Volatility drag: why +20% then -20% leaves you 4% down

A zero average that lost money

Take ₹1,00,000. In year one it gains 20%. In year two it falls 20%. The simple average of +20% and −20% is exactly 0%, so you might expect to be back at ₹1,00,000.

You are not. After year one you hold ₹1,20,000. A 20% fall takes off ₹24,000, leaving ₹96,000. The fall is applied to a bigger base than the gain was, so it removes more rupees than the gain added.

The same effect is behind a 50% fall needing a 100% gain. Here we look at what it does across several years of ups and downs.

The effect grows with the swings

Compare two gains-and-losses of the same size at different scales:

Each row has the same 0% average. The bigger the swing, the larger the shortfall. Doubling the swing from 10% to 20% cut the loss from ₹1,000 to ₹4,000, which is four times as much, not twice. That is the signature of the effect: it grows with the square of the swing.

Four years, a worked example

Now use a more realistic run of yearly returns: +30%, −20%, +25%, −15%.

• The simple average is (30 − 20 + 25 − 15) ÷ 4 = 5% a year.
• Compounded: 1.30 × 0.80 × 1.25 × 0.85 = 1.105, so ₹1,00,000 becomes ₹1,10,500.

A steady 5% a year for four years would have given about ₹1,21,550. The bumpy path ends roughly ₹11,000 behind, because the real compound rate is only about 2.5% a year, half of the simple average.

These are made-up returns chosen to show the mechanism, not any fund's record.

A rule of thumb

For moderate swings, the compound rate is roughly the simple average minus half the variance, where variance is the standard deviation squared. A fund with a 20% standard deviation has a variance of 0.04, so about 2 percentage points a year is lost to drag. A fund with a 10% standard deviation loses only about 0.5 point.

This is an approximation, not an exact law, but it explains why two funds with the same average year can end in very different places.

What this means when you read a fund

• Prefer CAGR to a yearly average. The CAGR versus absolute return post explains why CAGR is the growth you actually received.
• Check the volatility figure. A fund's page shows annualised volatility, which is a standard deviation of daily returns. This guide explains how to read it.
• Smoother can win on the same average. If two funds average the same return, the lower-volatility one compounds to more. That is the quiet case for diversification.
• Sequence matters when you withdraw. Drag is bigger still when you take money out during falls; see sequence of returns risk.

Five bad years in a row

To see how stubborn it is, repeat the +20%, −20% pair five times, ten years in all. Each pair multiplies your money by 1.20 × 0.80 = 0.96. Five pairs give 0.96 to the power of five, about 0.815, so ₹1,00,000 becomes roughly ₹81,500 with an average return of exactly zero the whole way.

The takeaway

Volatility is not only a feeling; it is a cost that shows up in arithmetic. It does not make risk wrong, because higher-risk assets are meant to pay more. It does mean that the average return printed in a brochure and the money in your account can differ, and the gap widens as returns swing. Judge funds by compounded returns, and by how bumpy the ride was getting there.

This post is educational, not financial advice. The returns above are invented for illustration and are not forecasts or any fund's record.