Multi-period Setting Research Articles

Multiperiod mean-variance efficient portfolios with endogenous liabilities

We study the optimal policies and mean-variance frontiers (MVF) of a multiperiod mean-variance optimization of assets and liabilities (AL). This makes the analysis more challenging than for a setting based on purely exogenous liabilities, in which the optimization is only performed on the assets while keeping liabilities fixed. We show that, under general conditions for the joint AL dynamics, the optimal policies and the MVF can be decomposed into an orthogonal set of basis returns using exterior algebra. This formalism, novel to financial applications, allows us to study analytically the structure of optimal policies and MVF representations under endogenous liabilities in a multidimensional and multiperiod setting. Using a numerical example, we illustrate our methodology by analysing the impact of the rebalancing frequency on the MVF and by highlighting the main differences between exogenous and endogenous liabilities.

Capital Budget Renegotiations and the Adverse Consequences of Delegating Investment Decision Rights

In this paper, we empirically examine the capital budgeting process of a large multi-divisional firm and the implications of the dynamics that underlie this process. Although investment decisions are one of the most important decisions made by firms, relatively little is known about the capital allocation process that triggers these investment decisions. Despite the prevalence of multi-stage budget processes in practice, prior studies mostly assume only a single negotiation period and provide no clear indication how agents behave in multi-period settings. To fill this void, we examine how information and agency problems affect the allocation of capital to individual investment projects over time, starting from the initial investment proposal moving to subsequent renegotiations. We argue that information asymmetry and uncertainty about private consumption preferences affect the budgeting behavior of managers when they have investment decision rights, and that the specific type of behavior is time-dependent. Based on capital budget data from a large, multi-divisional firm, we find that managers incorporate more slack into budgets during renegotiations the more the principal delegates investment decision rights to the manager. This occurs to a higher extent during the earlier stages of the investment when the principal has less information about the true nature of the investment. We further find that the manager takes advantage of multi-period budget processes to shift budgetary slack between investment stages of a project. He does so to a higher extent the more decision rights are delegated and during the more mature stages of the investment when uncertainty about his consumption preferences has been resolved. These results indicate that, for a manager with delegated investment decision rights, cost escalation is the dominant budgeting behavior during the early stages of the investment, while cost shifting is the dominant budgeting behavior during the more mature stages.

Can Cheap Talk Be as Effective at Mitigating Agency Problems as Reputation Building? An Experimental Test in the Presence of a Noisy Performance Measure

Given traditional agency theory assumptions and unobservable effort in a single-period setting, a moral hazard arises in which the agent is expected to shirk and provide the miminal possible effort after contracting with the principal. Traditional solutions to this agency problem include paying the agent a financial incentive tied to some noisy measure of performance or allowing the agent to develop a reputation over multiple periods. As the noisiness of the performance measure increases, however, these traditional solutions become increasingly costly and ineffective. In many single- and multi-period agency settings in the firm, however, the agent can communicate a promised level of effort to the principal prior to contracting. We document that this pre-contract communication, which is non-enforceable and therefore considered “cheap talk” by traditional economic theory, can be highly effective in mitigating the moral hazard problem in agency theory. In a repeating single-period experimental setting where production is observable but is a very noisy indicator of effort, communication of a promised level of effort results in higher pay for the agent, higher effort, and higher expected profit for the principal than the control group. When the principal and agent interact over multiple periods, reputation building is ineffective but cheap talk continues to yield superior outcomes. These results are consistent with recent economic theory incorporating social norms such as the norm of promise-keeping.

A multi-period inventory model with multi-dimensional procurement bidding

We consider a multi-period inventory model with raw material procurements carried out via a reverse auction. Bids are multi-dimensional, and they consist of supplier information of price, shortage quantity and lead time. This work is an extension of our earlier work that has focused on multi-dimensional procurement auctions in single-period inventory models, to multi-period settings. The new model is based on a hybrid approach combining stochastic dynamic programming and simulation.

An Experimental Examination of the House Money Effect in a Multi-Period Setting

There is evidence that risk-taking behavior is influenced by prior monetary gains and losses. When endowed with house money, people become more risk taking. This paper is the first to report a house money effect in a dynamic, financial setting. Using an experimental method, we compare market outcomes across sessions that differ in the level of cash endowment (low and high). Our experimental results provide support for a house money effect. Traders’ bids, price predictions, and market prices are influenced by the amount of money that is provided prior to trading. However, dynamic behavior is difficult to interpret due to conflicting influences.

Tax Shield, Bankruptcy and Interest Ceiling

This paper analyses the tax shield under realistic assumptions: no immediate refund and potential corporate bankruptcy for different financing policies. Assuming a German setting, we additionally investigate the impact of the interest ceiling (“Zinsschranke”) introduced by the German Tax Reform Act 2008 on the tax shield value. Our analysis rests on an option pricing model in a single period setting and on a Monte Carlo Simulation model in a multiperiod setting. We find the introduction of possible bankruptcy to have a significant impact on the tax shield; in contrast the effect of the interest ceiling is negligible.

On a multi-period supply chain system with supplementary order opportunity

This paper considers a supplementary supply–order system in a multi-period situation. In each period, the buyer first places an initial order based on the demand prediction; he has the opportunity to place a supplementary order with the supplier after the demand of that period is realized. The supplier maintains an inventory, and decides the quantity to be produced and the quantity to be provided for the supplementary order in each time period. We formulate the problem as a multi-period inventory game, and derive the optimal production and order policies for the supplier and buyer, respectively. The existence and uniqueness of Nash equilibrium is proved in the generalized multi-period setting, and the closed-form Nash equilibrium solution is obtained when the parameters are stationary. Numerical study is performed to reveal more managerial insights. We find that the supplementary supply–order mechanism, if designed properly, can effectively improve the multi-period supply chain performance.

Conditional value-at-risk constrained optimisation of a power portfolio

The deregulation of electricity markets is introducing risk and uncertainty into a sector of the economy that was traditionally state-regulated. In order to manage risk from market prices, consumers and producers use financial methods to support decentralised decision making under uncertainty. In this research, optimisation of portfolios of real and contractual assets is considered in a multi-period setting that includes transmission constraints. Fixed transmission rights are used as a measure of transmission congestion using data from the PJM Interconnection, a regional transmission organisation in the USA. The results show that transmission considerations in a power portfolio optimisation problem do have an impact on the profit function. Omitting transmission congestion may over-state expected profit. Companies should not only hedge the risk of unknown power prices but also unknown transmission congestion.

A Multi-Period Bank-Run Model for Liquidity Risk

We present a new dynamic bank run model for liquidity risk where a financial institution finances its risky assets by a mixture of short- and long-term debt. The financial institution is exposed to liquidity risk as its short-term creditors have the possibility not to renew their funding at a finite number of rollover dates. Besides, the financial institution can default due to insolvency at any time until maturity. We compute both insolvency and illiquidity default probabilities in this multi-period setting using a structural credit risk model approach. Firesale rates can be determined endogenously as expected debt value over current asset value. Numerical results illustrate the impact of various input parameters on the default probabilities.

Canonical Vine Copulas in the Context of Modern Portfolio Management: Are They Worth it?

In the context of managing downside correlations, we examine the use of multi-dimensional elliptical and asymmetric copula models to forecast returns for portfolios with 3 to 12 constituents. Our analysis assumes that investors have no short-sales constraints and a utility function characterized by the minimization of Conditional Value-at-Risk (CVaR). We examine the efficient frontiers produced by each model and focus on comparing two methods for incorporating scalable asymmetric dependence structures across asset returns using the Archimedean Clayton copula in an out-of-sample, long-run multi-period setting. For portfolios of higher dimensions, we find that modelling asymmetries within the marginals and the dependence structure with the Clayton canonical vine copula (CVC) consistently produces the highest-ranked outcomes across a range of statistical and economic metrics when compared to other models incorporating elliptical or symmetric dependence structures. Accordingly, we conclude that CVC copulas are ‘worth it’ when managing larger portfolios.

The strictest common relaxation of a family of risk measures

Operations which form new risk measures from a collection of given (often simpler) risk measures have been used extensively in the literature. Examples include convex combination, convolution, and the worst-case operator. Here we study the risk measure that is constructed from a family of given risk measures by the best-case operator; that is, the newly constructed risk measure is defined as the one that is as restrictive as possible under the condition that it accepts all positions that are accepted under any of the risk measures from the family. In fact we define this operation for conditional risk measures, to allow a multiperiod setting. We show that the well-known VaR risk measure can be constructed from a family of conditional expectations by a combination that involves both worst-case and best-case operations. We provide an explicit description of the acceptance set of the conditional risk measure that is obtained as the strictest common relaxation of two given conditional risk measures.

Effects on Strategy Development of Including Relative Performance Information in Incentive Scheme

Companies commonly use income as the basis for short-term incentives designed to motivate performance. Managing income is a complex task, particularly in multi-period settings. Strategy development is necessary to maximize income in a complex task, and requires trade-offs between current and future periods. In addition, Relative Performance Information (RPI) is often provided, or available as feedback, to motivate performance. While firms have the option of taking the additional step and contracting on RPI, many do not. We separately investigate how providing RPI and contracting on RPI affect strategy development in a multi-period experimental setting where income is the basis for short-term incentives. The results show that only providing RPI reduces strategy development and performance. However, contracting on RPI mitigates these effects. Our results suggest a potential cost to this ‘middle ground’ between eliminating RPI and contracting on RPI. We conclude that employers incenting their managers to maximize income in a multi-period setting should avoid the dissemination of RPI as ex post information only.

Supply chain coordination for the joint determination of order quantity and reorder point using credit option

Decisions regarding order quantity and reorder point are two major challenges in supply chain inventory management. In this paper, a coordination model of the joint determination of these two decision variables is proposed. A decentralized supply chain consisting of one buyer and one supplier in a multi-period setting is investigated. Demand and lead times are uncertain in our model. An incentive scheme based on credit option has been developed to encourage the buyer to participate in the coordination model. In this model, the downstream member has the option of using credit to purchase goods during the credit time, subject to its commitment to a jointly agreed order quantity and reorder point. The credit time is determined in such a way that the two parties have incentives to participate. The proposed incentive scheme can share the benefits of coordination between the two members based on their bargaining power. The proposed model shows that the coordination of the reorder point, together with order quantity, can increase the overall chain profitability as well as each member’s profitability.

Managing new and differentiated remanufactured products

We study a firm that makes new products in the first period and uses returned cores to make remanufactured products (along with new products) in future periods. The remanufactured product is differentiated from the new product, so the firm needs to choose differentiated prices. We analyze the monopoly environment in two-period, multi-period (three, four and five) and infinite planning horizons, and characterize the optimal remanufacturing and pricing strategy for the firm. In the process, we identify remanufacturing savings thresholds that determine the production and pricing strategy for the firm. Among other results, we find—counter to intuition—that in a finite-horizon, multi-period setting, the optimal policy is not necessarily monotone in remanufacturing savings.

Expected gain–loss pricing and hedging of contingent claims in incomplete markets by linear programming

Abstract We analyze the problem of pricing and hedging contingent claims in the multi-period, discrete time, discrete state case using the concept of a “λ gain–loss ratio opportunity”. Pricing results somewhat different from, but reminiscent of, the arbitrage pricing theorems of mathematical finance are obtained. Our analysis provides tighter price bounds on the contingent claim in an incomplete market, which may converge to a unique price for a specific value of a gain–loss preference parameter imposed by the market while the hedging policies may be different for different sides of the same trade. The results are obtained in the simpler framework of stochastic linear programming in a multi-period setting, and have the appealing feature of being very simple to derive and to articulate even for the non-specialist. They also extend to markets with transaction costs.

Public Debt Sustainability and Management in a Compound Option Framework

This paper introduces the Asset and Liability Management (ALM) compound option model. The model builds on the observation that the public sector net worth in a multi-period setting corresponds to the value of an option on an option on total government assets. Hence, the ALM compound option model is better suited for analyzing and evaluating the risk profile of public debt than existing one-period models, and is especially useful for analyzing the soundness of exit strategies from the large fiscal expansions undertaken by G-20 countries in the wake of the recent financial crisis. As an illustration, the model is used to analyze the risk profile and sustainability of Australia's public debt under different policies.

Public Debt Sustainability and Management in a Compound Option Framework

This paper introduces the Asset and Liability Management (ALM) compound option model. The model builds on the observation that the public sector net worth in a multi-period setting corresponds to the value of an option on an option on total government assets. Hence, the ALM compound option model is better suited for analyzing and evaluating the risk profile of public debt than existing one-period models, and is especially useful for analyzing the soundness of exit strategies from the large fiscal expansions undertaken by G-20 countries in the wake of the recent financial crisis. As an illustration, the model is used to analyze the risk profile and sustainability of Australia's public debt under different policies.

Public Debt Sustainability and Management in a Compound Option Framework

This paper introduces the Asset and Liability Management (ALM) compound option model. The model builds on the observation that the public sector net worth in a multi-period setting corresponds to the value of an option on an option on total government assets. Hence, the ALM compound option model is better suited for analyzing and evaluating the risk profile of public debt than existing one-period models, and is especially useful for analyzing the soundness of exit strategies from the large fiscal expansions undertaken by G-20 countries in the wake of the recent financial crisis. As an illustration, the model is used to analyze the risk profile and sustainability of Australia's public debt under different policies.

On the Extension of the Tax-CAPM to Multiperiod Settings

The CAPM or the Tax-CAPM are frequently applied to determine the cost of capital in business valuations. The Tax-CAPM extents the CAPM to include personal taxes and is advocated by the IDW (Institute of Public Auditors in Germany) for valuations required under corporate law or as part of contractual agreements. To derive a practically applicable version of Brennan’s Tax-CAPM (Brennan 1970), a model with homogenously taxed market participants is frequently used in the German academic literature. To date, a practical extension of this model to multiperiod settings could only be achieved by using simplifying assumptions on dividends. This paper shows that in the case of typified investors, the restrictive assumptions on dividends can be dropped and that the Tax-CAPM can be extended to multiperiod settings using a similar approach to that adopted in the multiperiod CAPM. As a result, a valuation formula is derived that can be used to explicitly include the effects of personal income taxes in multiperiod settings as recommended by the IDW for valuations required under corporate law or as part of contractual agreements.

Reputation Effects of Disclosure: An Experimental Investigation

This paper examines experimentally the sequential equilibrium theory of reputation and disclosure developed in Lunawat, 2009. It provides experimental evidence in support of the sequential equilibrium play and of the reputation building role played by disclosure. The said paper predicts higher investment in economies with disclosure as compared to those without. In testing this prediction, this paper introduces a two-stage experimental design which turns out also to be a contribution to experimental methodology. The two-stage design allows for construction of subject samples with uniform prior beliefs about a manager’s trustworthiness but different disclosure institutions. Data collected using this design provides support for the said prediction. This paper also sheds light on a related question of the reputation building role played by incremental disclosure. It introduces a multi-period setting that allows reinvestment of capital and provides for definition of incremental disclosure in an economy. It is shown that incremental disclosure results in even higher investment.