📊 How Diversification Can Increase Compound Growth

Finance & Statistics
Portfolio Theory · Correlation · Volatility · Compounding

💡 The Question

We have already seen that volatility can reduce compound growth through the volatility drag.

But what happens when we combine multiple assets?

Consider two assets with identical characteristics:

We build a portfolio:

50% Asset A + 50% Asset B

The expected return remains 7%.

What changes is their correlation.

1. No Real Diversification

Suppose the two assets are perfectly correlated:

ρ = 1

They always move together.

The portfolio therefore has:

Expected Return ≈ 7%
Volatility      ≈ 15%
CAGR            ≈ 5.9%

Combining the assets provides essentially no diversification benefit.

2. Real Diversification

Now assume:

ρ = 0.2

The assets no longer move perfectly together.

The expected return remains unchanged, but portfolio volatility falls:

Expected Return ≈ 7%
Volatility      ≈ 11%
CAGR            ≈ 6.4%

That’s approximately +0.5 percentage points of annual compound growth without increasing expected return.

3. Why?

For a two-asset portfolio:

σp² = wA²σA² + wB²σB² + 2wAwBσAσBρ

Correlation enters directly into portfolio variance.

Lower correlation → lower covariance → lower portfolio volatility.

And since compound growth can be approximated as:

CAGR ≈ μ - σ²/2

reducing volatility also reduces the volatility drag.

Lower correlation
       ↓
Lower portfolio volatility
       ↓
Lower volatility drag
       ↓
Higher compound growth

🎯 Key Takeaway

Diversification is not simply about owning more assets.

The important question is how those assets move relative to each other.

Two perfectly correlated investments provide little diversification benefit.

Combining assets with lower correlation can instead reduce portfolio volatility without necessarily reducing expected return.

And lower volatility means less volatility drag and potentially higher long-term compound growth.

Diversification doesn’t only make the journey smoother. It can make compounding more efficient.

🧰 Tools & Methods

Portfolio Theory · Statistics · Correlation · Covariance · Volatility · Compounding