Rule of 72’s cousin
At 3% inflation, purchasing power halves in ~24 years (72 ÷ 3). Real-return math is why that gap matters.
Real (exact) \(\displaystyle r = \frac{1+N}{1+\pi}-1\). Approx: \(r \approx N-\pi\) when rates are small.
\(\displaystyle \text{Real Growth Factor} = \frac{\frac{V_\text{end}}{V_\text{start}}}{\frac{\text{CPI}_\text{end}}{\text{CPI}_\text{start}}}\), \(\displaystyle \text{Real CAGR} = \left(\text{RGF}\right)^{1/T}-1\).
From Fisher: \(\displaystyle 1+N=(1+r)(1+\pi)\Rightarrow N=(1+r)(1+\pi)-1\).
A real return tells you how much your purchasing power has grown after removing the effect of inflation.
If your nominal return is N and inflation is π (both annualized), the exact Fisher relationship is
(1+real) = (1+N)/(1+π). This is more accurate than the simple approximation N − π when rates
are large or compounding spans multiple years. In practice, investors often care about real CAGR:
the annualized growth rate of wealth after dividing portfolio growth by the change in a price index (CPI/RPI/PCE) over the same period.
Why does this matter? Over long horizons, differences between nominal and real results can be dramatic. The long-running Global Investment Returns research (Dimson–Marsh–Staunton) shows that real returns vary widely across countries and asset classes, and that inflation regimes shape the gap between nominal and real performance. Their latest public summary (2025) updates a 35-market dataset back to 1900, documenting long-term real returns to equities, bonds, and bills and how they relate to local inflation histories. :contentReference[oaicite:0]{index=0}
Over short horizons, higher inflation is often associated with lower real stock returns (a negative co-movement), but at longer horizons the relationship can look more neutral or even turn positive as earnings and cash flows adjust. An IMF working paper (“Stock Returns and Inflation Redux”) finds a negative relation at the quarterly horizon across many countries, with evidence more consistent with the Fisher hypothesis as the horizon lengthens. :contentReference[oaicite:1]{index=1}
For bonds, the channel is different. Unexpected inflation typically hurts nominal Treasuries via higher yields (lower prices). Recent work on corporate bonds decomposes inflation exposure and shows that, while excess returns versus T-bills often carry negative inflation betas, credit spreads (relative to duration-matched Treasuries) can load positively on inflation, reflecting different risk premia. Index-linked bonds such as TIPS, by contrast, accrue principal with CPI and are designed to preserve purchasing power before taxes and fees; institutional primers provide detail on their mechanics, indexation lags, and use cases for hedging real liabilities. :contentReference[oaicite:2]{index=2}
Finally, expectations matter: market-implied breakeven inflation from TIPS and news about inflation both feed into real-rate and risk-premium dynamics. Research using large news corpora shows that inflation coverage influences inflation compensation and premia in inflation-protected markets—one reason real returns can diverge from simple “nominal minus CPI” rules of thumb in the short run. :contentReference[oaicite:3]{index=3}
At 3% inflation, purchasing power halves in ~24 years (72 ÷ 3). Real-return math is why that gap matters.
Since 1900, UK cash (T-bills) has delivered a slightly negative real return on average—quietly losing to prices.
The exact link is \((1+N)=(1+r)(1+π)\). The shortcut N−π can be off by whole percentage points when rates are chunky.
TIPS breakeven inflation is a market-implied vote on future CPI; real returns shift as that crowd forecast moves.
Paying 1% in fees when real returns are 2–3% eats a third to a half of your “true” gain.