Lo sagrado y lo profano como ámbitos recíprocamente excluyentes

The literature review has discussed the advantages and disadvantages of modelling two accounting variables, i.e. earnings and cash flows. In annual reports, earnings and cash flows are not necessarily equal to each other by construction, but accumulated earnings and cash flows throughout the life of a firm are considered to converge in the long run. Firms in a steady stage or with a short operating cash cycle tend not to have a substantial deviation between earnings and cash flow. In general, earnings with information of accrual terms provide a better indication of future income than cash flow whereas the cash flow measure has the advantage of less manipulation than earnings. Therefore, the financial analysis procedure that takes both items into account should be more informative than looking into either one of them separately.

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As measures of profit, prediction of earnings and cash flow is of great concern to financial market participants. Short term prediction of cash flow assists in judging a firm’s ability to carry on its day-to-day business and long-term cash flow prediction is necessary to evaluate a firm’s survival and equity value. For predicting earnings or cash flow, there have been studies in the time series properties of both measures. Earnings are likely to follow a submartingale process and changes in earnings seem to be independently random. Models of other ARIMA forms (submartingale could be a case of them) have also been applied to model and predict earnings. Cash flow is different from earnings because of the effect of accruals. Univariate models as applied to earnings are not sufficient for cash flow, since they ignore additional information embedded in other accounting variables. Cash flow is better predicted using past cash flow and accrual terms. Accrual level and accrual quality both affect the performance of the cash flow prediction model, which implies that the traditional linear regression model is of limited value in practice.

The studies reviewed here reported mixed results. The criteria for model comparison differ according to the researchers’ preference. A comprehensive study should not only look at the in-sample performance of models, but also should include out-of-sample prediction tests to reach a sounder conclusion. In the out-of-sample test, the prediction period should not be limited to only one period ahead because longer term prediction is of more value, both to academic researchers who aim to explore the data generating process of accounting incomes and to practitioners who rely on the prediction to make real world decisions. Moreover, accounting income prediction models ought to be examined in the stock market setting. Stock prices are considered to reflect the market expectation (prediction) of future incomes of relevant firms. Combinative study of both pure predictive test and market price association would serve the purpose of describing the underlying mechanism of market expectation that is unobservable.

Cash flow is a more complicated process than earnings. Due to the limitation of data, it is difficult to find the true cash flow generating process of firms. Few attempts are made to explore the time series property of cash flow and there is no clear and general conclusion about it. The linear models developed to predict cash flow have at least three limitations, where breakthrough might start, and no study has shed light on them all:

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Although there are common factors that firms tend to share, heterogeneity inevitably exists. It cannot be expected that firms within different sectors managed by different teams will have very close operational styles and activities.

2. Possible dynamic feature of cash flow process;

As firms grow into different stages in their life cycle, the income behaviour would be significantly different across the various stages. One static model would not be able to make an accurate prediction of the variable of interest, i.e. cash flow. 3. Criteria of comparing models;

Apart from the development of more advanced model, there is potential problem that different criteria may suit different models, which are optimal under their respective criteria. As the loss function depends on the specific economic application, it is hard to finally pick out a model that is universally optimal.

The main contributions of this thesis are threefold. First, drawbacks of the models used in prior studies will be explained and how the drawbacks could be eliminated will be suggested. The models in this thesis are built on the DKW and BCN models, the latter of which could be seen as an extension of the former. Therefore, this thesis will start from the derivation of DKW model and suggest potential improvements. In contrast with DKW and BCN models that use linear forms to capture the pattern of cash flow, it will be shown that there are likely to be dynamic and nonlinear components in the model that have been overlooked.

Nonlinear models will have more complication in their structures than linear models and sometimes brings in computational burdens for modellers, which is not helpful if the nonlinear model does not provide better performance. After all linear model in many cases may perform sufficiently well to capture a large variation in the empirical datasets. Cash flow prediction is a practical problem, and the features of empirical data have an impact on the estimation of the linear model. However previous research did not place much emphasis on the practical aspects because the studies were mainly focused on finding out the factors, or predictors, that are able to enhance the predictability of cash flow. Most studies of cash flow prediction use panel data. There are econometric methods that have been developed to deal with the panel data issues that are not resolvable in simple linear regression studies. Therefore, this thesis will introduce the panel models and explain why they are superior to simple regression in cash flow prediction studies. It will be a bridge

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leading from the BCN model to more advanced practical applications without changing the model’s structure.

Secondly, the main breakthrough of this thesis is the implementation and application of dynamic and nonlinear forms of the cash flow prediction model. The parameters in the original static model will be treated as time-varying (TV) state variables and a Bayesian updating method is applied to calculate the optimal prediction of these parameters and then cash flow given some certain prior distribution. The models are still within the range of linear form as the state variables are assumed to follow linear forms such as a random walk (RW) or autoregressive (AR) process. This limitation could also be relaxed and there will be no linear restrictions placed on the TV parameters. The nonlinearity of the parameter variables will be approximated by a tool known as a Padé approximant.

To make this thesis a more comprehensive study in cash flow prediction, two more issues that have not been emphasised much in previous studies will be discussed, i.e. long-term cash flow prediction and criteria adopted to compare models’ performance. The idea of vector autoregressive (VAR) model will be analogously extended to a nonlinear form, in order to adapt the developed cash flow models to the multiple-period setting. Besides, taking account of features of panel data, multiple criteria will be applied to compare the performance of models. One model could be better in one attribute but worse in another. The models that will be applied in the thesis will attempt to reach a balance point in terms of the criteria.

The third main contribution of this thesis is linking the results of these cash flow prediction models to an application in pricing equity. The cash flow prediction models will produce both predicted level of future cash flows and the uncertainty about the prediction. The cash flows of firms are associated with their equity price by the framework of the discounted cash flow (DCF) model that was mathematically formalised by Williams (1938). The DCF model is very theoretical and there are drawbacks for it in practice. Therefore, the model is usually used with simple assumptions on the cash flow process and the corresponding discount rates. For instance, in the Gordon growth model (Gordon and Shapiro, 1956 and Gordon, 1959), cash flows are assumed to grow by a constant rate beyond some period in the future. Even if all market participants agree identically on the same cash flow prediction, the rates to discount them might be determined individually with respect to

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subjective opinions, and thus the same stock would worth differently to them, which then leads to trading activities. The method developed in this thesis will distinguish itself with the previously designed models in the following two aspects. First, the cash flows used as the discounted amounts will be the output by statistical prediction models instead of a subjectively assumed process. The first issue, i.e. predicting cash flow into the infinite future, could be achieved by implementing the models discussed in this thesis. Secondly, the uncertainty of cash flow prediction has not been an issue of major concerned in the literature. It could be measured by the dispersion of the predicted distribution of future cash flows, which could be a crucial model input to decide the discount rates for firms. This thesis will place the uncertainty of cash flow prediction into the framework of expected utility theory, where the concept of risk aversion will be introduced and will contribute to the discount rates calculation. As an analytical form of solution may not be available, numerical solutions will be obtained through Monte Carlo simulation methods. Therefore, the process of implementing the model benefits from the development of computing power. The proposed method provides an alternative way to the well-known capital asset pricing model (see e.g. Sharpe, 1964) in the determination of discount rates. This is the first time the uncertainty of cash flow prediction is used to price equities.

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