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Erschienen in: Review of Accounting Studies 4/2013

01.12.2013

Dynamic risk, accounting-based valuation and firm fundamentals

verfasst von: Matthew R. Lyle, Jeffrey L. Callen, Robert J. Elliott

Erschienen in: Review of Accounting Studies | Ausgabe 4/2013

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Abstract

This study extends the accounting-based valuation framework of Ohlson (Contemp Acc Res 11(2):661–687, 1995) and Feltham and Ohlson (Acc Rev 74(2):165–183, 1999) to incorporate dynamic expectations about the level of systematic risk in the economy. Our model explains recent empirical findings documenting a strong negative association between changes in economy-wide risk and future stock returns. Importantly, the model also generates costs of capital that are solely a linear function of accounting variables and other firm fundamentals, including the book-to-market ratio, the earnings-to-price ratio, the forward earnings-to-price ratio, size and the dividend yield. This result provides a theoretical rationale for the inclusion of these popular variables in cost of capital (expected return) computations by the accounting and finance literatures and obviates the need to estimate costs of capital from unobservable (future) covariances. The model also generates an accounting return decomposition in the spirit of Vuolteenaho (J Finance 57(1):233–264, 2002). Empirically, we find that costs of capital generated by our model are significantly associated with future returns both in and out of sample in contrast to standard benchmark models. We further obtain significantly lower valuation errors in out-of-sample tests than traditional models that ignore dynamic risk expectations.

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Fußnoten
1
As we show further below, the dividend yield can be eliminated using the clean surplus relation in which case the cost of capital can be expressed solely (in addition to size) as a linear function of accounting numbers, namely, the past book-to-market ratio, the current book-to-market ratio, the earnings-price ratio, and the forward earnings-price ratio.
 
2
See Ohlson (2009) and the citations therein.
 
3
See their Corollary 3.
 
4
To the best of our knowledge, Morel (2003) is the first paper to decry this disconnect and attempt to deal with it.
 
5
The latter assumption is for simplicity. Relaxing this condition would increase the number of variables in the stock price equation by one.
 
6
Because our analysis is in discrete time, this specific form of discount factor may yield negative values. We assume that does not occur
 
7
This result obtains by assuming that the market portfolio has stochastic risk. This is a straightforward extension of the basic derivations in Cochrane (2001), Chapter 9.
 
8
We have also solved for a model where risk follows a mean-reverting process. The implications of our results do not change even when risk is assumed to mean-revert.
 
9
The result that λ1 is positive presumes a positive correlation (ρ) between shocks to abnormal earnings (\(\epsilon_{t+1}\)) and shocks to the stochastic discount factor (e t+1). On average it is unlikely to be otherwise as long as growth in the economy and growth in firm level abnormal earnings are positively correlated. To complete the argument note that the discount factor represents the marginal rate of consumption in the economy or growth in the economy—see “Appendix 1”. Therefore shocks to the discount rate factor are driven by shocks to aggregate consumption or shocks to aggregate growth, represented by e t+1 which, in turn, should be positively related to shocks to (abnormal) earnings \(\epsilon_{t+1}\).
 
10
Note that λ1 is the firm level driver of expected returns being a function of the persistence of abnormal earnings, the volatility of abnormal earnings, and the correlation between (shocks to) abnormal earnings and (shocks to) economy-wide systematic risk in the economy.
 
11
The restriction on earnings growth does not affect any of our results, if anything our results are stronger when we remove this restriction.
 
12
We prefer to use equation (11), which includes the dividend yield, rather than Eq. (12) because of the high correlation between current and past book-to-market ratios. We refer to Eq. (11) as the accounting-based model although size and the dividend yield are not accounting variables.
 
13
Particularly, we measure next period expected earning by multiplying 1 year ahead concensus IBES earnings by w d and 2 year ahead concensus IBES earnings by 1 − w d where w d is the difference between the firms ficscal year end date and the current forecast date divided by 365.
 
14
We assume that long-run abnormal earnings are cross-sectionally constant, consistent with the notion that, in the long-run, a firm will grow to the point where it resembles a cross-section of firms.
 
15
The results in this and the following tables are not sensitive to the size of the estimation window.
 
16
Letting \(Z_{t}=(R_{f}-1)\frac{VIX_{t}}{S_{t}}-\frac{\Updelta VIX_{t}}{S_{t}},\) we also include Z t-1 in the regression.
 
17
The firm-level \(\hat{\lambda}_{1},\) estimated market beta, and estimated FF factor betas are updated annually each April.
 
18
Since \(\hat{\lambda}_{1}\) is already an estimated coefficient, we force a coefficient of one for \(\frac{\hat{\lambda}_{1}VIX_{t}}{B_{t}}\) when estimating Eq. (18).
 
19
Industries are based on the Fama–French 48 industry classifications downloaded from Ken French’s website.
 
20
Specifically, the two RIM models used assume a functional form of \(S_{t}=B_{t}+\sum_{i=1}^{T}E_{t}[\frac{x_{t+i}^{a}}{(1+r)^{i}}]+E_{t}[\frac{x_{t+i}^{a}(1+g)}{(1+r)^{5}(r-g)}]\), where B t is book value, x t+i a is abnormal earnings at time t + i and g is growth in abnormal earnings. It is assumed that T = t + 5 and a long-term growth rate of 0. Various other assumptions of long-term growth tended to yield higher valuation errors than the assumption of zero growth.
 
21
The effects of winsorizing the data and constraining the absolute pricing error to 1 reduces the performance of our model relative to the benchmarks. If we do not apply these filters, our model does even better than what is presented in the tables relative to the benchmark models.
 
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Metadaten
Titel
Dynamic risk, accounting-based valuation and firm fundamentals
verfasst von
Matthew R. Lyle
Jeffrey L. Callen
Robert J. Elliott
Publikationsdatum
01.12.2013
Verlag
Springer US
Erschienen in
Review of Accounting Studies / Ausgabe 4/2013
Print ISSN: 1380-6653
Elektronische ISSN: 1573-7136
DOI
https://doi.org/10.1007/s11142-013-9227-x

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