Binomial basis for linear information dynamics: real options, dividends and the valuation of equity

Analytical research has confirmed that real options give rise to the kind of nonlinearities observed in practice between equity prices and the figures appearing on corporate financial statements. We develop these real option values in terms of a quasi 'supply-side' model of linear information dynamics based on simple discrete time binomial filtration processes. Our analysis shows that the linear models that pervade the empirical (and analytical) work of the area, will almost certainly suffer from an omitted variables problem. Parameter estimation will then be inconsistent and inefficient.     

Consumption-based equity valuation

Using a CCAPM-based risk-adjustment model, we perform yearly valuations of a large sample of stocks listed on NYSE, AMEX, and NASDAQ over a 30-year period. The model differs from standard valuation models in the sense that it adjusts forecasted residual income for risk in the numerator rather than through a risk-adjusted cost of equity in the denominator. The risk adjustments are derived based on assumptions about the time-series properties of residual income returns and aggregate consumption rather than on historical stock returns. We compare the performance of the model with several implementations of standard valuation models, both in terms of median absolute valuation errors (MAVE) and in terms of excess returns on simple investment strategies based on the differences between model and market prices. The CCAPM-based valuation model yields a significantly lower MAVE than the best performing standard valuation model. Both types of models can identify investment strategies with subsequent excess returns. The CCAPM-based valuation model yields time-series of realized hedge returns with more and higher positive returns and fewer and less negative returns compared with the time-series of realized hedge returns based on the best performing standard valuation model for holding periods from 1 to 5 years. In a statistical test of 1-year-ahead excess return predictability based on the models’ implied pricing errors, the CCAPM-based valuation model is selected as the better model. Using the standard series of aggregate consumption and the nominal price index, a reasonable level of relative risk aversion, and calibrated growth rates in the continuing value at each valuation date, the CCAPM-based valuation model produces small risk adjustments to forecasted residual income and low continuing values. Compared with standard valuation models, it relies less on estimated parameters and speculative elements when aggregating residual earnings forecasts into a valuation.     

Real (adaptation) options and the valuation of equity: some empirical evidence

Data from 1,374 firms across four broad industrial groupings are used to assess the contribution that real (adaptation) options make to overall equity values. The analysis indicates that real (adaptation) options make a significant contribution to the equity value of firms with a market to book ratio (of equity) of around unity or less. As the market to book ratio grows beyond this level, however, the contribution made by real (adaptation) options decays quickly away and equity values are mainly comprised of the present value of the dividends that firms are expected to pay. This means that for around one in every five of the firms in our sample real (adaptation) options make a significant contribution to overall equity value. Thus, while linear equity valuation models would seem to be appropriate for the substantial majority of firms on which our sample is based, there is a sizeable minority of firms where real (adaptation) options have a significant impact on equity values. For this latter group of firms there will be a non-linear relationship between equity value and its determining variables. This has important implications for the regression procedures that are applied in this area of accounting research.     

Familiarity bias and earnings-based equity valuation

Review of Quantitative Finance and Accounting - This study examines whether investors’ familiarity bias affects their earnings-based equity valuation. Building on theoretical and empirical...     

Pricing equity options everywhere

Finite difference methods are a popular technique for pricing American options. Since their introduction to finance by Brennan and Schwartz their use has spread from vanilla calls and puts on one stock to path-dependent and exotic options on multiple assets. Despite the breadth of the problems they have been applied to, and the increased sophistication of some of the newer techniques, most approaches to pricing equity options have not adequately addressed the issues of unbounded computational domains and divergent diffusion coefficients. In this article it is shown that these two problems are related and can be overcome using multiple grids. This new technique allows options to be priced for all values of the underlying, and is illustrated using standard put options and the call on the maximum of two stocks. For the latter contract, I also derive a characterization of the asymptotic continuation region in terms of a one-dimensional option pricing problem, and give analytic formulae for the perpetual case.     

Private equity valuation under time-inconsistent preferences

Our research expands on the private equity (PE) valuation theory by incorporating the limited partner’s (LP) time-inconsistent preferences. Our findings show that time inconsistency has a detrimental impact on the LP’s certainty-equivalent valuation, which is dependent on the duration of investment and the value of PE asset. Through a comparative static analysis of the risk-attitude parameter and the future self arrival intensity, we have determined that the negative effects of time inconsistency can be mitigated by a more conservative attitude on the part of LP, while a higher future self arrival intensity exacerbates the impact of LP’s time inconsistency on their certainty-equivalent valuation.     

A note on accounting conservatism in residual income and abnormal earnings growth equity valuation

The impact of conservative accounting on residual income (RI) and abnormal earnings growth (AEG) valuation models is investigated in this note. Limiting the analyses to information dynamics constrained models (the core models in Ohlson, 1995; Ohlson & Juettner-Nauroth, 2005), we find that both models can handle accounting conservatism if the persistence factors of residual income or abnormal earnings growth fulfil certain conditions. In a comparison of permissible time-series specifications, the AEG model can potentially handle more conservatively biased earnings in the first forecast period than the RI model. However, this requires that the growth of the conservative bias in the second forecast period is not too large. In a 0-NPV competitive equilibrium with a constant steady state growth, both models work equally well. Further elaborations indicate that, in the presence of accounting conservatism a reasonable value of the persistence factor of residual income in the RI model should be in the interval between 1.0 and R (where R = 1 + discount rate), whereas the persistence factor of abnormal earnings growth in the AEG model should be close to 1.0. This implies that the persistence factor in the RI model appears to have been understated while the persistence factor in the AEG model appears to have been overstated in previous empirical research.     

Accounting diversity and firm valuation

We examine accounting numbers and stock prices across three countries: Germany, Norway, and the United Kingdom (UK). The accounting systems in the three countries differ in faithfulness to clean surplus accounting and in conservatism. We address three questions. First, are there systematic differences across countries in the value relevance of accounting? Second, are there systematic differences in the incremental and relative value relevance of book values and earnings per shape (EPS) across the countries? Third, do future earnings realizations (proxies for expected earnings) explain current stock prices? We find that accounting book value and EPS are significantly related to current stock prices across all three countries. German accounting numbers have the lowest relation with stock prices (R² ≈ 40%) and UK accounting numbers the highest (R² ≈ 70%), while Norwegian accounting numbers are in between (R² ≈ 60%). Second, the incremental and relative explanatory power of book value and of EPS differs across time and across countries. Book values explain more than earnings in Germany and Norway, but less in the UK. Finally, future income realization explain little about market prices not already explained by current book value and EPS.     

The valuation of compound options

This paper presents a theory for pricing options on options, or compound options. The method can be generalized to value many corporate liabilities. The compound call option formula derived herein considers a call option on stock which is itself an option on the assets of the firm. This perspective incorporates leverage effects into option pricing and consequently the variance of the rate of return on the stock is not constant as Black-Scholes assumed, but is instead a function of the level of the stock price. The Black-Scholes formula is shown to be a special case of the compound option formula. This new model for puts and calls corrects some important biases of the Black-Scholes model.     

Rainbow trend options: valuation and applications

Asset selection and timing decisions are major investment concerns. To resolve these issues simultaneously, a new class of rainbow trend options is proposed. The diversification effect of rainbow options can reduce the importance of asset selection decisions and trend options can mitigate unfavorable effects on market entry and exit decisions. We consider a general framework to facilitate the derivation of analytic pricing formulas for simple, pure, and Asian rainbow trend options using the martingale pricing method. The properties of these options and their Greeks are analyzed. We also investigate the performance of the dynamic delta hedging strategy for issuers of rainbow trend options. Last, this paper explores the applications of rainbow trend options for hedging price risks, designing executive stock options, modifying countercyclical capital buffer proposed by Basel Committee, and acting as control variates of the Monte Carlo simulation.     

Seasonality and the valuation of commodity options

Price movements in many commodity markets exhibit significant seasonal patterns. However, given an observed futures price, a deterministic seasonal component at the price level is not relevant for the pricing of commodity options. In contrast, this is not true for the seasonal pattern observed in the volatility of the commodity price. Analyzing an extensive sample of soybean, corn, heating oil and natural gas options, we find that seasonality in volatility is an important aspect to consider when valuing these contracts. The inclusion of an appropriate seasonality adjustment significantly reduces pricing errors in these markets and yields more improvement in valuation accuracy than increasing the number of stochastic factors.     

Liquidation triggers and the valuation of equity and debt

Many bankruptcy codes implicitly or explicitly contain net-worth covenants, which provide the firm’s bondholders with the right to force reorganization or liquidation if the value of the firm falls below a certain threshold. In practice, however, default does not necessarily lead to immediate change of control or to liquidation of the firm’s assets by its debtholders. To consider the impact of this on the valuation of corporate securities, we develop a model in which liquidation is driven by a state variable that accumulates with time and severity of distress. We model a dynamic grace period for the liquidation event. Recent or severe distress events may have greater impact on the liquidation trigger. Our model can be applied to a wide array of bankruptcy codes and jurisdictions.     

The analytic valuation of American options

No analytic solution exists for the valuation of American optionswritten on futures contracts and foreign currencies for whichearly exercise may be optimal. This article formulates the Americanoption valuation problem in economically and mathematicallymeaningful ways. This enables us to derive valuation formulasfor American options. The properties associated with the optimalexercise boundary are examined, and a numerical technique toimplement the valuation formulas is presented.     

Using accounting information for consumption planning and equity valuation

This article develops a consumption-based valuation model that treats earnings and cash flow as complementary information sources. The model integrates three ideas that do not appear in traditional valuation models: (i) earnings provide information about future shocks to cash flow; (ii) earnings contain indiscernible transient accruals; and (iii) investors use cash flow and earnings to make allocation and consumption decisions and set price. Accordingly, the quality of earnings affects production and consumption as well as price. Among other implications, the model reveals that a valuation coefficient is not just a capitalization factor; it is the product of a capitalization factor and a structural factor reflecting earnings quality and accounting bias.     

The analysis and valuation of interest rate options

This paper provides a simple, alternative model for the valuation of European-style interest rate options. The assumption that drives the hedging argument in the model is that the forward prices of bonds follow an arbitrary two-state process. Later, this assumption is made more specific by postulating that the discount on a zero-coupon bond follows a multiplicative binomial process. In contrast to the Black-Scholes assumption applied to zero-coupon bonds, the limiting distribution of this process has the attractive features that the zero-bond price has a natural barrier at unity (thus precluding negative interest rates), and that the bond price is negatively skewed. The model is used to price interest rate options in general, and interest rate caps and floors in particular. The model is then generalized and applied to European-style options on bonds. A relationship is established between options on swaps and options on coupon bonds. The generalized model then provides a computationally simple formula, closely related to the Black-Scholes formula, for the valuation of European-style options on swaps.     

Exercise behavior,valuation, and the incentive effects of employee stock options

We use a large database on ESO exercises to document characteristics of exercise behavior and calibrate a utility-based model for measuring how differences in exercise behavior are manifested in option values and incentives. Option values and incentives computed from the model calibrations are compared to those computed from models used to value tradable options. Our analysis provides guidance to both academics and practitioners about how differences in exercise behavior and model choice affect measures of ESO values and incentives, and underscores the importance of gaining a thorough understanding of the underlying economic forces that affect the behavior of ESO holders.     

Residual income,value-relevant information and equity valuation: a simultaneous equations approach

The paper uses Ohlson (Contemp Account Res 11:661–687, 1995) and compares the relative predictability of the proposed simultaneous model for contemporaneous stock price with a traditional single equation model used by the previous studies. The paper also explores how residual income and value-relevant information affect firms’ equity price. The main results of the paper suggest that the predictive ability and estimation efficiency of the simultaneous models in explaining contemporaneous stock prices are better than those of the traditional single models. Moreover, investors will use the value-relevant information beyond accounting earnings, namely analysts’ earnings forecasts, bankruptcy cost and agency cost, in equity valuation to make decision. Note particularly, the higher the bankruptcy or agency cost is, the more important the role it plays in equity valuation and, on average, the higher the accuracy of price prediction is.

A fuzzy-based approach to residual income equity valuation

The decision of whether to buy, hold or sell equities depends on whether the current price reflects the stock’s intrinsic or fundamental value. The residual income valuation model expresses this fundamental value as a function of current book value of equity plus the sum of discounted expected residual income. Although past and present income and book value information is readily available to investors, values taken by essential parameters in this model are unknown ex ante, particularly the cost of equity or discount rate and future residual income. Any point estimate of equities’ fundamental value according to the model may therefore conceal considerable variation around the estimate, even in the presence of minor perturbations in the model’s inputs. In this paper, we introduce a fuzzy-based approach which reflects the imprecision inherent in certain parameters in equity valuation. We extend the limited prior fuzzy-based literature on investment analysis by introducing the concept of fuzzy fundamental equity value, initially on an illustrative example. To further demonstrate this fuzzy representation, illustrative financial statement data for individual UK companies are considered, with fuzzy fundamental equity values evaluated over progressive forecast horizons. Our series of illustrative applications (which encompasses the standard crisp approach) make the inherent uncertainty involved in estimating equity value immediately apparent.     

Accounting data and asset valuation: Theory

Firms and divisions which are not traded on organized exchanges are often valued without the benefit of market data. Accounting data is used instead. One suggested approach is to use accounting beta as a proxy for market return beta. In the context of the Arbitrage Pricing Theory, we provide a theoretical justification for such a procedure. Our results provide a set of sufficient conditions so that return betas and accounting betas are equal. Our results also suggest a general methodology for evaluating projects and untraded firms using accounting data. The method underlying the derivation here is very general and can be applied in deriving testable restrictions between fundamentals, broader in context than that of accounting variables.