💰 Lump Sum vs Dollar-Cost Averaging

Finance & Data Science
Monte Carlo Simulation · Compounding · Investment Timing · Python

💡 The Question

Suppose I have €34,000 to invest over a 10-year horizon.

Is it better to invest everything immediately or gradually enter the market?

To explore this question, I compared two strategies:

• Lump Sum (PIC): €34,000 invested immediately.
• Dollar-Cost Averaging (PAC): €10,000 initially + €200/month for 10 years.

1. The Simulation

I generated 20,000 Monte Carlo scenarios under the following assumptions:

Both strategies experience exactly the same simulated market path within each scenario.

The only difference is when capital enters the market.

2. The Results

The gradual strategy outperformed the lump-sum investment in only 2,332 out of 20,000 simulations (~12%).

Lump Sum produced higher expected wealth, but also a much wider distribution of outcomes.

3. Why Does Lump Sum Usually Win?

The reason is relatively simple.

If the asset has a positive expected return, investing earlier gives more capital more time to compound.

Lump Sum
€34,000 ──────────────────────────────→
          exposed for ~10 years

DCA
€10,000 ──────────────────────────────→
       + €200
          + €200
             + €200 ...

DCA reduces the amount exposed to the market early on.

That protects against investing everything immediately before a downturn, but also reduces participation in rising markets.

4. The Role of Return Sequence

The gradual strategy introduces another interesting effect: the order of returns matters.

With Lump Sum and no additional cash flows, rearranging the same set of returns does not change final wealth:

(1+r₁)(1+r₂)...(1+rₙ)

With DCA, however, each contribution experiences a different subset of future returns.

Therefore, two market paths with similar overall performance can produce different outcomes depending on when positive and negative returns occur relative to contributions.

In my simulations, some of the worst DCA outcomes followed an interesting pattern:

Strong returns early, followed by large losses later.

By the time the downturn arrives, much more capital has been accumulated and is exposed to the decline.

🎯 Key Takeaways

• Lump Sum generated higher wealth in roughly 88% of simulations.
• DCA produced a narrower distribution of outcomes.
• Investing earlier maximizes exposure to compound growth.
• Gradual investing reduces entry-timing risk, but sacrifices part of the potential upside.
• Return sequence matters for DCA because capital enters the market at different points in time.

The trade-off is therefore not simply:

Safe vs Risky

but rather:

Reducing timing risk vs maximizing time in the market.

🧰 Tools & Methods

Python · NumPy · Monte Carlo Simulation · Statistics · Compounding · Sequence of Returns

⚠️ Disclaimer

This is a simplified simulation created for educational purposes while studying personal finance.

It is not financial advice, and real markets are considerably more complex than the assumptions used here.