The Performance of the Three-Beta Model SUBMITTED IN

The Performance of the Three-Beta Model in the Period 1963-1997 by Serkan Arslanalp B.S., Electrical Engineering and Computer Science (1998) B.S., Economics (1998) Massachusetts Institute of Technology SUBMITTED TO THE DEPARTMENT OF ELECTRICAL ENGINEERING AND COMPUTER SCIENCE IN PARTIAL FULFILLMENT OF THE REQUIREMENTS FOR THE DEGREE OF MASTER OF ENGINEERING IN ELECTRICAL ENGINEERING AND COMPUTER SCIENCE AT THE MASSACHUSETTS INSTITUTE OF TECHNOLOGY JUNE 1999 @ 1999 Serkan Arslanalp All rights reserved The author hereby grants to MIT permission to reproduce and to distribute publicly paper and electronic copies of this thesis document in whole or in part Signature of Author ............................................. Department of Electrical Engineering and Comput'er Science May 21, 1999 .......................... Roy E. Welsch Prof sor of Statistics and Management Science -Thesis Supervisor Certified by........................... Accepted by.......................................... MASSACHUSETTS INSTI OF TECHNOLO JUL LIB S ........... '> ..- . . Arthur C. Smith Chairman, Department Committee on Graduate Theses The Performance of the Three-Beta Model in the Period 1963-1997 by Serkan Arslanalp Submitted to the Department of Electrical Engineering and Computer Science on May 21, 1999 in partial fulfillment of the requirements for the degree of Master of Engineering in Electrical Engineering and Computer Science ABSTRACT This thesis investigates the performance of the Three-Beta model in the period from January 1963 to December 1997. For this study, 10 tests were carried out. For each test, 10 assets were chosen randomly from a group of S&P500 stocks that have been continuously listed over the entire sample period. Each year, a set of three betas was calculated for every asset by using its daily returns. Using these betas as our measure of risk, an optimal portfolio was selected and then tested for the following year. The same tests were also conducted with the Sharpe model for comparison. In 7 out of the 10 tests, the Three-Beta model performed better than the Sharpe model. On average, the Three-Beta model produced 9.6% more profits than the Sharpe model during the period from 1963 to 1997. Thesis Supervisor: Roy E. Welsch Title: Professor of Statistics and Management Science 2 Acknowledgments First of all I wish to thank my supervisor Professor Roy Welsch for showing and communicating so much interest in my work. I would also like to express my gratitude to my family for their support throughout the years. Thanks to the Sloan Trading Room Research Laboratory for providing the CRSP Database for this research. Finally, I would like to thank everyone I met at MIT for giving me the opportunity to live such an enriching experience. Special thanks to Jessica Lin and Quinn Goldstein for the numerous helpful discussions on this project. All errors are my own responsibility. 3 List of Symbols p R r T t The expectation operator. Expectations are also often denoted with an overbar The base for natural logarithms and the exponential function. e ~ 2.71828. The dividend vector. The identity matrix. As a subscript it usually denotes the i* asset. As a subscript it usually denotes the jthaSSet. As a subscript it usually denotes the t investor. As a subscript or a superscript it usually denotes the market portfolio. The number of assets. The cumulative normal distribution function. The standard normal distribution function. The price vector. The riskless return (the interest rate plus one). The interest rate. r = R - 1. Some fixed number of days, often the number of business days in a year. Current day. W Wealth. w A vector of portfolio weights. wi is the fraction of the wealth in the iti* asset. The random return on portfolio w. The random returns on the assets. The expected returns on the assets. The actual returns on the assets. zti is the return on day t for asset i. A vector or a matrix whose elements are 0. A vector whose elements are 1. As a vector inequality each element of the left-hand vector is greater than or equal to the corresponding element of the right-hand vector, and at least one element is strictly greater. The expected instantaneous rate of return on assets. = Cov(z,zm). The beta of assets. The residual portion of the assets' returns. st,i is the return on day t for asset i. A correlation coefficient. The variance-covariance matrix of returns. A standard deviation, usually of the return on an asset. E E d I I k M N N(.) n(.) z 0 1 ; cc p F. p G Public information. Private information of investor k. 4 . Contents 1. INTRODUCTION......................................................-------..................................................6 RESEARCH OBJECTIVES ....................................................... 1.1. 6 ..................... 1.2. D ATA ........................................................----------------------------------......................................... 1.3. 2. ORGANIZATION OF THE THESIS ................................................... BACKGROUND ....................................................--------------------------------.............................. 6 7 8 8 2.1. THE RETURN OF AN ASSET ........................................................ 11 2.2. THE RISK OF AN ASSET.............................................................................. ...... 12 2.3. THE SHARPE MODEL.......................................................... 13 . ............................. 2.4. THE THREE-B ETA M ODEL ..................................................... 3. PORTFOLIO OPTIMIZATION....................................................- -........ 15 ---------------------------............................... - .. 3.1. INTRODUCTION .......................................................................... 3.2. THE SHARPE M ODEL......................................................... 3.3. THE THREE-BETA M ODEL ....................................................--................. 15 17 17 4. RESULTS ........................................-............----------------............................................... 18 5. CONCLUSION .....................................................--.......--.-----------------............................... 20 A. MATLAB CODES .......................................................................... B. TABLES................................................................... 5 -------------------------------............................... 21 27 Chapter 1 Introduction A cornerstone of finance is portfolio optimization theory, which tries to maximize returns for a given level of risk. An important question on this matter is how we actually measure the risk of a portfolio. Although there are other ones, beta is a popular measure of risk that was introduced by William F. Sharpe[7] who received the Nobel prize for this work. However this model is based on an unrealistic assumption: the normality of the distribution of asset returns. In reality, asset returns tend to exhibit non-normalities. For example, measured over a long interval, the distribution of returns is generally skewed (non-symmetrical) [1]. Moreover, previous research shows that U.S. stock returns exhibit kurtosis (more returns in the extreme tails of the distribution) [2],[3],[4],[5]. The Three-Beta model attempts to account for these non-normalities. The Three-Beta model which was introduced by Abdoul Karim Sylla [9] in collaboration with Roy Welsch uses three betas instead of a single beta to measure risk. This model -at least in theory- is superior to the Sharpe (or single-beta) model because it allows for non-normality of the distribution of asset returns by allowing for different betas for different ranges of market returns. Based on the Three-Beta and the Sharpe model, we will choose different portfolios in an optimal portfolio selection framework and test which one produces better results. 1.1. Research Objectives The main objective for this thesis is to test the performance of the Three-Beta model and compare it with the performance of the Sharpe (Single-Beta) model. 6 1.2. Data The data used for this research are the daily returns of the S&P500 stocks. The time frame spanned is from January 1963 to December 1997. The source of the data is the database of CRSP (The Center for Research in Security Prices) which carries unique issue identifiers that track a continuous history of securities, providing a seamless time-series examination of the issue's history. Thanks to the Sloan Trading Room Research Laboratory this database is conveniently available for research purposes at http://risk.mit.edu:8080/web/. The statistical analysis of the data, regression analysis, plots and optimizations were made by version 5.2 of MatlabTM, a data analysis software written by Mathworks, Inc. 1.3. Organization Of The Thesis In Chapter 2, a general background on the subject is given. Risk and Return are defined for a single asset and for many assets in a portfolio context. The Sharpe model (or the Single-Beta) model will be introduced along with some of the difficulties associated with its normality assumption of the distribution of asset returns. Lastly, the Three-Beta model will be presented to allow for the nonnormalities discussed previously. In Chapter 3, we will set up the method of selecting the optimal portfolio with the Sharpe model and with the Three-Beta model. In Chapter 4, we will analyze the performance of the Three-Beta model against the Sharpe model and see which one produces better results. Finally, we will make a general conclusion of this work and discuss some new possibilities of further research. An appendix showing the test results in more detail and the Matlab codes that we used for the tests will be included. 7 Chapter 2 Background This chapter presents the basic concepts that need to be introduced for an understanding of optimal portfolio selection. 2.1. The Return of an Asset Let us denote the return of a financial asset over a period by It. Then I, is a random variable with the following formula. (2.1) * 1,= p,_I where p t 1 is the current price, p, is the price at the end of the period, and at is the dividend that is given out during the period. While the first variable is known, the latter two are uncertain. Given that we observe z, the actual returns of an asset, for T periods, the expected return of this asset is defined as follows. Expected Re turn = E[]= 1 = -z'1 (2.2) A random variable is characterized by the values that it can take and the probability of each value being realized. Therefore one would need to investigate the values that the return of an asset can take. However this would require information about all the different states of the world and how they would relate to the return of the asset in question. Even if one can come up with a tableau of all the different states of the world, it is still doubtful whether one can really know how each state would affect the return of this asset. Fortunately though, one can still gain valuable information about the return of an asset by looking at its distribution.Let us see this in an example. Figure 2.1 shows the distribution of the daily returns of IBM in 1993. 8 60. . The daily rtuns d IBM in 1993 .. . . 4 6 50- 40- 30- 20- / 10- 0 -6 -4 -W U Z Daily un1() 8 Figure 2.1 To a first approximation, one can say that the distribution of IBM's returns can be described as a normal distribution. (which is plotted as a thin line in the figure). Although this might look like the end of the story, further investigation of the same data shows that it is not quite so. Let us look at the same data on a normal probability plot. If the returns of IBM were really distributed normally, then this plot would be linear. However as one can see from Figure 2.2, the returns of IBM deviate from the linear line at the two tails. Nomn rtbaility Plot d IBM 0.999. / 0.9970.99 0.98 - 4. + 0.95 0.90 0.75 - - 0.50 0.250.10 0.05 0.02 0.01 0.003 + UA" i -0.06 -0.04 -0.02 0 0.02 Feta Figure 2.2 9 0.04 0.06 0.08 In general, previous research has shown that, in fact, many asset returns have distributions that deviate from normality [2],[3],[4],[5]. A measure of deviation from normality is skewness. Skewness is a measure of non-symmetry in a distribution. Symmetrical distributions have a skewness value of zero. A distribution with negative skewness has more observations in the left tail (left of the peak or mode) and a distribution with positive skewness has more observations in the right tail. The skewness, or the normalized third moment, of an asset's return i with mean Y and variance a, is defined by S[(] E - 3) 3 (2.4) Another measure of deviation from normality is excess kurtosis. Kurtosis is a measure of the extent to which observed data fall near the center of a distribution or in the tails. A kurtosis value less that that of a standard, normal distribution indicates a distribution with a fat midrange on either side of the mean and a low peak - a platykurtotic distribution. A kurtosis value greater than that of a normal distribution indicates a high peak, a thin midrange and fat tails. The latter, a leptokurtotic distribution, is common in observed price, rate and return time series data. Asset returns are likely to have a leptokurtotic distribution if they are subject to frequent price jumps. The kurtosis, or normalized fourth moment is defined by K[4] EL 4 (2.5) The normal distribution has skewness equal to zero, as do all other symmetric distributions. The normal distribution has kurtosis equal 3, butfat-tailed distributions with extra probability mass in the tail areas have higher or even infinite kurtosis. Sample estimates of skewness for daily US stock returns tend to be negative for stock indexes but close to zero or positive for individual stocks. Sample estimates of excess kurtosis for daily US stock returns are large and positive for both indexes and individual stocks, indicating that returns have more mass in the tail areas than would be predicted by a normal distribution. However, most models (including the Sharpe model which we will discuss later in section 2.3) assume these non-normalities away. While this results in simpler mathematics (because the normal distribution has the property of being fully characterized by only two parameters; mean and standard deviation), it will also be misleading if these "non-normalities" actually have economic significance. 10 2.2. The Risk of An Asset The risk of holding an asset is associated with the possibility that the realized return will be less than the expected return. The cause of this problem is the failure of the asset price to materialize as expected. So, it becomes clear that the variability in prices affects the riskiness of the asset. Given this, it is natural that variance is a common measure of risk. Assuming that we can observe z, the actual returns of an asset, for T periods, the variance of an asset can be defined as follows. Risk = Var[i]= Z = zz - T T 2 z'11'z (2.5) It is also important to understand the sources of risk. Risk could be divided into two general categories. The risk that can potentially be eliminated by diversification is called unique risk.' Unique risk is the result of the fact that many of the perils that surround an individual company are specific to that company. But there is also some risk that you can not avoid however much you 2 diversify. This risk is generally called market risk. Market risk stems from the fact that there are other economy-wide perils which threaten all businesses. That is why stocks have a tendency to move together, and that is why investors are exposed to market uncertainties no matter how many stocks they hold. In Figure 2-3, we have computed the risk' of twenty stocks chosen randomly from the S&P500 stocks. In this picture, one can see how risk can be divided into these two parts - unique risk and market risk. For only a single stock unique risk is very important, but for a portfolio of ten or more stocks diversification has done the bulk of its work. For a reasonably well-diversified portfolio, only market risk matters. Therefore, the predominant source of uncertainty for a diversified investor is that the market will rise or plummet, carrying the investor's portfolio with it. 0.5 0.45- 0.40.350.3 - 0.25- 0.2- 0.15- 00 2 4 6 8 10 12 14 16 18 20 he nubr ofasets in the prtfdio Figure 2.3 Unique risk is also called unsystematic risk, specific risk, or diversifiable risk. Market risk is also called systematic risk, or undiversifiablerisk. 3 Risk is measured as the standard deviation of the portfolio. 2 11 Having discussed the return and risk of a single asset let us now think about the risk and return of many assets in a portfolio context. A portfolio is a combination of assets. Therefore the return of a portfolio is the weighted average of the returns of the component assets. Given that the portfolio weights are denoted as w = (wI, w2 , ... , wN), then the expected return and risk of the portfolio can be defined as follows 2.3. Expected Re turn of a Portfolio = z, = w'Z (2.6) Risk of a Portfolio = (T = w'Ew (2.7) The Sharpe Model The Sharpe model hypothesizes a model where an asset's return moves with the return of the market. This model can be written as follows. Z = a + Z.0 + 6 (2.8) It is conventional to use the notation a(alpha) and P(beta) for the coefficients of this model. It is assumed that C's are uncorrelated with the market return and with each other. The expected value of this equation is E[2]=a+ZmP -1 (2.9) The value of P in this model can be calculated directly. We take the covariance of both sides of (2.8) with zmn. This produces = (2.10) 2 and hence p (2.11) im Finally let us calculate the variance of an asset based on the Sharpe model. = E[ ((Zm -m)3+ = E (Zm = 2 pn( '@ + ZZm - -2 12 ) (zm m) mp+ )} }pF'P + E[c's] The first term on the left hand side is the previously mentioned market risk. This risk is associated with the movement of the market. Market risk cannot be diversified away and exposure to market risk is measured by beta. The Three-Beta Model 2.5. The Sharpe model we have discussed in the previous part is a linear model with a beta (p) that is constant for the whole range of market returns. The underlying assumption here is the normality of the distribution of asset returns. The Three-Beta allows for non-normality by defining three different betas for different ranges of market returns. This model assumes that the market returns have two structural breaks(knots or thresholds) at zm~ and zm*. We chose these structural breaks to be at the tenth and the ninetieth percentile of the market return distribution. This gave us the following three intervals for the market returns. I1 {(m such that 1m_ I2 {(zm such that z (im such that Im ,3 zm} or Negative Tail < Im < z}I > z} or Middle Part or Positive Tail At the heart of this model, there is a belief that the asset-market relationship changes at the tails of the market return distribution. The following regression model captures this idea. It is useful to note that if p- and P* are not significantly different than 0, then this model reduces to the Sharpe model. Z=a+Zm0+Zm-- where _ Zm-z; 10 "m- "+ 0 if Zm el, otherwise Zm ifzm e13 otherwise 13 +zm+' +E (2.13) Finally, here is the expected return and the variance based on the Three-Beta model. S1+ZmI01 z X I E[l] I a t2 + z m2P2 t3 +zm2 2 =- a 2f'j a 2 + a7 ,p s 2 3 a 2 a3 = = 3 zmi c a - z +m E[Im Eli] ami =Var(im Eli) ay = E I; "m E 13 P +P* = m 13 + a2 P2 = P3 m Zm =a - z mP Var(C eI;) 14 ( 2 .14) _'m E 12 + C1 2 where a Zm E1I + m E1 , 2 (2.15) Chapter 3 Portfolio Optimization 3.1. Introduction Optimization is a process by which we determine the most favorable tradeoff between competing interests, given the constraints we face. Within the context of portfolio optimization, the competing interests are risk reduction and return enhancement. We use an optimizer to identify the asset weights that produce the lowest risk for various levels of expected return. The main tool for portfolio optimization is diversification. Diversification is an approach to investment management analyzed and popularized by Harry Markowitz [6]. It is summarized by the popular saying: "Don't put all your eggs in one basket." With diversification, risk can be reduced relative to the average return of a portfolio by distributing assets among a variety of asset classes, such as stocks, bonds, money market instruments, and physical commodities, as well as by diversifying within these categories and across international boundaries. Diversification usually reduces portfolio risk because the returns on various asset classes are not perfectly correlated. An efficient portfolio is a portfolio whose risk/return characteristics fall on the efficient frontier; i.e. at a given level of risk no portfolio has a higher expected return, and for a given expected return no portfolio has a lower level of risk. The efficient frontier is a continuum of portfolios that have the highest expected returns for their given levels of standard deviation plotted in dimensions of expected return and standard deviation. Figure 3.1 shows an efficient frontier. 15 15 + 10 + D 5 6 7 8 9 Fisk 10 11 12 13 Figure 3.1 Finally let us put these ideas in mathematical form. Let us first assume that there are no short sales. This implies that w > 0. An optimal portfolio with an expected return of z*w is the solution to following problem. Minimize Risk = a2W z* subject to: w 'z w'1= 1 w 0 16 = w'Tw (3.1) 3.2. The Sharpe Model Now that we have discussed general portfolio optimization, let us focus on portfolio optimization based on the Sharpe Model. For this we substitute (2.12) in (3.1). The optimal portfolio is now the solution to the following problem. Minimize Risk = r= w'(ca. 'P + )w(3.2) subject to: w'z= zI I w'1= w 3.3. 0 The Three-Beta Model Similarly for the Three-Beta model, we substitute (2.15) in (3.1). So the solution to the following problem gives the optimal portfolio based on this model. Minimize Risk = T2 subject to: w'z = z* w'1=1 w 0 17 = 1i ,p (3.3) + )w Chapter 4 Results In this study, 10 tests were carried out to test the performance of the Three-Beta model. For each test, 10 assets were chosen randomly from a group of S&P500 stocks that have been continuously listed over our entire sample period. Each year, a set of three betas were calculated for every asset by using its daily returns. Using these betas as our measure of risk, an optimal portfolio was selected and then tested for the following year. The same tests were also conducted with the Sharpe model for comparison. 4 At the end of 1997 (after 34 years) the Three-Beta seems to be the winner. The results are summarized in Figure 4.1. As one can see from this figure, in 7 out of the 10 tests, the Three-Beta model performed better than the Sharpe model. On average, the Three-Beta model produced 9.6% more profits than the Sharpe model during the period from 1963 to 1997. The nch betterdoes the3-Betaprfm? 30 25 15 10 C I .i 11.11 -10 1 2 3 4 5 6 Test 7 8 9 10 Figure 4.1 4 Appendix B contains tables of the betas and the weights calculated for each test and each model. 18 These results were predictable because the Three-Beta model could be seen as a generalization of the Sharpe model and approximates better the behavior of asset returns. We believe that the normality assumption is the cause of the failure of the Sharpe model. 19 Chapter 5 Conclusion The purpose of this thesis was to investigate the performance of the Three-Beta model. In order to do this, we presented the fundamentals of risk and return for a single asset and for many assets in a portfolio context. This led to our introduction of the Sharpe (single-beta) model. Then we introduced the Three-Beta model which allowed for non-normality of the distribution of asset returns. We finally showed how to choose optimal portfolios based on the Sharpe and the Three-Beta model and tested their performances for the period from January 1963 to December 1997. The results obtained showed that on average the Three-Beta model performs better than the Sharpe model. This is a result which encourages future investigations and studies. Below we list some possible ways this work can be extended. The first limitation of this work is its arbitrary choice of knots (thresholds) for estimating betas. A possible work could concentrate on finding a rigorous and systematic way to find the optimal choice of knots. Another way this work can be extended is by using hourly return data instead of daily return data. The hourly return data yields more data points which might yield to better estimates of beta. Finally, the performance of Three-Beta model can also be tested with foreign stocks in addition to domestic stocks. If one decided to follow this approach, the S&P500 would not be a reasonable proxy for the market anymore, so a new proxy for the international market would be required. 20 Appendix A Matlab Codes The following Matlabfunctionsfind two optimalportfolios every yearfrom 1963 to 1997 based on the Three-Beta model, and the Sharpe Model. Then each portfolio is testedfor the following year. Comments are in italics. function test index = available(63,10); i = 1; k = zeros(34,2); for year=63:96 [vall, val3, weight, WEIGHT]=invest(year,index); k(i,1)=vall; k(i,2)=val3; i=i+1; end ts=cumprod(k); x--ts(:,1); X=ts(:,2); cf; Plots the performanceof the Three-Beta model for the periodfrom 1963 to 1997 plot(X, 'g'); hold on; Plots the performance of the Sharpe model for the periodfrom 1963 to 1997 plot(x, 'r'); function Ivall, vaI3, weight, WEIGHT] = invest(year, index) astmkt = getdata(year,1O,index); market = astmkt(:,end); assets = astmkt(:,1:end-1); target = mean(mean(assets)); [RISK ROR WTS] = threebetafrontier(astmkt,[],target); Calculatedthe weights for the optimalportfolio based on the Three-Beta model. Calculatedthe weights for the optimal portfolio based on the Sharpe model [risk ror wts] = onebetafrontier(astmkt,[],target); weight = wts(1,:); WEIGHT = WTS(1,:); astmkt = getdata(yeart l,10, index); market = astmkt(:,end); assets = astmkt(:,1:end-1); actual-returns = cumprod(assets+1); actual-mktrtn = cumprod(market+ I); x = portror(actual_returns, weight); X = portror(actual-returns, WEIGHT); Returns how much return is made at the end of the year with an optimal portfolio based on the Sharpe model val I = x(end); Returns how much return is made at the end of the year with an optimal portfolio based on the Three-Beta model val3 = X(end); 21 function [beta, predicted] = onebeta(astmkt) market = astmkt(:,end); assets = astmkt(:,1:end-1); [T S]= size(assets); I = ones(T, 1); indep-var = [I market]; for i = 1:S dep-var = assets(:,i); beta(:,i) = regress(dep var, indep var); end predicted = indep-var*beta; Calculates and returns the beta of an asset function Ibeta,predictedl = threebeta(astmkt, pdown, p-up,option) Calculates and returns the three betas of an asset market = astmkt(:,end); assets = astmkt(:,1:end-1); [T S]= size(assets); I = ones(T, 1); knotdown = prctile(market,pdown* 100); dummydown = unifpdf(market,min(market),knot-down)*(knot-down-min(market)); marketdown = diag(market*dummydown'); I_down = diag(I*dummy-down'); marketdownc = diag(((market-knot-down)*dummydown)); knot-up = prctile(market,pup* 100); dummy-up = unifpdf(marketknot_up,max(market))*(max(market)-knot_up); market-up = diag(market*dummy-up'); Lup = diag(I*dummy-up'); markeL-upc = diag(((market-knot_up)*dummy-up')); if option == 0 indep-var = [I Iup ILdown market market-up market-down]; elseif option == I indep-yar = [I market marketdownc market-upc]; end for i = :S depvar = assets(:,i); beta(:,i) = regress(dep-var, indep-yar); end predicted = indep-yar*beta; 22 function Iriskror,wts] = onebetafrontier(astmkt,pts,target) [RISK,ROR,WTS] = ONEBETAFRONTIER(ASTMKTPTS, TARGET) returns the annualized standarddeviations, RISK, and annualized rates of return,ROR, that comprise the efficientfrontier of a given portfolio, plus the weights of each asset, WTS, for each point on the frontier. ASTMKT is an M-by-N matrix qf time series data where each column represents a single asset.(the last column is the market). PTS specifies the number of efficient frontierpoints to be calculated. By default, PTS = 10. TARGET specifies the desired rate of return. When enteringa targetrate of return, enter PTS as an empty matrix. RISK and ROR are PTS-by-J vectors, and WTS is a PTS-by-(number of assets) matrix. ONEBETAFRONTIER(ASTMKT) plots the efficient frontier without returning any data to the MA TLAB workspace. [RISK,ROR, WTS] = ONEBETAFRONTIER(ASTMKTPTS) returns the standarddeviations,rates of return, and weights of each point on the efficient frontier. [RISK,ROR, WTS] = ONEBETAFRONTIER(ASTMKT,[], TARGET) returns the efficient frontierdata associatedwith a specific rate of return on thefrontier. if nargin < 2 pts = 10; end ifpts <2 pts=2; end if isempty(pts) pts = 2; end [beta pred] = onebeta(astmkt); market = astmkt(:,end); assets = astmkt(:,1:end-1); ret = mean(assets); [m,n] = size(assets); [row,col]= size(ret); beta0 = beta(1,:); betal = beta(2,:); resid = assets-pred; H = var(market)*(betal'*betal) + diag(var(resid)); f= zeros(1,n); A(1,:)= ones(1,n); A(2,:)= -A(1,:); A(3:n+2,:) = -eye(n); b='[l;-l;f']; if nargin == 3 numtar = length(target(:)); for j = 1:numtar A(3+n,:) = ret; A(4+n,:) = -ret; b(3+n,1)= target(j); b(4+n,1) = -target(j); wts(j,1:n) = qp(H,fA,b)'; risk(j) = sqrt(portvar(assets,wts(j,1:n))); ror(j) = portror(ret,wts(j,1:n)); end w=wts; i = find(abs(w)<1e-6); w(i)= zeros(size(i)); wts = w; return end % Weights for global minimum wrl = qp(H,fA,b)'; % Find minimum rate of return on frontier rl = portror(ret,wrl); % Find maximum rate of return on frontier r2 = max(ret); r = rl:(r2-rl)/(pts-1):r2; % Generate rates of return on frontier % Index used by for loop k = 1; % Preallocate for loop matrix w = zeros(pts,n); my = zeros(max(size(r)),l); % Preallocate for loop matrix % calculate weights for each rate of return for i = r A(3+n,:) = ret; A(4+n,:) = -ret; b(3+n,1)= i; b(4+n,1)= -i; 23 w(k,:) = qp(H,fA,b)'; mv(k) = portvar(assets,w(k,:)); k =k+l; end % Compare difference in rates if abs(rl -r2) < 1e-6 % If difference is negligible, create one point v = portvar(assets,w); r= rl; else % Else calculate risk for each point v = sqrt(mv); end if nargout == 0 % Get hold status of figure held = ishold; % Plot efficient frontier and minimum risk point plot(v*252,r*25200,'r','linewidth',3,'erasemode','nornal') hold on plot(min(v)*252,max(r(find(v=min(v))))*25200,'bo','inewidth',3,'erase','none') xlabel('Risk: Annualized Standard Deviation'); ylabel('Return: Annualized Expected Return (%)'); if ~held % Turn hold off if necessary hold off end end % Return output if nargout ~= 0 risk = v*252; ror = (r*25200)'; i = find(abs(w)<Ie-6); w(i)= zeros(size(i)); wts = w; end 24 function Iriskror,wts] = threebetafrontier(astmkt,pts,target) [RISK,ROR, WTS] = THREEBETAFRONTIER(ASTMKTPTS, TARGET) returns the annualized standarddeviations, RISK, and annualized rates qf return, ROR, that comprise the efficient frontierof a given portfolio, plus the weights of each asset, WTS, for each point on thefrontier. ASTMKT is an M-by-N matrix of time series data where each column representsa single asset.(the last column is the market). PTS specifies the number of efficient frontierpoints to be calculated. By default, PTS = 10. TARGET specifies the desired rate of return. When entering a target rate of return, enter PTS as an empty matrix. RISK and ROR are PTS-by-1 vectors, and WTS is a PTS-by-(number of assets) matrix. THREEBETAFRONTIER(ASTMKT) plots the efficient frontierwithout returningany data to the MA TLAB workspace. [RISK,ROR, WTS] = THREEBETA FRONTIER(ASTMKT,PTS) returnsthe standarddeviations, rates of return, and weights of each point on the efficient frontier. [RISKROR, WTS] = THREEBETAFRONTIER(ASTMKT,[], TARGET) returns the efficient frontierdata associated with a specific rate of return on the frontier. if nargin < 2 pts = 10; end ifpts<2 pts = 2; end if isempty(pts) pts = 2; end kI =0.1; k2= 0.9; [BETA PRED]= threebeta(astmkt,kl,k2, 1); market = astmkt(:,end); knotI = prctile(market,kl* 100); knot2 = prctile(market,k2* 100); assets = astmkt(:,1:end-1); ret = mean(assets); [m,n] = size(assets); [row,col] = size(ret); ALPHA1 = BETA(1,:)- BETA(3,:)*knotl; ALPHA2 = BETA(1,:); ALPHA3 = BETA(1,:)- BETA(4,:)*knot2; BETA 1 = BETA(2,:)+ BETA(3,:); BETA2 = BETA(2,:); BETA3 = BETA(2,:)+ BETA(4,:); RESID = assets-PRED; p= I; r= 1; q= 1; for i = 1:m if market(i) <= knoti mktI(p,1) = market(i); resI(p,:) = RESID(i,:); p = p+1; elseif market(i) >= knot2 mkt3(r,1)= market(i); res3(r,:) = RESID(i,:); r =r+1; else mkt2(q,1)= market(i); res2(q,:) = RESID(i,:); q = q+1; end end var.astsI= var(mktl)*(BETA '*BETA 1)+diag(var(res1)); varasts2= var(mkt2)*(BETA2'*BETA2)+diag(var(res2)); varasts3= var(mkt3)*(BETA3'*BETA3)+diag(var(res3)); H = (var astsI+varasts2+var asts3)./3; f= zeros(1,n); A(1,:)= ones(1,n); A(2,:) -A(1,:); A(3:n+2,:)= -eye(n); b = [1;-1;f'; if nargin == 3 25 numtar = length(target(:)); for j = 1:numtar A(3+n,:)= ret; A(4+n,:) = -ret; b(3+n,1)= target(j); b(4+n,1) = -target(j); wts(j,1:n) = qp(H,fA,b)'; risk(j) = sqrt(portvar(assets,wts(j,l:n))); ror(j) = portror(ret,wts(j,l:n)); end w-wts; i = find(abs(w)<l e-6); w(i) zeros(size(i)); wts = w; return end % Weights for global minimum wrl = qp(H,fA,b)'; % Find minimum rate of return on frontier rl = portror(ret,wrl); % Find maximum rate of return on frontier r2 = max(ret); r= rl:(r2-rl)/(pts-1):r2; % Generate rates of return on frontier % Index used by for loop k = 1; % Preallocate for loop matrix w = zeros(pts,n); my = zeros(max(size(r)),1); % Preallocate for loop matrix % calculate weights for each rate of return for i = r A(3+n,:) = ret; A(4+n,:) = -ret; b(3+n,1)= i; b(4+n,1)= -i; w(k,:) = qp(H,fA,b)'; mv(k) = portvar(assets,w(k,:)); k = k+ 1; end % Compare difference in rates if abs(rl -r2) < 1e-6 % If difference is negligible, create one point v = portvar(assets,w); r= rl; else % Else calculate risk for each point v = sqrt(mv); end if nargout == 0 % Get hold status of figure held = ishold; % Plot efficient frontier and minimum risk point plot(v*252,r*25200,'g','linewidth',3,'erasemode','normal') hold on minrisk = min(v)*252; minreturn = max(r(find(v==min(v))))*25200; plot(minrisk,minreturn,'bo','inewidth',3,'erase','none') xlabel('Risk: Annualized Standard Deviation'); ylabel('Return: Annualized Expected Return (%)'); %axis([(minrisk-0.2),(minrisk+0.2),(minreturn-2), (minreturn+2)]); if -held % Turn hold off if necessary hold off end end % Return output if nargout -= 0 risk = v*252; ror = (r*25200)'; i = find(abs(w)<l e-6); w(i)= zeros(size(i)); wts =w; end 26 Appendix B Tables This part contains the tables of betas and portfolio weights that were calculated for each test. Prior to giving these tables, we show some figures that show the performance of the Three-Beta model versus the Sharpe model over 35 years. The figures are in log scale. Test 1 $1 iritia irnestment oa 35 years 103 0 0 5 10 15 25 2D 30 35 Nuibr OfYears Betas IU.UO 0.48 0.38 U.+f/ U.0O 0.62 0.04 1.40 ".I 1.21 1.06 jU.00U.'+ IU.0 0.44 0.18 27 I I .f / 0.32 0.76 4 3.04 % 1.22 2.94 I .40 U.dU 1.41 1.14 U.04 U.1 / 0.73 0.38 U.3/ U.41 1 0.7 0.39 1.24 1.56 1.31 0.98 1.46 0.74 6 0.95 0.79 0.91 1.92 -0.7 2.25 6 0.51 0.91 0.54 1.49 2.36 0.96 1.04 1.52 0.63 -0.29 0.74 0.57 0.84 0.38 6 2.26 1.94 1.01 0.27 1.36 0.55 1.27 0.46 1.03 0.58 0.78 0.74 0.67 1.41 0.73 1.59 1.01 1.32 0.19 0.89 1.58 3.63 1.12 0.62 0.23 0.71 0.68 0.84 0.43 0.85 0.74 0.68 0.89 -0.31 -0.01 1.78 0.55 1.18 0.34 0.63 0.76 0.67 0.6 0.90 1.25 1.13 0.67 0.84 0.49 0.93 0.26 1.25 0.21 0.77 0.76 0.72 1.14 1.01 1.63 1.29 0.38 0.29 -0.03 0.60 1.3 0.35 0.37 1.55 0.11 0.21 1.23 0.59 0.67 0.6 -0.02 0.54 0.36 0.55 2.52 0.57 0.75 0.45 0.24 0.9 0.54 0.43 0.46 1.02 1.99 0.69 0.51 1.22 1.6 1.21 0.93 1.45 1.69 1.23 0.86 0.32 0.83 2.03 0.42 0.78 1.99 0.59 0.94 0.68 0.58 0.87 0.1 1.03 1.86 0.7 1.83 2.22 1.5 1.21 0.66 1.24 1.3 1.08 0.3 1.13 1.26 7 1.15 1.62 1.15 0.79 1.27 0.66 1.41 0.97 1.17 0.2 1.33 1.19 1.31 7 0.81 0.72 0.69 1.13 0.03 1.55 0.86 1.33 0.5 1.63 0.1 1.87 1.17 2.01 1.72 80 0.69 1.09 0.57 1.12 0.83 0.82 0.9 _ 1.45 1.03 2.21 1.01 0.1 1.04 0.11 1.34 0.1 1.23 2.25 1.04 -0.37 1.18 0.71 1.23 1.3 0.71 0.6 0.87 0.23 1.27 1.99 0.83 2.38 0.61 2.66 0.44 -0.49 1.80 1.61 1.71 -0.49 0.66 1.7 0.59 3.09 1.05 2.09 0.93 1.13 1.46 2.5 1.11 1.58 0.65 0.55 0.74 0.85 0.87 0.94 0.53 0.87 0.76 0.92 0.57 3.7 1.38 -0.28 1.33 1.5 1.23 1.49 1.00 1.9 0.85 0.99 0.70 1.66 0.28 1.68 0.83 1.13 0.93 -0.59 0.64 1.07 0.75 0.93 2.17 1.87 -0.46 1.20 0.1 1.35 0.80 -0.22 0.74 1.34 1.97 1.26 .1.04 1.43 0.83 0.28 0.87 0.91 1.27 1.95 0.93 0.18 0.62 -0.78 0.61 0.91 0.56 0.53 0.86 0.79 12.33 2.07 0.66 1.24 0.63 0.62 0.50 2.52 0.21 0.53 0.45 0.41 1.38 1.53 0.82 1.09 0.52 -0.22 0.53 0.3 0.66 0.99 0.59 0.46 -0.02 0.46 0.51 0.22 0.84 1.23 0.60 2.12 0.1 0.78 0.71 0.52 0.35 -0.08 0.64 0.38 0.86 1.15 0.42 0.28 0.49 0.94 0.63 0.67 1.66 0.61 0.97 -0.85 1.03 0.41 1.72 0.74 1.02 0.78 0.47 0.63 1.21 0.6 0.55 1.25 1 1.38 0.45 1.17 0.48 1.28 1.28 0.54 0.4 0.64 -0.5 0.93 1.37 0.94 0.29 2.02 -0.01 .0.17 1.93 1.86 1.82 0.36 0.82 0.26 0.92 1.22 0.65 2.43 0.48 1.86 1.84 1.06 2.09 0.99 1.25 0.48 1.16 0.52 0.53 0.35 0.67 1.75 1.06 0.92 0.48 1.26 0.64 1.01 1.13 1.00 1.43 0.94 0.91 0.62 -0.5 0.82 0.41 1.00 1.03 1.11 0.91 3.59 1.2.0.11 0.94 1.36 1.75 0.71 1.36 0.51 0.78 -0.22 0.98 0.07 0.84 1.00 0.12 0.97 2.21 0.78 1.12 0.95 .1.15 0.69 0.15 0.77 0.83 0.92 0.73 0.15 0.87 0.65 0.63 0.89 1.26 0.65 0.65 1.49 0.69 0.38 0.16 0.64 1.82 0.42 0.5 0.38 0.34 -0.03 0.59 -0.14 0.63 0.54 0.80 -0.24 1 0.65 0.58 1.03 0.61 1.82 0.45 0.19 0.67 0.83 0.51 0.98 0.48 0.72 0.45 0.31 0.37 0.66 0.65 1.37 0.67 0.76 0.55 0.4 0.23 0.7 0.4 2.95 0.34 1.53 0.45 0.01 0.56 0.05 0.96 0.66 1.22 0.79 0.42 0.28 0.07 0.69 0.66 2.13 0.79 1.19 1.10 -0.03 0.56 0.39 28 0.71 1.01 1.21 1.13 1.03 1.78 0.5 2.15 0.46 1.84 1.07 1.84 0.68 0.23 0.8 0.14 0.1 0.41 1.27 0.30.24 0.14 0.93 0.91 0.94 _ 0.34 1.17 0.19 0.01 0.84 2.05 0.37 0.48 1.22 0.31 1.4 -1.01 0.49 0.07 0.62 0.02 2.59 1.16 1.64 1.18 0.76 1.52 0.07 1.74 0.28 0.5 0.32 0.73 0.52 0.88 1.15 1.02 1.27 0.7 0.99 3.33 0.74 0.85 0.55 1.07 0.09 0.63 0.53 0.68 0.4 0.86 1.15 0.9 0.12 1.76 1.98 3.21 1.84 -0.6 0.66 1.51 0.59 0.41 0.53 1.1 0.31 0.94 0.53 1.58 0.3 1.09 0.31 1.14 1.63 0.83 0.17 1.13 0.69 0.72 0.7 0.82 0.38 0.67 0.04 0.83 0.07 2.55 1.71 3.33 1.05 0.13 0.98 0.28 1.38 1.04 0.45 1.19 0.87 0.96 1.53 0.83 1.55 1.14 0.33 1.32 0.77 1.05 0.67 1.12 0.9 0.96 0.46 1.08 0.39 1.38 0.63 1.54 0.79 1.53 1.7 1.59 0.95 1.44 0.17 1.68 0.58 0.76 0.19 1.1 0.29 0.80 0.42 0.84 1.00 226 0.68 0.61 1.12 1.35 1.1 0.82 0.67 1.5 0.46 0.87 0.85 1.04 1.53 1.02 1.09 1.66 0.89 0.22 7 0.71 0.61 0.64 0.75 0.5 0.77 0.82 0.93 0.68 0.85 0.44 -0.83 0.41 0.25 0.28 0.79 0.40 1.32 0.28 -0.09 0.79 -0.24 1.12 1.63 1.06 1.24 0.68 -0.12 0.93 1.64 1.03 1.59 0.98 0.7 0.26 0.75 0.14 0.17 -0.48 1.27 2.39 0.82 1.47 0.32 0.92 1.89 0.82 0.92 0.56 0.52 0.12 0.81 1.13 0.77 0.92 0.83 2.78 0.38 1.17 0.21 0.45 0.27 0.22 0.32 0.11 0.88 0.72 1.02 -0.37 0.73 1.19 0.67 0.75 0.69 0.98 0.67 0.69 0.57 1.86 0.33 1.5 0.72 2.25 0.41 1.87 1.07 1.45 1.01 1.16 1.05 1.63 0.54 1.81 0.98 0.04 1.2 0.72 1.05 1.35 0.85 0.71 0.72 0.8 0.33 1.19 1.76 0.91 2.76 1.61 1.63 1.26 -0.09 0.35 0.35 0.37 1.51 0.2 1.57 1.32 0.34 1.06 0.71 1.09 1.54 1.50 1.92 1.4 2.35 1.23 1.36 1.35 1.43 1.25 0.89 2.04 0.74 0.76 0.80 1.75 0.4 1.69 1.52 1.4 1.38 2.65 1.38 1.52 1.23 1.8 1.27 1.73 2.48 1.59 1.36 1.38 1.31 1.72 0.96 2.01 0.94 0.36 1.38 2.38 1.06 2.4 1.30 -0.77 0.96 1.92 1.41 1.48 -0.69 1.42 1.01 0.9 1.03 -0.1 1.17 1.13 1.17 1.57 1.13 0.21 1.18 1.51 0.98 1.82 1.14 1.3 1.04 1.51 1.11 1.59 1.01 0.45 1.20 1.08 1.3 0.78 0.57 0.52 0.64 0.12 1.08 0.53 1.37 0.23 1.13 1.46 1.12 0.12 1.27 1.44 1.12 2.05 1.17 1.42 1 1.89 1.26 1.48 1.17 1.36 0.86 0.88 0.77 1.38 1.35 1.53 1.46 1.58 1.33 1.50 1.53 1.58 0.60 0.84 0.31 1.21 1.3 1.08 1.48 1.85 0.64 1.30 1.3 1.28 1.28 1.13 1.44 1.39 1.52 1 1.04 1.09 1.35 1.21 0.45 1.19 0.99 0.85 1.05 1.37 1.73 1.05 1.54 1.77 1.55 1.50 1.16 1.56 0.39 0.37 0.38 1.05 0.92 1.23 1.01 1.88 1.14 1.84 0.49 0.66 1.05 0.78 1.1 1.73 2.04 1.34 1.21 1.04 1.26 1.19 1.27 1.05 0.96 0.85 1.08 0.76 0.72 0.8 1.36 1.41 1.87 1.39 1.4 1.52 1.42 1.81 1.23 1.01 0.81 1.37 2.2 1.27 1.85 1.38 1.47 0.9 -0.07 1.48 2.29 0.96 1.13 1.28 0.99 0.81 1.11 0.72 1.20 1.3 1.21 1.82 3.27 1.55 1.92 0.51 0.69 1.85 1.55 0.24 0.79 1.01 0.67 1.13 0.81 0.88 1.03 1.06 1.01 1.12 1.03 0.65 1 0.98 0.91 0.95 0.98 0.86 0.98 0.93 0.83 1.03 1.34 1.46 1.14 2.26 1.20 1.19 1.11 0.95 1.18 0.81 0.84 0.56 0.98 1.24 1.17 0.52 0.43 0.04 0.35 0.87 0.2 0.97 0.81 1.11 0.82 1.06 0.96 0.57 1.64 1.39 1.96 0.38 -0.12 0.77 0.79 0.71 0.47 0.87 0.67 1.08 1.07 2.4 0.94 1.05 -0.66 1.15 0.86 1.94 0.88 0.92 1.13 0.64 1.03 1.07 2.81 0.74 1.11 1.03 1.05 1.29 0.7 1.34 0.79 -0.66 1.39 1.19 0.22 1.28 1.08 1.48 0.69 1.18 -0.46 0.19 2.63 -0.8 0.96 0.13 1.24 0.59 0.67 0.48 0.73 1.64 0.2 0.80 2.03 0.31 0.63 1.33 0.49 2.31 0.47 0.36 0.88 1.05 2.01 1.38 0.24 0.83 0.33 1.21 0.93 0.4 1.37 0.87 1.3 0.83 1.17 0.74 1.57 1.01 0.19 1.17 0.80 1.88 0.5 2.04 -0.2 0.91 0.29 1.18 0.62 0.72 0.52 0.63 2.26 0.3 0.38 -0.05 0.63 0.47 1.05 0.43 0.34 0.65 0.82 0.65 0.97 0.33 0.95 0 1.82 1.75 0.83 1.06 1- 1.6 1.11 2.1 0.66 0.58 0.76 0.77 -0.48 0.73 0.77 0.8 0.81 0.79 -2.13 2.71 0.15 0.97 0.88 0.92 1.13 1.08 1.08 1.06 0.4 1.39 0.61 0.13 0.95 11.56 1.6 American Home Products Halliburton Co. SLE Sara Lee Corp. W 0.35 -0.01 1.53 0.53 0.65 0.39 0.68 0.73 0.3 0.78 0.93 0.96 1.08 0.36 0.34 0.59 -0.27 0.85 2.13 0.53 0.93 0.84 1.12 0.73 0.63 0.78 0.92 0.71 0.94 0.46 0.09 0.77 0.58 1.26 1.74 1 0.83 1.71 0.78 -0.78 -0.73 0.18 _ HAL AHP 0.45 1.06 1.19 0.83 1.72 1.21 0.73 1.34 -0.46 1.15 1.43 0.97 1.02 1.21 0.8 1.41 1.25 0.95 1.28 0.78 1.11 -0.56 1.03 0.96 1.13 1.39 0.79 1.11 1.29 1.13 -1.29 -0.27 0.86 0.48 0.9 1.44 -0.97 0.84 0.91 0.95 -0.18 Westvaco Corp. FRO Frontier Corp. KMB Kimberly-Clark TXT Textron Inc. DOW Dow Chemical PPG PPG Industries SUN Sunoco Inc. Weights 0.00 0.00 0.08 0.07 0.21 0.24 0.12 0.14 0.09 0.14 0.11 0.11 0.09 0.10 0.05 0.05 0.04 0.04 0.03 0.08 0.06 0.07 0.06 0.07 0.22 0.09 0.03 0.12 0.11 0.11 0.22 0.12 0.00 0.12 0.10 0.08 0.04 0.05 0.03 0.05 0.05 0.05 0.04 0.05 0.03 0.07 0.08 0.08 0.22 0.18 0.14 0.10 0.07 0.10 0.18 0.15 0.16 0.09 0.07 0.09 0.09 0.09 0.05 0.07 0.71 29 0.11 0.11 0.13 0.08 0.09 0.11 0.00 0.10 0.06 0.00 0.06 0.01 0.00 0.10 0.07 0.02 0.06 0.02 0.07 0.14 0.11 0.14 0.26 0.14 0.11 0.15 0.10 0.15 0.21 0.14 0.09 0.08 0.08 0.13 0.09 0.12 0.10 0.07 0.09 0.07 0.12 0.14 0.12 0.13 0.21 0.23 0.14 0.19 0.14 0.13 0.20 0.17 0.10 0.16 0.12 7 0.14 0.18 0.14 0.17 0.03 0.03 7 0.16 0.10 0.03 7 0.10 80 0.14 0.06 0.08 0.12 0.21 0.19 0.13 0.18 0.14 0.21 0.15 0.08 9 0.12 S0.10 0.27 9 0.17 0.05 0.12 0.11 0.17 0.16 0.20 0.08 0.11 0.09 0.12 0.11 0.11 0.12 0.14 0.15 0.14 0.18 0.21 0.12 0.24 0.13 0.34 0.19 0.08 0.11 0.11 0.22 0.12 0.06 0.00 0.01 0.05 0.09 0.12 0.13 0.07 0.02 0.00 0.00 0.08 0.04 0.08 0.00 0.00 0.11 0.03 0.03 0.0C 0.0C 0.C00 0.11 0.04 0.03 0.04 0.04 0.07 0.01 04 0.07 0.07 0.09 0.17 0.18 0.13 0.10 0.10 0.06 0.24 0.10 0.11 0.03 0.03 0.08 0.06 0.04 0.00 0.00 0.O0 0.08 0.08 0.04 0.08 0.04 0.07 0.02 0.09 0.07 0.16 0.10 0.07 0.06 0.03 0.11 0.19 0.21 0.18 0.09 0.12 0.16 0.14 0.06 0.07 0.12 0.0C 0.00 0.09 0.08 0.08 0.12 0.07 0.05 0.09 0.05 AHP American Home Products HAL Halliburton Co. SLE Sara Lee Corp. W Westvaco Corp. FRO Frontier Corp. KMB Kimberly-Clark TXT Textron Inc. DOW Dow Chemical PPG PPG Industries SUN Sunoco Inc. 0.08 0.06 0.16 0.06 0.08 0.09 0.04 0.09 0.11 0.13 0.16 0.10 0.12 0.12 0.11 0.07 0.07 0.10 0.00 0.00 0.08 0.11 0.10 0.15 0.09 0.04 0.12 0.12 0.01 0.07 0.0C 0.05 0.00 0.04 0.08 0.14 0.11 0.09 0.10 0.06 0.10 0.03 0.11 0.15 0.08 0.06 0.00 0.00 0.00 0.07 0.02 0.06 0.12 0.14 0.08 0.15 0.05 0.06 0.01 0.04 0.02 0.09 0.05 0.11 0.07 0.09 0.06 0.08 0.07 0.04 0.13 0.11 0.07 0.10 0.00 0.03 0.03 0.07 0.06 0.07 0.11 0.16 0.08 0.15 0.22 0.16 0.09 0.16 0.14 0.18 0.05 0.13 0.11 0.13 0.09 0.14 0.04 0.17 0.08 0.14 0.15 0.30 0.57 0.59 0.11 0.08 0.35 0.20 0.14 0.06 0.05 0.03 0 0.11 0.08 0.13 0.06 0.08 0.06 0.10 0.08 0.09 0.04 0.11 0.05 0.12 0.06 0.08 0.1C 0.20 0.52 0.55 0.10 0.07 0.23 0.13 0.16 0.05 0.06 0.04 30 0.17 0.21 0.06 0.04 0.09 0.02 0.16 0.11 0.11 0.22 0.14 0.25 0.21 0.22 0.20 0.22 0.20 0.13 0.05 0.02 0.31 0.15 0.17 0.11 0.13 0.10 0.08 0.15 0.11 0.16 0.08 0.05 0.09 0.05 0.12 0.08 0.14 0.14 0.14 0.20 0.17 0.20 0.19 0.22 0.11 0.22 0.01 0.04 0.2 0.14 0.19 0.12 0.15 0.16 0.08 0.13 0.03 0.00 0.03 0.09 0.00 0.09 0.07 0.14 0.08 0.10 0.06 0.07 0.19 0.21 0.15 0.03 0.06 0.07 0.0C 0.01 0. 00 0.08 0.13 0.11 0.10 0.09 0.16 0.07 0.06 0.00 0.04 0.06 0.06 0.05 0.08 0.12 0.09 0.11 0.04 0.06 0.12 0.15 0.09 0.07 0.08 0.06 0.00 0.00 0.0 0.08 0.11 0.11 0.10 0.08 0.19 0.08 0.15 0.15 0.14 0.19 0.03 0.00 0.13 0.05 0.08 0.00 0.00 0.00 0.12 0.00 0.00 0.04 0.06 0.05 0.21 0.24 0.07 0.00 0.04 0.07 0.12 0.10 0.11 0.25 0.18 0.23 0.13 0.24 0.07 0.08 0.20 0.12 0.10 0.00 0.06 0.09 0.13 0.05 0.07 0.08 0.11 0.06 0.23 0.22 0.04 0.04 0.05 0.08 0.06 0.10 0.11 0.14 0.07 0.06 0.13 0.10 0.04 0.07 0.15 0.12 0.03 0.03 0.26 0.24 0.06 0.02 0.08 0.11 0.18 0.15 0.21 0.10 0.22 0.13 0.24 0.17 0.22 0.16 0.15 0.07 0.01 0.08 0.15 0.11 0.11 0.08 0.11 0.10 0.10 0.13 0.14 0.15 0.10 0.07 0.15 0.09 0.21 0.12 0.00 0.02 0.07 0.05 0.02 0.05 0.00 0.02 0.13 0.13 0.14 0.12 0.06 0.07 0.02 0.07 0.02 0.05 0.08 0.09 0.09 0.11 0.07 0.05 0.03 0.05 0.0C 0.00 0.0C 0.0C 0.0C 0.00 0.0C 0.03 0.17 0.14 0.04 0.04 0.07 0.05 0.22 0.16 0.03 0.07 0.06 0.03 0.07 0.09 0.11 0.10 0.10 0.09 0.07 0.05 0.08 0.11 0.08 0.05 0.08 0.10 0.10 0.07 0.13 0.14 0.10 0.11 Test 2 $1 irital irnestmet a" 35 year 102 .; 10- 10- 0 5 10 15 30 25 2D 35 imber d Years Betas 0.3 0. 0.22 -0.02 0.25 -0.01 1.41 0.38 -0.55 U.59 1.14 V., I 1.09 0.94 0.71 0.51 2.18 1.22 1 0.65 0.88 1.58 0.62 1.66 0.71 0.59 0.58 0.66 -0.19 0.23-0.02 0.94 0.41 0.49 1.1 0.90 0.82 0.83 0.60 0.8 0.25 0.5 0.38 1.24 1.56 1.31 -0.7 0.31 1.47 0.29 1.41 -0.09 0.56 0.44 0.46 0.22 -0.29 0.48 -0.79 0.64 2.08 0.41 0.95 0.62 0.46 -1.61 -1.87 -0.96 -0.94 1.49 2.36 0.96 0.85 0.13 0.97 0.99 2.28 0.6 0.57 1.12 0.43 1.52 0.47 0.25 2.29 2.44 0.47 -0.34 0.51 -0.72 0.44 -0.25 0.86 0.58 0.74 0.66 0.35 0.74 1.36 1.07 1.27 0.48 0.44 1.02 -0.33 1.15 -0.01 0.72 10.6 7 -0.44 0.340.12 0.26 1.14 1.31 1.72 2.26 0.78 0.94 0.84 0.81 1.53 0.65 0.89 1.30 2.08 1.04 0.490.76 0.35 1.01 0.27 1.36 1.02 0.22 0.25 -0.03 0.57 0.58 0.35 0.58 -1 0.190.28 0.21 0.04 0.51 0.47 0.51 0.96 -0.09 0.45 011 0.32 1.121.63 1.06 _ -0.12 0.100.23 0.06 -0.05 0.34 1.20.11 1.46 1.81 1.13 0.43 0.58 2.19 0.73 1.52 0.59 0.440.84 0.28 2.34 3.44 2.03 0.87 1.54 1.64 0.68 0.15 1.53 0.37 0.76 0.63 0.71 0.59 0.89 0.31 1.11 0.79 1.43 0.55 1.03 159 0.98 0.57 0.58 0.72 0.52 0.49 0.45 0.650.18 0.6 0.92 1.75 0.81 0.71 0.96 10.58 0.79 -0.14 1.94 2.68 2.02 1.01 0.7 0.540.28 0.6 1.41 0.73 1.59 _ 0 0.50 0.32 0.48 _ 0.87 0.22 0.86 0.16 1.35 1.26 1.13 1.41 0.41 1.11 1.46 0.91 0.94 -095 1.1 2.4 2.153.52 1.82 1.88 1.79 1.92 1.99 0.4 0.52 0.17 0.77 0.39 0.83 0.78 0.02 1.62 2.13 0.31 0.42 0.37 0.97 1.26 1.12 0.29 0.950.96 1.21 0.24 1.34 0.690.56 0.68 0.98 0.28 1.38 0.50 1.16 0.34 0.34 0.64 0.36 0.67 0.46 0.77 0.66 0.5 0.54 0.63 0.11 0.48 1.16 2.28 0.37 -0.42 0.25 -0.07 0.92 0.65 ~0.430.34 1.64 2.12 0.32 1.69 0.04 0.29 0.7 0.3 0.9 1.38 1.33 3 1.07 0.8 0.07 0.81 0.92 1.04 0.45 _ 0.69 1.19 31 0.5 0.3 0.61 _ 1.982.21 1.85 0.05 0.29 -0.8 0.33 1.14 1.262.05 1.1 1.53 1.74 0.31 0.53 0.26 0.38 0.29 0.22 0.27 1.51 0.46 1.64 0.42 0.41 0.99 0.38 0.31 0.36 0.84 0.47 1.56 1.30 0.91 1.42 0.93 1.09 1.04 1.12 0.92 1.19 0.32 1.23 1.52 -0.83 1.25 1.36 1.05 0.98 0.94 1.12 0.07 0.64 0.88 0.36 2.51 1.33 1.66 1.19 1.58 1.66 0.77 1.53 0.44 1.21 1.33 1.25 0.71 0.88 0.81 0.88 1.13 0.89 2.66 0.33 1.28 1.30 1.14 1.4 0.45 0.95 0.92 0.98 0.81 1.40 1.53 1.43 11.23 1.15 1.69 1.07 1.16 0.44 1.06 0.3 1.03 0.68 0.92 0.97 0.85 1.62 0.55 1.69 0.28 0.81 0.25 1.78 0.65 1.12 0.41 0.32 0.43 0.3 0.68 0.51 0.66 0.98 -0.13 0.91 0.76 1.04 0.7 1.23 0.8 0.04 1.83 1.01 0.75 0.44 1.1 1.16 0.35 0.61 0.36 0.44 0.78 1.03 1.89 0.57 0.31 1.28 1.51 1.05 0.77 1.05 0.67 1.12 0.9 0.96 0.46 1.08 0.39 1.38 0.63 1.54 0.28 0.79 0.30 0.09 0.26 0.75 0.15 0.63 0.12 1.53 1.7 1.59 -0.04 0.38 0.84 0.24 0.27 0.28 0.41 0.22 0.68 0.48 0.43 0.63 0.95 1.44 0.17 1.68 1.31 1.13 0.03 1.55 0.86 1.33 0.5 1.63 0.1 1.87 1.17 2.01 2.63 1.36 2.73 -0.57 2.02 1.28 1.54 1.26 1.21 1.86 1.17 0.48 0.05 0.42 0.98 0.36 0 0.31 1.93 1.86 1.82 0.13 1.17 0.99 1.02 1.74 0.67 1.53 1.81 1.49 2.62 1.45 1.08 -0.04 0.59 2.38 0.3 0.87 0.89 2.06 0.98 -0.56 0.42 2.42 0.31 1 -0.17 1.75 1.03 0.86 0.94 0.34 1.16 1.04 0.96 1.53 _ 1.09 1.08 1.19 1.2 1.12 1.11 0.5 2.93 0.94 0.98 0.95 0.73 0.63 0.49 0.74 0.18 0.61 0.4 0.63 0.69 0.83 -0.07 0.97 1.04 0.99 1.34 1.09 1 2.43 0.71 -0.31 0.7 1.84 1.06 2.09 0.99 1.25 0.48 1.16 1.07 1.75 1.17 1.26 0.64 0.91 3.59 -0.45 0.96 0.98 1.14 1.3 1.04 0.95 0.66 0.81 0.84 1.09 0.74 0.39 0.82 0.66 0.54 0.86 0.55 -0.04 0.95 0.67 0.85 0.13 1.62 0.81 2.01 0.86 0.98 1.76 0.95 0.62 1.03 1.78 1.07 -0.35 2.65 0.77 0.49 0.76 1.77 1.33 2.06 0.69 0.86 1.06 1.06 2.38 0.91 0.84 0.64 0.77 1.31 0.36 1.4 1.02 1.09 1.33 1.37 1.27 1.46 1.22 0.80 0.79 0.84 1.53 1.19 1.61 1.26 2.18 0.74 0.51 .1.91 .2.84 0.79 0.27 1.5 1.94 2.44 1.36 1.06 0.94 1.15 1.34 1.18 1.26 1.63 1.68 0.72 1.17 1.41 1 1.37 1.07 1.64 1.5 1.08 0.77 1.11 1.10 1.27 0.99 0.83 0.53 0.81 1.73 2.04 1.34 0.63 0.63 0.31 0.77 3.67 2.25 3.27 1.01 2.11 1.21 0.50 -0.15 0.71 1.01 0.68 0.75 0.81 0.88 1.03 0.52 0.31 0.56 0.62 -0.46 1.11 -0.56 0.49 0.58 0.47 1.39 0.5 1.13 1.07 2.81 0.36 -0.2 0.41 0.74 0.76 1.11 0.79 -0.66 0.46 0.1 0.96 0.56 1.05 1.52 1.83 1.37 1.32 -0.02 0.43 0.77 0.12 0.92 0.6 0.77 1.7 0.62 0.67 0.58 0.65 0.79 0.62 0.54 0.56 1- 2.38 1.57 2.53 1.35 0.99 0.85 0.78 1.05 1.88 .0.57 1.09 1.55 1.1 1.91 0.37 1.22 1.32 1.08 -0.15 1.54 0.59 1.03 0.46 -0.61 0.5 0.64 0.23 0.8 1.48 1.41 3.07 1.22 1.26 1.86 0.53 0.36 0.68 1 2.4 0.82 1.66 1.92 1.24 1.2 -1.49 0.56 0.86 0.5 0.6 0.48 0.85 0.28 0.93 0.43 0.35 0.45 1.30 1.7 0.81 1.28 0.11 1.5 0.58 0.81 0.73 1.67 0.52 0.92 0.87 1.37 0.66 1.05 1.09 1.46 -0.17 2.95 1.68 2.21 1.63 1.76 1.21 1.83 1.33 0.66 -0.03 0.75 1.48 1.28 1.72 1.29 0.83 0.77 0.59 0.81 1.09 0.66 0.06 1.05 0.95 0.67 1.43 0.75 1.18 1.07 1.37 1.73 0.85 0.9 2.17 0.59 1.14 0.45 0.72 1.03 0.87 0.97 1.4 1.09 0.9 1.03 2.18 0.69 1.02 0.62 1.04 0.03 1.23 0.91 0.53 0.79 0.51 0.28 0.49 0.56 0.44 0.68 0.41 0.78 0.38 0.15 0.46 0.41 0.64 0.01 1.80 2.1 1.61 0.51 0.42 0.65 0.49 0.61 0.37 0.68 0.66 1.06 0.41 1.13 2 0.76 0.51 0.67 0.21 0.42 0.51 0.32 1.51 1.36 0.68 0.51 0.43 0.03 0.47 2.79 1.23 0.55 1.17 1.38 1.35 1.53 1.23 1.53 1.12 1.25 1.05 0.86 1.28 0.88 0.42 0.64 1.16 0.69 1.02 1.05 1.13 0.77 1.39 1.05 -0.7 1.42 0.3 -0.02 -0.49 1.10 1.42 0.54 0.66 1.17 2.17 1.09 0.51 0.91 1.22 2.51 4.36 2.41 0.87 2.67 0.57 -0.03 2.49 3.39 2.16 0.6 3.8 0.93 0.67 1.83 1.62 1.87 1.8 0.6 0.73 0.53 _ 0.68 0.32 1.27 2.53 1.34 0.77 0.64 0.72 0.78 1.20 1.18 1.25 1.09 0.3 1.34 0.89 2.1 0.93 0.23 0.88 0.15 0.25 1.52 -0.02 0.63 0.11 1.33 -0.01 0.08 0.67 1.05 0.62 0.69 0.35 -0.01 0.42 0.88 0.77 0.95 0.54 0.72 1.02 0.95 0.84 0.74 1.14 0.51 1.55 1.22 2.69 1.58 2.14 0.74 0.2 0.85 1.140.33 1.32 0.47 0.95 0.45 0.82 0.02 0.74 0.28 0.44 0.68 0.31 1.04 1.35 1.18 0.96 1.53 0.83 0.39 0.330.42 0.23 0.41 0.86 0.33 0.49 0.61 0.43 0.62 0.63 0.65 0.44 0.59 1.09 1.36 1.2 0.08 1.57 2.24 1.62 0.42 0.97 0.47 1.3 0.01 1.22 0.21 1.57 1.51 0.76 1.75 0.87 1.21 0.67 0.39 0.81 1.39 32 0.63 1 0.78 0.27 0.96 0.34 0.94 0.38 1.01 1.9 1.34 1.55 1.23 1.62 0.84 1.82 0.93 1.24 -1.2 0.89 0.66 1.10 0.43 0.92 1.55 1.45 1.6 0.92 0.76 1.34 -1.5 1.51 1.32 1.52 1.69 1.06 0.91 0.85 1.41 1.44 1.5 0.94 0.99 0.82 0.76 1.06 0.89 1.73 0.78 0.78 0.57 0.24 0.63 -0.11 1.31 2.08 1.18 0.78 1.30 1.34 1.34 0.85 1.31 1.33 1.35 0.90 1.26 0.66 1.49 0.44 0.9 0.11 2.11 0.74 0.8 0.69 OKE 0.67 0.41 0.79 0.37 0.96 0.67 0.62 0.9 0.5 1.01 .76 0.59 0.99 1.120.52 1.39 0.78 0.56 0.06 0.51 1.88 0.56 0.74 0.41 2.2 -0.13 149 1.32 1.43 1.99 1.15 1.73 1.14 0.24 1.307 1.42 0.86 0.21 1.03 2.26 1.04 0.63 0.47 0.21 0.12 0.06 1.05 1.5 -2.13 1.13 1.08 0.52 0.54 0.43 1.08 1.56 1.29 -0.6 0.85 0.78 ONEOK Inc. 1.08 1.48 0.69 1.37 1.72 1.44 _ 53 0.88 0.75 0.86 1.24 1.03 1.13 1.04 0.71 1.19 0.7 1.06 -0.16 1.1 0.16 0 0.51 0.53 0.63 0.59 ____ -0.11 1.72 1.21 0.63 0.09 0.73 1.74 0.88 2.5 1.36 1.41 0.82 0.26 1.04 1.45 0.49 0.59 1.13 0.43 1.47 1.33 0.71 1.47 ___ 1.67 1.11 2.68 0.91 -0.24 1.04 1.18 1.05 0.69 Deere & Co. DE Phillips Petroleum P PCG PG&E Corp. HAL Halliburton Co. TXU Texas Utilities Hldg.Cos. vo Seagram Co. Ltd. HI Household International HNZ Heinz (H.J.) BC Brunswick Corp. Weights uAU~ U.11 U-ui U.Uji U.1I5 U.e-1 U.1t) U.141 U.1/ U-141 U.UZ) U.U11 U.Iu U.U(j U1 U.111 U.U'1 U.Ubl U.U0 U.UZ~ 0.21 0.19 0.22 0.13 0.26 0.20 0.21 0.14 0.16 0.19 0.19 0.23 0.25 0.04 0.02 0.08 0.09 0.13 0.27 0.14 0.30 0.06 0.09 0.08 0.03 0.07 0.12 0.05 0.07 0.07 0.02 0.04 0.12 0.11 0.11 0.08 0.04 0.09 0.13 0.09 0.04 0.06 0.13 0.13 0.19 0.11 0.09 0.04 0.03 0.03 0.07 0.04 0.05 0.05 0.06 0.06 0.09 0.17 0.04 0.05 0.05 0.01 0.04 0.04 0.04 0.09 0.12 0.11 0.04 0.05 0.13 0.10 0.06 0.17 0.08 0.09 0.07 0.04 0.20 0.23 0.10 0.04 0.02 0.07 0.10 0.20 0.04 0.04 0.07 0.07 0.10 0.03 0.12 0.06 0.05 0.04 0.08 0.21 0.03 0.03 0.06 0.16 0.01 0.04 0.07 0.17 0.24 0.16 0.15 0.21 0.16 0.19 0.17 0.11 0.11 0.13 0.15 0.14 0.07 0.01 0.04 0.04 0.08 0.20 0.11 0.23 0.04 0.06 0.06 0.00 0.07 0.10 0.00 0.06 0.06 0.00 0.00 0.06 0.04 0.14 0.10 0.00 0.06 0.18 0.08 0.04 0.06 0.11 0.12 0.16 0.12 0.07 0.00 0.00 0.00 0.04 0.04 0.00 0.04 0.06 0.01 0.02 0.15 0.00 0.02 0.05 0.00 0.04 0.19 0.20 0.18 0.11 0.10 0.21 0.08 0.02 0.15 0.23 0.11 0.22 0.29 0.34 0.52 0.32 0.22 0.16 0.26 0.26 0.09 0.16 0.12 0.11 0.12 0.10 0.15 0.08 0.03 0.15 0.20 0.18 0.17 0.21 0.21 0.46 0.23 0.17 0.17 0.20 0.19 0.11 0.04 0.03 0.03 0.11 0.09 0.00 0.00 0.11 0.10 0.01 0.11 0.04 0.03 0.00 0.00 0.08 0.19 0.03 0.01 0.00 0.05 33 0.13 0.08 0.11 0.13 0.11 0.15 0.25 0.18 0.15 0.02 0.00 0.04 0.12 0.08 0.07 0.13 0.18 0.14 0.29 0.15 0.27 0.15 0.08 0.12 0.10 0.13 0.11 0.20 0.17 0.11 0.04 0.00 0.07 0.12 0.09 0.06 0.14 0.17 0.12 0.20 0.15 0.19 0.14 0.09 0.10 0.18 0.14 0.26 0.32 0.26 0.20 0.38 0.40 0.12 0.04 0.06 0.09 0.10 0.04 0.14 0.04 0.09 0.06 0.13 0.08 0.10 0.13 0.12 0.26 0.24 0.22 0.18 0.36 0.21 0.09 0.07 0.10 0.11 0.03 0.01 0.09 0.14 0.14 0.12 0.09 0.21 0.05 0.04 0.08 0.05 0.08 0.07 0.07 0.00 0.04 0.03 0.05 0.27 0.04 0.02 0.00 0.15 0.00 0.02 0.05 0.05 0.01 0.09 0.15 0.08 0.03 0.06 0.12 0.07 0.14 0.14 0.22 0.13 0.06 0.15 0.11 0.22 0.05 0.01 0.17 0.08 0.04 0.01 0.10 0.16 0.10 0.03 0.06 0.08 0.07 0.11 0.14 0.20 0.08 0.08 0.12 0.10 0.16 0.10 0.06 0.20 0.06 0.01 0.01 0.00 0.03 0.00 0.00 0.00 0.05 0.00 0.00 0.00 0.01 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.13 0.00 0.02 0.02 0.02 0.04 0.00 0.02 0.00 0.07 0.01 0.00 0.03 0.03 0.04 0.02 0.00 0.02 0.02 0.00 0.01 0.10 0.05 0.16 0.28 0.00 0.02 0.07 - 0.11 - 0.08 * 0.04 * 0.04 ' 0.13 * 0.12 . 0.16 0.13 0.20 0.00 0.01 0.06 0.08 0.07 0.04 0.05 0.12 0.10 0.12 0.10 0.03 0.12 0.11 0.04 0.16 0.00 0.01 0.11 0.01 0.09 0.01 0.11 0.04 0.10 0.12 0.09 0.13 0.04 0.02 0.10 0.04 0.08 0.04 OKE ONEOK Inc. DE Deere & Co. P Phillips Petroleum PCG 0.10 0.04 0.02 0.07 0.00 0.11 0.09 0.05 0.06 0.11 0.05 0.15 Halliburton Co. TXU Texas Utilities Hldg.Cos. vo Seagram Co. Ltd. HI Household International BC 0.21 0.16 0.00 0.21 0.22 0.00 0.18 0.23 0.27 0.07 0.17 0.05 0.17 0.15 0.00 0.19 0.18 0.03 0.16 0.21 0.23 0.09 0.16 0.07 10.04 0.02 0.00 0.00 0.00 0.02 0.04 0.01 0.04 0.06 0.09 0.03 0.06 0.02 0.00 0.00 0.00 0.04 0.05 0.03 0.05 0.03 0.10 0.04 0.22 0.27 0.74 0.36 0.41 0.27 0.39 0.43 0.31 0.15 0.26 0.33 0.16 0.26 0.56 0.35 0.35 0.19 0.27 0.36 0.27 0.14 0.25 0.22 0.04 0.04 0.00 0.00 0.16 0.21 0.18 0.02 0.08 0.11 0.04 0.06 0.10 0.09 0.05 0.02 0.20 0.31 0.28 0.04 0.09 0.16 0.06 0.09 30 35 PG&E Corp. HAL HNZ 0.07 0.05 0.00 0.05 0.00 0.06 0.07 0.06 0.08 0.10 0.06 0.13 Heinz (H.J.) Brunswick Corp. 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U 0.42 0.25 0.30 0.53 0.30.46 -0.72 11.92 0.51 0.91 1.16 1.28 0.74 0.72 0.9 0.63 0.54 0.08 3.25 -0.29 0.74 0.57 0.84 1.03 1.27 1.24 1.52 0.94 0.84 _ 0.38 0.07 0.79 -0.24 1.22 1.52 0.95 1.24 -0.12 0.93 1.64 0.7 1.03 0.78 0.74 0.67 1.53 0.71 0.61 V.D' 1.59 1.06 1.64 2.93 1.28 9.75 1.62 2.24 0.87 3.13 0.79 2.49 2.86 2.32 2.07 3.27 1.16 3.9 1.47 1.45 1.58 3.05 0.91 2.0812.11 1.76 3.75 2.19 0.32 2.42 1.34 3.05 0.7 -0.1 1.31 1.69 1.19 2.24 1.41 0.99 0.62 0.78 1.13 1.67 0.92 2.29 1.34 3.46 1.13 -0.07 0.90 0.17 1.12 1.42 0.12 0.39 0.74 1.34 0.70 0.31 1.25 3.04 1.05 _ 0.99 1.97 2.84 2.34 1.48 2.81 1.19 1.05 0.74 -0.03 1.01 -0.32 1.41 0.61 1.09 1.97 0.98 1.29 0.64 1.02 0.52 1.11 0.91 0.2 1.41 3.33 1.41 1.91 0.91 1.34 0.8 1.25 0.22 1.35 0.75 0.5 0.77 0.82 0.93 0.68 0.85 0.78 0.94 0.72 0.91 0.93 0.1 0.95 1.64 2.12 1.5 1.48 2.09 1.29 1.96 2.29 1.60 2.67 1.41 1.89 5.74 1.03 1.87 1.19 1.89 3.93 1.73 1.99 1.37 2.22 0.52 0.62 0.37 1.030.8 0.89 1.43 0.98 1.38 1.09 0.31 1.14 0.69 1.52 0.57 1.13 0.91 1.06 1.51 0.96 0.38 1.11 0.29 0.78 1.58 0.87 1.44 0.44 0.64 2.12 1.15 1.13 2.14 1.38 0.17 1.5 1.21 0.66 0.71 1.07 1.04 -0.48 1.13 1.37 0.44 0.32 0.66 0.43 0.54 1.04 1.46 1.61 1.55 0.92 0.4 0.93 1.50 0.4 1.57 1.24 1.3 1.08 0.3 1.13 2.24 1.37 2.82 2.27 4.16 1.14 1.05 1.49 0.97 0.55 1.02 1.53 1.99 1.48 1 2 1.86 1.78 1.39 2.41 1.19 1.69 0.25 1.84 1.9 1.09 0.92 1.13 0.96 1.97 1.14 0.89 1.21 1.05 1 1.12 1.68 1.04 1.14 0.93 1.15 2.45 5.13 2.39 1.16 2.17 4.7 1.76 2.42 2.79 1.74 1.18 1.69 1.26 12.83 1.32 1.23 0.33 0.54 0.27 1.230.55 1.17 0.48 2.37 0.28 1.44 0.57 1.59 1.01 1.80 2.21 1.68 1.15 1.62 1.15 1.02 1.22 0.98 0.97 1.68 0.79 0.79 1.18 1.76 1.27 0.66 1.41 1.20 1.56 1.01 1.06 2.21 0.81 1.26 2.44 1.19 0.93 1.33 1.67 1.22 1.76 1.74 0.73 0.59 2.18 10.47 0.39 0.87 0.3 0.69 1.02 0.62 0.81 0.47 0.98 0.44 0.83 0.25 0.99 0.05 1.58 1.27 1.71 0.1 0.45 0.68 1.02 1.12 0.05 2.24 1.83 0 0.97 1.17 0.2 2.14 1.29 0.41 1.6 1.10 2.11 0.5 1.27 1.96 1.33 1.41 0.93 1.9 0.12 1.21 2.5 1.19 1.41 1.1 1.75 1.97 0.66 1.23 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0.77 1.45 -1.14 1.18 1.33 1.12 1.3 1.15 1.92 1.01 .1.2 0.74 2.16 0.42 1.07 0.09 0.63 0.53 0.68 0.4 0.86 1.15 0.9 0.67 0.92 0.48 1.11 0.12 1.18 1.51 0.98 1.82 0.86 0.88 0.77 1.04 0.99 0.85 1.05 1.01 1.05 0.78 1.1 1.82 1.01 0.67 1.13 0.79 1.11 1.29 1.13 _ 0.92 1.15 1.43 0.97 1.2 2.1 0.62 0.95 0.62 1.32 1.69 1.15 1.1 0.61 0.76 1.25 0.65 1.87 1.25 1.13 0.83 0.39 0.43 1.18 0.76 0.63 1.81 1.1 0.75 1.87 1.36 2.13 1.15 -0.01 0.85 0.41 0.34 -4.1 1.29 1.01 1.22 0.33 1.12 2.12 1.77 -0.09 1.14 0.27 0.53 -0.93 1.13 0.59 1.13 1.44 1.02 0.89 1.17 1.37 1.63 1.21 031__-0.69 0___ 1.53 1.19 1.38 1.83 0.94 1.28 1.14 1.57 1.01 1.17 0.71 1.71 1.85 0.87 1.84 ___ 1_.04 0.93 0.47 1.04 0.68 0.70 0.64 1.20 1.07 1.68 1.45 0.97 1.28 0.73 1.33 0.24 1.46 1.63 1.67 1.10 1.33 0.93 1.44 1.24 1.23 1.57 1.32 0.81 1.39 0.51 0.74 1.75 -0.03 1.71 1.85 1.08 1.15 0.89 0.49 1.02 1.66 1.42 1.21.19 0.832_5 0.13 0.27 0.04 1.59 1.34 1.19 0.55 0.31 0.42 1.47 1.23 1.55 1.32 0.36 1.59 2.14 1.33 -0.13 _ .1.15 1.60 1.46 0.78 0.42 0.42 0.03 1.31 1.37 1.34 1.04 0.59 1.38 .2.79 -0.09 -0.05 0.99 1.10 0.2 0.64 0.39 0.67 0.84 1.81 1.74 1.28 0.6 0.78 1.7 ____ 1 0.94 1.39 1.02 1.21 0.98 0.54 1.09 0.8 1.1 -0.59 1.82 1.06 0.74 0.5 0.66 0.58 1.03 0.95 1.02 0.76 0.98 -0.18 0.3 1.41 0.97 2.24 0.38 -0.05 0.94 1.23 0.56 0.43 0.62 1.3 0.48 0.54 0.33 1.16 0.76 0.86 0.72 0.84 0.88 0.43 0.9 -0.48 0.68 0.3 0.8 0.65 0.49 0.65 0.36 0.82 0.56 0 0.66 1.46 1.93 1.77 0.79 2.78 1.61 0.84 0.49 0.68 0.4 _ 0.68 1.16 1.17 1.1 1.65 1.26 2.16 0.96 1.38 0.97 0.88 0.92 1.6 0.921.52 0.63 1.67 0.96 1.62 0.61 2.09 0.89 1.08 0.86 __ 0.62 PEP CR 2.7 1.55 2.04 1.19 2.66 1.22 1.11 1.32 0.93 0.58 1.33 0.38 0.7 0.850.9 0.97 -0.2 Southern Co. Household International NCE New Century Energies JNJ Johnson & Johnson EK Eastman Kodak AHP American Home Products PEP PepsiCo Inc. CR Crane Company RTN.B Raytheon Co. R Ryder System Weights Sto ckI so i NCE JNJ EK AHIP 36 RTNV.B R 0 0.18 0.17 0.11 0.07 0.11 0.08 0.14 0.03 0.05 0.18 0.32 0.27 0.27 0.35 0.32 0.20 0.22 0.21 0.20 0.38 0.30 0.09 0.16 0.18 0.08 0.16 0.13 0.26 0.18 0.29 0.28 0.10 0.09 0.07 0.14 0.15 0.19 0.12 0.13 0.20 0.05 0.08 0.1C 0.05 0.04 0.14 0.1( 0.07 0.04 0.15 0.06 0.08 0.12 0.13 0.27 0.01 0.19 0.03 0.17 0.02 0.25 0.06 0.25 0.25 0.09 0.16 0.17 0.21 0.03 0.14 0.15 0.27 0.01 0.25 0.00 0.10 0.01 0.15 0.05 0.21 0.17 0.05 0.0C 0.19 0.08 0.06 0.05 0.25 0.02 0.15 0.04 0.28 0.03 0.28 0.04 0.11 0.03 0.1(10.01 OH 0 0.17 0.13 0.15 0.05 0.05 0.10 0.08 0.15 0.02 0.16 0.07 0.05 0.02 0.11 0.19 0.11 0.07 0.09 0.13 0.04 0.04 0.04 0.07 0.14 0.0( 0.06 0.01 0.02 0.03 0.03 0.07 0.06 0.05 010 0.16 0.19 0.12 0.09 0.03 0.04 0.07 0.07 0.080.0E 0.20 0.18 0.12 0.10 0.05 0.09 0.07 0.08 0.15 0.11 0.22 0.14 0.41 0.24 0.24 0.13 0.17 0.13 0.19 0.14 0.24 0.21 0.10 0.04 0.13 0.09 0.15 0.12 0.28 0.20 0.29 0.24 0.26 0.18 0.16 0.12 0.11 0.08 0.38 0.21 0.56 0.46 0.47 0.39 0.39 0.30 0.27 0.23 0.29 0.24 0.22 0.16 0.14 0.12 0.2C 0.21 04 0.31 SO Southern Co. HI Household International NCE New Century Energies JNJ Johnson & Johnson EK Eastman Kodak AHP American Home Products PEP PepsiCo Inc. CR Crane Company RTN.B Raytheon Co. R Ryder System 0.00 0.00 0.06 0.06 0.14 0.10 0.29 0.21 0.22 0.19 0.10 0.09 0.09 0.09 0.00 0.02 0.14 0.14 0.10 0.1C 0.07 0.09 0.11 0.11 0.11 0.12 0.12 0.11 0.0C 0.12 0.00 0.12 0.19 0.23 0.22 0.15 0.02 0.08 0.00 0.04 0.04 0.05 0.06 0.08 0.06 0.08 0.02 0.12 0.00 0.0( 0.00 0.03 0.00 0.00 0.00 0.05 0.15 0.19 0.02 0.06 0.03 0.04 0.12 0.11 0.12 0.1C 0.03 0.07 0.18 0.20 0.02 0.18 0.2C 0.11 0.16 0.21 0.15 0.13 0.15 0.18 015 0.15 0.17 0.11 0.18 0.14 0.14 0.15 0.20 0.08 0.11 0.24 0.03 0.13 0.27 0.04 0.06 0.17 0.00 0.08 0.05 0.01 0.12 0.02 0.03 0.21 0.00 0.0C 0.04 0.04 0.07 0.07 0.10 0.00 0.02 0.07 0.00 0.09 0.16 0.09 0.10 0.10 0.05 0.13 0.10 0.00 0.06 0.13 0.09 0.09 0.13 0.19 0.11 0.19 0.02 0.06 0.15 0.14 0.13 0.11 0.00 0.00 0.18 0.00 0.00 0.11 0.06 0.08 0.11 0.00 0.03 0.06 0.00 0.00 0.19 0.11 0.09 0.07 0.01 0.03 0.11 0.08 0.09 0.20 0.04 0.05 0.15 0.02 0.03 0.08 37 0.00 0.10 0.09 0.22 0.1C 0.09 0.06 0.14 0.16 0.07 0.06 0.12 0.18 0.01 0.02 0.10 0.22 0.04 0.05 0.06 0.14 0.11 0.09 0.07 0.17 0.03 0.06 0.13 0.15 0.22 0.12 0.09 0.08 0.03 0.05 0.12 0.17 0.12 0.09 0.11 0.19 0.12 0.16 0.14 0.11 0.08 0.15 0.22 0.12 0.15 0.08 0.11 0.18 0.13 0.10 0.21 0.25 0.18 0.27 0.11 0.15 0.04 0.00 0.06 0.08 0.07 0.05 0.06 0.08 0.11 0.0C 0.0C 0.0C 0.00 0.00 0.00 0.04 0.11 0.04 0.08 0.04 0.16 0.20 0.16 0.19 0.11 0.09 0.13 0.06 0.00 0.10 0.07 0.06 0.06 0.07 0.19 0.12 0.04 0.08 0.0( 0.00 0.00 0.00 0.01 0.12 0.05 0.09 0.05 0.22 0.06 0.04 0.06 0.00 0.1 0.04 0.04 0.04 0.06 0.11 0.19 0.11 0.04 0.04 0.18 0.01 0.00 0.04 0.02 0.01 0.02 0.06 0.10 0.06 0.04 0.10 0.21 0.00 0.00 0.00 0.01 0.01 0.02 0.13 0.00 0 0.11 0.02 0.03 0.00 0.00 0.13 0.07 0.06 0.14 0.25 0.06 0.05 0.05 0.02 0.11 0.05 0.03 0.03 0.04 0.09 0.11 0.09 0.03 0.01 0.11 0.02 0.03 0.06 0.04 0.04 0.05 0.04 0.08 0.05 0.04 0.06 0.06 0.05 0.00 0.03 0.05 0.05 0.06 0.04 0.00 0.01 0.06 0.09 0.03 0.05 0.04 0.06 0.00 0.00 0.00 0.03 0.00 0.02 0.04 0.05 0.02 0.06 0.00 0.04 0.00 0.00 0.00 0.00 0.03 0.07 0.00 0.01 0.11 0.10 0.00 0.02 0.07 0.10 0.00 0.02 0.0C 0.03 0.00 0.01 0.13 0.14 0.16 0.10 0.12 0.14 0.00 0.0( 0.04 0.09 0.00 0.03 0.03 0.06 0.05 0.06 0.00 0.02 0.04 0.05 0.00 0.03 0.06 0.08 0.01 0.03 0.09 0.10 0.07 0.1C 0.04 0.05 0.18 0.09 0.1C 0.07 0.36 0.55 0.0C 0.00 0.06 0.04 0.0C 0.01 0.13 0.19 0.03 0.00 0.25 0.12 0.01 0.06 0.16 0.17 0.00 0.03 0.090.09 0.0C 0.02 1 0.02 0.10 0.10 0.24 0.19 0.01 0.03 0.23 0.19 0.03 0.03 0.04 0.06 0.09 0.11 Test 4 $1intial inestnwt ar 35 years 10 .2 5 0 10 20 15 10mber of Years 30 25 35 Betas WWW.- . U.b jU.4O 2.88 0.28 1.63 0.27 -0.14 0.71 1.07 0.51 0.47 1.15 2.42 0.67 U.' 0.67 1.36 10.74 0.94 1.62 0.92 0.67 0 15r 1.05 0.9 1.03 1.68 0.59 0.41 1.07 0.25 0.78 0.97 0.75 0.65 0.31 0.7 4.14 0.07 0.39 1.12 -0.75 0.99 0.33 1.34 0.64 0.84 0.43 0.81 0.80 0.92 0.65 1.24 0.90 1.15 0.58 0.28 0.05 0.42 0.08 0.43 1.36 0.32 1.87 3.22 1.43 1.42 1.42 1.42 1.39 0.02 1.55 0.84 1.62 0.00 -0.09 1.60 3.15 0.61 0.23 0.79 0.84 0.8 0.97 1.98 0.8 0.65 0.57 0.94 1.2 0.65 1.74 0.44 0.7 0.45 2.37 5.69 0.44 4.95 0.75 1.91 0.54 -0 AA 0.61 0.11 1.48 2.43 0.74 1.34 0.86 0.78 0.81 0.72 0.88 0.38 1.19 0.85 0.49 0.75 -0.77 0.92 0.22 1.2 0.6 0.97 2.22 0.83 0.78 0.83 0.7 0.81 . _ 1.03 -0.03 1.93 -1.12 4.64 1.02 0.19 1.10 0.74 0.41 0.23 2.07 4.19 0.48 0.76 1.21 1.24 1.33 0.59 0.5 .0.23 0.62 1.83 0.27 0.88 0.54 0.93 1.19 2.12 0.94 0.41 0.93 0.32 1.83 0.89 1.94 0.49 1.71 0.66 0.44 0.76 0.99 0.77 0.87 0.96 0.38 1.01 0.43 0.27 0.42 1.84 1.48 1.78 1.5 -1.29 1-2.31 -1.79 0.84 1.71 0.49 0.83 0.78 1.17 0.8 0.55 0.85 0.37 0.81 0.41 0.1 0.58 -0.15 0.45 0.9 0.47 _ 0.23 1.40 1.83 1.27 -0.29 0.49 1.49 1.01 -0.48 0.67 1.56 0.79 0.23 0.41 0.52 0.57 0.01 1.07 0.34 0.46 0.08 0.84 -0.12 1.06 0.18 1.21 0.87 0.53 0.72 0.49 1.47 0.31 0.65 -0.18 0.82 1.46 0.84 0.59 1.14 0.8 1.08 0.57 0.23 0.54 0.37 0.45 0.28 1.12 0.54 2.24 0.57 1.55 0.86 0.62 0.73 0.53 1.27 0.32 0.6 0.26 1.33 0.27 1.68 0.80 0.93 0.63 0.60 0.48 0.69 1.09 0.54 1.16 0.78 1.06 0.33 0.97 0.45 0.67 0.64 0.74 0.57 0.18 0.59 0.45 0.69 1.84 1.26 2.25 1.2 0.42 0.60 0.79 0.52 1.18 1.24 1.63 1.26 1.07 0.95 1.01 0.12 -0.69 0.25 0.43 1.94 -0.06 1.21 1.47 0.98 0.25 0.25 -1.41 0.88 1.53 2.35 1.16 1.71 1.49 0.86 1.59 0.95 0.68 0.75 0.73 2.07 3.02 2 0.7- 0.05 0.91 1.23 1.07 2.57 _ 1.51 1.81 _ U.33~ 1.03 2.03 0.5 1.57 0.85 1.62 0.7 1.9 0.54 0.52 _ 027 298R -A nq Ar W-,1 0.77 -0.99 0.38 38 _ 0.74 _ -1.1 1.3 1.15 1.03 1.09 1.17 0.73 1.44 1 1.99 0.37 1.15 2.15 0.89 1.03 0.8 0.75 0.63 0.77 1.34 0.94 1.24 1.65 1 0.65 1 2.96 1.04 0.93 0.550 .81 0.59 1.23 0.04 -0.07 1.20 0.57 0.48 -0.06 0.53 1.33 0.47 0.87 0.70 1.44 0.86 1.91 0.7 0.61 1.38 0.9 1.33 2.06 0.66 0.19 0.71 1.15 0.59 2.15 1.42 2.58 0.53 0.31 0.49 0.92 1.1 3.8 1.50 1.68 0.58 1.09 0.5 1.28 0.56 2.22 0.92 1.54 0.69 1.74 0.58 0.7 -0.76 0.94 0.55 1.82 0.24 1.09 0.16 0.35 -0.7 -0.11 0.57 0.73 0.63 1.01 0.51 0.63 0.85 -0.04 0.96 0.78 0.49 0.1 0.57 1.1 0.47 1.21 1.85 1.17 0.74 1.08 0.34 0.79 2.17 1.42 0.12 1.47 1.86 1.59 2.67 0.92 3.97 1.14 0.94 1.67 0.57 1.67 1.88 1.61 1.55 0.98 1.35 0.59 2.22 0.66 0.94 0.65 0.37 1.31 0.43 1.57 0.81 1.21 1.56 1.11 1.47 1.14 2.52 0.68 1.26 1.25 2.06 0.83 1.94 1.35 1.46 1.28 1.69 1.37 1.25 1.35 1.48 1.30 0.71 1.31 1.12 0.72 1.33 0.79 -0.03 1.36 1.9 1.21 0.92 1.37 1.39 1.31 1.48 1.33 1.05 1.68 0.57 1.29 1.57 1.01 .2.1 1.16 0.63 1.32 1.04 0.88 0.28 0.96 1.01 1.09 0.58 1.28 0.31 0.78 -0.13 0.93 1.47 0.52 0.18 0.65 0.45 1.11 1.76 1.67 2.07 1.76 0.91 0.38 0.87 1.61 1.04 -0.1 0.92 3.11 0.90 0.44 1.09 0.47 0.45 1 0.18 0.92 0.64 1.16 0.45 0.95 1.32 0.92 1.18 0.38 1.1 2.42 1.16 1.55 0.9 2.58 1.09 0.93 1.21 1.58 1.07 1.9 0.92 1.53 1.04 0.29 1.18 0.9 1.3 0.78 0.99 1.05 0.93 1.2 1.67 1.14 1.79 1.97 1.50 1.3 1.71 -0.1 1.14 1.41 1.09 .1.13 1.12 1.3 1.14 0.93 1.55 1.27 1.68 1 0.97 -0.31 1.42 2.51 0.64 -0.33 0.77 0.79 0.33 0.87 0.92 0.7 2.17 1.12 0.63 1.49 1.97 1.46 1.56 1.47 1.27 1.26 1.35 1.33 0.87 1.27 1.19 1.21 0.36 0.98 1.34 0.62 0.7 2.08 1.31 1.27 0.70 1.16 2.02 1.18 2.12 0.43 1.18 -0.11 0.84 1.17 0.47 0.76 0.7 1.51 1.96 1.14 2.52 1.71 2.11 1.68 1.5 1.24 0.24 1.44 0.73 1.27 1.35 1.2 0.30 1.34 1.61 1.04 1.93 0.25 -0.31 -0.18 0.53 0.41 1.44 3.02 1.3 0.56 0.73 0.48 0.34 0.08 1.28 0.96 1.32 0.45 1.33 0.1 0.430.83 0.99 0.91 0.76 0.25 2.51 0.69 0.30 0.56 1.08 1.88 0.94 0.24 1.56 1.20 0.74 1.3 1.53 1.00 0.26 1.16 0.91 1.05 0.77 1.12 0.93 1.10 0.8 1.13 1.15 0.38 0.72 -0.19 0.99 0.84 0.98 0.96 1.25 0.1 0.68 -0.36 1.10 1.76 0.55 0.65 1.09 0.37 1.17 1.24 1.40 1.5 1.25 2.03 1.05 0.27 0.98 1.82 0.8 2.01 1.56 1.25 -0.11 1.37 1.27 1.21 0.81 1.17 1.33 1.63 1.2 2.07 1.44 1.44 1.45 1.09 0.29 1.3 1.22 0.6 1.33 1.05 1.13 0.13 1.27 0.37 0.24 0.39 0.42 0.96 1.01 0.86 0.47 0.71 0.42 1.1 0.6 0.67 0.77 -0.02 0.77 1.71 0.64 0.72 1.21 1.61 1.19 0.59 0.43 0.78 0.94 1.20 1.35 1.12 39 2.67 1.45 -0.21 1.78 1.24 1.02 1.08 0.95 1.31 0.96 0.99 0.83 2.17 1.36 0.78 -0.22 0.78 0.78 0.77 0.86 1.63 1.12 1.69 1.83 2.03 0.04 0.38 0.16 1.55 1.28 0.88 1.11 0.92 1.57 0.43 0.56 1.65 0.31 0.22 -0.16 1.77 1.22 1.00 0.72 0.93 1.95 0.22 1.8 1.21 0.64 0.78 1.58 0.88 0.22 0.41 0.3 1.07 1.12 0.43 0.51 -0.48 0.39 0.05 1 1.02 0.56 0.82 0.54 1.36 1.04 1.38 0.94 0.52 0.56 0.59 1.38 0.21 0.38 1.7 1.03 1.00 1.14 0.72 1.38 1.28 2.18 0.94 0.35 0.99 0.7 1.35 1.82 0.58 1.82 0.74 0.42 1.05 1.13 1.33 0.69 0.6 1.16 1 0.73 1.12 0.49 1.26 0.94 1.43 1.06 1.6 1.15 0.85 0.73 0.70 0.2 0.73 0.72 0.86 1.09 1.34 1.5 1 1.58 1.29 0.93 0.81 0.91 0.95 0.91 1.02 0.86 0.97 0.83 1.12 0.82 0.31 2.08 1.51 0.44 0.79 0.39 1.01 0.85 1.01 2.02 0.87 1.33 0.92 0.78 0.38 -0.49 .0.6 0 0.86 0.45 0.26 0.84 0.09 1.07 0.59 1.36 1.1 0.53 0.71 0.15 0.27 0.28 0.53 0.68 0.45 -0.05 1.14 3.18 1.65 1.05 1.8 0.54 0.49 0.51.31 2.86 0.82 0.44 -0.14 0.65 0.45 0.79 -0.18 0.83 1.47 0.42 1.13 0.78 0.66 1.98 0.58 0.33 0.5 0.65 0.88 0.59 0.83 1.99 1.30 1.65 1.39 0.3 0.93 0.68 0.33 1.48 1.15 0.1 0.39 0.31 0.46 0.88 1.57 2.94 1.21 0.89 1.11 0.76 1.31 0.48 0.90 0.6 0.88 1.39 1.17 0.63 1.16 1.37 1.16 0.13 1.39 0.44 0.73 1.19 1.06 1.16 1.7 0.70 0.14 0.86 0.26 0.90 1.06 0.83 1.16 1.05 1.03 1.02 1.18 1.03 -0.08 1.09 1.89 1.01 0.07 1.22 0.71 1.16 1.71 1.36 -0.31 1.32 1.26 1.48 1.27 1.2 1.46 -0.17 1.36 1.23 1.24 1.4 1.75 1 1.48 0.88 0.99 1.64 1.9 1.15 0.49 1.15 1.5 1.35 1.10 1.32 1 1.35 1.58 1.13 1.58 1.19 1.44 -0.5 1.23 2.03 0.90 1.05 1.47 1.15 1.93 0.81 1.67 0.66 0.38 0.75 0.65 0.04 1.26 1 1.72 0.92 1.19 0.39 1.14 0.95 2.63 1.19 0.94 1.86 0.87 1.01 2.22 0.12 1.04 0.98 0.60 0.1 0.84 0.09 0.99 0.68 1.11 0.89 0.82 1.85 0.58 1.41 0.57 1.21 0.6 0.22 0.48 0.81 0.45 0.49 0.71 0.58 0.75 0.55 1.07 -1.01 1.38 1.08 0.61 -0.21 0.96 -0.22 0.53 0.63 0.44 0.91 0.31 0.71 0.15 0.95 0.40 0.44 0.49 -0.28 0.59 1.12 0.42 0.95 0.66 1.94 0.66 -0.89 0.49 1.12 0.54 0.14 0.47 0.58 0.49 0.27 0.72 0.84 0.64 1.13 0.54 0.38 1.06 -0.11 0.89 0.93 0.93 0.65 0.37 0.65 0.34 -0.67 0.99 1.24 1.12 -0.03 1.00 0.8 0.96 1.32 0.81 0.88 0.99 -0.58 0.55 0.61 0.67 -0.21 0.74 0.35 0.9 0.59 0.760.92 0.22 0.89 0.39 1.09 0.51 0.65 0.35 0.74 1.91 0.38 0.46 1.33 2.03 0.21 0.32 1.49 0.77 0.32 0.77 1.07 0.66 1.09 0.98 -0.54 0.66 0.84 0.64 0.35 0.88 0.94 0.88 0.72 0.69 0.39 0.8 0.57 1.08 0.96 0.94 2.42 41.12 0.8210.41 0.85 1.53 0.57 -0.27 0.61 1.28 0.51 0.57 0.58 -0.27 1.36 0.68 1.65 0.72 0.89 0.64 0.86 1.72 MAS Masco Corp. HSY Hershey Foods UK Union Carbide MOB Mobil Corp. NSP Northern States Power 1.10 1.41 1.07 0.34 1.84 -0.12 1.1 0.74 1.20 1.66 0.78 1.13 0.48 1.28 2.13 -0.39 Helmerich & Payne HP WHR Whirlpool Corp. SGP Schering-Plough MTC Monsanto Company BGG Briggs & Stratton Weights 0.00 0.01 0.02 0.02 0.04 0.12 0.07 0.04 0.03 0.11 0.03 0.05 0.00 0.16 0.01 0.02 0.00 0.08 0.11 0.10 0.00 0.01 0.04 0.01 0.00 0.00 0.00 0.07 0.09 0.21 0.03 0.09 0.00 0.04 0.04 0.13 0.14 0.06 0.07 0.12 0.06 0.11 0.0510.07 0.0910.08 0.04 0.05 0.10 0.06 0.02 0.14 0.12 0.06 0.02 0.10 0.02 0.14 0.00 0.16 0.06 0.10 0.10 0.14 0.11 0.05 0.04 0.15 0.03 0.11 0.04 0.04 0.05 0.11 0.00 0.05 0.00 0.00 0.00 0.00 0.10 0.20 0.04 0.13 0.12 0.10 0.05 0.08 0.10 0.05 0.05 0.16 0.09 0.04 0.0610.02 0.05 0.07 0.07 0.00 0.08 0.10 0.04 0.01 0.08 0.05 0.09 0.11 0.11 0.03 0.07 0.09 0.09 0.05 0.05 0.05 0.16 0.11 0.13 0.08 0.05 0.15 0.10 0.11 0.05 0.13 0.00 0.06 0.05 0.01 0.18 0.17 0.19 0.20 0.18 0.21 0.14 0.22 0.16 0.11 0.09 0.12 0.03 0.12 0.10 0.18 0.02 0.07 0.09 0.0510.08 0.13 0.14 0.05 0.01 0.09 0.08 0.10 0.21 0.12 0.12 0.17 0.12 0.09 0.22 0.22 0.03 0.16 0.00 0.13 0.10 0.14 0.04 0.12 0.00 0.13 0.05 0.11 0.08 0.10 0.16 0.15 0.00 0.02 0.14 0.12 0.15 0.13 0.10 0.07 0.24 0.05 0.17 0.14 0.18 0.04 0.22 0.12 0.33 0.1310.29 0.16 0.31 0.06 0.62 0.10 0.41 0.22 0.22 0.11 0.37 0.21 0.27 0.21 0.39 0.05 0.23 0.03 0.22 0.10 0.28 0.09 0.50 0.04 0.44 0.10 0.33 0.09 0.30 0.10 0.19 0.00 0.35 0.12 0.57 0.00 0.00 0.09 0.10 U.02 0.13 0.02 0.10 0.01 0.16 0.00 0.13 0.05 0.14 0.00 0.15 0.00 0.26 0.00 0.191 0.00 0.21 0.07 0.40 0.03 0.27 0.00 0.13 0.01 0.26 0.00 0.18 0.00 0.24 0.03 0.15 0.19 0.18 0.18 0.18 0.00 0.29 0.03 0.30 0.00 0.24 0.03 0.20 0.08 0.16 0.07 0.21 0.14 0.47 0.13 40 0.02 0.01 0.02 0.05 0.00 0.00 0.02 0.03 0.08 0.05 0.04 0.04 0.05 0.02 0.06 0.13 0.12 0.02 0.04 0.02 0.05 0.07 0.05 0.23 0.11 0.07 0.08 0.05 0.11 0.05 0.11 0.14 0.11 0.02 0.00 0.01 0.02 0.06 0.08 0.04 0.12 0.06 0.04 0.00 0.07 0.09 0.06 0.06 0.00 0.02 0.09 0.07 0.04 0.10 0.07 0.12 0.14 0.11 0.05 0.04 0.03 0.03 0.05 0.08 0.05 0.10 0.05 0.07 0.02 0.09 0.12 0.09 0.03 0.00 0.00 0.04 0.16 0.00 0.13 0.14 0.06 0.00 0.16 0.14 0.13 0.00 0.05 0.07 0.04 0.00 0.00 0.06 0.15 0.00 0.15 0.03 0.06 0.07 0.13 0.00 0.03 U.1b 0.05 0.12 0.18 0.11 0.04 0.07 0.11 0.04 0.12 0.10 0.08 0.08 0.03 0.05 0.2110.07 0.12 0.09 0.12 0.00 0.02 0.02 0.06 0.03 0.06 0.10 0.05 0.16 0.05 0.02 0.06 0.05 0.08 0.11 0.13 0.08 0.06 0.10 0.12 0.00 0.07 0.11 0.08 0.03 0.16 0.12 0.18 0.14 0.07 0.02 0.1b U.U U.U/ 0.13 0.14 0.08 0.19 0.08 0.28 0.06 0.21 0.09 0.19 0.15 0.21 0.06 0.25 0.101 0.09 0.09 0.07 0.06 0.09 0.15 0.24 0.12 0.23 0.14 0.11 0.13 0.16 0.32 0.18 0.14 0.17 0.16 0.04 0.07 0.06 0.20 0.16 0.10 0.06 0.11 0.11 0.08 0.14 0.06 0.14 0.13 0.16 0.15 0.18 0.11 0.08 0.12 0.08 0.06 0.12 0.04 0.13 0.09 0.16 0.19 0.23 0.09 0.11 0.07 0.08 0.14 0.09 0.12 0.02 0.11 0.04 0.16 0.00 0.06 ' 0.05 a 0.15 *0.00 S0.05 S0.02 0.06 S0.05 I.07 0.02 0.16 0.04 0.07 0.02 0.04 0.04 0.00 0.10 0.12 0.09 0.09 0.15 0.11 013 0.10 0.01 0.05 0.07 0.05 0.06 0.14 0.13 MAS Masco Corp. HSY Hershey Foods UK Union Carbide MOB Mobil Corp. NSP Northern States Power HP 0.05 0.16 0.13 0.09 0.17 0.14 0.13 014 0.06 0.31 0.17 0.10 0.16 0.20 0.13 13 06 T0 007 0.00 0.04 0.00 0.13 0.07 0.00 1 0.02 0.04 0.02 0.12 0.06 0 0.05 0.31 0.27 0.58 0.54 0.25 0.13 0.22 0.22 0.27 0.12 0.08 0.08 0.27 0.04 0.07 0.03 0.40 0.00 0.03 0.04 0.39 0.0055 0.00 0.21 0.05 0.08 0.09 0.14 0.09 0.07 0.06 0.23 0.08 0.07 0.04 018 0.14 0.14 0.05 0.07 0.09 0.22 0.09 0.05 0.20 0.23 0.04 0.00 0.06 0.05 0.08 0.05 0.04 0.06 0.04 0.09 0.02 0.04 0.08 0.07 0.05 0.00 0.04 0.00 0.04 0.07 0.06 0.06 0.01 0.03 0.13 013 0.14 0.16 0.09 0.11 0.12 0.07 0.13 0.14 0.13 0.06 0.13 0.09 0.10 0.15 0.12 0.06 0.10 0.05 0.08 0.06 0.07 0.09 0.06 Helmerich & Payne WHR Whirlpool Corp. 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W SHW Sherwin-Williams Weights U.U0I U.U41 U.Ul V., uI I 0.03 0.01 0.06 0.02 I 0.08 0.08 0.08 0.09 0.16 0.00 0.18 0.11 ________________________________ 0.181 0.00 0.16 0.09 0.28 0.27 0.38 0.18 0.20 0.27 0.28 0.14 0.09 0.11 0.09 0.05 0.09 0.09 0.07 0.06 0.01 0.09 0.00 0.05 - a~ 0.011 0.10 0.01 0.09 43 u 0.08 0.111 0.16 0.15 0.02 0.07 0.19 0.161 U.UI .Ui .zz U.zz 0.031 0.03 0.03 0.11 0.031 0.04 0.05 0.08 0.15 0.19 0.07 0.11 0.141 0.16 0.08 0.08 v.uz 0.06 0.03 0.05 0.09 u.ui U.U0I .1i 0.061 0.03 0.08 0.11 0.101 0.10 0.13 0.10 0.111 0.07 0.13 0.10 0.15 6 0.07 7 0.17 0.00 0.07 0.08 0.09 0.14 7 0.00 0.13 0.00 7 0.0C 80 0.07 0.01 0.06 0.11 0.07 0.10 86 0.07 0.11 0.05 0.00 90.23 9 0.06 9 0.04 9 0.05 94 0.05 9 0.10 0.07 0.15 0.09 0.18 0.02 0.10 0.07 0.16 0.21 0.07 0.15 0.02 0.04 0.05 0.03 0.06 0.12 0.11 0.10 0.05 0.04 0.00 0.00 0.17 0.08 0.04 0.05 0.04 0.11 0.07 0.22 0.29 0.21 0.21 0.10 0.15 0.12 0.26 0.22 0.35 0.24 0.17 0.21 0.22 0.13 0.11 0.10 0.09 0.00 0.27 0.09 0.00 0.06 0.08 0.06 0.01 0.17 0.12 0.03 0.18 0.24 0.18 0.18 0.11 0.15 0.07 0.13 0.20 0.24 0.22 0.20 0.11 0.23 0.12 0.11 0.09 0.08 0.01 0.55 0.09 0.00 0.11 0.1C 0.06 0.03 0.13 0.12 0.07 0.28 0.21 0.30 0.38 0.32 0.56 0.26 0.14 0.20 0.12 0.28 0.18 0.19 0.21 0.40 0.25 0.16 0.16 0.27 0.4C 0.35 0.23 0.10 0.34 0.27 0.20 0.10 0.16 0.18 MRO USA-Marathon Giroup WIN Winn-Dixie DTE DTE Energy Co. CHA Champion International WMB Williams Cos. TRW TRW Inc. TAN Tandy Corp. ETR Entergy Corp. W SHW 0.28 0.09 0.17 0.01 0.27 0.05 0.33 0.02 0.24 0.02 0.50 0.0C 0.17 0.02 0.05 0.10 0.14 0.08 0.12 0.06 0.25 0.04 0.12 0.03 0.19 0.02 0.17 0.11 0.35 0.00 0.21 0.00 0.1C 0.06 0.16 0.08 0.15 0.05 0.17 0.07 0.36 0.04 0.22 0.06 0.06 0.16 0.26 10.0 0.25 0.05 0.17 0.09 0.16 0.07 0.16 0.02 0.16 0.08 0.08 0.01 0.03 0.01 0.07 0.00 0.04 0.01 0.03 0.04 0.03 0.03 0.05 0.00 0.14 0.00 0.06 0.00 0.09 0.04 0.05 0.01 0.07 0.13 0.08 0.00 0.09 0.01 0.02 0.03 0.04 0.10 0.07 0.09 0.14 0.07 0.10 0.07 0.16 0.12 0.10 0.09 0.06 0.0C 0.14 0.06 0.07 10.0 0.06 0.04 0.09 0.05 0.09 0.03 0.05 0.03 0.07 0.11 0.01 0.02 0.0C 0.03 0.06 0.04 0.06 0.02 0.01 0.05 0.05 0.11 0.05 0.03 0.05 0.08 0.12 0.08 0.06 0.08 0.07 0.00 0.07 0.05 0.07 0.04 0.02 0.04 0.09 Westvaco Corp. Sherwin-Williams 44 0.05 0.07 0.06 0.04 0.12 0.02 0.10 0.07 0.07 0.05 005 0.14 0.14 0.19 0.09 0.19 0.21 0.24 0.16 0.03 0.30 0.21 0.10 0.09 0.11 0.18 0.17 0.10 0.13 0.06 0.00 0.02 0.04 0.09 0.07 0.07 0.10 0.04 0.00 0.05 0.03 0.03 0.09 0.10 0.13 0.08 0.01 0.04 0.13 0.04 0.00 0.01 0.09 0.06 0.03 0.06 0.13 0.11 0.05 0.06 0.11 0.13 0.04 0.05 0.12 0.11 0.00 0.02 0.14 0.33 0.09 0.00 0 0.18 0.0C 0.02 0.17 0.15 0.15 0.14 0.09 0.21 0.00 0.01 0.14 0.13 0.00 0.00 0.26 0.17 0.00 0.00 0.15 0.18 0.08 0.07 0.03 0.16 0.01 0.06 0.03 0.22 0.04 0.09 0.16 0.01 0.00 0.00 0.0C 0.24 0.01 0.05 0.06 0.20 0.17 0.20 0.15 0.08 0.02 0.06 0.24 0.08 0.04 0.06 0.29 0.12 0.01 0.03 0.36 0.18 0.03 0.05 0.25 0.14 0.04 0.03 0.06 0.15 0.07 0.07 0.14 0.14 0.00 0.03 0.18 0.04 0.07 0.10 0.08 0.11 0.06 0.07 0.10 0.05 0.11 0.08 0.07 0.16 0.01 0.02 0.12 0.11 0.05 0.06 0.15 0.09 0.00 0.01 0.07 0.11 0.05 0.13 0.21 0.11 0.08 0.07 0.06 0.11 0.16 0.14 0.11 0.13 0.06 0.05 0.06 0.26 0.04 0.04 0.00 0.08 0.13 0.1C 0.06 0.11 0.04 0.07 0.09 0.13 0.06 0.06 0.04 0.20 0.03 0.03 0.0C 0.16 0.08 0.09 0.01 0.06 0.20 0.16 0.00 0.04 0.09 0.09 0.13 0.14 0.14 0.15 0.05 0.0( 0.0C 0.00 0.0C 0.04 0.00 0.06 0.01 0.18 0.07 0.05 0.11 0.22 0.02 0.05 0.00 0.22 0.00 0.03 0.00 0.24 0.02 0.05 0.06 0.24 0.09 0.08 0.06 0.06 0.14 0.16 0.17 0.10 0.12 0.11 0.13 0.13 0.12 0.13 0.09 0.07 0.09 0.08 0.10 0.17 0.08 0.14 0.10 0.09 0.05 0.02 0.07 0.06 0.06 0.03 0.03 0.04 0.09 0.03 0.0( 0.00 0.10 0.04 0.03 0.07 0.08 0.16 0.10 0.11 Test 6 $1irtial imestmert omr 35 years 10 ;10 0 5 15 10 20 25 30 35 ramber df Yeas Betas U.UU 0.79 0.62 0.50 0.53 0.37 2 0.40 0.3 0.36 0.74 0.40 0.48 0.34 0.64 0.76 0.47 0.98 -0.04 0.65 0.3 0.81 0.47 0.79 0.04 0.9 0.75 0.94 1.13 0.56 2.12 0.48 0.58 0.45 0.5 1.02 1.09 1.05 0.7 U. /I U.03 U. 14 -U.UD 0.29 0.30.07 0.25 0.59 0.58 0.45 0.88 -0.16 -2 0.63 0.22 0.66 _-3.51 1.78 -0.19 0.18 0.24 0.36 0.33 0.60 0.8 0.28 0.36 0.25 -0.33 0.43 1.72 0.35 0.35 0.49 0.76 0.32 0.25 0.49 0.40.35 -0.44 0.06 0.96 0.74 1.56 0.45 0.11 0.26 0.15 0.24 0.35 0.32 2.23 -0.06 1.64 0.63 0.59 0.79 1.43 0.30 0.02 0.76 0.50.55 0.2 .0.17 0.96 0.50 0.36 0.54 0.28 0.53 0 0.56 0.56 0.6 0.19 0.83 0.39 0.48 0.49 0.69 0.56 0.45 0.26 0.53 0.56 0.68 0.29 0.19 0.8 0.70 1.17 0.81 0.92 0.34 0.64 0.62 0.25 0.69 0.72 0.46 1.16 0.44 1.06 0.30 -0.25 0.44 -0.32 0.5 0.51 0.3 0.93 -1.05 1.04 I 0.71 0.71 1.02 1.19 0.92 1.67 0.78 0.41 0.61 _ 0.72 0.34 I.00 U. I / 1.6 0.76 0.62 2.38 1.39 -2.08 1.41 2.10 1.56 -0.77 0.74 2.65 1.12 0.05 0.73 2.25 1.64 3.2 0.21 1.71 1.12 0.12 -1.17 1.29 0.82 -0.89 1.21 1.27 0.63 0.19 -1.22 1.64 1.41 -0.58 0.63 1.69 0.27 0.76 1 1.77 45 1.98 0.85 2.73 3.4 1.66 3.06 -1.26 3.98 2.1 4.17 0.67 2.58 2.78 1.34 1.78 1.87 0.26 1.43 1.32 0.64 1.32 1.47 0.51 1.54 2.62 0.81 1.86 1.1 U.o., -U.'+I 0.83 1.35 1.13 0.69 0.8 1.27 1.22 0.57 2.73 1.8 1.01 1.99 3.26 0.55 1.95 0.29 0.97 1.26 0.93 0.76 0.73 -0.2 0.95 0.91 0.93 1.06 1.03 -0.51 1.22 1.17 1.47 1.05 1.66 1.08 1.07 1.35 1.18 0.52 1.11 1.75 0.94 2.06 0.47 0.89 0.99 1.09 1.08 1.06 0.34 1.11 1.32 0.99 1 0.99 0.59 1.07 0.77 0.4 0.16 0.93 0.47 -0.51 0.64 0.92 0.42 0.92 1.13 1.79 0.79 1.16 2.24 0.68 1.85 1.32 1.04 1.17 I-' I. 1.74 1.73 1.38 0.90 1.16 1.19 0.70 0.91 1.02 1.25 1.33 1.18 1.86 2 0.69 1.78 0.86 0.54 0.84 1.64 1.07 1.17 1.21 0.36 1.2 2.1 0.47 0.79 0.37 0.54 1.1 0.48 1.45 1.27 -0.07 1.37 1.14 2.26 0.71 1.87 1.42 1.60 2.07 2.07 1.84 1.33 1.17 0.28 2.98 1.07 0.51 1.9 3.22 1.43 1.42 1.42 1.39 1.55 3.15 0.61 4.64 4.19 1.51 1.81 3.02 2 1.71 1.48 1.78 2.24 0.27 1.68 0.74 0.73 1.44 -1.1 0.15 -0.23 0.24 0.12 1.22 0.2- 0.69 1.54 0.25 1.84 0.03 2.27 1.13 0.54 1.15 1.56 1.82 0.8 2.01 1.27 1.12 1.17 0.90 -0.02 1.11 0.36 1.10 1.08 0.41 0.86 0.33 0.49 -0.11 1.38 2.77 0.71 1.44 2.03 1.56 0.61 0.43 0.53 -0.17 0.26 0.08 0.63 1.04 1.45 1.15 1.47 0.93 0.94 0.87 0.97 0.53 1.25 -0.11 1.14 0.62 1.41 1.77 1.48 1.61 1 0.7 1.02 0.63 0.65 0.44 0.59 0.45 1.13 0.64 0.95 0.90 0.06 0.95 1.37 1.27 1.77 0.7 1.81 0.61 0.14 0.69 0.36 0.68 0.64 0.6 0.80 0.88 0.79 0.8 1.28 1.31 1.26 0.69 1.2 0.18 0.2 0.6 0.62 2.06 0.32 1.12 1.22 4.07 1.89 0.90 0.27 0.93 0.47 0.95 0.45 0.28 0.30 0.09 0.26 0.75 0.15 0.63 0.12 0.42 1.72 0.17 0.38 0.21 0.34 0.8 0.69 0.43 0.76 0.49 1.01 2.29 0.83 0.88 0.84 1.39 0.72 1.13 0.92 0.45 1.03 0.56 0.88 0.19 0.99 0.89 0.54 0.32 0.62 0.5 -0.04 0.38 0.84 0.24 0.27 0.28 0.41 0.22 0.68 0.48 0.43 0.63 0.61 0.64 0.54 1.24 0.61 0.07 0.74 -0.57 0.5 0.84 0.77 0.48 0.05 0.42 0.89 0.98 0.69 0.69 -0.73 0.36 0 0.31 1 0.2 0.87 0.55 0.9 0.9 0.72 1.04 0.72 0.51 1.16 1.1 1.25 0.58 1.26 1.4 1.13 1.06 1.10 1.2 1.09 0.96 1.17 1.13 1.12 1.33 0.23 -0.44 0.37 -0.1 0.20 0.65 0.18 0.01 0.49 0.79 0.35 0.7 0.31 -0.23 0.42 0.34 0.36 0.35 0.36 0.37 0.37 0.61 0.26 0.69 0.39 0.21 0.34 0.97 1.17 0.71 -0.31 0.71 0.93 0.6 0.7 0.96 1.07 0.66 0.81 0.87 1.71 0.97 0.84 -0.45 0.96 0.98 0.95 -0.19 0.70 0.33 0.78 1.02 1.19 0.64 0.72 0.78 0.03 0.68 0.66 0.59 1.03 0.83 0.53 0.81 0.45 0.33 0.6 0.52 0.56 0.36 0.58 0.84 0.57 0.39 0.59 0.46 0.45 1.19 0.25 0.9 0.48 0.69 0.38 0.91 0.67 0.56 0.89 -0.67 0.73 0.79 0.79 0.38 0.75 0.97 0.72 0.36 0.80 0.36 1.67 0.22 1.27 0.48 1.65 1.25 1.64 2.25 1.18 1.40 1.44 1.35 0.71 1.01 0.68 0.43 0.67 0.58 0.71 1.37 0.5 0.91 0.60 0.54 0.65 0.61 0.69 0.79 0.62 0.54 0.56 0.59 0.69 0.1 0.84 0.36 0.56 0.34 0.51 0.88 0.54 0.02 0.84 1.63 0.88 1.14 1.14 2.14 0.79 2.42 1.21 1.10 0.39 1.42 0.67 0.39 0.81 0.41 1.12 0.52 1.39 0.78 0.58 1.26 0.33 1.42 1.98 1.21 1.11 0.21 1.43 1.02 2.2 -0.39 1.21 1.03 1.3 0.66 -0.53 _ 1.23 2.52 1.51 0.51 1.79 1.14 0.57 0.49 1.75 1.58 1.24 -0.21 1.54 1.69 1.07 0.84 1.31 1 2.08 1.8 0.9 1.42 1.32 1.75 -0.07 1.17 0.7 1.2 0.85 0.32 0.98 0.7 1.41 1.11 1.38 1.37 1.04 1.61 1.02 2.98 1.24 2.21 0.02 1.58 1.29 1.59 2.04 -0.06 0.86 0.98 1.25 0.28 1.47 1.03 1.57 1.13 1.77 0.59 2.01 1.23 2.1 1.34 2 1.25 0.75 0.11 0.97 .2.14 1.33 0.01 1.49 _ 1.87 2.01 0.34 2.07 0.8 1.29 0.47 1.64 0.01 2.57 - 1.24 -0.54 1.16 0.25 1.49 0.37 1.92 1.17 1.98 1.42 1.59 1.49 1.01 1.48 1.67 1.34 2.25 2.43 1.26 0.65 1.8- 1.52 1.24 1.74 0.96 1.64 1.28 1.47 _ 0.91 1.07 1.34 1.1 0.12 0.94 0.9 0.62 0.62 1.76 1.38 0.62 1.46 1.61 1.04 1.93 0.53 10.73 1.28 0.96 1.32 1.86 1 2.83 2.35 1.22 1.27 1.29 0.49 1.06 0.98 1.4 0.54 1.42 1.28 1.46 -0.22 0.12 1.87 1.65 1.78 1.72 1.04 1.02 0.86 .1.17 1.73 0.93 0.61 1.23 0.94 1.24 1.31 2.41 -0.54 1.25 1.74 1.44 1.6 1.56 1.31 0.59 0.28 1.02 0.98 1.17 0.8 1.30 1.3 1.36 1.55 -0.22 1.1 1.12 3.17 0.81 0.68 0.87 0.74 46 2.68 1.12 1.22 1.29 1.19 1.11 1.34 1.11 _ 1.31 1.41 0.74 1.14 1.14 0.4 1.14 2.2 1.23 0.7 1.05 1.64 0.39 -1.15 2.19 1.69 0.89 0.65 1 2.27 0.74 2.56 1.68 1.73 1.22 1.3 0.89 1.44 0.62 0.92 1.16 0.93 0.54 0.54 0.81 0.46 1.41 1.9 2.65 1 0.91 0.95 0.97 0.31 1.01 0.85 1.33 -0.49 0.84 0.09 0.8 0.94 0.14 2.68 1.5 1.53 0.79 -0.69 1.82 0.74 0.42 1 1.26 0.70 0.2 0.72 1.20 1.06 1.29 0.67 0.06 1.07 1.02 1.2 1.21 0.78 1.58 1.12 -0.48 0.54 1.36 0.52 0.21 0.72 1.38 0.35 1.22 0.91 1.36 0.79 0.45 1.26 1.15 1.64 0.75 1.09 .36 1.1 0.61 1.32 1.34 1.13 1.65 1.77 1.22 1.95 1.54 1.41 1.41 2.78 1.59 2.63 1.24 2.51 1.08 1.88 0.94 0.78 1.63 1.12 1.69 2.03 1.55 1.28 1.57 1.86 0.15 2.28 0.92 2.03 2.08 2.3 0.97 0.13 1.23 1.33 0.99 0.91 0.76 1.98 2.66 1.42 _ 1.09 0.33 1.31 0.65 1.56 1.18 1.55 1.52 1.22 1.73 1.31 1.17 1.3 1.44 3.02 1.3 0.90 0.73 0.81 1.34 0.56 0.28 0.7 0.3 0.90 0.45 0.88 11.17 0.69 -0.31 1.31 1.25 1.06 1.38 0.66 0.75 0.62 1.35 1.27 1.12 1.96 1.21 0.81 1.17 1.12 -1.26 1.27 0.89 1.43 1.39 0.76 1.41 0.77 1.32 1.36 1.32 0.61 1.57 1.22 1.82 0.11 -1.05 0.33 -0.12 1.23 2.31 0.52 0.2 0.66 0.08 0.8 -0.29 1.36 0.64 1.34 1.050.41 1.42 1.35 1.56 1.25 0.88 0.61 1 -0.15 1.48 0.05 1.53 0.8 0.78 0.6 1.65 1.63 0.82 1.62 2.15 0.65 0.41 1.27 1.43 0.46 2.03 1.45 2.14 1.29 0.69 1.00 0.21 1.60.14 1.07 0.51 1.23 0.99 0.68 0.32 0.95 1.12 0.39 0.65 1.26 0.74 1.04 1.42 1.1 0.27 1.14 3.18 0.54 1.59 2.07 1.72 -0.08 2.86 1.46 1.5 1.54 0.79 -0.18 1.13 0.51 0.94 0.58 1.29 1.12 1.48 1.53 0.09 2.02 0.83 1.99 0.3 0.66 1.47 1 1.48 S0.73 0.72 0.78 0.56 0.06 0.51 0.309 05607 0.41 0.87 1.4 1 1.29 Procter & Gamble PG PCG 0.98 2.01 0.32 1.81 3.17 1.63 1.97 0.73 2.03 0.92 1.4 0.8 0.76 0.32 1.16 0~680.4 I.30 1.40.932 19003 0.907 0.8 1.2 0.75 -0.59 1.42 0.81 1.57 -1 0.67 .0.42 1.19 --0.81- 1.39 0.9 0.61 1.28 1.331 0.51 0.64 -0.83 O~4054 1 055.9 1.06 1.05 0.88 0.72 PG&E Corp. DTE DTE Energy Co. BF.B Brown-Forman Corp. MZ Milacron Inc. MOT Motorola Inc. UCL Unocal Corp. N Inco, Ltd. F Ford Motor HP 0.71 0.37 0.66 Helmerich & Payne Weights 0.20 U.18 0.05 U.04 0.29 U.26 0.12 0.11 0.03 0.05 0.03 0.04 0.18 0.15 0.10 0.13 0.00 0.02 0.00 0.00 0.17 0.08 0.19 0.23 0.17 0.14 0.08 0.25 0.18 0.05 0.03 0.14 0.00 0.15 0.06 0.07 0.09 0.10 0.00 0.03 0.28 0.22 0.12 0.00 0.12 0.14 0.12 0.15 0.23 0.20 0.14 0.05 0.17 0.16 0.13 0.11 0.17 0.08 0.15 0.12 0.13 0.14 0.14 0.09 0.12 0.21 0.18 0.18 0.00 0.19 0.20 0.15 0.13 0.10 0.13 0.16 0.15 0.08 0.14 0.22 0.38 0.23 0.23 0.33 0.52 0.39 0.26 0.18 0.22 0.42 0.12 0.23 0.16 0.00 0.30 0.17 0.10 0.09 0.07 0.12 0.12 0.10 0.08 0.13 0.15 0.22 0.15 0.16 0.21 0.42 0.28 0.19 0.16 0.18 0.26 0.13 0.17 0.15 0.00 0.23 0.08 0.17 0.15 0.06 0.06 0.09 0.18 0.10 0.10 0.05 0.17 0.09 0.07 0.02 0.16 0.07 0.20 0.02 0.10 0.00 0.21 0.05 0.17 0.00 0.03 0.05 0.08 0.02 0.07 0.07 0.14 0.10 0.03 0.09 0.02 0.10 0.07 0.11 0.00 0.08 0.04 0.09 0.11 0.06 0.03 0.13 0.06 0.02 0.10 0.00 0.00 0.09 0.00 0.00 0.00 0.00 0.01 0.00 0.06 0.00 0.00 0.00 0.04 0.02 0.00 0.01 0.00 0.14 0.00 0.11 0.01 0.00 0.01 0.03 0.00 0.03 0.10 0.00 0.02 0.02 0.04 0.05 0.01 0.09 0.02 0.02 0.02 0.06 0.04 0.06 0.05 0.02 0.14 0.02 0.10 0.07 0.05 0.09 0.06 0.00 0.25 0.27 0.30 0.00 0.29 0.21 0.35 0.35 0.22 0.47 0.15 0.12 0.23 0.21 0.07 0.10 0.20 0.17 0.45 0.31 0.13 0.21 0.23 0.47 0.32 0.20 0.20 0.25 0.01 0.25 0.17 0.28 0.26 0.17 0.41 0.10 0.08 0.14 0.21 0.04 0.06 0.23 0.12 0.33 0.25 0.09 0.17 0.16 0.36 0.29 0.06 0.16 0.11 0.03 0.06 0.08 0.16 0.07 0.10 0.05 0.11 0.06 0.05 0.03 0.11 0.05 0.14 0.04 0.10 0.03 0.14 0.05 0.12 0.09 0.08 0.08 0.09 0.06 0.06 0.07 0.13 0.11 0.06 0.06 0.02 0.10 0.07 0.11 0.02 0.09 0.04 0.08 0.08 0.10 0.04 0.10 0.07 0.05 0.10 0.00 47 0.11 0.06 0.00 0.09 0.10 0.02 0.00 0.05 0.06 0.10 0.00 0.14 0.25 0.18 0.10 0.05 0.03 0.00 0.06 0.01 0.01 0.05 0.06 0.00 0.06 0.07 0.05 0.01 0.10 0.11 0.05 0.05 0.09 0.06 0.07 0.02 0.10 0.16 0.16 0.12 0.10 0.10 0.03 0.07 0.03 0.07 0.04 0.07 0.00 0.04 0.08 0.10 0.09 0.20 0.12 0.05 0.07 0.03 0.00 0.08 0.07 0.14 0.02 0.06 0.00 0.09 0.00 0.16 0.06 0.00 0.04 0.02 0.10 0.15 0.04 0.11 0.04 0.12 0.00 0.13 0.11 0.23 0.18 0.10 0.06 0.06 0.17 0.07 0.07 0.03 0.10 0.05 0.04 0.08 0.00 0.17 0.10 0.16 0.06 0.07 0.06 0.06 0.02 0.00 0.00 0.0801 0.00 0.00 0.15 0.08 0.07 0.00 0.02 0.09 0.07 0.00 0.06 0.00 0.09 0.00 0.13 0.20 0.03 0.00 0.11 0.02 0.06 0.00 0.19 0.00 0.20 0.07 0.08 0.00 0.19 0.00 0.14 0.00 0.20 0.00 0.11 0.11 0.02 0.01 0.11 0.00 0.19 0.00 0.11 0.01 0.08 0.00 0.0001 0.05 0.16 0.00 0.13 0.10 0.04 0.00 0.05 0.14 0.00 0.04 0.07 0.08 0.14 0.04 0.12 0.20 0.04 0.03 0.12 0.02 0.00 0.01 0.06 0.00 0.01 0.00 0.02 0.09 0.03 0.03 0.00 0.06 0.03 0.04 0.16 0.09 0.05 0.04 0.01 0.07 0.13 0.05 0.07 0.12 0.02 0.03 0.23 0.19 0.36 0.25 0.09 0.21 0.09 0.11 0.01 0.04 0.00 0.01 0.01 0.00 0.12 0.11 0.06 0.05 9 0.00 0.02 0.22 0.21 0.22 0.12 0.14 0.19 0.05 0.04 0.00 0.02 0.11 0.08 0.00 0.07 0.19 0.15 0.08 0.09 0.16 9 0.14 0.16 0.13 0.25 0.19 0.19 0.13 0.01 0.03 0.00 0.03 0.05 0.06 0.04 0.13 0.00 0.02 0.14 0.13 S0.0 0.081 0.26 0.21 0.15 0.20 0.18 0.15 0.03 0.03 0.18 0.18 0.02 0.03 0.00 0.0C 0.06 0.05 0.06 0.06 9 0.03 0.10 0.27 0.25 0.06 0.07 0.13 0.04 0.05 0.03 0.09 0.10 0.05 0.08 0.10 0.08 0.14 0.14 0.08 0.11 9 0.14 0.15 0.07 0.08 0.16 0.21 0.21 0.12 0.09 0.08 0.03 0.08 0.09 0.04 0.06 0.08 0.01 0.06 0.15 0.10 9 07 025 0.21 -0 0.07 0.09 0.06 0.04 1 0.03 0.04 0.06 0.18 0.19 0.15 0.14 0.12 0.13 0.26 0.22 0.02 0.07 0.03 0.04 0.01 PG Procter & Gamble PCG PG&E Corp. DTE DTE Energy Co. BF.B Brown-Forman Corp. MZ Milacron Inc. MOT Motorola Inc. UCL Unocal Corp. N Inco, Ltd. F Ford Motor HP Helmerich & Payne 48 0 0.06 0.07 0.08 0.09 0.17 0.12 0.12 0.14 0.08 0.07 0.08 0.08 0.12 0.09 Test 7 $1 iritial irnestment 2 owr 35 years 10 ; 10 0 0 5 10 15 2D Number ofYears 25 30 35 Betas 1 .1i 1.Ud$ 0.91 1.56 n -r;q 0l25 0.82 -0.86 0.93 0.26 1.27 1.17 U. 1.01 1.18 074 1.23 1.71 1.09 0.5 048 0.64 0.65 0.65 2.05 4.49 2.12 1.49 2.22 1.68 0.67 -0.09 2.44 0.27 -0.14 1.90 2.33 1.63 0.47 2.43 -1.03 1.32 0.44 3.05 -0.75 3.72 1.14 1.82 0.63 1.02 0.27 1.51 0.87 1.17 0.68 0.30 0.41 0.2 1.12 0.39 1.37 0.28 0.05 0.42 2.17 2.44 2.22 2.15 0.24 0.53 0.35 0.58 0.79 1.32 0.72 1.2 1.03 0.7 0.97 1.26 0.08 1.48 0.93 0.32 1.08 0.43 1.36 0.32 1.39 0.17 1.57 0.02 1.75 0.32 0.00 -0.09 1.49 1.21 1.25 0.23 0.87 0.8 0.93 0.56 1.74 0.51 .0.77 0.68 0.26 0.9 0.94 1.06 0.9 0.50 0.76 0.51 1.39 0.7 1.68 0.1 0.93 0.4 1.05 -1.12 3.22 0.65 2.73 2.24 0.41 0.23 0.5 1.38 2.28 0.8 1.07 0.98 1.2 2.17 1.87 1.38 0.99 0.62 0.78 -0.81 0.78 1.27 0.72 0.23 2.63 0.68 0.41 0.93 0.32 1.03 1.7 0.92 1.15 0.32 1.32 -0.1 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1.46 1.11 0.70 1.14 0.78 0.94 0.72 1.34 0.91 -1.7 1.66 -0.36 0.93 0.1 0.95 1.67 0.89 0.69 0.87 0.67 0.72 0.74 0.73 0.74 0.72 0.82 2.37 0.92 0.96 -0.04 0.77 1.18 0.63 1.17 1.28 1.08 1.04 0.08 0.84 0.62 0.56 1.77 0.75 0.56 0.81 1.12 1.1 1.04 0.66 1.17 0.45 0.67 1.35 0.58 0.43 1.32 1.88 1.21 0.79 1.28 1.06 1.24 1.17 0.12 0.6 0.69 0.71 0.57 -0.19 2.07 3.19 1.64 1.11 1.53 1.23 0.46 1.95 0.31 0.69 1.52 0.57 0.71 1.07 1.04 1.09 0.96 1.21 1.05 0.93 1.37 1.41 1.16 1.26 2.68 1.87 3.63 1.51 1.12 1.53 1.67 1 2.83 1.02 1.22 0.98 1.18 1.29 0.54 1.45 1 1.35 0.57 1.63 0.79 1.32 1.25 1.91 0.68 2.18 1.20 1.56 1.01 1.44 0.85 0.44 0.64 0.44 0.32 0.66 0.43 1.02 0.72 1.08 1.01 0.62 0.77 1.71 0.54 1.74 0.48 2.37 0.28 1.11 0.57 1.42 1.68 1.52 0.47 0.47 0.98 0.44 0.1 0.45 0.68 0.5 0.12 0.66 1.23 0.51 1.46 1.51 1.41 1.97 0.64 0.54 1.11 0.30 1.34 1.28 2.77 1.34 0.25 -0.32 -0.18 1.03 1.21 0.92 1.55 1.57 1.40 0.59 1.31 1.05 0.62 1.12 1.03 1.02 0.48 0.58 0.35 1.17 1.54 1.11 1 1.24 -0.28 1.15 1.27 1.16 1.71 0.95 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1.23 1.36 1.11 -0.67 1.01 0.95 1.25 0.69 1.29 1.04 1.35 1.52 0.9 1.38 0.28 1.23 -0.55 1.37 0.69 0.45 -0.05 0.91 2.6 1.6 1.86 0.21 0.49 0.53 -1.08 3.82 0.82 0.65 0.45 0.42 0.93 0.68 0.56 1.37 1.39 1.51 0.56 0.26 0.78 0.66 1.47 0.4 0.33 _ 0.88 0.59 0.95 1.29 1.14 0.93 1.06 1.48 0.81 1.53 0.87 0.93 0.45 0.26 0.53 1.68 0.73 1.63 1.67 1.57 1.75 1.71 1.85 1.42 3.25 1.59 1.34 1.55 2.14 1.60 1.46 1.34 2.79 1.10 0.2 1.28 1 0.98 0.54 1.1 1.06 1.0310.95 0.98 -1.1 0.53 1.57 0.32 0.21 0.79 1.29 0.64 0.78 1.52 0.46 0.96 0.35 0.42 1.23 1.73 0.92 2.34 -0.11 0.57 0.58 0.53 0.79 ~0.87 1.08 0.83 0.65 2.34 0.48 -0.03 0.69 0.6 0.73 0.47 0.58 1.46 0.49 0.68 0.83 1.37 0.8 0.4 0.16 0.68 0.78 0.57 -0.27 0.67 2.2 0.34 0.57 0.28 2.03 0.66 0.84 1.09 1.06 1.13 0.64 0.79 0.35 1.15 1.61 -0.38 1.390 .88 1.19 0.24 1.43 1.38 1.05 2.31 0.69 0.92 1.21 0.43 1.48 0.42 1.02 2.1 1.41 0.94 1.23 0.62 2.78 0.92 1.52 0.63 1.67 - Fortune Brands, Inc. MRK Merck & Co. XON Exxon Corp. NCE New Century Energies MRO USX-Marathon Group NSP Northern States Power CBS CBS Corp. Alcoa Inc. AA TAN Tandy Corp. PEP PepsiCo Inc. Weights 0.07 0.07 0.12 0.21 0.11 0.20 0.11 0.04 0.08 0.19 0.12 0.11 0.12 0.18 0.20 0.35 0.25 0.31 0.13 0.08 0.16 0.20 0.08 0.04 0.00 0.07 0.08 0.08 0.14 0.10 0.19 0.14 0.04 0.09 0.14 0.12 0.08 0.08 0.14 0.15 0.26 0.16 0.31 0.10 0.15 0.17 0.11 0.11 0.05 0.00 0.12 0.08 0.14 0.09 0.15 0.07 0.24 0.16 0.12 0.06 0.03 0.00 0.00 0.00 0.08 0.04 0.06 0.05 0.12 0.07 0.07 0.09 0.23 0.09 0.21 0.15 0.09 0.14 0.06 0.16 0.10 0.17 0.14 0.09 0.08 0.14 0.02 0.04 0.01 0.09 0.03 0.14 0.06 0.12 0.10 0.14 0.12 0.18 0.10 0.19 0.26 0.26 0.03 0.10 0.14 0.21 0.15 0.06 0.21 0.15 0.14 0.14 0.25 0.15 0.18 0.13 0.09 0.13 0.10 0.20 0.05 0.00 0.08 0.25 0.00 0.20 0.28 0.05 0.15 0.16 0.22 0.18 0.21 0.28 0.16 0.09 0.20 0.24 0.22 0.20 0.21 0.12 0.19 0.11 0.16 0.11 0.03 0.11 0.19 0.00 0.15 0.14 0.11 0.13 0.07 0.14 0.06 0.09 0.07 0.11 0.15 0.27 0.16 0.15 0.15 0.19 0.14 0.11 0.15 0.22 0.26 0.20 0.14 0.21 0.57 0.16 0.11 0.08 0.08 0.04 0.12 0.06 0.07 0.07 0.09 0.11 0.16 0.10 0.10 0.14 0.16 0.09 0.06 0.14 0.16 0.19 0.14 0.14 0.12 0.41 0.00 0.00 0.05 0.09 0.03 0.12 0.06 0.13 0.00 0.06 0.01 0.00 0.12 0.00 0.11 0.00 0.03 0.05 0.02 0.04 0.02 0.06 0.03 0.07 00 0.00 0.05 0.08 0.09 0.08 0.12 0.07 0.14 0.02 0.08 0.03 0.07 0.19 0.06 0.09 0.00 0.08 0.03 0.05 0.03 0.03 0.09 0.04 0.07 0.00 51 0.28 0.21 0.18 0.23 0.19 0.16 0.22 0.27 0.29 0.28 0.38 0.38 0.26 0.29 0.21 0.29 0.35 0.18 0.32 0.39 0.39 0.25 0.32 0.19 0.11 0.27 0.16 0.17 0.14 0.14 0.11 0.12 0.17 0.16 0.18 0.28 0.26 0.15 0.19 0.15 0.23 0.18 0.12 0.22 0.29 0.27 0.16 0.17 0.12 0.17 0.00 0.03 0.07 0.00 0.09 0.00 0.05 0.02 0.02 0.03 0.00 0.03 0.00 0.04 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.05 0.10 0.05 0.09 0.00 0.04 0.03 0.08 0.08 0.05 0.05 0.04 0.04 0.01 0.00 0.07 0.06 0.03 0.02 0.03 0.03 0.04 0.05 0.00 0.01 0.04 0.13 0.05 0.07 0.02 0.07 0.07 0.02 0.02 0.00 0.00 0.00 0.11 0.07 0.00 0.00 0.00 0.06 0.00 0.00 0.02 0.00 0.12 0.00 0.04 0.03 0.18 0.16 0.09 0.04 0.13 0.11 0.04 0.05 0.01 0.04 0.04 0.12 0.10 0.08 0.04 0.03 0.08 0.03 0.01 0.06 0.05 0.13 0.00 0.02 0.05 0.01 0.03 0.12 0.01 0.00 0.00 0.05 0.00 0.00 0.01 0.06 0.05 0.00 0.00 0.00 0.13 0.00 0.00 0.00 0.15 0.00 0.03 0.00 0.02 0.05 0.03 0.05 0.10 0.02 0.02 0.01 0.05 0.02 0.00 0.03 0.07 0.05 0.02 0.01 0.00 0.10 0.03 0.00 0.01 0.12 0.02 0.11 0.00 0.09 0.12 0.17 0.07 0.04 0.07 0.04 0.17 0.14 0.11 0.17 0.05 0.04 0.03 0.00 0.00 0.07 0.04 0.09 0.01 0.05 0.04 0.11 0.00 0.11 U.09 0.10 0.09 0.08 0.03 0.06 0.07 0.10 0.13 0.12 0.16 0.08 0.05 0.07 0.05 0.02 0.12 0.03 0.12 0.04 0.05 0.14 0.13 0.07 0.23 0.44 0.00 0.00 0.29 0.32 0.43 0.00 0.00 0.26 0.17 0.24 0.16 0.11 0.15 0.18 0.23 0.06 0.08 0.37 0.31 0.16 0.10 0.08 0.44 0.34 0.15 0.04 0.05 0.36 0.30 0.16 0.03 0.03 0.20 0.20 0.00 0.55 0.11 0.52 0.13 0.36 0.13 0.26 0.11 0.16 0.22 0.19 0.21 0.17 0.14 0.13 0.00 0.00 S0.11 0.14 0.03 0.07 0.07 0.10 0.01 0.03 0.09 0.10 0.00 0.03 0.00 0.00 0.08 0.02 0.08 0.02 0.00 0.14 0.10 0.06 0.18 0.00 0.12 0.11 0.12 0.02 0.20 0.07 0.26 0.13 0.11 0.08 0.08 0.15 0.13 0.25 0.24 0.07 0.08 0.22 0.20 0.10 FO 0.00 0.03 0.01 0.03 0.00 0.00 0.08 0.10 0.00 04 0.05 0.08 0.10 0.07 0.03 0.05 0.03 0.03 0.0 004 0.05 0.04 0.08 0.08 0.03 0.04 0.07 0.09 0.03 0.03 0.01 0.09 0.04 0.05 0.15 0.17 0.38 0.27 0.08 0.09 0.10 0.12 0.03 0.7 010 Fortune Brands, Inc. MRK Merck & Co. XON Exxon Corp. NCE New Century Energies MRO USX-Marathon Group NSP Northern States Power CBS CBS Corp. AA Alcoa Inc. TAN Tandy Corp. PEP PepsiCo Inc. Test 8 $1irtial irustmnt oar 35 years 100 0 0 5 10 15 2D frTber ofYeas Betas 52 25 30 35 0.02 0.04 0.00 0.00 0.01 0.04 0.00 0.00 0.00 0.02 0.00 0.00 0.03 000 0.01 0.03 0.06 0.02 0.03 0.02 0.00 0.00 0.05 0.04 0.00 0.02 0.08 0.08 0.03 0.02 0.03 0.05 0.06 08 000 03 002 0.2 1.23 U.34 -U.Ul 0.95 0.82 0.24 0.34 0.18 0.6 0.26 -0.04 0.54 -0.43 0.57 0.94 0.31 1.58 1.31 1.6 1.29 1 0.93 1.16 0.94 0.63 0.71 1.3 0.68 0.4 0.99 0.67 0.94 1.35 1.27 0.46 1.28 1.65 1.45 2.39 1.22 2.56 1.18 1.04 1.21 1.17 1.37 1.03 1.33 1.69 1.37 0.59 1.5 0.95 1.24 1.06 1.13 2.18 1.29 1.48 1.37 0.67 -0.15 0.41 1.07 0.25 0.81 0.07 0.94 1.2 0.65 0.91 0.44 0.7 0.45 0.11 0.78 0.81 0.72 1.03 0.54 0.52 0.48 0.76 0.62 1.83 0.27 1.83 0.66 0.44 0.76 0.45 0.57 0.18 0.59 1.43 1.74 0.69 0.60 0.79 0.52 1.18 0.55 0.81 0.59 0.04 0.79 1.68 0.39 1.14 1.25 0.65 1.24 2 0.39 1.23 2.78 1.16 1.43 1.15 0.57 1.44 1.13 2.04 0.91 1.46 0.41 1.62 1.3 1.40 0.53 1.5 1.57 0.99 -0.12 1.18 U./ 0.88 0.90 0.81 1.30 -U.U.3 0.94 0.65 1.58 0.62 1.66 0.82 0.83 1.31 1.53 0.65 0.89 2.08 1.04 1.54 0.89 0.31 1.11 0.71 0.28 1.94 2.68 2.02 0.42 0.35 0.56 -0.41 0.530.26 0.67 0.77 1.21 0.24 1.34 1.38 1.33 3 1.07 0.93 1.28 1.07 -0.29 1.30 1.14 1.38 1.4 -0.25 0.45 1.38 1.58 0.95 0.92 1.41 0.98 1.02 0.81 0.48 -0.06 0.91 1.07 0.53 0.82 0.47 1.23 0.86 1.91 0.83 1.69 0.7 0.68 1.38 1.41 0.66 0.19 0.97 0.72 0.71 0.99 1.40 1.53 1.43 1.23 1.15 1.69 1.07 1.35 1.09 1.36 1.2 0.59 0.95 0.53 0.31 0.78 0.95 0.49 0.71 0.5 1.1 1.14 1.20 0.21 0.58 1.09 0.75 0.41 1.4 0.5 0.73 1.07 0.56 1.05 1.04 0.79 0.69 1.74 0.65 0.96 1.03 0.58 0.61 1.58 -0.76 0.29 0.90 0.45 0.24 1.09 1.02 1.37 0.95 0.16 0.89 1.27 -0.7 1.66 0.91 -0.02 0.63 1.01 0.78 1.38 1.14 0.51 0.57 0.66 0.85 1.39 1.11 0.51 0.49 0.1 0.59 0.76 1.29 0.57 0.47 0.73 0.38 1.02 0.82 1.08 0.72 -0.19 0.76 1.78 0.73 0.96 0.67 1.13 0.1 0.18 1.04 1.13 0.68 -0.36 0.53 0.82 0.98 =.65 0.44 0.66 -0.24 0.35 -0.09 0.51 -0.09 0.47 0.51 0.24 11.42 0.57 0.52 0.57 0.62 0.26 0.59 0.25 -0.18 0.50 0.68 0.51 0.08 1.57 2.24 1.62 0.42 0.97 0.47 1.3 0.01 1.22 0.21 1.57 1.18 1.51 0.76 1.75 0.68 1.62 0.55 1.69 2.73 1.21 1.86 1.17 0.99 1.53 1.81 1.49 1.45 0.59 2.38 0.3 0.23 0.41 -0.06 0.41 0.64 U.b3 U.34 0.29 -0.09 13 1.08 -0.14 0.48 -0.79 1.33 0.95 2.34 -0.94 0.94 1.11 0.57 1.12 0.86 0.43 0.97 10.25 1.12 1.95 0.44 -0.25 0.98 0.58 0.97 0.43 1.44 1.35 0.73 1.52 1.33 0.59 2.15 0.37 2.23 1.46 0.65 0.18 2.07 0.6 3.77 1.41 1.21 1.57 0.94 -0.95 1.27 1.1 10.48 11.62 1.48 2.66 0.67 0.46 1.38 0.77 1.13 0.48 1.47 1.29 0.92 0.65 1.46 0.61 1.59 2.14 1.42 0.32 0.74 0.2 1.70.85 1.37 0.38 0.63 0.41 -0.29 0.01 0.12 0.12 1.04 0.85 0.26 1.1 -0.76 0.79 0.36 0.12 1.38 0.45 0.33 1.56 0.58 0.98 0.62 1.21 1.79 2.26 0.39 1.54 1.85 3.33 0.53 1.28 2.35 2.56 0.48 2.23 0.37 3.04 0.49 0.77 1.61 0.86 0.51 1.82 0.02 0.3 1.05 -0.7 1.42 0.3 1.17 2.17 1.09 1.12 1.28 1.51 1.05 2.79 1.23 0.55 1.17 12.18 0.69 1.02 0.62 0.86 0.81 0.29 -0.44 1.79 0.92 0.56 1.9 -0.3 1.97 0.54 1.08 1.41 0.22 0.21 1.65 1.4 2.41 0.30 -0.36 1.21 0.15 0.35 1.39 1.16 1.64 0.35 0.19 0.91 0.53 0.32 1.03 0.73 1.67 0.52 0.86 0.62 0.34 0.77 0.09 1.49 1.1 1.41 2.1 1.28 0.09 1.45 1.46 1.71 2.58 1.1 0.21 0.15 0.18 0.55 0.60 1.16 0.36 1 53 1.55 0.92 0.87 1.37 0.66 1.09 0.74 0.39 0.82 0.66 0.54 0.86 0.55 -0.04 0.95 0.67 0.85 1.54 1.26 1.86 1 2.4 1.03 1.78 - 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Phillips Petroleum P CIN ClNergy Corp. HON Honeywell Household International HI DCN Dana Corp. ITT Industries, Inc. IIN MAS Masco Corp. Weights 0.1: 0.111 0.241 0.301 0.151 0. 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DOW Dow Chemical BOL Bausch & Lomb MAY May Dept. Stores GTE GTE Corp. GM General Motors ETN Eaton Corp. T AT&T Corp. 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GLW Coming Inc. HI RTN.B F 0.37 0.34 0.35 0.37 0.39 0.57 0.59 0.36 0.52 0.72 0.58 0.37 0.29 0.19 0.36 0.38 0.17 0.05 0.06 0.00 0.01 0.03 0.10 0.17 0.23 0.15 0.18 0.09 0.07 0.13 0.15 0.14 0.12 0.20 0.20 0.05 0.03 0.09 0.12 0.01 0.11 0.10 0.11 0.0( 0.04 0.10 0.09 0.04 0.04 0.00 0.00 0.00 0.05 0.05 0.09 0.08 0.07 0.12 0.10 0.10 0.11 0.29 0.24 0.04 0.06 0.09 0.10 0.00 0.00 0.22 0.19 0.00 0.00 0.0C 0.05 0.07 0.14 0.00 0.04 0.06 0.09 0.09 0.09 0.080.08 0.17 0.16 0.11 0.00 0.00 0.10 0.07 0.01 0.04 0.26 0 0.00 0.00 0.12 0.06 0.00 0.03 0.19 0.14 0.02 0.04 0.11 0.06 0.00 0.00 0.05 0.05 0.00 0.03 0.05 0.04 0.17 0.13 0.08 0.07 0.01 0.06 0.03 0.12 0.00 0.04 0.01 0.0C 0.02 0.08 0.00 0.04 0.16 0.13 0.0C 0.07 0.09 0.08 0.0C 0.14 0.09 0.09 0.02 0.08 0.00 0.02 0.00 0.05 0.00 0.06 0.0C 0.11 0.05 0.05 0.00 0.10 0.17 0.16 0.05 0.17 0.18 0.11 0.06 0.00 0.61 0.70 0.20 0.05 0.34 0.19 0.0( 0.08 0.22 0.31 0.07 0.02 0.37 0.20 0.14 0.05 0.29 0.25 0.00 0.05 0.23 0.17 0.04 0.10 0.20 0.17 0.03 0.08 0.31 0.24 0.00 0-00 0-03 0.29 0.19 0.05 0.05 0.08 0.10 0.07 0.10 0.16 0.06 0.14 0.13 0.14 0.04 0.02 0.02 0.03 0.13 0.01 0.06 0.04 0.16 0.10 0.06 0.09 0.12 0.21 0.00 0.12 0.14 0.0( 0.03 0.09 0.07 0.06 Household International Raytheon Co. Ford Motor PBY Pep Boys GLK Great Lakes Chemical P 0.27 0.30 0.33 0.33 0.28 0.44 0.42 0.20 0.38 0.52 0.52 0.26 1 0.20 0.26 0.23 0.15 0.12 0.06 0.00 0.21 0.09 0.12 0.17 0.24 0.12 0.12 0.11 0.09 Phillips Petroleum 62 0.12 0.07 0.11 0.00 0.20 0.10 0.09 0.00 0.06 0.24 0.16 0.02 0.28 0.18 0.11 0.00 0.13 0.10 0.09 0.02 0.08 0.16 0.07 0.00 0.11 0.13 0.10 0.00 0.15 0.16 0.10 0.16 0.09 0.12 0.07 0.00 0.08 0.05 0.03 0.03 0.00 0.11 0.10 0.18 0.05 0.22 0.15 0.08 0.0( 0.37 0.20 0.10 0.07 0.05 0.04 0.13 0.04 0.34 0.21 0.09 0.07 0.08 0.07 0.20 0.06 0.18 0.15 0.03 0.10 0.18 0.11 0.11 0.10 0.08 0.07 0.12 0.25 0.00 0.00 0.08 0.02 0.04 0.00 0.03 0.06 0.07 0.03 0.23 0.12 0.00 0.01 0.00 0.02 0.02 0.02 0.23 0.06 0.01 0.04 0.05 0.05 0.01 0.03 0.11 0.05 0.03 0.06 0.01 0.06 0.07 0.07 0.15 0.09 0.01 0.02 0.12 0.03 0.13 0.14 0.0C 0.0C 0.03 0.03 0.0C 0.01 0.02 0.02 0.00 0.00 0.13 0.01 0.03 0.09 0.04 0.06 0.10 0.10 0.16 0.03 0.09 0.07 0.02 0.05 0.18 0.03 0.12 0.07 0.10 0.03 0.15 0.13 0.02 0.06 0.04 0.00 0.00 0 0.00 0.00 0.12 0.00 0.00 0.00 0.0C 0.10 0.14 0.06 0.01 0.03 0.00 0.17 0.05 0.10 0.09 0.10 0.15 0.17 0.04 0.07 0.08 0.04 0.03 0.04 0.03 0.09 0.19 0.04 0.03 0.03 0.04 0.08 0.08 0.07 0.00 0.01 0.00 0.11 0.06 0.08 0.11 0.08 0.13 0.13 Bibliography [1] Brealey, Richard A. and Stewart C. Myers. Principlesof CorporateFinance, 4 th ed., McGraw- Hill, 1991 [2] Aggarwal, Raj and Ramesh Rao. "Institutional Ownership and Distribution of Equity Returns." FinancialReview 25(May 1990):211-229. [3] Barnea, Amir and David H. Downes. "A Re-examination on the Empirical Distribution of Stock Price Changes." Journal of the American StatisticalAssociation 68 (June 1973): 348-313 [4] Farina, Eugene F. "The Behavior of Stock Market Prices." Journalof Business 38(January 1965):34-105. [5] Officer, Robert. "The Distribution of Stock Returns." Journalof the American Statistical Association 67(December 1972): 807-812. [6] Markowitz, H. M. "Portfolio Selection." JournalofFinance 7(March 1952): 77-91. [7] Sharpe, W. F. "Capital Asset Prices: A Theory of Market Equilibrium under Conditions of Risk." JournalofFinance 19(September 1964): 425-442. [8] Lintner, J. "The Valuation of Risk Assets and the Selection of Risky Investments in Stock Portfolios and Capital Budgets." 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