Volatility harvesting

The surprising truth about diversification

You probably know that diversification reduces risk. Fewer investors know that it can also increase long-term return — without choosing riskier assets, and even when both assets have exactly the same expected return.

This is the essence of volatility harvesting — also called the rebalancing bonus or diversification return — and it is one of the structural reasons why well-diversified portfolios have historically outperformed expectations.

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A simple example

Imagine two assets, A and B:

• Both are expected to return roughly 7 % per year on average
• Both are volatile — swinging up or down by as much as 30 % in a single year
• But they move out of step: when A rises sharply, B might be flat or falling, and vice versa

What happens if you hold them 50/50 and rebalance every year?

Each year you sell a little of whichever has risen and buy a little of whichever has fallen. Sell high, buy low — automatically and mechanically, with no forecasting required.

The result: the portfolio outperforms either asset held alone — not because you picked better assets, but because you systematically exploited the swings between them.

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The essence — no maths required

The maths — which you can read further down — is simply the proof of what already makes intuitive sense: systematic “buy low, sell high” works.

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Why it works: systematic buy-low, sell-high

Rebalancing enforces a mechanical discipline that requires no predictions:

• When A has risen relative to B → trim A, buy more B (sell high, buy low)
• When B has risen relative to A → trim B, buy more A (sell high, buy low)

In each rebalancing cycle you capture part of the spread between the two assets. No forecasting. No market timing. Just arithmetic.

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Interactive simulation

Try it yourself. Both assets in the simulator below have identical parameters — same expected return, same volatility. The only difference is:

• Single asset (buy & hold) — 100 % in one asset, never rebalanced
• Rebalanced 50/50 — both assets in equal weight, rebalanced annually

The blue band shows the spread of outcomes for the single-asset strategy — from the 10th to the 90th percentile across all simulated paths. The green band shows the same for the rebalanced strategy. The solid lines show the median outcome for each strategy.

Notice that the blue band is wider than the green: the single asset has higher volatility, so outcomes stretch further in both directions. The green band is narrower because rebalancing reduces combined portfolio swings. The bands can overlap — that simply reflects the different risk profiles of the two strategies, not that they end up in the same place.

Things to try:

• Raise the volatility slider. The premium scales with $\sigma^2$, so moving from 15 % to 30 % volatility quadruples the theoretical premium.
• Slide the correlation toward +1. As the assets move together, diversification disappears and the gap between the two median lines shrinks to zero.
• Slide toward −1. The assets are nearly perfectly opposed — the premium becomes very large and portfolio volatility approaches zero.
• Run the same settings twice. The simulated premium fluctuates around the theoretical value — sometimes above, sometimes below.

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What drives the premium?

Factor	Effect on premium
Higher individual volatility	Larger premium
Lower correlation between assets	Larger premium
More frequent rebalancing	Captures premium faster, but increases transaction costs
More assets	Premium applies across all asset pairs

The strongest conditions: high individual volatility combined with low or negative correlation between assets.

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Real-world portfolios

The rebalancing premium is not just theory. Here are typical estimates for well-known combinations:

Portfolio	Typical correlation	Theoretical premium
60 % equities / 40 % bonds	ρ ≈ −0.3 to 0	~0.5–1.5 % per year
MSCI World / Emerging Markets	ρ ≈ 0.6–0.8	~0.2–0.5 % per year
Equities / Gold	ρ ≈ −0.1 to 0	~0.5–1.0 % per year
Two highly correlated equities	ρ ≈ 0.9	Below 0.1 % per year

The stocks/bonds combination is historically attractive because bonds tend to rise when equities fall — negative correlation that maximises the premium. This is one of the structural reasons the 60/40 portfolio has performed remarkably well over time.

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Real-world limits

The rebalancing premium is genuine, but can be eroded by:

Transaction costs

Every rebalancing trade has a cost — spread, commission, and potentially market impact. For small, frequent rebalances the cumulative cost can exceed the premium.

Taxes

In taxable accounts where gains are realised on sale, every rebalancing trade can trigger a tax event. The tax payment removes capital from the portfolio that can no longer compound.

In Denmark, this interaction between the rebalancing premium and realisation-based taxation is particularly important. See Rebalancing vs. Danish Taxation for a detailed analysis of how the two forces trade off against each other.

Correlation is not constant

The formula assumes a stable correlation. In practice, correlations shift over time and often spike toward +1 during market crises — precisely when diversification is most needed. The premium may be lower than the long-run average suggests.

The premium is statistical, not guaranteed

Over short horizons, random variation dominates. The premium only materialises reliably over long periods and across many independent return realisations.

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The maths — for the curious

Want to understand why it works? Here is the precise explanation.

The volatility drag

The arithmetic mean of returns overstates actual compounded growth. Suppose an asset rises 50 % one year and falls 33 % the next:

$\bar{r} = \frac{0.50 + (-0.33)}{2} = 8.5\%$

But the actual outcome after two years:

$1.50 \times 0.67 \approx 1.00$

The investor ends where they started. The real compounded return is 0 %, not 8.5 %. The gap is approximately:

$g \approx \bar{r} - \frac{\sigma^2}{2}$

Higher volatility means a larger gap and a lower real-world compounded return, for a given arithmetic average.

The rebalancing premium

A rebalanced 50/50 portfolio of two assets has lower combined variance than either asset alone. Lower variance → smaller gap → higher compounded return. That is the source of the premium.

The approximate annual premium from rebalancing two equal-weight identical assets:

$\text{rebalancing premium} \approx \frac{\sigma^2}{4}(1 - \rho)$

• $\sigma$: the annual volatility of each asset
• $\rho$: the correlation between the two assets

Example with $\sigma = 20\,\%$ and $\rho = 0$:

$\text{premium} \approx \frac{0.04}{4} \times 1 = 1\,\%\ \text{per year}$

Over 20 years, a 1 % annual premium compounds to roughly 22 % more final wealth — for exactly the same expected return in both assets.

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Summary

• Rebalancing between uncorrelated assets generates a return premium independent of their expected returns
• The source is portfolio variance reduction below the individual asset variance
• The annual premium is approximately $\frac{\sigma^2}{4}(1-\rho)$ for two equal-weight assets
• For typical stock/bond parameters, this is roughly 0.5–1.5 % per year before costs
• Volatility and low correlation are the two key drivers
• Taxes and transaction costs can erode or eliminate the premium in taxable accounts

Volatility harvesting is one of the few genuine free lunches in portfolio management — but only when costs and taxes are managed carefully enough to keep the lunch worth eating.