VALUE INVESTING, RISK AND
RISK MANAGEMENT

Part II

1 October 2000

...continued from Part I

Is it more serious to convict an innocent man or to acquit a guilty one? That will depend on the consequences of the error. Is the punishment death or fine? What is the danger to the community of released prisoners? What are the current ethical views on punishment? From the point of view of mathematical theory, all that we can do is to show how the risk of the errors can be controlled....

J. Neyman and E. Pearson,
“On the Problem of the Most Efficient Form
of Statistical Hypothesis,”
Philosophical Transactions of the Royal Society, 1933

Conclusion #1: The Generally-Futile Hunt for ‘Minimum Overall Risk’

Consider a familiar event: a man is accused of a serious criminal offence and undergoes trial by jury. Clearly, the accused is either guilty or innocent. Seldom, however, can complete and incontrovertible evidence be brought to bear in order to decide a criminal matter. Accordingly, members of the jury must evaluate imperfect and incomplete information which has been put to them indirectly (i.e., by the prosecution and defence). Influenced by such evidence, they must then deliberate and render a judgement about the defendant’s guilt or innocence. Innate uncertainty, combined with incomplete and imperfect information and the possibility that this information is presented and interpreted erroneously, thereby ensures – despite their best intentions – that some percentage of juries' verdicts are mistaken.

Setting aside mistrials, hung juries and the like, in any given trial the jury must either convict or acquit. Four possible outcomes, set out in Table 1, therefore present themselves. Two are usually regarded as ‘good’: that in which a guilty defendant is convicted and that in which an innocent defendant is acquitted. The third, in which a guilty party is acquitted, is usually regarded as ‘bad.’ And the fourth, in which an innocent one is convicted, is (given the presumption of innocence which underlies the Anglo-Saxon trial by jury), regarded as even worse. Two risks thus inhere in any jury’s verdict. The first is the possibility that it acquits a guilty defendant (thereby leaving a crime unpunished and its perpetrator free to commit further offences). The second is the possibility that it convicts an innocent defendant (thereby depriving the defendant unjustly of his liberty and leaving the culprit at large to commit further offences).

Table 1: The Jury Process:
Four Possible Outcomes and Two Inherent Risks

Consider now an ‘experiment’ which consists of one jury, 100 defendants and a series of trials which, one by one, tries the defendants. Let us say that you are perfectly omniscient, are not a member of the jury and have no contact with its members. You know which of the 100 defendants is guilty and which is innocent, but you cannot give jury members the benefit of this knowledge. Let us also say that 50 defendants are guilty and 50 are innocent, that the jury’s conviction rate across the 100 trials is 50% and that it is able to ascertain the guilt or innocence of any particular defendant with 75% accuracy.

The results of your and the jurors’ decisions, if they were repeated over a large number of ‘experiments’ of 100 jury trials, would approximate those set out in Table 2a. As an omniscient observer, your decisions (the cells of the table labelled “100% Accurate”) would correctly identify each of the 50 guilty defendants and correctly ‘convict’ them; similarly, you would correctly identify each of the 50 innocent defendants and correctly ‘acquit’ them.

Table 2a: Expected Risks Arising from 100 Jury Trials
With a 50-50 Conviction Rate

The members of the jury, however, are fallible. For the 100 defendants as a whole, the jury’s 50-50 conviction rate (bottom row) corresponds exactly to the true numbers of guilty and innocent defendants (fourth column). With respect to individual defendants, however, either because perfect and complete information is not put to them, they misinterpret it or they let biases prejudice their judgement (or some combination of these and other factors), the jurors make mistakes. Given the jury’s accuracy rate (labelled “75% Accurate” in the table), on average it will correctly convict 37.5 of the 50 guilty defendants but erroneously acquit the other 12.5. Similarly, on average it will accurately acquit 37.5 of the 50 innocent defendants but mistakenly convict the other 12.5. As a result, the two risks identified in Table 1 come to fruition: one-quarter of the defendants (12.5+12.5) are either wrongly convicted or wrongly acquitted.

Assume now that another series of 100 jury trials, using the same jury, takes place. Before the first trial begins, however (perhaps on the basis of new evidence, a confession or some other development), one or more of the wrongful convictions in Table 2a comes to light and is overturned. The jury, being human, is chastened. It cannot know with absolute certainty which of the 100 new defendants is guilty and which is innocent. But in order to lessen the likelihood that it wrongfully convicts an innocent man, it decides to raise the bar against wrongful conviction by reducing its willingness to convict. Assume that it lowers its overall conviction from 50-50 to 40-60. All else, however, remains equal: you are omniscient, 50 of the defendants are guilty and the jury’s accuracy rate remains at 75%.

The results of your and their decisions, if taken under these assumptions over a large number of sequences of 100 trials, would approximate those set out in Table 2b. As an omniscient observer, your decisions continue to identify correctly each of the 50 guilty defendants and correctly to ‘convict’ them; similarly, you continue to identify correctly each of the 50 innocent defendants and correctly to ‘acquit’ them.

Table 2b: Expected Risks Arising from 100 Jury Trials

Again, however, the members of the jury are not omniscient. Note that at the aggregate level their 40-60 conviction rate (bottom row) no longer corresponds to the true numbers of guilty and innocent defendants (fourth column). With respect to the individual defendants, then, for this and the aforementioned reasons the jurors will continue to make mistakes. Given their 40-60 conviction rate they convict 40 defendants; and given their 75% accuracy rate 30 of these 40 are accurately identified as guilty. They thereby correctly convict 30 of the 50 guilty defendants – and erroneously acquit 20 others. Analogously, they correctly acquit 40 of the 50 innocent defendants but mistakenly acquit 10 guilty ones.

The lower conviction rate, in light of an unchanged number of guilty and innocent defendants, thus has two consequences. First, it causes the sum of the two risks – i.e., average total risk – to increase from 25 (12.5+12.5 in Table 2a) to 30 (10+20 in Table 2b). It also causes the distribution among the two risks to change. The jury tends wrongfully to convict fewer innocent defendants – 10 in Table 2b versus 12.5 in Table 2a – and thereby mitigates the extent of Risk #1 (the ‘worst outcome’ identified in Table 1). At the same time, however, it tends wrongfully to acquit more guilty defendants – 20 in 2b versus 12.5 in 2a – and thereby exacerbates the extent of Risk #2 (the ‘bad outcome’ in Table 1). The jury, in other words, makes a subjective ‘trade-off’ whereby one risk which many people regard as more ethically undesirable is ‘exchanged’ for another which many regard as less undesirable. This exchange, however, comes at the cost of a greater number of mistaken jury verdicts.

The three premises in Part I thus generate a startling conclusion: given the information to hand at a particular point in time, the overall risk which inheres in a series of decisions cannot be minimised or even reduced. In this critical respect, risk cannot be ‘managed.’ Poor choices, however, can increase total risk and thereby magnify the likelihood of loss. With the information at one’s disposal, the best that one can do is to ‘exchange’ a specific risk which is regarded as very salient or most undesirable for another which is regarded as less salient or less undesirable. It is in this limited respect that risk can be ‘managed.’ Not just objective consequences but also subjective and ethical considerations are thus bound inextricably into one’s decisions.

Conclusion #2: Long-Term ‘Risk Management’

A second series of conclusion emerges from the three premises set out in Part I. Over the longer term, the only means whereby jurors – and decision-makers more generally – can reduce the total risk which inheres in their decisions is to increase the average accuracy of their decisions. This, in turn, implies either

1. an increase in the quality and quantity of the information to which they have access,
   
2. an improvement in their ability to interpret this information,
   
3. a reduction in the psychological biases which mar their judgement (see, for example, Massimo Piattelli-Palmarini’s excellent book Inevitable Illusions: How Mistakes of Reason Rule Our Minds)
   
4. or some combination of these factors.

Part III applies this framework and its two sets of conclusions to an investment setting. Straight off the bat, however, some of these results’ implications are rather obvious. It is not surprising, for example, that Graham-and-Dodd value investors tend to be voracious consumers of primary information (i.e. raw statistical data, company financial statements and so on) and either discount or ignore secondary information. Just as jurors could do without lawyers (who act as brokers and possibly unwitting distorters of primary information), value investors seek primary source material and eschew that which has been mediated by brokers, advisors, analysts and journalists (see The Mass Media and Value Investing: Part II). Equally unsurprising is value investors’ familiarity (whether it is innate or learnt) with the principles of behavioural finance – a field which combines insights from economics and psychology in order to illuminate the sources of financial misjudgements and ‘malinvestments.’

...continued in Part III

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