The maths of buying the dip: why a 20% fall needs a 25% recovery

A crypto asset falls 20%, then gains 20%. Is it back where it started? No. An initial $100 would fall to $80, then recover to $96. The same percentage describes two different dollar amounts because the second move starts from a smaller base.

All prices in this explainer are hypothetical. They illustrate percentage changes, not a forecast for Bitcoin, Ether or any other asset.

After a fall from $100 to $80, the asset needs to gain $20 to reach its original price. That $20 is 25% of the remaining $80. The recovery required is therefore 25%, even though the initial loss was 20%.

For a loss below 100%, the calculation is:

Required recovery (%) = loss (%) / (100 - loss (%)) × 100

The gap grows as the loss gets larger:

• A 10% fall requires an 11.11% recovery.
• A 20% fall requires a 25% recovery.
• A 25% fall requires a 33.33% recovery.
• A 50% fall requires a 100% recovery.
• A 75% fall requires a 300% recovery.

Figures are rounded to two decimal places. A complete loss leaves no remaining value on which to earn a percentage recovery.

Suppose someone buys one unit for $100 and another after the price falls to $80. They now own two units at a total cost of $180, or an average of $90 per unit. A rise from $80 to $90 would bring that position back to its purchase cost before fees.

That lower average comes with another $80 committed to the asset. If the price then falls to $60, the two units are worth $120 against the $180 spent. Adding to a position changes both the break-even price and the amount exposed to further losses.

The formula says how far a price must rise to recover a loss. It says nothing about whether that rise will happen, how long it could take, or whether the original price represented fair value. Fees and other costs can also move an investor's actual break-even point above the simple price calculation.

In its September 2024 investor bulletin on Bitcoin and Ether exchange-traded products, the SEC's Office of Investor Education and Advocacy describes the underlying assets as highly speculative and discusses their price volatility. Read the investor bulletin.

When comparing a dip with a rebound, check the starting price for each percentage. A 20% gain after a 20% loss still leaves the original position 4% below its starting value.