We establish an algorithm that produces an optimal strategy for retirees to withdraw funds between their tax‐deferred accounts (TDAs), like traditional IRA/401(k) accounts, and their Roth IRA/401(k) accounts, in the context of a financial model based on American tax law. This optimal strategy follows a geometrically simple, intuitive approach that can be used to maximize the size of a retiree's bequest to an heir or, alternatively, to maximize a retiree's portfolio longevity. We give examples where retirees following the approach currently implemented by major investment firms, like Fidelity and Vanguard, will reduce their bequests by approximately 10% or lose 18 months of portfolio longevity compared to our optimal approach. Further, our strategy and algorithm can be extended to many cases where the retiree has additional, known yearly sources of money, such as income from part‐time work, taxable investment accounts, and Social Security.
Commodity price driven valuation models require a stochastic price input if the value of managerial flexibility, such as the option to defer investment until the optimal time and the option to abandon a project, is to be estimated. The risk-neutral version of the stochastic price model is typically used in academic work; however, risk-adjusted models of the expected spot price are often used in practice. These two approaches are connected by a risk premium which is unfortunately often difficult to estimate. In this work, we use natural gas futures prices in a Kalman filter approach with maximum likelihood estimation to parameterize the Schwartz and Smith (2000) stochastic price model, and then apply an asset pricing model to address the large uncertainty of the risk premia parameter estimates. To evaluate the impact of the risk premia and other parameters in the two-factor price model on project valuation, we apply the price model to a prototypical shale gas investment, both for a base reference case as well as for cases where there are real options to optimally time decisions to invest or to abandon the project. Using this approach, we are able to determine the implied risk-adjusted discount rate that would be used with the spot price forecast, given the two-factor model risk premia, and we also discuss the impact of the risk premia on project value relative to other model parameters.
scite is a Brooklyn-based organization that helps researchers better discover and understand research articles through Smart Citations–citations that display the context of the citation and describe whether the article provides supporting or contrasting evidence. scite is used by students and researchers from around the world and is funded in part by the National Science Foundation and the National Institute on Drug Abuse of the National Institutes of Health.