Definition of Risk from "Risk Less and Prosper"

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bobcat2
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Definition of Risk from "Risk Less and Prosper"

Post by bobcat2 » Fri Dec 30, 2011 10:07 pm

I see a new thread has started with confusing, inconsistent, and convoluted definitions of risk and uncertainty. http://www.bogleheads.org/forum/viewtop ... 10&t=87759

For example, some Bogleheads continue to espouse the distinction between risk and uncertainty that economist Frank Knight developed over 90 years ago. Knight’s definition of risk vs. uncertainty had been discarded by most of the economics profession by the 1940s, but apparently his definition still holds sway over many investment enthusiasts even today, over six decades after economists had rejected it.

In his new book on personal finance, Risk Less and Prosper, Zvi Bodie clearly and concisely states the standard economics definition of risk.
Defining Risk

To start, we need to define what we mean by risk. To build your own insight, ask yourself what risk means to you, based on your own exposures to risks – financial or otherwise. A few proposed definitions of risk that commonly surface include: the unknown; the chance that something harmful may happen; uncertain outcomes that may cause loss; and uncertainty that arouses fear.

Let’s discard the idea that risk is nothing but the unknown, because risk is more than the ordinary uncertainty that surrounds our lives. By referring to harm, loss, and fear, the next three suggestions reflect one fundamental property of risk: Somebody has to care about the consequences if uncertainty is to be understood as risk.

The notion of “caring” or “mattering” is central. It captures both the potential (objective) impact of uncertainty as well as its (subjective) bite. This brings us close to the definition we will adopt. Investment risk is uncertainty that matters. There are two prongs to this definition – the uncertainty, and what matters about it – and both are significant. So beyond the odds of hitting a rough patch, there are the consequences of loss to consider.
Page 50.

Notice that the above simple standard definition of risk in economics encapsulates the two aspects of risk, often called the components of risk, that VictoriaF discusses in the other thread.
This definition easily maps into a common financial risk formula:
Risk = Consequences x Probability of occurrence.

In the NIST formulation, consequences are referred to as "(iii) impact (i.e., harm)" and probabilities are referred to as "likelihood that harm will occur." The likelihood of harm occurring is related to the probabilities of "(i) threats" and "(ii) vulnerabilities." Note the use of the words "harm," "threats," and "vulnerabilities."
Consequences - how much the risk "matters"
Probability of occurrence - the degree of uncertainty the risk entails



Why risk, which is such an important and basic element of finance, continues to be so confusing to many people knowledgeable in general about finance and investments is puzzling. But how can we hope to effectively manage risk if we don't know what it is?

I also find it odd that people continue to confuse a method of measuring investment risk, standard deviation, with the definition of investment risk. It seems obvious to me anyway that a method of measuring a phenomenon is not the same thing as the definition of the phenomenon.

BobK
In finance risk is defined as uncertainty that is consequential (nontrivial). | The two main methods of dealing with financial risk are the matching of assets to goals & diversifying.

peter71
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Re: Definition of Risk from "Risk Less and Prosper"

Post by peter71 » Fri Dec 30, 2011 10:35 pm

Hi Bob,

Why not take your crusade against Knightian uncertainty to the Wikipedia page devoted to it, complete with cites to all the major economists who discredited the definition beginning in the 40's?

http://en.wikipedia.org/wiki/Knightian_uncertainty

I only skimmed the rest of your post, but per your last question see here (for starters) re the distinction between a "theoretical definition" and an "operational definition".

http://en.wikipedia.org/wiki/Operational_definition

I can also re-link to the top 5 selling econ textbooks and their diverse definitions of risk if you like . . .

Best,
Pete

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Dick Purcell
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Re: Definition of Risk from "Risk Less and Prosper"

Post by Dick Purcell » Fri Dec 30, 2011 11:04 pm

BobK –

WondeRful stuff!

In that other thread, Bob90245 requested your participation. (I think he was hoping for a Fourth-of-July fireworks exhibition for New Year’s.) And VictoriaF echoed his invitation.

But why did you have to undermine your marvelous essay with that short absurd last paragraph?

Standard deviation does not measure risk, and therefore is not a measure of risk. It does not address the first of the two requirements in your definition of risk, the consequence of an event. And it does not even measure the second requirement, probability, either, because it does not define what it deviates from.

Of course, the issue in the other thread to which you refer is the mislabeling of standard deviation as “risk” and the effects of doing so in serving the interests of the financial industry and the high priests of investment “education” to the detriment of the mission of Bogle and the interests of the investing public.

Misuse of the label “risk” certainly enables the other Bodie to add emotional grab to an assortment of Greeky symbols in his BKM textbook. Have the Two Bodies ever met to settle the contradiction between the Bodian definition of risk you present above and the “risk” in the BKM textbook?

Otherwise, great stuff. Huzzah!

Dick Purcell
Last edited by Dick Purcell on Sat Dec 31, 2011 1:18 am, edited 2 times in total.

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bobcat2
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Frank Knight

Post by bobcat2 » Fri Dec 30, 2011 11:12 pm

It's not my crusade, it's simply a fact of life. Whether investment enthusiasts know this or not, or like it or not, the economics profession rejected Knightian risk and Knightian uncertainty a very long time ago. This is yet another situation where a huge gap has developed between economists and investment professionals and investment enthusiasts.

By the 1940s Knight's approach to risk had been replaced by the expected utility approach to risk pioneered by von Neumann and Morganstern. The modern definition of risk in economics follows from the risk foundation developed by von Neumann and Morganstern, not from the much earlier work by Knight.

Knight did make a lasting contribution to economics in this vein however. Knight was the first to truly stress that many economic decisions are made when we are not certain of the outcomes. Before that nearly all of economics was concerned with situations where the outcome was known with certainty.

We can see how Knight unintentionally has affected modern finance by how Robert Merton defines finance.
- Finance is the study of how to allocate scarce resources over time under conditions of uncertainty.

Now Merton is using the modern definition of uncertainty in his definition of finance, but certainly the definition stresses that finance is not about deterministic outcomes.

I say that Knight unintentionally had a huge impact on finance because Knight's work on risk and uncertainty was concerned by decisions made by government officials and business managers and the effects of those decisions on the overall economy. None of Knight's work on risk and uncertainty dealt with financial assets.

BobK
In finance risk is defined as uncertainty that is consequential (nontrivial). | The two main methods of dealing with financial risk are the matching of assets to goals & diversifying.

peter71
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Re: Definition of Risk from "Risk Less and Prosper"

Post by peter71 » Fri Dec 30, 2011 11:43 pm

Bob,

As you may know there's no shortage of dogmatic charlatans asserting that it's just "a fact of life" that experimental economics/neuroeconomics has struck a death blow to expected utility theory . . . not so much people at the center of the field, to be sure, but people on the periphery in various ways (including people in my own field of political science).

Happily, it's getting harder and harder to get published merely for confidently spouting dogma across the social sciences: not coincidentally, semantic debates which might once have been found in peer-reviewed journals are now relegated to forums like this one, while academics (and particularly younger academics) focus on operationalizing concepts in multiple ways so as to better understand our (complicated!) social world.

Best,
Pete

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Re: Definition of Risk from "Risk Less and Prosper"

Post by beardsworth » Fri Dec 30, 2011 11:51 pm

Never heard of this man Frank Knight, or the adjective "Knightian" until the past 24 hours, as this thread comes along just after I started reading The Only Guide You'll Ever Need for the Right Financial Plan (2010), by Larry Swedroe, who is certainly an "investment professional" rather than an economist per se. Its opening paragraphs include this:

"Investing deals with both risk and uncertainty. In 1921, University of Chicago professor Frank Knight wrote . . . the classic book Risk, Uncertainty, and Profit. An article from the Library of Economics and Liberty described Knight's definitions of risk and uncertain as follows: 'Risk is present when future events occur with measurable probability. Uncertainty is present when the likelihood of future events is indefinite or incalculable.' . . . During crises, the perception about equity investing shifts from one of risk to one of uncertainty. We often hear commentators use expressions like, 'There is a lack of clarity or visibility.' Since investors prefer risky bets (where they can calculate the odds) to uncertain bets (where the odds cannot be calculated), when investors see markets as uncertain, the risk premium demanded rises. That causes severe bear markets. . . . Investors have demonstrated the unfortunate tendency to sell well after market declines have already occurred and to buy well after rallies have long begun. The result is they dramatically underperform the very mutual funds in which they invest. That is why it is so important to understand that investing is always about uncertainty and about never choosing an allocation exceeding your risk tolerance."

But this thread seems to argue that the distinction between "risk" and "uncertainty" is old thinking. So I'm confused. It's not the first time and won't be the last. :)

Marc

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Dick Purcell
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Re: Definition of Risk from "Risk Less and Prosper"

Post by Dick Purcell » Sat Dec 31, 2011 12:22 am

BobK –

The Knightian view of risk v. uncertainty certainly should be rejected based on unacceptable misuse of the word risk. It’s a distinction between more and less “knowable” uncertainties, not risk.

But while grievously mislabeled, Knight’s distinction is important — terribly important. And in most investment-probabilities stuff, overlooked. That was Larry’s point in his launching that other thread, and I continue to regret obscuring it in my diversion of most of that thread’s discussion to the equally important point of misuse of the word risk.

But –- on your claim that the Knightian view has been rejected by economists since the 1940s, you better tell your friend Merton and the others at MIT. In the paper “Physics envy may be hazardous to your wealth” by MIT’s Professor Andrew Lo and Mark Mueller, published just last year, the introduction says this:
Motivated by Knight’s (1921) distinction between “risk” (randomness that can be fully captured by probability and statistics) and “uncertainty” (all other types of randomness), we propose a slightly finer taxonomy—fully reducible, partially reducible, and irreducible uncertainty—that can explain some of the key differences between finance and physics. Fully reducible uncertainty is the kind of randomness that can be reduced to pure risk given sufficient data, computing power, and other resources. Partially reducible uncertainty contains a component that can never be quantified, and irreducible uncertainty is the Knightian limit of unparametrizable randomness. While these definitions may seem like minor extensions of Knight’s clear-cut dichotomy, they underscore the fact that there is a continuum of randomness in between risk and uncertainty, and this nether region is the domain of economics 1and business practice. In fact, our taxonomy is reflected in the totality of human intellectual pursuits, which can be classified along a continuous spectrum according to the type of uncertainty involved, with religion at one extreme (irreducible uncertainty), economics and psychology in the middle (partially reducible uncertainty) and mathematics and physics at the other extreme (certainty).
All of the following, notably including your friend Merton, are thanked for review and comments on the paper:
We thank Jerry Chafkin, Peter Diamond, Arnout Eikeboom, Doyne Farmer, Gifford Fong, Jacob Goldfield, Tom Imbo, Jakub Jurek, Amir Khandani, Bob Lockner, Paul Mende, Robert Merton, Jun Pan, Roger Stein, Tina Vandersteel for helpful comments and discussion.
Please tell Merton and those other MIT types they are 60 or 70 years behind in the field of economics. Or at least, put an end to their dreadful Knightian misuse of the word risk.

Dick Purcell

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bobcat2
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Re: Definition of Risk from "Risk Less and Prosper"

Post by bobcat2 » Sat Dec 31, 2011 10:20 am

There is nothing inconsistent between the standard definition of risk and the paper by Lo et al. Lo is simply saying that some risky situations are more uncertain than others and we always need to be very cognizant of that fact. Lo is not saying that some uncertain situations should be called risk and other situations uncertainty. All the uncertain situations are risky, but some are riskier are others. I don't see anything new in the view that some risky situations are more risky than other risky situations. What is new is that Lo wants to establish a finer taxonomy among the different levels of risk (uncertainty).

According to Lo, Knight's definition of risk is trivial when it comes to economics and so when we come to assessing risk in economics we have only what Knight described as uncertainty, but Lo feels that Knight's uncertainty needs to be further refined. I think nearly all economists would agree with Lo that if we take Knightian risk seriously, that is, that risk is only situations where the odds are well known, then we are basically left with games of chance such as tossing coins and rolling dice. This would leave nearly everything we are seriously concerned about in economics in the realm of Knightian uncertainty. So Knight's dichotomy between risk and uncertainty for economic phenomena is uninteresting given that Knightian risk in economics is for all practical purposes the null set.

Here is how Lo puts it in his paper.
Level 2

This level of randomness is Knight’s (1921) definition of risk: randomness governed by a known probability distribution for a completely known set of outcomes. At this level, probability theory is a useful analytical framework for risk analysis. Indeed, the modern axiomatic foundations of probability theory—due to Kolmogorov, Wiener, and others—is given precisely in these terms, with a specified sample space and a specified probability measure. No statistical inference is needed, because we know the relevant probability distributions exactly, and while we do not know the outcome of any given wager, we know all the rules and the odds, and no other information relevant to the outcome is hidden. This is life in a hypothetical honest casino, where the rules are transparent and always followed. This situation bears little resemblance to financial markets.


BobK
In finance risk is defined as uncertainty that is consequential (nontrivial). | The two main methods of dealing with financial risk are the matching of assets to goals & diversifying.

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