## An Example Bond Pricing

We discussed earlier an 8 coupon, 30-year maturity bond with par value of 1,000 paying 60 semiannual coupon payments of 40 each. Suppose that the interest rate is 8 annually, or r 4 per six-month period. Then the value of the bond can be written as Price J (1.04) + (1.04)60 (14.3) 40 X Annuity factor (4 , 60) + 1,000 X PV factor (4 , 60) It is easy to confirm that the present value of the bond's 60 semiannual coupon payments of 40 each is 904.94 and that the 1,000 final payment of par value has...

## Measurement Error in Beta

Roll's critique tells us that CAPM tests are handicapped from the outset. But suppose that we could get past Roll's problem by obtaining data on the returns of the true market portfolio. We still would have to deal with the statistical problems caused by measurement error in the estimates of beta from the first-stage regressions. It is well known in statistics that if the right-hand-side variable of a regression equation is measured with error (in our case, beta is measured with error and is...

## Separation of Ownership and Management

Many businesses are owned and managed by the same individual. This simple organization, well-suited to small businesses, in fact was the most common form of business organization before the Industrial Revolution. Today, however, with global markets and large-scale production, the size and capital requirements of firms have skyrocketed. For example, General Electric has property, plant, and equipment worth about 35 billion. Corporations of such size simply could not exist as owner-operated...

## Systematic Risk versus Firm Specific Risk

The success of a portfolio selection rule depends on the quality of the input list, that is, the estimates of expected security returns and the covariance matrix. In the long run, efficient portfolios will beat portfolios with less reliable input lists and consequently inferior reward-to-risk trade-offs. Suppose your security analysts can thoroughly analyze 50 stocks. This means that your input list will include the following n 50 estimates of expected returns n 50 estimates of variances (n2 -...

## Financial Intermediation

Recall that the financial problem facing households is how best to invest their funds. The relative smallness of most households makes direct investment intrinsically difficult. A small investor obviously cannot advertise in the local newspaper his or her willingness to lend money to businesses that need to finance investments. Instead, financial intermediaries such as banks, investment companies, insurance companies, or credit unions naturally evolve to bring the two sectors together....

## How Pension Funds Lost In Market Boom

In one of the happiest reports to come out of Detroit lately, General Motors proclaimed Tuesday that its U.S. pension funds are now fully funded on an economic basis. Less noticed was GM's admission that, in accounting terms, it is still a few cents well, 3 billion shy of the mark. Wait a minute. If GM's pension plans were 9.3 billion in the hole when the year began, and if the company, to its credit, shoveled in 10.4 billion more during the year, how come its pension deficit wasn't wiped out...

## Calculation of Expected Return and Variance

Several software packages can be used to generate the efficient frontier. We will demonstrate the method using Microsoft Excel. Excel is far from the best program for this purpose and is limited in the number of assets it can handle, but working through a simple portfolio optimizer in Excel can illustrate concretely the nature of the calculations used in more sophisticated black-box programs. You will find that even in Excel, the computation of the efficient frontier is fairly easy. We will...

## Duration and Convexity of Callable Bonds

Look at Figure 16.7, which depicts the price-yield curve for a callable bond. When interest rates are high, the curve is convex, as it would be for a straight bond. For example, at an interest rate of 10 , the price-yield curve lies above its tangency line. But as rates fall, there is a ceiling on the possible price The bond cannot be worth more than its call price. So as rates fall, we sometimes say that the bond is subject to price compression its value is compressed to the call price. In...

## Bond Indentures

A bond is issued with an indenture, which is the contract between the issuer and the bondholder. Part of the indenture is a set of restrictions on the firm issuing the bond to protect the rights of the bondholders. Such restrictions include provisions relating to collateral, sinking funds, dividend policy, and further borrowing. The issuing firm agrees to these so-called protective covenants in order to market its bonds to investors concerned about the safety of the bond issue. Sinking Funds...

## Taxation Of Mutual Fund Income

Investment returns of mutual funds are granted pass-through status under the U.S. tax code, meaning that taxes are paid only by the investor in the mutual fund, not by the fund itself. The income is treated as passed through to the investor as long as the fund meets several requirements, most notably that at least 90 of all income is distributed to shareholders. In addition, the fund must receive less than 30 of its gross income from the sale of securities held for less than three months, and...

## Life Cycles and Multistage Growth Models

As useful as the constant-growth DDM formula is, you need to remember that it is based on a simplifying assumption, namely, that the dividend growth rate will be constant forever. In fact, firms typically pass through life cycles with very different dividend profiles in different phases. In early years, there are ample opportunities for profitable reinvestment in the company. Payout ratios are low, and growth is correspondingly rapid. In later years, the firm matures, production capacity is...

## Inflation And Equity Valuation

What about the effects of inflation on stock prices We start with an inflation-neutral case in which all real variables, and therefore the stock price, are unaffected by inflation. We then explore the ways in which reality might differ. Consider the case of Inflatotrend, a firm that in the absence of inflation pays out all earnings as dividends. Earnings and dividends per share are 1, and there is no growth. We will use asterisked (*) letters to denote variables in the no-inflation case, or...

## The Price Earnings Ratio and Growth Opportunities

Much of the real-world discussion of stock market valuation concentrates on the firm's price-earnings multiple, the ratio of price per share to earnings per share, commonly called the P E ratio. Our discussion of growth opportunities shows why stock market analysts focus on the P E ratio. Both companies considered, Cash Cow and Growth Prospects, had earnings per share (EPS) of 5, but Growth Prospects reinvested 60 of earnings in prospects with an ROE of 15 , whereas Cash Cow paid out all...

## Predicting Betas

We saw in the previous section that betas estimated from past data may not be the best estimates of future betas Betas seem to drift toward 1 over time. This suggests that we might want a forecasting model for beta. One simple approach would be to collect data on beta in different periods and then estimate a regression equation Current beta a + b (Past beta) (10.14) Given estimates of a and b, we would then forecast future betas using the rule Forecast beta a + b (Current beta) There is no...

## Sensitivity to the Business Cycle

Once the analyst forecasts the state of the macroeconomy, it is necessary to determine the implication of that forecast for specific industries. Not all industries are equally sensitive to the business cycle. For example, consider Figure 17.9, which is a graph of automobile production and shipments of cigarettes, both scaled so that 1963 has a value of 100. Clearly, the cigarette industry is virtually independent of the business cycle. Demand for cigarettes does not seem affected by the state...

## Mutual Fund Investment Performance A First Look

We noted earlier that one of the benefits of mutual funds for the individual investor is the ability to delegate management of the portfolio to investment professionals. The investor retains control over the broad features of the overall portfolio through the asset allocation decision Each individual chooses the percentages of the portfolio to invest in bond funds versus equity funds versus money market funds, and so forth, but can leave the specific security selection decisions within each...

## Tests of the CAPM

Early tests of the CAPM performed by John Lintner,1 later replicated by Merton Miller and Myron Scholes,2 used annual data on 631 NYSE stocks for 10 years, 1954 to 1963, and produced the following estimates (with returns expressed as decimals rather than percentages) Coefficient 70 .127 71 .042 72 .310 Standard These results are inconsistent with the CAPM. First, the estimated SML is too flat that is, the 71 coefficient is too small. The slope should be rM - rf .165 (16.5 per year), but it is...

## Capital Allocation Across Risky And Riskfree Portfolios

History shows us that long-term bonds have been riskier investments than investments in Treasury bills, and that stock investments have been riskier still. On the other hand, the riskier investments have offered higher average returns. Investors, of course, do not make all-or-nothing choices from these investment classes. They can and do construct their portfolios using securities from all asset classes. Some of the portfolio may be in risk-free Treasury bills, some in high-risk stocks. The...

## Fees and Mutual Fund Returns

The rate of return on an investment in a mutual fund is measured as the increase or decrease in net asset value plus income distributions such as dividends or distributions of capital gains expressed as a fraction of net asset value at the beginning of the investment period. If we denote the net asset value at the start and end of the period as NAV0 and NAVj, respectively, then NAVj - NAV0 + Income and capital gain distributions For example, if a fund has an initial NAV of 20 at the start of...

## Expected versus Realized Returns

In a recent working paper, Fama and French23 offer one possible interpretation of the puzzle. They work with an expanded sample period, 1872-1999, and report the average risk-free rates, average return on equity (represented by the S& P 500 index), and the resultant risk premium for the overall period and subperiods The difference in results before and after 1949 suggests that the equity premium puzzle is really a creature of modern times. Fama and French (FF) suspect that estimating the...

## Betas and Expected Returns

Because nonfactor risk can be diversified away, only factor risk commands a risk premium in market equilibrium. Nonsystematic risk across firms cancels out in well-diversified portfolios, so that only the systematic risk of a portfolio of securities can be related to its expected returns. The solid line in Figure 11.1A plots the return of a well-diversified Portfolio A with (3A 1 for various realizations of the systematic factor. The expected return of Portfolio A is 10 this is where the solid...

## Estimating Beta Coefficients

The spreadsheet Betas, which you will find on the Online Learning Center (www.mhhe.com bkm), contains 60 months' returns for 10 individual stocks. Returns are calculated over the five years ending in December 2000. The spreadsheet also contains returns for S& P 500 Index and the observed risk-free rates as measured by the one-year Treasury bill. With this data, monthly excess returns for the individual securities and the market as measured by the S& P 500 Index can be used with the...

## Stock Prices and Investment Opportunities

Consider two companies, Cash Cow, Inc., and Growth Prospects, each with expected earnings in the coming year of 5 per share. Both companies could in principle pay out all of these earnings as dividends, maintaining a perpetual dividend flow of 5 per share. If the market capitalization rate were k 12.5 , both companies would then be valued at D1 k 5 .125 40 per share. Neither firm would grow in value, because with all earnings paid out as dividends, and no earnings reinvested in the firm, both...

## Flotation Therapy

Nothing gets online traders clicking their buy icons so fast as a hot IPO. Recently, demand from small investors using the Internet has led to huge price increases in shares of newly floated companies after their initial public offerings. How frustrating, then, that these online traders can rarely buy IPO shares when they are handed out. They have to wait until they are traded in the market, usually at well above the offer price. Now, help may be at hand from a new breed of Internet-based...

## Financial Leverage and ROE

An analyst interpreting the past behavior of a firm's ROE or forecasting its future value must pay careful attention to the firm's debt-equity mix and to the interest rate on its debt. An example will show why. Suppose Nodett is a firm that is all-equity financed and has total assets of 100 million. Assume it pays corporate taxes at the rate of 40 of taxable earnings. Table 19.4 shows the behavior of sales, earnings before interest and taxes, and net profits under three scenarios representing...

## Tests of Predictability in Stock Market Returns

Returns over Short Horizons Early tests of efficient market were tests of the weak form. Could speculators find trends in past prices that would enable them to earn abnormal profits This is essentially a test of the efficacy of technical analysis. The already cited work of Kendall and of Roberts,7 both of whom analyzed the possible existence of patterns in stock prices, suggests that such patterns are not to be found. One way of discerning trends in stock prices is by measuring the serial...

## Buying On Margin

When purchasing securities, investors have easy access to a source of debt financing called brokers' call loans. The act of taking advantage of brokers' call loans is called buying on margin. Purchasing stocks on margin means the investor borrows part of the purchase price of the stock from a broker. The broker, in turn, borrows money from banks at the call money rate to finance these purchases, and charges its clients that rate plus a service charge for the loan. All securities purchased on...

## Managed Investment Companies

There are two types of managed companies closed-end and open-end. In both cases, the fund's board of directors, which is elected by shareholders, hires a management company to manage the portfolio for an annual fee that typically ranges from .2 to 1.5 of assets. In many cases the management company is the firm that organized the fund. For example, Fidelity Management and Research Corporation sponsors many Fidelity mutual funds and is responsible for managing the portfolios. It assesses a...

## Convergence of Price to Intrinsic Value

Now suppose that the current market price of ABC stock is only 48 per share and, therefore, that the stock now is undervalued by 2 per share. In this case the expected rate of CHAPTER 18 Equity Valuation Models 569 price appreciation depends on an additional assumption about whether the discrepancy between the intrinsic value and the market price will disappear, and if so, when. One fairly common assumption is that the discrepancy will never disappear and that the market price will continue to...

## Contingent Immunization

Contingent immunization is a mixed passive-active strategy suggested by Liebowitz and Weinberger.11 To illustrate, suppose that interest rates currently are 10 and that a manager's portfolio is worth 10 million right now. At current rates the manager could lock in, via conventional immunization techniques, a future portfolio value of 12.1 million after two years. Now suppose that the manager wishes to pursue active management but is willing to risk losses only to the extent that the terminal...

## Risk And Risk Premiums

Risk means uncertainty about future rates of return. We can quantify that uncertainty using probability distributions. For example, suppose you are considering investing some of your money, now all invested in a bank account, in a stock market index fund. The price of a share in the fund is currently 100, and your time horizon is one year. You expect the cash dividend during the year to be 4, so your expected dividend yield (dividends earned per dollar invested) is 4 . Your total holding-period...

## The Security Market Line

We can view the expected return-beta relationship as a reward-risk equation. The beta of a security is the appropriate measure of its risk because beta is proportional to the risk that the security contributes to the optimal risky portfolio. Risk-averse investors measure the risk of the optimal risky portfolio by its variance. In this world we would expect the reward, or the risk premium on individual assets, to depend on the contribution of the individual asset to the risk of the portfolio....

## Bond Prices And Yields

In the previous chapters on risk and return relationships, we have treated securities at a high level of abstraction. We assumed implicitly that a prior, detailed analysis of each security already had been performed, and that its risk and return features had been assessed. We turn now to specific analyses of particular security markets. We examine valuation principles, determinants of risk and return, and portfolio strategies commonly used within and across the various markets. We begin by...

## Short Sale

The accompanying spreadsheet is set up to measure the return on investment from a short sale. The spreadsheet is based on the example in Section 3.7. The spreadsheet calculates the price at which additional margin would be required and presents return analysis for a range of ending stock prices. Additional problems using this spreadsheet are available at www.mhhe.com bkm. 1933 act requires full disclosure of relevant information relating to the issue of new securities. This is the act that...

## The Constant Growth DDM

Equation 18.3 as it stands is still not very useful in valuing a stock because it requires dividend forecasts for every year into the indefinite future. To make the DDM practical, we need to introduce some simplifying assumptions. A useful and common first pass at the problem is to assume that dividends are trending upward at a stable growth rate that we will call g. Then if g .05, and the most recently paid dividend was D0 3.81, expected future dividends are D1 D0(1 + g) 3.81 X 1.05 4.00 D2...

## Forecasting the Stock Market

What can we learn from all of this about the future rate of return on stocks First, a note of optimism. Although timing the stock market is a very difficult and risky game, it may not be impossible. For example, we saw in Chapter 12 that some variables such as the market dividend yield seem to predict market returns. However, if market history teaches us anything at all, it is that the market has great variability. Thus, although we can use a variety of methods to derive a best forecast of the...

## Net Worth Immunization

Many banks and thrift institutions have a natural mismatch between asset and liability maturity structures. Bank liabilities are primarily the deposits owed to customers, most of which are very short-term in nature and, consequently, of low duration. Bank assets by contrast are composed largely of outstanding commercial and consumer loans or mortgages. These assets are of longer duration than are deposits, and their values are correspondingly more sensitive to interest rate fluctuations. In...

## Realized Compound Yield versus Yield to Maturity

We have noted that yield to maturity will equal the rate of return realized over the life of the bond if all coupons are reinvested at an interest rate equal to the bond's yield to maturity. Consider, for example, a two-year bond selling at par value paying a 10 coupon once a year. The yield to maturity is 10 . If the 100 coupon payment is reinvested at an interest rate of 10 , the 1,000 investment in the bond will grow after two years to 1,210, as illustrated in Figure 14.5, A. The coupon paid...

## Determinants of Bond Safety

Bond rating agencies base their quality ratings largely on an analysis of the level and trend of some of the issuer's financial ratios. The key ratios used to evaluate safety are 1. Coverage ratios Ratios of company earnings to fixed costs. For example, the times-interest-earned ratio is the ratio of earnings before interest payments and taxes to interest obligations. The fixed-charge coverage ratio adds lease payments and sinking fund payments to interest obligations to arrive at the ratio of...

## Decomposition of ROE

To understand the factors affecting a firm's ROE, including its trend over time and its performance relative to competitors, analysts often decompose ROE into the product of a series of ratios. Each component ratio is in itself meaningful, and the process serves to focus the analyst's attention on the separate factors influencing performance. This kind of decomposition of ROE is often called the Du Pont system. One useful decomposition of ROE is Net profits Pretax profits EBIT Sales Assets ROE...

## Why Do Investors Like Convexity

Convexity is generally considered a desirable trait. Bonds with greater curvature gain more in price when yields fall than they lose when yields rise. For example in Figure 16.6 bonds A and B have the same duration at the initial yield. The plots of their proportional price changes as a function of interest-rate changes are tangent, meaning that their sensitivities to changes in yields at that point are equal. However, bond A is more convex than bond B. It enjoys greater price increases and...

## Industry Life Cycles

Examine the biotechnology industry and you will find many firms with high rates of investment, high rates of return on investment, and low dividend payout rates. Do the same for the public utility industry and you will find lower rates of return, lower investment rates, and higher dividend payout rates. Why should this be The biotech industry is still new. Recently, available technologies have created opportunities for highly profitable investment of resources. New products are protected by...

## Interest Rate Sensitivity

The sensitivity of bond prices to changes in market interest rates is obviously of great concern to investors. To gain some insight into the determinants of interest rate risk, turn to Figure 16.1, which presents the percentage change in price corresponding to changes in yield to maturity for four bonds that differ according to coupon rate, initial yield to maturity, and time to maturity. All four bonds illustrate that bond prices decrease when yields rise, and that the price curve is convex,...

## Initial Public Offerings

Investment bankers manage the issuance of new securities to the public. Once the SEC has commented on the registration statement and a preliminary prospectus has been distributed to interested investors, the investment bankers organize road shows in which they travel around the country to publicize the imminent offering. These road shows serve two purposes. First, they attract potential investors and provide them information about the offering. Second, they collect for the issuing firm and its...

## Interest Rate Swaps

An interest rate swap is a contract between two parties to exchange a series of cash flows similar to those that would result if the parties instead were to exchange equal dollar values 514 PART IV Fixed-Income Securities of different types of bonds. Swaps arose originally as a means of managing interest rate risk. The volume of swaps has increased from virtually zero in 1980 to about 40 trillion today. Interest rate swaps do not have anything to do with the Homer-Liebowitz bond swap taxonomy...

## An Illustration Of Financial Statement Analysis

In her 2003 annual report to the shareholders of Growth Industries, Inc., the president wrote 2003 was another successful year for Growth Industries. As in 2002, sales, assets, and operating income all continued to grow at a rate of 20 . We can evaluate her statement by conducting a full-scale ratio analysis of Growth Industries. Our purpose is to assess GI's performance in the recent past, to evaluate its future prospects, and to determine whether its market price reflects its intrinsic value....

## Intrinsic Value Versus Market Price

The most popular model for assessing the value of a firm as a going concern starts from the observation that an investor in stock expects a return consisting of cash dividends and capital gains or losses. We begin by assuming a one-year holding period and supposing that ABC stock has an expected dividend per share, E D1 , of 4, the current price of a share, P0, is 48, and the expected price at the end of a year, E P1 , is 52. For now, don't worry about how you derive your forecast of next...

## Industry Structure and Performance

The maturation of an industry involves regular changes in the firm's competitive environment. As a final topic, we examine the relationship among industry structure, competitive strategy, and profitability. Michael Porter2 has highlighted these five determinants of competition threat of entry from new competitors, rivalry between existing competitors, price pressure from substitute products, bargaining power of buyers, and bargaining power of suppliers. Threat of Entry New entrants to an...

## Financial Engineering And Interest Rate Derivatives

New financial instruments created through financial engineering can have highly unusual risk and return characteristics that offer both opportunities and challenges for fixed-income portfolio managers. To illustrate the possibilities opened up by financial engineering, consider the inverse floater, which is a bond that pays a lower coupon payment when a reference interest rate rises. For example, an inverse floater may pay a coupon rate equal to 10 minus the rate on one-year Treasury bills....

## The Market Index

In what has become known as Roll's critique, Richard Roll3 pointed out that 1. There is a single testable hypothesis associated with the CAPM The market portfolio is mean-variance efficient. 2. All the other implications of the model, the best-known being the linear relation between expected return and beta, follow from the market portfolio's efficiency and therefore are not independently testable. There is an if and only if' relation between the expected return-beta relationship and the...

## Spot And Forward Yields

The spreadsheet entitled SPOTYA.XLS, found on the Online Learning Center www.mhhe.com bkm , can be used to estimate spot rates from coupon bonds and to calculate the forward rates for both single-year and multiyear bonds. The spreadsheet demonstrates a methodology to bootstrap spot rates from coupon bonds. The model sequentially solves for the spot rates that are associated with each of the periods. The methodology is similar to but slightly different from the regression methodology described...

## Find The Equilibrium Expected Excess Return On This Stock Using The

We have assumed so far that there is only one systematic factor affecting stock returns. This simplifying assumption is in fact too simplistic. It is easy to think of several factors driven by the business cycle that might affect stock returns interest rate fluctuations, inflation rates, oil prices, and so on. Presumably, exposure to any of these factors will affect a stock's risk and hence its expected return. We can derive a multifactor version of the APT to accommodate these multiple sources...

## Dont Ignore Lucks Role In Stock Picks

When stock-market investors take a hit, they rail at their stupidity and question their investment strategy. But when lottery ticket buyers lose, they shrug off their bad luck and pony up for another ticket. Maybe those lottery players have the right idea. Sure, if you lose a bundle in the stock market, it could be your fault. But there is a fair chance that the real culprits are bad luck and skewed expectations. Examples Consider these three Picking on Yourself If one of your stocks craters,...

## Portfolios Of One Risky Asset And One Riskfree Asset

In this section we examine the risk-return combinations available to investors. This is the technological part of asset allocation it deals only with the opportunities available to in- CHAPTER 7 Capital Allocation between the Risky Asset and the Risk-Free Asset 187 Figure 7.1 Spread between three-month CD and T-bill rates. vestors given the features of the broad asset markets in which they can invest. In the next section we address the personal part of the problem the specific individual's...

## Time For Investings Fourletter Word

What four-letter word should pop into mind when the stock market takes a harrowing nose dive Risk is the potential for realizing low returns or even losing money, possibly preventing you from meeting important objectives, like sending your kids to the college of their choice or having the retirement lifestyle you crave. But many financial advisers and other experts say that these days investors aren't taking the idea of risk as seriously as they should, and they are overexposing themselves to...

## Implications Of The Emh For Investment Policy Technical Analysis

Technical analysis is essentially the search for recurrent and predictable patterns in stock prices. Although technicians recognize the value of information regarding future economic prospects of the firm, they believe that such information is not necessary for a successful trading strategy. This is because whatever the fundamental reason for a change in stock price, if the stock price responds slowly enough, the analyst will be able to identify a trend that can be exploited during the...

## Passive Strategies The Capital Market Line

The CAL is derived with the risk-free and the risky portfolio, P. Determination of the assets to include in risky portfolio P may result from a passive or an active strategy. A passive strategy describes a portfolio decision that avoids any direct or indirect security analysis.4 At first blush, a passive strategy would appear to be naive. As will become apparent, however, forces of supply and demand in large capital markets may make such a strategy a reasonable choice for many investors. In...

## Diversification And Portfolio Risk

Suppose your portfolio is composed of only one stock, Compaq Computer Corporation. What would be the sources of risk to this portfolio You might think of two broad sources of uncertainty. First, there is the risk that comes from conditions in the general economy, such as the business cycle, inflation, interest rates, and exchange rates. None of these macroeconomic factors can be predicted with certainty, and all affect the rate of return on Compaq stock. In addition to these macroeconomic...

## Survivorship Bias And Tests Of Market Efficiency

We've seen that survivorship bias might be one source of the equity premium puzzle. It turns out that survivorship bias also can affect our measurement of persistence in stock market returns, an issue that is crucial for tests of market efficiency. For a demonstration of the potential impact of survivorship bias, imagine that a new group of mutual funds is set up. Half the funds are managed aggressively and the other conservatively however, none of the managers are able to beat the market in...

## The Index Model and the Expected Return Beta Relationship

Recall that the CAPM expected return-beta relationship is, for any asset i and the theoretical market portfolio, where p, Cov R,, Rm ctM. This is a statement about the mean of expected excess returns of assets relative to the mean excess return of the theoretical market portfolio. If the index M in equation 10.9 represents the true market portfolio, we can take the expectation of each side of the equation to show that the index model specification is A comparison of the index model relationship...

## Estimating the Index Model

Equation 10.3 also suggests how we might go about actually measuring market and firm-specific risk. Suppose that we observe the excess return on the market index and a specific asset over a number of holding periods. We use as an example monthly excess returns on the S amp P 500 index and GM stock for a one-year period. We can summarize the results for a sample period in a scatter diagram, as illustrated in Figure 10.1. CHAPTER 10 Single-Index and Multifactor Models 297 CHAPTER 10 Single-Index...

## Well Diversified Portfolios

Now we look at the risk of a portfolio of stocks. We first show that if a portfolio is well diversified, its firm-specific or nonfactor risk can be diversified away. Only factor or systematic risk remains. If we construct an n-stock portfolio with weights w , 1, then the rate of return on this portfolio is as follows is the weighted average of the p of the n securities. The portfolio nonsystematic component which is uncorrelated with F is which similarly is a weighted average of the e of the n...

## Expected Returns on Individual Securities

The CAPM is built on the insight that the appropriate risk premium on an asset will be determined by its contribution to the risk of investors' overall portfolios. Portfolio risk is what matters to investors and is what governs the risk premiums they demand. 268 PART III Equilibrium in Capital Markets Remember that all investors use the same input list, that is, the same estimates of expected returns, variances, and covariances. We saw in Chapter 8 that these covariances can be arranged in a...

## Portfolios Of Two Risky Assets

In the last section we considered naive diversification using equally weighted portfolios of several securities. It is time now to study efficient diversification, whereby we construct risky portfolios to provide the lowest possible risk for any given level of expected return. Portfolios of two risky assets are relatively easy to analyze, and they illustrate the principles and considerations that apply to portfolios of many assets. We will consider a portfolio comprised of two mutual funds, a...

## Event Studies

The notion of informationally efficient markets leads to a powerful research methodology. If security prices reflect all currently available information, then price changes must reflect new information. Therefore, it seems that one should be able to measure the importance of an event of interest by examining price changes during the period in which the event occurs. An event study describes a technique of empirical financial research that enables an observer to assess the impact of a particular...

## Finding Funds That Zig When The Blue Chips

Investors hungry for lower risk are hearing some surprising recommendations from financial advisers mutual funds investing in less-developed nations that many Americans can't immediately locate on a globe. funds specializing in small European companies with unfamiliar names. funds investing in commodities. All of these investments are risky by themselves, advisers readily admit. But they also tend to zig when big U.S. stocks zag. And that means that such fare, when added to a portfolio heavy in...

## The Industry Version Of The Index Model

Not surprisingly, the index model has attracted the attention of practitioners. To the extent that it is approximately valid, it provides a convenient benchmark for security analysis. A modern practitioner using the CAPM, who has neither special information about a security nor insight that is unavailable to the general public, will conclude that the security is properly priced. By properly priced, the analyst means that the expected return on the security is commensurate with its risk, and...

## Stock Investors Pay High Price For Liquidity

Given a choice between liquid and illiquid stocks, most investors, to the extent they think of it at all, opt for issues they know are easy to get in and out of. But for long-term investors who don't trade often which includes most individuals that may be unnecessarily expensive. Recent studies of the performance of listed stocks show that, on average, less-liquid issues generate substantially higher returns as much as several percentage points a year at the extremes. . . . Among the academic...

## Capital Allocation and the Separation Property

Now that we have the efficient frontier, we proceed to step two and introduce the risk-free asset. Figure 8.14 shows the efficient frontier plus three CALs representing various Figure 8.14 Capital allocation lines with various portfolios from the efficient set. portfolios from the efficient set. As before, we ratchet up the CAL by selecting different portfolios until we reach Portfolio P, which is the tangency point of a line from F to the efficient frontier. Portfolio P maximizes the...

## Futures Contracts

A futures contract calls for delivery of an asset or in some cases, its cash value at a specified delivery or maturity date for an agreed-upon price, called the futures price, to be paid Figure 2.14 Financial futures listings. DJ INDUSTRIAL AVERAGE CBOT -SIO times average Lifetime Open Open High Low Settle Change High Low Interest Sect 10575 10700 50555 10675 10 12126 9995 13,472 Dec 10745 10822 10745 10B19 101 1218Q 8100 2,S10 Est vol 13,000 vol Mon 9,322 open Int 15,590, 147, Idxprl HI...

## Shorter Clearer Mutualfund Disclosure

Mutual-fund investors are about to get shorter and clearer disclosure documents under new rules adopted by the Securities and Exchange Commission earlier this week. But despite all the hoopla surrounding the improvements including a new profile prospectus and an easier-to-read full prospectus there's still a slew of vital information fund investors don't get from any disclosure documents, long or short. Of course, more information isn't necessarily better. As it is, investors rarely read fund...

## Real Assets Versus Financial Assets

The material wealth of a society is determined ultimately by the productive capacity of its economy the goods and services that can be provided to its members. This productive capacity is a function of the real assets of the economy the land, buildings, knowledge, and machines that are used to produce goods and the workers whose skills are necessary to use those resources. Together, physical and human assets generate the entire spectrum of output produced and consumed by the society. In...

## The Index Model and Realized Returns

We have said that the CAPM is a statement about ex ante or expected returns, whereas in practice all anyone can observe directly are ex post or realized returns. To make the leap from expected to realized returns, we can employ the index model, which we will use in excess return form as We saw in Section 10.1 how to apply standard regression analysis to estimate equation 10.9 using observable realized returns over some sample period. Let us now see how this framework for statistically...

## Empirical Models and the ICAPM

The empirical models using proxies for extramarket sources of risk are unsatisfying for a number of reasons. We discuss these models further in Chapter 13, but for now we can summarize as follows 1. Some of the factors in the proposed models cannot be clearly identified as hedging a significant source of uncertainty. 2. As suggested by Black, the fact that researchers scan and rescan the database of security returns in search of explanatory factors an activity often called data-snooping may...

## Review of Portfolio Mathematics

Consider the problem of Humanex, a nonprofit organization deriving most of its income from the return on its endowment. Years ago, the founders of Best Candy willed a large block of Best Candy stock to Humanex with the provision that Humanex may never sell it. This block of shares now comprises 50 of Humanex's endowment. Humanex has free choice as to where to invest the remainder of its portfolio.2 The value of Best Candy stock is sensitive to the price of sugar. In years when world sugar crops...

## Risk Aversion Expected Utility And The St Petersburg Paradox

We digress here to examine the rationale behind our contention that investors are risk averse. Recognition of risk aversion as central in investment decisions goes back at least to 1738. Daniel Bernoulli, one of a famous Swiss family of distinguished mathematicians, spent the years 1725 through 1733 in St. Petersburg, where he analyzed the following coin-toss game. To enter the game one pays an entry fee. Thereafter, a coin is tossed until the first head appears. The number of tails, denoted by...

## Real Versus Nominal Risk

The distinction between the real and the nominal rate of return is crucial in making investment choices when investors are interested in the future purchasing power of their wealth. Thus a U.S. Treasury bond that offers a risk-free nominal rate of return is not truly a risk-free investment it does not guarantee the future purchasing power of its cash flow. An example might be a bond that pays 1,000 on a date 20 years from now but nothing in the interim. Although some people see such a...

## Criticisms Of Indexing Dont Hold Up

Amid the stock market's recent travails, critics are once again taking aim at index funds. But like the firing squad that stands in a circle, they aren't making a whole lot of sense. Indexing, of course, has never been popular in some quarters. Performance-hungry investors loathe the idea of buying index funds and abandoning all chance of beating the market averages. Meanwhile, most Wall Street firms would love indexing to fall from favor because there isn't much money to be made running index...

## Normal and Lognormal Distributions

Modern portfolio theory, for the most part, assumes that asset returns are normally distributed. This is a convenient assumption because the normal distribution can be described completely by its mean and variance, consistent with mean-variance analysis. The argument has been that even if individual asset returns are not exactly normal, the distribution of returns of a large portfolio will resemble a normal distribution quite closely. The data support this argument. Table 6A.1 shows summaries...

## The CAPM with Restricted Borrowing The Zero Beta Model

The CAPM is predicated on the assumption that all investors share an identical input list that they feed into the Markowitz algorithm. Thus all investors agree on the location of the efficient minimum-variance frontier, where each portfolio has the lowest variance among all feasible portfolios at a target expected rate of return. When all investors can borrow and lend at the safe rate, r, all agree on the optimal tangency portfolio and choose to hold a share of the market portfolio. However,...

## The Optimal Risky Portfolio with Two Risky Assets and a Risk Free Asset

What if our risky assets are still confined to the bond and stock funds, but now we can also invest in risk-free T-bills yielding 5 We start with a graphical solution. Figure 8.6 shows the opportunity set based on the properties of the bond and stock funds, using the data from Table 8.1. Two possible capital allocation lines CALs are drawn from the risk-free rate rf 5 to two feasible portfolios. The first possible CAL is drawn through the minimum-variance portfolio A, which is invested 82 in...

## Computer Networks

The Internet and other advances in computer networking are transforming many sectors of the economy, and few moreso than the financial sector. These advances will be treated in greater detail in Chapter 3, but for now we can mention a few important innovations online trading, online information dissemination, automated trade crossing, and the beginnings of Internet investment banking. Online trading connects a customer directly to a brokerage firm. Online brokerage firms can process trades more...

## Appendix C The Fallacy Of Time Diversification

The insurance story just discussed illustrates a misuse of rate of return analysis, specifically the mistake of comparing portfolios of different sizes. A more insidious version of this error often appears under the guise of time diversification. Consider the case of Mr. Frier, who has 100,000. He is trying to figure out the appropriate allocation of this fund between risk-free T-bills that yield 10 and a risky portfolio that yields an annual rate of return with E rP 15 and o gt 30 . Mr. Frier...

## S S Covr rj

We can express portfolio variance as Now examine the effect of diversification. When the average covariance among security returns is zero, as it is when all risk is firm-specific, portfolio variance can be driven to zero. We see this from equation 8A.3 The second term on the right-hand side will be zero in this scenario, while the first term approaches zero as n becomes larger. Hence when security returns are uncorrelated, the power of diversification to limit portfolio risk is unlimited....

## Optimal Portfolios With Restrictions On The Riskfree Asset

The availability of a risk-free asset greatly simplifies the portfolio decision. When all investors can borrow and lend at that risk-free rate, we are led to a unique optimal risky portfolio that is appropriate for all investors given a common input list. This portfolio maximizes the reward-to-variability ratio. All investors use the same risky portfolio and differ only in the proportion they invest in it versus in the risk-free asset. What if a risk-free asset is not available Although T-bills...

## Treasury Bills

Treasury bills T-bills, or just bills, for short are the most marketable of all money market instruments. T-bills represent the simplest form of borrowing The government raises money by selling bills to the public. Investors buy the bills at a discount from the stated maturity value. At the bill's maturity, the holder receives from the government a payment equal to the face value of the bill. The difference between the purchase price and ultimate maturity value constitutes the investor's...