Inflation


Inflation erodes the purchasing power of money; a euro today does not buy as much bread and butter as a euro did ten years ago. We may wish to account for inflation in order to make investment models more accurate.

Inflation Rate


Inflation is due to the general increase in prices with time. It is desribed by an inflation rate f. Prices one year from now will on average be today's prices multipied by a factor (1 + f). Inflation compounds the same way as interest does, and after k years of inflation at rate f, prices will be (1 + f)k times their value today.

In other words, the value of money decreases. If the inflation rate is f, then the value of one euro next year is only 1/(1 + f), and after k years it is 1/(1 + f)k, assuming the inflation rate is constant.

In Denmark the national bureau of statistics (Statistics Denmark) is responsible for measuring the price index and calculating the inflation rate (Fig. 1). They participate in a European collaboration to create socalled Harmonised Indices of Consumer Prices (HICP), which are published on the Eurostat homepage. In November 2011 the overall HICP inflation rate for the EU is 3.4% (Denmark 2.5%).

FigInflation.png
Fig. 1. Inflation in Denmark from the year 1900 to 2010 (Danmarks Statistik,
Statistikbanken).


Real Euros


Each cash flow at year k in a cash flow stream must be multiplied by 1/(1 + f)k in order to account for inflation. After multiplication, the amounts we look at are no longer the actual euros we really use in transactions, but they are 'equivalent euros' according to purchasing power. If the starting point for the inflation series is today, the amounts are in real euros. That is, they are in today's euros corresponding to today's general price level, as opposed to actual euros (current prices).

This point is a turning point. As long as cash flows concern actual inflows and actual outflows, including interest, then the monetary unit is actual euros. But as soon as we include inflation -- and other concepts related to value -- then the monetary unit becomes hypothetical. It is no longer its face value, but its present worth to the owner.

Real Interest Rate


The real interest rate is then the nominal interest rate i adjusted by the inflation rate f. Money in the bank increases nominally by the factor (1 + i), but its purchasing power is deflated by 1/(1 + f). Therefore, due to the inflation rate f, the real interest rate i0 is determined by

      (1)               1 + i0 = (1 + i)/(1 + f),


or

      (2)               i0 = (1 + i)/(1 + f) - 1


For small inflation rates f the real interest rate i0 is approximately equal to (i - f) (Luenberger 1998).

In other words, if we wish to account for inflation, we choose the real interest rate instead of the nominal interest rate i. That is, we use i0 as a substitute for i.

Usually the interest rate in a bank is higher than the inflation rate, so that there is an incentive to make a deposit. In other words, the real interest rate is usually positive (i0 > 0).

  1. Eurostat: Inflation dashboard
  2. Wikipedia Inflation



The original document is available at http://seacourse.dk/wiki/tiki-index.php?page=Inflation