To lift your returns, swap these risks

Overview

Investors inevitably make mistakes. That’s because investment unavoidably entails risk and uncertainty. (By “risk” I mean known potential outcomes and estimates of their likelihoods; uncertainty, in contrast, entails outcomes that are unknown and whose probabilities therefore can’t be estimated). Successful investment presupposes a realistic conception of risk and its competent management. Like its corporate governance, incentive structure, etc., so too Leithner & Company’s conception and management of risk: they’re certainly distinctive and perhaps unique. This article details them.

It extends and elaborates two key results of Warren Buffett’s 25 biggest mistakes – and 4 lessons they teach (21 November 2024): first, more than two-thirds of his self-acknowledged investment mistakes have been errors of commission, and less than one-third have been errors of omission; second, Buffett’s costliest mistakes have been errors of commission.

• Errors of commission are decisions to invest which produce losses and therefore destroy capital. Because they reduce the wherewithal available for subsequent profitable investments, they’re worse than errors of omission.
• Errors of omission are failures to grasp opportunities for profitable investment, or premature sales of investments; they produce foregone gains.

Over time and as I’ll show, investors can increase their number of bearable (by some empirical or ethical standard) mistakes in order to mitigate intolerable ones.

The objective of investment risk management, as Leithner & Company practices it, is therefore to reduce as much as reasonably possible the ratio of errors of commission to errors of omission.

Our Definition of Investment – and of Risk

Investment is the act of entrepreneurship which combines capital, land and labor; its purpose is the production of capital or consumer goods. A subset of this process provides a definition which suits our purposes: to invest is to exchange one asset – typically cash – for another (such as a stock, bond, title to a block of land, etc.). In any such transaction, the investor incurs inconvenience: the funds expended to purchase the security can’t (until it’s sold) buy consumer goods or services. 

Investment therefore defers current gratification. The opportunity cost of investment is present consumption foregone; its purpose is its prospective reward – greater future consumption. It’s a trade-off: less jam in the present in exchange for the hope of more jam in the future.

The investor foregoes some consumption and waits because, she believes, over time her investment will generate benefits which outweighs its present inconvenience. She’s postponed the consumption of a given quantity of jam today so that, she hopes, she or her heirs can consume a greater quantity in the future.

Although they’re often tacit, investors necessarily make certain assumptions about the past, present and the future. Yet they frequently misinterpret the past and misunderstand the present; moreover, tomorrow is uncertain, and next week, month and year ever more so.

As a result, investors’ assumptions virtually never correspond perfectly to reality. Almost invariably – some bonds, such as U.S. Treasury Inflation-Protected Securities (“TIPS”), are partial exceptions – today’s outlay almost certainly won’t generate the exact stream of income and/or growth of capital that the investor expects. In particular, there’s usually a significant chance that an investment’s return will fall well short of expectations; it’s also possible that return of capital as well as return on capital will fail to eventuate.

“Risk” refers to known possible outcomes and estimates of their likelihoods, and it can’t be avoided – or even, at a given point in time, reduced. In particular, the highly likely chance that one’s assumptions are either false or to some extent significantly awry accompanies any investment. Crucially, however, risk can be managed.

Our Conception of Risk Management

“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 …”

So wrote Jerzy Neyman and Egon Pearson in the Philosophical Transactions of the Royal Society (1933). There’s a close parallel between jury trials and Leithner & Company’s conception and practice of risk management share several key attributes:

• Faulty premises, invalid reasoning and unreliable evidence magnify the likelihood of poor decisions.
• Some mistakes are, empirically, ethically and subjectively, more undesirable than others.
• Over time, investors can choose to swap one kind of mistake for another, i.e., to accept the likelihood of a larger number of more tolerable errors in exchange for the probability of a smaller number of more objectionable ones. In this limited but crucial respect, risk can be managed.
• Accordingly, the management of investment risk necessarily entails not just objective consequences but also subjective and ethical considerations.

To grasp these points, let’s start with a simple example: a man undergoes trial by jury. Seldom can absolute certainty be brought to bear in order to decide such matters. Accordingly, members of the jury must evaluate the imperfect and incomplete information that the judge permits the prosecution and defence to present. Influenced by the defence’s and prosecution’s (mis)interpretation of evidence, as well as its own, the jury then deliberates and renders a judgement.

Incomplete, biased and irrelevant information, as well as the possibility that the jury misinterprets whatever valid and reliable information it considers, etc., ensure that some percentage of juries’ verdicts has always been, presently is and will always be mistaken.

Ethically, such miscarriages of justice are deeply regrettable. Realistically, given the fallibility of jurors, lawyers and judges, the incomplete and possibly biased evidence they consider, etc., their total elimination is impossible. A reduction of these miscarriages is, however, feasible. Setting aside the possibility of mistrial, hung jury and the like, the jury must either convict or acquit. Accordingly, one of four possible outcomes occurs (Table 1).

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

Two of these outcomes, ethically speaking, are good: a guilty defendant is convicted and an innocent one is acquitted. The third, the acquittal of a guilty defendant, is bad. And the fourth, the conviction of an innocent one, is (given the presumption of innocence which underlies Anglo-American jurisprudence) even worse.

Two specific risks thus accompany 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).

Consider now a thought experiment that comprises one jury, 100 defendants and a series of 100 trials – each of which tries one defendant. Let’s say that you’re 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 can’t give jury members the benefit of this knowledge. Let’s also say that 50 defendants are guilty and 50 are innocent, that (by coincidence) 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.

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

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

The members of the jury, however, are fallible. For the 100 defendants as a whole, the jury’s 50-50 conviction rate (bottom row) happens by a happy co-incidence to correspond exactly to the true numbers of guilty and innocent defendants (fourth column). With respect to individual defendants, however, either because perfect and complete information isn’t put to them, they misinterpret it or let biases prejudice their judgement, the jurors make mistakes. Given the jury’s accuracy rate (labelled “75% Accurate”), 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 occur: 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 or some other development), one or more of the wrongful convictions in Table 2 comes to light. 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.

Let’s say 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 3.

Table 3: Expected Risks Arising from 100 Jury Trials with a 40-60 Conviction Rate

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.

Yet the jury’s members aren’t omniscient. 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, given an unchanged number of guilty and innocent defendants, thus has two crucial consequences. It causes the sum of the two risks – average total risk – to increase from 25 (12.5 + 12.5 in Table 2) to 30 (10 + 20 in Table 3). It also changes the distribution of the two risks.

The jury tends wrongfully to convict fewer innocent defendants – 10 in Table 3 versus 12.5 in Table 2 – and thereby mitigates Risk #1 (the “worst outcome” identified in Table 1). At the same time, however, it tends wrongfully to acquit more guilty defendants – 20 in Table 3 versus 12.5 in Table 2 – and thus exacerbates Risk #2 (the “bad outcome” in Table 1).

Over the longer term, the only means whereby jurors can reduce the total risk that inheres in their decisions is to increase the average accuracy of their decisions. How can they do that? One or more of two ways: (1) increase the quality and quantity of the information which they access; (2) improve their ability to interpret this information, i.e., reduce the biases which mar their judgement.

Investing: Four Possible Outcomes and Two Inherent Risks

Let’s now apply these results to derive a framework with which to construct and manage an investment portfolio. Suppose that you’re a one-person “jury” and that you must evaluate a security as a potential addition to your portfolio. It either will or won’t generate the stream of earnings that your assumptions and analysis ascribe to it; and it either is or isn’t available at a sensible price. Accordingly, it either does or doesn’t suit your purposes. Clearly, however, evidence from the past and present never shed incontestable light upon the results that a potential investment will achieve in the future. 

Adding to the difficulty is delayed feedback – only in several years’ time will its (un)suitability become apparent. You must therefore use imperfect and incomplete information about the past and present; you must also make assumptions about an imperfectly predictable and perhaps uncertain future. As a result, it’s likely that some and perhaps many of your decisions will prove to be erroneous.

Assume that in five years you’ll know whether this investment opportunity is sound. The trouble is that you must decide today whether to act. Four possible outcomes (Table 4) therefore present themselves.

Table 4: The Investment Process: Four Possible Outcomes and Two Types of Risk

Two are usually regarded as good: a sound investment opportunity is grasped and an unsound one is rejected. The third outcome (a sound opportunity is declined) is bad. And the fourth (an unsound investment is purchased) is even worse.

Table 4 therefore shows that two risks accompany every investment decision. The first is a sin of omission. This is the possibility that a sound opportunity is declined and a gain foregone. The second is a sin of commission, i.e., the possibility that an unsound investment is grasped and a loss eventually incurred (see also Warren Buffett’s 25 biggest mistakes – and 4 lessons they teach, 21 November 2024).

Thought Experiment #1

Consider now a thought experiment that includes you, 100 potential investments, 100 decisions and me. Let’s say that you’re perfectly prescient: your crystal ball can gaze five years into the future and determine with perfect precision which of the opportunities is (for my purposes) sound and unsound. Unfortunately for me, however, you don’t give me the benefit of your knowledge.

Let’s assume that 50 opportunities are sound and 50 are unsound, that my “accuracy rate” is 50% (i.e., my assumptions and analysis can ascertain the soundness or otherwise of each opportunity with 50% accuracy) and that my “acceptance rate” is also 50% (i.e., given an assessment of a sound opportunity, the likelihood that I act upon it is 50-50).

The results of our investment decisions, if they were repeated over a large number of experiments, would approximate those set out in Table 5. As an omniscient observer, your decisions (the cells labelled “100% Accurate”) would correctly identify each of the 50 sound assets and correctly “purchase” them; similarly, they would correctly identify each of the 50 unsound assets and correctly refrain from “buying” them.

Table 5: Expected Risks Arising from a Series of Investment Decisions with a 50-50 Acceptance Rate and a 50-50 Accuracy Rate

But my decisions, remember, are fallible. At the aggregate level, the true numbers of sound and unsound assets (fourth column) correspond exactly to the total numbers that I actually buy and decline to buy (bottom row). With respect to individual investment decisions, however, I make mistakes. Given that each of my decisions is, on average, 50% accurate (labelled “50% Accurate” in the table), I will tend correctly to purchase 25 of the sound investments but erroneously decline to purchase the other 25. Similarly, on average I‘ll rightly decline to purchase 25 of the 50 unsound investments but mistakenly buy the other 25.

As a result, the two investment risks come to fruition: one-half of the assets (25+25) are either wrongly purchased or wrongly declined. My results under these circumstances are no different from those that would occur if I simply tossed a fair coin.

Thought Experiment #2

Assume that five years later I face another series of 100 investment decisions. Given the results in Table 5, I’m chastened. I can’t be certain which of the 100 new opportunities is sound and which is unsound.

During the past five years, however, I’ve learnt that if I decrease the “acceptance rate” then I can reduce my portfolio’s expected number of loss-making investments.

Let’s say that I lower this rate from 50-50 to 20-80. I’ve also realised that one can cut the total risk in a series of investment decisions by increasing the average accuracy of each decision. I’ve therefore increased the quality and quantity of the information that I use to make decisions; improved my ability to interpret this information; and reduced the psychological and other biases that mar my judgement.

Table 6: Expected Risks Arising from a Series of Investment Decisions with a 20-80 “Acceptance Rate” and 75% “Accuracy Rate”

Let’s suppose that these improvements have increased my average accuracy from 50% to 75%. Otherwise all else remains equal: you’re omniscient and 50 of the 100 investment opportunities are sound. The results of our decisions, if taken under these assumptions over a large number of sequences of 100 trials, would approximate those in Table 6.

As an omniscient observer, you continue to identify each of the 50 sound investment opportunities and to act upon them; similarly, you continue to identify each of the 50 unsound investments and to avoid them. Again, however, I’m not omniscient. Note that at the aggregate level my 20-80 acceptance rate (bottom row) no longer corresponds to the true numbers of sound and unsound investments (fourth column).

Further, I continue to make mistakes. Given my more stringent acceptance rate, I act upon just 20 opportunities; and given my 75% accuracy rate, 15 of these 20 are assessed correctly. I thereby invest correctly in 15 of the 50 sound investments – and mistakenly forego 35 others. On the other hand, I correctly avoid 45 of the 50 unsound opportunities and mistakenly accept the other five.

Assuming a much lower “acceptance rate” and a higher “accuracy rate,” in other words, I’ll tend to accept far fewer unsound investment opportunities and thereby commit far fewer “sins of commission” (5 in Table 6 versus 25 in Table 5). I’ll also tend to forego more sound opportunities (35 in Table 6 versus 25 in Table 5) and thus commit more “sins of omission.”

The distribution of the two competing investment risks thus changes substantially: there is a decrease in the occurrence of real financial losses and an increase in the forfeiture of hypothetical financial benefits. In consequence, the ratio of “sound” to “unsound” investments increases from 1-to-1 (i.e. 25:25) in Table 5 to 3-to-1 (i.e., 15:5) in Table 6.

At the same time, given better standards of analysis and more stringent criteria of decision-making, total investment risk – that is to say, my total number of erroneous investment decisions (25+25 in Table 5, 5+35 in Table 6) – FALLS from 50 to 40.

As with jury decisions, so too with the management of investment risk: the major difference between Tables 5 and 6 is a subjective “trade-off” of risks that has occurred whereby fewer dud investments are purchased but more sound ones are foregone. Leithner & Company exchanges one risk which we regard as intolerable for another we regard as undesirable but nonetheless bearable.

Here, then, are two key characteristics of our conception and management of risk: 

1. The acceptance rate denotes the extent to which we prioritise our options and act only upon those which appear to have the best odds of achieving their intended long-run consequences.
2. The accuracy rate of successful decisions quantifies the extent to which we can ascertain whether a particular security’s price is significantly lower than a conservative, subjective but justifiable estimate of its value.

 Leithner & Company use logic and evidence to identify discrepancies between prices and our estimates of values. We act only upon the widest incongruities, which thereby increases our decisions’ overall accuracy rate. Concentrating our portfolios upon the widest discrepancies – where the odds of loss are apparently low, and thus the likelihood of gain seemingly stacked in our favour – crimps our acceptance rate. Our assumptions, analyses and behaviour thus tend to create what Benjamin Graham has called a “margin of safety.”

“Thus,” wrote Graham in The Intelligent Investor: A Book of Practical Counsel, “in sum we say that to have a true investment there must be present a true margin of safety. And a true margin of safety is one that can be demonstrated by figures, by persuasive reasoning, and by reference to a body of actual experience.”

Conclusions and Implications

If you’re an experienced investor, it’s inevitable and unavoidable: you’ve already made, are making and will continue to make errors. Leithner & Company certainly has, and even Warren Buffett has erred repeatedly (see Warren Buffett’s 25 biggest mistakes – and 4 lessons they teach, 21 November 2024). We don’t agonise over ours (“Why on earth did we do X? Why didn’t we do Y?”). We do, however, investigate and try to learn from them; even more importantly, we choose which kind we endeavour to avoid – and, as a result, which type we’re prepared to tolerate.

It's counter-intuitive: investors must accept more errors of commission in order to commit fewer errors of commission. Yet the two actions which underpin this trade-off – attaining a high accuracy rate and maintaining a low acceptance rate – reflect Benjamin Graham’s commonsensical emphasis upon margin of safety.

“What” wrote Graham in The Intelligent Investor (4^th rev. ed., 2008, p. 8), “will we aim to accomplish in this book? Our main objective will be to guide the reader against the (risk of) substantial error ...” In his “Note About Benjamin Graham” (p. xii), Jason Zweig averred: “only by insisting on ... the ‘margin of safety’ ... can you minimize your odds of error.”

In his Commentary on Chap. 20 (p. 530), Zweig elaborated: “as Graham has reminded you in every chapter of this book, the intelligent investor must focus not just on getting the analysis right. You must also ensure against loss if your analysis turns out to be wrong – as even the best analyses will be at least some of the time ... However, you do have (some) control over the consequences of being wrong.”

This article has derived, detailed and justified this insight. Leithner & Company constantly seeks to increase the quality and quantity of the evidence which underpins our analyses. We also continually strive to improve our ability to interpret information – and particularly to detect and reject invalid data and unreliable assertions. We conduct our own analyses of primary data (i.e., raw statistics from the ABS and RBA and elsewhere, corporate financial statements, etc.), and either heavily discount or (usually) completely ignore secondary information (which has been mediated by brokers, advisors, “analysts” and journalists).

By these and other means, over the years we’ve increased the accuracy rate of our investment decisions; that is, the extent to which we’ve been able consistently to ascertain whether a security’s price is significantly lower than a cautious estimate of its value. Particularly when the crowd is exuberant, we’ve also slashed our acceptance rate: we act only upon those opportunities whose disparities between price and our estimates of value are widest.

By committing ever fewer loss-making big errors, we’ve necessarily allowed more gain-foregoing small ones. We’ve benefitted from the exchange. The effects of errors of commission are long-lasting, whereas those of errors of omission are ephemeral: if you overlook or decline a sound opportunity today, no problem; it’s likely that before long another will appear.

Consequently, we gladly swap risks: we allow a greater number of errors of omission in order to abate the risk that we commit errors of commission. We’ve increased one type of risk whose consequence we regard as a less severe in order to mitigate another which we regard as more damaging.

In conclusion, over the decades we’ve become better at choosing our mistakes: our trade-off of risks has produced a distribution of resultant errors which has greatly mitigated our permanent losses and thereby enhanced our long-term returns.

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