The Math of Finance: Part II — Inflation

Photo by Imelda on Unsplash

Photo by Imelda on Unsplash

What is inflation?

When most people talk about inflation, they talk about how the prices for certain goods seem to be increasing over time, i.e. things get more and more expensive. 

But this is not what economists and bankers mean when they talk about inflation. For them, inflation is the reduction of the purchasing power of a single unit of currency. I know that sounds complicated so let me explain it with an example:

Let’s say you want to buy a pencil. A pencil doesn’t spoil, and you can store it for years. That pencil costs USD 1.00 today. But just five years ago you could buy the same type of pen for USD 0.90.

The pencil today is still the same type as it was five years ago. It hasn’t changed. But what has changed is that your money has lost in value. USD 0.90 is now worth less than a pencil. Economists call this a “loss in purchasing power” which most people call inflation.

What causes inflation?

Demand-Pull Inflation

A classic example of Demand-Pull inflation would be the change in house prices over time. 

There is only a limited number of houses and apartments available. And if more and more people want to buy a place of their own, this means that more and more people compete for the same limited number of houses. They start offering more and more money when bidding for real estate and drive up the price for everyone. Demand is pulling the prices up.

But if fewer and fewer people want to buy, say because of a financial crisis or recession prices go down, because people are not willing to pay as much for a house as during “the good times”.

Cost-Push Inflation

Sometimes companies are forced to raise prices for their products because it costs more to make them than before. For example, raw materials could cost more, or the employees demand higher salaries. Cost increases push the prices up as companies want to preserve their profit margins.

Built-In Inflation

The underlying assumption, in this case, is that people are used to prices going up. So they expect that any given item will cost more in the future and that their salaries will always be higher in the future.

Everyone assumes that there will be inflation. Employees expect that they will receive annual salary increases and companies raise prices now and then.

So your money loses value every year because people think “this is the way how the economy works”. It is a self-fulfilling prophecy.

What are the effects of inflation?

Inflation means that salaries loose purchasing power every year. You can buy fewer things for the same currency amount. Therefore employees need periodical pay rises to compensate for this loss in purchasing power.

At the same time, keeping large amounts as cash reduces your wealth over time, as inflation will slowly erode the value of your cash.

As an individual or a family, you need a sound financial strategy on how best to manage your money and where to invest it to protect you from the effects of inflation.

How is inflation measured?

How do you calculate inflation?

There are two ways to calculate inflation. 

The first one simply compares prices from one period to another to calculate the inflation rate. For example:

Year 1: 1 litre of milk costs USD 2.00

Year 2: 1 litre of milk costs USD 2.10

Inflation is calculated as follows:

(Price year 2 / Price year 1) - 1 = Inflation Rate

2.10 / 2.00 = 1.05

1.05 - 1 = 0.05 = 5% inflation rate

The second one involves picking a base year and comparing prices in all future years to this base year to calculate the cumulative impact of inflation. 

(Price current year / price base year) x 100 = inflation index = cumulative inflation compared to the base year

Let me give you an example:

2010: 1 gallon of milk costs USD 2.00

2011: 1 gallon of milk costs USD 2.10 (+5% from 2010)

2012: 1 gallon of milk costs USD 2.16 (+3% from 2011)

2013: 1 gallon of milk costs USD 2.31 (+7% from 2012)

The cumulative effect is:

2010: 100 (Base year)

2011: 105 (+5% inflation)

2012: 108 (+8% cumulative inflation: 5% + 3%)

2013: 115 (+15% cumulative inflation: 5% + 3% + 7%)

What is the Consumer Price Index (CPI)?

National statics agencies and various international bodies (like the OECD or the IMF) publish multiple reports on the rate of inflation for different groups of goods. The most well known, and widely used measurement is the “Consumer Price Index”. 

Instead of measuring the inflation of individual items, several goods and services are grouped into so-called “baskets”. These groups represent items and services that consumer (i.e. you and me) buy and the composition can change over time. For example, the consumer price index (CPI) in the 1970s wouldn’t include mobile phone contracts, because mobile phones hadn’t been invented yet. 

To measure the inflation, you select a base year (the starting point of your measurement) and then track how the prices change over time, compared to the base year. Let me explain this with an example:

  • Let’s pick 2015 as our base year. And the goods in our basket cost USD 50. The base year index is always set at 100.

  • In 2016 the same products cost USD 51. Using the formula from above ((price current year / price base year) x 100) we calculate (51/50) x 100 = 102. So the CPI in 2016 is 102.

  • In 2017 our goods cost USD 55. So the CPI (55/50) x 100 = 110 compared to the base year 2015.

From time to time, you need to pick a new base year; otherwise, your numbers become too big. Most people are only interested in tracking inflation over a few years. An additional benefit of selecting a new base year is that you can adjust the products and services that are included in your basket.

The CPI is often used to index (i.e. adjust for inflation) wages, salaries, commercial rents or other kinds of contracts.

Are there other measurements?

Depending on where you live or the purpose of the report you are interested in there are different indices compiled to measure inflation. The Retail Price Index (RPI) is a common statistic in the UK. And there are measurements for various industrial sectors like energy or commodities.

While they take different goods into account when calculating the inflation rate, they all use the same methodology as the CPI.

What is the role of the Central Bank?

Why is the Central Bank important?

The underlying assumption of our economic system is that we need to continuously grow how much we produce (our output) and our productivity. This will ensure that we will be more prosperous in the future. 

In the previous article about interest rates, I mentioned that the Central Bank of a country raises or lowers its lending rate to make debt cheaper or more expensive.

The assumption is that when debt is cheap, companies and people borrow more to invest and to buy more things or services, so there is more demand. This drives up economic growth and increases the inflation rate at the same time. (See the paragraph about Demand-Pull-Inflation above) The reverse is also true. If new debt is more expensive, people borrow less and buy less and inflation slows down as there is less demand.

Central Banks try to keep the inflation rate in a 2% - 3% range and adjust the lending rate accordingly to stimulate or slow down economic growth.

Why do Central Banks target slow but steady inflation?

A slow but steady growth rate implies that prices rise at a reasonable pace. You avoid a so-called “bubble” in which prices would rise sharply only to be followed by a recession and falling prices when the bubble bursts.

I will explain the ideas behind economic growth models and what causes growth, bubbles and recessions in the next article.

How does this article help me?

Impact on your every day lives

The effect most of us feel is that prices go up over time. So you need pay rises to be able to keep the same lifestyle over time.

Impact on your savings/investment strategy

If the interest rate a bank is paying you is lower than the inflation rate, your money will lose in value every year. 

For example, you have USD 100.00 in savings and the bank pays you 1% in interest (your return) and the inflation rate is 4%. This means that after the first year, you earned USD 1.00 in interest. But at the same time, your money lost USD 4.00 in purchasing power. So your money lost a total of USD 3.00 in value even if you actually have more Dollars in your account.

This is the reason why financial advisors urge people to invest in different things like bonds, stocks or real estate. These sectors tend to earn long-term returns that are higher than the long-term inflation rate.

So if you want to put your money into a savings account or any other form of investment, compare the interest rate with the inflation rate.

Impact on your debt

If you have debt with a fixed interest rate (like an average consumer loan from your bank), inflation will slowly erode the purchasing power of the amount you owe. Your future salary will likely be higher, but the outstanding balance of the loan will not go up with inflation, making it easier for you to pay back the debt.

If you have debt with a variable interest rate (meaning the lender can increase the interest rate), the outstanding balance of the loan will also be “reduced” by inflation. But the lender will increase the interest rate when the inflation rate goes up to compensate for it. In this case, inflation will not help you ease your debt burden.

What will be the next article in the series?

In the next article, I will explain what economists mean when they talk about growth, bubbles, recessions and trade.