Valuation Equation Research Articles

Understanding Policy in the Great Recession: Some Unpleasant Fiscal Arithmetic

I use the valuation equation of government debt to understand fiscal and monetary policy in and following the great recession of 2008-2009, to think about whether the US is headed for a fiscal inflation, and what that inflation will look like. I emphasize that a fiscal inflation can come well before large deficits or monetization are realized, and is likely to come with stagnation rather than a boom.

Structural Default Modeling: A Lattice-Based Approach

That the stockholders’ right to default on corporate debt is an option has been understood since Merton’s seminal 1974 article. Later work by Geske and others applied Merton’s insight to more complex, and more realistic, capital structures and default criteria. Unfortunately, while it is not too hard to write down valuation equations for a firm with multiple classes of risky debt, the equations typically involve high-order multivariate normal distributions, which are quite difficult to evaluate computationally. In this article, Jabbour, Kramin, and Young propose a lattice model in which the default risk in complex capital structures becomes easier to deal with. One key to their approach is to build survival probabilities directly into the tree.

Diversification, Refocusing and Firm Value

Abstract At any point in time a firm faces three restructuring choices: diversify, refocus, or do nothing. This study analyses the causes and the consequences of these actions in a unified framework using the appropriate methodologies. Various factors, such as firm's characteristics and multinational nature, its industry's characteristics, its exchange and index inclusion, and divested (or acquired) segment(s)' industry conditions, are considered as the determinants of the diversifying and the refocusing decisions. The estimation results from the corresponding multinomial logit model suggest that refocusing occurs generally due to firm‐specific reasons, and diversification due to outside factors, such as industry and economic conditions. Added or dropped segment's industry profitability, its relationship to the core business of the firm, and its relatedness to the businesses of the conglomerate's other segments have a nontrivial effect on either decision. In a related analysis, the paper explicitly models and estimates the valuation consequences that are sustained by the firm after it undertakes a refocusing or a diversification action. To isolate the changes in firm's value that are due to these decisions only, a 2SLS estimation is used to control for endogeneity that arises because the factors that affect a firm's value are likely to have also induced the firm to make the corresponding decision. The novelty of my approach is in its inclusion of variables measuring the consequences due to both actions, the diversification and the refocusing, in the same valuation equation. Contrary to some earlier findings, I find no evidence of ‘diversification discount’ or ‘refocusing premium.’ The choice of this paper to analyse all corporate restructuring decisions in a unified framework yields valuable business insights into the reasons for undertaking such corporate events.

A note on the integrability of the classical portfolio selection model

We revisit the classical Merton portfolio selection model from the perspective of integrability analysis. By an application of a nonlocal transformation the nonlinear partial differential equation for the two-asset model is mapped into a linear option valuation equation with a consumption dependent source term. This result is identical to the one obtained by Cox–Huang [J.C. Cox, C.-f. Huang, Optimal consumption and portfolio policies when asset prices follow a diffusion process, J. Econom. Theory 49 (1989) 33–88], using measure theory and stochastic integrals. The nonlinear two-asset equation is then analyzed using the theory of Lie symmetry groups. We show that the linearization is directly related to the structure of the generalized symmetries.

Two ways to solve, using Lie group analysis, the fundamental valuation equation in the double-square-root model of the term structure

Two approaches based on Lie group analysis are employed to obtain the closed-form solution of a partial differential equation derived by Francis A. Longstaff [J Financial Econom 1989;23:195–224] for the price of a discount bond in the double-square-root model of the term structure.

Present Value with Random Stopping Times

Discounting an income stream with a random stopping time produces a formula similar to one for a perpetuity, except that a risk premium is added to the discount rate. This results in a valuation equation that is convenient to apply to complex multi-phase income streams. It suggests a framework for empirical research that includes, for example, bankruptcy rates derived from company fundamentals to estimate the expected stopping time of a business, and offers an additional perspective on the role of interest rates in the economy.

Accounting Earning, Book Value and Cash Flow in Equity Valuation: An Empirical Study on CNX NIFTY Companies

Way back in 1934, Graham and Dodd observed the importance of earning power in investment theory. According to them, history of actual earning with a reasonable expectation should be approximated in future. The empirical study of Ball and Brown (1968) contends that - of all the sources of information as regards the working of a firm during a year, income number reported in the annual income statement captures one-half or more.In the backdrop of relevance of accounting numbers for equity valuation, Ohlson (1995) and Feltham & Ohlson (1995) provide an objective valuation model based on abnormal earning. According to the models, the fundamental of valuation depends on abnormal earning (NIa) - an autoregressive process of the first order [AR (1)] - that is related to the abnormal earning of the previous period. Along with abnormal earning there may be other variables like book value of the equity, operating cash flow, accruals and other information [all of them being autoregressive - AR (1) process] can be used severally and jointly for predicting equity value.In the present paper we have made an attempt to taste the forecasting ability of equity share value of CNXNIFTY companies of the National Stock Exchange of India empirically for a period covering altogether10 years (1999 to 2008) by pooling cross-sectional data on abnormal earning, book value and operating cash flow in line with the forecasting and valuation equation models of Ohlson (1995) and Feltham & Ohlson (1995). Our findings suggest that abnormal earning ,book value and operating cash flow component of earning respectively follow an autoregressive process. Information on abnormal earning and book value aid in predicting equity value. The findings are consistent with Ohlson model.

Cost of capital equations under the Australian imputation tax system

AbstractSince the introduction of the Australian imputation tax system, there have been problems both in the measurement of the market value of franking (imputation tax) credits and in their application to estimating cash flows and the cost of capital. In the present paper, we provide a convenient and robust resolution to the above problems in the context of an internally consistent set of equations for the cost of capital, asset valuation and the capital asset pricing model (CAPM). The equations apply under both classical and imputation tax systems and under differential taxation of dividends, capital gains and interest. The simple form of the CAPM presented here is shown to encompass more complex versions of the CAPM, which attempt to accommodate the effect of personal taxes. The valuation equations require an estimate of the market value of $1 of the firm's dividends, within which is embedded the market value of the imputation tax credits. Separate estimates of the value of imputation tax credits, or Officer's gamma factor, are not required.

Closed‐Form Mortgage Valuation Using Reduced‐Form Model

Valuing mortgage‐related securities is more complicated than valuing regular defaultable claims due to the borrower's prepayment behavior as well as the possibility of default. Some researchers use a structural‐form model to obtain the closed‐form formulas for the mortgage value. With this method, however, it is difficult to identify the critical region of early exercise. As an alternative, the reduced‐form model developed in this article is able to value the mortgage without setting boundary conditions, and it can thereby accurately handle the multidimensional space of correlated state variables. The purpose of this article is to derive a closed‐form solution of the mortgage valuation equation under a general reduced‐form model that embeds relevant economic variables. This new approach enables portfolio managers to undertake sophisticated portfolio optimization and hedging analyses. An implementation procedure for the model is also provided to demonstrate how the valuation framework can be utilized in practical applications.

The Theory of Finance in a Nutshell

Using a few simple and basic principles, the main results of the modern theory of finance are obtained, from CAPM to option prices, from risk neutral valuation to intertemporal model, non-expected utility and behavioral finance. The basic intuition inside the valuation equation is that the price of any asset is the sum of the prices of the moments of its probability distribution multiplied by their quantity. This set-up can lead to classical results but it is also capable of several important and easy-to-think generalizations which can be proved useful from both theoretical and practical points of views.

The value of knowledge spillovers in the U.S. semiconductor industry

This paper aims at quantifying the economic value of knowledge spillovers by exploring information contained in patent citations. We estimate a market valuation equation of the U.S. semiconductor firms during the 1980s and 1990s, and find an average value of $0.6 to 1.2 million “R&D-equivalent” dollars for knowledge spillovers embodied in one patent citation. For an average semiconductor firm, such an estimate implies that the total value of knowledge spillovers the firm received during the sample period can be as high as half of its actual total R&D expenditures in the same period. This provides a direct measure of the economic value of social returns or externalities of relevant technological innovations. We also find that the value of knowledge spillovers declines as the size of firm's patent portfolio increases, and that self citations are more valuable than external citations, indicating a significant amount of tacit knowledge or know-how spillovers that occur within the firm.

Calibration Risk for Exotic Options

For academic modelers, the major objective is typically to derive a valuation equation for a derivative instrument, while computing Greek letter risks is only a secondary consideration. For users of models in the real world, however, the market provides the correct value and the parameters of the theoretical pricing model are calibrated to match the market, in order to generate risk assessment and risk management strategies consistent with the way the market is currently pricing the security. But calibration can be done in a number of ways. Do we want parameters that minimize the overall discrepancy between model values and market prices in dollars, or in percent? Alternatively, should we focus on the crucial but unobservable volatility parameter and minimize aggregate differences between the implied volatility from the model and Black-Scholes implied volatility, either in volatility points or in percentages? This might make sense because the latter are often used in setting option price quotes in the market. In this paper, the authors examine what impact this choice has on the results of model calibration, taking as examples the Heston stochastic volatility model and the Bates model, which allows price jumps as well. They find considerable difference among parameters estimated by using absolute price differences versus one of the other techniques. The paper demonstrates that the choice of calibration method can have a substantial impact on pricing of exotic option contracts and on model risk. One result is that calibration based on absolute price discrepancies produces quite different parameter estimates than the other three methods. <b>TOPICS:</b>Options, VAR and use of alternative risk measures of trading risk, volatility measures

Discussion of “Using accounting information for consumption planning and equity valuation”

This paper discusses Yee (2007), who investigates the role of accounting information for consumption planning and equity valuation. Higher earnings quality increases investor welfare and ex ante stock prices as well as the weight on earnings in valuation equations based on both cash flows and earnings. The former is due to improved consumption smoothing through more informed production choices, while the latter is due to the impact on the relative information content of current cash flows versus earnings about future cash flows.

Valuation of derivatives based on single-factor interest rate models

The CKLS [Chan, K.C., Karolyi, G.A., Longstaff, F.A., & Sanders, A.B. (1992). An empirical comparison of the short-term interest rate, Journal of Finance, 1(7), 1209–1227] short-term risk-free interest rate process leads to a valuation model for both default-free bonds and contingent claims that can only be solved numerically for the general case. Valuation equations of this nature in the past have been solved using the Crank Nicolson scheme. In this paper, we introduce a new numerical scheme — the Box method, and compare it with the traditional Crank Nicolson scheme. We find that in specific cases of the CKLS process where analytical prices are available, the new scheme leads to more accurate results than the Crank Nicolson scheme.

The Tax-CAPM With Stochastic Dividends (Das Tax-CAPM Mit Stochastischen Dividenden)

The IDW (Institut der Wirtschaftsprufer in Deutschland) proposes to derive the cost of capital, that are required for valuation with the DCF-approach, by using the Tax-CAPM. The original version of the model assumes deterministic dividends. To valuate stochastic cash-flows however, a Tax-CAPM with stochastic dividends is required. The paper deals with integrating stochastic dividends into the Tax-CAPM. In the first part of the paper, the equilibrium equation of the Tax-CAPM with stochastic dividends is derived for different assumptions concerning the tax system. A former version of an equilibrium equation, that does not model the influence of taxation on the beta-factor appropriately, is corrected. In the second part, an interpretation of the equilibrium equation is given. In the third part, single-period valuation equations are derived.

VALUATION OF EVENT‐CONTINGENT OPTIONS

AbstractI study a new class of investment options, event‐contingent options. These are options to invest and divest in projects that are dependent on other projects of the same firm or that are conditioned by projects of other firms in its value chain. I construct payoff functions and derive closed‐form solutions for the value of options to invest contingent on investment (OICI), options to invest contingent on divestment (OICD), options to divest contingent on divestment (ODCD), and options to divest contingent on investment (ODCI). I also derive analytical comparative statics for these option valuation equations and examine their implications on the firm's wealth. I offer examples of event‐contingent options in a global context.

The economics of using forests to increase carbon storage

Changes in forest-management practices have the potential to increase forest land carbon storage, which would help to reduce CO2 concentrations in the atmosphere linked to climate change and contribute to Kyoto Protocol targets for signatory countries. However, successfully increasing carbon storage while maintaining economic profitability is challenging because of the long planning horizons required for many forest activities and slow carbon sequestration rates in northern forests. The literature on the economics of forest management for carbon storage is unfortunately sparse and, in many instances, confused and misleading. Three carbon valuation equations are widely used that give contradictory results, with two of them (flow summation and average storage) ignoring the time-value carbon benefits and other essential data. Only the discounted carbon equation gives reasonably interpretable economic results. As well, many studies have omitted essential economic gradients that result in structurally questionable results. I review the literature, highlighting deficiencies in equations and how analyses are structured with the intent to produce a reasonable method of interpreting previous work and advice for future studies.

Corporate Failure and Equity Valuation

An important problem for portfolio managers is how to adjust the valuation of equity for the risk that the company may fail. Traditional adjustments seem ad hoc, and previous research on the topic has ignored the irreversible nature of failure. Here, a standard equity valuation model is extended to include a parsimonious but rigorous correction for a stationary annual probability of failure. Although the correction is nonlinear, it can be reduced to an equivalent function that enters the valuation equation in the traditional additive way. Empirical benchmarking suggests that, even without assuming risk-averse investors, this approach comes closer to predicting observed equity premiums than the traditional approach.

The Value of Knowledge Spillovers

This paper aims at quantifying the economic value of knowledge spillovers by exploring information contained in patent citations. We estimate a market valuation equation for semiconductor firms during the 1980s and 1990s, and find an average value in the amount of $0.6 to 1.2 million R&D-equivalent dollars for the knowledge spillovers as embodied in one patent citation. For an average semiconductor firm, such an estimate implies that the total value of knowledge spillovers the firm received during the sample period could be as high as half of its actual total R&D expenditures in the same period. This provides a direct measure of the economic values of the social returns or externalities of relevant technological innovations. We also find that the value of knowledge spillovers declines as the size of the firm's patent portfolio increases, and that self citations are more valuable than external citations, indicating a significant amount of tacit knowledge or know-how spillovers that occur within the firm.

Accruals, Accounting-Based Valuation Models, and the Prediction of Equity Values

This study uses out-of-sample equity value estimates to determine whether earnings disaggregation, imposing linear information valuation model (LIM) structure and separate industry estimation of valuation model parameters aid in predicting contemporaneous equity values. We consider three levels of earnings disaggregation: aggregate earnings, cashflow and total accruals and cash flow and four major components of accruals. For pooled estimations, imposing the LIM structure results in significantly smaller prediction errors; for by-industry estimations, it does not. However, by-industry prediction errors are substantially smaller, suggesting that the by-industry estimations are better specified. Mean squared and absolute prediction errors are smallest when earnings are disaggregated into cash flow and major accrual components; median prediction errors are smallest when earnings are disaggregated into cash flow and total accruals. These findings suggest that (1) if concern is with errors in the tails of the equity value prediction error distribution, then earnings should be disaggregated into cash flow and the major accrual components; otherwise earnings should be disaggregated only into cash flow and total accruals; (2) imposing the LIM structure neither increases nor decreases prediction errors, which supports the efficacy of drawing inferences from valuation equations based on residual income models that do not impose the structure implied by the model; (3) valuation of abnormal earnings, accruals, accrual components, equity book value, and other information varies significantly across industries.