Volatility Drag Explained: Why +20% and −20% Still Produce a Loss

Volatility Drag Explained: Why +20% and −20% Still Produce a Loss

Investment returns compound from a changing base. A 20% gain followed by a 20% loss does not return capital to its starting point: £100 becomes £120, then falls to £96. The arithmetic average return is zero, but the compounded result is a 4% loss.

বাংলায় পড়ুন: Volatility Drag: কেন +20% ও −20%-এর পরও Loss হয়

Learning objective: By the end of this tutorial, you should be able to distinguish arithmetic and geometric returns, calculate the effect of alternating gains and losses, explain why leverage magnifies the gap and avoid common performance-reporting mistakes.

1. Returns act on the latest account value

Suppose a portfolio starts at £100:

1. It gains 20%: £100 × 1.20 = £120.
2. It then loses 20%: £120 × 0.80 = £96.

The two percentage moves have the same size, but the second move acts on a larger base. The total return is:

(1 + 0.20) × (1 − 0.20) − 1 = −0.04, or −4%.

For equal positive and negative moves of size x:

(1 + x)(1 − x) = 1 − x².

That squared term explains the loss. At ±10%, the two-period result is −1%. At ±20%, it is −4%. At ±40%, it is −16%.

2. Arithmetic mean and geometric mean answer different questions

Arithmetic mean

Add the periodic returns and divide by the number of periods. For +20% and −20%:

Arithmetic mean = (20% − 20%) ÷ 2 = 0%.

This describes the average of the two observations. It does not describe the investor's compounded growth rate.

Geometric mean

Multiply the growth factors and take the appropriate root:

Geometric mean = √(1.20 × 0.80) − 1 = √0.96 − 1 ≈ −2.02% per period.

Compounding −2.02% for two periods produces the same final £96. For evaluating a multi-period investment path, the geometric return is usually the more relevant measure.

3. A worked comparison with the same arithmetic average

Consider two hypothetical two-year paths, both with an arithmetic average return of 5%:

Path	Year 1	Year 2	Ending value from £100	Two-year return	Annualised geometric return
Smooth	+5%	+5%	£110.25	+10.25%	+5.00%
Volatile	+20%	−10%	£108.00	+8.00%	+3.92%

The average of +20% and −10% is 5%, but the compounded annual growth rate is only about 3.92%. Greater dispersion around the same arithmetic mean reduced the geometric result in this example.

This gap is often called volatility drag. It is a mathematical consequence of compounding, not a management fee deducted from the account.

4. Loss recovery is asymmetric

After a loss, the required recovery percentage is measured from a smaller base:

Loss	Capital remaining from £100	Gain needed to recover to £100
−10%	£90	+11.11%
−20%	£80	+25.00%
−30%	£70	+42.86%
−50%	£50	+100.00%

The recovery formula is:

Required gain = 1 ÷ (1 − loss) − 1.

This is why large drawdowns deserve disproportionate attention. Avoiding one severe loss can matter more to long-run compounding than adding several small winning periods.

5. Leverage magnifies the compounding gap

Assume an index falls 10% on day one and rises 10% on day two:

• Index: £100 × 0.90 × 1.10 = £99, a 1% loss.
• Hypothetical 2× daily exposure: £100 × 0.80 × 1.20 = £96, a 4% loss.

The leveraged result is not simply twice the index's two-day loss. The product targets twice each daily return, and each daily move compounds from the new value.

The US SEC and FINRA investor alert uses this same two-day structure to explain why daily-reset leveraged and inverse ETFs can differ significantly from a simple multiple of their benchmark over periods longer than one day. The divergence can become larger when volatility and the holding period increase.

Fees, financing, tracking error and rebalancing costs can create additional differences beyond the pure compounding shown here.

6. The order of ordinary returns and path dependence

For an unleveraged investment with no deposits, withdrawals or rebalancing, multiplying the same set of periodic returns produces the same final value regardless of their order. +20% then −10% ends at the same £108 as −10% then +20%.

The lived path can still matter because investors may add or withdraw money, face margin calls, rebalance, use stop-losses or change exposure after a drawdown. Daily-reset leveraged products also adjust their exposure repeatedly, which makes their multi-day outcome dependent on the sequence of underlying daily returns.

Use “path dependence” precisely. Compounding alone creates a gap between arithmetic and geometric returns; cash flows, dynamic exposure and risk constraints make the order of returns operationally important.

7. Volatility drag does not mean volatility always causes a loss

A persistent trend can compound favourably. Two consecutive +10% returns turn £100 into £121, a 21% gain. A daily leveraged product can outperform a simple multiple during a consistent trend because gains compound on a rising base.

The lesson is conditional:

• Alternating gains and losses create a compounding penalty.
• Higher leverage magnifies both favourable and unfavourable compounding.
• The final result depends on return size, sequence, costs and any exposure reset.
• A positive expected return can still overcome volatility drag, but the required edge rises as variance and costs increase.

Volatility drag is a risk lens, not a forecast that an asset must fall.

8. How traders can use the concept

Compare strategies with geometric returns

When reviewing multi-period performance, use cumulative return and annualised geometric return beside the arithmetic average. A high average with violent swings may compound less efficiently than a slightly lower but steadier series.

Size positions for survival

Large percentage losses require increasingly large recoveries. Position sizing and portfolio limits should prevent one trade or correlated cluster from creating a drawdown that changes the entire recovery problem.

Evaluate leverage at the correct horizon

Check whether a product targets daily, monthly or point-to-point exposure. Never assume a 2× daily product will deliver exactly twice the benchmark's monthly or annual return.

Include costs in the growth factors

Net return compounds after spread, commission, financing, management fees and taxes where applicable. Small recurring costs become material over many periods.

Review cash-flow timing

Money-weighted returns can differ from time-weighted returns when deposits and withdrawals occur. A large deposit just before a loss changes the investor's result even if the fund's published time-weighted return is unchanged.

9. Common mistakes

Adding returns across periods

Adding +20% and −20% to get zero ignores the changing capital base. Multiply growth factors instead.

Using the arithmetic mean as CAGR

Arithmetic average is not annualised compound growth. Use the geometric mean for a completed multi-period path.

Assuming equal loss and gain cancel

A 20% loss needs a 25% gain to recover. The percentages use different bases.

Treating volatility drag as a fee

It is a compounding effect. Actual fees and financing costs are separate and should be added to the analysis.

Generalising a daily leverage target

A daily objective applies to one day. Multi-day results depend on daily compounding and may depart sharply from the stated multiple.

Ignoring survivorship and liquidation

An average return is irrelevant if leverage or a margin call forces the position to close before the expected recovery arrives.

10. Practical checklist

• Convert each return into a growth factor: 1 + return.
• Multiply growth factors to calculate cumulative performance.
• Use the geometric mean or CAGR for multi-period compound growth.
• Compare drawdown size with the gain required for recovery.
• Review both average return and volatility; neither is sufficient alone.
• Identify whether leverage resets daily or at another interval.
• Include spread, fees, financing and tracking difference.
• Stress-test alternating moves, gaps and repeated losing periods.
• Check whether cash flows, rebalancing or margin rules make the sequence important.
• Report the measurement period and whether returns are gross or net.

The core lesson

Percentages do not cancel symmetrically because gains and losses act on different capital bases. Arithmetic return summarises observations; geometric return measures what happened to wealth. The gap becomes more important as volatility, leverage, costs and holding time increase.

For traders and investors, protecting the compounding base is part of return generation—not a separate task.

Educational risk disclosure

This tutorial was prepared with AI-assisted research and writing under The Money Man editorial workflow. All portfolio examples are hypothetical and exclude taxes unless stated. This is educational information, not personalised investment advice or a recommendation to use leverage or buy any exchange-traded product. Leveraged and inverse products can produce rapid losses, may not match a simple multiple over longer periods and can lose most or all invested capital.