
That investors should invest only in Europe.
That investors should invest only is Asia.
Nothing.
Correlations between U.S. investment grade bonds are
a) Low because of the equity characteristics of high yield bonds.
b) Low because yields on investment grade bonds are determined by
systematic interest rate variables.
c) High because of the equity characteristics of high yield bonds.
d) High because yields on investment grade bonds are determined by
systematic interest rate variables.
e) None of the above.
(a)
10
Correlations between U.S. investment grade bonds and high yield bonds are
a) Low because of the equity characteristics of high yield bonds.
b) Low because yields on investment grade bonds are determined by
systematic interest rate variables.
c) High because of the equity characteristics of high yield bonds.
d) High because yields on investment grade bonds are determined by
systematic interest rate variables.
e) None of the above.
352
MULTIPLE CHOICE PROBLEMS
USE THE FOLLOWING INFORMATION FOR THE NEXT 12 PROBLEMS
Stock
W
X
Y
Z
31-Dec-03 31-Dec-0331-Dec-0431-Dec-04
Price
Shares
Price
Shares
$ 75.00 10000 $ 50.00 30000
$ 150.00 5000
$ 65.00 15000
$ 25.00 20000 $ 35.00 20000
$ 40.00 25000 $ 50.00 25000
Stocks W and X had 3 for 1 splits on December 31, 2003 at the end of trading.
(c)
1
Calculate the price weighted series for Dec 31, 2003, prior to the splits.
a)
b)
c)
d)
e)
(a)
2
Calculate the price weighted series for December 31, 2003 after the splits.
a)
b)
c)
d)
e)
(e)
3
4
72.5
100.0
119.25
121.25
103.57
Calculate the price weighted series for Dec 31, 2004.
a)
b)
c)
d)
e)
(a)
103.57
100.0
72.5
121.25
119.25
121.25
119.25
100.0
72.5
103.57
Calculate the percentage return in the price weighted series for the period
Dec 31, 2003 to Dec 31, 2004.
a)
b)
c)
d)
e)
42.86%
20.00%
21.76%
33.33%
40.00%
353
(d)
5
Calculate the value weighted index for Dec 31, 2003, prior to the splits.
Assume a base index value of 100. The base year is Dec 31, 2003.
a)
b)
c)
d)
e)
(c)
6
Calculate the value weighted index for Dec 31, 2003, after the splits.
Assume a base index value of 100. The base year is Dec 31, 2003.
a)
b)
c)
d)
e)
(e)
7
8
9
12.68%
47.50%
21.76%
33.33%
40.00%
Calculate the unweighted index for Dec 31, 2003, prior to the splits.
Assume a base index value of 100. The base year is Dec 31, 2003.
a)
b)
c)
d)
e)
354
121.25
100.0
81.69
72.5
147.5
Calculate the percentage return in the value weighted index for the period
Dec 31, 2003 to Dec 31, 2004.
a)
b)
c)
d)
e)
(a)
72.5
81.69
100.0
147.5
121.25
Calculate the value weighted index for Dec 31, 2004. Assume a base index
value of 100. The base year is Dec 31, 2003.
a)
b)
c)
d)
e)
(b)
147.5
81.69
72.5
100.0
121.25
100.0
200.0
150.0
120.0
175.0
(c)
10
Calculate the unweighted index for Dec 31, 2003, after the splits. Assume a
base index value of 100. The base year is Dec 31, 2003.
a)
b)
c)
d)
e)
(a)
11
Calculate the unweighted index (geometric mean) for Dec 31, 2004.
Assume a base index value of 100. The base year is Dec 31, 2003.
a)
b)
c)
d)
e)
(a)
12
110.0
200.0
100.0
120.0
150.0
146.05
121.25
151.25
148.75
100.25
Calculate the percentage return in the unweighted index (geometric mean)
for the period Dec 31, 2003 to Dec 31, 2004. Assume a base index value of
100. The base year is Dec 31, 2003.
a)
b)
c)
d)
e)
46.05%
21.25%
51.25%
48.75%
100.25%
USE THE FOLLOWING INFORMATION FOR THE NEXT THREE PROBLEMS
You are given the following information regarding prices
for a sample of stocks:
Stock
A
B
C
(b)
Number of Shares
1,000,000
10,000,000
25,000,000
13
PriceT
50
30
20
PriceT+1
60
35
25
Using a price-weighted series approach, what is the percentage change in
the series for the period from T to T + 1.
a) 1.20%
355
b)
c)
d)
e)
(d)
14
Using a value-weighted series approach, what is the percentage change in
the series for the period from T to T + 1.
a)
b)
c)
d)
e)
(c)
20.00%
21.76%
33.33%
40.00%
15
1.22%
20.00%
20.55%
21.76%
33.33%
Construct an unweighted series (arithmetic mean) assuming $1,000 is
invested in each stock. What is the percentage change in wealth for this
portfolio?
a)
b)
c)
d)
e)
1.21%
20.00%
20.56%
21.76%
33.33%
USE THE FOLLOWING INFORMATION FOR THE NEXT THREE PROBLEMS
Price
COMPANY
Day 1
Day 2
Day 3
Day 4
Shares
A
12
10
8
9
B
23
22
26
25
*Split at Close of Day 2
(c)
16
17
B
350
350
350
350
C
250
250
250**
750
**Split at Close of Day 3
13.000
19.000
29.000
87.000
100.000
Calculate a Dow Jones Industrial Index for Day 4.
a) 11.2389
356
A
500
500*
1000
1000
Calculate a Dow Jones Industrial Index for Day 1.
a)
b)
c)
d)
e)
(c)
C
52
55
51
19
b)
c)
d)
e)
(e)
18
21.3343
31.2389
41.6890
None of the above
Calculate a Standard & Poor's Index for Day 3 if the base period is Day 1
with an initial index value is 100.
a)
b)
c)
d)
e)
90.351
91.035
95.234
101.628
110.351
CHAPTER 7
ANSWERS TO MULTIPLE CHOICE PROBLEMS
1
PRICE WEIGHTED SERIES DEC 2003 = (75 + 150 + 25 + 40)/4 = 72.5
2
POST SPLIT SERIES = 72.5 = (25 + 50 + 25 + 40)/X
The new divisor, X = 1.931
3
PRICE WEIGHTED SERIES DEC 2004 = (50 + 65 + 35 + 50)/1.931 = 103.57
4
Return on series = (103.57 – 72.5)/72.5 = 42.86%
5
Value weighted series Dec 2003 =
 750000  750000  500000  1000000 

 x100  100
 750000  750000  500000  1000000 
6
Value weighted post split = 100. Not affected by splits.
7
Value weighted series Dec 2004 =
 1500000  975000  700000  1250000 

 x100  147.5
 750000  750000  500000  1000000 
8
9
SINCE THE BASE VALUE IS 100 AND THE CURRENT INDEX VALUE IS
147.5, the percentage return is 47.5%.
The index value Dec 2003 is 100
357
10
Post split the index value is 100
11
Index Dec 2004 = (2 + 1.3 + 1.40 + 1.25)1/4 (100) = 146.05
12
The return on the index is 46.05%
13
Given a three security series and a price change from period T to T+1, the percentage
change in the price weighted series would be
A
B
C
Sum
Divisor
Average
Period T
$50
30
20
$100
3
33.33
Period T+1
$60
35
25
$120
3
40.00
Percentage change = (40.00 - 33.33)/33.33 = 20.00%
14
Period T
Stock
Price/Share
A
$50
B
30
C
20
Total
# of Shares
1,000,000
10,000,000
25,000,000
Market Value
$50,000,000
300,000,000
500,000,000
$850,000,000
Period T+1
Stock Price/Share
A
$60
B
35
C
25
Total
# of Shares
1,000,000
10,000,000
25,000,000
Market Value
$60,000,000
350,000,000
625,000,000
$1,035,000,000
Percentage change = (1,035 – 850)/850 = 21.76%
15
Period T
Stock Price/Share
A
$50
B
30
C
20
Total
Period T+1
Stock Price/Share
A
$ 60
B
35
C
25
358
# of Shares Market Value
20.00
$1,000.00
33.33
1,000.00
50.00
1,000.00
$3,000.00
# of Shares
20.00
33.33
50.00
Market Value
$1,200.00
1,166.55
1,250.00
Total
$3,616.55
Percentage change = (3,616.55 - 3,000)/3,000 = 20.56%
16
Day 1 Index = (12 + 23 + 52)/3.0000 = 29.000
17
Day 2 Index = (10 + 22 + 55)/3.0000 = 29.000
Adjusted Day 2 Index = (5 + 22 + 55)/X = 29.000
X = 2.8276 (new divisor)
Day 3 Index = (8 + 26 + 51)/2.8276 = 30.0608
Adjusted Day 3 Index = (8 + 26 + 17)/Y = 30.0608
Y = 1.6966 (new divisor)
Day 4 Index = (9 + 25 + 19)/1.6966 = 31.2389
18
Base = ($12 x 500) + ($23 x 350) + ($52 x 250) = $27,050
Day 3 ($8 x 1000) + ($26 x 350) + ($51 x 250) = $29,850
Index = ($29,850/$27,050) x 100 = 110.351
CHAPTER 8
359
AN INTRODUCTION TO PORTFOLIO MANAGEMENT
TRUE/FALSE QUESTIONS
(t)
1
Risk is defined as the uncertainty of future outcomes.
(t)
2
A basic assumption of the Markowitz model is that investors base decisions solely
on expected return and risk.
(t)
3
The yield spread between yields on AAA bonds and BAA bonds is evidence that
investors are risk averse.
(t)
4
Standardizing the covariance by the individual standard deviation yields the
correlation coefficient.
(t)
5
The covariance is a measure of the degree to which two variables (e.g., rates of
return) move together over time relative to their means.
(f)
6
For a two stock portfolio containing Stocks i and j, the correlation coefficient of
returns (ri,j) is equal to the square root of the covariance (covi,j).
(f)
7
To reduce the standard deviation of a portfolio it is necessary to increase the
relative weight of assets with low volatility (small standard
deviation of returns).
(t)
8
Increasing the correlation among assets in a portfolio results in an increase in the
standard deviation of the portfolio.
(f)
9
A basic assumption of portfolio theory is that an investor would want to maximize
risk subject to a given level of return.
(t)
10
Most investors hold a diversified portfolio in order to reduce portfolio risk.
(f)
11
other.
360
Most assets of the same type have negative covariances of returns with each
MULTIPLE CHOICE QUESTIONS
(a)
1
The optimal portfolio is identified at the point of tangency between the
efficient frontier and the
a)
b)
c)
d)
e)
(d)
2
An individual investor’s utility curves specify the tradeoffs he or she is willing to
make between
a)
b)
c)
d)
e)
(c)
3
4
approaches a horizontal straight line.
bends out.
bends in.
approaches a vertical straight line.
none of the above.
A portfolio manager is considering adding another security to his portfolio. The
correlations of the 5 alternatives available are listed below. Which security
would enable the highest level of risk diversification
a)
b)
c)
d)
e)
(b)
high risk and low risk assets.
high return and low return assets.
covariance and correlation.
return and risk.
efficient portfolios.
As the correlation coefficient between two assets decreases, the shape of the
efficient frontier
a)
b)
c)
d)
e)
(d)
highest possible utility curve.
lowest possible utility curve.
middle range utility curve.
steepest utility curve.
flattest utility curve.
5
0.0
0.25
-0.25
-0.75
1.0
A positive covariance between two variables indicates that
a)
b)
c)
d)
the two variables move in different directions.
the two variables move in the same direction.
the two variables are low risk.
the two variables are high risk.
361
e) the two variables are risk free.
(c)
6
A positive relationship between expected return and expected risk is consistent
with
a)
b)
c)
d)
e)
(d)
7
What information must you input to a computer program in order to derive the
portfolios that make up the efficient frontier
a)
b)
c)
d)
e)
(d)
8
investors being risk seekers.
investors being risk avoiders.
investors being risk averse.
all of the above.
none of the above.
Expected returns, covariances and correlations.
Standard deviations, variances and covariances.
Expected returns, standard deviations and variances.
Expected returns, variances and correlations.
Covariances, correlations and variances.
The Markowitz model is based on several assumptions regarding investor
behavior. Which of the following is an assumption of the Markowitz model?
a) Investors consider investment alternative as being represented by a joint
probability distribution of expected returns over some holding period.
b) Investors minimize one-period expected utility.
c) Investors estimate the risk of the portfolio on the basis of their utility
functions.
d) Investors base decisions solely on expected return and risk.
e) None of the above.
(a)
9
As the correlation coefficient between two assets increases, the shape of the
efficient frontier
a)
b)
c)
d)
e)
(d)
10
The probability of an adverse outcome is the
a)
b)
c)
d)
362
approaches a horizontal straight line.
bends out.
bends in.
approaches a vertical straight line.
none of the above.
Statistics.
Variance.
Random.
Risk.
definition of:
e) Semivariance.
(c)
11
Which of the following is a measure of risk?
a)
b)
c)
d)
e)
(b)
12
Semivariance, when applied to portfolio theory, is concerned with the
a)
b)
c)
d)
e)
(a)
13
14
Square root of deviations from the mean.
Deviations below the mean.
Deviations above the mean.
All deviations (above and below the mean).
Summation of the squared deviations from the mean.
With low, zero or negative correlations it is possible to derive portfolios that have
a)
b)
c)
d)
e)
(d)
Range of standard deviations
Expected return
Standard deviation
Covariance
Correlation
Lower risk than the individual securities in the portfolio.
Lower risk than the highest risk individual security in the portfolio.
Higher risk than the individual securities that make up the portfolio.
Higher risk than the highest risk individual security in the portfolio.
None of the above.
Which of the following statements are correlation coefficient is false?
a) The values range between -1 to +1.
b) A value of +1 implies that the returns for the two stocks move together in a
completely linear manner.
c) A value of -1 implies that the returns move in a completely opposite direction.
d) A value of zero means that the returns are zero.
e) None of the above (that is, all statements are true)
(a)
15
In a two stock portfolio, if the correlation coefficient between two stocks were to
decrease over time everything else remaining constant the portfolio's risk would
a)
b)
c)
d)
e)
Decrease.
Remain constant.
Increase.
Fluctuate positively and negatively.
Be a negative value.
363
(d)
16
Given the following correlations between pairs of stocks, a portfolio constructed
from which pair will have the lowest standard deviation?
Correl(A,B) = 0, Correl(C,D) = 1, Correl(E,F) = 0.75, Correl(G,H) = -0.75,
Correl(I,J) = -0.50.
a)
b)
c)
d)
e)
(c)
17
Given a portfolio of stocks the envelope curve containing the set of best possible
combinations is known as the
a)
b)
c)
d)
e)
(d)
18
19
Expected security returns.
Standard deviations of expected returns.
Correlations of expected returns.
All of the above.
None of the above.
A portfolio is considered to be efficient if:
a)
b)
c)
d)
e)
364
Efficient portfolio.
Utility curve.
Efficient frontier.
Last frontier.
Capital asset pricing model.
Estimation error refers to potential errors that arise from estimating
a)
b)
c)
d)
e)
(a)
Pair A,B
Pair C,D
Pair E,F
Pair G,H
Pair I,J
No other portfolio offers higher expected returns with the same risk.
No other portfolio offers lower risk with lower expected return.
There is no portfolio with a higher return.
There is no portfolio with lower risk.
None of the above
MULTIPLE CHOICE PROBLEMS
(d) 1
Consider two securities, A and B. Security A and B have a correlation coefficient of 0.65. Security A has standard deviation
of 12, and security B has standard deviation of 25. Calculate the covariance between these two securities.
a)
b)
c)
d)
e)
(a)
2
300
461.54
261.54
195
200
Calculate the expected return for a three asset portfolio with the following
Asset
A
B
C
a)
b)
c)
d)
e)
(c)
3
Exp. Ret.
0.0675
0.1235
0.1425
Given the following weights and expected security returns, calculate the expected
return for the portfolio.
a)
b)
c)
d)
e)
4
Weight
0.25
0.35
0.40
11.71%
11.12%
15.70%
14.25%
6.75%.
Weight
.20
.25
.30
.25
(d)
Std. Dev
0.12
0.1675
0.1835
Expected Return
.06
.08
.10
.12
.085
.090
.092
.097
None of the above
the standard deviation for stock A is 0.15 and for stock B, it is 0.20. The
covariance between returns for these stocks is 0.01. The correlation coefficient
between these two stocks is:
a) -0.125
b) 0.195
c) -0.285
365
d) 0.333
e) 0.405
USE THE FOLLOWING INFORMATION FOR THE NEXT TWO PROBLEMS
Given: E(R1) = .10
E(SD1) = .03
W1 = .30
(d)
5
6
W2 = .70
Calculate the expected return of the two stock portfolio.
a)
b)
c)
d)
e)
(c)
E(R2) = .15
E(SD2) = .05
.105
.115
.125
.135
None of the above
Calculate the expected standard deviation of the two stock portfolio when the
correlation is 0.40.
a)
b)
c)
d)
e)
.0016
.0160
.0395
.1558
.3950
USE THE FOLLOWING INFORMATION FOR THE NEXT FOUR PROBLEMS
Given the following information about two stocks:
E(R1) = 0.12
E(SD1) = 0.08
(a)
7
Calculate the expected return a two stock portfolio when w1 = 0.75.
a)
b)
c)
d)
e)
(d)
366
8
E(R2) = 0.16
E(SD2) = 0.15
0.13
0.136
0.14
0.125
0.16
Calculate the expected standard deviation of a two stock portfolio when w1 =
0.75
and the covariance between stock 1 and stock 2 is -0.009.
a)
b)
c)
d)
e)
(b)
9
Calculate the expected return a two stock portfolio when w1 = 0.60.
a)
b)
c)
d)
e)
(c)
10
0.1025
0.0705
0.0906
0.0404
0.0623
0.13
0.136
0.14
0.125
0.16
Calculate the expected standard deviation of a two stock portfolio when w1 =
0.60
and the covariance between stock 1 and stock 2 is 0.8.
a)
b)
c)
d)
e)
0.1025
0.0705
0.0906
0.0404
0.0623
CHAPTER 8
ANSWERS TO MULTIPLE CHOICE PROBLEMS
1.
Cov(A, B) = (0.65)(12)(25) = 195
2.
E(R) = (0.25)(0.0675) + (0.35)(0.1235) + (0.40)(0.1425) = 0.1171 or 11.71%
3.
E(R) = (0.20)(0.06) + (0.25)(0.08) + (0.30)(0.10) + (0.25)(0.12) = 0.092 or 9.2%
4.
Correlation = (0.01)(0.15 x 0.20) = 0.3333
5.
E(R) = (.3 x .10) + (.7 x .15) = .135
6.
SD= [(.3)2(.03)2+ (.7)2(.05)2+ 2(.3)(.7)(.03)(.05)(.4)]1/2 = 0.03947
7.
8.
E(R) = (.75 x .12) + (.25 x .16) = 0.13
SD = [(.75)2(.04)2+ (.25)2(.06)2+ 2(.75)(.25)(-.0009)]1/2 = 0.0404
9.
10.
E(R) = (.60 x .12) + (.40 x .16) = 0.136
SD= [(.6)2(.04)2+ (.4)2(.06)2+ 2(.6)(.4)(.8)]1/2 = 0.0906
367
CHAPTER 9
AN INTRODUCTION TO ASSET PRICING MODELS
TRUE/FALSE QUESTIONS
(t)
1
One of the assumptions of Capital Market Theory is that investors can borrow or
lend at the risk-free rate.
(f)
2
An assumption of Capital Market Theory is that buying or selling of assets entails
no taxes, but entails significant transaction costs.
(t)
3
A risky asset is an asset with uncertain future returns, and uncertainty (or risk) is
measured by the variance or standard deviation of returns.
(t)
4
The standard deviation of a portfolio that combines the risk-free asset with risky
assets is the linear proportion of the standard deviation of the risky asset portfolio.
(t)
5
The Capital Market Line (CML) is the line from the intercept point that represents
the risk-free rate tangent to the original efficient frontier.
(t)
6
The market portfolio consists of all risky assets.
(f)
7
All portfolios on the CML are perfectly negatively correlated, which means that
all portfolios on the CML are perfectly negatively correlated with the
completely diversified market portfolio since it lies on the CML.
(t)
8
Diversification reduces the unsystematic risk in a portfolio.
(f)
9
The Capital Asset Pricing Model (CAPM) is a technique for determining the
expected risk on an asset.
(t)
10
Beta is a standardized measure of systematic risk.
(t)
11
Multifactor models of risk and return can be broadly grouped into models that use
macroeconomic factors and models that use microeconomic factors.
(f)
12
Arbitrage Pricing Theory (APT) specifies the exact number of risk factors and
their identity
368
MULTIPLE CHOICE QUESTIONS
(d)
1
Which of the following is not an assumption of the Capital Market Theory?
a)
b)
c)
d)
e)
(e)
2
The market portfolio consists of all
a)
b)
c)
d)
e)
(c)
3
4
New York Stock Exchange stocks.
International stocks and bonds.
Stocks and bonds.
U.S. and non-U.S. stocks and bonds.
Risky assets.
The separation theorems divides decisions on
a)
b)
c)
d)
e)
(d)
All investors are Markowitz efficient investors.
All investors have homogeneous expectations.
There are no taxes or transaction costs in buying or selling assets.
There are no risk-free assets.
All investors have the same one period time horizon.
from decisions on
.
Lending, borrowing
Risk, return
Investing, financing
Risky assets, risk free assets
Buying stocks, buying bonds
When identifying undervalued and overvalued assets, which of the following
statements is false?
a) An asset is properly valued if its estimated rate of return is equal to
required rate of return.
b) An asset is considered overvalued if its estimated rate of return is below
required rate of return.
c) An asset is considered undervalued if its estimated rate of return is above
required rate of return.
d) An asset is considered overvalued if its required rate of return is below
estimated rate of return.
e) None of the above (that is, all are true statements)
(b)
5
its
its
its
its
Utilizing the security market line an investor owning a stock with a beta of (-2)
would expect the stock's return to
in a market that
was expected to decline 10 percent.
a) Rise or fall an indeterminate amount
b) Rise by 20.0%
369
c) Fall by 20.0%
d) Rise by 10.2%
e) Fall by 10.2%
(d)
6
The Capital Market Line (CML) refers to the efficient formed by creating
portfolios that
a)
b)
c)
d)
e)
(e)
7
Invest solely in the market portfolio M.
Lend at the risk free asset and invest in the market portfolio.
Borrow at the risk free asset and invest in the market portfolio.
Lend and borrow at the risk free rate and invest in the market portfolio.
Short sell the market portfolio.
As the number of stocks in a portfolio increases
a) The expected return of the portfolio increases because systematic
decreases.
b) The expected return of the portfolio increases because unsystematic
decreases.
c) The standard deviation of the portfolio increases because systematic
increases.
d) The standard deviation of the portfolio decreases because systematic
increases.
e) The standard deviation of the portfolio decreases because unsystematic
decreases.
(a)
8
9
10
risk
risk
Risk and required return on an asset.
Systematic risk and required return on an asset.
Risk and return on a diversified portfolio of assets.
Unsystematic risk and required return on an asset
Systematic risk and required return on a diversified portfolio of assets.
Confidence risk.
Maturity risk.
Expected inflation risk.
Call risk.
Return difference between small capitalization and large capitalization stocks.
In a multifactor model, confidence risk represents
a) Unanticipated changes in the level of overall business activity.
370
risk
In a macro-economic based risk factor model the following factor would be one
of many appropriate factors
a)
b)
c)
d)
e)
(d)
risk
The Security Market Line (SML) represents the relation between
a)
b)
c)
d)
e)
(a)
risk
b) Unanticipated changes in investors’ desired time to receive payouts.
c) Unanticipated changes in short term and long term inflation rates.
d) Unanticipated changes in the willingness of investors to take on investment
risk.
e) None of the above.
(b)
11
In a multifactor model, time horizon risk represents
a)
b)
c)
d)
Unanticipated changes in the level of overall business activity.
Unanticipated changes in investors’ desired time to receive payouts.
Unanticipated changes in short term and long term inflation rates.
Unanticipated changes in the willingness of investors to take on investment
risk.
e) None of the above.
(e)
12
In a micro-economic based risk factor model the following factor would be one
of many appropriate factors
a)
b)
c)
d)
e)
Confidence risk.
Maturity risk.
Expected inflation risk.
Call risk.
Return difference between small capitalization and large capitalization stocks.
MULTIPLE CHOICE PROBLEMS
(b)
1
Consider an asset that has a beta of 1.5. The return on the risk-free asset is 6.5%
and the expected return on the stock index is 15%. The estimated return on the
asset is 20%. Calculate the alpha for the asset.
a)
b)
c)
d)
e)
(b)
2
19.25%
0.75%
–0.75%
9.75%
9.0%
The table below provides factor risk sensitivities and factor risk premia for
a three factor model for a particular asset where factor 1 is MP the growth
rate in U.S. industrial production, factor 2 is UI the difference between
actual and expected inflation, and factor 3 is UPR the unanticipated change
in bond credit spread.
Risk Factor
Factor
Sensitivity(β)
Risk
Premium(λ)
371
MP
UI
UPR
1.76
-0.8
0.87
0.0259
-0.0432
0.0149
Calculate the expected excess return for the asset.
a)
b)
c)
d)
e)
(a)
3
The variance of returns for a risky asset is 25%. The variance of the error
term, Var(e) is 8%. What portion of the total risk of the asset, as measured
by variance, is unsystematic?
a)
b)
c)
d)
e)
(c)
4
5
5.2%
8.0%
3.2%
4.0%
1.2%
An investor wishes to construct a portfolio by borrowing 35% of his
original wealth and investing all the money in a stock index. The return on
the risk-free asset is 4.0% and the expected return on the stock index is
15%. Calculate the expected return on the portfolio.
a)
b)
c)
d)
e)
372
32%
8%
68%
25%
75%
An investor wishes to construct a portfolio consisting of a 40% allocation to
a stock index and a 60% allocation to a risk free asset. The return on the
risk-free asset is 2% and the expected return on the stock index is 10%. The
standard deviation of returns on the stock index 8%. Calculate the expected
standard deviation of the portfolio.
a)
b)
c)
d)
e)
(b)
12.32%
9.32%
4.56%
6.32%
8.02%
18.25%
18.85%
9.50%
15.00%
11.15%
(d)
6
An investor wishes to construct a portfolio consisting of a 70% allocation to
a stock index and a 30% allocation to a risk free asset. The return on the
risk-free asset is 4.5% and the expected return on the stock index is 12%.
Calculate the expected return on the portfolio.
a)
b)
c)
d)
e)
(d)
7
A stock has a beta of the stock is 1.1. The risk free rate is 2.5% and the return on
the market is 12%. The estimated return for the stock is 14%. According to the
CAPM you should
a)
b)
c)
d)
e)
(b)
8
9
10
1.0
0.0
-1.0
0.5
-0.5
The expected return for a stock, calculated using the CAPM, is 10.5%. The
market return is 9.5% and the beta of the stock is 1.50. Calculate the
implied risk-free rate.
a)
b)
c)
d)
e)
(d)
Sell because required return is 9.95%.
Sell because required return is 16.5%.
Buy because required return 11.5%.
Buy because required return is 12.95%.
Short because it is undervalued.
Consider a risky asset that has a standard deviation of returns of 15.
Calculate the correlation between the risky asset and a risk free asset.
a)
b)
c)
d)
e)
(a)
8.25%
16.50%
17.50%
9.75%
14.38%
7.50%
13.91%
17.50%
21.88%
14.38%
The expected return for a stock, calculated using the CAPM, is 25%. The
risk free rate is 7.5% and the beta of the stock is 0.80. Calculate the implied
return on the market.
a) 7.50%
b) 13.91%
c) 17.50%
373
d) 21.88%
e) 14.38%
(c)
11
The expected return for Zbrite stock calculated using the CAPM is 15.5%.
The risk free rate is 3.5% and the beta of the stock is 1.2. Calculate the
implied market risk premium.
a)
b)
c)
d)
e)
(d)
12
5.5%
6.5%
10.0%
15.5%
12.0%
Calculate the expected return for Express Inc. which has a beta of .69 when
the risk free rate is.09 and you expect the market return to be .14.
a)
b)
c)
d)
e)
0.05%
13.91%
10.92%
12.45%
14.25%
USE THE FOLLOWING INFORMATION FOR THE NEXT THREE PROBLEMS
You expect the risk-free rate (RFR) to be 5 percent and the market return to be 9 percent. You
also have the following information about three stocks.
STOCK
X
Y
Z
(b)
13
BETA
1.50
0.50
2.00
CURRENT
PRICE
$ 22
$ 40
$ 45
EXPECTED
PRICE
$ 23
$ 43
$ 49
EXPECTED
DIVIDEND
$ 0.75
$ 1.50
$ 1.00
What are the expected (required) rates of return for the three stocks (in the order
X, Y, Z)?
a)
b)
c)
d)
e)
(a)
374
14
16.50%, 5.50%, 22.00%
11.00%, 7.00%, 13.00%
7.95%, 11.25%, 11.11%
6.20%, 2.20%, 8.20%
15.00%, 3.50%, 7.30%
What are the estimated rates of return for the three stocks (in the order X, Y, Z)?
a)
b)
c)
d)
e)
(e) 15
7.95%, 11.25%, 11.11%
6.20%, 2.20%, 8.20%
16.50%, 5.50%, 22.00%
11.00%, 7.00%, 13.00%
15.00%, 3.50%, 7.30%
What is your investment strategy concerning the three stocks?
a)
b)
c)
d)
e)
Buy stock Y, it is undervalued.
Buy stock X and Z, they are undervalued.
Sell stocks X and Z, they are overvalued.
Sell stock Y, it is overvalued.
Choices a and c
USE THE FOLLOWING INFORMATION FOR THE NEXT FOUR PROBLEMS
Year
1
2
3
4
5
6
(a)
16
17
18
0.4255
0.5929
5.6825
9.4163
0.3333
Compute the correlation coefficient between GBC and the Market Index.
a)
b)
c)
d)
e)
(b)
Return for
Market
12
13
17
-15
-8
9
Compute the beta for GBC Company using the historic returns presented above.
a)
b)
c)
d)
e)
(e)
Return for
GBC
25
10
5
-13
11
-20
0.4255
0.5929
5.6825
9.4163
0.3333
Compute the intercept of the characteristic line
375
a)
b)
c)
d)
e)
(d)
19
0.4255
1.013
1.4385
0.5875
0.5219
The equation of the characteristic line is
a)
b)
c)
d)
e)
RGBC + 1.013 = 0.4255(RMarket)
RGBC = 1.013 - 0.4255(RMarket)
RMarket = 1.013 + 0.4255(RGBC)
RGBC = 1.013 + 0.4255(RMarket)
RMarket = 1.013 - 0.4255(RMarket)
CHAPTER 9
ANSWERS TO PROBLEMS
1
6.5 + 1.5(15 – 6.5) = 19.25%
alpha = 20 –19.25 = 0.75%
2
The table below shows the relevant calculations
Risk
Factor
Factor
Sensitivity(β)
MP
1.76
UI
-0.8
UPR
0.87
Expected return
Risk
Premium(λ)
0.0259
-0.0432
0.0149
(β)x(λ)
0.0456
0.0346
0.013
0.1232
3
8%/25% = 0.32. = 32% unsystematic.
4
0.4(0.08) = 0.032 or 3.2%
5
-0.35(4) + 1.35(15) = 18.85%
6
E(R)= 0.3(4.5) + 0.7(12) = 9.75%
7
E(R)= 2.5 + 1.1(12 – 2.5) = 12.95%. Buy the stock is undervalued.
8
The correlation between a risky asset and a risk-free
asset is always zero.
9
10.5 = X + 1.5(9.5 – X). X = 7.5%.
376
10
25 = 7.5 + 0.8(X). X = 14.38%. Return on market = 14.38 + 7.5 = 21.88%
11
15.5 = 3.5 + 1.2(X). X = 10%.
12
k = .09 + .69 (.14 - .09) = .1245 = 12.45%
For problems 13 - 15
STOCK
REQUIRED
ESTIMATED
EVALUATION
X
.05 + 1.50(.09 - .05) = 11%
(23 - 22 + 0.75)/22 = 7.95%
Overvalued
Y
.05 + 0.50(.09 -.05) = 7%
(43 - 40 + 1.50)/40 = 11.25%
Undervalued
Z
.05 + 2.00(.09 - .05) = 13%
(49 - 45 + 1.00)/45 = 11.11%
Overvalued
For problems 16 – 19
The table below shows the relevant calculations.
16
(1)
(2)
(3)
Year
1
2
3
4
5
6
Total
Average
Variance
Std. Dev.
Covariance
Correlation
Beta
GBC
25
10
5
-13
11
-20
18
3.0000
Market
12
13
17
-15
-8
9
28
4.67
(4)
GBC
(R-E(R ))2
484.00
49.00
4.00
256.00
64.00
529.00
1386.00
(5)
Market
(R-E(R ))2
53.73
69.39
152.03
386.91
160.53
18.75
841.33
277.20
16.65
168.27
12.97
(6)
GBC
R-E(R )
22.00
7.00
2.00
-16.00
8.00
-23.00
(7)
Market
R-E(R )
7.33
8.33
12.33
-19.67
-12.67
4.33
(8)
(6) x (7)
161.26
58.31
24.66
314.72
-101.36
-99.59
358.00
71.60
0.33
0.4255
Beta for GBC Computer is computed as follows:
Beta = Cov(GBC, Market)/ VarianceMarket
Beta = 18.40/82 = 0.2244
17
The correlation coefficient can be computed as follows:
377
Correlation = Cov(GBC, Market)/(SDGBC x SDMarket)
= 71.6/(16.65 x 12.97) = 0.33
Where:
SDGBC = [1386/5]1/2 = 16.65
SDMarket = [841.33/5]1/2 = 12.97
Cov(GBC, Market) = 358/5 = 71.60
18
The alpha or intercept of the characteristic line is computed as follows:
alpha = 3.0 - [(0.4255)(4.67)] = 1.013%
19
378
RGBC = 1.013 + 0.4255(RMarket)