Annualization

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There are a number of ways of taking a one month or six month percentage change and stating it in annual terms, for apples-to-apples comparisons. The simplest method is to just multiply by 12 in the case of one month or 2 in the case of the six month percentage change. I call that simple annualization, though it could also be called multiplicative annualization. It does not reflect compounding: twelve consecutive monthly percentage changes of 1% will result in a percentage change of 12.68% over an entire year, somewhat over 12.00%.

To take compounding into account, use a formula like this for monthly percentage changes:

\( Geometrically \, Annualized \, Inflation = \left [ \left ( \frac{P_m}{P_{m-1}} \right )^{12}-1 \right ] *100 \)

A similar formula could be used to annualized 6 month percentage changes:

\( Geometrically \, Annualized \, Inflation = \left [ \left ( \frac{P_m}{P_{m-6}} \right )^{2}-1 \right ] *100 \)

Above, the current month’s prices are divided by prices 6 months ago. To inflate them, they are taken to the power of 2 (since there are 2 six-month periods in a year). Further discussion and a more general formula are presented in the paper. Simple annualization isn’t an awful approximation for geometric annualization, but there’s no reason not to insert the proper formula into your spreadsheet.