Chapter 6. Case three: the class drawn from the past

6.1The claim

Knight's chapter ends its survey with a limit on the law of large numbers itself: pooling can share losses out and render them predictable without shrinking them, and only so far as the contingencies repeat. Where knowledge is partial, any change in the conditions of judgment changes the worth of the judgment, so the class drawn from past cases may not hold for the next. The section reads that closing passage and then the invalidation lines of both records, each of which names a past-based class to be discarded or divided. The case adds to the first account of the tail, the one that places it outside prior classes, a pair of records that do not give up measurement but ask that it be cut differently. Whether that cutting reaches the tail or only marks where it was last seen is the question the case leaves open.

6.2Knight's closing limit

After his survey of devices, Knight draws the chapter toward its conclusion in a passage that restates the whole problem. The basic uncertainties of economic life, he says, are the errors made in forecasting the future and in adjusting present arrangements to fit it. Where not knowing what comes next is owed to a genuine indeterminacy in nature, nothing is left but large-number pooling, and pooling can share the losses out and render them predictable without shrinking them at all. And even that recourse is available only so far as the contingencies can be gathered into homogeneous groups, which is to say only so far as they recur.

Where ignorance is only partial, a matter of knowledge that is incomplete and inference that is imperfect, Knight continues, cases cannot be sorted on objective grounds, and altering the circumstances in which a judgment is reached will very likely alter how good that judgment is. The point holds, he adds, even when one entrepreneur pools by taking on a larger volume of business, since how well that person estimates is bound up with how many estimates there are and how much material they involve. Pooling by specialisation is subject to the same limit with more force.

Two ideas are joined here. The first is that pooling needs recurrence: the cases in the group must be cases of something that happens again. The second is that the act of judging many cases changes the judging. A larger pool is not simply more of the same; it is a different pool, and the estimates within it are of different quality. Knight states the second idea for the entrepreneur's own estimates, but it applies equally to any class formed from past cases and used for future ones. The class is formed under certain conditions. If the conditions change, the class may no longer describe the cases.

Knight's remark on a sixth factor of uncertainty belongs here too. Earlier in the chapter, after listing the ways in which people differ in their relation to uncertainty, he adds for completeness a category of events so revolutionary and so unexpected by anyone that they hardly count as errors of judgment at all. Knight does not connect them to classes drawn from the past. This article reads them as marking the edge of any such class: events of that kind are not cases of a class.

6.3The first record's revisit line

The first record's invalidation line has two parts. The first states when the judgment would change:

The second states what to check next:

The second sentence is the record's version of Knight's closing limit. The worst historical loss is a class drawn from the past: the set of all losses the strategy has suffered, of which the largest is taken as the ceiling. To assume it is an upper bound is to assume the contingencies recur, that the next crisis will be no worse than the worst so far. The record instructs that this assumption be removed.

Taleb (2007) is concerned with rare events of extreme impact that are explained after the fact as if they had been predictable. His note says nothing about loss ceilings. Applying it to them is a step taken here: a worst historical loss is a rare event already explained, and treating it as a ceiling takes the explanation of the last surprise as a forecast of the next. The record's instruction refuses that, and so refuses to let the past's worst case close the class.

The first sentence of the revisit line moves the other way. It does not say that crisis risk cannot be measured. It says that if crisis risk, including crisis conditions, falls within a budget set in advance and is supported by an independent check, limited use is considered. This is measurement under constraint, and it fits the description in Power (2007) of risk management as turning uncertainty into objects an organisation can manage and account for. The pre-set budget is such an object; the independent verification is another.

The two sentences can be read as in tension. The second says the past's worst case is not a bound; the first says crisis risk can be fitted inside a budget. If the worst historical loss is not a ceiling, the question of what figure the budget is to be compared with is open. The record does not close it. The recommendation Kay and King (2020) make, to prefer strategies robust and resilient to what cannot be foreseen over optimising on invented numbers, bears on the gap. The record's word limited, in limited application, points in that direction. It does not say adoption in full once the budget is met. It says a bounded use is considered, which leaves room for being wrong.

The record's revisit condition, like most in the parent study, contains no number, threshold or time. The pre-set budget is named but not stated. The ledger's code did not count this condition as observable, and the two coders did not agree on how hard the restriction would be to lift. The record leaves the size of the budget to whoever sets it.

6.4The second record's revisit line

The second record's invalidation line also has two parts:

The phrase offsetting effect is the Korean "상쇄 효과". It is the same idea Knight calls the cancelling of gains and losses across pooled cases. The record's condition for recognising diversification is that the offsetting hold in two kinds of period: in independent periods, and under stress. The first is Knight's ordinary pooling. The second is the test his fire sentence implies but does not state: offsetting that holds only when nothing is burning is not offsetting the pool can rely on.

The next check divides the past into two classes. One correlation table is drawn from normal periods; another from periods of concentrated losses. This is a reclassification, and it is the most Knightian move in either record. Knight's chapter describes insurers responding to imperfect classes in two ways, by dividing them more finely and by adjusting rates within them by judgment. The second record divides finely: not by strategy, which is how its question first framed the pool, but by period, which is how the dependence actually shows itself.

This move sits closer to the second account of the tail than the first. It assumes that the stress-period dependence can be measured from past stress periods, which is to say that stress recurs often enough to form a class. If the tail lies outside any prior class, as the first account holds, then the stress-period table will describe the last crisis and not the next. If the tail is made by the pool's own coupling, as the second account holds, then the stress-period table may capture the coupling, provided the coupling persists. The record proposes the table without saying which of these it expects.

Knight's closing limit applies to the table as much as to the worst historical loss. The stress-period correlation is drawn under certain conditions. If the portfolio's strategies change, or if other firms adopt similar strategies, the conditions change, and so may the correlation. Set beside Daníelsson's note, that the use of risk models changes the market and makes risk endogenous, Knight's remark looks like a narrower relative. Knight states his point for one entrepreneur's estimates; the note speaks of a market of firms using the same models. The kinship is drawn here; neither text claims it.

6.5Two records, one gesture

The two revisit lines make the same gesture from different sides. The first removes a ceiling drawn from the past. The second divides a table drawn from the past. Both treat the past as a source of classes that may be wrong for the decision at hand, and both respond by changing how the past is used rather than abandoning it.

Neither record claims that the change will capture the tail. The first says limited application is considered if conditions are met. The second says diversification is recognised if offsetting holds under stress. Both are conditional, and both leave the conditions to be checked by someone the record does not name. The ledger's coders found no decider stated in either record. Both read the decider in the first as a team or organisation, from the setting; in the second they agreed on the same reading. Neither record has a deadline.

Clarke (1999) and Power (2004) mark a risk in this kind of gesture. A plan written to show that the risk is under control can persuade its authors as well as others, and defensive documentation can take the place of judgment. A separated correlation table and a pre-set budget are both documents. Whether they would serve as instruments of judgment or as certificates that judgment was exercised is not something the records can show, since the records end at the moment of decision.

6.6What the case adds

To the first account of the tail, this case brings two records that accept its premise in part and resist its conclusion. Both records refuse to let the past close the class: one removes the worst historical loss as a ceiling, the other separates calm from stress. In that respect they agree with Taleb (2007) and Kay and King (2020) that a class drawn from past cases can mislead at the tail. But neither gives up on measurement. Both propose a new way of cutting the past, and the second proposes one that makes sense chiefly on the second account, where stress-period dependence recurs often enough to be counted. Knight's closing limit, that pooling holds only so far as contingencies recur and that judging many cases changes the judging, describes the risk both proposals carry. The records name the risk; they do not resolve it.