Diversification stops working when you need it

One bet of 4,000, or forty bets of 100. Same total, same odds on each, same edge.

Almost everyone knows the second is safer. Rather fewer can say by how much, and almost nobody can say what has to be true for the safety to exist — which is the part that matters, because in the conditions where you most want the safety, the thing that has to be true stops being true.

Watch the spread narrow

A bet that wins 100 with a 55% chance and loses 100 otherwise. A small genuine edge, ten units per trial, and a spread far larger than the edge.

Move the number of trials and watch two things: the expected total, which rises in a straight line, and the chance the total is still negative, which falls much more slowly than most people expect.

Expected value

≈ Hypothetical model, not a forecast

The average outcome of a repeated two-sided bet, and how widely the total can still land around it.

It assumes

• Every trial is independent, which is the assumption this whole lesson is about.
• The odds are exactly as stated and do not change at any point.
• The stake is identical on every trial regardless of what happened before.
• The spread at the end uses a normal approximation to the total.

It ignores

• Ruin — this model happily continues past a balance of zero
• Any change in bet size after a win or a loss
• Correlation between trials, and odds that shift over time
• Costs of playing, such as a commission on each trial

Holding the win chance at 55, find the number of independent trials at which the chance the total is still negative falls below one in twenty. Note how large that number is for such a clear edge.

Chance of winning55%

Number of trials10

Expected result per trial

10

Expected total

100

Spread of one trial

99.5

Spread of the total

315

Chance the total is still negative

0.375

Win chance that makes this fair

50%

• Expected total
• One spread above
• One spread below

◷ Not there yet — keep moving the controls.

Somewhere around two hundred and seventy trials before the chance of a losing total drops below one in twenty. With a ten percent edge on every single one.

That is the honest scale of it: diversification works, it works slowly, and the benefit arrives in square roots rather than in proportion. Going from one holding to ten does most of the available work; going from ten to a hundred does a good deal less; and none of it happens at all without the condition in the assumptions.

Now drag the trials back to one and look at the chance of a losing outcome. It is close to a coin toss. Forty holdings that all do the same thing are that number, not the other one.

Predict

A portfolio is spread across many holdings, chosen carefully so that they normally move quite independently of each other. A severe market fall arrives. What happens to the relationships between them during the fall?

Choose one answer

They hold — the holdings were chosen precisely to be differentThey tighten, and the holdings fall togetherThey reverse — some holdings rise as others fallThey become unmeasurable during the fall

Lock in answer

Why the relationships tighten

Three mechanisms, and none of them is mysterious.

One reason replaces many. In ordinary conditions each holding moves for its own reasons: this company's results, that building's tenant, this borrower's prospects. In a severe fall a single reason arrives that applies to all of them at once — the price of money changed, or everybody needs cash — and it swamps the individual stories.

Selling is not selective. A holder who must raise cash sells whatever can be sold, which is not the same as whatever they wanted to sell. That transmits pressure from the assets people wanted to leave into the assets they merely could leave, which is how unrelated things start falling together.

The buyers step back at the same moment. Falls are as much about the disappearance of bids as the arrival of offers. The people who would have bought each of your different holdings are frequently the same people, and they become cautious simultaneously.

So the diversification thins out exactly in the conditions it was bought for. That is not a reason to abandon it — thinner is not zero, and the portfolio that fell together still fell less than the single holding would have. It is a reason to stop treating it as a defence against the worst case.

What still helps when it tightens

Being precise about what survives is more useful than a warning.

Genuinely different cash flows. Holdings whose money comes from different payers, in different economies, for different reasons, tighten less than holdings that merely have different names. The test from the ownership track applies: write down the sentence that would have to be true for each one to have a bad decade, and count how many distinct sentences you wrote.

Instruments at different points in the queue. Lending to something and owning it are different exposures to the same enterprise, and they behave differently in trouble because one gets paid first.

Things that are not assets. Cash does not fall when everything falls. This is not a clever hedge, it is the absence of a position, and its value in a crash is precisely that it stops you being a forced seller.

Time. Money arriving to be invested at intervals over decades is spread across market conditions in a way a single lump is not. It is the one form of diversification that costs nothing and that nobody can take away.

Check

Somebody holds twenty different assets and says they are well diversified. What single question tests the claim fastest?

Choose one answer

How many are there, and in what proportions?What would have to happen for all twenty to have a bad decade at once?How have they moved together over the last five years?Are they in different countries?

Check answer

Worth remembering

• Diversification leaves the expected return alone and narrows the spread around it.
• The narrowing follows a square root, so the benefit arrives slowly and the early holdings do most of the work.
• The whole effect depends on the holdings varying independently of one another.
• In a severe fall almost everything moves together, which is close to a definition of a crash rather than a surprise.
• Cash, genuinely different cash-flow sources, different places in the payment queue, and time are what still help when relationships tighten.