Value creation with Dye’s disclosure option: optimal risk-shielding with an upper tailed disclosure strategy

Abstract

Dye [J Account Res 23 (1985) 123] showed that the optimal disclosure policy, when a manager is randomly endowed with perfect private information, is upper tailed, i.e., the manager only discloses firm value above an appropriate cutoff level. We interpret this strategically as an optimal exercise by management of the embedded formal option to report value. Given any disclosure cutoff level, we value the corresponding option using contingent claims analysis. It is shown that the Dye disclosure cutoff value maximizes the formal option value. We find it to be the minimum possible conditional valuation (conditioned by non-disclosure) which is thus consistent with the intuition that investors should value conservatively. We show how the Dye cutoff can be interpreted as a strike price in a ‘protective put’ which offers a shield against risk of disclosure of low value. The strategic analysis is further extended by allowing the probability level that the manager is informed to be a choice variable. We show that the manager will never choose to be perfectly endowed with information, and is likely to be more endowed than unendowed. We also present a simple worked example which shows how the total value of the firm changes once the Dye option is formally incorporated.

Appendices

Appendix: proof of the marginal values theorem

Working from the identity

$$ V(t){\mathbb{P}}(N(t))=E_{{\mathbb{P}}}[{\mathbb{X}}1_{N(t)}]=\int_{N(t)} {\mathbb{X}}d{\mathbb{P(\omega)}}, $$

differentiation gives

$$ dV(t){\mathbb{P}}(N(t))+V(t)d{\mathbb{P}}(N(t))=dE_{{\mathbb{P}}}[{\mathbb{X}} {{\mathbf{1}}}_{N(t)}]=td{\mathbb{P}}(N(t)), $$

so that

$$ dV(t){\mathbb{P}}(N(t))=(t-V(t))d{\mathbb{P}}(N(t)). $$

Since $d{\mathbb{P}}(N(t))=qdF(t),$ we can write this explicitly as

$$ V^{\prime}(t)=\left(t-V(t)\right) \frac{q}{p+qF(t)}f(t), $$

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where F(t) denotes the cumulative distribution function (for the probability law of the random variable X) and is assumed to be of the form

$$ F(t)=\int_{0}^{t}f(x)\,dx, $$

for some continuous f(x). Hence

$$ W^{\prime}(t)=\left(V(t)-t\right) \frac{pq}{p+qF(t)}f(t). $$

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Acknowledgement

We gratefully acknowledge the comments of Sudipto Bhattacharya, Nick Bingham and Bjorn Jorgensen.