Drawdown recovery math: why losses hurt more than gains help

A drawdown is a decline from a previous peak. If your portfolio rises to $10,000 and then falls to $8,000, it is in a 20% drawdown, even if it is still above what you originally put in. Drawdowns are a normal part of investing. What surprises many people is how much larger the gain needs to be to recover from them.

The formula

If an investment loses a fraction L of its value, the gain needed to get back to the starting value is:

Required gain = L ÷ (1 − L)

The reason is that the recovery starts from a smaller base. After a 20% loss, $100 becomes $80. To get back to $100, the $80 must grow by $20, which is 25% of $80, not 20%.

The recovery table

Small losses are easy to recover from. Large ones are not. The required gain rises slowly at first and then very steeply. Somewhere between a 30% and a 50% loss, recovery stops being a matter of patience and starts requiring an exceptional result.

Time is the hidden cost

The table shows the size of the required gain, but not how long it might take. A portfolio that has to double just to get back to even may need many years to do it, depending on what it earns, and there is no guarantee it ever will. Meanwhile, money you need for a goal with a fixed date, such as a home purchase or retirement, may not have that time. This is why the same percentage loss is far more dangerous close to the date you need the money.

What this means for managing risk

The asymmetry has practical consequences:

• Limit how much any single position can lose. A rule like the one in our position sizing guide keeps a single mistake from producing a deep portfolio drawdown.
• Watch concentration. If one holding is 40% of your account and it halves, your whole portfolio falls 20%, which then needs a 25% gain to recover.
• Know your own pain threshold. Decide in advance the portfolio drawdown at which you will review your plan, rather than discovering it during a sell-off.
• Keep cash you need out of the market. Being forced to sell during a drawdown locks in the loss and removes the chance to recover.

A portfolio example

An illustrative example: a $20,000 portfolio holds five equal positions of $4,000 each. One falls 50%, losing $2,000. The portfolio falls 10%, to $18,000, and needs about 11.1% to recover. Now imagine the same loss when that one stock was half the portfolio, $10,000: the loss is $5,000, a 25% portfolio drawdown that needs a 33.3% gain to recover. Same stock, same move, very different damage. Our guide to managing investment risk covers the other tools that limit this.

Measuring your own drawdowns

Track the value of your portfolio at regular intervals and record its running peak. Drawdown at any time is the current value divided by the running peak, minus one. Keep the record over time. It tells you how deep your real declines have been, how long they lasted and how you behaved during them, which is far more useful than a generic risk score.

Common misunderstandings

• "It went down 30% and then up 30%, so I am back to even." No. $100 falls to $70, and a 30% gain on $70 is $21, leaving $91, still 9% below the start.
• "I have not lost anything until I sell." The value of the portfolio has fallen whether or not you sell. Selling decides whether you can participate in any recovery; it does not change what the holding is worth today.
• "Average returns tell me how I did." A year of −50% followed by a year of +50% averages 0%, but $100 becomes $50 and then $75, a 25% loss. Compound results, not averages, are what you actually experience.

Working these numbers out yourself once is the fastest way to make the asymmetry stick. Try it with your own largest holding: if it fell 40% tomorrow, how much would your whole portfolio fall, and what gain would that need?

The takeaway

Avoiding large losses does more for long-run results than chasing large gains, because large losses are so hard to climb back from. That does not mean avoiding all risk; it means choosing how much you take, deliberately.

Drawdowns and portfolio risk are the first chapter of our ebook How to Choose Investments, Manage Risk, and Build a Portfolio: With the Money You Have, because everything else builds on protecting the money you cannot afford to lose.