Hybrid units of wealth (and a surprising guarantee)

Suppose you have some New Zealand dollars ($\mathrm{NZD}$) and some other valuable, fungible, relatively divisble items called, say, $\mathrm{XYZ}$. If the value of $\mathrm{XYZ}$ increases, then the value of your portfolio (measured in $\mathrm{NZD}$) increases.

But the value of $\mathrm{XYZ}$ increasing is indistinguishable from the value of $\mathrm{NZD}$ decreasing, so if you measure the value of your portfolio in $\mathrm{XYZ}$, then an increase in the value of $\mathrm{XYZ}$ appears as a decrease in the value of your portfolio.

So which is correct? Has your portfolio increased in value, or decreased in value? Well, it depends on whether $\mathrm{XYZ}$ or $\mathrm{NZD}$ is more useful to you. But what if they’re equally useful to you? What if $\mathrm{XYZ}$ is another currency that you use as often as $\mathrm{NZD}$? Continue reading Hybrid units of wealth (and a surprising guarantee)