finance theory by r merton

Finance Theory Robert C Merton Table of Contents I Introduction II On the Arithmetic of Compound Interest: The Time Value of Money III On the Theory of Accumulation and Intertemporal Consumption Choice by Households in an Environment of Certainty 34 On the Role of Business Firms, Financial Instruments and Markets in an Environment of Certainty 57 The "Default-Free" Bond Market and Financial Intermediation in Borrowing and Lending 76 VI The Value of the Firm Under Certainty 115 VII The Firm's Investment Decision Under Certainty: Capital Budgeting and Ranking of New Investment Projects 134 VIII Forward Contracts, Futures Contracts and Options 151 IX The Financing Decision by Firms: Impact of Capital Structure Choice on Value 165 X The Investor's Decision Under Uncertainty: Portfolio Selection 185 XI Implications of Portfolio Theory for the Operation of the Capital Markets: The Capital Asset Pricing Model 225 XII Risk-Spreading via Financial Intermediation: Life Insurance 241 XIII Optimal Use of Security Analysis and Investment Management 249 XIV Theory of Value and Capital Budgeting Under Uncertainty 270 XV Introduction to Mergers and Acquisitions: Firm Diversification 287 XVI The Financing Decision by Firms: Impact of Dividend Policy on Value 296 XVII Security Pricing and Security Analysis in an Efficient Market 312 IV V Copyright © 1982 by Robert C Merton These Notes are not to be reproduced without the author’s written permission All rights reserved I INTRODUCTION Output Product Markets Consumption Manufacturing or Business Firms Labor Markets Households Savings Capital Markets • Stock • Bond • Money • Futures Investment Capital Savings Financial Intermediaries (Borrowings) Domain of Finance This course is an introduction to the theory of optimal financial management of households, business firms, and financial intermediaries For the term "optimal" to have meaning, a criterion for measuring performance must be established For households, it is assumed that each consumer has a criterion or "utility" function representing his preferences among alternatives, and this set of preferences is taken as "given" (i.e., as exogenous to the theory) This traditional approach to households and their tastes does not extend to economic organizations and institutions That is, they are regarded as existing primarily because of the functions they serve instead of functioning primarily because they exist Economic organizations and institutions, unlike households and their tastes, are endogenous to the theory Hence, in the theory of the firm, it is not a fruitful approach to treat the firm as an "individual" with exogenous preferences Rather, it is assumed that firms are created as means to the ends of consumer-investor welfare, and therefore, the criterion function for judging optimal management of the firm will be endogenous In a modern large-scale economy, it is neither practical nor necessary for management to "poll" the owners of the firm to make decisions Instead certain data gathered from the capital markets can be used as "indirect" signals for the determination of the optimal investment and financing decisions What the labor and product markets are to the marketing, production and Robert C Merton product-pricing managers, the capital markets are to the financial manager Hence, a good financial manager must understand how capital markets work Since the capital markets are central, it is quite natural to begin the study of Finance with the theory of capital markets To derive the functions of financial markets and institutions, we investigate the behavior of individual households Using portfolio selection theory, the households' demand functions for assets and financial securities are derived to develop the demand side of capital markets Taking as given the supply of available assets (i.e., the investment and financing decisions of business firms), the demands of households are aggregated and equated to aggregate supplies to determine the equilibrium structure of returns of assets traded in the capital market Inspection of the structure of these demand functions leads in a natural way to an introductory theory for the existence and optimal management of financial intermediaries In the second part of the course, the supply side of the capital markets is developed by studying the optimal management of business firms (given the demand functions of households) The two elements which make Finance a nontrivial subject are time and uncertainty Capital investments often require substantial commitments of resources to earn uncertain cash flows which may not be generated before some distant future date It is the financial manager's responsibility to determine under what conditions such investments should be taken and to ensure that sufficient funds will be available to take the investments Because future flows and rates of return are not known with certainty, to make good decisions, the financial manager must have a thorough understanding of the tradeoff between risk and return While the basic mode of approach has universal application, it should be understood that the assumed environment is the (reasonably) large corporation in a large-scale economy with welldeveloped capital markets and institutions similar to those in the United States Although the emphasis is on the private sector, most of the analysis can be applied directly to public sector financing and investment decisions However, certain assumptions made in developing the theory (which are quite reasonable in the assumed environment) will require modification before being applied to small businesses with limited access to the capital markets or to foreign countries with significantly different institutional and social structures Finance Theory Summary of Different Parts of Finance Households (Personal Finance) Taken as Given: A criterion function for choice among alternative consumption programs To be Determined: Initial endowments Optimal consumption-saving decision Optimal allocation of savings (portfolio selection) Manufacturing or Business Firms (Corporate Finance) Taken as Given: Owners of the firm are households [either directly or through financial intermediaries] Proper management is to operate the firm in the best interests of the owners or shareholders The technology or "blueprints" of available projects (including cost and revenue forecasts) are known either as point values (certainty) or as probability distributions To be Determined: An operation criterion for measuring good management Investment decision in physical assets (capital budgeting) a Which assets to invest in b How much to invest in total The long-term financing decision a Dividend policy b Capital structure decisions and the cost of capital The short-term financing decision a Management of working capital and cash Robert C Merton Mergers and Acquisitions: Firm diversification Taxation and its impact on 2-5 (above) Financial Intermediaries (Financial Institutions) Taken as Given: Owners of the intermediary are households [either directly or through other financial intermediaries] Proper management is to operate the intermediary in the best interests of the owners or shareholders To be Determined: Why they exist and what services they provide How the management of financial intermediaries differs from the management of business firms Efficient management and measurement of performance The role of market makers Capital Markets and Financial Instruments (Capital Market Finance) To be Determined: Why they exist and what services they provide The characteristics of an "efficient" capital market How an efficient capital market permits decentralization of decision making The role of capital markets as a source of information (or "signals") for efficient decision making by households and managers of business firms and financial intermediaries The empirical testing of finance theories using capital market data Finance Theory Basic Methodology and Approach of the Course How should the system work? Does it work that way? If not, is there an opportunity for improvement (and hence, a profit opportunity)? If you and the market "disagree," then who is right? Frequently-Used Concepts Equilibrium: To understand each element of the system, one must frequently analyze the whole system To so, we look at the aggregated resultant of the actions of each unit If each unit is choosing the "best" plan possible and the aggregation of the actions implied by these plans are such that the market clears (i.e., supply equals demand for every item), then these "best" plans can be realized, and the market is said to be in equilibrium In general, it will be assumed that the markets are in or tending toward equilibrium Competition: The basic paradigm adopted is that markets operate such that the very best at their "job" will earn a "fair" return and those that are not will earn a less-than-fair return This is in contrast to the view that anyone can earn a "fair" return and the "smart" people will earn a "super" return In certain situations, it will be assumed that the capital markets satisfy the technical conditions of pure competition "Perfect" or "Frictionless" Markets: At times, we will use the abstract concept of a perfect market That is, there are no transactions costs or other frictions; that there are no institutional restrictions against market transactions of any sort; there are no divisibility problems with respect to the scale of transactions; that equal information is available to all market participants In some cases, actual markets will be sufficiently "close" to this abstraction to use the resulting analysis directly In other cases, it provides a "benchmark" for the study of imperfections Robert C Merton Summary 53-Year Return Experience: Stocks and Bonds (1926–1978) Source: “Stocks, Bonds, Bills, and Inflation: Historical Returns (1926–1978),” R.G Ibbotson and R.A Sinquefield, Financial Analysts Foundation (1979) Average Annual Return Standard Deviation Common Stocks (S&P 500) 11.2% 22.2% $89,592 (8.9%) Long-Term Corporate Bonds 4.1% 5.6% $ 7,807 (4.0%) Long-Term Government Bonds 3.4% 5.7% $ 5,342 (3.2%) U.S Treasury Bills 2.5% 2.2% $ 3,728 (2.5%) Type Growth of $1000 (Average Compound Return) “Inflation-Adjusted” (Consumers Price Index) (“Real”) Returns Type Average Annual Return Standard Deviation 22.3% Growth of $1000 (Average Compound Return) Common Stocks (S&P 500) 8.7% Long-Term Corporate Bonds 1.6% NA $ 2,018 (1.3%) Long-Term Government Bonds 0.9% NA $ 1,377 (0.6%) U.S Treasury Bills 0.0% 4.6% $23,399 (6.1%) $ 965 (0.0%) Finance Theory II ON THE ARITHMETIC OF COMPOUND INTEREST: THE TIME VALUE OF MONEY From our everyday experiences, we all recognize that we would not be indifferent to a choice between a dollar to be paid to us at some future date (e.g., three years from now) or a dollar paid to us today Indeed, all of us would prefer to receive the dollar today The assumption implicit in this common-sense choice is that having the use of money for a period of time, like having the use of an apartment or a car, has value The earlier receipt of a dollar is more valuable than a later receipt, and the difference in value between the two is called the time value of money This positive time value of money makes the choice among various intertemporal economic plans dependent not only on the magnitudes of receipts and expenditures associated with each of the plans but also upon the timing of these inflows and outflows Virtually every area in Finance involves the solution of such intertemporal choice problems, and hence a fundamental understanding of the time value of money is an essential prerequisite to the study of Finance It is, therefore, natural to begin with those basic definitions and analytical tools required to develop this fundamental understanding The formal analysis, sometimes called the arithmetic of compound interest, is not difficult, and indeed many of the formulas to be derived may be quite familiar However, the assumptions upon which the formulas are based may not be so familiar Because these formulas are so fundamental and because their valid application depends upon the underlying assumptions being satisfied, it is appropriate to derive them in a careful and axiomatic fashion Then, armed with these analytical tools, we can proceed in subsequent sections with the systematic development of finance theory Although the emphasis of this section is on developing the formulas, many of the specific problems used to illustrate their application are of independent substantive importance A positive time value of money implies that rents are paid for the use of money For goods and services, the most common form of quoting rents is to give a money rental rate which is the dollar rent per unit time per unit item rented A typical example would be the rental rate on an apartment which might be quoted as "$200 per month (per apartment)." However, a rental rate can be denominated in terms of any commodity or service For example, the wheat rental rate Finance Theory Their results seem somewhat surprising in the light of our proof that dividend policy does not matter in the absence of transactions costs and personal taxes Since both exist in the real world, one's prior might be that γ1 > I.e., investors prefer low-dividend yielding stocks The Black-Scholes explanation of this result is as follows: because payout policies are not randomly distributed across the firms and risk classes, to achieve dividend yields that are significantly different from the market's, the investor must hold a less-than-well-diversified portfolio Thus, to achieve a higher (or lower) dividend-yielding portfolio, one must pay a price in the form of increased variance Because dividend-yield is only a small fraction of the total return on the market and the maximum tax-saving is even smaller, it does not pay to adjust one's portfolio to avoid dividends Moreover, unless a taxpayer is in the maximum tax bracket, he does not know if he would prefer high or low-dividend paying portfolios unless he knows the "spread" between pre-tax yields Hence, they conclude that for stock portfolios (in the world as it is) investors neglect tax differentials between dividends and capital gains 311 XVII SECURITY PRICING AND SECURITY ANALYSIS IN AN EFFICIENT MARKET Consider the following somewhat simplified description of a typical analyst-investor's actions in making an investment decision First, he collects the information or "facts" (both fundamental and technical) about the company and related matters which may affect the company Second, he analyzes this information in such a way so as to determine his best estimate (as of today, time "zero") of the stock price at a future date (time "one") This best estimate is the expected stock price at time one which we denote by P (1) From looking at the current stock price, P(0), he can estimate an expected return on the stock, Z , which is Z = P(1) P(0) However, his analyst's job is not finished Because he recognizes that his information is not perfect (i.e., subject to error, unforeseen events which may occur, etc.), he must also give consideration to the range of possible future prices In particular, he must estimate how dispersed this range is about his best estimate and how likely is a deviation of a certain size from this estimate This analysis then gives him an estimate of the deviations of the rate of return from the expected rate and the likelihood of such deviations Obviously, the better his information, the smaller will be the dispersion and the less risky the investment Third, armed with his estimates of the expected rate of return and the dispersion, he must make an investment decision and determine how much of the stock to buy or sell How much will depend on how good the risk-return tradeoff on this stock is in comparison with alternative investments available and on how much money he has to invest (either personally or as a fiduciary) The higher the expected return and the more money he has (or controls), the more of the stock he will want to buy The larger the dispersion (i.e., the less accurate the information that he has), the smaller the position he will take in the stock To see how the current market price of the stock is determined, we look at the aggregation of all analysts' estimates, and assume that on the average the market is in equilibrium I.e., on average, the price will be such that total (desired) demand equals total supply Analysts' estimates may differ for two reasons: (1) they may have access to different 312 Finance Theory amounts of information (although presumably public information is available to all); (2) they may analyze the information differently with regard to its impact on future stock prices Nonetheless, each analyst comes to a decision as to how much to buy or sell at a given market price, P(0) The aggregation of these decisions gives us the total demand for shares of the company at the price, P(0) Suppose that the price were such that there were more shares demanded than supplied (i.e., it is too low), then one would expect the price to rise, and vice versa, if there were more shares available at a given price than were demanded Hence, the market price of the stock will reflect a weighted average of the opinions of all analysts The key question is: what is the nature of this weighting? Because "votes" in the marketplace are cast with dollars, the analysts with the biggest impact will be the ones who control the larger amounts of money, and among these, the ones who have the strongest "opinions" about the stock will be the most important Note: the ones with the strongest "opinions" have them because (they believe that) they have better information (resulting in a smaller dispersion around their best estimate) Further, because an analyst who consistently overestimates the accuracy of his estimates will eventually lose his customers, one would expect that among the analysts who control large sums, the ones that believe that they have better information, on average, probably From all this, we conclude that the market price of the stock will reflect the weighted average of analysts' opinions with heavier weights on the opinions of those analysts with control of more than the average amount of money and with better than average amounts of information Hence, the estimate of "fair" or "intrinsic" value provided by the market price will be more accurate than the estimate obtained from an average analyst Now, suppose that you are an analyst and you find a stock whose market price is low enough that you consider it a "bargain" (if you never find this situation, then there is no point being in the analyst business) From the above discussion, there are two possibilities: (1) you have a bargain─your estimate is more accurate than the market's I.e., you have either better than average information about future events which may affect stock price and/or you a better than average job of analyzing information Or, (2) others have better information than you or 313 Robert C Merton process available information better, and your "bargain" is not a bargain One's assessment of which it is, depends on how good the other analysts are relative to oneself There are important reasons why one would expect the quality of analysts to be high: (1) the enormous rewards to anyone who can consistently beat the average attract large numbers of intelligent people to the business; (2) the relative ease of entry into the (analyst) business implies that competition will force the analysts to get better information and better techniques for processing this information just to survive; (3) the stock market has been around long enough for these competitive forces to take effect Unfortunately, the tendency is to underestimate the capabilities of other analysts Ask any analyst if he is better than average, and invariably he answers "yes." Clearly, this cannot be true for all analysts by the very definition of average If the analysts are so good, why aren't most of them rich? Precisely because they compete with each other, the market price becomes a better and better estimate of "fair value," and it becomes more difficult to find profit opportunities To stay ahead, the analyst must develop new ideas continually As the limiting case of this process, one would expect that as market prices become better estimates of "fair value" in the sense of fully reflecting all relevant known information, the fluctuations of stock prices around the expected "fair return" will be solely the result of unanticipated events and new information Hence, these fluctuations are random and not forecastable And it is in this sense that the fluctuations in stock prices can be described by a random walk This also explains why the performance of most "managed" portfolios will be no better than the performance of an "unmanaged" well-diversified portfolio In fact, the "unmanaged" portfolio, because it takes market prices as the best estimate of value, is equivalent to a "managed" portfolio whose manager is a no-worse-than-average analyst! The investor who buys such a portfolio is simply "piggy-backing" on the actions taken by active analyst-investors competing with each other This is essentially the story behind the "Random Walk Theory." It does not imply that a better-than-average analyst cannot make greater than fair returns It does not imply that all analysts should quit their jobs, and in fact, its cornerstone is that enough analysts remain and 314 Finance Theory actively compete so that market prices are good estimates of "fair" value It is only in this way that the "piggy-backing" by investors can be justified Further, it does not imply that all investors should hold "unmanaged" portfolios If an investor can identify an analyst with above-average capabilities and is willing to bear the risk of his capabilities, then a "bargain" can be struck so that both are rewarded for the effort The theory does imply that to make "extra" profits, one must have superior techniques which process information in a way not generally known in the market and that the longer that the market is in existence, the greater the number of participants, the more difficult it is to make these "extra" profits An Example to Illustrate the Efficient Market Concept Consider a firm in a cyclical business whose earnings are completely predictable but vary in the following fashion: If the earnings per share this period are $50, then next period's earnings per share will be $100, and if the earnings per share this period are $100, then next period's earnings per share will be $50 I.e., if Et denotes earnings in period t , and if E0 = $50 then E1 = 100, E = 50, E3 = 100, or t E t +1 = E t + (-1) 50 If the firm pays out all earnings as dividends (Dt = E t ) and if the required return ("fair market return") is 20% per period, then the correct price per share, St (ex-dividend) is given by S0 = $386.36, S1 = $363.64, S2 = $386.36, S3 = $363.64, St +1 = St + (-1) t +1 22.72 I.e., the return per dollar from investing in the shares from time to time 1, Z1 = D1 + S1 100 + 363.64 = = 1.20, and from time to time 2, 386.36 S0 Z2 = D2 + S2 50 + 386.36 = = 1.20, and so forth 363.4 S1 315 Robert C Merton Suppose that investors are myopic and assume that current earnings (and hence, current dividends) are permanent I.e., their best guess of future dividends is that they will be equal to ' current dividends If St denotes price per share under this belief, then 50 100 D0 D = = $250; S1' = = = $500, r r 2 50 100 D2 D3 = = = $250; S3' = = = $500, r r t ' St' +1 = St + (-1) 250 S0' = S 2' or The return per dollar from investing in the shares from time to time under this pricing is Z1' = ' 100 + 500 D1 + S1 = = 2.4 or 140% ' 250 S0 ' and from time to time , Z is Z 2' = ' 50 + 250 D + S2 = = 0.6 or - 40% ' 500 S1 and it continues to alternate 316 Finance Theory Empirical Studies of Capital Market Theory In Sections IX and X, we developed a theory for the capital markets based on essentially rational behavior and optimal portfolio selection Specifically, by applying the mean-variance model and aggregating demands, we deduced the Capital Asset Pricing model, which provided a specification for equilibrium expected returns among securities Based on this model, we deduced a naive or benchmark portfolio strategy From our analysis of an efficient speculative market, we deduced a rationale for random selection of securities or the naive strategy as possible portfolio strategies Since these models have important implications for both corporate finance and financial intermediation, it is most important that empirical testing of the models is performed Basically, there are three questions to be answered: (i) How does the "random walk" theory hold up against the data? (ii) Is the security market line specification a reasonable description of returns on securities? (iii) How does the performance of the naive strategy compare with managed portfolio strategies? 317 Robert C Merton The answer to (i) is simply that a large number of technical trading strategies (filtering, serial correlation, charting services, volume analysis, etc.) have produced no evidence to refute the random walk hypothesis To the extent that any serial correlation in the returns were present, it was of such small magnitude and "short-lived" nature that no profitable trading was possible Other studies of brokerage house and general service recommendations, dividend announcements and earning reports have shown no evidence of providing trading profits "Dart throwing" or more careful random selection of portfolios provide no evidence against the random walk hypothesis In the study of managed portfolio performance, both the random walk hypothesis and the asset pricing model are implicitly tested Returns on the "Market" NYSE index: value-weighted index of all stocks on the New York Stock Exchange ≈80% in market value of all securities) S&P index: Standard & Poors 500-stock index including the largest companies (in 1965 representing ≈80% of market value of NYSE stocks) Random Selection of Stocks (Fisher & Lorie): Equally-weighted portfolio of all stocks on the New York Stock Exchange 1926-1965 Average Return (1-year): including dividends, no taxes, or commissions Years Average Annual Return (Arithmetic Average) Standard Deviation (Annual) 1926-1945 17.8% 41.2% 1946-1965 15.1% 19.8% 1926-1965 16.5% 32.3% 318 Finance Theory "Market" (in this sense) was much more volatile in the pre-war versus post-war period Average Compound Return: including dividends, no taxes, but including purchase commissions: Years Average Compound Return (Geometric Average) 1926-1945 6.3% 1946-1965 12.6% 1926-1965 9.3% All Stocks on the New York Stock Exchange: Value-Weighted Cowles (1871-1937): Average Compound Return: 6.6% Since the Fisher Lorie results for average performance of randomly selected portfolios is as good as managed portfolios on average over the same period, this is additional evidence in favor of the Random Walk 319 Simulated Rate of Return Experience for Successful Market Timing* Monthy Forecasts: P = Probability of Correct Forecast January 1927 – December 1978 Per Month P=1.0 P=.90 Market Timing P=.75 P=.60 P=.50 NYSE Stocks Average Rate of Return 2.58% 2.17% 1.56% 0.94% 0.53% 0.85% Standard Deviation 3.82% 3.98% 4.13% 4.19% 4.18% 5.89% Highest Return 38.55% 38.27% 37.61% 36.41% 35.12% 38.55% Lowest Return -0.06% -17.05% -22.02% -24.52% -25.64% -29.12% 2.51% 2.10% 1.47% 0.85% 0.44% 0.68% Average Compound Return Growth of $1,000 $5,362,212,000 $418,902,144 $9,146,722 $199,718 $15,602 $67,527 Average Annual Compound Return 34.65% 28.32% 19.14% 10.69% 5.41% 8.47% *Buy the market when the forecast is for stocks to better than bonds Buy bonds when the forecast is for bonds to better than stocks 320 Robert C Merton Average Annual Compound Return on the Market (value-weighted, including reinvesting dividends, no commissions, or taxes) (Scholes) Years Total: 10 Years: Years: 1953-1972 1953-1962 1963-1972 1953-1957 1958-1962 1963-1967 1968-1972 NYSE Average Return Avg Excess Return S&P Average Return Avg Excess Return 11.98% 13.11% 10.86% 12.25% 13.99% 14.53% 7.31% 7.57% 10.00% 5.15% 9.45% 10.52% 9.70% 0.71% 11.63% 13.38% 9.90% 13.50% 13.26% 12.34% 7.52% 7.22% 10.25% 4.19% 10.70% 9.79% 7.50% 0.92% Jensen Performance of Mutual Funds Study 1945-1964 Testing 115 Funds ability to Forecast (relative to Security Market Line): Model Specification: Z j (t) = R(t) + β j[ ZM (t) - R(t)] + α j (t) Test: ~ (t) = R(t) + β [ ~ (t) - R(t)] + (t) + ~ (t) αj εj Zj j ZM E(~ε j (t)) = 0; Cov(~ε j (t), ~ε i (t - k)) = i, j = 1, k = 1,2, Assumes: β j is stationary Suppose not: ~ ~ β j (t) = β j + U j (t) estimated ~ ,~ ) > ) < βj if you can forecast the market, then Cov ( U which would imply E(β j j ZM and biases tests in favor of superior performance (i.e., larger α j ) 321 Robert C Merton 115 Funds Studied Returns net of all costs including management fees 76 funds had measured α j < 39 funds had measured α j ≥ Average α = – 011 = – 1.1% The statistical significance of the positive α j were no more than would have been expected by chance when the true α j = average α Using Returns Gross of Management Fees 55 funds had measured α j < 60 funds had measured α j ≥ Average α = – 004 = –0.4% Statistical significance of the positive α j were no more than would have been expected by change when the true α j = Conclusions: Funds taken as a whole not show evidence of superior forecasting capability; and, of course, not show evidence of sufficient superior forecasting to cover costs What about individual funds? Even if funds as a whole not show evidence of superior forecasting, what about the overtime performance of particular funds? Is it true that funds with observed positive α j in the past tend to have positive α j in the future? Jensen & Black studied the 115 funds for the years 1955-1964 computing the realized α j for each year (a total of 10 × 115 = 1150 observations) The differential returns were computed gross of management fees The results were 322 Finance Theory Number of Successive Years of Observed Positive "α" Number of Times Observed Percent of Cases Followed by Another Positive "α" 574 50.4% 312 52.0% 161 53.4% 79 55.8% Conclusion: It appears that funds that did well in the past show little evidence of continuing to so Jensen also found that there was no significant evidence of serial correlation in the return series in support of the Random Walk Hypothesis With respect to providing efficient (or well-diversified) portfolios, on average, Jensen found that 85% of the variance of the funds' returns were due to market movements I.e., σp ≈ (1.085) σM βp = 1.085 ρpM σp or ρpM ≈ = 9216 1.085 Further, on the whole, funds tended to keep about the same level of βp or σp through time Overall Summary Over the last forty years, randomly selected portfolios have returns greater than or equal to randomly selected managed portfolios Most mutual funds are reasonably well diversified (i.e., have reasonably low nonsystematic risk) On average, funds did not perform, before expenses, any better than a naive strategy portfolio with the same beta 323 Robert C Merton On average, funds did worse, after expenses, than the naive strategy portfolio with the same beta Few, if any, individual funds showed any consistent performance superior to the naive strategy over time Most funds spend too much money trying to forecast returns on stocks: either explicitly in analyst salaries and support and implicitly through brokerage commissions and spreads through excess turnover Investment prescription: Since these results did not include sales commissions on "load" funds which run from 1½ - 8½%, clearly one should buy "no load" funds (with no sales commissions) To achieve an efficient investment strategy, choose a mix of a few well-diversified, no load funds Select funds with the lowest costs (management fees and turnover) (ii) Testing the Capital Asset Pricing Model (Miller and Scholes; Black-Jensen-Scholes) The capital asset pricing model specifies that E( Z j) = R + β j [E( ZM ) - R] and E( ZM) > R I.e., investors are risk-averse; expected excess return on a security is proportional to its beta; it is dependent only on beta; is linear in beta The Black-Jensen-Scholes paper is one of the most sophisticated tests of the capital asset pricing model Using monthly returns from 1931-1965 on 600-1100 securities, they found the following: The expected return on the market is greater than the riskless rate ( ZM > R) Expected return on individual securities (portfolios) is an increasing function of its beta and the excess returns are linear in beta Expected return depends on beta 324 Finance Theory The empirical Security Market Line is too "flat." I.e., the returns on "low beta" (β < 1) stocks were higher than predicted by the Capital Asset Pricing Model and the returns on "high beta" (β > 1) stocks were lower than predicted by the Capital Asset Pricing Model Results 1-3 are consistent with the capital asset pricing model, result is not, and has been the cause for much concern as well as new research in this area To analyze this problem, BJS constructed a "zero-beta" portfolio by combining stocks only (so it has variance), and this portfolio had realized returns significantly greater than the riskless rate I.e., Z0-β > R where Z0-β is the expected return on the minimum-variance, zero-beta portfolio constructed from stocks The specification that they fit was Z j - R = β j( Z M - R) + γ(β j)( Z 0-β - R) , where γ(1) = and dγ < dβ While there are many possible theoretical and empirical explanations for this finding, such analyses are beyond the level of this course It is evident that the simple form of the Capital Asset Pricing Model as a means for estimating expected returns on individual securities is not sufficient; however, the main results implied by that model (1-3) seem to describe returns and, as a good approximation, its specification is not unreasonable 325 ... Efficient Market 312 IV V Copyright © 1982 by Robert C Merton These Notes are not to be reproduced without the author’s written permission All rights reserved I INTRODUCTION Output Product Markets... common per period rate will be Robert C Merton denoted by r Although no specific institutional structure for borrowing or lending is presumed, the reader may find it helpful to think of the described... after-tax rate of interest, (1 - τ )r Because property taxes can be deducted from income 27 Robert C Merton for federal income tax purposes, the after-tax outflow for property taxes each year is