Measuring the unmeasurable: an application of uncertainty quantification to Treasury bond portfolios

We extract from the yield curve a new measure of fundamental economic uncertainty, based on McDiarmid’s diameter and related methods for optimal uncertainty quantification (OUQ). OUQ seeks analytical bounds on a system’s behaviour, even where aspects of the underlying data-generating process and system response function are not completely known. We use OUQ to stress test a simple fixed-income portfolio, certifying its safety—i.e. that potential losses will be ‘small’ in an appropriate sense. The results give explicit tradeoffs between: scenario count, maximum loss, test horizon, and confidence level. Unfortunately, uncertainty peaks in late 2008, weakening certification assurances just when they are needed most.