Solution Manual For Investments, 12th Edition
Solution Manual For Investments, 12th Edition makes solving textbook questions easier with expertly crafted solutions.
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CHAPTER 1: THE INVESTMENT ENVIRONMENT
1-1
CHAPTER 1: THE INVESTMENT ENVIRONMENT
PROBLEM SETS
1. While it is ultimately true that real assets determine the material well-being of an
economy, financial innovation in the form of bundling and unbundling securities
creates opportunities for investors to form more efficient portfolios. Both
institutional and individual investors can benefit when financial engineering creates
new products that allow them to manage their portfolios of financial assets more
efficiently. Bundling and unbundling create financial products with new properties
and sensitivities to various sources of risk that allows investors to reduce volatility
by hedging particular sources of risk more efficiently.
2. Securitization requires access to a large number of potential investors. To attract
these investors, the capital market needs:
1. a safe system of business laws and low probability of confiscatory
taxation/regulation;
2. a well-developed investment banking industry;
3. a well-developed system of brokerage and financial transactions; and
4. well-developed media, particularly financial reporting.
These characteristics are found in (indeed make for) a well-developed financial
market.
3. Securitization leads to disintermediation; that is, securitization provides a means
for market participants to bypass intermediaries. For example, mortgage-backed
securities channel funds to the housing market without requiring that banks or
thrift institutions make loans from their own portfolios. Securitization works well
and can benefit many, but only if the market for these securities is highly liquid.
As securitization progresses, however, and financial intermediaries lose
opportunities, they must increase other revenue-generating activities such as
providing short-term liquidity to consumers and small business and financial
services.
4. The existence of efficient capital markets and the liquid trading of financial assets
make it easy for large firms to raise the capital needed to finance their investments
in real assets. If Ford, for example, could not issue stocks or bonds to the general
public, it would have a far more difficult time raising capital. Contraction of the
supply of financial assets would make financing more difficult, thereby increasing
the cost of capital. A higher cost of capital results in less investment and lower
real growth.
1-1
CHAPTER 1: THE INVESTMENT ENVIRONMENT
PROBLEM SETS
1. While it is ultimately true that real assets determine the material well-being of an
economy, financial innovation in the form of bundling and unbundling securities
creates opportunities for investors to form more efficient portfolios. Both
institutional and individual investors can benefit when financial engineering creates
new products that allow them to manage their portfolios of financial assets more
efficiently. Bundling and unbundling create financial products with new properties
and sensitivities to various sources of risk that allows investors to reduce volatility
by hedging particular sources of risk more efficiently.
2. Securitization requires access to a large number of potential investors. To attract
these investors, the capital market needs:
1. a safe system of business laws and low probability of confiscatory
taxation/regulation;
2. a well-developed investment banking industry;
3. a well-developed system of brokerage and financial transactions; and
4. well-developed media, particularly financial reporting.
These characteristics are found in (indeed make for) a well-developed financial
market.
3. Securitization leads to disintermediation; that is, securitization provides a means
for market participants to bypass intermediaries. For example, mortgage-backed
securities channel funds to the housing market without requiring that banks or
thrift institutions make loans from their own portfolios. Securitization works well
and can benefit many, but only if the market for these securities is highly liquid.
As securitization progresses, however, and financial intermediaries lose
opportunities, they must increase other revenue-generating activities such as
providing short-term liquidity to consumers and small business and financial
services.
4. The existence of efficient capital markets and the liquid trading of financial assets
make it easy for large firms to raise the capital needed to finance their investments
in real assets. If Ford, for example, could not issue stocks or bonds to the general
public, it would have a far more difficult time raising capital. Contraction of the
supply of financial assets would make financing more difficult, thereby increasing
the cost of capital. A higher cost of capital results in less investment and lower
real growth.
CHAPTER 1: THE INVESTMENT ENVIRONMENT
1-1
CHAPTER 1: THE INVESTMENT ENVIRONMENT
PROBLEM SETS
1. While it is ultimately true that real assets determine the material well-being of an
economy, financial innovation in the form of bundling and unbundling securities
creates opportunities for investors to form more efficient portfolios. Both
institutional and individual investors can benefit when financial engineering creates
new products that allow them to manage their portfolios of financial assets more
efficiently. Bundling and unbundling create financial products with new properties
and sensitivities to various sources of risk that allows investors to reduce volatility
by hedging particular sources of risk more efficiently.
2. Securitization requires access to a large number of potential investors. To attract
these investors, the capital market needs:
1. a safe system of business laws and low probability of confiscatory
taxation/regulation;
2. a well-developed investment banking industry;
3. a well-developed system of brokerage and financial transactions; and
4. well-developed media, particularly financial reporting.
These characteristics are found in (indeed make for) a well-developed financial
market.
3. Securitization leads to disintermediation; that is, securitization provides a means
for market participants to bypass intermediaries. For example, mortgage-backed
securities channel funds to the housing market without requiring that banks or
thrift institutions make loans from their own portfolios. Securitization works well
and can benefit many, but only if the market for these securities is highly liquid.
As securitization progresses, however, and financial intermediaries lose
opportunities, they must increase other revenue-generating activities such as
providing short-term liquidity to consumers and small business and financial
services.
4. The existence of efficient capital markets and the liquid trading of financial assets
make it easy for large firms to raise the capital needed to finance their investments
in real assets. If Ford, for example, could not issue stocks or bonds to the general
public, it would have a far more difficult time raising capital. Contraction of the
supply of financial assets would make financing more difficult, thereby increasing
the cost of capital. A higher cost of capital results in less investment and lower
real growth.
1-1
CHAPTER 1: THE INVESTMENT ENVIRONMENT
PROBLEM SETS
1. While it is ultimately true that real assets determine the material well-being of an
economy, financial innovation in the form of bundling and unbundling securities
creates opportunities for investors to form more efficient portfolios. Both
institutional and individual investors can benefit when financial engineering creates
new products that allow them to manage their portfolios of financial assets more
efficiently. Bundling and unbundling create financial products with new properties
and sensitivities to various sources of risk that allows investors to reduce volatility
by hedging particular sources of risk more efficiently.
2. Securitization requires access to a large number of potential investors. To attract
these investors, the capital market needs:
1. a safe system of business laws and low probability of confiscatory
taxation/regulation;
2. a well-developed investment banking industry;
3. a well-developed system of brokerage and financial transactions; and
4. well-developed media, particularly financial reporting.
These characteristics are found in (indeed make for) a well-developed financial
market.
3. Securitization leads to disintermediation; that is, securitization provides a means
for market participants to bypass intermediaries. For example, mortgage-backed
securities channel funds to the housing market without requiring that banks or
thrift institutions make loans from their own portfolios. Securitization works well
and can benefit many, but only if the market for these securities is highly liquid.
As securitization progresses, however, and financial intermediaries lose
opportunities, they must increase other revenue-generating activities such as
providing short-term liquidity to consumers and small business and financial
services.
4. The existence of efficient capital markets and the liquid trading of financial assets
make it easy for large firms to raise the capital needed to finance their investments
in real assets. If Ford, for example, could not issue stocks or bonds to the general
public, it would have a far more difficult time raising capital. Contraction of the
supply of financial assets would make financing more difficult, thereby increasing
the cost of capital. A higher cost of capital results in less investment and lower
real growth.
CHAPTER 1: THE INVESTMENT ENVIRONMENT
1-2
5. Even if the firm does not need to issue stock in any particular year, the stock market
is still important to the financial manager. The stock price provides important
information about how the market values the firm's investment projects. For example,
if the stock price rises considerably, managers might conclude that the market
believes the firm's future prospects are bright. This might be a useful signal to the
firm to proceed with an investment such as an expansion of the firm's business.
In addition, shares that can be traded in the secondary market are more attractive to
initial investors since they know that they will be able to sell their shares. This in
turn makes investors more willing to buy shares in a primary offering and thus
improves the terms on which firms can raise money in the equity market.
Remember that stock exchanges like those in New York, London, and Paris are the
heart of capitalism, in which firms can raise capital quickly in primary markets
because investors know there are liquid secondary markets.
6. a. No. The increase in price did not add to the productive capacity of the
economy.
b. Yes, the value of the equity held in these assets has increased.
c. Future homeowners as a whole are worse off, since mortgage liabilities have
also increased. In addition, this housing price bubble will eventually burst and
society as a whole (and most likely taxpayers) will suffer the damage.
7. a. The bank loan is a financial liability for Lanni, and a financial asset for the bank.
The cash Lanni receives is a financial asset. The new financial asset created is
Lanni's promissory note to repay the loan.
b. Lanni transfers financial assets (cash) to the software developers. In return,
Lanni receives the completed software package, which is a real asset. No
financial assets are created or destroyed; cash is simply transferred from one party
to another.
c. Lanni exchanges the real asset (the software) for a financial asset, which is 1,250
shares of Microsoft stock. If Microsoft issues new shares in order to pay Lanni,
then this would represent the creation of new financial assets.
d. By selling its shares in Microsoft, Lanni exchanges one financial asset (1,250
shares of stock) for another ($125,000 in cash). Lanni uses the financial asset of
$50,000 in cash to repay the bank and retire its promissory note. The bank must
return its financial asset to Lanni. The loan is "destroyed" in the transaction, since it
is retired when paid off and no longer exists.
1-2
5. Even if the firm does not need to issue stock in any particular year, the stock market
is still important to the financial manager. The stock price provides important
information about how the market values the firm's investment projects. For example,
if the stock price rises considerably, managers might conclude that the market
believes the firm's future prospects are bright. This might be a useful signal to the
firm to proceed with an investment such as an expansion of the firm's business.
In addition, shares that can be traded in the secondary market are more attractive to
initial investors since they know that they will be able to sell their shares. This in
turn makes investors more willing to buy shares in a primary offering and thus
improves the terms on which firms can raise money in the equity market.
Remember that stock exchanges like those in New York, London, and Paris are the
heart of capitalism, in which firms can raise capital quickly in primary markets
because investors know there are liquid secondary markets.
6. a. No. The increase in price did not add to the productive capacity of the
economy.
b. Yes, the value of the equity held in these assets has increased.
c. Future homeowners as a whole are worse off, since mortgage liabilities have
also increased. In addition, this housing price bubble will eventually burst and
society as a whole (and most likely taxpayers) will suffer the damage.
7. a. The bank loan is a financial liability for Lanni, and a financial asset for the bank.
The cash Lanni receives is a financial asset. The new financial asset created is
Lanni's promissory note to repay the loan.
b. Lanni transfers financial assets (cash) to the software developers. In return,
Lanni receives the completed software package, which is a real asset. No
financial assets are created or destroyed; cash is simply transferred from one party
to another.
c. Lanni exchanges the real asset (the software) for a financial asset, which is 1,250
shares of Microsoft stock. If Microsoft issues new shares in order to pay Lanni,
then this would represent the creation of new financial assets.
d. By selling its shares in Microsoft, Lanni exchanges one financial asset (1,250
shares of stock) for another ($125,000 in cash). Lanni uses the financial asset of
$50,000 in cash to repay the bank and retire its promissory note. The bank must
return its financial asset to Lanni. The loan is "destroyed" in the transaction, since it
is retired when paid off and no longer exists.
CHAPTER 1: THE INVESTMENT ENVIRONMENT
1-3
8. a.
Assets Liabilities &
Shareholders’ Equity
Cash $ 70,000 Bank loan $ 50,000
Computers 30,000 Shareholders’ equity 50,000
Total $100,000 Total $100,000
Ratio of real assets to total assets = $30,000/$100,000 = 0.30
b.
Assets Liabilities &
Shareholders’ Equity
Software product* $ 70,000 Bank loan $ 50,000
Computers 30,000 Shareholders’ equity 50,000
Total $100,000 Total $100,000
*Valued at cost
Ratio of real assets to total assets = $100,000/$100,000 = 1.0
c.
Assets Liabilities &
Shareholders’ Equity
Microsoft shares $125,000 Bank loan $ 50,000
Computers 30,000 Shareholders’ equity 105,000
Total $155,000 Total $155,000
Ratio of real assets to total assets = $30,000/$155,000 = 0.19
Conclusion: when the firm starts up and raises working capital, it is characterized by
a low ratio of real assets to total assets. When it is in full production, it has a high
ratio of real assets to total assets. When the project "shuts down" and the firm sells it
off for cash, financial assets once again replace real assets.
9. a. For commercial banks, the ratio is: $134.3/$17,532.8 = 0.0077
b. For nonfinancial firms, the ratio is: $23,678/$45,464 = 0.5208
c. The difference should be expected primarily because the bulk of the
business of financial institutions is to make loans and the bulk of the
business of non-financial corporations is to invest in equipment,
manufacturing plants, and property. The loans are financial assets for
financial institutions, but the investments of non-financial corporations are
real assets.
10. a. Primary-market transaction in which gold certificates are being offered to
public investors for the first time by an underwriting syndicate led by JW Korth
Capital.
1-3
8. a.
Assets Liabilities &
Shareholders’ Equity
Cash $ 70,000 Bank loan $ 50,000
Computers 30,000 Shareholders’ equity 50,000
Total $100,000 Total $100,000
Ratio of real assets to total assets = $30,000/$100,000 = 0.30
b.
Assets Liabilities &
Shareholders’ Equity
Software product* $ 70,000 Bank loan $ 50,000
Computers 30,000 Shareholders’ equity 50,000
Total $100,000 Total $100,000
*Valued at cost
Ratio of real assets to total assets = $100,000/$100,000 = 1.0
c.
Assets Liabilities &
Shareholders’ Equity
Microsoft shares $125,000 Bank loan $ 50,000
Computers 30,000 Shareholders’ equity 105,000
Total $155,000 Total $155,000
Ratio of real assets to total assets = $30,000/$155,000 = 0.19
Conclusion: when the firm starts up and raises working capital, it is characterized by
a low ratio of real assets to total assets. When it is in full production, it has a high
ratio of real assets to total assets. When the project "shuts down" and the firm sells it
off for cash, financial assets once again replace real assets.
9. a. For commercial banks, the ratio is: $134.3/$17,532.8 = 0.0077
b. For nonfinancial firms, the ratio is: $23,678/$45,464 = 0.5208
c. The difference should be expected primarily because the bulk of the
business of financial institutions is to make loans and the bulk of the
business of non-financial corporations is to invest in equipment,
manufacturing plants, and property. The loans are financial assets for
financial institutions, but the investments of non-financial corporations are
real assets.
10. a. Primary-market transaction in which gold certificates are being offered to
public investors for the first time by an underwriting syndicate led by JW Korth
Capital.
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CHAPTER 1: THE INVESTMENT ENVIRONMENT
1-4
b. The certificates are derivative assets because they represent an investment in
physical gold, but each investor receives a certificate and no gold. Note that
investors can convert the certificate into gold during the four-year period.
11. a. A fixed salary means that compensation is (at least in the short run)
independent of the firm's success. This salary structure does not tie the manager’s
immediate compensation to the success of the firm, so a manager might not feel
too compelled to work hard to maximize firm value. However, the manager
might view this as the safest compensation structure and therefore value it more
highly.
b. A salary that is paid in the form of stock in the firm means that the manager earns
the most when the shareholders’ wealth is maximized. Five years of vesting helps
align the interests of the employee with the long-term performance of the firm. This
structure is therefore most likely to align the interests of managers and shareholders.
If stock compensation is overdone, however, the manager might view it as overly
risky since the manager’s career is already linked to the firm, and this undiversified
exposure would be exacerbated with a large stock position in the firm.
c. A profit-linked salary creates great incentives for managers to contribute to the
firm’s success. However, a manager whose salary is tied to short-term profits will be
risk seeking, especially if these short-term profits determine salary or if the
compensation structure does not bear the full cost of the project’s risks. Shareholders,
in contrast, bear the losses as well as the gains on the project and might be less
willing to assume that risk.
12. Even if an individual shareholder could monitor and improve managers’ performance
and thereby increase the value of the firm, the payoff would be small, since the
ownership share in a large corporation would be very small. For example, if you own
$10,000 of Ford stock and can increase the value of the firm by 5%, a very ambitious
goal, you benefit by only: 0.05 $10,000 = $500. The cost, both personal and
financial to an individual investor, is likely to be prohibitive and would typically
easily exceed any accrued benefits, in this case $500.
In contrast, a creditor, such as a bank, that has a multimillion-dollar loan outstanding
to the firm has a big stake in making sure that the firm can repay the loan. It is clearly
worthwhile for the bank to spend considerable resources to monitor the firm.
13. Mutual funds accept funds from small investors and invest, on behalf of these
investors, in the domestic and international securities markets.
Pension funds accept funds and then invest in a wide range of financial securities, on
behalf of current and future retirees, thereby channeling funds from one sector of the
economy to another.
1-4
b. The certificates are derivative assets because they represent an investment in
physical gold, but each investor receives a certificate and no gold. Note that
investors can convert the certificate into gold during the four-year period.
11. a. A fixed salary means that compensation is (at least in the short run)
independent of the firm's success. This salary structure does not tie the manager’s
immediate compensation to the success of the firm, so a manager might not feel
too compelled to work hard to maximize firm value. However, the manager
might view this as the safest compensation structure and therefore value it more
highly.
b. A salary that is paid in the form of stock in the firm means that the manager earns
the most when the shareholders’ wealth is maximized. Five years of vesting helps
align the interests of the employee with the long-term performance of the firm. This
structure is therefore most likely to align the interests of managers and shareholders.
If stock compensation is overdone, however, the manager might view it as overly
risky since the manager’s career is already linked to the firm, and this undiversified
exposure would be exacerbated with a large stock position in the firm.
c. A profit-linked salary creates great incentives for managers to contribute to the
firm’s success. However, a manager whose salary is tied to short-term profits will be
risk seeking, especially if these short-term profits determine salary or if the
compensation structure does not bear the full cost of the project’s risks. Shareholders,
in contrast, bear the losses as well as the gains on the project and might be less
willing to assume that risk.
12. Even if an individual shareholder could monitor and improve managers’ performance
and thereby increase the value of the firm, the payoff would be small, since the
ownership share in a large corporation would be very small. For example, if you own
$10,000 of Ford stock and can increase the value of the firm by 5%, a very ambitious
goal, you benefit by only: 0.05 $10,000 = $500. The cost, both personal and
financial to an individual investor, is likely to be prohibitive and would typically
easily exceed any accrued benefits, in this case $500.
In contrast, a creditor, such as a bank, that has a multimillion-dollar loan outstanding
to the firm has a big stake in making sure that the firm can repay the loan. It is clearly
worthwhile for the bank to spend considerable resources to monitor the firm.
13. Mutual funds accept funds from small investors and invest, on behalf of these
investors, in the domestic and international securities markets.
Pension funds accept funds and then invest in a wide range of financial securities, on
behalf of current and future retirees, thereby channeling funds from one sector of the
economy to another.
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CHAPTER 1: THE INVESTMENT ENVIRONMENT
1-5
Venture capital firms pool the funds of private investors and invest in start-up firms.
Banks accept deposits from customers and loan those funds to businesses or use the
funds to buy securities of large corporations.
14. Treasury bills serve a purpose for investors who prefer a low-risk investment.
The lower average rate of return compared to stocks is the price investors pay
for predictability of investment performance and portfolio value.
15. With a top-down investing style, you focus on asset allocation or the broad
composition of the entire portfolio, which is the major determinant of overall
performance. Moreover, top-down management is the natural way to establish a
portfolio with a level of risk consistent with your risk tolerance. The disadvantage of
an exclusive emphasis on top-down issues is that you may forfeit the potential high
returns that could result from identifying and concentrating in undervalued securities
or sectors of the market.
With a bottom-up investing style, you try to benefit from identifying undervalued
securities. The disadvantage is that investors might tend to overlook the overall
composition of your portfolio, which may result in a non-diversified portfolio or a
portfolio with a risk level inconsistent with the appropriate level of risk tolerance. In
addition, this technique tends to require more active management, thus generating
more transaction costs. Finally, the bottom-up analysis may be incorrect, in which case
there will be a fruitlessly expended effort and money attempting to beat a simple buy-
and-hold strategy.
16. You should be skeptical. If the author actually knows how to achieve such returns, one
must question why the author would then be so ready to sell the secret to others.
Financial markets are very competitive; one of the implications of this fact is that
riches do not come easily. High expected returns require bearing some risk, and
obvious bargains are few and far between. Odds are that the only one getting rich from
the book is its author.
17. Financial assets provide for a means to acquire real assets as well as an expansion
of these real assets. Financial assets provide a measure of liquidity to real assets
and allow for investors to more effectively reduce risk through diversification.
18. Allowing traders to share in the profits increases the traders’ willingness to
assume risk. Traders will share in the upside potential directly in the form of
higher compensation but only in the downside indirectly in the form of potential
job loss if performance is bad enough. This scenario creates a form of agency
conflict known as moral hazard, in which the owners of the financial institution
share in both the total profits and losses, while the traders will tend to share more
of the gains than the losses.
1-5
Venture capital firms pool the funds of private investors and invest in start-up firms.
Banks accept deposits from customers and loan those funds to businesses or use the
funds to buy securities of large corporations.
14. Treasury bills serve a purpose for investors who prefer a low-risk investment.
The lower average rate of return compared to stocks is the price investors pay
for predictability of investment performance and portfolio value.
15. With a top-down investing style, you focus on asset allocation or the broad
composition of the entire portfolio, which is the major determinant of overall
performance. Moreover, top-down management is the natural way to establish a
portfolio with a level of risk consistent with your risk tolerance. The disadvantage of
an exclusive emphasis on top-down issues is that you may forfeit the potential high
returns that could result from identifying and concentrating in undervalued securities
or sectors of the market.
With a bottom-up investing style, you try to benefit from identifying undervalued
securities. The disadvantage is that investors might tend to overlook the overall
composition of your portfolio, which may result in a non-diversified portfolio or a
portfolio with a risk level inconsistent with the appropriate level of risk tolerance. In
addition, this technique tends to require more active management, thus generating
more transaction costs. Finally, the bottom-up analysis may be incorrect, in which case
there will be a fruitlessly expended effort and money attempting to beat a simple buy-
and-hold strategy.
16. You should be skeptical. If the author actually knows how to achieve such returns, one
must question why the author would then be so ready to sell the secret to others.
Financial markets are very competitive; one of the implications of this fact is that
riches do not come easily. High expected returns require bearing some risk, and
obvious bargains are few and far between. Odds are that the only one getting rich from
the book is its author.
17. Financial assets provide for a means to acquire real assets as well as an expansion
of these real assets. Financial assets provide a measure of liquidity to real assets
and allow for investors to more effectively reduce risk through diversification.
18. Allowing traders to share in the profits increases the traders’ willingness to
assume risk. Traders will share in the upside potential directly in the form of
higher compensation but only in the downside indirectly in the form of potential
job loss if performance is bad enough. This scenario creates a form of agency
conflict known as moral hazard, in which the owners of the financial institution
share in both the total profits and losses, while the traders will tend to share more
of the gains than the losses.
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CHAPTER 1: THE INVESTMENT ENVIRONMENT
1-6
19. Answers may vary, however, students should touch on the following: increased
transparency, regulations to promote capital adequacy by increasing the frequency
of gain or loss settlement, incentives to discourage excessive risk taking, and the
promotion of more accurate and unbiased risk assessment.
1-6
19. Answers may vary, however, students should touch on the following: increased
transparency, regulations to promote capital adequacy by increasing the frequency
of gain or loss settlement, incentives to discourage excessive risk taking, and the
promotion of more accurate and unbiased risk assessment.
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Chapter 2 - Asset Classes and Financial Instruments
2-1
CHAPTER 2: ASSET CLASSES AND FINANCIAL
INSTRUMENTS
PROBLEM SETS
1. Preferred stock is like long-term debt in that it typically promises a fixed payment
each year. In this way, it is a perpetuity. Preferred stock is also like long-term debt
in that it does not give the holder voting rights in the firm.
Preferred stock is like equity in that the firm is under no contractual obligation to
make the preferred stock dividend payments. Failure to make payments does not set
off corporate bankruptcy. With respect to the priority of claims to the assets of the
firm in the event of corporate bankruptcy, preferred stock has a higher priority than
common equity but a lower priority than bonds.
2. Money market securities are called cash equivalents because of their high level
of liquidity. The prices of money market securities are very stable, and they can
be converted to cash (i.e., sold) on very short notice and with very low
transaction costs. Examples of money market securities include Treasury bills,
commercial paper, and banker's acceptances, each of which is highly marketable
and traded in the secondary market.
3. (a) A repurchase agreement is an agreement whereby the seller of a security
agrees to “repurchase” it from the buyer on an agreed upon date at an agreed
upon price. Repos are typically used by securities dealers as a means for
obtaining funds to purchase securities.
4. Spreads between risky commercial paper and risk-free government securities
will widen. Deterioration of the economy increases the likelihood of default on
commercial paper, making them more risky. Investors will demand a greater
premium on all risky debt securities, not just commercial paper.
5.
Corp. Bonds Preferred Stock Common Stock
Voting rights (typically) Yes
contractual obligation Yes
Perpetual payments Yes Yes
Accumulated dividends Yes
Fixed payments (typically) Yes Yes
Payment preference First Second Third
2-1
CHAPTER 2: ASSET CLASSES AND FINANCIAL
INSTRUMENTS
PROBLEM SETS
1. Preferred stock is like long-term debt in that it typically promises a fixed payment
each year. In this way, it is a perpetuity. Preferred stock is also like long-term debt
in that it does not give the holder voting rights in the firm.
Preferred stock is like equity in that the firm is under no contractual obligation to
make the preferred stock dividend payments. Failure to make payments does not set
off corporate bankruptcy. With respect to the priority of claims to the assets of the
firm in the event of corporate bankruptcy, preferred stock has a higher priority than
common equity but a lower priority than bonds.
2. Money market securities are called cash equivalents because of their high level
of liquidity. The prices of money market securities are very stable, and they can
be converted to cash (i.e., sold) on very short notice and with very low
transaction costs. Examples of money market securities include Treasury bills,
commercial paper, and banker's acceptances, each of which is highly marketable
and traded in the secondary market.
3. (a) A repurchase agreement is an agreement whereby the seller of a security
agrees to “repurchase” it from the buyer on an agreed upon date at an agreed
upon price. Repos are typically used by securities dealers as a means for
obtaining funds to purchase securities.
4. Spreads between risky commercial paper and risk-free government securities
will widen. Deterioration of the economy increases the likelihood of default on
commercial paper, making them more risky. Investors will demand a greater
premium on all risky debt securities, not just commercial paper.
5.
Corp. Bonds Preferred Stock Common Stock
Voting rights (typically) Yes
contractual obligation Yes
Perpetual payments Yes Yes
Accumulated dividends Yes
Fixed payments (typically) Yes Yes
Payment preference First Second Third
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Chapter 2 - Asset Classes and Financial Instruments
2-2
6. Municipal bond interest is tax-exempt at the federal level and possibly at the
state level as well. When facing higher marginal tax rates, a high-income
investor would be more inclined to invest in tax-exempt securities.
7. a. You would have to pay the ask price of:
101.9297% of par value of $1,000 = $1,019.297
b. The coupon rate is 3.000%; implying coupon payments of $30.00 annually
or, more precisely $15.00 (semiannually).
c. The yield to maturity on a fixed income security is also known as its required
return and is reported by The Wall Street Journal and others in the financial
press as the ask yield. In this case, the yield to maturity is 2.902%. An investor
buying this security today and holding it until it matures will earn an annual
return of 2.902%. Students will learn in a later chapter how to compute both
the price and the yield to maturity with a financial calculator.
8. Treasury bills are discount securities that mature for $10,000. Therefore, a specific T-
bill price is simply the maturity value divided by one plus the semi-annual return:
P = $10,000/1.02 = $9,803.92
9. The total before-tax income is $4. After the 50% exclusion for preferred stock
dividends, the taxable income is: 0.50 $4 = $2.00
Therefore, taxes are: 0.30 $2.00 = $0.60
After-tax income is: $4.00 – $0.60 = $3.40
Rate of return is: $3.40/$40.00 = 8.50%
10. a. You could buy: $5,000/$57.94 = 86.30 shares. Since it is not possible to trade
in fractions of shares, you could buy 86 shares of Herbalife.
b. Your annual dividend income would be: 86 $1.20 = $103.20
c. The price-to-earnings ratio is 47.75 and the price is $57.94. Therefore:
$57.94/Earnings per share = 47.75 Earnings per share = $1.21
d. Herbalife closed today at $57.94, which was $1.39 lower than yesterday’s
price of $59.33.
2-2
6. Municipal bond interest is tax-exempt at the federal level and possibly at the
state level as well. When facing higher marginal tax rates, a high-income
investor would be more inclined to invest in tax-exempt securities.
7. a. You would have to pay the ask price of:
101.9297% of par value of $1,000 = $1,019.297
b. The coupon rate is 3.000%; implying coupon payments of $30.00 annually
or, more precisely $15.00 (semiannually).
c. The yield to maturity on a fixed income security is also known as its required
return and is reported by The Wall Street Journal and others in the financial
press as the ask yield. In this case, the yield to maturity is 2.902%. An investor
buying this security today and holding it until it matures will earn an annual
return of 2.902%. Students will learn in a later chapter how to compute both
the price and the yield to maturity with a financial calculator.
8. Treasury bills are discount securities that mature for $10,000. Therefore, a specific T-
bill price is simply the maturity value divided by one plus the semi-annual return:
P = $10,000/1.02 = $9,803.92
9. The total before-tax income is $4. After the 50% exclusion for preferred stock
dividends, the taxable income is: 0.50 $4 = $2.00
Therefore, taxes are: 0.30 $2.00 = $0.60
After-tax income is: $4.00 – $0.60 = $3.40
Rate of return is: $3.40/$40.00 = 8.50%
10. a. You could buy: $5,000/$57.94 = 86.30 shares. Since it is not possible to trade
in fractions of shares, you could buy 86 shares of Herbalife.
b. Your annual dividend income would be: 86 $1.20 = $103.20
c. The price-to-earnings ratio is 47.75 and the price is $57.94. Therefore:
$57.94/Earnings per share = 47.75 Earnings per share = $1.21
d. Herbalife closed today at $57.94, which was $1.39 lower than yesterday’s
price of $59.33.
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Chapter 2 - Asset Classes and Financial Instruments
2-3
11. a. At t = 0, the value of the index is: (90 + 50 + 100)/3 = 80
At t = 1, the value of the index is: (95 + 45 + 110)/3 = 83.333
The rate of return is: (83.333/80) − 1 = 4.17%
b. In the absence of a split, Stock C would sell for 110, so the value of the
index would be: (95+45+110)/3 = 250/3 = 83.333 with a divisor of 3.
After the split, stock C sells for 55. Therefore, we need to find the divisor
(d) such that: 83.333 = (95 + 45 + 55)/d d = 2.340. The divisor fell,
which is always the case after one of the firms in an index splits its
shares.
c. The return is zero. The index remains unchanged because the return for
each stock separately equals zero.
12. a. Total market value at t = 0 is: ($9,000 + $10,000 + $20,000) = $39,000
Total market value at t = 1 is: ($9,500 + $9,000 + $22,000) = $40,500
Rate of return = ($40,500/$39,000) – 1 = 3.85%
b. The return on each stock is as follows:
rA = (95/90) – 1 = 0.0556
rB = (45/50) – 1 = –0.10
rC = (110/100) – 1 = 0.10
The equally weighted average is:
[0.0556 + (-0.10) + 0.10]/3 = 0.0185 = 1.85%
13. The after-tax yield on the corporate bonds is: 0.09 (1 – 0.30) = 0.063 = 6.30%
Therefore, municipals must offer a yield to maturity of at least 6.30%.
14. Equation (2.2) shows that the equivalent taxable yield is: r = rm /(1 – t), so simply
substitute each tax rate in the denominator to obtain the following:
a. 4.00%
b. 4.44%
c. 5.00%
d. 5.71%
2-3
11. a. At t = 0, the value of the index is: (90 + 50 + 100)/3 = 80
At t = 1, the value of the index is: (95 + 45 + 110)/3 = 83.333
The rate of return is: (83.333/80) − 1 = 4.17%
b. In the absence of a split, Stock C would sell for 110, so the value of the
index would be: (95+45+110)/3 = 250/3 = 83.333 with a divisor of 3.
After the split, stock C sells for 55. Therefore, we need to find the divisor
(d) such that: 83.333 = (95 + 45 + 55)/d d = 2.340. The divisor fell,
which is always the case after one of the firms in an index splits its
shares.
c. The return is zero. The index remains unchanged because the return for
each stock separately equals zero.
12. a. Total market value at t = 0 is: ($9,000 + $10,000 + $20,000) = $39,000
Total market value at t = 1 is: ($9,500 + $9,000 + $22,000) = $40,500
Rate of return = ($40,500/$39,000) – 1 = 3.85%
b. The return on each stock is as follows:
rA = (95/90) – 1 = 0.0556
rB = (45/50) – 1 = –0.10
rC = (110/100) – 1 = 0.10
The equally weighted average is:
[0.0556 + (-0.10) + 0.10]/3 = 0.0185 = 1.85%
13. The after-tax yield on the corporate bonds is: 0.09 (1 – 0.30) = 0.063 = 6.30%
Therefore, municipals must offer a yield to maturity of at least 6.30%.
14. Equation (2.2) shows that the equivalent taxable yield is: r = rm /(1 – t), so simply
substitute each tax rate in the denominator to obtain the following:
a. 4.00%
b. 4.44%
c. 5.00%
d. 5.71%
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Chapter 2 - Asset Classes and Financial Instruments
2-4
15. In an equally weighted index fund, each stock is given equal weight regardless of its
market capitalization. Smaller cap stocks will have the same weight as larger cap
stocks. The challenges are as follows:
• Given equal weights placed to smaller cap and larger cap, equal-
weighted indices (EWI) will tend to be more volatile than their market-
capitalization counterparts;
• It follows that EWIs are not good reflectors of the broad market that they
represent; EWIs underplay the economic importance of larger
companies.
• Turnover rates will tend to be higher, as an EWI must be rebalanced
back to its original target. By design, many of the transactions would be
among the smaller, less-liquid stocks.
16. a. The ten-year Treasury bond with the higher coupon rate will sell for a higher
price because its bondholder receives higher interest payments.
b. The call option with the lower exercise price has more value than one with a
higher exercise price.
c. The put option written on the lower priced stock has more value than one
written on a higher priced stock.
17. a. You bought the contract when the futures price was $3.96 (see Table
2.8). The contract closes at a price of $4.06, which is $0.10 more than the
original futures price. The contract multiplier is 5000. Therefore, the gain will
be: $0.08 5000 = $400.00
18. a. The call option gives you the right, but not the obligation to buy at $100; the
stock is trading in the secondary market at $103. Since the stock price
exceeds the exercise price, you exercise the call.
The payoff on the option will be: $103 - $100 = $3
The cost was originally $3.81, so the profit is: $3 - $3.81 = -$.81
b. Since the stock price is greater than the exercise price, you will exercise the call.
The payoff on the option will be: $103 - $95 = $8
The option originally cost $7.65, so the profit is $8 - $7.65 = $.35.
c. Owning the put option gives you the right, but not the obligation, to sell at $105, but
you could sell in the secondary market for $03 if you exercise the call the payoff on
the option will be: $105 - $103 = $2.
The option originally cost $4.79, so the profit is $2.00-$4.79 = -$2.79.
2-4
15. In an equally weighted index fund, each stock is given equal weight regardless of its
market capitalization. Smaller cap stocks will have the same weight as larger cap
stocks. The challenges are as follows:
• Given equal weights placed to smaller cap and larger cap, equal-
weighted indices (EWI) will tend to be more volatile than their market-
capitalization counterparts;
• It follows that EWIs are not good reflectors of the broad market that they
represent; EWIs underplay the economic importance of larger
companies.
• Turnover rates will tend to be higher, as an EWI must be rebalanced
back to its original target. By design, many of the transactions would be
among the smaller, less-liquid stocks.
16. a. The ten-year Treasury bond with the higher coupon rate will sell for a higher
price because its bondholder receives higher interest payments.
b. The call option with the lower exercise price has more value than one with a
higher exercise price.
c. The put option written on the lower priced stock has more value than one
written on a higher priced stock.
17. a. You bought the contract when the futures price was $3.96 (see Table
2.8). The contract closes at a price of $4.06, which is $0.10 more than the
original futures price. The contract multiplier is 5000. Therefore, the gain will
be: $0.08 5000 = $400.00
18. a. The call option gives you the right, but not the obligation to buy at $100; the
stock is trading in the secondary market at $103. Since the stock price
exceeds the exercise price, you exercise the call.
The payoff on the option will be: $103 - $100 = $3
The cost was originally $3.81, so the profit is: $3 - $3.81 = -$.81
b. Since the stock price is greater than the exercise price, you will exercise the call.
The payoff on the option will be: $103 - $95 = $8
The option originally cost $7.65, so the profit is $8 - $7.65 = $.35.
c. Owning the put option gives you the right, but not the obligation, to sell at $105, but
you could sell in the secondary market for $03 if you exercise the call the payoff on
the option will be: $105 - $103 = $2.
The option originally cost $4.79, so the profit is $2.00-$4.79 = -$2.79.
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Chapter 2 - Asset Classes and Financial Instruments
2-5
19. There is always a possibility that the option will be in-the-money at some time prior to
expiration. Investors will pay something for this possibility of a positive payoff.
20.
Value of Call at Expiration Initial Cost Profit
a. 0 4 -4
b. 0 4 -4
c. 0 4 -4
d. 5 4 1
e. 10 4 6
Value of Put at Expiration Initial Cost Profit
a. 10 6 4
b. 5 6 -1
c. 0 6 -6
d. 0 6 -6
e. 0 6 -6
21. A put option conveys the right to sell the underlying asset at the exercise price. A
short position in a futures contract carries an obligation to sell the underlying asset
at the futures price. Both positions, however, benefit if the price of the underlying
asset falls.
22. A call option conveys the right to buy the underlying asset at the exercise price. A
long position in a futures contract carries an obligation to buy the underlying asset
at the futures price. Both positions, however, benefit if the price of the underlying
asset rises.
CFA PROBLEMS
1. (d) There are tax advantages for corporations that own preferred shares.
2. The equivalent taxable yield is: 6.75%/(1 − 0.34) = 10.23%
3. (a) Writing a call entails unlimited potential losses as the stock price rises.
4. a. The taxable bond. With a zero tax bracket, the after-tax yield for the
2-5
19. There is always a possibility that the option will be in-the-money at some time prior to
expiration. Investors will pay something for this possibility of a positive payoff.
20.
Value of Call at Expiration Initial Cost Profit
a. 0 4 -4
b. 0 4 -4
c. 0 4 -4
d. 5 4 1
e. 10 4 6
Value of Put at Expiration Initial Cost Profit
a. 10 6 4
b. 5 6 -1
c. 0 6 -6
d. 0 6 -6
e. 0 6 -6
21. A put option conveys the right to sell the underlying asset at the exercise price. A
short position in a futures contract carries an obligation to sell the underlying asset
at the futures price. Both positions, however, benefit if the price of the underlying
asset falls.
22. A call option conveys the right to buy the underlying asset at the exercise price. A
long position in a futures contract carries an obligation to buy the underlying asset
at the futures price. Both positions, however, benefit if the price of the underlying
asset rises.
CFA PROBLEMS
1. (d) There are tax advantages for corporations that own preferred shares.
2. The equivalent taxable yield is: 6.75%/(1 − 0.34) = 10.23%
3. (a) Writing a call entails unlimited potential losses as the stock price rises.
4. a. The taxable bond. With a zero tax bracket, the after-tax yield for the
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Chapter 2 - Asset Classes and Financial Instruments
2-6
taxable bond is the same as the before-tax yield (5%), which is greater than
the yield on the municipal bond.
b. The taxable bond. The after-tax yield for the taxable bond is:
0.05 (1 – 0.10) = 4.5%
c. You are indifferent. The after-tax yield for the taxable bond is:
0.05 (1 – 0.20) = 4.0%
The after-tax yield is the same as that of the municipal bond.
d. The municipal bond offers the higher after-tax yield for investors in tax
brackets above 20%.
5. If the after-tax yields are equal, then: 0.056 = 0.08 × (1 – t)
This implies that t = 0.30 =30%.
2-6
taxable bond is the same as the before-tax yield (5%), which is greater than
the yield on the municipal bond.
b. The taxable bond. The after-tax yield for the taxable bond is:
0.05 (1 – 0.10) = 4.5%
c. You are indifferent. The after-tax yield for the taxable bond is:
0.05 (1 – 0.20) = 4.0%
The after-tax yield is the same as that of the municipal bond.
d. The municipal bond offers the higher after-tax yield for investors in tax
brackets above 20%.
5. If the after-tax yields are equal, then: 0.056 = 0.08 × (1 – t)
This implies that t = 0.30 =30%.
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CHAPTER 3: HOW SECURITIES ARE TRADED
3-1
CHAPTER 3: HOW SECURITIES ARE TRADED
PROBLEM SETS
1. Limit buy order: an order that purchases stock if the price falls below a
predetermined level. Limit sell order: sells stock when the price rises above a
predetermined level. Limite orders are not guaranteed to execute since the price
may not reach the trigger point. Market order: either a buy or sell order that is
executed immediately at the current market price
2. In response to the potential negative reaction to large [block] trades, trades will be split
up into many small trades, effectively hiding the total number of shares bought or sold.
3. The use of leverage necessarily magnifies returns to investors. Leveraging
borrowed money allows for greater return on investment if the stock price increases.
However, if the stock price declines, the investor must repay the loan, regardless of
how far the stock price drops, and incur a negative rate of return. For example, if an
investor buys an asset at $100 and the price rises to $110, the investor earns 10%.
If an investor takes out a $40 loan at 5% and buys the same stock, the return will be
13.3%, computed as follows: $10 capital gain minus $2 interest expense divided by
the $60 original investment. Of course, if the stock price falls below $100, the
negative return will be greater for the leveraged account.
4.
a. False: An investor who wishes to sell shares immediately should ask his or her
broker to enter a market order.
b. False: The ask price is greater than the bid price. (note: the opposite is true for
yields)
c. False: An issue of additional shares of stock to the public by Microsoft would be
called seasoned offering.
d. True
5. (a) A broker market consists of intermediaries who have the discretion to trade
for their clients. A large block trade in an illiquid security would most likely
trade in this market as the brokers would have the best access to clients
interested in this type of security.
The advantage of an electronic communication network (ECN) is that it can
execute large block orders without affecting the public quote. Since this
security is illiquid, large block orders are less likely to occur and thus it would
not likely trade through an ECN.
3-1
CHAPTER 3: HOW SECURITIES ARE TRADED
PROBLEM SETS
1. Limit buy order: an order that purchases stock if the price falls below a
predetermined level. Limit sell order: sells stock when the price rises above a
predetermined level. Limite orders are not guaranteed to execute since the price
may not reach the trigger point. Market order: either a buy or sell order that is
executed immediately at the current market price
2. In response to the potential negative reaction to large [block] trades, trades will be split
up into many small trades, effectively hiding the total number of shares bought or sold.
3. The use of leverage necessarily magnifies returns to investors. Leveraging
borrowed money allows for greater return on investment if the stock price increases.
However, if the stock price declines, the investor must repay the loan, regardless of
how far the stock price drops, and incur a negative rate of return. For example, if an
investor buys an asset at $100 and the price rises to $110, the investor earns 10%.
If an investor takes out a $40 loan at 5% and buys the same stock, the return will be
13.3%, computed as follows: $10 capital gain minus $2 interest expense divided by
the $60 original investment. Of course, if the stock price falls below $100, the
negative return will be greater for the leveraged account.
4.
a. False: An investor who wishes to sell shares immediately should ask his or her
broker to enter a market order.
b. False: The ask price is greater than the bid price. (note: the opposite is true for
yields)
c. False: An issue of additional shares of stock to the public by Microsoft would be
called seasoned offering.
d. True
5. (a) A broker market consists of intermediaries who have the discretion to trade
for their clients. A large block trade in an illiquid security would most likely
trade in this market as the brokers would have the best access to clients
interested in this type of security.
The advantage of an electronic communication network (ECN) is that it can
execute large block orders without affecting the public quote. Since this
security is illiquid, large block orders are less likely to occur and thus it would
not likely trade through an ECN.
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CHAPTER 3: HOW SECURITIES ARE TRADED
3-2
Electronic limit-order markets (ELOM) transact securities with high trading
volume. This illiquid security is unlikely to be traded on an ELOM.
6. a. The stock is purchased for: 300 $40 = $12,000
The amount borrowed is $4,000. Therefore, the investor put up equity, or
margin, of $8,000.
b. If the share price falls to $30, then the value of the stock falls to $9,000. By
the end of the year, the amount of the loan owed to the broker grows to:
$4,000 1.08 = $4,320
Therefore, the remaining margin in the investor’s account is:
$9,000 − $4,320 = $4,680
c. The percentage margin is now: $4,680/$9,000 = 0.52, or 52% > 30%.
Therefore, the investor will not receive a margin call.
d. Using an end price of $30, the rate of return on the investment over the year
is:
(Ending equity in the account − Initial equity)/Initial equity
= ($4,680 − $8,000)/$8,000 = −0.415, or −41.5%
Alternatively, divide the initial equity investments into the change in value
plus the interest payment:
($3,000 loss + $320 interest)/$8,000 = -0.415.
7. a. The initial margin was: 0.50 1,000 $40 = $20,000
As a result of the increase in the stock price Old Economy Traders loses:
$10 1,000 = $10,000
Therefore, margin decreases by $10,000. Moreover, Old Economy Traders
must pay the dividend of $2 per share to the lender of the shares, so that the
margin in the account decreases by an additional $2,000. Therefore, the
remaining margin is:
$20,000 – $10,000 – $2,000 = $8,000
b. The percentage margin is: $8,000/$50,000 = 0.16, or 16%
So there will be a margin call.
3-2
Electronic limit-order markets (ELOM) transact securities with high trading
volume. This illiquid security is unlikely to be traded on an ELOM.
6. a. The stock is purchased for: 300 $40 = $12,000
The amount borrowed is $4,000. Therefore, the investor put up equity, or
margin, of $8,000.
b. If the share price falls to $30, then the value of the stock falls to $9,000. By
the end of the year, the amount of the loan owed to the broker grows to:
$4,000 1.08 = $4,320
Therefore, the remaining margin in the investor’s account is:
$9,000 − $4,320 = $4,680
c. The percentage margin is now: $4,680/$9,000 = 0.52, or 52% > 30%.
Therefore, the investor will not receive a margin call.
d. Using an end price of $30, the rate of return on the investment over the year
is:
(Ending equity in the account − Initial equity)/Initial equity
= ($4,680 − $8,000)/$8,000 = −0.415, or −41.5%
Alternatively, divide the initial equity investments into the change in value
plus the interest payment:
($3,000 loss + $320 interest)/$8,000 = -0.415.
7. a. The initial margin was: 0.50 1,000 $40 = $20,000
As a result of the increase in the stock price Old Economy Traders loses:
$10 1,000 = $10,000
Therefore, margin decreases by $10,000. Moreover, Old Economy Traders
must pay the dividend of $2 per share to the lender of the shares, so that the
margin in the account decreases by an additional $2,000. Therefore, the
remaining margin is:
$20,000 – $10,000 – $2,000 = $8,000
b. The percentage margin is: $8,000/$50,000 = 0.16, or 16%
So there will be a margin call.
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CHAPTER 3: HOW SECURITIES ARE TRADED
3-3
c. The equity in the account decreased from $20,000 to $8,000 in one year, for a
rate of return of: (−$12,000/$20,000) = −0.60, or −60%
8. a. The buy order for FinTrade will be filled at the best limit-sell order price:
$50.25
b. The next market buy order will be filled at the next-best limit-sell
order price: $51.50
c. You would want to increase your inventory. There is considerable buying
demand at prices just below $50, indicating that downside risk is limited. In
contrast, limit sell orders are sparse, indicating that a moderate buy order could
result in a substantial price increase.
9. a. You buy 200 shares of Telecom for $10,000. These shares increase in value by
10%, or $1,000. You pay interest of: 0.08 $5,000 = $400
The rate of return will be:$1, 000 $400 0.12 12%
$5, 000
− = =
b. The value of the 200 shares is 200P. Equity is (200P – $5,000). You will
receive a margin call when:P
P
200
000,5$200 −
= 0.30 when P= $35.71 or lower
10. a. Initial margin is 50% of $5,000, or $2,500.
b. Total assets are $7,500 ($5,000 from the sale of the stock and $2,500 put up for
margin). Liabilities are 100P. Therefore, equity is ($7,500 – 100P). A margin
call will be issued when:P
P
100
100500,7$ −
= 0.30 when P = $57.69 or higher
11. The total cost of the purchase is: $20 1,000 = $20,000
You borrow $5,000 from your broker and invest $15,000 of your own funds.
Your margin account starts out with equity of $15,000.
a. (i) Equity increases to: ($22 1,000) – $5,000 = $17,000
3-3
c. The equity in the account decreased from $20,000 to $8,000 in one year, for a
rate of return of: (−$12,000/$20,000) = −0.60, or −60%
8. a. The buy order for FinTrade will be filled at the best limit-sell order price:
$50.25
b. The next market buy order will be filled at the next-best limit-sell
order price: $51.50
c. You would want to increase your inventory. There is considerable buying
demand at prices just below $50, indicating that downside risk is limited. In
contrast, limit sell orders are sparse, indicating that a moderate buy order could
result in a substantial price increase.
9. a. You buy 200 shares of Telecom for $10,000. These shares increase in value by
10%, or $1,000. You pay interest of: 0.08 $5,000 = $400
The rate of return will be:$1, 000 $400 0.12 12%
$5, 000
− = =
b. The value of the 200 shares is 200P. Equity is (200P – $5,000). You will
receive a margin call when:P
P
200
000,5$200 −
= 0.30 when P= $35.71 or lower
10. a. Initial margin is 50% of $5,000, or $2,500.
b. Total assets are $7,500 ($5,000 from the sale of the stock and $2,500 put up for
margin). Liabilities are 100P. Therefore, equity is ($7,500 – 100P). A margin
call will be issued when:P
P
100
100500,7$ −
= 0.30 when P = $57.69 or higher
11. The total cost of the purchase is: $20 1,000 = $20,000
You borrow $5,000 from your broker and invest $15,000 of your own funds.
Your margin account starts out with equity of $15,000.
a. (i) Equity increases to: ($22 1,000) – $5,000 = $17,000
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CHAPTER 3: HOW SECURITIES ARE TRADED
3-4
Percentage gain = $2,000/$15,000 = 0.1333, or 13.33%
(ii) With price unchanged, equity is unchanged.
Percentage gain = zero
(iii) Equity falls to ($18 1,000) – $5,000 = $13,000
Percentage gain = (–$2,000/$15,000) = –0.1333, or –13.33%
The relationship between the percentage return and the percentage change in
the price of the stock is given by:
% return = % change in price equityinitialsInvestor'
investmentTotal = % change in price 1.333
For example, when the stock price rises from $20 to $22, the percentage change in
price is 10%, while the percentage gain for the investor is:
% return = 10% 000,15$
000,20$ = 13.33%
b. The value of the 1,000 shares is 1,000P. Equity is (1,000P – $5,000). You will
receive a margin call when:P
P
000,1
000,5$000,1 −
= 0.25 when P = $6.67 or lower
c. The value of the 1,000 shares is 1,000P. But now you have borrowed $10,000
instead of $5,000. Therefore, equity is (1,000P – $10,000). You will receive a
margin call when:P
P
000,1
000,10$000,1 −
= 0.25 when P = $13.33 or lower
With less equity in the account, you are far more vulnerable to a margin call.
e.By the end of the year, the amount of the loan owed to the broker grows to:
$5,000 1.08 = $5,400
The equity in your account is (1,000P – $5,400). Initial equity was $15,000.
Therefore, your rate of return after one year is as follows:
(i)000,15$
000,15$400,5$)22$000,1( −− = 0.1067, or 10.67%
(ii)000,15$
000,15$400,5$)20$000,1( −− = –0.0267, or –2.67%
(iii)000,15$
000,15$400,5$)18$000,1( −− = –0.1600, or –16.00%
3-4
Percentage gain = $2,000/$15,000 = 0.1333, or 13.33%
(ii) With price unchanged, equity is unchanged.
Percentage gain = zero
(iii) Equity falls to ($18 1,000) – $5,000 = $13,000
Percentage gain = (–$2,000/$15,000) = –0.1333, or –13.33%
The relationship between the percentage return and the percentage change in
the price of the stock is given by:
% return = % change in price equityinitialsInvestor'
investmentTotal = % change in price 1.333
For example, when the stock price rises from $20 to $22, the percentage change in
price is 10%, while the percentage gain for the investor is:
% return = 10% 000,15$
000,20$ = 13.33%
b. The value of the 1,000 shares is 1,000P. Equity is (1,000P – $5,000). You will
receive a margin call when:P
P
000,1
000,5$000,1 −
= 0.25 when P = $6.67 or lower
c. The value of the 1,000 shares is 1,000P. But now you have borrowed $10,000
instead of $5,000. Therefore, equity is (1,000P – $10,000). You will receive a
margin call when:P
P
000,1
000,10$000,1 −
= 0.25 when P = $13.33 or lower
With less equity in the account, you are far more vulnerable to a margin call.
e.By the end of the year, the amount of the loan owed to the broker grows to:
$5,000 1.08 = $5,400
The equity in your account is (1,000P – $5,400). Initial equity was $15,000.
Therefore, your rate of return after one year is as follows:
(i)000,15$
000,15$400,5$)22$000,1( −− = 0.1067, or 10.67%
(ii)000,15$
000,15$400,5$)20$000,1( −− = –0.0267, or –2.67%
(iii)000,15$
000,15$400,5$)18$000,1( −− = –0.1600, or –16.00%
Loading page 17...
CHAPTER 3: HOW SECURITIES ARE TRADED
3-5
The relationship between the percentage return and the percentage change in
the price of Xtel is given by:
% return =
equityinitialsInvestor'
investmentTotal
priceinchange%
− equityinitialsInvestor'
borrowedFunds
%8
For example, when the stock price rises from $40 to $44, the percentage
change in price is 10%, while the percentage gain for the investor is:
000,15$
000,20$
%10
− 000,15$
000,5$
%8
=10.67%
e. The value of the 1000 shares is 1,000P. Equity is (1,000P – $5,400). You will
receive a margin call when:P
P
000,1
400,5$000,1 −
= 0.25 when P = $7.20 or lower
12. a. The gain or loss on the short position is: (–1,000 ΔP)
Invested funds = $15,000
Therefore: rate of return = (–1,000 ΔP)/15,000
The rate of return in each of the three scenarios is:
(i) Rate of return = (–1,000 $2)/$15,000 = –0.1333, or–13.33%
(ii) Rate of return = (–1,000 $0)/$15,000 = 0%
(iii) Rate of return = [–1,000 (–$2)]/$15,000 = +0.1333, or+13.33%
b. Total assets in the margin account equal:
$20,000 (from the sale of the stock) + $15,000 (the initial margin) = $35,000
Liabilities are 500P. You will receive a margin call when:P
P
000,1
000,1000,35$ −
= 0.25 when P = $28 or higher
c. With a $1 dividend, the short position must now pay on the borrowed shares:
($1/share 1000 shares) = $1000. Rate of return is now:
[(–1,000 ΔP) – 1,000]/15,000
(i) Rate of return = [(–1,000 $2) – $1,000]/$15,000 = –0.2000, or –
20.00%
(ii) Rate of return = [(–1,000 $0) – $1,000]/$15,000 = –0.0667, or –6.67%
3-5
The relationship between the percentage return and the percentage change in
the price of Xtel is given by:
% return =
equityinitialsInvestor'
investmentTotal
priceinchange%
− equityinitialsInvestor'
borrowedFunds
%8
For example, when the stock price rises from $40 to $44, the percentage
change in price is 10%, while the percentage gain for the investor is:
000,15$
000,20$
%10
− 000,15$
000,5$
%8
=10.67%
e. The value of the 1000 shares is 1,000P. Equity is (1,000P – $5,400). You will
receive a margin call when:P
P
000,1
400,5$000,1 −
= 0.25 when P = $7.20 or lower
12. a. The gain or loss on the short position is: (–1,000 ΔP)
Invested funds = $15,000
Therefore: rate of return = (–1,000 ΔP)/15,000
The rate of return in each of the three scenarios is:
(i) Rate of return = (–1,000 $2)/$15,000 = –0.1333, or–13.33%
(ii) Rate of return = (–1,000 $0)/$15,000 = 0%
(iii) Rate of return = [–1,000 (–$2)]/$15,000 = +0.1333, or+13.33%
b. Total assets in the margin account equal:
$20,000 (from the sale of the stock) + $15,000 (the initial margin) = $35,000
Liabilities are 500P. You will receive a margin call when:P
P
000,1
000,1000,35$ −
= 0.25 when P = $28 or higher
c. With a $1 dividend, the short position must now pay on the borrowed shares:
($1/share 1000 shares) = $1000. Rate of return is now:
[(–1,000 ΔP) – 1,000]/15,000
(i) Rate of return = [(–1,000 $2) – $1,000]/$15,000 = –0.2000, or –
20.00%
(ii) Rate of return = [(–1,000 $0) – $1,000]/$15,000 = –0.0667, or –6.67%
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CHAPTER 3: HOW SECURITIES ARE TRADED
3-6
(iii) Rate of return = [(–1,000) (–$2) – $1,000]/$15,000 = +0.067, or
+6.67%
Total assets are $35,000, and liabilities are (1,000P + 1,000). A margin call will
be issued when:P
P
000,1
000,1000,1000,35 −−
= 0.25 when P = $27.2 or higher
13. The broker is instructed to attempt to sell your Marabel, Inc. stock as soon as the
Marabel, Inc. stock trades at a bid price of $70 or less. Here, the broker will attempt
to execute but may not be able to sell at $70, since the bid price is now $69.95. The
price at which you sell may be more or less than $70 because the stop-loss becomes
a market order to sell at current market prices.
14. a. $55.50
b. $55.25
c. The trade will not be executed because the bid price is lower than the price
specified in the limit-sell order.
d. The trade will not be executed because the asked price is greater than the price
specified in the limit-buy order.
15. a. You will not receive a margin call. You borrowed $20,000 and with another
$20,000 of your own equity you bought 1,000 shares of Ixnay at $40 per
share. At $35 per share, the market value of the stock is $35,000, your equity
is $15,000, and the percentage margin is: $15,000/$35,000 = 42.9%
Your percentage margin exceeds the required maintenance margin.
b. You will receive a margin call when:P
P
000,1
000,20$000,1 −
= 0.35 when P = $30.77 or lower
16. The proceeds from the short sale (net of commission) were: ($21 100) – $50 = $2,050
A dividend payment of $200 was withdrawn from the account.
Covering the short sale at $15 per share costs (with commission): $1,500 + $50 =
$1,550
Therefore, the value of your account is equal to the net profit on the transaction:
$2,050 – $200 – $1,550 = $300
3-6
(iii) Rate of return = [(–1,000) (–$2) – $1,000]/$15,000 = +0.067, or
+6.67%
Total assets are $35,000, and liabilities are (1,000P + 1,000). A margin call will
be issued when:P
P
000,1
000,1000,1000,35 −−
= 0.25 when P = $27.2 or higher
13. The broker is instructed to attempt to sell your Marabel, Inc. stock as soon as the
Marabel, Inc. stock trades at a bid price of $70 or less. Here, the broker will attempt
to execute but may not be able to sell at $70, since the bid price is now $69.95. The
price at which you sell may be more or less than $70 because the stop-loss becomes
a market order to sell at current market prices.
14. a. $55.50
b. $55.25
c. The trade will not be executed because the bid price is lower than the price
specified in the limit-sell order.
d. The trade will not be executed because the asked price is greater than the price
specified in the limit-buy order.
15. a. You will not receive a margin call. You borrowed $20,000 and with another
$20,000 of your own equity you bought 1,000 shares of Ixnay at $40 per
share. At $35 per share, the market value of the stock is $35,000, your equity
is $15,000, and the percentage margin is: $15,000/$35,000 = 42.9%
Your percentage margin exceeds the required maintenance margin.
b. You will receive a margin call when:P
P
000,1
000,20$000,1 −
= 0.35 when P = $30.77 or lower
16. The proceeds from the short sale (net of commission) were: ($21 100) – $50 = $2,050
A dividend payment of $200 was withdrawn from the account.
Covering the short sale at $15 per share costs (with commission): $1,500 + $50 =
$1,550
Therefore, the value of your account is equal to the net profit on the transaction:
$2,050 – $200 – $1,550 = $300
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CHAPTER 3: HOW SECURITIES ARE TRADED
3-7
te that your profit ($300) equals (100 shares profit per share of $3). Your net
proceeds per share were:
$21 selling price of stock
–$15 repurchase price of stock
–$ 2 dividend per share
–$ 1 2 trades $0.50 commission per share
$ 3
CFA PROBLEMS
1. a. In addition to the explicit fees of $70,000, FBN appears to have paid an
implicit price in underpricing of the IPO. The underpricing is $3 per share, or
a total of $300,000, implying total costs of $370,000.
b. No. The underwriters do not capture the part of the costs corresponding
to the underpricing. The underpricing may be a rational marketing
strategy. Without it, the underwriters would need to spend more resources
in order to place the issue with the public. The underwriters would then
need to charge higher explicit fees to the issuing firm. The issuing firm
may be just as well off paying the implicit issuance cost represented by
the underpricing.
2. (d) The broker will sell, at current market price, after the first transaction at
$55 or less.
3-7
te that your profit ($300) equals (100 shares profit per share of $3). Your net
proceeds per share were:
$21 selling price of stock
–$15 repurchase price of stock
–$ 2 dividend per share
–$ 1 2 trades $0.50 commission per share
$ 3
CFA PROBLEMS
1. a. In addition to the explicit fees of $70,000, FBN appears to have paid an
implicit price in underpricing of the IPO. The underpricing is $3 per share, or
a total of $300,000, implying total costs of $370,000.
b. No. The underwriters do not capture the part of the costs corresponding
to the underpricing. The underpricing may be a rational marketing
strategy. Without it, the underwriters would need to spend more resources
in order to place the issue with the public. The underwriters would then
need to charge higher explicit fees to the issuing firm. The issuing firm
may be just as well off paying the implicit issuance cost represented by
the underpricing.
2. (d) The broker will sell, at current market price, after the first transaction at
$55 or less.
Loading page 20...
CHAPTER 4: MUTUAL FUNDS AND
OTHER INVESTMENT COMPANIES
4-1
CHAPTER 4: MUTUAL FUNDS AND
OTHER INVESTMENT COMPANIES
PROBLEM SETS
1. The unit investment trust should have lower operating expenses. Because the
investment trust portfolio is fixed once the trust is established, it does not have to
pay portfolio managers to constantly monitor and rebalance the portfolio as
perceived needs or opportunities change. Because the portfolio is fixed, the unit
investment trust also incurs virtually no trading costs.
2. a. Unit investment trusts: Diversification from large-scale investing, lower
transaction costs associated with large-scale trading, low management fees,
predictable portfolio composition, guaranteed low portfolio turnover rate.
b. Open-end mutual funds: Diversification from large-scale investing, lower
transaction costs associated with large-scale trading, professional management
that may be able to take advantage of buy or sell opportunities as they arise,
record keeping.
c. Individual stocks and bonds: No management fee; ability to coordinate
realization of capital gains or losses with investors’ personal tax situations;
capability of designing portfolio to investor’s specific risk and return profile.
3. Open-end funds are obligated to redeem investor's shares at net asset value and thus
must keep cash or cash-equivalent securities on hand in order to meet potential
redemptions. Closed-end funds do not need the cash reserves because there are no
redemptions for closed-end funds. Investors in closed-end funds sell their shares
when they wish to cash out.
4. Balanced funds keep relatively stable proportions of funds invested in each asset
class. They are meant as convenient instruments to provide participation in a range
of asset classes. Life-cycle funds are balanced funds whose asset mix generally
depends on the age of the investor. Aggressive life-cycle funds, with larger
investments in equities, are marketed to younger investors, while conservative life-
cycle funds, with larger investments in fixed-income securities, are designed for
older investors. Asset allocation funds, in contrast, may vary the proportions
invested in each asset class by large amounts as predictions of relative performance
across classes vary. Asset allocation funds therefore engage in more aggressive
market timing.
OTHER INVESTMENT COMPANIES
4-1
CHAPTER 4: MUTUAL FUNDS AND
OTHER INVESTMENT COMPANIES
PROBLEM SETS
1. The unit investment trust should have lower operating expenses. Because the
investment trust portfolio is fixed once the trust is established, it does not have to
pay portfolio managers to constantly monitor and rebalance the portfolio as
perceived needs or opportunities change. Because the portfolio is fixed, the unit
investment trust also incurs virtually no trading costs.
2. a. Unit investment trusts: Diversification from large-scale investing, lower
transaction costs associated with large-scale trading, low management fees,
predictable portfolio composition, guaranteed low portfolio turnover rate.
b. Open-end mutual funds: Diversification from large-scale investing, lower
transaction costs associated with large-scale trading, professional management
that may be able to take advantage of buy or sell opportunities as they arise,
record keeping.
c. Individual stocks and bonds: No management fee; ability to coordinate
realization of capital gains or losses with investors’ personal tax situations;
capability of designing portfolio to investor’s specific risk and return profile.
3. Open-end funds are obligated to redeem investor's shares at net asset value and thus
must keep cash or cash-equivalent securities on hand in order to meet potential
redemptions. Closed-end funds do not need the cash reserves because there are no
redemptions for closed-end funds. Investors in closed-end funds sell their shares
when they wish to cash out.
4. Balanced funds keep relatively stable proportions of funds invested in each asset
class. They are meant as convenient instruments to provide participation in a range
of asset classes. Life-cycle funds are balanced funds whose asset mix generally
depends on the age of the investor. Aggressive life-cycle funds, with larger
investments in equities, are marketed to younger investors, while conservative life-
cycle funds, with larger investments in fixed-income securities, are designed for
older investors. Asset allocation funds, in contrast, may vary the proportions
invested in each asset class by large amounts as predictions of relative performance
across classes vary. Asset allocation funds therefore engage in more aggressive
market timing.
Loading page 21...
CHAPTER 4: MUTUAL FUNDS AND
OTHER INVESTMENT COMPANIES
4-2
5. Unlike an open-end fund, in which underlying shares are redeemed when the fund
is redeemed, a closed-end fund trades as a security in the market. Thus, their prices
may differ from the NAV.
6. Advantages of an ETF over a mutual fund:
• ETFs are continuously traded and can be sold or purchased on margin.
• There are no capital gains tax triggers when an ETF is sold (shares are just
sold from one investor to another).
• Investors buy from brokers, thus eliminating the cost of direct marketing
to individual small investors. This implies lower management fees.
Disadvantages of an ETF over a mutual fund:
• Prices can depart from NAV (unlike an open-end fund).
• There is a broker fee when buying and selling (unlike a no-load fund).
7. The offering price includes a 6% front-end load, or sales commission, meaning that
every dollar paid results in only $0.94 going toward purchase of shares. Therefore:
Offering price =06.01
70.10$
Load1
NAV
−
=
− = $11.38
8. NAV = Offering price (1 –Load) = $12.30 .95 = $11.69
9. Stock Value Held by Fund
A $ 7,000,000
B 12,000,000
C 8,000,000
D 15,000,000
Total $42,000,000
Net asset value =000,000,4
000,30$000,000,42$ − = $10.49
10. Value of stocks sold and replaced = $15,000,000
Turnover rate =000,000,42$
000,000,15$ = 0.357, or 35.7%
OTHER INVESTMENT COMPANIES
4-2
5. Unlike an open-end fund, in which underlying shares are redeemed when the fund
is redeemed, a closed-end fund trades as a security in the market. Thus, their prices
may differ from the NAV.
6. Advantages of an ETF over a mutual fund:
• ETFs are continuously traded and can be sold or purchased on margin.
• There are no capital gains tax triggers when an ETF is sold (shares are just
sold from one investor to another).
• Investors buy from brokers, thus eliminating the cost of direct marketing
to individual small investors. This implies lower management fees.
Disadvantages of an ETF over a mutual fund:
• Prices can depart from NAV (unlike an open-end fund).
• There is a broker fee when buying and selling (unlike a no-load fund).
7. The offering price includes a 6% front-end load, or sales commission, meaning that
every dollar paid results in only $0.94 going toward purchase of shares. Therefore:
Offering price =06.01
70.10$
Load1
NAV
−
=
− = $11.38
8. NAV = Offering price (1 –Load) = $12.30 .95 = $11.69
9. Stock Value Held by Fund
A $ 7,000,000
B 12,000,000
C 8,000,000
D 15,000,000
Total $42,000,000
Net asset value =000,000,4
000,30$000,000,42$ − = $10.49
10. Value of stocks sold and replaced = $15,000,000
Turnover rate =000,000,42$
000,000,15$ = 0.357, or 35.7%
Loading page 22...
CHAPTER 4: MUTUAL FUNDS AND
OTHER INVESTMENT COMPANIES
4-3
11. a.40.39$
000,000,5
000,000,3$000,000,200$
NAV =
−
=
b. Premium (or discount) =NAV
NAVicePr − =40.39$
40.39$36$ − = –0.086, or -8.6%
The fund sells at an 8.6% discount from NAV.
12.1 0
0
NAV NAV Distributions $12.10 $12.50 $1.50 0.088, or 8.8%
NAV $12.50
− + − +
= =
13. a. Start-of-year price: P0 = $12.00 × 1.02 = $12.24
End-of-year price: P1 = $12.10 × 0.93 = $11.25
Although NAV increased by $0.10, the price of the fund decreased by $0.99.
Rate of return =1 0
0
Distributions $11.25 $12.24 $1.50 0.042, or 4.2%
$12.24
P P
P
− + − +
= =
b. An investor holding the same securities as the fund manager would have
earned a rate of return based on the increase in the NAV of the portfolio:1 0
0
NAV NAV Distributions $12.10 $12.00 $1.50 0.133, or 13.3%
NAV $12.00
− + − +
= =
14. a. Empirical research indicates that past performance of mutual funds is not
highly predictive of future performance, especially for better-performing
funds. While there may be some tendency for the fund to be an above average
performer next year, it is unlikely to once again be a top 10% performer.
b. On the other hand, the evidence is more suggestive of a tendency for poor
performance to persist. This tendency is probably related to fund costs and
turnover rates. Thus if the fund is among the poorest performers, investors
should be concerned that the poor performance will persist.
15. NAV0 = $200,000,000/10,000,000 = $20
Dividends per share = $2,000,000/10,000,000 = $0.20
NAV1 is based on the 8% price gain, less the 1% 12b-1 fee:
NAV1 = $20 1.08 (1 – 0.01) = $21.384
Rate of return =20$
20.0$20$384.21$ +− = 0.0792, or 7.92%
OTHER INVESTMENT COMPANIES
4-3
11. a.40.39$
000,000,5
000,000,3$000,000,200$
NAV =
−
=
b. Premium (or discount) =NAV
NAVicePr − =40.39$
40.39$36$ − = –0.086, or -8.6%
The fund sells at an 8.6% discount from NAV.
12.1 0
0
NAV NAV Distributions $12.10 $12.50 $1.50 0.088, or 8.8%
NAV $12.50
− + − +
= =
13. a. Start-of-year price: P0 = $12.00 × 1.02 = $12.24
End-of-year price: P1 = $12.10 × 0.93 = $11.25
Although NAV increased by $0.10, the price of the fund decreased by $0.99.
Rate of return =1 0
0
Distributions $11.25 $12.24 $1.50 0.042, or 4.2%
$12.24
P P
P
− + − +
= =
b. An investor holding the same securities as the fund manager would have
earned a rate of return based on the increase in the NAV of the portfolio:1 0
0
NAV NAV Distributions $12.10 $12.00 $1.50 0.133, or 13.3%
NAV $12.00
− + − +
= =
14. a. Empirical research indicates that past performance of mutual funds is not
highly predictive of future performance, especially for better-performing
funds. While there may be some tendency for the fund to be an above average
performer next year, it is unlikely to once again be a top 10% performer.
b. On the other hand, the evidence is more suggestive of a tendency for poor
performance to persist. This tendency is probably related to fund costs and
turnover rates. Thus if the fund is among the poorest performers, investors
should be concerned that the poor performance will persist.
15. NAV0 = $200,000,000/10,000,000 = $20
Dividends per share = $2,000,000/10,000,000 = $0.20
NAV1 is based on the 8% price gain, less the 1% 12b-1 fee:
NAV1 = $20 1.08 (1 – 0.01) = $21.384
Rate of return =20$
20.0$20$384.21$ +− = 0.0792, or 7.92%
Loading page 23...
CHAPTER 4: MUTUAL FUNDS AND
OTHER INVESTMENT COMPANIES
4-4
16. The excess of purchases over sales must be due to new inflows into the fund.
Therefore, $400 million of stock previously held by the fund was replaced by new
holdings. So turnover is: $400/$2,200 = 0.182, or 18.2%.
17. Fees paid to investment managers were: 0.007 $2.2 billion = $15.4 million
Since the total expense ratio was 1.1% and the management fee was 0.7%, we
conclude that 0.4% must be for other expenses. Therefore, other administrative
expenses were: 0.004 $2.2 billion = $8.8 million.
18. As an initial approximation, your return equals the return on the shares minus the
total of the expense ratio and purchase costs: 12% − 1.2% − 4% = 6.8%.
But the precise return is less than this because the 4% load is paid up front, not at
the end of the year.
To purchase the shares, you would have had to invest: $20,000/(1 − 0.04) = $20,833.
The shares increase in value from $20,000 to: $20,000 (1.12 − 0.012) = $22,160.
The rate of return is: ($22,160 − $20,833)/$20,833 = 6.37%.
19.
Assume $1,000 investment Loaded-Up Fund Economy Fund
Yearly growth (r is 6%)(1 .01 .0075)r+ − −(.98) (1 .0025)r + −
t = 1 year $1,042.50 $1,036.35
t = 3 years $1,133.00 $1,158.96
t = 10 years $1,516.21 $1,714.08
20. a.$450,000,000 $10,000000 $10
44,000,000
− =
b. The redemption of 1 million shares will most likely trigger capital gains taxes
which will lower the remaining portfolio by an amount greater than $10,000,000
(implying a remaining total value less than $440,000,000). The outstanding shares
fall to 43 million and the NAV drops to below $10.
21. Suppose you have $1,000 to invest. The initial investment in Class A shares is
$940 ( = $1000 × [1-.06]) net of the front-end load. After four years, your portfolio will
be worth:
$940 (1.10)4 = $1,376.25
Class B shares allow you to invest the full $1,000, but your investment performance
net of 12b-1 fees will be only 9.5%, and you will pay a 1% back-end load fee if you
sell after four years. Your portfolio value after four years will be:
$1,000 (1.095)4 = $1,437.66
OTHER INVESTMENT COMPANIES
4-4
16. The excess of purchases over sales must be due to new inflows into the fund.
Therefore, $400 million of stock previously held by the fund was replaced by new
holdings. So turnover is: $400/$2,200 = 0.182, or 18.2%.
17. Fees paid to investment managers were: 0.007 $2.2 billion = $15.4 million
Since the total expense ratio was 1.1% and the management fee was 0.7%, we
conclude that 0.4% must be for other expenses. Therefore, other administrative
expenses were: 0.004 $2.2 billion = $8.8 million.
18. As an initial approximation, your return equals the return on the shares minus the
total of the expense ratio and purchase costs: 12% − 1.2% − 4% = 6.8%.
But the precise return is less than this because the 4% load is paid up front, not at
the end of the year.
To purchase the shares, you would have had to invest: $20,000/(1 − 0.04) = $20,833.
The shares increase in value from $20,000 to: $20,000 (1.12 − 0.012) = $22,160.
The rate of return is: ($22,160 − $20,833)/$20,833 = 6.37%.
19.
Assume $1,000 investment Loaded-Up Fund Economy Fund
Yearly growth (r is 6%)(1 .01 .0075)r+ − −(.98) (1 .0025)r + −
t = 1 year $1,042.50 $1,036.35
t = 3 years $1,133.00 $1,158.96
t = 10 years $1,516.21 $1,714.08
20. a.$450,000,000 $10,000000 $10
44,000,000
− =
b. The redemption of 1 million shares will most likely trigger capital gains taxes
which will lower the remaining portfolio by an amount greater than $10,000,000
(implying a remaining total value less than $440,000,000). The outstanding shares
fall to 43 million and the NAV drops to below $10.
21. Suppose you have $1,000 to invest. The initial investment in Class A shares is
$940 ( = $1000 × [1-.06]) net of the front-end load. After four years, your portfolio will
be worth:
$940 (1.10)4 = $1,376.25
Class B shares allow you to invest the full $1,000, but your investment performance
net of 12b-1 fees will be only 9.5%, and you will pay a 1% back-end load fee if you
sell after four years. Your portfolio value after four years will be:
$1,000 (1.095)4 = $1,437.66
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CHAPTER 4: MUTUAL FUNDS AND
OTHER INVESTMENT COMPANIES
4-5
After paying the back-end load fee, your portfolio value will be:
$1,437.66 .99 = $1,423.28
Class B shares are the better choice if your horizon is four years.
With a 15-year horizon, the Class A shares will be worth:
$940 (1.10)15 = $3,926.61
For the Class B shares, there is no back-end load in this case since the horizon is
greater than five years. Therefore, the value of the Class B shares will be:
$1,000 (1.095)15 = $3,901.32
At this longer horizon, Class B shares are no longer the better choice. The effect of
Class B's 0.5% 12b-1 fees accumulates over time and finally overwhelms the 6%
load charged to Class A investors.
22. a. After two years, each dollar invested in a fund with a 4% load and a portfolio
return equal to r will grow to: $0.96 (1 + r – 0.005)2.
Each dollar invested in the bank CD will grow to: $1 1.062.
If the mutual fund is to be the better investment, then the portfolio return (r)
must satisfy:
0.96 (1 + r – 0.005)2 > 1.062
0.96 (1 + r – 0.005)2 > 1.1236
(1 + r – 0.005)2 > 1.1704
1 + r – 0.005 > 1.0819
1 + r > 1.0869
Therefore: r > 0.0869 = 8.69%
b. If you invest for six years, then the portfolio return must satisfy:
0.96 (1 + r – 0.005)6 > 1.066 = 1.4185
(1 + r – 0.005)6 > 1.4776
1 + r – 0.005 > 1.0672
r > 7.22%
The cutoff rate of return is lower for the six-year investment because the
“fixed cost” (the one-time front-end load) is spread over a greater number of
years.
OTHER INVESTMENT COMPANIES
4-5
After paying the back-end load fee, your portfolio value will be:
$1,437.66 .99 = $1,423.28
Class B shares are the better choice if your horizon is four years.
With a 15-year horizon, the Class A shares will be worth:
$940 (1.10)15 = $3,926.61
For the Class B shares, there is no back-end load in this case since the horizon is
greater than five years. Therefore, the value of the Class B shares will be:
$1,000 (1.095)15 = $3,901.32
At this longer horizon, Class B shares are no longer the better choice. The effect of
Class B's 0.5% 12b-1 fees accumulates over time and finally overwhelms the 6%
load charged to Class A investors.
22. a. After two years, each dollar invested in a fund with a 4% load and a portfolio
return equal to r will grow to: $0.96 (1 + r – 0.005)2.
Each dollar invested in the bank CD will grow to: $1 1.062.
If the mutual fund is to be the better investment, then the portfolio return (r)
must satisfy:
0.96 (1 + r – 0.005)2 > 1.062
0.96 (1 + r – 0.005)2 > 1.1236
(1 + r – 0.005)2 > 1.1704
1 + r – 0.005 > 1.0819
1 + r > 1.0869
Therefore: r > 0.0869 = 8.69%
b. If you invest for six years, then the portfolio return must satisfy:
0.96 (1 + r – 0.005)6 > 1.066 = 1.4185
(1 + r – 0.005)6 > 1.4776
1 + r – 0.005 > 1.0672
r > 7.22%
The cutoff rate of return is lower for the six-year investment because the
“fixed cost” (the one-time front-end load) is spread over a greater number of
years.
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CHAPTER 4: MUTUAL FUNDS AND
OTHER INVESTMENT COMPANIES
4-6
c. With a 12b-1 fee instead of a front-end load, the portfolio must earn a rate of
return (r) that satisfies:
1 + r – 0.005 – 0.0075 > 1.06
In this case, r must exceed 7.25% regardless of the investment horizon.
23. The turnover rate is 50%. This means that, on average, 50% of the portfolio is sold
and replaced with other securities each year. Trading costs on the sell orders are
0.4% and the buy orders to replace those securities entail another 0.4% in trading
costs. Total trading costs will reduce portfolio returns by: 2 0.4% 0.50 = 0.4%
24. For the bond fund, the fraction of portfolio income given up to fees is:%0.4
%6.0
= 0.150, or 15.0%
For the equity fund, the fraction of investment earnings given up to fees is:%0.12
%6.0
= 0.050, or 5.0%
Fees are a much higher fraction of expected earnings for the bond fund and
therefore may be a more important factor in selecting the bond fund.
This may help to explain why unmanaged unit investment trusts are concentrated in
the fixed income market. The advantages of unit investment trusts are low turnover,
low trading costs, and low management fees. This is a more important concern to
bond-market investors.
25. Suppose that finishing in the top half of all portfolio managers is purely luck, and
that the probability of doing so in any year is exactly ½. Then the probability that
any particular manager would finish in the top half of the sample five years in a row
is (½)5 = 1/32. We would then expect to find that [350 (1/32)] = 11 managers
finish in the top half for each of the five consecutive years. This is precisely what
we found. Thus, we should not conclude that the consistent performance after five
years is proof of skill. We would expect to find 11 managers exhibiting precisely
this level of "consistency" even if performance is due solely to luck.
OTHER INVESTMENT COMPANIES
4-6
c. With a 12b-1 fee instead of a front-end load, the portfolio must earn a rate of
return (r) that satisfies:
1 + r – 0.005 – 0.0075 > 1.06
In this case, r must exceed 7.25% regardless of the investment horizon.
23. The turnover rate is 50%. This means that, on average, 50% of the portfolio is sold
and replaced with other securities each year. Trading costs on the sell orders are
0.4% and the buy orders to replace those securities entail another 0.4% in trading
costs. Total trading costs will reduce portfolio returns by: 2 0.4% 0.50 = 0.4%
24. For the bond fund, the fraction of portfolio income given up to fees is:%0.4
%6.0
= 0.150, or 15.0%
For the equity fund, the fraction of investment earnings given up to fees is:%0.12
%6.0
= 0.050, or 5.0%
Fees are a much higher fraction of expected earnings for the bond fund and
therefore may be a more important factor in selecting the bond fund.
This may help to explain why unmanaged unit investment trusts are concentrated in
the fixed income market. The advantages of unit investment trusts are low turnover,
low trading costs, and low management fees. This is a more important concern to
bond-market investors.
25. Suppose that finishing in the top half of all portfolio managers is purely luck, and
that the probability of doing so in any year is exactly ½. Then the probability that
any particular manager would finish in the top half of the sample five years in a row
is (½)5 = 1/32. We would then expect to find that [350 (1/32)] = 11 managers
finish in the top half for each of the five consecutive years. This is precisely what
we found. Thus, we should not conclude that the consistent performance after five
years is proof of skill. We would expect to find 11 managers exhibiting precisely
this level of "consistency" even if performance is due solely to luck.
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CHAPTER 5: INTRODUCTION TO RISK, RETURN, AND
THE HISTORICAL RECORD
5-1
CHAPTER 5: INTRODUCTION TO RISK, RETURN, AND
THE HISTORICAL RECORD
PROBLEM SETS
1. The Fisher equation predicts that the nominal rate will equal the equilibrium
real rate plus the expected inflation rate. Hence, if the inflation rate increases
from 3% to 5% while there is no change in the real rate, then the nominal rate
will increase by 2%. On the other hand, it is possible that an increase in the
expected inflation rate would be accompanied by a change in the real rate of
interest. While it is conceivable that the nominal interest rate could remain
constant as the inflation rate increased, implying that the real rate decreased
as inflation increased, this is not a likely scenario.
2. If we assume that the distribution of returns remains reasonably stable over
the entire history, then a longer sample period (i.e., a larger sample) increases
the precision of the estimate of the expected rate of return; this is a
consequence of the fact that the standard error decreases as the sample size
increases. However, if we assume that the mean of the distribution of returns
is changing over time but we are not in a position to determine the nature of
this change, then the expected return must be estimated from a more recent
part of the historical period. In this scenario, we must determine how far
back, historically, to go in selecting the relevant sample. Here, it is likely to
be disadvantageous to use the entire data set back to 1880.
3.Nominal
Real Real
1 1 .45
1 1.1154 11.54%
1 1 .30
r
r r
i
+ +
+ = = = → =
+ +
4. For the money market fund, your holding-period return for the next year
depends on the level of 30-day interest rates each month when the fund rolls
over maturing securities. The one-year savings deposit offers a 5% holding
period return for the year. If you forecast that the rate on money market
instruments will increase significantly above the current 3% yield, then the
money market fund might result in a higher HPR than the savings deposit.
The 20-year Treasury bond offers a yield to maturity of 5% per year, which is
100 basis points higher than the rate on the one-year savings deposit;
however, you could earn a one-year HPR much less than 4% on the bond if
long-term interest rates increase during the year. If Treasury bond yields rise
above 5%, then the price of the bond will fall, and the resulting capital loss
will wipe out some or all of the 5% return you would have earned if bond
yields had remained unchanged over the course of the year.
THE HISTORICAL RECORD
5-1
CHAPTER 5: INTRODUCTION TO RISK, RETURN, AND
THE HISTORICAL RECORD
PROBLEM SETS
1. The Fisher equation predicts that the nominal rate will equal the equilibrium
real rate plus the expected inflation rate. Hence, if the inflation rate increases
from 3% to 5% while there is no change in the real rate, then the nominal rate
will increase by 2%. On the other hand, it is possible that an increase in the
expected inflation rate would be accompanied by a change in the real rate of
interest. While it is conceivable that the nominal interest rate could remain
constant as the inflation rate increased, implying that the real rate decreased
as inflation increased, this is not a likely scenario.
2. If we assume that the distribution of returns remains reasonably stable over
the entire history, then a longer sample period (i.e., a larger sample) increases
the precision of the estimate of the expected rate of return; this is a
consequence of the fact that the standard error decreases as the sample size
increases. However, if we assume that the mean of the distribution of returns
is changing over time but we are not in a position to determine the nature of
this change, then the expected return must be estimated from a more recent
part of the historical period. In this scenario, we must determine how far
back, historically, to go in selecting the relevant sample. Here, it is likely to
be disadvantageous to use the entire data set back to 1880.
3.Nominal
Real Real
1 1 .45
1 1.1154 11.54%
1 1 .30
r
r r
i
+ +
+ = = = → =
+ +
4. For the money market fund, your holding-period return for the next year
depends on the level of 30-day interest rates each month when the fund rolls
over maturing securities. The one-year savings deposit offers a 5% holding
period return for the year. If you forecast that the rate on money market
instruments will increase significantly above the current 3% yield, then the
money market fund might result in a higher HPR than the savings deposit.
The 20-year Treasury bond offers a yield to maturity of 5% per year, which is
100 basis points higher than the rate on the one-year savings deposit;
however, you could earn a one-year HPR much less than 4% on the bond if
long-term interest rates increase during the year. If Treasury bond yields rise
above 5%, then the price of the bond will fall, and the resulting capital loss
will wipe out some or all of the 5% return you would have earned if bond
yields had remained unchanged over the course of the year.
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CHAPTER 5: INTRODUCTION TO RISK, RETURN, AND
THE HISTORICAL RECORD
5-2
5. a. If businesses reduce their capital spending, then they are likely to
decrease their demand for funds. This will shift the demand curve in
Figure 5.1 to the left and reduce the equilibrium real rate of interest.
b. Increased household saving will shift the supply of funds curve to the
right and cause real interest rates to fall.
c. Open market purchases of U.S. Treasury securities by the Federal
Reserve Board are equivalent to an increase in the supply of funds (a
shift of the supply curve to the right). The FED buys treasuries with
cash from its own account or it issues certificates which trade like
cash. As a result, there is an increase in the money supply, and the
equilibrium real rate of interest will fall.
6. a. The “Inflation-Plus” CD is the safer investment because it guarantees the
purchasing power of the investment. Using the approximation that the real
rate equals the nominal rate minus the inflation rate, the CD provides a real
rate of 1.5% regardless of the inflation rate.
b. The expected return depends on the expected rate of inflation over the next
year. If the expected rate of inflation is less than 3.5% then the conventional
CD offers a higher real return than the inflation-plus CD; if the expected rate
of inflation is greater than 3.5%, then the opposite is true.
c. If you expect the rate of inflation to be 3% over the next year, then the
conventional CD offers you an expected real rate of return of 2%, which is
0.5% higher than the real rate on the inflation-protected CD. But unless you
know that inflation will be 3% with certainty, the conventional CD is also
riskier. The question of which is the better investment then depends on your
attitude towards risk versus return. You might choose to diversify and invest
part of your funds in each.
d. No. We cannot assume that the entire difference between the risk-free
nominal rate (on conventional CDs) of 5% and the real risk-free rate (on
inflation-protected CDs) of 1.5% is the expected rate of inflation. Part of the
difference is probably a risk premium associated with the uncertainty
surrounding the real rate of return on the conventional CDs. This implies
that the expected rate of inflation is less than 3.5% per year.
7. E(r) = [0.35 × 44.5%] + [0.30 × 14.0%] + [0.35 × (–16.5%)] = 14%
2 = [0.35 × (44.5 – 14)2] + [0.30 × (14 – 14)2] + [0.35 × (–16.5 – 14)2] = 651.175
= 25.52%
The mean is unchanged, but the standard deviation has increased, as the
probabilities of the high and low returns have increased.
THE HISTORICAL RECORD
5-2
5. a. If businesses reduce their capital spending, then they are likely to
decrease their demand for funds. This will shift the demand curve in
Figure 5.1 to the left and reduce the equilibrium real rate of interest.
b. Increased household saving will shift the supply of funds curve to the
right and cause real interest rates to fall.
c. Open market purchases of U.S. Treasury securities by the Federal
Reserve Board are equivalent to an increase in the supply of funds (a
shift of the supply curve to the right). The FED buys treasuries with
cash from its own account or it issues certificates which trade like
cash. As a result, there is an increase in the money supply, and the
equilibrium real rate of interest will fall.
6. a. The “Inflation-Plus” CD is the safer investment because it guarantees the
purchasing power of the investment. Using the approximation that the real
rate equals the nominal rate minus the inflation rate, the CD provides a real
rate of 1.5% regardless of the inflation rate.
b. The expected return depends on the expected rate of inflation over the next
year. If the expected rate of inflation is less than 3.5% then the conventional
CD offers a higher real return than the inflation-plus CD; if the expected rate
of inflation is greater than 3.5%, then the opposite is true.
c. If you expect the rate of inflation to be 3% over the next year, then the
conventional CD offers you an expected real rate of return of 2%, which is
0.5% higher than the real rate on the inflation-protected CD. But unless you
know that inflation will be 3% with certainty, the conventional CD is also
riskier. The question of which is the better investment then depends on your
attitude towards risk versus return. You might choose to diversify and invest
part of your funds in each.
d. No. We cannot assume that the entire difference between the risk-free
nominal rate (on conventional CDs) of 5% and the real risk-free rate (on
inflation-protected CDs) of 1.5% is the expected rate of inflation. Part of the
difference is probably a risk premium associated with the uncertainty
surrounding the real rate of return on the conventional CDs. This implies
that the expected rate of inflation is less than 3.5% per year.
7. E(r) = [0.35 × 44.5%] + [0.30 × 14.0%] + [0.35 × (–16.5%)] = 14%
2 = [0.35 × (44.5 – 14)2] + [0.30 × (14 – 14)2] + [0.35 × (–16.5 – 14)2] = 651.175
= 25.52%
The mean is unchanged, but the standard deviation has increased, as the
probabilities of the high and low returns have increased.
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CHAPTER 5: INTRODUCTION TO RISK, RETURN, AND
THE HISTORICAL RECORD
5-3
8. Probability distribution of price and one-year holding period return for a 30-
year U.S. Treasury bond (which will have 29 years to maturity at year-end):
Economy Probability YTM Price
Capital
Gain
Coupon
Interest HPR
Boom 0.20 11.0% $ 74.05 −$25.95 $8.00 −17.95%
Normal growth 0.50 8.0 100.00 0.00 8.00 8.00
Recession 0.30 7.0 112.28 12.28 8.00 20.28
9. E(q) = (0 × 0.25) + (1 × 0.25) + (2 × 0.50) = 1.25
σq = [0.25 × (0 – 1.25)2 + 0.25 × (1 – 1.25)2 + 0.50 × (2 – 1.25)2]1/2 = 0.8292
10. (a) With probability 0.9544, the value of a normally distributed
variable will fall within 2 standard deviations of the mean; that is,
between –40% and 80%. Simply add and subtract 2 standard
deviations to and from the mean.
11. From Table 5.4, the average risk premium Big/Value for the period 1927-
2018 was: 11.69% per year.
Adding 11.69% to the 3% risk-free interest rate, the expected annual HPR for
the Big/Value portfolio is: 3.00% + 11.69% = 14.69%.
12.
(01/1930-6/1974)
Small Big
Low 2 High Low 2 High
Average 0.99% 1.17% 1.48% 0.76% 0.81% 1.19%
SD 8.29% 8.38% 10.17% 5.70% 6.72% 8.89%
Skew 1.30 1.63 2.35 0.17 1.75 1.77
Kurtosis 9.74 13.10 17.69 7.06 17.80 14.64
(07/1974-12/2018)
Small Big
Low 2 High Low 2 High
Average 1.00% 1.35% 1.45% 0.99% 1.05% 1.13%
SD 6.69% 5.28% 5.49% 4.70% 4.35% 4.90%
Skew -0.43 -0.55 -0.47 -0.33 -0.43 -0.54
Kurtosis 2.08 3.60 4.30 1.99 2.57 2.96
THE HISTORICAL RECORD
5-3
8. Probability distribution of price and one-year holding period return for a 30-
year U.S. Treasury bond (which will have 29 years to maturity at year-end):
Economy Probability YTM Price
Capital
Gain
Coupon
Interest HPR
Boom 0.20 11.0% $ 74.05 −$25.95 $8.00 −17.95%
Normal growth 0.50 8.0 100.00 0.00 8.00 8.00
Recession 0.30 7.0 112.28 12.28 8.00 20.28
9. E(q) = (0 × 0.25) + (1 × 0.25) + (2 × 0.50) = 1.25
σq = [0.25 × (0 – 1.25)2 + 0.25 × (1 – 1.25)2 + 0.50 × (2 – 1.25)2]1/2 = 0.8292
10. (a) With probability 0.9544, the value of a normally distributed
variable will fall within 2 standard deviations of the mean; that is,
between –40% and 80%. Simply add and subtract 2 standard
deviations to and from the mean.
11. From Table 5.4, the average risk premium Big/Value for the period 1927-
2018 was: 11.69% per year.
Adding 11.69% to the 3% risk-free interest rate, the expected annual HPR for
the Big/Value portfolio is: 3.00% + 11.69% = 14.69%.
12.
(01/1930-6/1974)
Small Big
Low 2 High Low 2 High
Average 0.99% 1.17% 1.48% 0.76% 0.81% 1.19%
SD 8.29% 8.38% 10.17% 5.70% 6.72% 8.89%
Skew 1.30 1.63 2.35 0.17 1.75 1.77
Kurtosis 9.74 13.10 17.69 7.06 17.80 14.64
(07/1974-12/2018)
Small Big
Low 2 High Low 2 High
Average 1.00% 1.35% 1.45% 0.99% 1.05% 1.13%
SD 6.69% 5.28% 5.49% 4.70% 4.35% 4.90%
Skew -0.43 -0.55 -0.47 -0.33 -0.43 -0.54
Kurtosis 2.08 3.60 4.30 1.99 2.57 2.96
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CHAPTER 5: INTRODUCTION TO RISK, RETURN, AND
THE HISTORICAL RECORD
5-4
. The distributions from (01/1930–06/1974) and (07/1974–12/2018) periods
have distinct characteristics due to systematic shocks to the economy and
subsequent government intervention. While the returns from the two periods do not
differ greatly, their respective distributions tell a different story. The standard
deviation for all six portfolios is larger in the first period. Skew is also positive, but
negative in the second, showing a greater likelihood of higher-than-normal returns
in the right tail. Kurtosis is also markedly larger in the first period.
13. anominal nominal
real
1 0.80 0.70
1 0.0588, 5.88%
1 1 1.70
r r i
r or
i i
+ − −
= − = = =
+ +
b.nominal .80 .70 .10 realr i r− = − =
Clearly, the approximation gives a real HPR that is too high.
14. From Table 5.3, the average real rate on T-bills has been 0.46%.
a. T-bills: 0.46% real rate + 3% inflation = 3.46%
b. Expected return on Big/Value:
3.46% T-bill rate + 11.69% historical risk premium = 15.15%
c. The risk premium on stocks remains unchanged. A premium, the
difference between two rates, is a real value, unaffected by inflation.
15. Real interest rates are expected to rise. The investment activity will shift
the demand for funds curve (in Figure 5.1) to the right. Therefore the
equilibrium real interest rate will increase.
16. a. Probability distribution of the HPR on the stock market and put:
STOCK PUT
State of the
Economy Probability
Ending Price
+ Dividend HPR
Ending
Value HPR
Excellent 0.25 $ 131.00 31.00% $ 0.00 −100%
Good 0.45 114.00 14.00 $ 0.00 −100
Poor 0.25 93.25 −6.75 $ 20.25 68.75
Crash 0.05 48.00 −52.00 $ 64.00 433.33
Remember that the cost of the index fund is $100 per share, and the cost
of the put option is $12.
THE HISTORICAL RECORD
5-4
. The distributions from (01/1930–06/1974) and (07/1974–12/2018) periods
have distinct characteristics due to systematic shocks to the economy and
subsequent government intervention. While the returns from the two periods do not
differ greatly, their respective distributions tell a different story. The standard
deviation for all six portfolios is larger in the first period. Skew is also positive, but
negative in the second, showing a greater likelihood of higher-than-normal returns
in the right tail. Kurtosis is also markedly larger in the first period.
13. anominal nominal
real
1 0.80 0.70
1 0.0588, 5.88%
1 1 1.70
r r i
r or
i i
+ − −
= − = = =
+ +
b.nominal .80 .70 .10 realr i r− = − =
Clearly, the approximation gives a real HPR that is too high.
14. From Table 5.3, the average real rate on T-bills has been 0.46%.
a. T-bills: 0.46% real rate + 3% inflation = 3.46%
b. Expected return on Big/Value:
3.46% T-bill rate + 11.69% historical risk premium = 15.15%
c. The risk premium on stocks remains unchanged. A premium, the
difference between two rates, is a real value, unaffected by inflation.
15. Real interest rates are expected to rise. The investment activity will shift
the demand for funds curve (in Figure 5.1) to the right. Therefore the
equilibrium real interest rate will increase.
16. a. Probability distribution of the HPR on the stock market and put:
STOCK PUT
State of the
Economy Probability
Ending Price
+ Dividend HPR
Ending
Value HPR
Excellent 0.25 $ 131.00 31.00% $ 0.00 −100%
Good 0.45 114.00 14.00 $ 0.00 −100
Poor 0.25 93.25 −6.75 $ 20.25 68.75
Crash 0.05 48.00 −52.00 $ 64.00 433.33
Remember that the cost of the index fund is $100 per share, and the cost
of the put option is $12.
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CHAPTER 5: INTRODUCTION TO RISK, RETURN, AND
THE HISTORICAL RECORD
5-5
b. The cost of one share of the index fund plus a put option is $112. The
probability distribution of the HPR on the portfolio is:
State of the
Economy Probability
Ending Price
+ Put +
Dividend HPR
Excellent 0.25 $ 131.00 17.0% = (131 − 112)/112
Good 0.45 114.00 1.8 = (114 − 112)/112
Poor 0.25 113.50 1.3 = (113.50 − 112)/112
Crash 0.05 112.00 0.0 = (112 − 112)/112
c. Buying the put option guarantees the investor a minimum HPR of 0.0%
regardless of what happens to the stock's price. Thus, it offers insurance
against a price decline.
17. The probability distribution of the dollar return on CD plus call option is:
State of the
Economy Probability
Ending Value
of CD
Ending Value
of Call
Combined
Value
Excellent 0.25 $ 114.00 $16.50 $130.50
Good 0.45 114.00 0.00 114.00
Poor 0.25 114.00 0.00 114.00
Crash 0.05 114.00 0.00 114.00
18.
a. Total return of the bond is (100/84.49)-1 = 0.1836. With t = 10, the annual
rate on the real bond is (1 + EAR) = = 1.69%.
b. With a per quarter yield of 2%, the annual yield is = 1.0824, or
8.24%. The equivalent continuously compounding (cc) rate is ln(1+.0824)
= .0792, or 7.92%. The risk-free rate is 3.55% with a cc rate of ln(1+.0355)
= .0349, or 3.49%. The cc risk premium will equal .0792 - .0349 = .0443, or
4.433%.
c. The appropriate formula is ,
where . Using solver or goal seek, setting the
target cell to the known effective cc rate by changing the unknown variance
(cc) rate, the equivalent standard deviation (cc) is 18.03% (excel may
yield slightly different solutions).
d. The expected value of the excess return will grow by 120 months (12
months over a 10-year horizon). Therefore the excess return will be 120 ×
4.433% = 531.9%. The expected SD grows by the square root of time
THE HISTORICAL RECORD
5-5
b. The cost of one share of the index fund plus a put option is $112. The
probability distribution of the HPR on the portfolio is:
State of the
Economy Probability
Ending Price
+ Put +
Dividend HPR
Excellent 0.25 $ 131.00 17.0% = (131 − 112)/112
Good 0.45 114.00 1.8 = (114 − 112)/112
Poor 0.25 113.50 1.3 = (113.50 − 112)/112
Crash 0.05 112.00 0.0 = (112 − 112)/112
c. Buying the put option guarantees the investor a minimum HPR of 0.0%
regardless of what happens to the stock's price. Thus, it offers insurance
against a price decline.
17. The probability distribution of the dollar return on CD plus call option is:
State of the
Economy Probability
Ending Value
of CD
Ending Value
of Call
Combined
Value
Excellent 0.25 $ 114.00 $16.50 $130.50
Good 0.45 114.00 0.00 114.00
Poor 0.25 114.00 0.00 114.00
Crash 0.05 114.00 0.00 114.00
18.
a. Total return of the bond is (100/84.49)-1 = 0.1836. With t = 10, the annual
rate on the real bond is (1 + EAR) = = 1.69%.
b. With a per quarter yield of 2%, the annual yield is = 1.0824, or
8.24%. The equivalent continuously compounding (cc) rate is ln(1+.0824)
= .0792, or 7.92%. The risk-free rate is 3.55% with a cc rate of ln(1+.0355)
= .0349, or 3.49%. The cc risk premium will equal .0792 - .0349 = .0443, or
4.433%.
c. The appropriate formula is ,
where . Using solver or goal seek, setting the
target cell to the known effective cc rate by changing the unknown variance
(cc) rate, the equivalent standard deviation (cc) is 18.03% (excel may
yield slightly different solutions).
d. The expected value of the excess return will grow by 120 months (12
months over a 10-year horizon). Therefore the excess return will be 120 ×
4.433% = 531.9%. The expected SD grows by the square root of time
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Subject
Finance