The persistence of earnings per share

The persistence of innovations to accounting earnings per share, EPS, has important implications for equity valuation, yet it remains a largely neglected subject. This paper employs various empirical tests in order to measure the persistence of shocks to EPS for the S&P 500 index. Within the I(0)/I(1) paradigm the empirical evidence rejects the I(1) specification, supporting instead a trend-stationary representation. When fractional orders of integration are considered, the results indicate that the detrended series is long memory (d  >  0) and mean reverting (d < 1). The responses decay slowly to zero, albeit 50 quarters after an initial shock the responses remain significantly different from zero. Likewise, the variance ratio evidence suggests that the effect of a shock persists over time spans characteristic of the business cycle.

Discounting Mean Reverting Cash Flows with the Capital Asset Pricing Model

Discounting cash flows requires an equilibrium model to determine the cost of capital. The CAPM of Sharpe and the intertemporal asset pricing model of Merton (1973) offer a theoretical justification for discounting at a constant risk adjusted rate. Two problems arise with this application. First, for mean reverting cash flows the risk adjustment is unknown, and second, if the present value is compounded forward then the distribution of future wealth is likely right skewed. I develop equilibrium discount rates for cash flows whose level or growth rate is mean reverting. Serial correlation also largely eliminates the skewness problem.     

Is integration I(d) applicable to observed economics and finance time series?

The method of cointegration in regression analysis is based on an assumption of stationary increments. Stationary increments with fixed time lag are called ‘integration I(d)’. A class of regression models where cointegration works was identified by Granger and yields the ergodic behavior required for equilibrium expectations in standard economics. Detrended finance market returns are martingales, and martingales do not satisfy regression equations. We ask if there exist detrended processes beyond standard regression models that satisfy integration I(d). We show that stationary increment martingales are confined to the Wiener process, and observe that martingales describing finance data admit neither the integration I(d) nor the ergodicity required for long time equilibrium relationships. In particular, the martingales derived from finance data do not admit the time (or ‘space’) translational invariance required for increment stationarity. Our analysis explains the lack of equilibrium observed earlier between FX rates and relative price levels.     

Occasional structural breaks and long memory with an application to the S&P 500 absolute stock returns

This paper shows that occasional breaks generate slowly decaying autocorrelations and other properties of I(d) processes, where d can be a fraction. Some theory and simulation results show that it is not easy to distinguish between the long memory property from the occasional-break process and the one from the I(d) process. We compare two time series models, an occasional-break model and an I(d) model to analyze S&P 500 absolute stock returns. An occasional-break model performs marginally better than an I(d) model in terms of in-sample fitting. In general, we found that an occasional-break model provides less competitive forecasts, but not significantly. However, the empirical results suggest a possibility such that, at least, part of the long memory may be caused by the presence of neglected breaks in the series. We show that the forecasts by an occasional break model incorporate incremental information regrading future volatility beyond that found in I(d) model. The findings enable improvements of volatility prediction by combining I(d) model and occasional-break model.     

Evidence on the Mean-Reverting Tendencies of Closed-End Fund Discounts

Closed‐end fund (CEF) discounts vary widely over time due to changes in share price, net asset value (NAV), or both. Prior studies suggest discounts are mean‐reverting. We examine the mean‐reversion issue by employing cointegration procedures. Specifically, we identify bond and equity CEFs that exhibit stationary time‐series properties and find statistically significant error correction terms that quantify the speed of mean reversion. The results indicate that mean reversion is caused by changes in both share price and NAVs. However, CEFs can only provide excess returns when the discount narrows due to share price increases.     

Arbitrage Bounds and the Time Series Properties of the Discount on UK Closed-End Mutual Funds

Abstract:  In a dataset of weekly observations over the period since 1990, the discount on UK closed-end mutual funds is shown to be nonstationary, but reverting to a nonzero long run mean. Although the long run discount could be explained by factors like management expenses etc., its short run fluctuations are harder to reconcile with an arbitrage-free equilibrium. In time series terms, there is evidence of long memory in discounts consistent with a bounded random walk. This conclusion is supported by explicit nonlinearity tests, and by results which suggest the behaviour of the discount is perhaps best represented by one of the class of Smooth-Transition Autoregressive (STAR) models.     

Uncovering the US term premium: An alternative route

The estimates of the US term premium crucially depend upon the ex-ante decision on whether the short-term rate is either an I(0) or an I(1) process. In this paper we estimate a fractionally integrated (I(d)) model which simultaneously determines both the order of integration of the short-term rate and the associated term premium. We show that the term premium experienced a sharp increase from essentially zero in mid-2007 to almost 3% in 2009. We also show that unemployment and term premium dynamics exhibit a very significant positive co-movement.     

On the convergence rate of fixed-width sequential confidence intervals

Abstract

Let X _f1, X _f2, ... be a sequence of i.i.d. random variables with mean µ and variance σ²∈ (0, ∞). Define the stopping times N(d)=min {n:n ^?1 Σ ⁿ _i=1} (X _i&#x2212;X _n)²+n ^?1?nd ²/a ²}, d>0, where X n =n ^?1 Σ ⁿ _i=1} Xi and (2π)^?½ ∫ ^a _?a exp (?u ²/2) du=α ∈(0,1). Chow and Robbins (1965) showed that the sequence I_n,d =[X_n ?d, X _n + d], n=1,2, ... is an asymptotic level -α fixed-width confidence sequence for the mean, i.e. lim_d→0 P(µ∈I_N(d),d )=α. In this note we establish the convergence rate P(µ∈I_N(d),d )=α + O(d½?δ) under the condition E|X₁|^3+?+5/(28) < ∞ for some δ ∈ (0, ½) and ??0. The main tool in the proof is a result of Landers and Rogge (1976) on the convergence rate of randomly selected partial sums.     

Real options with a double continuation region

If the average risk-adjusted growth rate of the project's present value V overcomes the discount rate but is dominated by the average risk-adjusted growth rate of the cost I of entering the project, a non-standard double continuation region can arise: The firm waits to invest in the project if V is insufficiently above I as well as if V is comfortably above I. Under a framework with diffusive uncertainty, we give exact characterization to the value of the option to invest, to the structure of the double continuation region, and to the subset of the primitives' values that support such a region.     

On the Equivalence between the APV and the wacc Approach in a Growing Leveraged Firm

While in a steady state framework the choice between the wacc approach ( Modigliani‐Miller, 1963 ) and the adjusted present value (APV) approach ( Myers, 1974 ) is irrelevant since the two approaches provide the same result, however, in a growing firm context the wacc equation seems to be inconsistent with the APV result. In this paper we propose a simple model to evaluate the tax savings in a growing firm in order to show under which assumptions the two approaches lead to the same results. We demonstrate that the use of the wacc model in a steady‐growth scenario gives rise to some unusual assumptions with regard to the discount rates to be used in calculating tax shields. We show that the widely used wacc formula, if used, as it is in most cases, in a growth context, implies that a) debt tax shield related to already existing debt are discounted using k_d; b) debt tax shield related to new debt, due to company's growth, are discounted, according to a mixed procedure, using both k_u and k_d. We discuss the inconsistency of such a discounting procedure and the preferred features of the APV approach.     

A note on different models of stochastic processes dealt with in the collective theory of risk

Abstract

1. For the definition of general processes with special regard to those concerned in Collective Risk Theory reference is made to Cramér (Collective Risk Theory, Skandia Jubilee Volume, Stockholm, 1955). Let the independent parameter of such a process be denoted by τ, with the origin at the point of departure of the process and on a scale independent of the number of expected changes of the random function. Denote with p(τ, n)dt the asymptotic expression for the conditional probability of one change in the random function while the parameter passes from τ to τ + dτ: relative to the hypothesis that n changes have occurred, while the parameter passes from 0 to τ. Assume further—unless the contrary is stated—that the probability of more than one change, while the parameter passes from τ to τ + dτ, is of smaller order than dτ.     

When are investment projects in the same risk class?

If two investments have the same pay‐off covariance with the market but one has higher expected pay‐off, which asset according to the CAPM has most risk? One answer is that as far as risk goes the two assets are the same, because they have the same covariance with the market. The correct answer, pointed out nearly four decades ago by Eugene Fama, but long overlooked, is that investments have the same risk, the same returns beta and the same CAPM discount rate if and only if they have the same ratio of ex ante pay‐off covariance to pay‐off mean. This insight clarifies much of the conventional wisdom that surrounds capital budgeting and ‘risk‐adjusted’ discount rates, while also displaying the mechanics by which information arrival affects the CAPM cost of capital.     

The monetary model in the presence of I(2) components: long-run relationships, short-run dynamics and forecasting of the Greek drachma

This paper re-examines the long-run properties of the monetary exchange rate model using data for the drachma–dollar and drachma–mark exchange rates under the hypothesis that the system contains variables that are I(2). Using the recent I(2) test by Paruolo (On the determination of integration indices in I(2) systems. J. Economet. 72 (1996) 313–356) to examine the presence of I(2) and I(1) components in a multivariate context we find that the system contains two I(2) variables in both cases and this finding is reconfirmed by the estimated roots of the companion matrix (Do purchasing power parity and uncovered interest rate parity hold in the long-run? An example of likelihood inference in a multivariate time-series model. Juselius, J. Economet. 69 (1995) 211–240). The I(2) component led to the transformation of the estimated model by imposing long-run but not short-run proportionality between domestic and foreign money. Two statistically significant cointegrating vectors were found and, by imposing linear restrictions on each vector as suggested by Johansen and Juselius (Identification of the long-run and the short-run structure: an applicaion to the ISLM model. J. Economet. 63 (1994) 7–36) and Johansen (Identifying restrictions of linear equations with applications to simultaneous equations and cointegration. J. Economet. 69 (1995b) 111–132), the order and rank conditions for identification are satisfied, but the test for overidentifying restrictions was not significant only for the case of the drachma/mark rate. The main findings suggest that we reject the forward-looking version of the monetary model for the drachma/dollar case but not when the drachma/mark rate is used, a result that is attributed to the monetary and exchange rate policy followed by the Greek authorities since Greece's joining of the European Union. Furthermore, we test for parameter stability using the tests developed by Hansen and Johansen (Recursive estimation in cointegrated VAR-models. Working paper (1993) University of Copenhagen) and it is shown that the dimension of the cointegration rank is sample independent while the estimated coefficients do not exhibit instabilities in recursive estimations. Finally, it is shown that the monetary model outperforms the random walk model in an out-of-sample forecasting contest.     

A Reconsideration of Tax Shield Valuation

A quarter‐century ago, Miles and Ezzell (1980) solved the valuation problem of a firm that follows a constant leverage ratio L = D/S. However, to this day, the proper discounting of free cash flows and the computation of WACC are often misunderstood by scholars and practitioners alike. For example, it is common for textbooks and fairness opinions to discount free cash flows at WACC with beta input β _S = [1 + (1 ? τ)L]β_u, although the latter is not consistent with the assumption of constant leverage. This confusion extends to the valuation of tax shields and the proper implementation of adjusted present value procedures. In this paper, we derive a general result on the value of tax shields, obtain the correct value of tax shields for perpetuities, and state the correct valuation formulas for arbitrary cash flows under a constant leverage financial policy.     

An analysis of real-estate risk using the present value model

The current study uses a present value model that allows for a time-varying expected discount rate in conjunction with a VAR process to decompose real-estate risk. The study finds that the variance ofunexpected returns accounts for most of the total risk with cash-flow risk accounting for twice as much of the unexplained real-estate risk although discount rate risk is also an important factor. This dominance of cash-flow risk is found to result in a weaker mean reversion process for real estate relative to stocks. Another finding is that real estate investors tend to become apprehensive about the future when news on future cash flow is good, and thus they demand higher expected future returns.     

When does the dividend–price ratio predict stock returns?

If the dividend–price ratio becomes I(1) while stock returns are I(0), the unbalanced predictive regression makes the predictability test more likely to indicate that the dividend–price ratio has no predictive power. This might explain why the dividend–price ratio evidences strong predictive power during one period, while it exhibits weak or no predictive power at other times. Using international data, this paper demonstrates that the dividend–price ratio generally has predictive power for stock returns when both are I(0). However, this paper also shows that the dividend–price ratio loses its predictive power when it becomes I(1). The results are shown to be robust across countries.     

Forecasting Medical Net Discount Rates

Determining the present value of future medical costs is an important issue for a variety of public and private entities. This article examines the time‐series properties of medical net discount rates and considers the implications for forecasting. The article provides evidence that the standard autoregressive moving average forecasting model may be improved by modeling the time‐varying volatility characteristics of the medical net discount rates.     

Long memory versus structural breaks in modeling and forecasting realized volatility

We explore the possibility of structural breaks in the daily realized volatility of the Deutschemark/Dollar, Yen/Dollar and Yen/Deutschemark spot exchange rates with observed long memory behavior. We find that structural breaks in the mean can partly explain the persistence of realized volatility. We propose a VAR-RV-Break model that provides superior predictive ability when the timing of future breaks is known. With unknown break dates and sizes, we find that a VAR-RV-I(d) long memory model provides a robust forecasting method even when the true financial volatility series are generated by structural breaks.     

Commentary: Some Further Evidence on Discount Rate Selection in the Context of Goodwill Impairment Testing

In an earlier edition of this journal, we published evidence relating to the nature of discount rates chosen by a sample of large Australian‐listed firms in the context of their goodwill impairment testing ( Carlin and Finch 2009 ). We argued that our evidence suggested that the rigour of the International Financial Reporting Standards (IFRS) goodwill impairment testing process was being undermined by inappropriate choice of discount rates on the part of many firms. In a commentary published alongside our article, questions were raised as to the validity of our conclusions and the methodology we applied in our study ( Gallery 2009 ). Subsequently, Bradbury has also contributed to the debate, raising similar concerns to those voiced by Gallery ( Bradbury 2010 ). In this brief paper, we provide further and better particulars in relation to our original dataset in a bid to assist those who have taken an interest in this debate to further inform their view of the merits (or otherwise) of the case we made in our original article.     

THE ROBUSTNESS OF ABNORMAL RETURNS FROM THE EARNINGS YIELD CONTRARIAN INVESTMENT STRATEGY

We examine the sensitivity of the abnormal profitability of the earnings' yield (E/P)‐based contrarian investment strategy to the following two risk measurement issues: (a) return‐measurement interval over which systematic risk is estimated and (b) time variation in systematic risk. We conduct our analysis using the capital asset pricing model to parameterize risk. We find that the estimates of systematic risk of E/P‐ranked portfolios are not sensitive to the return‐measurement interval. Consequently the abnormal profits to the E/P‐based contrarian investment strategy observed in prior studies are not artifacts of the return‐measurement interval. Furthermore, although both the raw and abnormal returns to E/P‐ranked portfolios exhibit mean reversion, time variation in systematic risk ensuing from this mean‐reverting behavior does not substantially affect abnormal profits to E/P‐ranked portfolios. JEL classification: G11, G12, G14