Showing papers in "Journal of Financial and Quantitative Analysis in 1981"
TL;DR: The authors developed a model of bank margins or spreads in which the bank is viewed as a risk-averse dealer and demonstrated that an interest spread or margin would always exist, and that this was the result of transactions uncertainty faced by the bank.
Abstract: This paper has developed a model of bank margins or spreads in which the bank is viewed as a risk-averse dealer. It was demonstrated that an interest spread or margin would always exist, and that this was the result of transactions uncertainty faced by the bank. Moreover, it was shown that this pure spread depended on four factors: the degree of managerial risk aversion; the size of transactions undertaken by the bank; bank market structure; and the variance of interest rates. The model implied that liability and asset structures had to be analyzed together since they were directly interrelated through transactions uncertainty. It was shown that because of this transactions uncertainty, hedging behavior was perfectly rational within an expected utility maximizing framework. Extending the model from a structure with one kind of loan and deposit to loans and deposits with many maturities should lead to further interesting insights into margin determination especially as “portfolio” effects may become apparent.
823 citations
TL;DR: In a world of heterogeneous investors, a competitive financial market has two major functions: the first is the mechanism by which ownership of the existing supply of risky assets is distributed among investors; the second is to aggregate the diverse information held by different investors into a single price as discussed by the authors.
Abstract: In a world of heterogeneous investors, a competitive financial market has two major functions. First, it is the mechanism by which ownership of the existing supply of risky assets is distributed among investors. This is the role which is analyzed in detail by the standard Capital Asset Pricing Model (CAPM) and its many extensions. The second important market function is to aggregate the diverse information held by different investors into a single price. Most versions of the CAPM eliminate the information aggregation function by assuming that investors hold homogeneous beliefs with respect to the probability distribution of asset returns. Exceptions which deal with some aspects of the problem are Lintner [7], Grossman [4], Grossman and Stiglitz [5], and Figlewski [1, 3 ].
426 citations
TL;DR: The adequacy of the capital asset pricing models (CAPM) as empirical representations of capital market equilibrium is now seriously challenged (see Ball [1], Banz [2], Basu [3], Cheng and Graver [8], Gibbons [15], Marsh [18], Reinganum [22], and Thompson [20]).
Abstract: The adequacy of the capital asset pricing models (CAPM) of Sharpe [27], Lintner [17], and Black [4] as empirical representations of capital market equilibrium is now seriously challenged (for example, see Ball [1], Banz [2], Basu [3], Cheng and Graver [8], Gibbons [15], Marsh [18], Reinganum [22], and Thompson [20]). Yet, the influence of earlier empirical studies (such as Black, Jensen, and Scholes [5] and Fama and MacBeth [11]) still remains; the current consensus seems to be that a security's beta is still an important economic determinant of equilibrium pricing even though it may not be the sole determinant. In light of the recent empirical evidence, however, the claim that a security's beta is an important determinant of equilibrium pricing should be reexamined.
272 citations
TL;DR: In this paper, the authors extended the Pareto optimal general insurance contract to the optimal investment portfolio insurance contract, which is a contract whose payoff depends upon the investment performance of some specified portfolio of common stocks.
Abstract: The form of the Pareto optimal general insurance contract has been investigated by Borch [5], Arrow [3], and Raviv [16]. This paper extends their work to the consideration of the optimal investment portfolio insurance contract. This is a contract whose payoff depends upon the investment performance of some specified portfolio of common stocks. Portfolio insurance differs from general insurance in two important ways. First, investment portfolio insurance lacks the property of stochastic independence between losses on different contracts which is characteristic of general insurance, and this has led some actuaries to question whether portfolio insurance contracts should be sold in view of the risks they pose for the solvency of insurance companies. Recent developments in the theory of option pricing suggest, however, that under certain assumptions an insurance company will be able to eliminate the risks associated with portfolio insurance contracts by following an appropriately defined investment strategy. Secondly, there exists a market for the pricing of investment risks, the securities market; and, under appropriate assumptions, the equilibrium price of portfolio insurance contracts may be determined without specification of the preferences of insurance companies. This permits consideration of insurance company preference functions to be dispensed with, in marked contrast to the earlier literature concerned with general insurance, which treats insurance company preferences symmetrically with those of the insurance purchaser. In addition, since the characteristics of the insured portfolio are known to the insurer, and the performance of the portfolio is beyond the control of the insured, portfolio insurance is not prone to the problems of adverse selection and moral hazard which are liable to arise in general insurance.
184 citations
TL;DR: In this article, the risk-return characteristics of investments in the common stocks of U.S.-based multinational corporations and national corporations (NATLs) were compared using the framework of the capital asset pricing model (CAPM).
Abstract: This study focuses on the risk-return characteristics of investments in the common stocks of U.S.–based multinational corporations (MNCs) and U.S. national corporations (NATLs). Findings follow from a comparison of the risk-adjusted performance of MNCs and NATLs using the framework of the capital asset pricing model (CAPM). Results of this comparison challenge assertions of earlier writers that marginal benefits or advantages accrue from investments in MNCs as compared to NATLs.
161 citations
TL;DR: The mean-variance model is precisely consistent with the expected utility hypothesis only in the special cases of normally distributed security returns or quadratic utility functions as mentioned in this paper, however, there is little evidence that security returns follow normal distributions, exhibiting increasing absolute risk aversion in the Pratt [ll]-arrow [1, 2] sense and displaying negative marginal utility after some finite wealth level.
Abstract: The mean-variance model is precisely consistent with the expected utility hypothesis only in the special cases of normally distributed security returns or quadratic utility functions. There is little evidence, however, that security returns follow normal distributions (see [13] for references) and quadratic preferences can be shown to generate implausible results, exhibiting increasing absolute risk aversion in the Pratt [ll]–Arrow [1, 2] sense and displaying negative marginal utility after some finite wealth level. In addition, Hakansson [4] has shown that single–period, mean-variance-efficient portfolios can have disastrous consequences over time—even when return distributions are stationary. Such criticisms of the mean-variance approach within the Von Neumann-Morgenstern framework have prompted several writers to suggest that investors maximize the expected value of utility functions with more “realistic” properties, while others have criticized the single-period focus of the model. One popular alternative utility function is the logarithmic function which exhibits decreasing absolute risk aversion and (conveniently) leads to myopic decision processes through time (i.e., investors treat each period as if it were the last, basing investment decisions on that period's wealth and return distributions only [8, 4]). (Other utility functions with constant relative risk aversion—such as the power function—also imply myopic decision rules within a multiperiod setting.)
149 citations
TL;DR: In this article, an empirically based composite indicator of a country's ability and willingness to honor its foreign debt service obligations during some future time period is presented. But the model is intended to complement, not replace, a thorough country analysis which examines nonquantifiable factors, such as the debt service ratio, the foreign exchange reserves to imports ratio, and the ratio of net noncommercial foreign exchange inflows to debt service payments.
Abstract: This article, Projecting Debt Servicing Capacity of Developing Countries, was reprinted with permission from the December 1981 issue of the Journal of Financial and Quantitative Analysis. Many less developed countries rely on foreign loans to fuel their economic development. In the wake of the oil crisis of 1973, many countries have experienced enormous growth in external indebtedness. Some have required loan deferral or rearrangement. This article aims to devise an empirically based composite indicator of a country's ability and willingness to honor its foreign debt service obligations during some future time period. The examined factors are the debt service ratio, the foreign exchange reserves to imports ratio, the ratio of net noncommercial foreign exchange inflows to debt service payments, the ratio of commercial foreign exchange inflows to debt service payments, the exports to gross national product ratio, and the real per capita gross national product to U.S. per capita gross national product ratio. The model projects a country's debt servicing capacity based on empirical data. The predictive model is intended to complement, not replace, a thorough country analysis which examines nonquantifiable factors.
113 citations
TL;DR: The search for a distribution which accurately describes the behavior of stock price returns has generated a considerable amount of controversy as mentioned in this paper. But none of the alternatives that have been proposed over the years (Stable Paretian-Mandelbrot [5], Poisson mixture of; lognormal distributions-Press [10], scaled T distribution-Praetz [9], lognormality with nonstationary variance-Rosenberg [11], subordinate stochastic process-Clark [2]) has gained general acceptance.
Abstract: The search for a distribution which accurately describes the behavior of stock price returns has generated a considerable amount of controversy. While it is well known that the traditionally used assumption of lognormality deviates in systematic ways from the empirically observed—the latter has fatter tails and a larger concentration of mass near zero—none of the alternatives that have been proposed over the years (Stable Paretian—Mandelbrot [5], Poisson mixture of; lognormal distributions—Press [10], scaled T distribution—Praetz [9], lognormal with nonstationary variance—Rosenberg [11], subordinate stochastic process—Clark [2]) has gained general acceptance.
104 citations
TL;DR: In this article, a major controversy has formed in the finance literature regarding the empirical evidence of the informational content of dividends, and a major issue of the dispute has centered on the identification and control of contemporaneous earnings information.
Abstract: In recent years a major controversy has formed in the finance literature regarding the empirical evidence of the informational content of dividends. Despite considerable support for the position of dividend nontriviality by various studies, the work by Watts [13] represents a formidable challenge. Because of the close proximity of the firm's earnings and dividend announcement dates, the major issue of the dispute has centered on the identification and control of contemporaneous earnings information. In an attempt to settle this controversy, the present study evaluates and extends Watts' methodology.
93 citations
TL;DR: In this paper, prices of corporate bonds are decomposed into elements associated with the pure price of time, the default risk of the agency rating class to which the bond is assigned, and the unique risk and ancillary features of the bond itself.
Abstract: In this paper prices of corporate bonds are decomposed into elements associated with (1) the pure price of time, (2) the default risk of the agency rating class to which the bond is assigned, and (3) the unique risk and ancillary features of the bond itself.
92 citations
TL;DR: The authors discusses the covariance of a bond's return with the returns of other assets, but does not discuss what is, from a portfolio theoretic view, the risk of the bond.
Abstract: This statement presents the usual perception of bond risk. It is striking in that it does not discuss what is, from a portfolio theoretic view, the risk of a bond––the covariance of its return with the returns of other assets. This is in contrast to the typical discussion of the riskiness of common stocks, where we find some discussion of systematic risk and the role it plays in determining equilibrium expected security returns.
TL;DR: In this paper, the authors examine the market response to information about firms whose future is assessed as being extremely problematic, and show that the market responds to such information with a strong negative bias.
Abstract: A recent issue of the Journal of Financial Economics (June/September 1978) is devoted to reporting anomalous evidence regarding market efficiency. This study may qualify under the same heading. Here we examine the market response to information about firms whose future is assessed as being extremely problematic.
TL;DR: In this article, it was shown that no known trading rule or security selection strategy which uses only publicly available information would provide an investor with the ability to earn, on average, positive "abnormal" returns in a market that is efficient in the semi-strong sense.
Abstract: In an efficient capital market, prices fully reflect available information and adjust to new information in a rapid and unbiased fashion. As a result, prices provide unbiased estimates of the underlying values. No known trading rule or security selection strategy which uses only publicly available information would provide an investor with the ability to earn, on average, positive “abnormal” returns in a market that is efficient in the semi-strong sense. Thus, a finding that common stocks selected, using a readily available, widely disseminated set of rules which requires only publicly available information for decision-making purposes, earn, on average, positive abnormal returns represents strong contradictory evidence regarding the semi-strong form of the efficient markets hypothesis.
TL;DR: A growing number of studies examine the optiraality of financial decisions when the assumption of perfect and costless information is replaced by allowing for informational asymmetry as discussed by the authors, where the asymmetry is assumed to exist between corporate insiders who possess superior information about the firm's future earnings prospects and outside investors.
Abstract: As is shown in the financial literature, the assumption of perfect and costless information often leads to the conclusion that corporate financial decisions are inconsequential to the value of the firm (e.g., Stiglitz [20] and Fama [6]). This conclusion seems to be in direct contradiction with the observed behavior of corporations that allocate real resources to implement financial policies. The gap between theory and observed behavior is bridged by introducing various frictions and market imperfections. A growing number of studies examine the optiraality of financial decisions when the assumption of perfect and costless information is replaced by allowing for informational asymmetry. The asymmetry is assumed to exist between corporate insiders who possess superior information about the firm's future earnings prospects and outside investors. The emphasis in this literature is on the ability of financial instruments to serve as signaling devices through which the true value of the firm can be revealed to the market without moral hazard or disclosure of confidential information. Although the signaling process is typically considered to be costly, it is advocated that firms may be better off if they employ this mechanism rather than reveal reliable, but confidential information, or not disclose at all.
TL;DR: In this article, the authors investigate the relationship between the variability of the beta coefficient and portfolio residual risk, and hence to provide a real picture of the process of portfolio diversification under the condition of beta nonstationarity.
Abstract: Over the past years the beta coefficient has been widely used as a measure of systematic risk in investment and portfolio analysis. The validity of using the beta coefficient as the proper measure of systematic risk is dependent upon the assumption that the beta coefficient is stationary over time. Unfortunately, this assumption has been challenged by a number of empirical studies which have found the beta coefficient to be unstable over time. Examples of such empirical investigations are those documented by Blume [4], Levy [12], Levitz [11], Baesel [2], Altman, Jacquillat, and Levasseur [1], and Roenfelt, Griepentrong, and Pflaum [16]. Most recently, Fabozzi and Francis [9] reported that some security beta coefficients tend to be random over time. Their findings also support the regression tendency of the beta coefficients towards the mean over time, as found by Blume [4]. Thus, because the beta coefficient is changing over time, the use of the ordinary least-squares (OLS) method in investment and portfolio analysis will yield an inefficient estimate of systematic risk. Furthermore, the OLS estimates of security and portfolio residual risks will be influenced by the variability of beta coefficient. Therefore, the purpose of this paper is to investigate the relationship between the variability of the beta coefficient and portfolio residual risk, and hence to provide a real picture of the process of portfolio diversification under the condition of beta nonstationarity. It is shown that the use of the OLS method to estimate security and portfolio residual risks will produce an incorrect conclusion that larger residual risks tend to be associated with higher variability in the beta coefficient.
TL;DR: In this article, the authors focus on whether yield differentials between bonds which differ in default risk vary systematically over the business cycle and find that during a cyclical upswing the yield differential (or risk premium) narrows, while during a downswing the differential widens.
Abstract: In recent years much research has centered upon whether yield differentials between bonds which differ in default risk vary systematically over the business cycle. Theory suggests that during a cyclical upswing the yield differential (or risk premium) narrows, while during a downswing the differential widens. The cyclical behavior of yield spreads is well documented in the corporate bond market [4, 8, 12, 16]. This effect has only recently been given attention in the tax-exempt bond market [1, 11]. In addition, the municipal bond market may be segmented. If tax-exempt borrowers and investors are unable to substitute between tax-exempt securities of varying default risk, changes in the relative supply of and demand for these classes of securities could produce systematic fluctuations in tax-exempt yield differentials. These effects could be produced by regulatory statutes which require that banks purchase high-grade securities and the fixed nature of bond ratings.
TL;DR: Ho and Saunders as mentioned in this paper applied a model that has been used to analyze dealer spreads to banking to analyze the institutional structure of the two problem areas and found that the risk of a mechanical application is that no real insights are gained.
Abstract: In this paper Ho and Saunders apply a model that has been used to analyze dealer spreads to banking.A potential contribution to a field can arise whenever a well-developed framework of analysis in one problem area is applied to another field. The risk of a mechanical application, however, is that the institutional structure of the two problem areas is so different that no real insights are gained. What are the facts here?
TL;DR: In this paper, the authors investigated how the measured stationarity of beta factors changes over data sets of varying lengths and derived analytic expressions to explain how and when this empirical phenomenon arises.
Abstract: The stationarity of beta factors has received considerable attention in the financial economics literature. One particular area of study has been to investigate how the measured stationarity of beta factors changes over data sets of varying lengths. By increasing the length of the estimation period, sampling fluctuations may be reduced; however, the probability of beta factors having changed will increase. The optimal data set length, then, involves a trade-off between these two opposing phenomena. Baesel [2] reported the empirical finding that the stationarity of beta was, indeed, dependent upon the estimation period length over which beta factors were estimated. He found, using transition matrices that beta stationarity was an increasing function of the calendar period used for beta estimation. In this paper, analytic expressions will be derived to explain how and when this empirical phenomenon arises. Conditions will be presented for beta stationarity to increase with calendar period length, and it will be demonstrated that beta stationarity will not increase indefinitely with estimation period length. An identical condition is required for beta stationarity to be an increasing function of the subsequent calendar period length. This phenomenon was empirically investigated by Roenfeldt, Griepentrog, and Pflaum [6], and the analysis presented here explains, in part, their findings.
TL;DR: The past two decades have seen a proliferation of mathematically sophisticated portfolio selection models such as mean variance (MV), expected utility, and growth optimal (GO) models have received the bulk of attention as mentioned in this paper.
Abstract: The past two decades have seen a proliferation of mathematically sophisticated portfolio selection models. Of these, the mean variance (MV), expected utility, and growth optimal (GO) models have received the bulk of attention.
TL;DR: In this paper, the authors apply this literature to an analysis of the market for bank loan commitments and explain the use of various payment options such as fees and compensating balance requirements associated with loan commitments.
Abstract: The idea that various characteristics of financial contracts and institutions can be explained as a rational response to problems created by information asymmetries has received a great deal of attention recently. A central theme of the literature in this area is that while moral hazard may hamper the direct transfer of information between market participants, information may be conveyed indirectly through the actions of market participants. For example, the characteristics of the insurance contract purchased may convey information as to riskiness of the insured. Recognition of the possible effects of information asymmetries has provided valuable insights into the role of financial intermediaries and the characteristics of the contracts they offer. In this paper we apply this literature to an analysis of the market for bank loan commitments. Through our analysis we are able to explain the use of various payment options such as fees and compensating balance requirements associated with loan commitments. Extensions of our analysis into the pricing of other bank services are also explored.
TL;DR: In this article, a fair and orderly market in the securities listed on an exchange is described, where a market maker is responsible for maintaining a fair, orderly market for the securities traded on the exchange.
Abstract: Markets for exchange typically evolve over time, and the organized security exchanges in the United States have evolved in such a manner as to give specialists a major role as market makers. Specialists are responsible for maintaining a fair and orderly market in the securities listed on an exchange. They specify prices to reflect supply and demand and adjust these prices in response to shifts in supply and demand.
TL;DR: The importance of accounting information on security price determination is of interest to both security analysts and accountants as discussed by the authors, however, none of this research has explicitly investigated how the empirical results can be affected by alternative accounting profitability measures within an industry simultaneously.
Abstract: The importance of accounting information on security price determination is of interest to both security analysts and accountants. Beaver [3], Downes and Dyckman [6], Gonedes [12], Beaver and Manegold [4], and others have investigated the possible relationships between accounting information and market information. Rosenberg [26] has shown the existence of extra-market components of covariance in security returns while Simkowitz and Logue (S–L) [28] have derived the interdependent structure of security returns. However, none of this research has explicitly investigated how the empirical results can be affected by alternative accounting profitability measures within an industry simultaneously.
TL;DR: In this article, Miller argues persuasively that at a point in time, a stock's price does not reflect the expectations of all potential investors, but rather the expectation of only the most optimistic minority who are trading the issue, as long as this minority can absorb the entire supply of stock, an increase (decrease) in divergence of opinion-leaving the average expectation unchanged-will increase the market clearing price.
Abstract: Edward Miller [5], expanding on the work of Williams [8], Smith [6], and Lintner [4], has proposed a direct relationship between a stock's “risk†and its “divergence of opinion.†Under conditions of uncertainty, potential investors in a stock arrive at different assessments of expected return. Thisvariation in expectations is characterized as the stock's divergence of opinion. Miller argues persuasively that at a point in time a stock's price does not reflect the expectations of all potential investors, but rather the expectations of only the most optimistic minority who are trading the issue. As long as this minority can absorb the entire supply of stock, an increase (decrease) in divergence of opinion-leaving the average expectation unchanged-will increase (decrease) the market clearing price.
TL;DR: In this paper, the authors explored the relative merits of negotiation versus competitive bidding in the underwriting of corporate bonds, particularly bonds issued by public utilities, in the context of the SEC's posture vis a vis its Rule U-50.
Abstract: Over the past decade, a number of papers [1, 2, 3, 6, 7, 9] have explored the relative merits of negotiation versus competitive bidding in the underwriting of corporate bonds, particularly bonds issued by public utilities. Interest in this subject has been stimulated principally by an important public policy issue—namely, the SEC's posture vis a vis its Rule U–50. Originally promulgated in 1940, this rule required competitive bidding on certain classes of utility bonds. In 1974, however, it was “temporarily” suspended on the grounds that chaotic conditions in the market for these securities called for more flexibility in the way issues could be underwritten. While this suspension continues in effect, Rule U–50 could be reinstated at any time by the SEC.
TL;DR: For example, this article showed that preferred stock ranks well below common stock and bond issues as a source of financing in the private capital market, and that the preferred stock burdens the issuer with a fixed financing cost without benefiting the stock holder with the tax deductability associated with interest payments.
Abstract: Historically, preferred stock ranks well below common stock and bond issues as a source of financing in the private capital market. Relative to issuance of bonds, the issuance of preferred stock burdens the issuer with a fixed financing cost without benefitingthe issuer with the tax deductability associated with interest payments.
TL;DR: In this paper, a two-parameter model for portfolio decisions, attributed to Markowitz [11], has individuals maximizing an objective function, ϕ [E(Y), V(Y)], of mean and variance of end-of-period wealth subject to a constraint imposed by initial wealth.
Abstract: The familiar two-parameter model for portfolio decisions, attributed to Markowitz [11], has individuals maximizing an objective function, ϕ [E(Y), V(Y)], of mean and variance of end-of-period wealth, subject to a constraint imposed by initial wealth. In the usual version there is an arbitrary number, n, of risky assets with stochastic end-of-period values (price plus dividend) represented by the vector X with exogenously given mean vector μ and nonsingular variance matrix σ. There is also one riskless asset, whose certain end-of-period value per dollar invested is p. Final wealth, as constrained by initial wealth, W, is given by Y = WP + a' (X – OP), where a and P are vectors of risky asset quantities and prices. Assuming ϕE > 0 (wealth preference), ϕV < 0 (risk aversion), and that the Hessian of $ is negative and semidefinite, portfolio optimum calls for ϕE(μ − OP) + 2ϕVσa = 0, or
TL;DR: Lanstein and Sharpe as mentioned in this paper showed that duration may be associated with unsystematic risk and that any relation between duration and systematic risk is more complex than implied in [3] and [6].
Abstract: Boquist, Racette, and Schlarbaum [3] and Livingston [6] show that a security systematic risk may be expressed as a function of its duration. These results have led to research examining the role of duration in explaining systematic risk, but Lanstein and Sharpe [5] indicate that Livingston's expression relies on the implicit assumption that extra-market covariances between securities are insignificant. Lanstein and Sharpe argue that such an assumption is unwarranted. They find a significant negative relationship between extra-market covariances and differences in duration between paired samples of common stock. Their paper suggests that duration may be associated with unsystematic risk and that any relation between duration and systematic risk is more complex than implied in [3] and [6].
TL;DR: In this article, the amount of funds to contribute to the pension fund in any given period and the selection of a particular mix of assets for that fund are discussed, and two decisions facing firms with defined benefit, trusteed pension plans.
Abstract: This paper is concerned with two decisions facing firms with defined benefit, trusteed pension plans: the amount of funds to contribute to the pension fund in any given period; and the selection of a particular mix of assets for that fund. The pension decision area is of importance for many firms today due to the recent rapid growth in pension costs in absolute terms and as a percent of firm profits. Unfunded liabilities (pension benefits payable net of pension assets) have become a sizable component of the capital structure of many firms. Pension funds (assets) also have grown rapidly due to liberalizationof pension benefits, inflation, the higher funding requirements of the pension reform law (ERISA), and the overall aging of the labor force.
TL;DR: In this article, the authors provide a theoretical framework for interpreting the long-term empirical data which does not violate the notion of a monotone increasing expected terminal wealth-beta relationship.
Abstract: Empirical tests of the Sharpe [36]–Lintner [23]–Black [3] Capital Asset Pricing Model (CAPM) have generally concluded that there is a positive, approximately linear, trade-off between average return and systematic risk (beta) for portfolio returns of common stocks. Most of the empirical studies, however, have reported data for short, usually monthly, time intervals. Exceptions to this rule include Blume and Friend [8] and Sharpe [38, pp. 289–292]. Their data provide evidence that long-term wealth ratios are concave, possibly nonmonotonic, functions of beta. These data are surprising since, if returns are intertemporally independent and the linear return model of CAPM is correct, expected multiperiod terminal wealth is a convex, monotone increasing function of beta. The results of this paper provide a theoretical framework for interpreting the long-term empirical data which does not violate the notion of a monotone increasing expected terminal wealth-beta relationship.
TL;DR: The Sturm-Kaplan method has the power to count all zeros on the real axis between any two specified limits as mentioned in this paper, which is known as Sturm's theorem.
Abstract: The algorithm leading to a solution of the above question has been known at least since Kaplan's 1965 tutorial [5] on Sturm's theorem. The Sturm-Kaplan method has the power to count all zeros on the real axis between any two specified limits. A significant problem may arise, however, when one tries to generate the Sturmian functions which play a central part in the Sturm-Kaplan method. The rather arduous nature of the task derives from the necessity to perform several polynomial (synthetic) divisions. As the number of cash flows involved in the analysis increases, the time and effort required to determine the Sturmian functions increase as well.