SOLUTIONS MANUAL For Investment Analysis and Portfolio Management 12 Edition. Frank Reilly, Keith Br by digitaldownload87

would probably be a dissaver as income decreases (transition from a regular income to income from a pension). Of course, the earlier that this individual can start saving, the better off s/he will be. Your goal should be to start saving once you finish school. 4. The saving–borrowing pattern would vary by profession to the extent that compensation patterns vary by profession and time spent in school also varies. For most white-collar professions (for example, lawyers), income would tend to increase with age. Thus, lawyers would tend to be borrowers in the early segments (when income is low) and savers later in life. Alternatively, for bluecollar professions (for example, plumbers), in which skill is often physical, compensation tends to remain constant or decline with age. Thus, plumbers would tend to be savers in the early segments and dissavers in the later segments (when their income declines). 5. The difference is because of the definition and the measurement of return. In the case of the Wall Street Journal, they only refer to the current dividend yield on common stocks, whereas in the case of the University of Chicago studies, they talk about the total rate of return on common stocks, which is the dividend yield plus the capital gain or loss yield during the period. In the long run, the dividend yield has been 4–5 percent, and the capital gain yield has averaged about the same. In recent years, the dividend yield has been closer to 2 percent (and the amount of share repurchases has increased). Therefore, it is important to compare alternative investments based on total return. 6. The variance of expected returns represents a measure of the dispersion of actual returns around the expected value. Everything else remaining constant, the larger the variance is, the greater the dispersion of expectations and the greater the uncertainty, or risk, of the investment. The purpose of the variance is to help measure and analyze the risk associated with a particular investment. A greater variance implies a greater possibility of returns that are very different from your expected return—and that is risk. 7. An investor’s required rate of return is a function of the economy’s risk-free rate (RFR), an inflation premium that compensates the investor for the loss of purchasing power, and a risk premium that compensates the investor for taking the risk. The RFR is the pure time value of money and is the compensation an individual demands for deferring consumption. More objectively, the RFR can be measured in terms of the long-run real growth rate in the economy because the investment opportunities available in the economy influence the RFR. We think of Treasury yields (i.e., the cost of government borrowing) as the RFR. The inflation premium is the additional protection an individual requires to compensate for the erosion in purchasing power resulting from increasing prices. Because the return on all investments is not certain as it is with T-bills, the investor requires a premium for taking on additional risk. The risk premium can be examined in terms of business risk, financial risk, liquidity risk, exchange rate risk, and country risk.

8. The three main factors that influence the nominal RFR are the real growth rate of the economy, the expected rate of inflation, and liquidity (i.e., supply and demand for capital in the economy). The real growth rate and inflationary expectations have positive relationships with the nominal RFR. In other words, the higher the real growth rate, the higher the nominal RFR, and the higher the expected level of inflation, the higher the nominal RFR. Liquidity has an inverse relationship with the nominal RFR, meaning that lower liquidity results in higher yields. It is unlikely that the economy’s long-run real growth rate will change dramatically during a business cycle. However, liquidity depends upon the government’s monetary policy and would change depending upon what the government considers to be the appropriate stimulus. Besides, the demand for business loans would be greatest during the early and middle parts of the business cycle. Inflation can also change significantly during a business cycle. 9. The five factors that influence the risk premium on an investment are business risk, financial risk, liquidity risk, exchange rate risk, and country risk. Business risk is a function of sales volatility and operating leverage, and the combined effect of the two variables can be quantified in terms of the coefficient of variation of operating earnings. Financial risk is a function of the uncertainty introduced by the financing mix. The inherent risk involved is the inability to meet future contractual payments (interest on bonds, etc.) or the threat of bankruptcy. Financial risk is measured in terms of a debt ratio (for example, debt/equity ratio) and/or the interest coverage ratio. Liquidity risk is the uncertainty an individual faces when he or she decides to buy or sell an investment. The two uncertainties involved are: (1) how long it will take to buy or sell this asset and (2) what price will be received. The liquidity risk on different investments can vary substantially (for example, real estate versus T-bills). Exchange rate risk is the uncertainty of returns on securities acquired in a different currency. The risk applies to the global investor or multinational corporate manager who must anticipate returns on securities in light of uncertain future exchange rates. A good measure of this uncertainty would be the absolute volatility of the exchange rate or its beta with a composite exchange rate. Country risk is the uncertainty of returns caused by the possibility of a major change in the political or economic environment of a country. The analysis of country risk is much more subjective and must be based on the history and current environment in the country. 10. The increased use of debt increases the fixed interest payment. Since this fixed contractual payment will increase, the residual earnings (net income) will become more variable. The required rate of return on the stock will increase since the financial risk (as measured by the debt/equity ratio) has increased. 11. According to the Capital Asset Pricing Model (which will be discussed in later chapters), all securities are located on the Security Market Line, with securities’ risk on the horizontal axis and securities’ expected return on the vertical axis. As to the locations of the five types of investments on the line, the U.S. government

bonds should be located to the left of the other four, followed by the U.K. government bonds, low-grade corporate bonds, common stock of large firms, and common stocks of Japanese firms. The U.S. government bonds have the lowest risk and the required rate of return simply because they virtually have no default risk at all. The U.K. government bonds are perceived to be default risk-free but expose the U.S. investor to exchange rate risk. Low-grade corporates contain business, financial, and liquidity risks but should be lower in risk than equities. Japanese stocks are riskier than U.S. stocks due to exchange rate risk.

12. An investor seeks a return that gives him or her a real rate of return plus compensation for inflation. If a market’s real RFR is, say, 3 percent, then the investor will require a 3 percent return on an investment because this will compensate him or her for deferring consumption. If there is no expected inflation, both the real and the nominal RFR would be 3 percent. However, if the expected inflation rate is 4 percent, the investor would be worse off in real terms if he or she invests at a rate of return of 3 percent. For example, you would receive $103, but the cost of $100 worth of goods at the beginning of the year would be $104 at the end of the year, which means that you could consume less real goods. Thus, for an investment to be desirable, it should have a return of 7.12 percent (1.03  1.04 ) − 1 or an approximate return of 7 percent (3% + 4%). In other words, you must receive both a real rate of return (3 percent) and compensation for inflation (4 percent). 13. Both changes cause an increase in the required return on all investments. Specifically, an increase in the real growth rate will cause an increase in the economy’s RFR because of a higher level of investment opportunities. In addition, the increase in the rate of inflation will result in an increase in the nominal RFR. Because both changes affect the nominal RFR, they will cause an equal increase in the required return on all investments of 5 percent. The following graph shows a parallel shift upward in the capital market line of 5 percent.

14. Such a change in the yield spread would imply a change in the market risk premium because, although the risk levels of bonds remain relatively constant, investors have changed the spreads they demand to accept this risk. In this case, because the yield spread (risk premium) declined, it implies a decline in the slope of the SML, as shown in the following graph. This also implies that there would be a lower risk premium for stocks. With a lower required rate of return, you would expect stock prices to increase.

15. The ability to buy or sell an investment quickly without a substantial price concession is known as liquidity. An example of a liquid investment asset would be a United States Government Treasury Bill. A T-bill can be bought or sold in minutes at a price almost identical to the quoted price. In contrast, an example of an illiquid asset would be a specialized machine or a parcel of real estate in a remote area. In both cases, it might take a considerable period of time to find a potential seller or buyer, and the actual selling price could vary substantially from expectations.

ANSWERS TO PROBLEMS Ending Value of Investment (Including Cash Flows) Beginning Value of Investment 39 + 1.50 40.50 = = = 1.191 1. 34 34 HPY = HPR − 1 = 1.191 − 1 = 0.191 = 19.1% HPR =

61 + 3 64 = = −0.985 2. 65 65 HPY = HPR − 1 = 0.985 − 1 = −0.015 = −1.5% HPR =

3. $4,000 used to purchase 80 shares = $50 per share (59  80) + (5  80) 4,720 + 400 5,120 = = = 1.280 4,000 4,000 4,000 HPY = HPR − 1 = 1.280 − 1 = 0.280 = 28%

HPR =

59  80 4,720 = = 1.180 4,000 4,000 HPY (Price Increase Alone) = 1.180 − 1 = 0.180 = 18%

HPR (Price Increase Alone) =

Therefore, HPY ( Total ) = HPY (Price Increase ) + HPY (Div ) 0.280 = 0.180 + HPY (Div ) 0.10 = HPY (Dividends )

4. “Real” Rate of Return =

Holding Period Return −1 1 + Rate of Inflation

For Problem #1:HPR = 1.191

1.191 1.191 −1 = − 1 = 1.145 − 1 = 0.145 = 14.5% 1 + .04 1.04 1.191 1.191 at 8% inflation: −1 = − 1 = 1.103 − 1 = 0.103 = 10.3% 1 + .08 1.08

at 4% inflation:

For Problem # 2:HPR = 0.985

0.985 − 1 = 0.947 − 1 = −0.053 = −5.3% 1.04 0.985 at 8% inflation: − 1 = 0.912 − 1 = −0.088 = −8.8% 1.08

at 4% inflation:

For Problem # 3: HPR = 1.280

1.280 − 1 = 1.231 − 1 = 0.231 = 23.1% 1.04 1.280 at 8% inflation: − 1 = 1.185 − 1 = 0.185 = 18.5% 1.08

at 4% inflation:

HPYi n i =1 (0.19) + (0.08) + (−0.12) + (−0.03) + (0.15) AMT = 5 0.27 = = 0.054 5 (0.08) + (0.03) + (−0.09) + (0.02) + (0.04) AMB = 5 0.08 = = 0.016 5

Arithemetic Mean (AM) = 

5(a).

Stock T is more desirable because the arithmetic mean annual rate of return is higher.

5(b). Standard Deviation ( ) =

 [R − E(R )] / n i =1

VarianceT = (0.19 − 0.054)2 + (0.08 − 0.054)2 + (−0.12 − 0.054)2 + (−0.03 − 0.054)2 + (0.15 − 0.054)2 = 0.01850 + 0.00068 + 0.03028 + 0.00706 + 0.00922 = 0.06574

 = 0.06574 / 5 = 0.01315 2

 T = 0.01314 = 0.11467 B = (0.08 − 0.016)2 + (0.03 − 0.016)2 + (−0.09 − 0.016)2 + (0.02 − 0.016)2 + (0.04 − 0.016)2 = 0.00410 + 0.00020 + 0.01124 + 0.00002 + 0.00058 = 0.01614

 = 0.01614 / 5 = 0.00323 2

 B = 0.00323 = 0.05681 By this measure, B would be preferable. Standard Deviation of Returns Expected Rate of Return 0.11466 CVT = = 2.123 0.054 0.05682 CVB = = 3.5513 0.016

Coefficient of Variation (CV) =

5(c).

By this measure, T would be preferable.

Geometric Mean ( GM) = π1/ n – 1 where π = Product of the HRs

5(d).

GMT = (1.19 ) (1.08 ) ( 0.88 ) ( 0.97 ) (1.15 ) 

1/5

−1

= [1.26160]1/5 – 1 = 1.04757 – 1 = 0.04757 GMB = (1.08 ) (1.03 ) ( 0.91 ) (1.02 ) (1.04 ) 

1/5

−1

= [1.07383]1/5 – 1 = 1.01435 – 1 = 0.01435

Stock T has more variability than Stock B. The greater the variability of returns, the greater the difference between the arithmetic and geometric mean returns.

7. 8.

E ( RMBC ) = ( 0.30 ) ( −0.10 ) + ( 0.10 ) ( 0.00 ) + ( 0.30 ) ( 0.10 ) + ( 0.30 ) ( 0.25) = ( −0.03) + 0.000 + 0.03 + 0.075 = 0.075

E ( RLCC ) = ( 0.05) ( −0.60 ) + ( 0.20 ) ( −0.30 ) + ( 0.10 ) ( −0.10 ) + ( 0.30 ) ( 0.20 ) + ( 0.20 ) ( 0.40 ) + ( 0.15) ( 0.80 ) = ( −0.03) + ( −0.06 ) + ( −0.01) + 0.06 + 0.08 + 0.12 = 0.16 Lauren’s range of possible returns is much wider ranging from −0.60 to 0.80 than that of Madison (from −0.10 to 0.25). The expected return is also higher for Lauren at 0.16 than that of Madison at 0.075. It presents a greater risk than the Madison Beer Company as an investment.

CPIn+1 − CPIn CPIn where CPI = the Consumer Price Index

Rate of Inflation =

172 − 160 12 = = 0.075 160 160 HPR Real Rate of Return = −1 1 + Rate of Inflation 1.055 U.S. Government T-Bills = − 1 = 0.9814 − 1 = −0.0186 1.075 1.075 U.S. Government LT Bonds = −1 = 0 1.075 1.1160 U.S. Common Stocks = − 1 = 1.0381 − 1 = 0.0381 1.075

Rate of Inflation =

10. NRFR = (1 + 0.03) (1 + 0.04 ) – 1 = 1.0712 – 1 = 0.0712 (An approximation would be the growth rate plus the inflation rate or 0.03 + 0.04 = 0.07.)

11. Return on Common Stock = 7.12% + 5% = 12.12% (An approximation would be 0.03 + 0.04 + 0.05 = 0.12 or 12%.) As an investor becomes more risk averse, the investor will require a larger risk premium to own common stock. As risk premium increases, so too will the required rate of return. In order to achieve a higher rate of return, stock prices should decline. Nominal Rate on T-Bills (or Risk-Free Rate) = (1 + 0.03) (1 + 0.05) – 1

12.

= 1.0815 – 1 = 0.0815 or 8.15%

(An approximation would be 0.03 + 0.05 = 0.08.) The required rate of return on common stock is equal to the RFR plus a risk premium. Therefore, the approximate risk premium for common stocks implied by these data is 0.14 − 0.0815 = 0.0585 or 5.85%. (An approximation would be 0.14 − 0.08 = 0.06.)

APPENDIX 1: ANSWERS TO PROBLEMS 1(a).

Expected Return = (Probability of Return)(Possible Return) n

E (RGDC ) =  Pi [Ri ] i =1

= (0.25)(−0.10) + (0.15)(0.00) + (0.35)(0.10) + (0.25)(0.25) = (−0.025) + (0.000) + (0.035) + (0.0625) = (0.0725) n

 2 =  Pi [Ri − E (Ri )]2 i =1

= (0.25)(−0.100 − 0.0725)2 + (0.15)(0.00 − 0.0725)2 + (0.35)(0.10 − 0.0725)2 + (0.25)(0.25 − 0.0725)2 = (0.25)(0.02976) + (0.15)(0.0053) + (0.35)(0.0008) + (0.25)(0.0315) = 0.0074 + 0.0008 + 0.0003 + 0.0079 = 0.0164

 GDC = 0.0164 = 0.128 1(b).

Standard deviation can be used as a good measure of relative risk between two investments that have the same expected rate of return.

1(c).

The coefficient of variation must be used to measure the relative variability of two investments if there are major differences in the expected rates of return.

2(a)

E ( RKCC ) = ( 0.15 )( −0.60 ) + ( 0.10 )( −0.30 ) + ( 0.05 )( −0.10 ) + ( 0.40 )( 0.20 ) + ( 0.20 )( 0.40 ) + ( 0.10 )( 0.80 ) = ( −0.09 ) + ( −0.03 ) + ( −0.005 ) + 0.08 + 0.08 + 0.08 = 0.115

 = ( 0.15 )( −0.60 − 0.115 ) + ( 0.10 )( −0.30 − 0.115 ) 2

+ ( 0.05 )( −0.10 − 0.115 ) + ( 0.40 ) ( 0.20 − 0.115 ) 2

+ ( 0.20 )( 0.40 − 0.115 ) + ( 0.10 )( 0.80 − 0.115 ) 2

= ( 0.15 )( −0.715 ) + ( 0.10 )( −0.415 ) + ( 0.05 )( −0.215 ) 2

+ ( 0.40 )( 0.085 ) + ( 0.20 )( 0.285 ) + ( 0.10 )( 0.685 ) 2

= ( 0.15 )( 0.5112 ) + ( 0.10 )( 0.1722 ) + ( 0.05 )( 0.0462 ) + ( 0.40 )( 0.0072 ) + ( 0.20 )( 0.0812 ) + ( 0.10 )( 0.4692 ) = 0.007668 + 0.01722 + 0.00231 + 0.00288 + 0.01624 + 0.04692 = 0.16225

 KCC = 0.16225 = 0.403

2(b).

Based on [E(Ri)] alone, Kayleigh Computer Company’s stock is preferable because of the higher return available.

2(c).

Based on standard deviation alone, the Gray Disc Company’s stock is preferable because of the likelihood of obtaining the expected return because it has a lower standard deviation. Standard Deviation Expected Return 0.128 CVGDC = = 1.77 0.0725 0.403 CVKCC = = 3.50 0.115

CV =

2(d).

Based on CV, Kayleigh Computer Company’s stock return has approximately twice the relative dispersion of Gray Disc Company’s stock return. A lower CV is better. 0.063 + 0.081 + 0.076 + 0.090 + 0.085 0.395 = = 0.079 5 5 0.150 + 0.043 + 0.374 + 0.192 + 0.106 0.865 AMU.K. = = = 0.173 5 5 AMU.S. =

3(a).

Standard deviation of U.S. T-bills: 0.92% or 0.0092. Standard deviation of U.K. common stock: 11.2% or 0.112. 3(b).

The average return of U.S. government T-bills is lower than the average return

of U.S. common stocks because U.S. government T-bills are riskless; therefore, their risk premium would equal 0. The U.S. common stocks are subject to the following types of risks: business risk, financial risk, liquidity risk, exchange rate risk, and, to a limited extent, country risk. The standard deviation of the T-bills and their range (9% to −6.3%) is much less than the standard deviation and range (37.4% to −4.3%) of the U.S. common stocks.

3(c).

GM = π1/ n – 1

πU.S. = (1.063) (1.081) (1.076 ) (1.090 ) (1.085) = 1.462 GMU.S. = (1.462 )

1/5

– 1 = 1.079 – 1 = 0.079

πU.K. = (1.150 ) (1.043) (1.374 ) (1.192 ) (1.106 ) = 2.1727 GMU.K. = ( 2.1727 )

1/5

– 1 = 1.1679 – 1 = 0.1679

In the case of the U.S. government T-bills, the arithmetic and geometric means are approximately equal (0.079), which indicates a small standard deviation (which, as we saw in 3(a), equals 0.0092). The geometric mean (0.1679) of the U.S. common stocks is lower than the arithmetic mean (0.173); this is always the case when the standard deviation is nonzero. A larger standard deviation means that the difference between the arithmetic and geometric means will be larger.

Solution and Answer Guide: Frank K. Reilly, Keith, C. Brown, Sanford J. Leeds, Investment Analysis & Portfolio Management, 12th Edition, © 2025, 9780357988176; Chapter 2: Asset Allocation and Secutiry Selection

Solution and Answer Guide

TABLE OF CONTENTS Answers to Questions..........................................................................................................1 Answers to Problems ......................................................................................................... 8 Appendix 2: Answers to Problems.................................................................................... 11

ANSWERS TO QUESTIONS 1. In answering this question, one assumes that the young person has a steady job, adequate insurance coverage, and sufficient cash reserves. The young individual is in the accumulation phase of the investment life cycle. During this phase, an individual should consider moderately high-risk investments, such as common stocks, because he or she has a long investment horizon and much earning ability over time. 2. In answering this question, one assumes that the 63-year-old individual has adequate insurance coverage and a cash reserve. Depending on her income from social security, she may need some current income from her retirement portfolio to meet living expenses. At the same time, she will need to protect herself against inflation. Removing money from her company’s retirement plan and investing it in money market funds and bond funds would satisfy the investor’s short-term and income needs. However, some long-term investments, such as common stock mutual funds, are needed to provide the investor with needed inflation protection. 3. Typically, investment strategies change during an individual’s lifetime. In the accumulating phase, the individual is accumulating net worth to satisfy shortterm needs (for example, house and car purchases) and long-term goals (for example, retirement and children’s college needs). In this phase, the individual is willing to invest in moderately high-risk investments in order to achieve aboveaverage rates of return. In the consolidating phase, an investor has paid off many outstanding debts and typically has earnings that exceed expenses. In this phase, the investor is becoming more concerned with the long-term needs of retirement or estate planning. Although the investor is willing to accept moderate portfolio risk, he or she is not willing to jeopardize the “nest egg.” In the spending phase, the typical investor is retired or semiretired. This investor wishes to protect the nominal value of his/her savings, but at the same time must

make some investments for inflation protection. The gifting phase is often concurrent with the spending phase. The individual believes that the portfolio will provide sufficient income to meet expenses, plus a reserve for uncertainties. If an investor believes there are excess amounts available in the portfolio, he/she may decide to make “gifts” to family or friends, institute charitable trusts, or establish trusts to minimize estate taxes. 4. A policy statement is important for both the investor and the investment advisor. A policy statement assists the investor in establishing realistic investment goals, as well as providing a benchmark by which a portfolio manager’s performance may be measured. 5. The 45-year-old uncle and 35-year-old sister differ in terms of time horizon. However, each has some time before retirement (20 versus 30 years). Each should have a substantial proportion of his/her portfolio invested in equities, with the 35year-old sister possibly having more equity investments in small firms or international firms (i.e., can tolerate greater portfolio risk). These investors could also differ in current liquidity needs (such as children and education expenses), tax concerns, and/or other unique needs or preferences. 6. Before constructing an investment policy statement, the financial planner needs to clarify the client’s investment objectives (for example, capital preservation, capital appreciation, current income, or total return) and constraints (for example, liquidity needs, time horizon, tax factors, legal and regulatory constraints, and unique needs and preferences). Data on current investments, portfolio returns, and savings plans (future additions to the portfolio) are helpful as well. 7. Student Exercise 8. CFA Examination III (1993) 8(a). At this point, we know (or can reasonably infer) that Mr. Franklin is •

unmarried (a recent widower)

•

childless

•

70 years of age

•

in good health

•

possessed a large amount of (relatively) liquid wealth intending to leave his estate to a tax-exempt medical research foundation, to whom he is also giving a large current cash gift

•

free of debt (not explicitly stated, but neither is the opposite)

•

in the highest tax brackets (not explicitly stated, but apparent)

•

not skilled in the management of a large investment portfolio, but also not a

complete novice because he owned significant assets of his own prior to his wife’s death •

not burdened by large or specific needs for current income

•

not in need of large or specific amounts of current liquidity

Taking this knowledge into account, his Investment Policy Statement will reflect these specifics: Objectives: Return requirements: The incidental throw-off of income from Mr. Franklin’s large asset pool should provide a more than sufficient flow of net spendable income. If not, such a need can easily be met by minor portfolio adjustments. Thus, an inflation-adjusted enhancement of the capital base for the benefit of the foundation will be the primary return goal (i.e., real growth of capital). Tax minimization will be a continuing collateral goal. Risk tolerance: Account circumstances and the long-term return goal suggest that the portfolio can take somewhat above-average risk. Mr. Franklin is acquainted with the nature of investment risk from his prior ownership of stocks and bonds, he has a still long actuarial life expectancy and is in good current health, and his heir—the foundation, thanks to his generosity—is already possessed of a large asset base. Constraints: Time horizon: Even disregarding Mr. Franklin’s still-long actuarial life expectancy, the horizon is long term because the remainder of his estate, the foundation, has a virtually perpetual life span. Liquidity requirement: Given what we know and the expectation of an ongoing income stream of considerable size, no liquidity needs that would require specific funding appear to exist. Taxes: Mr. Franklin is no doubt in the highest tax brackets, and investment actions should take that fact into account on a continuing basis. Appropriate tax-sheltered investments (standing on their own merits as investments) should be considered. Tax minimization will be a specific investment goal. Legal and regulatory: Investments, if under the supervision of an investment management firm (i.e., not managed by Mr. Franklin himself) will be governed by state law and the prudent person rule. Unique circumstances: The large asset total, the foundation as their ultimate recipient, and the great freedom of action enjoyed in this situation (i.e., freedom from confining considerations) are important in this situation, if not necessarily unique. 8(b). Given that stocks have provided (and are expected to continue to provide) higher risk-adjusted returns than either bonds or cash, and considering that the return goal is for long-term, inflation-protected growth of the capital base, stocks will be allotted the majority position in the portfolio. This is also consistent with Mr. Franklin’s absence of either specific current income needs (the ongoing cash flow should provide an adequate level for current spending) or specific liquidity needs. It is likely that income will accumulate to some extent and, if so, will automatically build a liquid emergency fund for Mr. Franklin as time passes. © 2025 Cengage Learning, Inc. All Rights Reserved. May not be scanned, copied or duplicated, or posted to a publicly accessible website, in whole or in part.

Because the inherited warehouse and the personal residence are significant (15 percent) real estate assets already owned by Mr. Franklin, no further allocation to this asset class is made. It should be noted that the warehouse is a source of cash flow, a diversifying asset and, probably, a modest inflation hedge. For tax reasons, Mr. Franklin may wish to consider putting some debt on this asset, freeing additional cash for alternative investment use. Given the long-term orientation and the above-average risk tolerance in this situation, about 70 percent of total assets can be allocated to equities (including real estate) and about 30 percent to fixed-income assets. International securities will be included in both areas, primarily for their diversification benefits. Municipal bonds will be included in the fixed-income area to minimize income taxes. There is no need to press for yield in this situation, nor any need to deliberately downgrade the quality of the issues utilized. Venture capital investment can be considered, but any commitment to this (or other “alternative” assets) should be kept small. The following is one example of an appropriate allocation that is consistent with the Investment Policy Statement and the historical and expected return and other characteristics of the various available asset classes: Current Range (%) Target (%) Cash/money market 0–5 0 U.S. fixed income 10–20 15 Non-U.S. fixed income 5–15 10 U.S. stocks (large cap) 30–45 30 (small cap) 15–25 15 Non-U.S. stocks 15–25 15 Real estate 10–15 15* Other 0–5 0 100 *Includes the Franklin residence and warehouse that together comprise the proportion of the total assets shown. 9. The major advantage of investing in common stocks is that generally, an investor would earn a higher rate of return than on corporate bonds over the long term. Also, while the return on bonds is prespecified and fixed, the return on common stocks can be substantially higher if the investor can pick a “winner,” that is, if the company’s performance turns out to be better than current market expectations. The main disadvantage of common stock ownership is the higher risk. While the income on bonds is certain (except in the extreme case of bankruptcy), the return on stocks will vary depending upon the future performance of the company and could well be negative. The coupon income from bonds will be taxed each year. The shareholder will be taxed for dividends (at a lower rate if the investor holds the stock for a period long enough to be considered a “qualified dividend”) and will not be taxed for any gains until the stock is sold. A line graph of returns over time should indicate a lower average level of return and lower variability of returns over time for bonds than for common stock. 10. The three factors are: (1) Limiting oneself to the U.S. securities market would imply effectively ignoring more than 50 percent of the world securities market. While U.S. markets are © 2025 Cengage Learning, Inc. All Rights Reserved. May not be scanned, copied or duplicated, or posted to a publicly accessible website, in whole or in part.

still the largest single sector, foreign markets have been growing in absolute and relative size since 1969. (2) The rates of return available on non-U.S. securities often have substantially exceeded those of U.S. securities. (3) Diversification with foreign securities reduces portfolio risk. 11. International diversification reduces portfolio risk because of the low correlation of returns among the securities from different countries. This is due to differing international trade patterns, economic growth, fiscal policies, and monetary policies among countries. 12. There are different correlations of returns between securities from the U.S. and alternate countries because there are substantial differences in the economies of the various countries (at a given time) in terms of inflation, international trade, monetary and fiscal policies, and economic growth. 13. The correlations between U.S. stocks and stocks for different countries should change over time because each country has a fairly independent set of economic policies. Factors influencing the correlations include international trade, economic growth, fiscal policy, and monetary policy. A change in any of these variables will cause a change in how the economies are related. For example, the correlation between U.S. and Japanese stocks will change as the balance of trade shifts between the two countries. Closer economic ties and increased trade will likely result in higher correlations between financial markets. For example, we expect larger correlations between the U.S. and Canada; Canada is the largest trading partner of the U.S. 14. The major risks that an investor must consider when investing in any bond issue are business risk, financial risk, and liquidity risk. Additional risks associated with foreign bonds, such as Japanese or German bonds, are exchange rate risk and country risk. Country risk is not a major concern for Japanese or German securities. Exchange rate risk is the uncertainty that arises from floating exchange rates between the U.S. dollar and the Japanese yen or euro. 15. The additional risks that some investors believe international investing introduces include foreign exchange risk and country risk. As an example, if you invested in Japan in 2021, you would have been hurt if you had sold that investment during much of 2022 because the yen weakened significantly during that period. In addition, if you invested in Ukraine prior to Russia’s invasion, you would have lost 65 percent for the year ended November 30, 2022. 16. There are four alternatives to direct investment in foreign stocks available to investors: (1) purchase of American Depository Receipts (ADRs) (2) purchase of American shares

(3) direct purchase of foreign shares listed on a foreign or U.S. exchange (4) purchase of international mutual funds 17. Unlike corporate bonds, interest on municipal bonds is exempt from taxation by the federal government and by the state that issued the bond, provided the investor is a resident of that state. For instance, a marginal tax rate of 35 percent means that a regular bond with an interest rate of 8 percent yields a net return after taxes of only 5.20 percent [0.08  (1 − 0.35)] . A tax-free bond with a 6 percent yield would be preferable. 18. The convertible bond of the growth company would have a lower yield. This is intuitive because there is a greater potential for the price of the growth company stock to increase, which would make the conversion feature of the bond extremely attractive. Thus, the investor would be willing to trade-off the higher upside potential resulting from conversion for the lower yield. 19. Liquidity is the ability to buy or sell an asset quickly at a price similar to the prior price assuming no new information has entered the market. Common stocks have the advantage of liquidity because it is very easy to buy or sell a small position (there being a large number of potential buyers) at a price not substantially different from the current market price. Raw land is relatively illiquid because it is often difficult to find a buyer immediately and often the prospective buyer will offer a price that is substantially different from what the owner considers to be the true market value. A reason for this difference is that while common stock data are regularly reported in a large number of daily newspapers and several magazines and closely watched by a large number of individuals, raw land simply lacks this kind of interest. Further, the speculative nature of raw land investment calls for high risk and longer maturity before profits can be realized. Finally, the initial investment on a plot of raw land would be substantially greater than a round lot in most securities. As a result, the small investor is generally precluded from this kind of investment. 20. Art and antiques are considered illiquid investments because in most cases they are sold at auctions. The implication of being traded at auctions rather than on a developed exchange is that there is tremendous uncertainty regarding the price to be received and it takes a long time to contact a buyer who offers the “right” price. Besides, many buyers of art and antiques are accumulators rather than traders, and this further reduces trading. Coins and stamps are more liquid than art and antiques because an investor can determine the “correct” market price from several weekly or monthly publications. There is no such publication of current market prices of the numerous unique pieces of art and antiques and owners are forced to rely on dealer estimates. Further, while a coin or stamp can be readily disposed of to a dealer at a commission of about 10– 15 percent, the commissions on paintings range from 30 to 50 percent. To sell a portfolio of stocks that are listed on the New York Stock Exchange, an investor simply contacts his/her broker to sell the shares. The cost of trading stocks

varies depending on whether the trade is handled by a full-service broker or a discount broker. 21. Emerging market stocks will not be perfectly correlated with U.S. stocks. As a result, if these stocks are fairly priced, they could reduce the volatility of your portfolio. It is possible, however, that these stocks will be less liquid. 22. International stocks versus U.S. stocks—problems: (1) Information about foreign firms is often difficult to obtain on a timely basis and once obtained can be difficult to interpret and analyze due to language and presentation differences. (2) Financial statements are not comparable from country to country. Different countries use different accounting principles. Even when similar accounting methods are used, cultural, institutional, political, and tax differences can make cross-country comparisons hazardous and misleading. Stock valuation techniques useful in the United States may be less useful in other countries. Stock markets in different countries value different attributes. (3) Currency and political risk must be considered when selecting non-U.S. stocks for a portfolio. (4) Increased costs: custody, management fees, and transaction expenses are usually higher outside the United States. 23. Arguments in favor of adding international securities include the following: (1) Benefits gained from broader diversification, including economic, political, and/or geographic sources. (2) Expected higher returns at the same or lower (if properly diversified) level of portfolio risk. (3) Advantages accruing from improved correlation and covariance relationships across the portfolio’s exposures. (4) Improved asset allocation flexibility, including the ability to match or hedge non-U.S. liabilities. (5) A wider range of industry and company choices for portfolio construction purposes. (6) A wider range of managers through whom to implement investment decisions. (7) Diversification benefits are realizable despite the absence of non-U.S. pension liabilities. At the same time, there are a number of potential problems associated with moving away from a domestic-securities-only orientation: (1) Possible higher costs, including those for custody, transactions, and management fees. (2) Possibly reduced liquidity, especially when transacting in size. (3) Possible unsatisfactory levels of information availability, reliability, scope, timeliness, and understandability. (4) Risks associated with currency management, convertibility, and regulations/controls. (5) Risks associated with possible instability/volatility in both markets and governments. (6) Possible tax consequences or complications. (7) Recognition that overseas investments may underperform U.S. investments.

ANSWERS TO PROBLEMS 1.

Most experts recommend that about six months’ worth of living expenses be held in cash reserves. Although these funds are identified as “cash,” it is recommended that they be invested in instruments that can easily be converted to cash with little chance of loss in value (for example, money market mutual funds, etc.). Most experts recommend that an individual should carry life insurance equal to 7–10 times an individual’s annual salary, but the final determination needs to include the expected expenses and needs facing one’s dependents over their lifetime. An unmarried individual may not need coverage but should consider purchasing some insurance while they are “insurable,” meaning that they are young and have fewer health issues that may make obtaining insurance more difficult or expensive. A married individual with two children should definitely have coverage (possibly 9–10 times their salary as a starting point, to be refined after considering the living expenses of loved ones, desire to provide for the college education of children, and so on).

2(a). $10,000 invested in a 9 percent tax-exempt IRA (assuming annual compounding) in 5 years : $10,000 (FVIF @ 9% ) = $10,000 (1.5386 ) = $15,386

in 10 years : $10,000 (FVIF @ 9% ) = $10,000 (2.3674 ) = $23,674 in 20 years : $10,000 (FVIF @ 9% ) = $10,000 ( 5.6044 ) = $56,044 After-tax yield = Before-tax yield (1 − Tax rate)

2(b).

= 9%(1 − 0.36) = 5.76% $10,000 invested at 5.76 percent (assuming annual compounding) in 5 years : $10,000(FVIF @ 5.76%) =$13,231 in10 years : $10,000(FVIF @ 5.76%) =$17,507

in 20 years : $10,000(FVIF @ 5.76%) =$30,650

3(a).

$10,000 invested in a 10 percent tax-exempt compounding) in 5 years : $10,000(FVIF @10%) =$10,000(1.6105) =$16,105 in10 years : $10,000(FVIF @10%) =$10,000(2.5937) =$25,937

IRA

(assuming

annual

in 20 years : $10,000(FVIF @10%) =$10,000(6.7275) =$67,275

After-tax yield = Before-tax yield (1 − Tax rate)

3(b).

= 10%(1 − 0.15) = 8.50%

$10,000 invested at 8.50 percent (assuming annual compounding) in 5 years : $10,000(FVIF @8.50%) =$15,037

in10 years : $10,000(FVIF @8.50%) =$22,610 in 20 years : $10,000(FVIF @8.50%) =$51,120 .

With inflation growing at 3 percent annually, the above figures need to be deflated by the following factors: in 5 years : (1.03)5 = 1.1593 in10 years : (1.03)5 = 1.3439 in 20 years : (1.03)5 = 1.8061

The real values of the answers from 4(a) are: $10,000 invested in a 9 percent taxexempt IRA (assuming annual compounding). in 5 years : $15,386/1.1593 =$13,271.80 in10 years : $23,674/ 1.3439 =$17,615.89 in 20 years : $56,044/ 1.8061 =$31,030.40

The real values of the answers from 5(a) are: $10,000 invested in a 10 percent taxexempt IRA (assuming annual compounding). in 5 years: $16,105/ 1.1593=$13,892.00 in10 years: $25,937/1.3439 = $19,299.80 in 20 years: $67,275/1.8061 =$37,248.77

5. 6. 7. 8(a).

Student Exercise Student Exercise Student Exercise The arithmetic average assumes the presence of simple interest, while the geometric average assumes compounding or interest-on-interest. As long as there is variation in returns, the geometric mean will always be smaller than the arithmetic mean. In addition, the greater the standard deviation, the greater the disparity between the arithmetic and geometric means. The arithmetic mean is our best prediction for a single-period return. The geometric mean is our best prediction of how money will compound. The geometric mean internal rate of return is a critical concept in security and portfolio selection as well as performance measurement in a multiperiod framework. 8(b). Ranking is best accomplished by using the coefficient of variation (standard deviation/arithmetic mean, multiplied by 100): Real estate 47.42 Treasury bills 90.40 Long govt. bonds 125.49 Long corp. bonds 161.34 Common stocks 164.40

Expected mean plus or minus two standard deviations: Arithmetic:10.28%  16.9%(2) = − 23.52% to + 44.08% 9.

If inflation is 3 percent, Realrate of return = (1 + return)/(1+ inflationrate) − 1 T-bills:realreturn = 1.035/1.03 − 1 = 0.0049 Large-cap common stock:realreturn = 1.1175/1.03 − 1 = 0.0850 Long-term corporate bond:realreturn = 1.0550/1.03 − 1 = 0.0243 Long-term government bond:realreturn = 1.0490/1.03 − 1 = 0.0184 Small-cap common stock:realreturn = 1.1310/1.03 − 1 = 0.0981

APPENDIX 2: ANSWERS TO PROBLEMS Lauren’s average return

(5 + 12 − 11 + 10 + 12) 5 = 28 / 5 = 5.6

Kayleigh’s average return (5 + 15 + 5 + 7 − 10) 5 = 22 / 5 = 4.4

L−L

K −K

5 − 5.6 = − 0.6

5 − 4.4 =0.6

12 − 5.6 = 6.4

15 − 4.4 = 10.6

−11 − 5.6 = − 16.6

5 − 4.4 = 0.6

10 − 5.6 = 4.4

7 − 4.4 = 2.6

12 − 5.6 = 6.4

−10 − 4.4 = − 14.4

(L − L) (K − K) N (−0.6)(0.6) + (6.4)(10.6) + (−16.6)(0.6) + (4.4)(2.6) + (6.4)(−14.4) = 5 −23.2 = = −4.64 5

CovLK =

3. Calculation of correlation coefficient (L − L ) 1 −0.6 2 6.4 3 −16.6 4 4.4 5 6.4 377.2 = 75.44 5

(K − K )2 0.36 112.36 6.76 0.36 207.36 327.20 327.2  K2 = = 65.44 5

 L = 75.44 = 8.69

 K = 65.44 = 8.09

 L2 =

rLK =

Cov LK

 L K

(L − L )2 0.36 40.96 275.56 19.36 40.96 377.20

(K − K ) 0.6 10.6 2.6 0.6 −14.4

−4.64 = −0.066 (8.69)(8.09)

While there is a slight negative correlation, the two securities are essentially uncorrelated. Thus, even though the two companies produce similar products, their historical returns suggest that holding both of these securities would help reduce risk through diversification.

Solution and Answer Guide: Frank K. Reilly, Keith, C. Brown, Sanford J. Leeds, Investment Analysis & Portfolio Management, 12th Edition, © 2025, 9780357988176; Chapter 3: Organization And Functioning Of Securities Markets

Solution and Answer Guide

TABLE OF CONTENTS Answers to Questions...........................................................Error! Bookmark not defined. Answers to Problems ......................................................................................................... 4

ANSWERS TO QUESTIONS 1. A market is a means whereby buyers and sellers are brought together to aid in the transfer of goods and/or services. While it generally has a physical location, it need not necessarily have one. Secondly, there is no requirement of ownership by those who establish and administer the market—they need only to provide a cheap, smooth transfer of goods and/or services for a diverse clientele. A good market should provide accurate information on the price and volume of past transactions and current supply and demand. Clearly, there should be rapid dissemination of this information. Adequate liquidity is desirable so that participants may buy and sell their goods and/or services rapidly at a price that reflects the supply and demand. The costs of transferring ownership and middleman commissions should be low. Finally, the prevailing price should reflect all available information. 2. This is a good discussion question for class because you could explore with students what are some of the alternatives that are used by investors with regard to other assets, such as art and antiques. One primary concern is that you as a seller may not know what a fair price is for your stock. In order to try to sell the shares, one possibility is to put an ad in the paper of your local community or in large cities. Another obvious alternative is an auction or the use of a website such as eBay. With an ad, you would have to specify a price or be ready to negotiate with a buyer. With an auction (internet-based or otherwise), you would be very uncertain of what you would receive. In all cases, there would be a substantial time problem—it may take days, weeks, or longer before you obtain an acceptable price for your shares. 3. Liquidity is the ability to sell an asset quickly at a price not substantially different from the current market, assuming no new information is available. A share of AT&T is very liquid, while an antique would be a fairly illiquid asset. A share of AT&T is highly liquid because an investor could convert it into cash within a few cents of the current market price. An antique is illiquid because it is relatively difficult to find a buyer, and you are uncertain as what price the prospective buyer will offer. U.S. Treasury securities are usually considered to be the most liquid assets in the world.

4. The primary market in securities is where new issues are sold by corporations to acquire new capital via the sale of bonds, preferred stock, or common stock. The sale typically takes place through an investment banker. The secondary market is simply trading in outstanding securities. It involves transactions between owners after the issue has been sold to the public by the company. Consequently, the proceeds from the sale do not go to the company, as is the case with a primary offering. Thus, the price of the security is important to the buyer and the seller. The functioning of the primary market would be seriously hampered in the absence of a good secondary market. A good secondary market provides liquidity to an investor if he or she wants to alter the composition of his or her portfolio from securities to other assets (i.e., house, etc.). Thus, investors would be reluctant to acquire securities in the primary market if they felt they would not subsequently be able to sell the securities quickly at a known price. 5. An example of an initial public offering (IPO) would be a small company selling company stock to the public for the first time. By contrast, a seasoned equity refers to an established company, such as Google, offering a new issue of common stock to an existing market for the stock. The IPO involves greater risk for the buyer because there is not an established secondary market for the small firm. Without an established secondary market, the buyer incurs additional liquidity risk associated with the IPO. 6. Student Exercise 7. In competitive-bid underwriting, the issuer is responsible for specifying the type of security to be offered, the timing, and so on, and then soliciting competitive bids from investment banking firms wishing to act as an underwriter. The high bids will be awarded the contracts. Negotiated underwritings are contractual arrangements between an underwriter and the issuer wherein the underwriter helps the issuer prepare the security issue with the understanding that they have the exclusive right to sell the issue. 8. NASDAQ is the largest U.S. secondary market in terms of the number of issues traded and in the amount of trading. NYSE stocks, however, have a larger aggregate market capitalization. In 2022, there were 3,200 stocks trading on the NYSE and 4,800 stocks trading on the NASDAQ. 9(a). A market order is an order to buy/sell a stock at the most profitable ask/bid prices prevailing at the time the order hits the exchange floor or the quote system on the trading platform. A market order implies the investor wants the transaction completed quickly at the prevailing price. Example: I read good reports about AT&T and I’m certain the stock will go up in value. When I call my broker and submit a market buy order for 100 shares of AT&T, the prevailing asking price is 60. The total cost for my shares will be $6,000 plus commission. 9(b). A limit order specifies a maximum price that the individual will pay to purchase the stock or the minimum he will accept to sell it. Example: If AT&T is selling for $60, then I would put in a limit buy order for one week to buy 100 shares at $59. Or, I could put in a limit order to sell at $61. Whether you are placing a limit order to buy or a limit order to sell, you are effectively saying that you only want to enter into a transaction if you can obtain a more attractive price than currently is quoted (i.e., you can buy for less than the current price or sell for more than the

current price). 9(c).

A short sale is the sale of stock that is not currently owned by the seller with the intent of purchasing it later at a lower price. This is done by borrowing the stock from another investor through a broker. Example: If I expect AT&T to go to $48, then I would sell it short at $60 and hope to replace it when it gets to $55.

9(d).

A stop-loss order is a conditional order whereby the investor indicates that he wants to sell the stock if the price drops to a specified price, thus protecting himself from a large and rapid decline in price. Example: If I buy AT&T at $60 and put in a stop loss at $57, then that (hopefully) protects me from a major loss if it starts to decline. It is always possible that a stock will “gap down” and start trading at a much lower level after bad news is released. Imagine, for example, bad news comes out and the stock drops to $40. Since the stock went below $57, the stop loss order has effectively told the broker to sell the stock at the current market price ($40).

10.

The designated market maker (or “specialist”) acts as a broker in handling limit orders placed with member brokers. Being constantly in touch with current prices, he is in a better position to execute limit orders because they are entered into his books and executed as soon as appropriate. Second, he maintains a fair and orderly market by trading on his own account when there is inadequate supply or demand. If the spread between the bid and ask is substantial, he can place his own bid or ask in order to narrow the spread. This helps provide a continuous market with orderly price changes. On a call market exchange, a designated market maker would call the roll of stocks and ask for interest in one stock at a time. After determining the available buy and sell orders, exchange officials would specify a single price that will satisfy most of the orders, and all orders are transacted at this designated price. The NYSE, which is a continuous market, also employs a call-market mechanism at the open and during trading suspensions. The specialist obtains income from both his functions: commissions as a broker and outperforming the market in his dealer function using the monopolistic information he has on limit orders.

11(a). Dark Pools—Orders put into a dark pool are not displayed to other market participants in order to reduce information leakage and minimize market impact costs and are sold to anonymous buyers. The participants on both sides of the trade are generally in the pool by invitation. The advantage to participants beyond anonymity is better pricing (at the midpoint of the bid–ask spread) and lower transaction fees. In terms of regulation, dark pools are registered as ATSs. Finally, they report their transactions on the composite tape, and it is estimated that they are responsible for about 25 percent of trading volume. 11(b). Broker/Dealer Internalization—Internalization is when retail brokers/dealers internally transact an order by buying or selling the stock against their own account on a consistent basis. Put another way, the firm is the counterparty to all transactions and uses its own capital. It is considered “dark liquidity” because the brokers are acting as OTC market makers and are not required to display quotes prior to execution. These firms are also allowed to report all trades to the consolidated tape, so there is post-trade information and account for about 18 percent of total trading volume and almost 100 percent of all retail marketable order flow.

11(c). High-Frequency Traders—HFTs are professionals and institutions who use AT to create programs that are traded thousands of times a day for small profits. They bring significant liquidity to the market, smaller bid–ask spreads, and substantially lower transaction costs. It is estimated that about 50 percent of all trading volume is attributable to HFTs. They are reviled because they bring added volatility to the market because their algorithms can cause significant shifts in the volume of trading and prices. Also, they contribute to a short-term attitude toward investing when capital markets are meant to determine intrinsic value based on cash flows over very long horizons. 11(d). Algorithmic Trading—Algorithmic trading is basically creating computer programs to make trading decisions. The decisions have become more sophisticated and complex, including simultaneously buying in one market and selling in another for a small profit or programming that would trade based on important company news (for example, earning surprises or merger announcements) or macroeconomic events, such as Federal Reserve decisions or domestic or international political news.

ANSWERS TO PROBLEMS 1(a).

Assume you pay cash for the stock: Number of shares you could purchase = $40,000/$80 = 500 shares. (1)

If the stock is later sold at $100 a share, then the total share proceeds would be

$100  500 shares = $50,000 . Therefore, the rate of return from investing in the stock is as

follows: $50,000 − $40,000 = 25% $40,000

(2)

If the stock is later sold at $40 a share, then the total share proceeds would be $40  $500 shares = $20,000 . Therefore, the rate of return from investing in the stock

would be: =

$20,000 − $40,000 = −50% $40,000

1(b). Assuming you use the maximum amount of leverage in buying the stock, the leverage factor for a 60 percent margin requirement is = 1/percentage margin requirement = 1/0.60 = 5/3. Thus, the rate of return on the stock if it is later sold at $100 a share = 25%  5 / 3 = 41.67% . In contrast, the rate of return on the stock if it is sold for $40 a share: = −50%  5 / 3 = −83.33%.

2(a).

Because the margin is 40 percent and Lauren currently has $50,000 on deposit in her margin account, if Lauren uses the maximum allowable margin, then her $50,000 deposit must

represent 40 percent of her total investment. Thus, $50,000 = 0.4x and x = $125,000. This sum represents $50,000 of her own funds (equity) and $75,000 of borrowed funds. Because the shares are priced at $35 each, Lauren can purchase $125,000 / $35 = 3,571 shares (rounded).

Total Profit = Total Return − Total Investment

2(b).

If the stock rises to $45 / share, Lauren’s total return is: 3,571 shares  $45 = $160,695. Total profit = $160,695 − $125,000 = $35,695.

(1)

Lauren’s profit is computed as : $160,695 − $75,000 borrowing = $85,695; because her initial equity was $50,000, her profit is $85,695 − $50,000 = $35,695, which is the same as computed above. If the stock falls to $25 / share, Lauren’s total return is: 3,571 shares  $25 = $89,275.

(2)

Total loss = $89,275 − $125,000 = −$35,725.

2(c)

Margin =

Market Value − Debit Balance , Market Value

where Market Value = Price per Share  Number of Shares.

Initial Loan Value = Total Investment − Initial Margin = $125,000 − $50,000 = $75,000

Therefore, if the maintenance margin is 30 percent, 0.30 =

(3,571 shares  Price) − $75,000 (3,571 shares  Price)

0.30 ( 3,571  Price ) = ( 3,571  Price ) − $75,000 1,071.3  Price = ( 3,571  Price ) − $75,000 − 2,499.7  Price = −$75,000 Price = $30.00

3. Profit = Ending Value − Beginning Value + Dividends − Transaction Costs − Interest Beginning Value of Investment = $20  100 shares = $2,000

Your Investment = Margin Requirement = ( 0.55  $2,000 ) = $1,100 Ending Value of Investment = $27  100 shares = $2,700 Dividends = $0.50  100 shares = $50.00 Transaction Costs = $0

Interest = 0.05  ( 0.45  $2,000 ) = $45.00 Therefore, Profit = $2,700 − $2,000 + $50 −$45 = $705

The rate of return on your investment of $1,100 is: $706 / $1,100 = 64.1%

Profit on a Short Sale = Begin Value − Ending Value − Dividends − Trans. Costs − Interest

Beginning Value of Investment = $56.00  100 shares = $5,600

( sold under a short sale arrangement) Your Investment = Margin Requirement = ( 0.45  $5,600 ) = $2,520

Ending Value of Investment = $45.00  100 = $4,500

( Cost of closing out position) Dividends = $2.50  100 shares = $250.00 Transaction Costs = $0

Interest = 0.08  $5,600) = $448 ( an investor pays interest on the total value of the shares borrowed) Therefore, Profit = $5,600 − $4,500 − $250 − $448 = $402

The rate of return on your investment of $2,520 is: $402 / $2,520 = 15.95%

5(a).

I want to protect some of the profit I have; should prices drop I will still have a profit of $15/share. This is assuming that the stock is sold at $40. It is always possible that a stock can “gap down” and trade much lower. There is nothing guaranteeing you the ability to sell at $40.

5(b).

With the stop loss : ( $40 − $25 ) / $25 = 60%. Again, this is assuming that the stock is sold at $40. It is always possible that a stock can “gap down” and trade much lower. There is nothing guaranteeing you the ability to sell at $40.

6(a).

Assuming that you pay cash for the stock:

Rate of Return =

($45  300) − ($30  300) 13,500 − 9,000 = = 50% ($30  300) 9,000

This is the return earned over two years, so the annualized return is (1 + 0.50 )

1/2

6(b).

− 1 = 22.47% .

Assuming that you used the maximum leverage in buying the stock, the leverage factor for a 60 percent margin requirement is = 1/margin requirement = 1/.60 = 1.67. Thus, the rate of return on the stock if it is later sold at $45 a share = 50%  1.67 = 83.33% .

The annualized return is (1 + 0.8333 )

1/2

– 1 = 35.4%

Limit order @ $24: Assuming that the stock traded continuously from $28 down to $20, your order was executed at $24. Then, the price went to $36.

Rate of Return = ( $36 − $24 ) / $24 = 50% Assuming market order @ $28: Buy at $28, the price goes to $36.

Rate of Return = ( $36 − $28 ) / $28 = 28.57% Limit order @ $18: Because the market did not decline to $18 (the lowest price was $20), the limit order was never executed.

Solution and Answer Guide: Frank K. Reilly, Keith, C. Brown, Sanford J. Leeds, Investment Analysis & Portfolio Management, 12th Edition, © 2025, 9780357988176; Chapter 4: Security Market Indexes And Index Funds

Solution and Answer Guide

ANSWERS TO QUESTIONS 1. The purpose of security market indexes is to provide a general indication of the aggregate market changes or market movements. More specifically, the indexes are used to derive market returns for a period of interest and then used as a benchmark for evaluating the performance of alternative portfolios. A second use is in examining the factors that influence aggregate stock price movements by forming relationships between market (series) movements and changes in the relevant variables in order to illustrate how these variables influence market movements. A third use is by technicians who use past aggregate market movements to predict future price patterns. A fourth use is to provide the basis for an index fund (or an ETF) that tracks the index and gives investors a low-cost opportunity to earn the returns that an index earned during a period. Finally, a very important use is in portfolio theory, where the systematic risk of an individual security is determined by the relationship between the rates of return for the individual security and the rates of return for a market portfolio of risky assets. Here, a representative index is used as a proxy for the market portfolio of risky assets. 2. A characteristic that differentiates alternative market indexes is the sample—the size of the sample (how representative of the total market it is) and the source (whether securities are of a particular type or a given segment of the population [NYSE, TSE]). The weight given to each member plays a discriminatory role—with diverse members in a sample, it would make a difference whether the index is price-weighted, value-weighted, or unweighted. Finally, the computational procedure is used for calculating return, that is, whether arithmetic mean, geometric mean, etc. 3. A price-weighted series is an arithmetic average of the current prices of the securities included in the sample, that is, closing prices of all securities are summed and divided by the number of securities in the sample. Over time, as a result of stock splits, the divisor will move away from the number of stocks that are in the index. The divisor will be adjusted so that a stock split does not change the value of an index. For example, we wouldn’t want the Dow Jones Industrial Average to decrease in value simply because a member stock did a stock split. A $100 security will have a greater influence on the series than a $25 security because a 10 percent increase in the former increases the numerator by $10, while it takes a 40 percent increase in the price of the latter to have the same effect. Said differently, a 10 percent increase

in the higher-priced stock results in a 10-point increase in the numerator, while a 10 percent increase in the lower-priced stock results in a $2.50 increase in the numerator. 4. A value-weighted index begins by deriving the initial total market value of all stocks used in the series (market value equals number of shares outstanding multiplied by current market price). The initial value is typically established as the base value and assigned an index value of 100. Subsequently, a new market value is computed for all securities in the sample, and this new value is compared to the initial value to derive the percent change, which is then applied to the beginning index value of 100. 5. Given a four-security series and a 2-for-1 split for security A and a 3-for-1 split for security B, the divisor would change from 4 to 2.8 for a price-weighted series. Stock

Before Split Price

After Split Prices

$20

$10

Total

100/4 = 25

70/x = 25 x = 2.8

The price-weighted series adjusts for a stock split by deriving a new divisor that will ensure that the new value for the series is the same as it would have been without the split. The adjustment for a value-weighted series due to a stock split is automatic. The decrease in stock price is offset by an increase in the number of shares outstanding. Before Split Stock

Price/Share

# of Shares

Market Value

$20

1,000,000

$20,000,000

500,000

15,000,000

2,000,000

40,000,000

3,500,000

105,000,000

Total

$180,000,000

The $180,000,000 base value is set equal to an index value of 100. After Split Stock

Price/Share

# of Shares

Market Value

$10

2,000,000

$20,000,000

1,500,000

15,000,000

2,000,000

40,000,000

3,500,000

105,000,000

Total

$180,000,000

Current Market Value  Beginning Index Value Base Value 180,000,000 =  100 180,000,000 = 100 which is precisely what one would expect because there has been no change in prices other than the split. 6. In an unweighted price index series (perhaps more appropriately called an “unweighted” or “equally weighted” index), all stocks carry equal weight irrespective of their price and/or value. One way to visualize an unweighted series is to assume that equal dollar amounts are invested in each stock in the portfolio, for example, an equal amount of $1,000 is assumed to be invested in each stock. Therefore, the investor would own 25 shares of GM ($40/share) and 40 shares of Coors Brewing ($25/share). An unweighted price index that consists of these two stocks would be constructed as follows: New Index Value =

Stock

Price/Share

# of Shares

Market Value

$40

$1,000

Coors

1,000

Total

$2,000

A 20% price increase in GM: Stock

Price/Share

# of Shares

Market Value

$48

$1,200

Coors

1,000

Total

$2,200

A 20% price increase in Coors: Stock

Price/Share

# of Shares

Market Value

$40

$1,000

Coors

1,200

Total

$2,200

Therefore, a 20 percent increase in either stock would have the same impact on the total value of the index (i.e., in all cases the index increases by 10 percent). An alternative treatment is to compute percentage changes for each stock and derive the average of these percentage changes. In this case, the average would be 10 percent [(20% + 0%) / 2 = 10%]. So in the case of an unweighted price-index series, a 20 percent price increase in GM would have the same impact on the index as a 20 percent price increase in Coors Brewing. 7. All three of these indexes are value-based (i.e., based on market capitalization). The Dow Jones Total Stock Market Index includes all U.S.-listed public stocks. The NYSE composite includes all stocks listed on the New York Stock Exchange. Finally, the NASDAQ composite index includes all stocks listed on the NASDAQ. In March 2023, the market capitalization of the NYSE composite

index was ~$25 trillion and the market cap of the NASDAQ composite was ~$19 trillion. Since the NYSE and NASDAQ composites are each subset of the Dow Jones Total Stock Market Index, we would expect that the larger subset (the NYSE composite index) would be more highly correlated with the Dow Jones Total Stock Market Index. 8. The high correlations between returns for alternative NYSE price index series can be attributed to the source of the sample (i.e., stock traded on the NYSE). The four series differ in sample size, that is, the DJIA has 30 securities, the S&P 400 has 400 securities, the S&P 500 has 500 securities, and the NYSE composite has over 2,800 stocks. The DJIA differs in computation from the other series, that is, the DJIA is a price-weighted series, whereas the other three series are value-weighted. Even so, there is a strong correlation between the series because of the similarity of types of companies. 9. Because the equal-weighted series implies that all stocks carry the same weight, irrespective of price or value, the results indicate that on average all stocks in the index increased by 23 percent. On the other hand, the percentage change in the value of a large company has a greater impact than the same percentage change for a small company in the value-weighted index. Therefore, the difference in results indicates that for this given period, the smaller companies in the index outperformed the larger companies. 10. The bond-market series are more difficult to construct due to the wide diversity of bonds available. Also, bonds are hard to standardize because their maturities and market yields are constantly changing. In order to better segment the market, you could construct five possible subindexes based on coupon, quality, industry, maturity, and special features (such as call features, warrants, convertibility, etc.). 11. The Russell 1000 and Russell 2000 represent two different samples of stocks, segmented by size. The fact that the Russell 2000 (which is composed of the smallest 2,000 stocks in the Russell 3000) increased more than the Russell 1000 (composed of the 1,000 largest capitalization U.S. stocks) indicates that small stocks performed better during this time period. 12. We should expect a high-yield index to be more highly correlated with the S&P 500. Junk bonds are more “equity-like.” Junk bonds are closer to equity in the capital structure. 13. Indexes with the broadest representation of U.S. stocks include the Wilshire 5000, the NYSE composite, and the Dow Jones Total Stock Market Index. These indexes would be appropriate benchmarks for portfolio managers wishing to construct a broadly diversified portfolio. In addition, the S&P 500 and Russell 1000 are large-cap indexes, but they will include approximately 80 percent of the market cap of U.S. stocks (although they ignore small-cap stocks). 14. Two investment products that managers may use to track the S&P 500 index include index mutual funds, such as Vanguard’s 500 Index Fund (VFINX) and SPY, an ETF that tracks the S&P 500. Per the textbook, the more accurate means of tracking the S&P 500 index has been VFINX; the SPDR “shares do not track the index quite as closely as did the VFINX fund.”