Sizing from the worst case backwards

There are two ways to arrive at a number.

Forwards: this could return three times my money, I am fairly confident, so a large amount is justified. The size comes out of the hoped-for return, and confidence does the arithmetic.

Backwards: if this went to zero I would still need to make rent for eighteen months, so the most that can be in it is this. The size comes out of the worst case, and the hoped-for return is not consulted at all.

Both produce a number. Only one of them produces a number that is still valid after the bad case arrives.

Why the order changes the answer

Forwards reasoning has a structural defect: the upside and your confidence in it come from the same place.

The reason you believe this position could triple is the same reason you believe it is unlikely to fail. One belief, doing two jobs, and it sets both the numerator and the denominator. When it is wrong it is wrong in both directions at once.

Backwards reasoning breaks that link. The survivable loss is a fact about your obligations, your reserve and your income — none of which have any opinion about the position. It can be worked out on a Tuesday with no view on anything.

What would you do

You have 60,000 in savings. Fixed commitments run to 2,000 a month, and your income covers them with about 400 a month to spare. No dependants, no debt beyond the ordinary.

Someone you have worked with for six years is raising money for a business you understand well. You think it is genuinely good. It is private, so there is no way out for at least five years, and if it fails the money is gone completely rather than partly.

Optimising for

Still being able to make every fixed commitment for twelve months if this position goes to zero.

You cannot know

• Whether your income continues uninterrupted for the next five years
• How much worse than expected the business could get before it stops
• Whether another opportunity you would want this badly arrives next year
• What you would think of this decision if the answer were already known

Choose an option

Put in 40,000 — the conviction is high and the size should reflect it.Put in 12,000 — a fifth of savings, sized so that a total loss changes nothing structural.Put in nothing, and keep the whole reserve.Put in 12,000 now and agree to put in 12,000 more each year it survives.

Making the worst case worse on purpose

The second step in the method has a deliberate distortion built into it, and it is there for a reason.

Whatever you believe the worst plausible outcome to be, that belief was formed from the outcomes you have seen or read about. The genuinely worst outcomes tend not to be in that sample, because they happen rarely and because the people they happened to talk about them less.

So the working rule is to take the worst case you can imagine and assume the real one is meaningfully worse — a holding that could fall by half could fall by more; a business that could take eighteen months could take three years; an illness that could cost six months of income could cost two years.

This is not pessimism. It is a correction for a sample you know to be biased in one direction.

What would you do

A small business has 90,000 of cash and monthly costs of 15,000, of which 9,000 is people and 6,000 is everything else. Revenue currently covers about 11,000 of that.

A supplier offers a discount worth roughly 1,200 a month, in exchange for a 50,000 order paid now instead of the usual monthly purchasing.

Optimising for

Keeping the business trading through a twelve-month period where revenue is a third lower than planned.

You cannot know

• Whether revenue holds, grows or falls over the next twelve months
• Whether the supplier would still be there if you asked again in six months
• How quickly the stock would sell if the order turned out to be wrong
• What a lender would charge if cash got tight, and whether one would lend at all

Choose an option

Take the full order. The discount is real, recurring, and pays for itself inside four years.Take a quarter of the order and keep the rest of the cash.Decline, and revisit once revenue covers costs.Take the full order and cut a role to protect the runway.

Check

What is the most common way downside-first sizing fails in practice, even for people who believe in it?

Choose one answer

The positions are sized correctly one at a time, and nobody checks what happens if several bad cases land in the same yearPeople are too pessimistic about the worst case and end up taking no risk at allThe method is too slow to use on time-limited opportunitiesIt gives a smaller answer than the forwards method

Check answer

Worth remembering

• Sizing forwards starts from the hoped-for return; sizing backwards starts from the loss you could absorb without your commitments changing.
• Forwards reasoning lets one belief set both the upside and the confidence, so when it is wrong it is wrong twice.
• The survivable loss depends on obligations, reserves and income, none of which have an opinion about the position.
• Whatever worst case you can imagine, assume the real one is worse, because your sample of outcomes systematically omits the worst ones.
• Positions sized correctly one at a time can still fail together, because bad cases tend to share a cause.