A fall of 50 percent needs a rise of 100 percent to get back to where it started. That asymmetry is the entire reason drawdown is reported separately from return, and it is why a series can post impressive-looking gains and still be underwater.
Everything below is arithmetic on synthetic series, chosen to isolate one property at a time. None of it describes any real asset and none of it is a forecast.
The asymmetry, stated exactly
Take a series that goes 100, then 50, then back to 100.
Max drawdown is 0.5. Max run-up is 1.0. The decline and the recovery are the same movement in price and different numbers, because they have different denominators: the fall is measured against the peak of 100, the rise against the trough of 50.
The recovery required from a given drawdown is drawdown divided by one minus drawdown. From 0.5 that is 1.0. From 0.8 it is 4.0 — an 80 percent fall needs a 400 percent rise. This is why deep drawdowns are qualitatively different from shallow ones rather than just larger.
The running peak resets, and that hides things
Drawdown is measured against a running peak, not the starting value. Consider 100, 50, 200, 150.
The largest fall in percentage terms is the first one, 100 down to 50, which is 0.5. The later fall from 200 to 150 is only 0.25, even though it destroyed more value in absolute terms. Max drawdown for the series is 0.5.
Meanwhile max run-up is 3.0, because the trough of 50 to the peak of 200 is a quadrupling. A single number for the series conceals that its worst decline and its best advance happened in different halves.
Drawdown and volatility measure different things
A series that only rises has a max drawdown of 0. Take 100, 105, 110, 115, 120: drawdown is 0, run-up is 0.2, and realised volatility is small but not zero, because the period returns vary slightly.
A flat series of 100, 100, 100, 100 has drawdown 0, run-up 0, and volatility exactly 0.
Now take 100, 130, 80, 125, 85, 120 — a series that ends higher than it started. Max drawdown is 0.384615, run-up is 0.5625, and realised volatility is 0.436287. It finished up 20 percent while spending most of its life recovering from falls.
Reporting only the start-to-end return on that last series would tell you almost nothing about what holding it was like.
Why volatility here is not annualised
The realised volatility figures above are the sample standard deviation of the period returns, and nothing more. They are not annualised, because annualising requires knowing what a period is, and these series do not carry one.
That is a general point rather than a limitation of the examples. An annualised volatility figure quoted without its sampling frequency is not interpretable, and converting between frequencies assumes returns are independent, which is an assumption rather than a fact.
What to take from it
Drawdown answers what the worst decline from a high-water mark was. Run-up answers what the best advance from a low was. Volatility answers how much period-to-period returns scattered. Return answers where it ended up. Four different questions, and only the fourth is the one usually quoted.
If you are comparing anything, quote the window with the number. A drawdown figure without its measurement period is close to meaningless, because a long enough window will always contain a deeper one.
For working these through on a series of your own, the drawdown and volatility notes go through the arithmetic.