Do Dual Discounting Equations Reconcile Exponential Banks with Their Hyperbolic Customers?

There is an apparent rift between the way banks calculate and the way humans think.

On the one hand, exponential discounting has played a centuries-long, lead role in financial analysis. On the other hand, experiments by behavioral economists demonstrate that hyperbolic discounting is better than exponential at explaining human inter-temporal behavior. The result is scope for misunderstanding between financial institutions and their customers because many financial products involve calculations alien to consumer thinking. Calls for improving consumer financial literacy are symptoms of this disconnect.

This article queries past experimental results by examining the underlying theory using the concept of duality. Two dual expressions are derived: one expression is dual to the exponential discounting equation and the other is dual to the hyperbolic. Each dual contains the full array of interest rates implied by every root solving its source equation. An array includes the negative and complex-valued interest rates ignored for centuries on the grounds that they lack economic meaning. Recent research, however, demonstrates that an array of rates does possess economic meaning. This finding legitimizes the duals, removing a barrier to their inclusion in financial analysis.

Duality offers possible reconciliation between the two approaches to discounting. The two dual expressions display a similarity and a difference. The similarity is in their structure, implying the two approaches to discounting are not as different as experimentalists suppose. The difference is in their components, this difference suggesting new experiments that may support or deny the proposed reconciliation.

Dual equations also suggest policy advice.