Maximum Drawdown: Depth, Duration and Recovery Time

Maximum drawdown is the largest fall from a peak to a later trough inside a stated window. Duration is how long the fall took and recovery time is how long the climb back took. The Anantara Multi-Asset Portfolio fell 9.7 per cent at worst in the stated year against the composite benchmark's 8.1 per cent, and regaining 9.7 per cent needs a rise of 10.74 per cent.

Ask a holder what the year was like and the answer is rarely the annual return. The answer is the worst part of it. Naming the worst part is not a failure of memory, it is a sensible answer to a different question, and maximum drawdown is the measure that answers it.

The running example throughout is the Anantara Multi-Asset Portfolio, an invented discretionary mandate of Rs 500 crore run by Faiz Ahmad Ansari for an invented charitable endowment whose investment committee is chaired by Rukmini Deshpande. The mandate is measured against a composite benchmark, described and never named, of a broad equity index and a broad bond index. In one stated twelve month period the Anantara Multi-Asset Portfolio fell 9.7 per cent from its highest point to its lowest before recovering, and the composite benchmark fell 8.1 per cent over the same window. A depth belongs to the one twelve month period it was measured inside, and one twelve month period is not evidence about what any approach achieves.

Volatility, beta and simple ratios are set out separately. Underneath all three sits the quantity that gets quoted worst: a single number, produced by one realised path, that most reports print without the two facts that would make it usable.

What exactly is a maximum drawdown, and how many numbers is it?

Start with the shape rather than the definition. A value series rises for a while, turns, falls, bottoms out, and climbs back. Maximum drawdownThe largest fall from a high point to a later low point in a value series, measured as a percentage of that high point, inside a window that must be stated. is the deepest of those falls inside a stated window, measured from the high point down to the low point that follows it.

Here is the part that gets lost. A fall is not one number, it is three. The depth is how far the value dropped below the peakThe highest value the series had reached at that moment. Every drawdown is measured downwards from a peak, so the peak is what fixes the base., expressed as a percentage of that peak. The duration is how long it took to get from the peak down to the troughThe lowest value the series reached before it started climbing again. The distance from the peak down to the trough is the depth.. The recovery time is the further stretch from the trough back up to the level of the old peak. Depth, duration and recovery time are three quantities with three different units. Almost every report quotes the depth alone, and the depth describes about a third of what happened.

Think of a shop that loses trade when the road outside is dug up. The owner can say how bad it got, how many weeks it took to get that bad, and how many months it took before takings were back where they had been. Three answers. The second and third are the ones that decide whether the shop survives, and it is the first one that ends up in the conversation.

The picture forces one thing into the open. The depth is a vertical distance and the other two are horizontal distances, so no single number can carry all three. A report that says the worst fall was 9.7 per cent has answered the vertical question and left both horizontal ones open, and the horizontal ones are usually the ones a holder was asking about.

Volatility vs Drawdown: which of the two says what the year felt like?

Both get called risk measures and they are not measuring the same object. Volatility is a dispersion of period returns around their mean. Squaring the deviations gives a gain and a loss of the same size identical weight, so volatility is symmetric by construction.

A drawdown is a different kind of object entirely. A drawdown is a single distance along one realised path. The measure uses only the falls and ignores every gain except in so far as gains set the peak the fall runs from. A drawdown also depends completely on the order the returns arrived in, and volatility has no such dependence. The dependence on order has a name: path dependenceA quantity is path dependent when reshuffling the same set of period returns into a different order changes its value. The end value and the volatility do not change; the worst fall does..

The cleanest demonstration available takes one shuffle. Take twelve monthly returns and compute their standard deviation. Now put the same twelve returns in a different order and compute it again. The standard deviation has not moved. A standard deviation does not know which month came first. The ending value has not moved either, and the same twelve multiplications simply happen in a different sequence. But the worst fall has moved a long way. Two portfolios with identical monthly returns in a different order have identical volatility, identical ending value and different maximum drawdowns. No cleaner proof exists that the two measure different things.

So the two answer different questions. Volatility answers how spread out the period returns were. A drawdown answers how bad it got along the way that actually happened. A holder who never sells feels the first one. A holder who might have to sell feels the second, and that difference is what decides things.

Why does the same portfolio show a different worst fall in a different window?

Because a drawdown is defined peak to trough inside a stated window, and moving the window moves both ends of that definition. A measurement windowThe stretch of time a figure is computed over, with a stated start and a stated end. Two windows over the same path are two different measurements. is part of the figure in the way that a unit is part of a length.

Two consequences follow directly, and both are one line of reasoning each. Lengthen a window and the answer can only stay the same or get deeper. Every fall the shorter window contained is still inside the longer one, and the longer one may contain worse. Shorten a window and it may cut the peak off one end, or the trough off the other, or both, and report a fall that never bothered anyone. A window sitting entirely inside a recovery reports no drawdown at all on a path that had one.

A drawdown quoted with no window attached is not merely thin, it cannot be used for anything, and presenting one that way is the ordinary practice rather than a rare lapse. The practice appears in almost any monitoring pack: a worst fall in a summary row with no start date, no end date, and a reader left to assume the row means the same thing as the row above it.

The control below can display twenty two different windows over that one path, and the twenty two answers are worth seeing laid out together.

Does it matter whether the values are daily or month end?

Frequency matters more than most readers expect, and most reports leave it out. A drawdown is computed from a series of observations, so it can only ever find a trough that one of those observations landed on. The measurement frequencyHow often the value series was observed: daily, weekly, month end. A drawdown can only find a low point that one of the observations actually recorded. therefore sets the resolution of the answer.

Picture a fall that opened after the tenth of a month, reached its worst point on the twentieth, and had largely reversed by the last working day. A month end series records the value on the last working day. A month end series never sees the twentieth. A daily series over exactly the same path sees all of it. A daily series on an identical path reports a fall at least as deep as a monthly one and usually deeper, so laying a daily figure beside a monthly figure is not a comparison at all. The Anantara depth of 9.7 per cent for the stated year is computed on month end values, and that fact travels with the figure exactly as the window does.

A table invites a reader to subtract one row from another, so the practical damage shows up the moment two frequencies land in the same table.

Why does climbing out always take more than the fall took?

The climb back is arithmetic, and the arithmetic is worth doing slowly. Here is where a depth figure stops being linear in how much it hurts. Suppose a value falls by d, expressed as a fraction. The remainder is one less d. The rise is measured on the smaller base the fall left behind, so getting back to the old level needs that remainder to rise by d divided by one less d.

The two numbers this guide carries run as follows. A fall of 9.7 per cent leaves 90.3 per cent standing, and 0.097 divided by 0.903 is 0.10742, so the climb back is 10.74 per cent. A fall of 8.1 per cent leaves 91.9 per cent standing, and 0.081 divided by 0.919 is 0.08814, so the climb back is 8.81 per cent. The widening is arithmetic rather than market behaviour. A gap of 1.6 points in depth therefore opens into a gap of 1.93 points in the climb out.

In rupees it is easier to feel. Take an illustrative peak at the mandate's stated size of Rs 500 crore. A fall of 9.7 per cent is Rs 48,50,00,000/-, leaving Rs 4,51,50,00,000/-. Earning that Rs 48,50,00,000/- back is now a gain of 10.74 per cent on the smaller amount, not 9.7 per cent, and the deeper the hole the wider that wedge gets. At a fall of 30 per cent the climb back is 42.86 per cent, and at 50 per cent it is 100 per cent.

How to Review a Portfolio Drawdown: what order do the seven steps go in?

Reviewing a fall properly is a fixed order of operations, and the order matters because each step supplies what the next one needs. Skip the first and every later number is unanchored. Skip the last and the review reads as though nothing were missing.

The seventh step, writing down what the data cannot show, is a step of the review and not an apology at the end of it. A review that ends with three absences named is more usable than one that ends with three estimates nobody can check, and it is the step most likely to be dropped because it looks like weakness rather than method.

Step six is the one most often missing. Before anyone calls a fall excessive, it should be set against what the exposure the mandate already carries would have produced on its own. The Anantara mandate carries a beta of 1.08 against its composite benchmark for the stated year, so a fall in the benchmark is expected to arrive amplified. Calling the amplified part excessive is charging a manager for a shape the holder chose.

The amplification is not special to a fall of 8.1 per cent either. The amplification is the same eighth on any fall the benchmark takes. A property of the mandate, then, rather than news about the year.

How Drawdowns Affect Portfolio Decisions: what changes when money must go out?

Everything, and this is why the measure exists rather than being a curiosity beside volatility. A drawdown is what a holder actually experiences and it is what an obligation to pay money out actually runs into. An annual return is a summary of the whole year that only somebody who was never forced to act ever receives.

Follow the mechanism honestly. A holder who has to fund a payment while the value is down sells units at the depressed level. The units sold are gone. When the value climbs back, the units that were sold are not there to climb with it, so the holder takes the fall and receives none of the recovery. The fall and the pattern of money going out together decide whether a fall was survivable or permanent, so a drawdown figure belongs beside that pattern rather than beside the return. The technical word for the stretch between the peak and the recovery is under waterThe stretch of time during which a value sits below a previous peak. A holder is under water from the moment the peak is passed until the old peak is regained., and how long a holder is under water is the question the depth alone cannot touch.

The under water stretch can be drawn directly, and most monitoring packs leave that drawing out.

The household version is exact and everybody has lived near it. A household running on one salary with three months of expenses set aside does not care about the average of its year. The household cares about the worst week it has to get through, and whether the roof needs repairing during that week. If the repair lands in the bad week, savings meant for later get spent at the worst possible moment and never get the chance to recover. Same mechanism, different scale.

What did the Anantara portfolio's worst fall actually say?

The window comes first, and the window is the discipline at issue. Inside one stated twelve month period, measured on month end values, the Anantara Multi-Asset Portfolio fell 9.7 per cent from its highest point to its lowest before recovering, and the composite benchmark fell 8.1 per cent over the identical window.

Start with the comparison every reader reaches for. Divide 9.7 by 8.1 and the result is 1.20, so at its worst the portfolio fell about a fifth further than the benchmark did. The ratio of two depths is a true statement about two depths, and most reviews stop there.

Now the comparison almost nobody runs, and it is the one worth the space. The portfolio carries a beta of 1.08 against that composite benchmark for the stated year. An exposure of that size alone would have produced a fall of 1.08 times 8.1 per cent, or 8.75 per cent. The realised 9.7 per cent is 0.95 points deeper than that. Most of the extra depth was already priced by the exposure the mandate itself set, and only 0.95 points sits beyond it.

Resist explaining that 0.95. A beta measured across a whole year does not have to hold inside its worst stretch, and one realised path cannot settle whether it did. The honest statement is that 0.95 points sits beyond what a whole year beta accounts for, and that the record does not contain what would be needed to say why.

Next the recovery arithmetic in full. Getting back from a 9.7 per cent fall needs 0.097 divided by 0.903, or 10.74 per cent. Getting back from an 8.1 per cent fall needs 0.081 divided by 0.919, or 8.81 per cent. So the portfolio's hole is 1.6 points deeper and the climb out of it is 1.93 points longer, and the second gap is larger than the first because the asymmetry compounds with depth.

This record holds a trap for a reader skimming rows. The 1.60 point gap between the two depths is not the only 1.60 in it.

Now the part that has to be stated rather than filled. The record carries the depth of both falls and carries no peak date, no trough date and no recovery date. Duration and recovery time therefore cannot be computed from it. The absence is the demonstration rather than a gap in it. A drawdown quoted as one number is exactly what the record contains, and one number cannot answer the question a holder actually has: how long they would have been under water.

What can a drawdown figure never reveal?

One realised path produces exactly one maximum drawdown. One depth is a single observation and not a distribution, and no amount of arithmetic performed on a single observation turns it into a property of the thing observed. A drawdown deeper than the benchmark's is a fact about the year that happened and is not evidence about how the portfolio behaves in general.

Keeping the units straight helps too. A depth is a distance travelled along a path, measured as a percentage of a peak. A depth is not a share of variance, not a probability and not an expectation, and a percentage sign is the only thing it has in common with any of those. Reading a depth as though it were one of them is how a fact about one year turns into a claim about a portfolio's character.

How does anybody use this in a room, on a Tuesday?

Take the committee first. Rukmini Deshpande's committee does not open the monitoring pack to admire the annual return. The committee opens it to decide whether the mandate is still the right shape for an endowment that has payments to make. A depth of 9.7 per cent with a window and a frequency attached, set beside the 8.75 per cent that the exposure alone accounts for, supports that conversation. A depth with nothing attached supports a mood.

A lender does the same work in a different vocabulary. Anyone lending against a portfolio wants to know two things: how far the collateral can fall before a margin call arrives, a question about depth, and how long it might sit down there, a question about duration and recovery. The lender therefore asks for the worst fall over a long window rather than the recent one. A longer window can only report a fall at least as deep, and the lender is deliberately buying the more conservative answer.

A household with a pen runs the identical review. Write down the highest the savings pot ever reached, the lowest it reached afterwards, the difference as a percentage of the high, and the two dates. Then write down whether any spending had to happen between those two dates. Whether spending had to happen between those two dates decides whether a fall was something lived through or something paid for, and that holds whether the pot is a savings account or a Rs 500 crore mandate.

The three readers do not want the same thing out of the fall, and it is worth being precise about which of the three quantities each of them is actually short of.