🎭 Compound Interest and Its Evil Twin

Finance & Data Science
Inflation · Compounding · Monte Carlo · AR(1) Process

💡 The Problem

Compound interest is one of the most powerful forces in long-term investing.

But it has an evil twin:

Compound inflation.

Imagine investing €30,000 today at 7% per year.

After 30 years:

Nominal Wealth ≈ €228,000

Impressive.

But with average inflation of 3%, those €228,000 would have the purchasing power of roughly:

Real Wealth ≈ €94,000

The portfolio grew enormously in nominal terms, but inflation absorbed a large part of that growth.

1. Adding Uncertainty

Inflation is not constant.

To explore its long-term impact, I generated 5,000 Monte Carlo simulations over 30 years.

Market

Expected Return: 7%
Volatility:      15%

Inflation

Instead of assuming constant inflation, I modeled it as an AR(1) process with persistence:

ρ = 0.5

This gives inflation “memory”: after a shock, inflation tends to remain elevated before gradually returning toward its long-term level.

I also introduced:

Inflation target: 2%
Annual shock probability: 5%
Shock magnitude: +4%

2. Nominal Wealth vs Real Wealth

The simulation produces two very different pictures.

Nominal Wealth

This is what the portfolio statement shows:

Initial Capital
      ↓
Market Returns
      ↓
Nominal Final Wealth

Real Wealth

This measures what that money can actually buy:

Nominal Final Wealth
        ↓
Accumulated Inflation
        ↓
Real Purchasing Power

After 30 years, the median real wealth is approximately half the nominal value.

Inflation silently absorbs a significant part of long-term compound growth.

In some particularly unfavorable simulations, real final wealth can even fall below the initial purchasing power.

3. Why Does Inflation Hurt So Much?

Because inflation compounds too.

Real wealth is approximately:

Real Wealth =
Nominal Wealth / (1 + inflation)^t

A seemingly small annual inflation rate becomes substantial over long horizons.

At 3% inflation:

€1 today
≈
€2.43 in 30 years

just to maintain the same purchasing power.

🎯 Key Takeaway

Long-term investing is not only about maximizing nominal returns.

The real objective is:

Preserving and increasing purchasing power.

Compound returns work in your favor.

Compound inflation works against you.

This is why nominal wealth alone can provide a misleading picture of long-term financial outcomes.

What matters is not how many euros you will have, but what those euros will be able to buy.

🧰 Tools & Methods

Python · Monte Carlo Simulation · Time Series · AR(1) · Inflation · Compounding