Optimal Payout Research Articles

Optimal payout strategies when Bruno de Finetti meets model uncertainty

Model uncertainty is ubiquitous and plays an important role in insurance and financial modeling. While a substantial effort has been given to studying optimal consumption, portfolio selection and investment problems in the presence of model uncertainty, relatively little attention is given to investigating optimal payout policies taking account of the impacts of model uncertainty. As one of the early attempts, this paper studies the optimal payout control problem under the classical risk model taking into account of model uncertainty about the claims arrival intensity. We aim to provide insights into understanding optimal decisions incorporating model uncertainty and to examine key impact of model uncertainty. We find that the optimal strategy robust to model uncertainty is of a band type. However, the presence of the model uncertainty alters the qualitative behavior of the optimal strategy in the sense that the optimal robust policy is no longer a barrier strategy for some particular cases. We provide numerical examples to illustrate the theoretical results and examine the impact of model uncertainty on optimal payout policies. We also provide examples that use real insurance data for calibration. We discover that the decision maker takes more conservative strategies under model uncertainty, which is consistent with the findings in the economic field and has not been addressed in the existing optimal payout problems without model uncertainty.

An Analytic Framework for Interpreting Investment Regressions in the Presence of Financial Constraints

Abstract We derive analytic solutions for the valuation, optimal investment, and optimal payout of a financially constrained firm. While marginal $q$ and average $q$ would be identically equal in the absence of financial constraints, they differ when financial constraints bind. We use analytic solutions to characterize the properties of regressions of investment on average $q$ and cash flow. The coefficient on cash flow is positive, but does not isolate the impact of the financial constraint, since it also partially reflects the impact of persistent profitability. The coefficient on average $q$ understates the impact of persistent profitability.

Dynamic financing and hedging under model uncertainty

ABSTRACT We extend the classic framework to investigate a firm's optimal financing, investment, payout and hedging strategies under model uncertainty (or ambiguity). It shows that model uncertainty has essentially different effects on liquidity policies compared to traditional business risk. A firm facing model uncertainty prefers refinancing less and payout earlier, and the marginal value may be increased when the refinancing option is in the money. Moreover, our model demonstrates that hedging tools play an important role in mitigating the negative impacts on firm value caused by model uncertainty, which illustrates an interesting result that traditional risk management method works well not only on business risk but also on model uncertainty.

Interdependent lotteries and the jackpot model of lottery demand

Bettors may view different gambles either as substitutes or complements. Assuming that the grand prize is the main driver of the demand for multi-prize lottery bets, this paper presents a theory of lottery sales maximization considering possible complementarity or substitutability among different lottery gambles offered by a single operator. Optimal payout ratios are derived accounting not only for interrelation among games but also for their relative popularity. The new profit optimization rule is then applied to a dataset of two Greek lotteries.

Elasticity of Demand and Optimal Prize Distribution for Instant Lottery Games

This study explores the optimal payout structure and prize distribution of instant (scratch-off) lottery games. Using ticket sales data for 185 instant lottery games sold between 2007 and 2011 by the Maryland State Lottery and Gaming Control Agency, we calculate the price elasticity of demand across a range of ticket denominations. Our findings suggest that increasing the payout rate of instant tickets will increase revenue, particularly among low denomination tickets. We also find that reallocating the current prize distributions within a game towards fewer, but more valuable, low-tier prizes will increase the number of tickets sold.

Coordinating Supply and Demand on an On-Demand Platform: Price, Wage, and Payout Ratio

Consider a situation when an on-demand service platform uses earnings-sensitive independent providers with heterogeneous reservation price (for work participation) to serve its wait-time and price sensitive customers with heterogeneous valuation of the service. As such, both the supply and demand are “endogenously” dependent on the price the platform charges its customers and the wage the platform pays its independent providers. In this paper, we present a queueing model with endogenous supply (number of participating agents) and endogenous demand (customer request rate) to model this on-demand service platform. To coordinate endogenous demand with endogenous supply, we use the steady state performance in equilibrium to characterize the optimal price, optimal wage and optimal payout ratio (i.e., the percentage of the platform’s revenue that is paid to the providers) that maximize the profit of the platform (as well as the total welfare). We find that it is optimal for the platform to charge a higher price, pay a higher wage, and offer a higher payout ratio (i.e., the ratio of wage over price) when the potential customer demand increases. Furthermore, when customers become more time-sensitive, the same result holds except that the platform would need to charge a lower price in order to sustain the customer demand.

Interrelation between payout and financing decisions: evidence from emerging markets

Nikita Konstantinovich Pirogov - HSE.
 E-mail: npirogov@hse.ru
 Artem Eduardovich Anilov - HSE.
 E-mail: tema_anilov@mail.ru
 Financing and payout decisions generally affect company’s economic performance: they have impact (both directly and indirectly) on the free cash flow and, thus, on company’s and shareholders’ value. Search for optimal capital structure and optimal payout policy strategy that are likely to maximize shareholders’ utility resulted in the papers, dedicated to determinants of capital structure and payout policy. In such papers, one of the policies is usually treated as a determinant for another one. This bound does not let researchers to make some conclusions about existence or absence of interrelation between payout and financing choices. To capture this interrelation, simultaneous regression analysis should be performed. Researchers, though, cannot come up with unified conclusion about the existence and direction of such interrelation.The absence of certain results as well as low level of research done on emerging markets make this topic rather relevant.The results of recent research on the interrelation between payout and financing decisions are discussed in this paper. We also develop an econometric model that allows us to check the existence of interrelation in emerging markets and to compare the results to those obtained from developed markets.The article contributes to the existed literature in the following directions: first, two debt variables are taken into account (total and long-term debt) as well as two payout policy variables (total payout and dividend payout). Second, macroeconomic variables are controlled. Third, the results obtained from the companies from emerging countries are compared to those obtained from developed markets.

Optimal contract theory with time-inconsistent preferences

This paper incorporates managers' time-inconsistent preferences into the classical DeMarzo and Sannikov (2006) contract model to study corresponding impacts on the optimal contract, corporate financial policies, and the optimal capital structure. The extended model shows that the impatience of the time-inconsistent agent has positive effects on the optimal payout decision which is opposite to DeMarzo and Sannikov (2006) and consequently provides a guideline to tailor the contract between investors and the agent. It also shows in the optimal capital structure, the total debt capacity shrinks with the degree of the agent's time inconsistency, and the long-term one shrinks more. In addition, our model predicts that the agent's time inconsistency not only imposes significant limits on the use of long-term debt but also has great effects on firms' capital structures. Thus our finding can potentially explain observed cross-sectional differences in firms' capital structures.

Optimal retirement income tontines

Tontines were once a popular type of mortality-linked investment pool. They promised enormous rewards to the last survivors at the expense of those died early. While this design appealed to the gambling instinct, it is a suboptimal way to generate retirement income. Indeed, actuarially-fair life annuities making constant payments–where the insurance company is exposed to longevity risk–induce greater lifetime utility. However, tontines do not have to be structured the historical way, i.e. with a constant cash flow shared amongst a shrinking group of survivors. Moreover, insurance companies do not sell actuarially-fair life annuities, in part due to aggregate longevity risk.We derive the tontine structure that maximizes lifetime utility. Technically speaking we solve the Euler–Lagrange equation and examine its sensitivity to (i) the size of the tontine pool n, and (ii) individual longevity risk aversion γ. We examine how the optimal tontine varies with γ and n, and prove some qualitative theorems about the optimal payout. Interestingly, Lorenzo de Tonti’s original structure is optimal in the limit as longevity risk aversion γ→∞. We define the natural tontine as the function for which the payout declines in exact proportion to the survival probabilities, which we show is near-optimal for all γ and n. We conclude by comparing the utility of optimal tontines to the utility of loaded life annuities under reasonable demographic and economic conditions and find that the life annuity’s advantage over the optimal tontine is minimal.In sum, this paper’s contribution is to (i) rekindle a discussion about a retirement income product that has been long neglected, and (ii) leverage economic theory as well as tools from mathematical finance to design the next generation of tontine annuities.

Capital Supply Uncertainty, Cash Holdings, and Investment

We develop a dynamic model of investment, financing, and cash management decisions in which investment is lumpy and firms face capital supply uncertainty. We characterize optimal policies explicitly, demonstrate that smooth-pasting conditions may not guarantee optimality, and show that firms may not follow standard single barrier policies. In the model, firms with high investment costs differ in their behaviors from firms with low investment costs, financing policy does not follow a strict pecking order, and the optimal payout policy may feature several regions with both incremental and lumpy dividend payments.

Commitment Driven Investing: The Essentials

Commitment Driven Investing (CDI) is a theoretical framework designed to generate optimal asset allocation, contribution, and payout strategies for institutional and individual investors with financial commitment to fund. This paper introduces the basic analytical tools and presents the economic foundation of CDI.The term "financial commitment" is defined as a series of future asset values at different points in time. Financial commitments can be out-flows (the asset values to be funded) and in-flows (contributions, or savings). Financial commitments can also be certain or uncertain in terms of their timing and magnitude.Financial commitments play a special role in investing. Investors do not invest in a vacuum – they invest and take a multitude of risks primarily to fund their financial commitments. A typical funding problem involves an investor that has made commitments to contribute and invest assets in order to make pre-determined payments and/or accumulate pre-determined asset values. The investor's challenges include the selection of optimal policy portfolio as well as the determination of optimal payout and contribution strategies.

Sustainable growth rate, optimal growth rate, and optimal payout ratio: A joint optimization approach

This study investigates the investment decision and dividend policy jointly from a non-steady state to a steady state. We extend Higgins’ (1977, 1981, 2008) sustainable growth rate model and develop a dynamic model which jointly optimizes the growth rate and payout ratio. We optimize the firm value to obtain the optimal growth rate in terms of a logistic equation and find that the steady state growth rate can be used as the benchmark for the mean-reverting process of the optimal growth rate. We also investigate the specification error of the mean and variance of dividend per share when introducing the stochastic growth rate. Empirical results support the mean-reverting process of the growth rate and the importance of covariance between the profitability and the growth rate in determining dividend payouts. The intertemporal behavior of the covariance may shed some light on the fact of disappearing dividends over decades.

Service guarantee and optimal payout models

Abstract This paper evaluates both the optimal service level and optimal economic payout in service payout models. A service guarantee level is explicitly taken into consideration to obtain the optimal payout. In this study, we consider a generic model to provide insights into the dynamic interaction between the service guarantee and optimal payout levels. Parametric analyses show that when the demand payout coefficient is high, the impact of the payout is positive only if the payout rate is high enough.

Optimal payout ratio under uncertainty and the flexibility hypothesis: Theory and empirical evidence

Following the dividend flexibility hypothesis used by DeAngelo and DeAngelo (2006), Blau and Fuller (2008), and others, we theoretically extend the proposition of DeAngelo and DeAngelo (2006) optimal payout policy in terms of the flexibility dividend hypothesis. In addition, we also introduce growth rate, systematic risk, and total risk variables into the theoretical model. To test the theoretical results derived in this paper, we use the data collected in the US from 1969 to 2009 to investigate the impact of the growth rate, systematic risk, and total risk on the optimal payout ratio in terms of the fixed-effect model. We find that based on flexibility considerations, a company will reduce its payout when the growth rate increases. In addition, we find that a nonlinear relationship exists between the payout ratio and the risk. In other words, the relationship between the payout ratio and the risk is negative (or positive) when the growth rate is higher (or lower) than the rate of return on total assets. Our theoretical model and empirical results can therefore be used to identify whether flexibility or the free cash flow hypothesis should be used to determine the dividend policy.

Optimal Payout Ratio under Uncertainty and Flexibility Hypothesis: Theory and Empirical Evidence

Following the flexibility dividend hypothesis used by DeAngelo and DeAngelo (2006), Blau and Fuller (2008), and others, we theoretically extend the proposition of DeAngelo and DeAngelo’s (2006) optimal payout policy in terms of flexibility dividend hypothesis. In addition, we also introduce growth rate, systematic risk, and total risk variables into the theoretical model.To test our theoretical results derived in this paper, we use the U.S. data during 1969 to 2009 to investigate the impact of growth rate, systematic risk, and total risk on the optimal payout ratio in terms of fixed effects model. We find that a company will reduce its payout when the growth rate increases for the flexibility concern. In addition, we find that there exists a nonlinear relationship between the payout ratio and the risk. In other words, the relationship between the payout ratio and risk is negative (or positive) when the growth rate is higher (or lower) than the rate of return on total assets. Therefore, our theoretical model and empirical results can be used to identify whether flexibility or free cash flow hypothesis should be used to determine the dividend policy.

Capital Supply Uncertainty, Cash Holdings, and Investment

We develop a model of investment, financing, and cash management decisions in which investment is lumpy and firms face uncertainty regarding their ability to raise funds in the capital markets. We characterize optimal policies explicitly and show that the smooth-pasting conditions used in prior contributions are necessary, but may not be sufficient, for an optimum. Instead of the standard Miller and Orr (1966) double-barrier policy for financing and payout, firms may optimally raise outside funds before exhausting internal resources and the optimal payout policy may feature several regions, with both smooth and discrete dividend payments. In the model, firms with high investment costs are qualitatively as well as quantitatively different in their investment, financing, and payout behaviors from firms with low investment costs. Finally, investment and payout do not always increase with slack, challenging the use of investment-cash flow sensitivities or payout ratios as measures of financing constraints.

Costly Financing, Optimal Payout Policies and the Valuation of Corporate Debt

We present a cash-flow based model of corporate debt valuation that incorporates two novel features. First, we allow for the separation and optimal determination of the firm's debt-service and dividend policies; in particular, the firm is allowed to maintain cash reserves to meet future debt obligations. Second, our model admits the possibility that raising resources through issuance of new equity could be a costly procedure. In contrast, much of the previous literature has considered only dividend polices that are the consequences of debt-service policy, and has assumed new equity issuance costs are either zero or infinite. We provide an analytical characterization of equilibrium behavior in our model. Numerical analysis of the equilibrium reveals that our model predicts substantially higher yield spread than the canonical Merton-type model. More importantly, we find that the two novel features of our model are crucial determinants of not only the overall spread that result but also of the marginal impact of allowing for debt-service to be strategic. Specifically: (a) assuming residual rather than optimal dividend policies can result in a significant upward bias in the yield spread predicted by the model; (b) the size of this bias depends in a central way on the costs of equity issuance; (c) the marginal impact of strategic debt-service is substantial, in general, only for low equity-issuance costs, and (d) under optimally-determined dividends, strategic debt-service can actually result in a narrowing of yield spreads. In summary, our results indicate that endogenizing dividend policy and allowing for equity-issuance costs can enhance the model's content substantially, while ignoring these factors could introduce non-trivial biases into the valuation.

Optimal payout policy in presence of downside risk

We analyze the determination of a value maximizing dividend payout policy for a broad class of cash reserve processes modeled as spectrally negative jump diffusions. We extend previous results based on continuous diffusion models and characterize the value of the optimal dividend distribution strategy explicitly. We also characterize explicitly the values as well as the optimal dividend thresholds for a class of associated optimal liquidation and sequential lump sum dividend control problems. Our results indicate that both the value as well as the marginal value of the optimal policies are increasing functions of policy flexibility in the discontinuous setting as well.

The economic analysis of lotteries

Lotteries Determinants of ticket sales and the optimal payout rate This paper considers policy issues arising in the design, regulation and taxation of lotteries, focusing on the market for an on‐line lottery game. Demand determines who buys lottery tickets and in what quantities. The design of lotteries affects the terms on which tickets are supplied. UK data suggest that its lottery may be priced too high to maximize lottery revenue – more revenue might be raised if the proportion of sales allocated to tax and other levies were smaller. Having established the positive economics of lotteries, the paper then assesses their welfare implications. Pari‐mutuel lotteries enjoy scale economies and, as natural monopolies, are invariably run either by government agencies or a regulated licensee. I estimate consumer surplus and identify the excess burden that arises from existing (over)taxation of lotteries. The large price elasticity of demand implies that revenue raised from the lottery is raised very inefficiently. Moreover, the demand for lottery tickets is inferior (and there is some evidence that such games are contagious and addictive). So using lotteries as a vehicle for raising revenue is extremely regressive. Finally, I consider other policy implications: induced effects on charitable giving and on other forms of gambling; the impact on the government budget; perceptions of risk; and distributional considerations. —Ian Walker

Payout Policy, Capital Structure, and Compensation Contracts when Managers Value Control

The optimal contract between managers and investors is endogenously derived when managers have preferences for both monetary compensation and corporate resources under their control. When the optimal payout is privately known to managers, they can be induced to make payouts by linking their compensation to the payout. Public equity is a claim on this discretionary payout. If investors can obtain new information about the firm's optimal payout level, it can be utilized by transferring the control from management to investors. The new information allows the firm to achieve a more efficient allocation through recontracting. We show that the new information will be obtained if and only if the payout falls below a promised level. Article published by Oxford University Press on behalf of the Society for Financial Studies in its journal, The Review of Financial Studies.