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Return predictability and shareholders’ real options

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Abstract

This study re-interprets the properties of the residual income model by highlighting the shareholders’ abandonment (liquidation or adaptation) option. We estimate the value of this real option as an explicit component of abnormal earnings in the residual income model and test the improvement in valuation after incorporating it into the model. Relative to the traditional specification of the residual income model, this real options model has a stronger predictive power for future abnormal stock returns. We also find that the superior return predictability of the real options model is pronounced in the set of firms with a high probability of exercising liquidation options (for example, those with low profitability, low growth opportunities, high underlying asset volatility, and low intangible assets), which is consistent with the importance of shareholders’ abandonment option in equity valuation. The results are robust to extensive sensitivity checks.

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Notes

  1. We assume that there is no agency problem between shareholders and managers. Therefore, the optimal point (T) is determined by managers on behalf of shareholders without any bias due to private incentives. Managers are expected to take all positive NPV projects and reject negative NPV projects to maximize shareholders’ wealth.

  2. Ohlson (1995, p. 670) introduces the model in Eq. (7): \( P_{t} = k(\phi x_{t} - d_{t} ) + (1 - k)y_{t} + \alpha_{2} \upsilon_{t} , \) where \( \phi = R_{f} /(R_{f} - 1), \) and \( k = (R_{f} - 1)\alpha_{1} = (R_{f} - 1)\omega /(R_{f} - \omega ) \) (x t is earnings; y t is book value; d t is dividend; υ t is “other information” at time t; ω is the persistence of residual income in its information dynamics in Eq. (A3); \( R_{f} \)is one plus the risk-free interest rate, and \( 0 \le \omega \le 1 \), \( 0 \le k \le 1 \)). Prior empirical studies report a positive value of ω in general (e.g., ω is 0.62 in Dechow, Hutton, and Sloan (1999)), thereby resulting in a positive k. However, ω becomes zero in a corner solution for liquidating firms as defined above. In this case, k becomes zero, and P t is determined solely by y t , the adaptation value of a firm.

  3. According to their definition, “recursion value is the value which results from discounting the stream of future earnings under the assumption that the firm continues to apply its current business technology to its resources. Adaptation value is the value of the firm’s resources independent of the firm’s current business technology; this value exists whenever resources can be adapted to alternative uses” (Burgstahler and Dichev 1997, p. 188).

  4. Some papers approximate the recursion value as the future earnings stream rather than dividend stream. However, the recursion value estimated by future earnings is overvalued if a firm does not pay out all of its earnings. We can see that the correct measure to use for this purpose is dividends, not earnings, from the PVED formula.

  5. The net asset value does not indicate the general meaning of firm value that is closely related to the long-term profitability (i.e., the present value of future dividend stream). Rather, it indicates the cash equivalent of liquidating the firm’s net assets or the value of net assets when they are used for purposes other than the current business. This net asset value or adaptation value is totally unrelated to the expected profitability under the current business.

  6. Some caution is warranted in using the traditional Black–Scholes option-pricing model to empirically measure the value of shareholders’ real options. Black and Scholes (1973) assume the “ideal conditions” in the market for the stock and the option. Among their assumptions, the most critical one is that the stock price follows a random walk in continuous time, and the distribution of possible stock prices at the end of any finite interval is log-normal. We assume that the analysts’ earnings forecast is efficient in the sense that it reflects all of the available relevant information at a particular point in time. Thus, the underlying asset of CO, the capitalized future dividends (cE) using this earnings forecast, is regarded as following a random walk, and the distribution of the possible cE at the end of any finite interval is log-normal. The measurement error of CO will increase proportionally to the extent that cE violates this assumption. Another concern arises from the exercise price in that it is fixed in the traditional Black–Scholes option-pricing model. However, the exercise price of the shareholders’ abandonment option is variable. Theoretically, the exercise price of CO is the adaptation value (AV), which varies continuously during the maturity of CO. Empirically, the proxy for AV is the book value of equity (BV). It also varies once per year during the maturity of CO. Hence, a modified option-pricing model such as that of Johnson and Tian (2000) with an “indexed stock option formula” should be used to reflect this variability of the exercise price. The main results are unchanged when this alternative formula is used. In relation, P t  = BV t · e −RFt · T + CO t to be mathematically more precise based on the put-call parity relationship. We simplify the specification as in Eq. (3) because BV is anyway not fixed during the option maturity.

  7. The underlying asset value in the real options model is the present value of the future dividend (i.e., cash flow for shareholders) stream, which is the firm value in PVED or RIM. Thus, it should equal Vf. If a firm has an extremely low probability of liquidation, the value of its shareholders’ abandonment option becomes zero, and the value of the firm is totally determined by the recursion value. In such a case, Vo converges with Vf. If the underlying asset (Vf) is significantly larger than the exercise price (BV), C (Vf, BV) becomes Vf–BV. Thus, Vo = BV + C (Vf, BV) = BV + (Vf–BV) = Vf. From this, we can see that Vo converges to Vf for such a firm.

  8. This prediction is contrasted with the assumption of market efficiency for both the short and long term. The return predictability of the V/P ratio in this case indicates that V/P is an unidentified risk proxy. Then, a high V/P ratio in the current period will predict a high future “expected” return.

  9. We do not claim that any valuation model can measure the true intrinsic value on an absolute basis but suggest that a model can do it better than other models on a relative basis. This reasoning is consistent with that of Penman (2006).

  10. The sample’s starting fiscal year shifts from 1976 to 1980 because a minimum of five recent fiscal years including the current fiscal year is required to calculate the standard deviations of cE change, and the sample’s ending fiscal year shifts from 2005 to 2001 to use year t + 1 stock prices and analysts’ forecast data and to calculate future 36-month buy-and-hold abnormal returns.

  11. For example, the mean (median) total assets (TA) are $6.55 ($1.23) billion for our sample, which is more than two times larger than $3.00 ($0.14) billion for Compustat populations. The same inference can be drawn from the book value (BV), market capitalization (MC), and sales. Compared to the mean (median) ROE of 8.9% (10.4%) for the Compustat populations, it is higher at 14.8% (15.4%) for our sample. This better profitability is also found through higher ROA and EPS. The mean (median) fiscal year-end stock price per share (FYP) of our sample is $32.63 ($28.50) compared with $17.70 ($12.88) for the Compustat populations. We can also observe this higher market value through market capitalization.

  12. For earnings, this is contrary to the previous results, which report negative skewness in general. That negative skewness results from some firms reporting huge losses due to increasing accounting conservatism. Our sample seems to have a survivorship bias because a firm must survive for at least 6 years to be included. As a result, many firms with huge losses might be excluded, and a positive skewness could emerge.

  13. This result is consistent with the result in Table 6 of Ali et al. (2003). They compare the return predictability of the residual income model under three specifications–the residual income model (RIM) using analysts’ earnings forecasts, the RIM using historical earnings, and the Ohlson and Juettner-Nauroth (2005) model. V/P from the RIM using historical data loses its significance when BV/P is included as a control variable because it does not contain additional information beyond the historical earnings information that is already included in the book value. In contrast, V/P from either the RIM that uses analysts’ earnings forecasts or the Ohlson and Juettner-Nauroth (2005) model maintains its significance even after BV/P is included.

  14. When the PEG model and MPEG model in Easton and Monahan (2005) are used, the coefficient of Vf/P in Column (5) of Table 3 is statistically significant at the 0.01 level. However, its magnitude is much smaller than that of Vo/P.

  15. Because the market beta, size, and book-to-market ratio are already controlled for in the expected returns of the Fama and French (1992) three-factor model, these three risk factors are excluded from Eq. (6) in this sensitivity analysis.

  16. Specifically, we compute the value of option (CO) using various option maturities such as 3, 5, 7, 10, 20, and 50 years. As expected, CO increases in its maturity but not in a sensitive way ($6.61, $7.47, $8.14, $8.93, $10.49, and $11.90, respectively). Vo and Vo/P also increase in maturity, but Vo/P does not exceed 1.3, even at a 50-year maturity. We repeat the analysis in Column (5) in Panel B of Table 3 using these various maturities. The magnitude of the Vo/P coefficient decreases (but not very much) as the option maturity lengthens (0.2893, 0.2866, 0.2795, 0.2705, 0.2656, and 0.2068, respectively), but its statistical significance is maintained at the 0.05 level, except for the 50-year maturity. Moreover, the adjusted R2 is fairly stable at around 2.5%, and Vf/P is not significant at any conventional level for all maturities.

  17. This marginal significance (0.10 level) is due to the multicollinearity because Vf/P and Vo/P are fundamentally the same variable in this subsample.

  18. The real options model converges to the model of Burgstahler and Dichev (1997) when cE volatility approaches zero. In this case, the call option, CO, is simplified to “max(Vf–BV, 0).” Even in this case, the valuation estimate is more accurate than that of the traditional empirical setting of the residual income model.

  19. For example, discounting the future cash flow stream is significantly affected by the assumption about the cost of equity, long-term growth, and terminal value. More importantly, the volatility of underlying assets, one of the core factors for estimating option values, is not as realistic as in financial options. cE is so stable that its measured volatility could generate errors in option value estimation. Fortunately, however, the results of this study are biased toward zero by this low volatility-related measurement error. If the true volatility of underlying assets, which is expected to be higher than what is used here, can be measured accurately it will produce a more precise estimation of shareholder option values, thereby making the results of this study stronger.

  20. For example, cE, the underlying asset of the real options, is not tradable. Therefore, the Black–Scholes formula for pricing tradable financial options is limited if applied to the real options.

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Acknowledgments

For their valuable comments and suggestions we thank James Ohlson (editor), two anonymous reviewers, Joseph Weintrop, Bin Ke, John Courtis, Charles Chen, Xijia Su, Steve Lim, Francis Kim, Zhaoyang Gu, Su-Keun Kwak, Woon-Oh Jung, Jae Ho Cho, Seung Weon Yoo, Daniel Norris, Jong Chan Park, Jay Junghun Lee, Woo-Jong Lee, and seminar participants at City University of Hong Kong and Seoul National University. Hwang appreciates financial support by the Institute of Management Research at Seoul National University. Sohn’s work described in this paper was fully supported by a grant from City University of Hong Kong.

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Authors and Affiliations

  1. College of Business Administration, Seoul National University, 599 Gwanak-ro, Gwanak-gu, Seoul, 151-742, Republic of Korea

    Lee-Seok Hwang

  2. Department of Accountancy, City University of Hong Kong (CityUHK), 83 Tat Chee Avenue, Kowloon Tong, Kowloon, Hong Kong, China

    Byungcherl Charlie Sohn

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  1. Lee-Seok Hwang
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Correspondence to Byungcherl Charlie Sohn.

Appendix

Appendix

The residual income model can be interpreted as containing the shareholders’ abandonment option in its abnormal earnings. We show that more formally here using the definitions in the main text. Vf = BV + RI, and Vo = BV + CO as shown in Eqs. (2) and (3) (the time subscript is omitted for brevity). When a firm’s long-term earnings are expected to be smaller than its cost of equity, RI is negative, that is, Vf < BV. In this case, CO = 0 because the underlying asset value is lower than the exercise price (the time value of the option is ignored for brevity). Thus, Vo can be expressed as follows (note that RI itself is negative here):

$$ \begin{aligned} Vo = & BV + CO = BV \\ = & BV + RI-RI \\ = & Vf-RI. \\ \end{aligned} $$

When the underlying asset value is lower than the exercise price, the put option value becomes the difference, that is, PUT (Vf, BV) = BV−Vf = −RI, where PUT (u, x) denotes the put option value with the underlying asset of u and the exercise price of x. Therefore,

$$ \begin{aligned} Vo = & Vf-RI \\ = & Vf + {\text{PUT }}\left( {Vf, \, BV} \right) \\ = & \left( {BV + RI} \right) + Put \\ = & BV + \left( {RI + Put} \right) \\ = & BV + RI^\prime = Vf^\prime . \\ \end{aligned} $$
(RIM′)

We can see that the valuation estimate from the real options model (Vo) is the same as that from the re-interpreted residual income model (Vf’′or RIM′). As shown in the second last line, RI′, the abnormal earnings of RIM′, has two components. One is RI, which is the abnormal earnings from recursion value, and the other is Put, which is the abnormal earnings attributable to the abandonment option. A similar derivation can be done to reach the same conclusion when Vf ≥ BV.

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Hwang, LS., Sohn, B.C. Return predictability and shareholders’ real options. Rev Account Stud 15, 367–402 (2010). https://doi.org/10.1007/s11142-010-9119-2

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