Integrating profitability prospects within cash management policies
Jean-Paul Décamps (Toulouse School of Economics, France)
Joint work with Stéphane Villeneuve

Tuesday June 3, 16:30-17:00 | session 3.8 | Stochastic Analysis | room 1+2

Two of the most important dimensions of the firms' financial policy are liquidity and profitability. Despite some attempts, liquidity and profitability concerns have been studied separately in the corporate finance literature. We do not have tractable models of corporate cash management with liquidity and profitability concerns. We study this issue in a dynamic model of a cash constrained firm which learns about its long-term profitability by observing earnings. The firm is confronted to internal agency costs and external financing costs and cope both a profitability concern (the risk to run a non-profitable project) and a liquidity concern (the risk to be forced to liquidate a profitable project). At each date, shareholders decide the amount of dividends, and whether or not to continue the project. The firm value is obtained as the value function of a bi-dimensional problem that combines singular control and stopping. The two-dimensional feature of the control problem emerges from Bayesian up-dating on a partially observable diffusion. We prove that the value function associated to the control problem satisfies $C^2$-smooth-fit across a free moving boundary characterized as the solution to an ordinary differential equation which represents the optimal dividend boundary.
We solve the model explicitly and obtain a rich set of theoretical implications. The uncertainty about the long run prospect impacts the corporate cash policy, which, in terms of target cash level changes as the firm learns about its profitability. The model predicts a positive relationship between cash holdings and shareholders’ belief. The model also exhibits a path-dependence property of the shareholders’ belief. It predicts that beliefs are all the more high because the firm reached several times its target cash levels. This provides a new explanation on how a young firm with unclear profitability becomes a mature firm with low uncertainty about its long-run prospect. The model shows that the cost of holding cash impacts the profitability threshold under which the project is not undertaken. Thus, because of liquidity concern, the shareholders’ decision to abandon the project cannot be first best. The model yields a non-monotonic relationship between cash holdings and the volatility of the cash flows. Thereby, the model explains why young and mature firms have different risk management policies. The model exhibits both concavity and convexity properties which lead to a non-monotonic relationship between cash holdings and the risk of profitability. The model leads to an endogenous dynamics for stock prices. The model predicts that, keeping constant the amount of liquid assets, the more often the firm has paid dividends, the higher the stock prices are. The model shows that the joint impact of profitability and liquidity concerns yields a non-monotonic behavior of volatility of stock prices as a function of stock prices.

Optimal stopping when the absorbing boundary is following after
Masahiko Egami (Kyoto University, Japan)
Joint work with Tadao Oryu

Tuesday June 3, 17:00-17:30 | session 3.8 | Stochastic Analysis | room 1+2

We study a new type of optimal stopping problems where the absorbing boundary moves as the state process X attains new maxima S. Specifically, we set the absorbing boundary as S-b where b is a certain constant. We examine this constrained optimization in a spectrally negative Levy model. The problem is two-dimensional and the threshold strategy given by the path of just X is not optimal. We reduce the problem to an infinite number of one-dimensional ones by using excursion theory and obtain an explicit solution with optimal rules. We illustrate our method by solving a real-life problem where even a big bank (high leverage) can easily fail because, as the bank grows, the absorbing boundary is following after. The deterioration of leverage ratio corresponds to an excursion in our model.