Foundations · F7 · 9 min
Inflation and real rates
Work out inflation from a price index, spot a base effect coming, and read the inflation rate priced into bonds.
In the news: Inflation day: the monthly price figures that move interest rates, the pound and share prices.
The essentials
- CPI inflation
- The yearly rise in the price of a typical household basket, published monthly and worked out from index levels: an index of 123.0 against 120.0 a year earlier is 2.5% inflation.
- Base effects
- Each month, the new monthly change enters the yearly rate and the same month last year drops out. If last year’s 1% jump is replaced by a 0.2% rise, yearly inflation falls about 0.8 points.
- Core inflation
- Inflation without volatile food and energy prices: a steadier guide to underlying pressure. The Bank of England aims for 2% inflation and watches core and services prices, which mostly follow wages.
- Real interest rate
- The interest rate minus inflation. Savings at 5% with 3% inflation earn about 2% real; at 4% with 6% inflation the real rate is −2%, so the money buys less each year.
- Breakeven inflation
- pay a on top of inflation. The gap to an ordinary ’s , such as 4.6% against 1.2%, is breakeven inflation: 3.4%, a market estimate plus a little for risk.
Inflation and breakevens
inflation = index now ÷ index a year ago − 1; breakeven = nominal − real
- index
- the price-index level, such as 123.0
- nominal
- yield on an ordinary bond
- real
- real yield on the matching inflation-linked bond
How it works
1. Prices going up
If a basket of shopping cost £100 a year ago and £103 today, prices rose 3% in a year. The yearly rise in the price of a typical household basket is , published every month.
2. Working from an index
Statisticians track prices with an index: say 120.0 a year ago and 123.0 now. Inflation = index now ÷ index a year ago − 1 = 123 ÷ 120 − 1 = 2.5%. Official rates are always worked out from the index levels like this.
3. Money loses value
At 3% inflation, £100 buys about 3% less after a year, and the loss compounds. The rule of 72 gives the time for prices to double: 72 ÷ the inflation rate. At 6% a year, prices double in about 12 years; at 2%, in about 36.
4. Today’s money
To compare money across years, scale it by the index. A £20,000 salary when the index was 80 is worth £20,000 × 120 ÷ 80 = £30,000 in today’s money, if the index is now 120.
5. Base effects
Each month, this month’s price change enters the yearly rate and the same month last year drops out. If prices jumped 1% in a month last year and rise 0.2% this month, yearly inflation falls by about 0.8 points, though nothing unusual happened. That is a .
6. Core inflation
Food and energy prices jump around with harvests, weather and wars. Strip them out and you get , a steadier guide to underlying price pressure. The Bank of England aims for 2% inflation and watches core, and services prices, which mostly follow wages.
7. Real interest rates
If your savings earn 5% while prices rise 3%, you are only about 2% better off. That 2% is the real rate: the interest rate minus inflation. Savings at 4% with inflation at 6% have a real rate of −2%: they buy less each year.
8. Bonds that track inflation
An ordinary government bond pays a fixed amount, whatever happens to prices. An raises its payments with inflation, so it pays a fixed return above inflation: its .
9. Breakeven inflation
Take the yield on an ordinary bond and subtract the real yield on the matching inflation-linked bond: 4.6% − 1.2% = 3.4%. That is , the inflation rate at which both pay the same. It is a market estimate of future inflation, plus a little extra for risk.
Worked example
Yearly inflation is 3.0%. Next month prices are expected to rise 0.3%; in the same month last year they rose 0.8%. The 10-year gilt yields 4.6% and the 10-year index-linked gilt 1.2% real. (Illustrative figures.)
- Last year’s 0.8% drops out and this year’s 0.3% comes in.
- New yearly rate ≈ 3.0% + 0.3% − 0.8% = 2.5%, with nothing unusual happening this month.
- Breakeven = 4.6% − 1.2% = 3.4%.
- If inflation averages more than 3.4%, the index-linked gilt does better; if less, the ordinary gilt does.
Inflation falls to about 2.5% on the base effect alone, and the market prices inflation of about 3.4% a year for ten years.
Check yourself
9 quick questions on the explanation above.
Practice
New numbers every set. Misses and guesses go into your review deck.
In the interview
Answer out loud in under a minute, then compare.
Why do central banks watch core inflation when people pay headline prices?
What does a 10-year breakeven tell you, and what else is in it?
A surprise jump in services inflation: what happens to gilts and sterling?
Remember
Breakeven = nominal yield − real yield
Inflation is a ratio of index levels, so the month that drops out matters as much as the one coming in.
Sources
Definitions and maths are standard textbook material; dated facts link to the sources above. Worked numbers are illustrative.