555003_投资学（全英）

This hyper-text book introduces the foundations of investment decision-making. Beginning with portfolio theory and the tradeoff between risk and return, it shows how the definition of investor risk depends crucially upon diversification. It explains modern asset pricing models currently used to determine the expected rate of return on investments and finally it presents evidence about what information can be used for strategic investment advantage. The book is designed for use in a four-week teaching module for master's students studying introductory Finance. It assumes some knowledge of statistics and a familiarity with the concepts of net present value. Please feel free to link to this text, but do not download or reproduce the material without my permission, since it is copyrighted. Chapter I Capital Markets: Investment Performance Chapter II Basics of Return and Risk: Efficient Frontier Chapter III Preferences and Investor Choice Chapter IV CAPM: The Portfolio Approach to Risk Chapter V Understanding Security Market Line Chapter VI Arbitrage Pricing Theory Chapter VII Betas, Leverage, Discount Rate Chapter VIII Information & Efficiency of Capital Markets SUMMARY Short Summary of Chapters For Study Acknowledgements I wish to thank the students in my 1996 Financial Management class for working with the notes to this book in the development phase, Ken Gray for his invaluable programming assistance and Zika Abzuk for system adminstration. I wish to thank my colleagues N. Prabhala, Geert Rouwenhorst and Campbell Harvey for their useful suggestions. I wish to thank Ibbotson Associates for the use of their Encorr software in the preparation of figures for this text. All errors are the sole responsibility of the author. © William N. Goetzmann YALE School of Management Chapter I: Capital Markets and Investment Performance Overview Suppose you find a great investment opportunity, but you lack the cash to take advantage of it. This is the classic problem of financing. The short answer is that you borrow -- either privately from a bank, or publicly by issuing securities. Securities are nothing more than promises of future payment. They are initially issued through financial intermediaries such as investment banks, which underwrite the offering and work to sell the securities to the public. Once they are sold, securities can often be re-sold. There is a secondary market for many corporate securities. If they meet certain regulatory requirements, they may be traded through brokers on the stock exchanges, such as the NYSE, the AMEX and NASDAQ, or on options exchanges and bond trading desks. Securities come in a bewildering variety of forms - there are more types of securities than there are breeds of cats and dogs, for instance. They range from relatively straightforward to incredibly complex. A straight bond promises to repay a loan over a fixed amount of interest over time and the principal at maturity. A share of stock, on the other hand, represents a fraction of ownership in a corporation, and a claim to future dividends. Today, much of the innovation in finance is in the development of sophisticated securities: structured notes, reverse floaters, IO's and PO's -- these are today's specialized breeds. Sources of information about securities are numerous on the world-wide web. For a start, begin with the Ohio State Financial Data Finder. All securities, from the simplest to the most complex, share some basic similarities that allow us to evaluate their usefulness from the investor's perspective. All of them are economic claims against future benefits. No one borrows money that they intend to repay immediately; the dimension of time is always present in financial instruments. Thus, a bond represents claims to a future stream of pre-specified coupon payments, while a stock represents claims to uncertain future dividends and division of the corporate assets. In addition, all financial securities can be characterized by two important features: risk and return. These two key measures will be the focus of this second module. I. Finance from the Investor's Perspective Most financial decisions you have addressed up to this point in the term have been from the perspective of the firm. Should the company undertake the construction of a new processing plant? Is it more profitable to replace an old boiler now, or wait? In this module, we will examine financial decisions from the perspective of the purchaser of corporate securities: shareholders and bondholders who are free to buy or sell financial assets. Investors, whether they are individuals or institutions such as pension funds, mutual funds, or college endowments, hold portfolios, that is, they hold a collection of different securities. Much of the innovation in investment research over the past 40 years has been the development of a theory of portfolio management, and this module is principally an introduction to these new methods. It will answer the basic question, What rate of return will investors demand to hold a risky security in their portfolio? To answer this question, we first must consider what investors want, how we define return, and what we mean by risk. II. Why Investors Invest What motivates a person or an organization to buy securities, rather than spending their money immediately? The most common answer is savings -- the desire to pass money from the present into the future. People and organizations anticipate future cash needs, and expect that their earnings in the future will not meet those needs. Another motivation is the desire to increase wealth, i.e. make money grow. Sometimes, the desire to become wealthy in the future can make you willing to take big risks. The purchase of a lottery ticket, for instance only increases the probability of becoming very wealthy, but sometimes a small chance at a big payoff, even if it costs a dollar or two, is better than none at all. There are other motives for investment, of course. Charity, for instance. You may be willing to invest to make something happen that might not, otherwise -- you could invest to build a museum, to finance low-income housing, or to re-claim urban neighborhoods. The dividends from these kinds of investments may not be economic, and thus they are difficult to compare and evaluate. For most investors, charitable goals aside, the key measure of benefit derived from a security is the rate of return. III. Definition of Rates of Return The investor return is a measure of the growth in wealth resulting from that investment. This growth measure is expressed in percentage terms to make it comparable across large and small investors. We often express the percent return over a specific time interval, say, one year. For instance, the purchase of a share of stock at time t, represented as Pt will yield P t+1 in one year's time, assuming no dividends are paid. This return is calculated as: R t = [ P t+1 - Pt]/ Pt. Notice that this is algebraically the same as: Rt= [P t+1/ Pt]-1. When dividends are paid, we adjust the calculation to include the intermediate dividend payment: Rt=[ P t+1 - Pt+Dt]/ Pt. While this takes care of all the explicit payments, there are other benefits that may derive from holding a stock, including the right to vote on corporate governance, tax treatment, rights offerings, and many other things. These are typically reflected in the price fluctuation of the shares. IV. Arithmetic vs. Geometric Rates of Return There are two commonly quoted measures of average return: the geometric and the arithmetic mean. These rarely agree with each other. Consider a two period example: P0 = $100, R1 = -50% and R2 = +100%. In this case, the arithmetic average is calculated as (100-50)/2 = 25%, while the geometric average is calculated as: [(1+R1)(1+R2)]1/2-1=0%. Well, did you make money over the two periods, or not? No, you didn't, so the geometric average is closer to investment experience. On the other hand, suppose R1 and R2 were statistically representative of future returns. Then next year, you have a 50% shot at getting $200 or a 50% shot at $50. Your expected one year return is (1/2)[(200/100)-1] + (1/2)[(50/100)-1] = 25%. Since most investors have a multiple year horizon, the geometric return is useful for evaluating how much their investment will grow over the long- term. However, in many statistical models, the arithmetic rate of return is employed. For mathematical tractability, we assume a single period investor horizon. V. Capital Market History The 1980's was one of the greatest decades for stock investors in the history of the U.S. capital markets. (Courtesy Ibbotson Associates) We measure stock market performance by the total return to investment in the S&P 500, which is a standard index of 500 stocks, weighted by the market value of the equity of the company. Dividends paid by S&P 500 companies are assumed to be re-invested in shares of stock. This provides a measure of total investor return, before individual taxes are paid. The 1930's was one of the worst decades for U.S. stock investors. (Courtesy Ibbotson Associates) In the 1930's stock markets crashed all over the globe. U.S. stock investors experienced a zero percent return for the eleven-year period from 12/1929 to 12/1939. U.S. Capital Markets over the Long Term: 1926 - 1995 Over the past 68 years, A stock investment in the S&P increased from $1 to $800 (Courtesy Ibbotson Associates) VI. Risk Premium Notice in the preceding figure that a dollar invested in stock grew to $889 over the period, while a dollar invested in corporate bonds grew to $40. Why the big difference? This return differential is commonly attributed to a difference in the risk associated with stocks as opposed to bonds. Notice that the stock line is "shakier" than the bond line. Wealth invested in stocks since 1926 was more volatile than wealth invested in bonds. Despite the higher return, the risks were higher as well. An investor typically cares about the riskiness of an investment. If, for instance, you are saving for a home purchase sometime in the next year, then you really care whether your $100,000 nest egg has a significant probability of dropping to $50,000 in twelve months. As a matter of fact, you might be willing to trade a lower rate of investment return for "insurance" that your principal will be secure. This is called risk-aversion -- and all things being equal, most investors prefer less risk to more. Summary Statistics of U.S. Investments from 1926 through March, 1995. Source:Ibbotson Associates Investment geom. mean arith.mean std high ret. low ret. S&P total return 10.30 12.45 22.28 42.56 -29.73 U.S. Small Stock TR 12.28 17.28 35.94 73.46 -36.74 U.S. LT Govt TR 4.91 5.21 8.00 15.23 -8.41 U.S. LT Corp. TR 5.49 5.73 7.16 13.76 -8.90 U.S. 30 day T-Bills 3.70 3.70 .96 1.35 -0.06 The difference between the S&P total return and the U.S. 30 day T-Bill return is called the equity premium. It is the amount of return that investors demand for holding a risky security such as stocks, as opposed to a riskless security, such as T-Bills. The annual equity premium is about 9% arithmetic, and 6% geometric, over the 1926 - 1995 period. VII. Standard Deviation as a Measure of Risk Stock returns may be riskier or more volatile, but this concept is a difficult one to express simply. To do so, we borrow a concept from statistics, called standard deviation. standard deviation is a summary measure about the average spread of observations. It is the square root of the variance, which is calculated as: The standard deviation of one-year S&P 500 returns is about 22.28%. If S&P returns are normally distributed, this means that about 2/3 of the time we should observe an annual return within the range (12.45-22.28)= -9.93 and (12.45+22.28)= 34.73. A histogram of S&P 500 annual returns shows that returns are approximately normally distributed, or are they? A normal distribution should allow returns lower than -100%. Stocks do not. In fact, the log of the variable being normally distributed is a better approximation. However, there is evidence to suggest that even this is not quite right. The tails of stock returns are a bit "fatter" than should be observed if returns were log-normally distributed. This lends some support to the hypothesis advanced by Benoit Mandelbrot that stock returns follow a "stable" distribution, with undefined variance. Have a look at the S&P 500 histogram yourself: How well does standard deviation capture the notion of investor risk? It equally weights high returns with low returns. It heavily weights extreme observations. It is not concerned with the shape of the distribution. All of these are valid criticisms. However the benefits to using standard deviation are large. It is a single measure, allowing us to quantify asset returns by risk. As we will see in the next chapter, it also provides the basis for investor decisions about portfolio choice. Chapter II: The Geography of the Efficient Frontier In the previous chapter, we saw how the risk and return of investments may be characterized by measures of central tendency and measures of variation, i.e. mean and standard deviation. In fact, statistics are the foundations of modern finance, and virtually all the financial innovations of the past thirty years, broadly termed "Modern Portfolio Theory," have been based upon statistical models. Because of this, it is useful to review what a statistic is, and how it relates to the investment problem. In general, a statistic is a function that reduces a large amount of information to a small amount. For instance, the average is a single number that summarizes the typical "location" of a set of numbers. Statistics boil down a lot of information to a few useful numbers -- as such, they ignore a great deal. Before modern portfolio theory, the decision about whether to include a security in a portfolio was based principally upon fundamental analysis of the firm, its financial statements and its dividend policy. Finance professor Harry Markowitz began a revolution by suggesting that the value of a security to an investor might best be evaluated by its mean, its standard deviation, and its correlation to other securities in the portfolio. This audacious suggestion amounted to ignoring a lot of information about the firm -- its earnings, its dividend policy, its capital structure, its market, its competitors -- and calculating a few simple statistics. In this chapter, we will follow Markowitz' lead and see where the technology of modern portfolio theory takes us. I. The Risk and Return of Securities Markowitz's great insight was that the relevant information about securities can be summarized by three measures: the mean return (taken as the arithmetic mean), the standard deviation of the returns and the correlation with other assets' returns. The mean and the standard deviation can be used to plot the relative risk and return of any selection of securities. Consider six asset classes: (Courtesy Ibbotson Associates) This figure was constructed using historical risk and return data on Small Stocks, S&P stocks, Corporate and Government Bonds, and an international stock index called MSCI, or Morgan Stanley Capital International World Portfolio. The figure shows the difficulty an investor faces about which asset to choose. The axes plot annual standard deviation of total returns, and average annual returns over the period 1970 through 3/1995. Notice that small stocks provide the highest return, but with the highest risk. In which asset class would you choose to invest your money? Is there any single asset class that dominates the rest? Notice that an investor who prefers a low risk strategy would choose T-Bills, while an investor who does not care about risk would choose small stocks. There is no one security that is best for ALL investors. II. Portfolios of Assets Typically, the answer to the investment problem is not the selection of one asset above all others, but the construction of a portfolio of assets, i.e. diversification across a number of different securities. The key to diversification is the correlation across securities. Recall from data analysis and statistics that the correlation coefficient is a value between -1 and 1, and measures the degree of co-movement between two random variables, in this case stock returns. It is calculated as: Where the sigma AB is the covariance of the two securities. Here is how to use correlation in the context of portfolio construction. Consider two securities, A and B. Security A has a mean of 10% and an STD of 15%. Security B has a mean of 20% and an STD of 30%. We can calculate the standard deviation of a portfolio composed of different mixtures of A & B using this equation: The mean return is not as complicated. It is a simple weighted average of the means of the two assets: mean p = W A RA + W B R B. Notice that a portfolio will typically have a weight of one, so usually, W A + W B = 1. What if the correlation of A&B = 0 ? Notice that a portfolio of 80% A and 20% B has a standard deviation of: sqrt(.82*.152+.22.32+2*0*.8*.2*.15*.3) = 13.4 % In other words, a mixture of 20% of the MORE RISKY SECURITY actually decreases the volatility of the portfolio! This is a remarkable result. It means you can reduce risk and increase return by diversifying across assets. What if the correlation of A&B = 1 ? In this case, the perfect correlation between the two assets means there is no diversification. The portfolio std of of the 80/20 mix is 18%. this is equal to a linear combination of the standard deviations: (.8)(.15)+(.2)(.30) = 18% What if the correlation of A&B = -1 ? This is an unusual case, because it means that when A moves up, B always moves down. Take a mixture of .665 A and (1-.665) B. sqrt(.6652*.152+(1-.665)2.32+2*0*(.665)*(1- .665)*.15*.3) = .075%, Which is very close to zero. In other words, A is nearly a perfect hedge for B. One of the few real-life negative correlations you will find is a short position in a stock offsetting the long position. In this case, since the mean returns are also the same, the expected return will be zero. These extremes of correlation values allow us to describe an envelope within which all combinations of two assets will lie, regardless of their correlations. (Courtesy Campbell Harvey) III. More Securities and More Diversification Now consider what will happen as you put more assets into the portfolio. Take the special case in which the correlation between all assets is zero, and all of them have the same risk. You will find that you can reduce the standard deviation of the portfolio by mixing across several assets rather than just two. Each point represents an equally-weighted combination of assets; from a single stock to two, to three, to thirty, and more. Notice that, after 30 stocks, diversification is mostly achieved. There are enormous gains to diversification beyond one or two stocks. (Courtesy Campbell Harvey) If you allow yourself to vary the portfolio weights, rather than keeping them equal, the benefits are even greater, however the mathematics is more challenging. You not only have to calculate the STD of the mixture between A&B, but the STD of every conceivable mixture of the securities. None-the-less, If you did so, you would find that there is a set of portfolios which provide the lowest level of risk for each level of return, and the highest level of return for each level of risk. By considering all combinations of assets, a special set of portfolios stand out -- this set is called the efficient frontier. The efficient frontier, shown in blue, is the set of dominant portfolios, at least from the perspective of a risk averse investor. For ANY level of risk, the efficient frontier identifies a point that is the highest returning portfolio in its risk class. By the same token, for any level o