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 ReturnBeta 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...
WellDiversified 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 Zag
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...
Investment Bankers and Underwriting
Public offerings of both stocks and bonds typically are marketed by investment bankers, who in this role are called underwriters. More than one investment banker usually markets the securities. A lead firm forms an underwriting syndicate of other investment bankers to share the responsibility for the stock issue. The bankers advise the firm regarding the terms on which it should attempt to sell the securities. A preliminary registration statement must be filed with the Securities and Exchange...
Empirical Evidence On Security Returns
In this chapter, we consider the empirical evidence in support of the CAPM and APT. At the outset, however, it is worth noting that many of the implications of these models already have been accepted in widely varying applications. Consider the following 1. Many professional portfolio managers use the expected return-beta relationship of security returns. Furthermore, many firms rate the performance of portfolio managers according to the reward-to-variability ratios they maintain and the...
So Are Markets Efficient
There is a telling joke about two economists walking down the street. They spot a 20 bill on the sidewalk. One starts to pick it up, but the other one says, Don't bother if the bill were real someone would have picked it up already. The lesson is clear. An overly doctrinaire belief in efficient markets can paralyze the investor and make it appear that no research effort can be justified. This extreme view is probably unwarranted. There are enough anomalies in the empirical evidence to justify...
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 May
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...
History Of Interest Rates And Risk Premiums
Individuals must be concerned with both the expected return and the risk of the assets that might be included in their portfolios. To help us form reasonable expectations for the performance of a wide array of potential investments, this chapter surveys the historical performance of the major asset classes. It uses a risk-free portfolio of Treasury bills as a benchmark to evaluate that performance. Therefore, we start the chapter with a review of the determinants of the risk-free interest rate,...
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...
A 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...
Treasury Notes and Bonds
The U.S. government borrows funds in large part by selling Treasury notes and Treasury bonds. T-note maturities range up to 10 years, whereas bonds are issued with maturities ranging from 10 to 30 years. Both are issued in denominations of 1,000 or more. Both make semiannual interest payments called coupon payments, a name derived from pre-computer days, when investors would literally clip coupons attached to the bond and present a coupon to an agent of the issuing firm to receive the interest...
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...
Theoretical Foundations of Multifactor Models
The CAPM presupposes that the only relevant source of risk arises from variations in stock returns, and therefore a representative market portfolio can capture this entire risk. As a result, individual-stock risk can be defined by the contribution to overall portfolio risk hence the risk premium on an individual stock is determined solely by its beta on the market portfolio. But is this narrow view of risk warranted Consider a relatively young investor whose future wealth is determined in large...
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...
APPENDIX A A DEFENSE OF MEANVARIANCE ANALYSIS Describing Probability
The axiom of risk aversion needs little defense. So far, however, our treatment of risk has been limiting in that it took the variance or, equivalently, the standard deviation of portfolio returns as an adequate risk measure. In situations in which variance alone is not adequate to measure risk this assumption is potentially restrictive. Here we provide some justification for mean-variance analysis. The basic question is how one can best describe the uncertainty of portfolio rates of return. In...
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...
Risk Tolerance And Asset Allocation
We have shown how to develop the CAL, the graph of all feasible risk-return combinations available from different asset allocation choices. The investor confronting the CAL now must choose one optimal portfolio, C, from the set of feasible choices. This choice entails a trade-off between risk and return. Individual investor differences in risk aversion imply that, given an identical opportunity set that is, a risk-free rate and a reward-to-variability 2 Margin purchases require the investor to...
The CAPM with Restricted Borrowing The ZeroBeta 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 RiskFree 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...
Empirical Evidence on Security Returns Chapter 13
This chapter contains substantial new material on the equity premium puzzle. It reviews new evidence questioning whether the historical-average excess return on the stock market is indicative of future performance. The chapter also examines the impact of survivorship bias in our assessment of security returns. It considers the potential effects of survivorship bias on our estimate of the market risk premium as well as on our evaluation of the performance of professional portfolio managers.
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...
The Passive Strategy Is Efficient
In Chapter 7 we defined the CML capital market line as the CAL capital allocation line that is constructed from a money market account or T-bills and the market portfolio. Perhaps now you can fully appreciate why the CML is an interesting CAL. In the simple world of the CAPM, M is the optimal tangency portfolio on the efficient frontier, as shown in Figure 9.4. In this scenario the market portfolio that all investors hold is based on the common input list, thereby incorporating all relevant...
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...
The Money Market
The money market is a subsector of the fixed-income market. It consists of very short-term debt securities that usually are highly marketable. Many of these securities trade in large denominations, and so are out of the reach of individual investors. Money market funds, however, are easily accessible to small investors. These mutual funds pool the resources of many investors and purchase a wide variety of money market securities on their behalf. Figure 2.1 is a reprint of a money rates listing...
Treasury Bills
U.S. 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...