Encyclopedia of Finance Part 11 docx

Chapter 19 MEAN VARIANCE PORTFOLIO ALLOCATION CHENG HSIAO, University of Southern California, USA SHIN-HUEI WANG, University of Southern California, USA Abstract The basic rules of balancing the expected return on an investment against its contribution to portfolio risk are surveyed. The related concept of Capital Asset Pricing Model asserting that the expected return of an asset must be linearly related to the covariance of its return with the return of the market portfolio if the market is efficient and its statistical tests in terms of Arbitraging Price Theory are also surveyed. The intertemporal generalization and issues of estimation errors and portfolio choice are discussed as well. Keywords: mean–variance efficiency; covariance; capital asset pricing model; arbitrage pricing the- ory; Sharpe ratio; zero-beta portfolio; volatility; minimum variance portfolio; value at risk; errors of estimation 19.1. Introduction Stock prices are volatile. The more volatile a stock, the more uncertain its future value. Investment success depends on being prepared for and being willing to take risk. The insights provided by mod- ern portfolio theory arise from the interplay be- tween the mathematics of return and risk. The central theme of modern portfolio theory is: ‘‘In constructing their portfolios investors need to look at the expected return of each investment in rela- tion to the impact that it has on the risk of the overall portfolio’’ (Litterman et al., 2003). To balance the expected return of an investment against its contribution to portfolio risk, an invest- ment’s contribution to portfolio risk is not just the risk of the investment itself, but rather the degree to which the value of that investment moves up and down with the values of the other investments in the portfolio. This degree to which these returns move together is measured by the statistical quan- tity called ‘‘covariance,’’ which is itself a function of their correlation along with their volatilities when volatility of a stock is measured by its stand- ard deviation (square root of variance). However, covariances are not observed directly; they are inferred from statistics that are notoriously un- stable. In Section 19.2, we summarize the Markowitz (1952, 1959) mean–variance allocations rule under the assumption that the correlations and volatilities of investment returns are known. Section 19.3 de- scribes the relationship between the mean variance efficiency and asset pricing models. Section 19.4 discusses issues of estimation in portfolio selection. 19.2. Mean–Variance Portfolio Selection The basic portfolio theory is normative. It con- siders efficient techniques for selecting portfolios based on predicted performance of individual se- curities. Marschak (1938) was the first to express preference in terms of indifference curves in a mean–variance space. Von Neumann and Morgen- stern (1947) provided an axiomatic framework to study the theory of choice under uncertainty. Based on these developments, Markowitz (1952, 1959) developed a mean–variance approach of asset allocation. Suppose there are N securities indexed by i, i ¼ 1, , N. Let R 0 ¼ (R 1 , , R N ) denote the re- turn of these N securities. Let m ¼ ER and S be the mean and the nonsingular covariance matrix of R. A portfolio is described by an allocation vector X 0 ¼ (x 1 , , x N ) of quantity x i for the ith secur- ity. In the mean–variance approach, an investor selects the composition of the portfolio to maxi- mize her expected return while minimizing the risk (i.e. the variance) subject to budget constraint. Since these objectives are contradictory, the in- vestor compromises and selects the portfolio that minimizes the risk subject to a given expected re- turn, say d. A portfolio X is said to be the min- imum-variance portfolio of all portfolios with mean (or expected) return d if its portfolio weight vector is the solution to the following constrained minimization: min x X 0 SX (19:1) subject to X 0 m ¼ d, (19:2) and X 0 i ¼ 1, (19:3) where i is an N Â1 vector of ones. Solving the Lagrangian L ¼ X 0 SX þ l 1 d À X 0 m ½ þ l 2 1 À X 0 i ðÞ , (19:4) yields the optimal portfolio X p ¼ 1 D m 0 S À1 m  S À1 i À i 0 S À1 m  S À1 m hin þdi 0 S À1 i  S À1 m À i 0 S À1 m  S À1 i hio , (19:5) where D ¼ mS À1 m  i 0 S À1 i  À i 0 S À1 m  2 : (19:6) From Equation (19.5), we have: Proposition 1: Any two distinct minimum-vari- ance portfolios can generate the minimum variance frontier. Proposition 2: Let portfolio o as the portfolio with the smallest possible variance for any mean return, then the global minimum variance portfolio has X 0 ¼ 1 i 0 S À1 i  S À1 i, m 0 ¼ ER 0 ¼ EX 0 0 R ¼ i 0 S À1 m i 0 S À1 i , ¼ 1 i 0 S À1 i (19:7) Proposition 3: The covariance of the return of the global minimum-variance portfolio o with any port- folio p is Cov R o , R p ÀÁ ¼ 1 iS À1 i : (19:8) that is, the correlation of them is positive, corr(R 0 , R p ) > 0 for any portfolio p. Proposition 4: If the covariance of the returns of two portfolios p and q equal to 0, Cov(R p , R q ) ¼ 0, then portfolios p and q are called orthogonal portfo- lios and the portfolio q is the unique portfolio which is orthogonal to p. Proposition 5: All portfolios on positively slope part of mean–variance frontier are positively correl- ated. When a risk-free asset with return R f is present, the expected return of investing in the N þ 1 assets will be m a ¼ (1 À a)R f þ aX 0 m, (19:9) where 0 < a < 1 is the proportion of investment in the risky assets. The minimum-variance portfolio with the expected return of investing in both N 458 ENCYCLOPEDIA OF FINANCE risky assets and the risk-free asset equal to d, m a ¼ d, is the solution of a 2 X 0 SX (19:10) subject to Equations (19.3) and (19.9) equal to d, X Ã p ¼ 1 i 0 S À1 m À R f iðÞ S À1 m À R f iðÞ, (19:11) a ¼ i 0 S À1 m À R f iðÞ m À R f iðÞS À1 m À R f iðÞ (d ÀR f ): (19:12) Thus, when there is a risk-free asset, all min- imum-variance portfolios are a combination of a given risky asset portfolio with weights propor- tional to X Ã p and the risk-free asset. This portfolio of risky assets is called the tangency portfolio be- cause X Ã p is independent of the level of expected return. If we draw the set of minimum-variance portfolios in the absence of a risk-free asset in a two-dimensional mean-standard deviation space like the curve GH in Figure 19.1, all efficient port- folios lie along the line from the risk-free asset through portfolio X Ã p . Sharpe (1964) proposes a measure of efficiency of a portfolio in terms of the excess return per unit risk. For any asset or portfolio with an expected return m a and standard deviation s a , the Sharpe ratio is defined as sr a ¼ m a À R f s a (19:13) The tangency portfolio X Ã p is the portfolio with the maximum Sharpe ratio of all risky portfolios. Therefore, testing the mean–variance efficiency of a given portfolio is equivalent to testing if the Sharpe ratio of that portfolio is maximum of the set of Sharpe ratios of all possible portfolios. 19.3. Mean–Variance Efficiency and Asset Pricing Models 19.3.1. Capital Asset Pricing Models The Markowitz mean–variance optimization framework is from the perspective of individual investor conditional on given expected excess re- turns and measure of risk of securities under con- sideration. The Capital Asset Pricing Model (CAPM) developed by Sharpe (1964) and Lintner (1965) asks what values of these mean returns will be required to clear the demand and supply if markets are efficient, all investors have identical information, and investors maximize the expected return and minimize volatility. An investor maximizing the expected return and minimizing risk will choose portfolio weights for which the ratio of the marginal contribution to portfolio expected return to the marginal contribu- tion to risk will be equal. In equilibrium, expected excess returns are assumed to be the same across investors. Therefore, suppose there exists a risk- free rate of interest, R f , and let Z i ¼ R i R f be the excess return of the ith asset over the risk-free rate (R f ) then the expected excess return for the ith asset in equilibrium is equal to E[Z i ] ¼ b im E[Z m ], (19:14) and b im ¼ Cov(Z i , Z m ) Var(Z m ) , (19:15) where Z m is the excess return on the market port- folio of assets, Z m ¼ R m R f , with R m being the return on the market portfolio. In the absence of a risk-free asset, Black (1971) derived a more general version of the CAPM. In Variance Mean Rf Figure 19.1. Mean–Variance frontier with risk-free asset MEAN VARIANCE PORTFOLIO ALLOCATION 459 the Black version, the expected return of asset i in equilibrium is equal to E[R i ] ¼ E[R om ] þ b im {E[R m ] À E[R om ]}, (19:16) and b im ¼ Cov(R i , R m ) Var(R m ) , (19:17) where R om is the return on the zero-beta portfolio associated with m. The zero-beta portfolio is de- scribed as the portfolio that has the minimum vari- ance among all portfolios that are uncorrelated with m. Closely related to the concept of trade-off be- tween risk and expected return is the quantification of this trade-off. The CAPM or zero-beta CAPM provides a framework to quantify this relationship. The CAPM implies that the expected return of an asset must be linearly related to the covariance of its return with the return of the market portfolio and the market portfolio of risky assets is a mean–vari- ance efficient portfolio. Therefore, studies of market efficiency have been cast in the form of testing the Sharpe–Lintner CAPM and the zero-beta CAPM. Under the assumption that returns are independ- ently, identically (IID) multivariate normally dis- tributed, empirical tests of the Sharpe–Lintner CAPM have focused on the implication of Equation (19.14) that the regression of excess return of the ith asset at time t, Z it ¼ R it R ft on the market excess return at time t, Z mt ¼ R mt R ft , has intercept equal to zero. In other words for the regression model Z it ¼ c im þ b im Z mt þ « it , i¼1, , N, t¼1, , T: (19:18) The null hypothesis of market portfolio being mean–variance efficient is: H 0 : c 1m ¼ c 2m ¼ ¼ c Nm ¼ 0: (19:19) Empirical tests of Black (1971) version of the CAPM model note that Equation (19.15) can be rewritten as E[R i ] ¼ a im þ b im E[R m ], a im ¼ E[R om ](1 À b im ) 8i : (19:20) That is, the Black model restricts the asset-specific intercept of the (inflation adjusted) real-return market model to be equal to the expected zero- beta portfolio return times one minus the asset’s beta. Therefore, under the assumption that the real- return of N assets at time t, R t ¼ (R it , , R Nt ) 0 is IID (independently identically distributed) multi- variate normal, the implication of the Black model is that the intercepts of the regression models R it ¼ a im þ b im R mt þ « it , i¼1, , N, t¼1, , T, (19:21) are equal to a im ¼ (1 À b im )g, (19:22) where the constant g denotes the expected return of zero-beta portfolio. 19.3.2. Arbitrage Pricing Theory Although CAPM model has been the major frame- work for analyzing the cross-sectional variation in expected asset returns for many years, Gibbons (1982) could not find empirical support for the substantive content of the CAPM using stock returns from 1926 to 1975. His study was criti- cized by a number of authors from both the statistical methodological point of view and the empirical difficulty of estimating the unknown zero beta return (e.g. Britten-Jones, 1999; Camp- bell et al., 1997; Gibbons et al., 1989; Shanken, 1985; Stambaugh, 1982; Zhou, 1991). Ross (1977) notes that no correct and unambiguous test can be constructed because of our inability to ob- serve the exact composition of the true market portfolio. Using arbitrage arguments, Ross (1977) proposes the Arbitrage Pricing Theory (APT) as a testable alternative. The advantage of the APT is that it allows for multiple risk factors. It also does not require the identification of the market port- folio. Under the competitive market the APT assumes that the expected returns are functions of an un- known number of unspecified factors, say K(K < N): 460 ENCYCLOPEDIA OF FINANCE R i ¼ E i þ b i1 d 1t þ þ b iK d Kt þ « it , i¼1, , N, t¼1, , T, (19:23) where R it is the return on asset i at time t, E i is its expected return, b ik are the factor loadings, d kt are independently distributed zero mean common factors and the « it are zero mean asset-specific disturbances, assumed to be uncorrelated with the d kt . As an approximation for expected return, the APT is impossible to reject because the number of factors, K, is unknown. One can always intro- duce additional factors to satisfy Equation (19.23). Under the additional assumption that market port- folios are well diversified and that factors are per- vasive, Connor (1984) shows that it is possible to have exact factor pricing. Dybvig (1985) and Grin- blatt and Titman (1987), relying on the concept of ‘‘local mean–variance efficiency’’, show that given a reasonable specification of the parameters of an economy, theoretical deviations from exact factor pricing are likely to be negligible. Thus, the factor portfolios estimated by the maximum likelihood factor analysis are locally efficient if and only if the APT holds (Roll and Ross, 1980, Dybvig and Ross, 1985). 19.3.3. Intertemporal Capital Asset Pricing Model (ICAPM) The multifactor pricing models can alternatively be derived from an intertemporal equilibrium argu- ment. The CAPM models are static models. They treat asset prices as being determined by the port- folio choices of investors who have preferences defined over wealth after one period. Implicitly, these models assume that investors consume all their wealth after one period. In the real world, investors consider many periods in making their portfolio decisions. Under the assumption that consumers maximize the expectation of a time- separable utility function and use financial assets to transfer wealth between different periods and states of the world and relying on the argument that consumers’ demand is matched by the exogen- ous supply, Merton (1973) shows that the efficient portfolio is a combination of one of mean– variance efficient portfolio with a hedging portfolio that reflects uncertainty about future consumption- investment state. Therefore, in Merton Intertem- poral Capital Asset Pricing Model (ICAPM) it usually lets market portfolio serve as one factor and state variables serve as additional factors. The CAPM implies that investors hold a mean– variance portfolio that is a tangency point between the straight line going through the risk-free return to the minimum-variance portfolios without risk- free asset in the mean-standard deviation space. Fama (1996) shows that similar results hold in multifactor efficient portfolios of ICAPM. 19.4. Estimation Errors and Portfolio Choice The use of mean variance analysis in portfolio selection requires the knowledge of means, vari- ances, and covariances of returns of all securities under consideration. However, they are unknown. Treating their estimates as if they were true param- eters can lead to suboptimal portfolio choices (e.g. Frankfurther et al., 1971; Klein and Bawa, 1976; Jorion, 1986) have conducted experiments to show that because of the sampling error, portfolios selected according to the Markowitz criterion are no more efficient than an equally weighted port- folio. Chopra (1991), Michaud (1989), and others have also shown that mean–variance optimization tends to magnify the errors associated with the estimates. Chopra and Zemba (1993) have examined the relative impact of estimation errors in means, vari- ances, and covariances on the portfolio choice by a measure of percentage cash equivalent loss (CEL). For a typical portfolio allocation of large U.S. pension funds, the effects of CEL for errors in means are about 11 times as that of errors in variances and over 20 times as that of errors in covariances. The sensitivity of mean–variance effi- cient portfolios to changes in the means of individ- ual assets was also investigated by Best and Grauer (1991) using a quadratic programming approach. MEAN VARIANCE PORTFOLIO ALLOCATION 461 The main argument of these studies appears to be that in constructing an optimal portfolio, good esti- mates of expected returns are more important than good estimates of risk (covariance matrix). How- ever, this contention is challenged by De Santis et al. (2003). They construct an example showing the estimates of Value at Risk (VaR), identified as the amount of capital that would be expected to be lost at least once in 100 months, using a $100 million portfolio invested in 18 developed equity markets to the sensitivity of different estimates of covariance matrix. Two different estimates of the covariance matrix of 18 developed equity markets are used – estimates using equally weighted 10 years of data and estimates giving more weights to more recent observations. They show that changes in estimated VaR can be between 7 and 21 percent. The main features of financial data that should be taken into account in estimation as summarized by De Santis et al. (2003) are: (i) Volatilities and correlations vary over time. (ii) Given the time-varying nature of second mo- ments, it is preferable to use data sampled at high frequency over a given period of time, rather than data sampled at low frequency over a longer period of time. (iii) When working with data at relatively high frequencies, such as daily data, it is import- ant to take into account the potential for autocorrelations in returns. (iv) Daily returns appear to be generated by a distribution with heavier tails than the nor- mal distribution. A mixture of normal distri- butions appear to approximate the data- generating process well. (v) Bayesian statistical method can be a viable alternative to classical sampling approach in estimation (e.g. Jorion, 1986). REFERENCES Best, M.J. and Grauer, R.R. (1991). ‘‘On the sensitivity of mean v ariance efficient portfolios to changes in asset means: some analytical and computational re- sults.’’ The Review of Financial Studies, 4(2): 315–342. Black, F. (1971). ‘‘Capital market equilibrium with restricted borrowing.’’ Journal of Business, 45: 444–454. Britten-Jones, M (1999). ‘‘The sampling error in esti- mates of mean efficient portfolio weight.’’ The Jour- nal of Finance, 54(2): 655–671. Campbell, J.Y., Lo, A.W., and MacKinley, A.C. (1997). The Econometrics of Financial Markets. Princeton, NJ: Princeton University Press. Chopra, Vijay K. (1991). ‘‘Mean variance revisited: near optimal portfolios and sensitivity to input vari- ations.’’ Russell Research Commentary. Chopra, V.K. and Ziemba, W.T. (1993). ‘‘The effect of errors in mean, variances, and covariances on opti- mal portfolio choice.’’ Journal of Portfolio Manage- ment, Winter, 6–11. Connor, G. (1984). ‘‘A unified beta pricing theory.’’ Journal of Economic Theory, 34: 13–31. De Santis, G., Litterman, B., Vesval, A., and Winkel- mann, K. (2003). ‘‘Covariance Matrix Estimation,’’ in Modern Investment Management, B. Litterman and the Quantitative Resources Group, Goldman Sachs Asset Management (ed.) Hoboken, NJ: Wiley. Dybvig, P.H. (1985). ‘‘An explicit bound on individual assets’ deviation from APT pricing in a finite eco- nomy.’’ Journal of Financial Economics, 12: 483–496. Dybvig, P.H. and Ross, S.A. (1985). ‘‘Yes, the APT is testable.’’ Journal of Fiance, 40: 1173–1183. Fama, E.F. (1996). ‘‘Multifactor portfolio efficiency and multifactor asset pricing.’’ Journal of Financial and Quantitative Analysis, 31(4): 441–465. Frankfurter, G.M., Phillips, H.E., and Seagle, J.P. (1971). ‘‘Portfolio selection : the effects of uncertain means, variances, and covariances.’’ Journal of Fi- nancial and Quantitative Analysis, 6(5): 1251–1262. Gibbons, M.R. (1982). ‘‘Multivariate tests of financial models: a new approach.’’ Journal of Financial Eco- nomics, 10: 3–27. Gibbons, M.R., Ross, S.A., and Shanken, J. (1989). ‘‘A test of efficiency of a given portfolio.’’ Econometrica, 57: 1121–4152. Grinblatt, M. and Titman, S. (1987). ‘‘The relation between mean-variance efficiency and arbitrage pri- cing.’’ Journal of Business, 60(1): 97–112. Jorion, P. (1986). ‘‘Bayes-Stein estimation for portfolio analysis.’’ Journal of Financial and Quantitative An- alysis, 21(3): 279–292. Klein, R.W. and Bawa,V.S. (1976). ‘‘The effect of esti- mation risk on optimal portfolio choice.’’ Journal of Financial Economics, 3: 215–231. 462 ENCYCLOPEDIA OF FINANCE Lintner, J. (1965). ‘‘The valuation of risk assets and the selection of risky investments in stock portfolios and capital budgets.’’ Review of Economics and Statistics, 47(1): 13–37. Litterman, B. and the Quantitative Resources Group, Goldman Sachs Asset Management (2003). Modern Investment Management. Hoboken, NJ: John Wiley. Markowitz, H.M. (1952). ‘‘Portfolio selection.’’ The Journal of Finance, 7: 77–91. Markowitz, H.M. (1959). Portfolio Selection: Efficient Diversification of Investments, New York: John Wiley . Marschak, J. (1938). ‘‘Money and the theory of assets.’’ Econometrica, 6: 311–325. Merton, R.C. (1973). ‘‘An intertemporal capital asset pricing model.’’ Econometrica, 41: 867–887. Michaud, R.O. (1989). ‘‘The Markowitz optimization enigma: Is ‘optimized’ optimal ?’’ Financial Analysis Journal, 45: 31–42. Roll, R. and Ross, S.A. (1980) . ‘‘An empirical investi- gation of the arbitrage pricing theory.’’ Journal of Finance, 33: 1073–1103. Ross, R. (1977). ‘‘A critique of the asset pricing theory’ s tests, part 1: One past and potential testability of the theory.’’ Journal of Financial Economics, 4: 129–176. Stambaugh, R.F. (1982). ‘‘ On the exclusion of assets from tests of the two parameter model.’’ Journal of Financial Economics, 10: 235–268. Shanken, J. (1982). ‘‘The arbitrage pricing theory: Is it testable?’’ Journal of Finance, 37(5): 1129–1140. Shanken, J. (1985). ‘‘Multivariate tests of the zero- beta.’’ Journal of Financial Economics, 14: 327–348. Sharpe, W.F. (1964). ‘‘Capital asset prices: a theory of market equilibrium under conditions of risk.’’ Jour- nal of Finance, 19: 425–442. Von Neumann, J. and Morgenstern, O. (1947). Theory of Games and Economic Behavior, 2nd edn. Prince- ton: Princeton University Press. Zhou, G. (1991). ‘‘Small samples tests of portfolio effi- ciency.’’ Journal of Financial Economics, 30: 165–191. MEAN VARIANCE PORTFOLIO ALLOCATION 463 Chapter 20 ONLINE TRADING CHANG-TSEH HSIEH, University of Southern Mississippi, USA Abstract The proliferation of the Internet has led to the rapid growth of online brokerage. As the Internet now allows individual investors access to information pre- viously available only to institutional investors, indi- vidual investors are profiting in the financial markets through online trading schemes. Rock-bottom fees charged by the online brokers and the changing atti- tude toward risk of the Internet-literate generation prompt the practitioners to question the validity of the traditional valuation models and statistics-based portfolio formulation strategies. These tactics also induce more dramatic changes in the financial mar- kets. Online trading, however, does involve a high degree of risk, and can cause a profitable portfolio to sour in a matter of minutes. This paper addresses the major challenges of trading stocks on the Internet, and recommends a decision support system for online traders to minimize the potential of risks. Keywords: Internet; day trading center; web-based brokers; online trading; valuation models; decision support systems; risks management; portfolio for- mulation strategies; financial market; stock invest- ment; institutional investors 20.1. Introduction In the past decade, one of the most phenomenal changes in investment markets is the burgeoning number of online brokers, and its subset, the so- called day-trading centers. Instead of doing busi- ness using the old style face-to-face approach, or over the phone with stockbroker, investors have been using the Web to explore a wealth of free information and have been making investment de- cisions with a new fleet of Internet-based brokers. Concepts of online trading have been around for quite some time. Before the proliferation of the Internet, however, online trading was primarily used as a vehicle for trading by institutional inves- tors. With the help of the Internet, individual investors are now able to access the stock markets in ways similar to those of the major players, the institutional investors (Barnett, 1999b; Smith, 1999a). The direct use of the Internet to trade stocks also raises doubt among investors about the validity of the traditional stock valuation models as well as portfolio formulation strategies. Inspired by the successful story of E * Trade, the pioneering Internet-based broker, many Web- based brokers have joined the throng that has forced traditional full-service firms to respond with bigger changes. Although, by the end of 1998, online brokers still controlled only $400 bil- lion of assets in customer accounts as compared with $3,200 billion managed by full-service brokers, transactions done through online traders now rep- resent more than 15 percent of all equity trades, a two-fold increase in just two years. And the online brokerage industry has doubled customer assets to more than $420 billion, and doubled accounts man- aged to 7.3 million by early 1999. The Internet has revolutionized the way in which consumers perform research and participate in the buying and selling of securities. As of Janu- ary 2003, there are an estimated 33 million U.S. consumer online trading accounts that control roughly $1.6 trillion in customer assets (Mintel International Group, 2002). The convenience of online trading has introduced millions of new con- sumers to the possibilities of online money man- agement. At the same time, the Internet and wireless devices have transformed the way in which capital markets operate and have made it possible for individual investors to have direct ac- cess to a variety of different markets, and to tools that were at one time reserved only for the invest- ment professional. 20.2. The Issues The proliferation of online trading sites has created major changes in the ways stocks are traded. Trad- itionally, an investor who wants to purchase a stock has to go through a broker. The broker will send a buy order to a specialist on the exchange floor, if the stock is listed on the NYSE. The specialist then looks for sellers on the trading floor or in his electronic order book. If the special- ist finds enough sellers to match his offer price, the specialist completes the transaction. Otherwise, the specialist may purchase at a higher price, with customer permission, or sell the stock to the cus- tomer out of his own inventory. If the stock is listed on the NASDAQ, the broker consults a trading screen that lists offers from the market makers for the said stock. The broker then picks up the market maker with the best price to complete the transaction. On the other hand, for buying stock online, the broker such as E * Trade simply collects order information, and completes the transaction through the electronic communication network (ECN). For traditional brokerage services, the broker usually charges hefty fees. For example, Morgan Stanley Dean Witter charges $40 per trade for customers with at least $100,000 in their accounts and if they make at least 56 trades per year. Merrill Lynch charges $56 per trade for a $100,000 account, with 27 trades per year. Typically, fees for a single trade at the full-service brokerage can be anywhere from $100 to $1000 depending upon the services involved. Charles Schwab, however, charges $29.95 per trade up to 1000 shares, and the champion of the online trader, E * Trade, charges merely $14.95 per market-order trade up to 5000 shares. Alternatively, the investor can choose unlimited number of trades and access to exclusive research and advice for a yearly fee (Thornton, 2000). The reduced cost offered by online trading has encouraged investors to increase the frequency of trading. Since the fee paid to complete a transac- tion through traditional brokerage is enough to cover fees of many trades charged online, the investor can afford to ride the market wave to try and realize a windfall caused by the price fluctu- ation on a daily basis. Perhaps, this helps explain why in two short years, Island, Instinet, and seven other ECNs, now control a whopping 21.6 percent of NASDAQ shares and nearly a third of the trades and are seeking to expand their operations to include NYSE company shares (Vogelstein, 1999a; Reardon, 2000). Although investors of all sizes could use online brokers, the most noteworthy change in financial markets is the increasing number of individual investors. These are the new breed of investors armed with the knowledge of information technol- ogy and a very different attitude toward risk in the investment market place (Pethokoukis, 1999). Their changing attitudes have contributed to sev- eral major changes in stock market strategies (Becker, 1998; Barnett, 1999a; Gimein, 1999; Pethokoukis, 1999; Vogelstein, 1999b; Sharma, 2000). 1. Webstock frenzies. Although day traders rep- resent a small percentage of all active traders on a daily market, the industry makes up about 15 percent of NASDAQ’s daily volume (Smith, 1999b). The aggressive trading be- havior of day traders, fueled by margin loans supplied by day-trading centers, is one of the ONLINE TRADING 465 driving forces behind the runaway price of many Internet-related stocks. Since the begin- ning of 1999, for example, Yahoo stock rose $40 in one day. eBay shares fell $30. Broad- cast.com gained $60 a share, and then lost $75 two days later. Webstocks as a whole gained 55 percent in the first days of trading in 1999, then a free-fall started in the early summer. Since April 1999, American Online stock price has dropped almost 67 percent. And the Goldman Sachs Internet Index currently stands nearly 43 percent below its all-time high in April. By Spring 2000, many of the tech stocks have recorded more than 80 per- cent of share price corrections. Some of these corrections actually happened in just a matter of few days (Cooper, 2001). These stocks have taught the online=day traders the real meaning of ‘‘volatility’’ (McLean, 1999). 2. Changing goals of investment. The easy money mentality has led to new goals for formulating investment portfolios. Traditional portfolio models have been based on a mean-variance modeling structure, and for years numerous variations of such models have filled the aca- demic journals. Today, however, investment professionals have been forced to abandon the investment strategies developed by aca- demics, focusing instead on strategies that achieve instant profits. As Net stocks became the horsepower to help pump the DJ index near to the 11,000 mark by early 2000, inves- tors have renounced traditional buy-and-hold strategies and have switched to holding stocks for minutes at a time. In addition, the chan- ging investment goals are partially caused by the change in the valuation system. 3. Different valuation models. Many of today’s hot stocks are not worth anywhere near where they trade For example, Netstock Amazon.com, one of the hottest, sold just $610 million in books and CDs in 1999 and is yet to make its first penny. However, its $20 billion market value makes it worth $5 billion more than Sears. In fact, with the exception of Yahoo, all Webstocks have infinite P=E ratios. This anomaly prompts practitioners to ques- tion traditional models of valuing the stock, and forecasters everywhere concede that old models are suspect (Weber, 1999). Online trading also engenders some changes in the traditional investing scenario. First, the wide variation in investor knowledge of the stock mar- ket and of trading is crucial in the online setting. The costs to investors of bad judgment are likely to be borne by new entrants to the world of individ- ual investing; these investors are pleased with the simplicity of the interactive user-friendly formats of e-brokerages, but are seldom proficient in the mechanisms and arrangements beyond the inter- face. Experienced investors can better identify the benefits and costs of choosing specific e-brokerages. Second, the frequency of online investor trading deserves special attention. Many market analysts suggest that the growing U.S. economy and the low commissions charged by e-brokerages influ- ence investors to trade more often. For example, an average Merrill Lynch (full-service broker) cus- tomer makes four to five trades per year while the core investors in an e-brokerage such as E * Trade make an average of 5.4 trades per quarter. Fre- quent trading is generally contrary to the recom- mendations of financial theory. Ultimately, it is possible for an e-brokerage to allow investors to trade frequently at very low or even zero costs per trade while earning large profits on the fraction of the increasingly large bid–ask spread that is pushed back by the market maker. At the same time, the investor may be unaware of the indirect costs in- curred with each trade. Third, the evolution of electronic trading may increase market fragmentation in the short run. E-brokerages may increasingly channel trades away from exchanges and toward market makers to compensate for lost revenue resulting from low direct commissions. Market fragmentation may have a negative impact on prices, increasing the bid–ask spread and potential for arbitrage oppor- 466 ENCYCLOPEDIA OF FINANCE [...]... if below, stocks are overvalued For example, over the next 12 months, the consensus earnings forecast of industry analysts for the S&P 500 is $52.78 per share This is a 19.1 percent increase over the latest available four-quarter trailing sum of earnings The fair value of the S&P 500 Index was 1 011. 11, derived as the 12-month forward earnings divided by the 10-year Treasury bond yield, assuming at 5.22... example, the long-term average of P=E is 15 Therefore, at its current ratio of over 33, the stock price is overvalued 3 Cornell model This model discounts future cash flows and compares that to the current market level The discount factor is a combination of the risk-free interest rate and a risk premium to compensate for the greater volatility of stocks When the value of the discounted cash flows is... deliver the bullet points of their business 468 ENCYCLOPEDIA OF FINANCE models to institutions at www.eoverview.com, Net Roadshow’s Web site These services may not bring individual investors up to par with institutional investors However, they are now able to make investment decisions based on information with similar quality and currency as the big investors The saved costs of trading through online... bird’s eye view of the activity on the NYSE floor One very useful source of information is from StarMine Investors can use this Web site to identify experts worth listening to, then use Multex to get the full detail of the relevant information (Mullaney, 2001) At Bestcalls.com, visitors can examine conference call information, and in the near future, individuals will be able to see corporate officers deliver... 2000) Trading online, however, involves an unusually high degree of risks Since most online traders are looking for profits in a relatively short period of time, their investing targets are primarily in techconcentrated NASDAQ markets where volatility is the rule (McNamee, 2000; Opiela, 2000) Yet, many online investors forget that online or off, disciplines for managing portfolio to minimize risk are still... Journal of Financial Economics, 18: 373–399 Campbell, J (1996) ‘‘Understanding risk and return.’’ Journal of Political Economy, 104: 298–345 Campbell, J and Shiller, R (1991) ‘‘Yield spreads and interest rate movements: a bird’s eye view.’’ Review of Economic Studies, 58: 495–514 Cooper, J (2001) ‘‘Hey, chicken littles, the sky isn’t falling.’’ Business Week, 12: 43 Farrell, C (2000) ‘‘Online or off,... Individual investors can enter their projected bond yield and estimated growth in corporate earnings to check the valuation of the stocks at Yardeni’s Web site 2 Campbell–Shiller model The valuation model developed by John Y Campbell of Harvard 467 University and Robert J Shiller of Yale University looks at price earnings ratios over time to determine a long-term market average (Campbell, 1987, 1996;... and Chung, 2000; Farrell, 2000) 20.4 Conclusion Online trading provides convenience, encourages increased investor participation, and leads to lower upfront costs In the long run, these will likely reflect increased market efficiency as well In the short run, however, there are a number of issues related to transparency, investors’ misplaced trust, and poorly aligned incentives between e-brokerages... which may impede true market efficiency For efficiency to move beyond the user interface and into the trading process, individual investors need a transparent window to observe the actual flow of orders, the time of execution, and the commission structure at various points in the trading process In this regard, institutional rules, regulations, and monitoring functions play a significant role in promoting... similar quality and currency as the big investors The saved costs of trading through online brokers might provide individual investors an edge over their big counterparts Since the individual investors’ activity usually involves only small volumes of a given stock, their decisions will not likely cause a great fluctuation in the price This will enable them to ride the market movement smoothly Nevertheless, . investi- gation of the arbitrage pricing theory.’’ Journal of Finance, 33: 1073 110 3. 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