Risk vs uncertainty

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Aptenodytes
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Re: Risk vs uncertainty

Post by Aptenodytes » Thu Dec 29, 2011 4:42 pm

Dick Purcell wrote:It is appalling, downright sickening, to see right here in Bogleheads there are people who persist in the deceptive malpractice of mislabeling return-rate standard deviation as “risk” –- thereby aiding the active-fund enemies of Bogle in keeping over 90% of the people’s fund money in actively managed funds. Your deceptive malpractice scares people into focusing on their short-term fears for the single year, where they cannot see the terrible long-term cost of active funds’ higher fees.

Rodc suggested the right label for standard deviation: “standard deviation.”

Why do you feel a need to change its label to some word that eliminates specification of what it is, in favor of greater deceptive emotional impact. Why??

Dick Purcell
Huh? How does paying attention to standard deviation contribute to a weakness for active management? I cannot imagine any way to implement a Bogle-consistent strategy without paying careful attention to standard deviation.

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bob90245
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Re: Risk vs uncertainty

Post by bob90245 » Thu Dec 29, 2011 4:47 pm

bob90245 wrote:I'll stay out, too.
Hey, congratulations, everyone! We're on the second page!

See you on page three! (As I watch from the sidelines...)
Ignore the market noise. Keep to your rebalancing schedule whether that is semi-annual, annual or trigger bands.

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Re: Risk vs uncertainty

Post by magician » Thu Dec 29, 2011 4:48 pm

Aptenodytes wrote:I cannot imagine any way to implement a Bogle-consistent strategy without paying careful attention to standard deviation.
Yes, but you're a penguin.

;)
Simplify the complicated side; don't complify the simplicated side.

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Aptenodytes
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Re: Risk vs uncertainty

Post by Aptenodytes » Thu Dec 29, 2011 4:50 pm

magician wrote:
Aptenodytes wrote:I cannot imagine any way to implement a Bogle-consistent strategy without paying careful attention to standard deviation.
Yes, but you're a penguin.

;)
busted. maybe I'll use that as my excuse to waddle away from this thread.

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DRiP Guy
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Re: Risk vs uncertainty

Post by DRiP Guy » Thu Dec 29, 2011 4:53 pm

Dick Purcell wrote:It is appalling, downright sickening, to see right here in Bogleheads there are people who persist in the deceptive malpractice

Your deceptive malpractice...

...change its label... in favor of greater deceptive emotional impact.
Dick, I think you've made your personal crusade well known here. I also think no one begrudges you the right to stake out that position, and even to conduct it here publicly. And finally, some here would likely even be willing allies in your efforts.

However, I feel I must step forward and say I lament your injection of morally loaded and emotionally charged attack language in your arguments.

Doing so seems unlikely to convince anyone, and IMHO simply degrades you and your cause, since I think few-to-none of the readers here really believe that we are observing purposeful deception for nefarious means by paid professionals right here in this thread, as you allude to.


So, c'mon, man. You can do better, and we deserve as much.

Thanks.
:sharebeer

peter71
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Re: Risk vs uncertainty

Post by peter71 » Thu Dec 29, 2011 4:58 pm

Dick,

Please take some time to review an introductory textbook on social science research methods. The bottom line is that there's absolutely nothing conspiratorial about the way in which academics have, at times, attempted to represent a complex semantic concept -- "risk" -- with a measurable operational definition -- "return-rate standard deviation." That's what academics do with all concepts -- see, e.g., research on much more complicated concepts like "happiness."

It's perfectly coherent to say either:

a) I think simple operational definition A should be replaced by simple operational definition B

OR

b) I think the entire enterprise of trying to quantitatively analyze the social world should be abandoned

But the idea that there's some master plan among academics and their flunkies to work wonders via a single operational definition is just crazy. If you don't have time to find a textbook, do some googling on "operational definitions," "validity" and "the drunkard's search problem."

Best,
Pete

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Re: Risk vs uncertainty

Post by LadyGeek » Thu Dec 29, 2011 5:04 pm

I would agree with others in the engineering field that risk has a negative intent which utilizes a likelihood x consequence. From the NASA Risk Management Handbook:
NASA wrote:Risk Statement - A concise description of an individual risk that can be understood and acted upon. Risk statements have the following structure: “Given that [CONDITION], there is a possibility of [DEPARTURE] adversely impacting [ASSET], which can result in [CONSEQUENCE].”
Website: NASA Risk Management Page

In my field, opportunities are those which have a positive impact. You take a risk if something is going to break function, cost, or schedule. An opportunity will improve functionality, save cost, or shorten the schedule.

I apply an engineering interpretation of risk to investing, unless it's highlighted otherwise. Variation in investment performance is volatility, with the impact to my portfolio as the consequence (thanks to bobcat2's tutorials). There is no conflict from my perspective.
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Re: Risk vs uncertainty

Post by VictoriaF » Thu Dec 29, 2011 5:34 pm

magician wrote:In my work in project risk management I frequently find that managers have a hard time identifying true opportunities: most often, they see a potentially negative event, and then identify the response to that event as an opportunity. ("If steel prices rise we could end up overrunning our budget, but we have the opportunity of avoiding those price increases by entering into futures / forward contracts." No, the risk is the threat of higher prices. The strategy to handle that risk is to transfer it to someone else by using financial derivatives. There is no opportunity.)
Some project managers may use bad terminology or not have an organized mind. The same is true for some Bogleheads ;-).

In the IT Risk Management process, after Risk Assessment is finished the next activity is Risk Mitigation. Mitigation approaches include risk reduction (e.g., by implementing countermeasures), risk transfer (usually, this refers to buying insurance), risk avoidance (not doing a risky thing), and risk acceptance (for example, if countermeasures are more expensive than the risk).

Nobody calls Risk Mitigation an opportunity. Risk is bad. It has to be dealt with. Risk mitigation deals with that "bad."

Victoria
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Re: Risk vs uncertainty

Post by happytrades » Thu Dec 29, 2011 6:21 pm

Insurance, risk & rates

Following up on the OP, an insurance man once told me there is no such thing as a bad risk, only a bad rate.

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Re: Risk vs uncertainty

Post by magician » Thu Dec 29, 2011 7:13 pm

VictoriaF wrote:
magician wrote:In my work in project risk management I frequently find that managers have a hard time identifying true opportunities: most often, they see a potentially negative event, and then identify the response to that event as an opportunity. ("If steel prices rise we could end up overrunning our budget, but we have the opportunity of avoiding those price increases by entering into futures / forward contracts." No, the risk is the threat of higher prices. The strategy to handle that risk is to transfer it to someone else by using financial derivatives. There is no opportunity.)
Some project managers may use bad terminology or not have an organized mind. The same is true for some Bogleheads ;-).
Some risk managers as well.
VictoriaF wrote:In the IT Risk Management process, after Risk Assessment is finished the next activity is Risk Mitigation. Mitigation approaches include risk reduction (e.g., by implementing countermeasures), risk transfer (usually, this refers to buying insurance), risk avoidance (not doing a risky thing), and risk acceptance (for example, if countermeasures are more expensive than the risk).

Nobody calls Risk Mitigation an opportunity. Risk is bad. It has to be dealt with. Risk mitigation deals with that "bad."
The PMBOK refers to that next step as Risk Handling; mitigation (reducing the probability or reducing the impact) is one approach to handling a threat, others being avoidance (changing the project so that the risky event cannot occur), transfer (giving the risk to a third party), sharing (developing a partnership that is better equipped to handle the risk), and acceptance (doing nothing unless and until the risk event occurs; this can be active (developing a contingency plan) or passive (winging it)).

I dislike the practice of referring to every risk-handling strategy as mitigation (I work with a subcontractor who does this); I prefer the narrower definition of mitigation (as above).
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Re: Risk vs uncertainty

Post by wifeofmarius » Thu Dec 29, 2011 7:39 pm

I am a long time lurker here so please be patient with my ignorance. My husband and I are in our mid 30's, he a full time IT specialist, and me, a stay at home Mom with too much time on her hands.

I am confused on how to measure standard deviation in our portfolio. Are we taking too much risk at this point in our lives?

Bewildered in Boston

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Dick Purcell
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Re: Risk vs uncertainty

Post by Dick Purcell » Thu Dec 29, 2011 7:40 pm

DRiPGuy and Peter71 –

Thanks for your responses.

I don’t think I said purposeful or conspiratorial deception or nefarious purposes or master plan for that. I did not intend to. And if I did (or even if I didn’t), I withdraw and renounce that implication.

But I durn well mean irresponsible.

And without evil intention, with mere irresponsibility, the effect is just as bad.

Dick Purcell

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Re: Risk vs uncertainty

Post by nisiprius » Thu Dec 29, 2011 8:40 pm

Well, Dick, what name do you suggest for "bidirectional fluctuation which is statistically somewhat lawful, somewhat bounded in a soft-edged way, and appropriately measured by the standard deviation?"

I don't like risk any more than you do. I don't think I like volatility. Fluctuation wouldn't be too bad except for one big problem: it doesn't have an adjectival form. An investment can be risky, it can be volatile, but... fluctuation-y? Flucty? Fluxable? Fluid?

How about turbulence? Stocks are turbulent, even over long holding periods. Nah, it's missing comparative forms, isn't it. Stocks are riskier than bonds, stocks are turbulentier then bonds? Nope.
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Re: Risk vs uncertainty

Post by peter71 » Thu Dec 29, 2011 8:59 pm

Hi Dick,

I don't think there's any shortage of academics selling their services and models to un-Bogle-esque financial enterprises, but I suspect they're mostly selling the sort of stuff you read about at Wilmott.com rather than MVO stuff.

In any case, there's a lot of economic problems in the world, and many that are getting worse, but I take heart in the fact that the "fleecing" of retail investors (as measured by fund fees and advising fees) seems to be a problem that's gotten less bad over the past 50 years. I suspect Markowitz, Sharpe etc. would argue that their simplistic risk = SD models actually deserve CREDIT for some of those fee reductions (given that their implication that people should diversify maximally undermined the case for broker/stockpickers) but even if you don't want to go that far I think it's tough to argue the rise of risk = annual SD models has been correlated with an increase in fees paid by investors.

Best,
Pete

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Re: Risk vs uncertainty

Post by LadyGeek » Thu Dec 29, 2011 9:54 pm

wifeofmarius wrote:I am a long time lurker here so please be patient with my ignorance. My husband and I are in our mid 30's, he a full time IT specialist, and me, a stay at home Mom with too much time on her hands.

I am confused on how to measure standard deviation in our portfolio. Are we taking too much risk at this point in our lives?

Bewildered in Boston
Welcome! This thread is not quite the right place to answer your question. Take a look at my post in this thread: Portfolio advice and analysis - it will explain the basics. Read the rest of that thread and prepare your portfolio in the format suggested. Then, start a new thread in the Investing - Help with Personal Investments forum and ask away. You'll get answers focused on exactly what you need.

To answer your immediate question - the definition of risk you are thinking of is related to the ratio of stocks/bonds a.k.a. asset allocation. You'll find that info in the post I mentioned.
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Re: Risk vs uncertainty

Post by Dick Purcell » Thu Dec 29, 2011 10:09 pm

Nisi –

I appreciate the question, and your sound-testing of options.

My first choice, by far, is Rodc’s proposal: call standard deviation “standard deviation.”That name is precisely correct, with no implications of meaning more than it means. I don’t think it should be the basis for investment selections –- instead, that it is an ingredient for assessing dollar-result probabilities as a valid basis for investment selection. The name standard deviation (for standard deviation) tends to put it in its appropriate place as a technical calculation component rather than decision basis.

If we need to call it something other than what it is (standard deviation), I like uncertainty. That’s a valid non-technical name of what it represents.

I agre with you that volatility is not great. It tends to imply short-term ups and downs as if they have no long-term implications, which is not right. For a given return-rate standard deviation, longer holding period means more uncertainty for the result, and volatility doesn’t capture that. My reactions to fluctuation and turbulence are similar.

Pete –

I’d like to disagree, in my usual diplomatic way.

Markowitz did indeed give great boost to three great ideas – diversification as you say, plus looking at investments’ prospects in terms of probabilities, plus understanding of the investment range of conservative-to-aggressive with higher means accompanied with more uncertainty.

But -- after receiving his Nobel, he exploited it in many years of on-the-Web endorsement to win acceptance for the original PC software product for applying his theory for spook and fleece, AllocationMaster. That product misleads the advisor and investor to (1) choose an asset-class allocation based on short-term fear of single-year standard deviation (aka “risk”), without comparing the options for the investor’s future; then (2) switch from the ill-chosen asset classes to any of thousands of actively managed funds or other gambles within the ill-chosen asset classes (de-diversifying).

And then it delivers a down-to-the-dollar projection of the investor’s future investment results through n years as if there were no uncertainty at all. I guess they would call that unexpected future “expected.”

That AllocationMaster product is still being sold to over 20,000 advisors advising millions, according to its purveyor. Fiduciary360 is teaching “fiduciary” investment advisors the same spook and fleece, starting with choice of asset classes based on single-year standard deviation (aka “risk”),and selling these advisors “fiduciary” certificates along with oceans of "data" on thousands of actively-managed funds for applying the full Markowitz-pioneered spook and fleece.

The Investment Company Institute reports that still today, less than 10% of people’s fund money is in index funds. And in a recent book Mr. Bogle estimated the annual financial industry extraction from people’s investments at $400 billion. I doubt that this figure is down from 50 years ago, or that it is declining. I think the terms of deception “risk” and "expected” (or just “return”) are key players in the deception that leads to such fleecing. I think prevailing use of those two terms is a principal barrier to the mission of Mr. Bogle.

Dick Purcell

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Re: Risk vs uncertainty

Post by peter71 » Thu Dec 29, 2011 10:39 pm

Hi Dick,

It's a complicated question of the sort that makes social science so difficult: namely, to what extent is the MVO advisor industry (for which I have no particular love) an important cause of investor "fleecing."

I'm skeptical that it's played a big role, and we can't ever really run the counterfactual of what a world without MVO and/or without Markowitz selling out would have looked like, but a good null hypothesis is that fleecing of various sorts has always existed . . .

Some additional thoughts:

1) You're certainly correct that the ABSOLUTE amount of fleecing has increased as AUM have increased, but social scientists rightly or wrongly often prefer proportional measures, e.g., "fleecing as a proportion of assets under management." Otherwise, if, e.g., VG is 10x larger than some crappy active management firm that charges 5x higher fees, that firm could still say that VG is responsible for 2x as much fleecing as they are.

2) You're also correct that the proportion of investor money that's indexed is relatively low, but here again an academic would point out that prior to the rise of MVO that proportion of indexed investor money was 0.

So your claim probably has to be that, even though positive trends toward indexing have increased and ER's have decreased during the MVO era, those positive trends would have been considerably stronger had it not been for MVO.

Best,
Pete

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Re: Risk vs uncertainty

Post by LadyGeek » Thu Dec 29, 2011 10:43 pm

I have one concern on the use of "standard deviation" instead of uncertainty. Most people who hear the term "standard deviation" would naturally assume a Gaussian (Normal) distribution. I don't think that's the case. My preference is volatility, which implies an unstable dynamic condition (it moves over time). Uncertainty implies a tolerance variation, which I can also live with.

What is MVO, as used in peter71's post?
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Re: Risk vs uncertainty

Post by peter71 » Thu Dec 29, 2011 11:02 pm

Hi Lady Geek,

MVO = Mean-variance optimization. I'm using it as shorthand for "designing portfolios by looking at a portfolio's mean and standard deviation over a relatively short period."

By the way, as far as I know Bobcat and other Bodie fans on here at least started out having a different beef with defining risk as SD than the one being expressed here.

Namely, it seems people here are saying "risk should refer to bad things rather than good things" (and I'm sympathetic to that, though in part as stocks tend to go up over time downward semideviation and volatility are highly correlated so I think it's kind of moot.

Anyway, I think the Bodie/bobcat/Norstad critique has typically focused on the "relatively short period" issue -- i.e., even if periodic SD goes down over time, terminal portfolio SD goes up (FWIW I think this is kind of moot/self-evident too).

And, for that matter, I don't think long-term unleveraged index investors need to worry about normal vs. non-normal distributions either.

Anyway, rant off. I know all you asked for was a definition of MVO. :D

Best,
Pete

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Re: Risk vs uncertainty

Post by GregLee » Fri Dec 30, 2011 12:10 am

William F. Sharpe has some discussion of standard deviation and measures of risk here: http://www.stanford.edu/~wfsharpe/mia/r ... .htm#other
Shortfall Measures

Some argue that standard deviation is a flawed measure of risk since it takes into account both happy and unhappy surprises, while most people associate the concept of risk with only the latter. Alternative measures focus on "downside risk" or likely "shortfall". Each requires the specification of an additional parameter -- the point from which shortfall is to be measured. This threshold may be zero, a riskless rate of return, or some level below which the Investor's disappointment with the outcome is assumed to be especially great.
... and concluding
In many cases it proves helpful to summarize the prospects of an investment strategy in terms of (1) its expected outcome and (2) a measure of downside risk or likely shortfall, even though the analysis leading to its choice utilized standard deviation as a measure of risk.
Greg, retired 8/10.

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Re: Risk vs uncertainty

Post by magician » Fri Dec 30, 2011 12:14 am

LadyGeek wrote:Most people who hear the term "standard deviation" would naturally assume a Gaussian (Normal) distribution.
What makes you think that?

Other distributions have standard deviations, most of them finite.
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Re: Risk vs uncertainty

Post by stlutz » Fri Dec 30, 2011 12:57 am

In other threads I've been one of the opponents of the "expected return" phrase. However, I really like Larry's original post in this thread. Investing in stocks is mainly about uncertainties. Investing in T-Bonds has fewer uncertainties (e.g. future inflation rates) and more quantifiable risks (duration). That distinction works well. I'm going to adopt Larry's terminology.

Standard deviation is a useful approximation for risk, or at least one way of looking at it. As with my comments on expected return, the errors in its use primarily effect professionals/academics as opposed to average investors. It's the experts who make the leap to defining risk completely in terms of volatility since that's easily calculated. To the average investor or person with a history degree (like me), standard deviation is still just an abstraction that's no more meaningful than Vanguard's 1-5 ranking..

A more useful explanation is to say that, based on history, there is a strong probability of a market decline of >50% twice in your investing lifetime. Or to put it another way, 2007-2009 was not a black swan event; one should anticipate that this will happen to them again..

So, stocks are "risky" because they are volatile. Their future returns are hard to predict because the future is "uncertain". Seems non-controversial to me.

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Re: Risk vs uncertainty

Post by 555 » Fri Dec 30, 2011 1:08 am

wifeofmarius wrote:I am a long time lurker here so please be patient with my ignorance. My husband and I are in our mid 30's, he a full time IT specialist, and me, a stay at home Mom with too much time on her hands.
I am confused on how to measure standard deviation in our portfolio. Are we taking too much risk at this point in our lives?
Bewildered in Boston
You probably should start a new thread.

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Re: Risk vs uncertainty

Post by 555 » Fri Dec 30, 2011 1:33 am

magician wrote:
LadyGeek wrote:Most people who hear the term "standard deviation" would naturally assume a Gaussian (Normal) distribution.
What makes you think that?
Other distributions have standard deviations, most of them finite.
You beat me to it. I'm definitely curious to hear the answer. Why would they assume that and why would it be natural?

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Re: Risk vs uncertainty

Post by LH » Fri Dec 30, 2011 8:13 am

Risk is just a very poor word. It essentially has no meaning.

Risk also has an upside. In on of the more rigorous definitions of risk = variance, the UPSIDE, like a fast stock boom, is also include in the definition of risk!

So contrary to what another poster said, Risk as commonly talked about in academic papers, actually includes events commonly construed as wonderful.

This does not really take away from what the other post said, but just further reiterates:

Risk as routinely used in finance is near meaningless, or at best, highly imprecise concept.

This is due to its lack of any consistent definition amongst different financial experts, and even a single financial expert, will use it inconsistently, switching between the different meanings without specifying exactly what he means when he says "risk". But if one is using risk=variance, then upside events ARE risk, according to that definition, and its one of the more well defined ones around. So conversely, one of the most precise definition, is also the one which also goes most strongly against the connotation of risk as bad. Its a beautiful thing in terms of its vagueness. Give me 80s, 90s variance "risk" for the rest of my life : )

I do like the engineer view of risk.

Its also great to point out uncertainty vs risk, Knight, its an important part of the problem. Which bears routine repeating. But risk is basically a semantics issue (coupled with difficulty of easily defining risk, or just making a verbal wall between risk and uncertainty, but no one OWNS the process/definitions, there is no way to do it, and being human, even someone who tries to make a wall themselves between risk and uncertainty, will end up using "risk" to essentially refer to uncertainty,its just human nature to do so), consequently tons of people just routinely talking past each other about "risk" and I do not foresee this changing.

I posit, you can post this post 10 years from now, and nothing will have changed in the meaning/lack of meaning/inconsistency of "risk" as talked about by financial humans.

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Re: Risk vs uncertainty

Post by nisiprius » Fri Dec 30, 2011 8:44 am

magician wrote:
LadyGeek wrote:Most people who hear the term "standard deviation" would naturally assume a Gaussian (Normal) distribution.
What makes you think that?

Other distributions have standard deviations, most of them finite.
Because it is by far the most common context. The association of "standard deviation" and "normal distribution" is deeply ingrained. The commonest use of standard deviation is to make at rough estimates of the probability of various departures from the mean, which assumes a normal distribution. Maybe it shouldn't be that way, but it is--just as surely as the word "stocks" in current parlance is always taken to mean "common stocks."

For example, when you hear that the founders of LTCM called what happened a "ten-sigma event," how do you interpret that statement? Random Googling turns up things like this (my boldface):

"The founders of LTCM later called the market conditions of 1998 'a ten-sigma event.' But obviously it was not that improbable."

Notice that the author did not say "But obviously the market was not following a normal distribution." The author interpreted LTCM's founds to mean, and I believe the founders did mean, that the market conditions of 1998 had only a one-septillionth chance of occurring.

I'll bet you could ask a hundred students "What is the probability of the return of an investment falling within two standard deviations of the mean," and eighty of them would say "95%." Frankly, I think I might, too, if I weren't in a situation where I was being forced to be careful.

And of course, don't forget that normality is not an unreasonable assumption if we know a priori that the thing we are looking at is the sum of many independent random variables--the central limit theorem applies. One of the huge and often ignored differences between financial application of statistics, and their use in science or manufacturing, is that in the later cases there really are many, practical, real-world situations where we know enough about the underlying characteristics of a system that we can say that it's reasonable to assume a sum of independent variables.

My statistics prof said that lack of independence was a far more common and more serious problem than lack of normality. We see this in real life in e.g. fault-tree calculations that don't allow properly for common causes, like "independent" engines whose fuel lines are not independently routed.
Last edited by nisiprius on Fri Dec 30, 2011 8:54 am, edited 3 times in total.
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Re: Risk vs uncertainty

Post by SP-diceman » Fri Dec 30, 2011 8:52 am

magician wrote: Some people (probably the majority of those who bother at all) define risk to include only negative possibilities; others define risk to include both negative and positive possibilities. Which definition you use isn't particularly important; i.e., both are eminently workable. Knowing which definition you use (and which the people with whom you're talking / working use) is vitally important.
I have to admit I have no idea what people are talking about,
it seems like another word ‘reward” is missing?

If I make a large bet on a coin toss the odds can be calculated exactly. (50/50)
(not sure why being able to calculate exact odds would matter except to assess risk)
That risk (I could lose) must have a reward/positive. ( I could win)
Why else would you take the risk?

(reminds me of that joke: tales I win, heads you lose)

The uncertainty is I can’t control results or the future.
(anything from loss, dishonesty, to the other side not having the money to back up the bet, to winning and having the earth hit be an asteroid)

Everything has risk/reward/uncertainty.

If someone wants to go bungee jumping, the
risk (I could get hurt) may not be worth the reward. (the excitement)
However, even taking the safe route and staying home, a plane could crash into my house. (uncertainty)


Thanks
SP-diceman

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Re: Risk vs uncertainty

Post by VictoriaF » Fri Dec 30, 2011 9:02 am

nisiprius wrote:
magician wrote:
LadyGeek wrote:Most people who hear the term "standard deviation" would naturally assume a Gaussian (Normal) distribution.
What makes you think that?

Other distributions have standard deviations, most of them finite.
Because it is by far the most common context. The association of "standard deviation" and "normal distribution" is deeply ingrained. The commonest use of standard deviation is to make at rough estimates of the probability of various departures from the mean, which assumes a normal distribution. Maybe it shouldn't be that way, but it is--just as surely as the word "stocks" in current parlance is always taken to mean "common stocks."
I checked Wikipedia's article on Standard Deviation. The first picture you see in the article is that of a normal distribution, and most initial text refers to normal distribution.

Later, the article includes relevant statements about other distributions such as
Wikipedia wrote:Not all random variables have a standard deviation, since these expected values need not exist. For example, the standard deviation of a random variable that follows a Cauchy distribution is undefined because its expected value μ is undefined.
and
Wikipedia wrote:In the case of a parametric family of distributions, the standard deviation can be expressed in terms of the parameters.
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Re: Risk vs uncertainty

Post by George-J » Fri Dec 30, 2011 10:41 am

Howard Marks' 2006 letter to Oaktree clients on Risk is a must read for clarity and common sense on this important topic
in part from the above link ..
What Is Risk?

According to the academicians who developed Capital Market Theory, risk equals volatility,
because volatility indicates the unreliability of an investment. I take great issue with this
definition of risk.

It’s my view that – knowingly or unknowingly – academicians settled on volatility as the proxy
for risk as a matter of convenience. They needed a number for their calculations that was
objective and could be ascertained historically and extrapolated into the future. Volatility fits the
bill, and most of the other types of risk do not. The problem with all of this, however, is that I
just don’t think volatility is the risk most investors care about.

There are many kinds of risk, and I’ll discuss some of them below. But volatility may be the
least relevant of them all. Theory says investors demand more return from investments that are
more volatile. But for the market to set the prices for investments such that more volatile
investments will appear likely to produce higher returns, there have to be people
demanding that relationship, and I haven’t met them yet. I’ve never heard anyone at Oaktree
– or anywhere else, for that matter – say, “I won’t buy it, because its price might show big
fluctuations,” or “I won’t buy it, because it might have a down quarter.” Thus it’s hard for me to
believe volatility is the risk investors factor in when setting prices and prospective returns.
In addition, volatility has a number of shortcomings that aren’t often addressed in the literature
but are obvious to investment practitioners:
and similar insightful comments in James Montier's 2009 letter Clear and present danger: the trinity of risk
Despite risk appearing to be one of finance’s favourite four letter words, it remains finance’s most misunderstood concept. Risk isn’t a number, it is a concept or a notion. From my perspective, risk equates to what Ben Graham called a “permanent loss of capital”. Three primary (although interrelated) sources of such danger can be identified: valuation risk, business/earnings risk, and balance sheet/financial risk. Rather than running around obsessing on the pseudoscience of risk management, investors should concentrate on understanding the nature of this trinity of risks."

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Re: Risk vs uncertainty

Post by kontango » Fri Dec 30, 2011 10:55 am

Couple of comments:

The normal distribution is used to illustrate Standard Deviation because: (1) it's familiar to most people (at least more familiar than other distributions), and (2) the standard deviation has a convenient interpretation if returns are normally distributed. Even if returns are not normally distributed (which they aren't), using a normal distribution is a "back-of-envelope" way to get a feel for uncertainty.

Second, I don't think anyone really believes returns are normally distributed. First, the normal distribution is a continuous distribution, whereas stock returns are discrete. Second, the normal distribution is a "thin-tailed" distribution whereas stock returns are fat-tailed. Last, the normal distribution allows for negative prices, since the x-axis runs from minus infinity to plus infinity! Clearly no one believes that (IMO).

Last, the distinction between two-sided risk vs one-sided risk (i.e., "downside risk") isn't that great. If standard deviation is not your preferred measure of risk, you can just use the semi-variance (semi-deviation) instead of variance (standard deviation). It measures the "downside" risk of an investment. Also, there is the Sortino Ratio that is exactly like the Sharpe Ratio except it only looks at downside risk (semi-deviation) instead of standard deviation.

I don't think using Sortino instead of Sharp (or semi-deviation instead of standard deviation) benefits you a whole lot in terms of asset allocation. It may be more intuitive to use, but I don't think it changes the results much.
Last edited by kontango on Fri Dec 30, 2011 11:11 am, edited 1 time in total.

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Re: Risk vs uncertainty

Post by peter71 » Fri Dec 30, 2011 11:06 am

nisiprius wrote:
magician wrote:
LadyGeek wrote:Most people who hear the term "standard deviation" would naturally assume a Gaussian (Normal) distribution.
What makes you think that?

Other distributions have standard deviations, most of them finite.
Because it is by far the most common context. The association of "standard deviation" and "normal distribution" is deeply ingrained. The commonest use of standard deviation is to make at rough estimates of the probability of various departures from the mean, which assumes a normal distribution. Maybe it shouldn't be that way, but it is--just as surely as the word "stocks" in current parlance is always taken to mean "common stocks."

For example, when you hear that the founders of LTCM called what happened a "ten-sigma event," how do you interpret that statement? Random Googling turns up things like this (my boldface):

"The founders of LTCM later called the market conditions of 1998 'a ten-sigma event.' But obviously it was not that improbable."

Notice that the author did not say "But obviously the market was not following a normal distribution." The author interpreted LTCM's founds to mean, and I believe the founders did mean, that the market conditions of 1998 had only a one-septillionth chance of occurring.

I'll bet you could ask a hundred students "What is the probability of the return of an investment falling within two standard deviations of the mean," and eighty of them would say "95%." Frankly, I think I might, too, if I weren't in a situation where I was being forced to be careful.

And of course, don't forget that normality is not an unreasonable assumption if we know a priori that the thing we are looking at is the sum of many independent random variables--the central limit theorem applies. One of the huge and often ignored differences between financial application of statistics, and their use in science or manufacturing, is that in the later cases there really are many, practical, real-world situations where we know enough about the underlying characteristics of a system that we can say that it's reasonable to assume a sum of independent variables.

My statistics prof said that lack of independence was a far more common and more serious problem than lack of normality. We see this in real life in e.g. fault-tree calculations that don't allow properly for common causes, like "independent" engines whose fuel lines are not independently routed.
Hi Nisi,

I agree with almost everything in this post, but I also think it's important to distinguish between the sort of leveraged shenanigans that LTCM was engaging in and the sort of behavior that most Bogleheads engage in. To use Taleb's term, I think that long term investors in total markets pretty much live in "Mediocristan." And while I think we probably underestimate the probability of a black swan / Knightian uncertainty alien / nanobot / asteroid event wiping out markets as we know it, it's reasonable to argue that you can't prepare for that stuff anyway.

So I guess the way I'd put things is this: for those of you who don't think that normal standard deviation is useful in describing what's likely to happen to the S&P next year, what sort of odds would you give me that next calendar year's returns will fall within 3 standard deviations of the mean?

i.e., 10.62 +/- 18.87(3) = -45.99 < x < 67.23

No doubt the normality assumption is indeed a bit off, and a year is a pretty short period, but would anyone, say, pay me $100 if it fell within that range in hopes of collecting $500 if it fell outside of it?

Best,
Pete

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Re: Risk vs uncertainty

Post by chisey » Fri Dec 30, 2011 11:16 am

LadyGeek and nisi--

There is no need to tie standard deviation to the normal distribution, and I too don't understand why you'd think most people make that leap (maybe it's an engineering thing?). I'm a statistician and have taught a lot of stat courses, and I can assure you that there's no need to associate the two concepts in an academic sense. Std. dev. is taught as a descriptive statistic just like mean, median, etc., and I would think most of its uses among non-statisticians are in that realm. Standard deviation measures dispersion and is useful in many kinds of distributions, known and unknown.

Properties of the normal distribution give standard deviation convenient uses in that context but that doesn't mean it's the only context people use it in. Just because it has nice meaning with one distribution doesn't mean we should tie the two concepts together. I will grant you that much of the statistical inference that involves standard deviation relies on assumptions of normality, but that is a separate concept from standard deviation itself.

As for the rest of the thread, I think it's widely accepted that std. dev. on its own is not a perfect quantifier of investment risk. To the extent that volatility causes or enhances certain kinds of risk, it is a useful measurement when analyzing investments. I don't know that there's any great attempt to hide the truth by interchanging "std. dev." and "risk," but we should be careful not to oversimplify the concept.

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Re: Risk vs uncertainty

Post by peter71 » Fri Dec 30, 2011 11:36 am

Hi Chisey,

I teach stats to social scientists and I can assure you I'm part of the problem in the sense that I just don't teach students much beyond normal distribution and the fact that it often doesn't hold (plus I also cover skewness and kurtosis). Thinking back to what I was myself taught in Prob Stats 101 in the math department, I can't recall even being taught about skewness and kurtosis (though with the popularization of black swan talk and power law talk by Taleb and Gladwell I suspect those concepts are now covered).

Best,
Pete

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Re: Risk vs uncertainty

Post by LadyGeek » Fri Dec 30, 2011 11:42 am

To the increasing posts responding to my comments on standard deviation, consider investors who don't have a strong mathematical background (a vast majority). If they wanted to know what standard deviation was, google turns up Wikipedia. Of course, the description is correct; but look at the picture on the right - your classic bell curve. That's all they would understand - the picture. (Supporting what VictoriaF said in a previous post.)

Gummy has a good tutorial - Standard Deviation: some comments on Volatility and Risk and Risk. He refers to William Sharpe's definition of risk.
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Re: Risk vs uncertainty

Post by chisey » Fri Dec 30, 2011 11:55 am

LadyGeek wrote:That's all they would understand - the picture. (What VictoriaF said in a previous post.)
If they are that lazy, they won't really understand the picture either. The Empirical Rule (68-95-99.7) seems to me to be at least as obscure to the common American as the definition of standard deviation is. I don't think they'd understand the picture without reading a little further.

Maybe most people really are that intellectually lazy . . . but it seems to me that someone who wants to understand a concept-- to the point of using it in investment strategy-- must have some desire to begin with and not be so incredibly lazy as to see a picture, read nothing, and go ahead and use it with something as important as their retirement money. But perhaps I overestimate people.

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Re: Risk vs uncertainty

Post by peter71 » Fri Dec 30, 2011 12:00 pm

Hi Again Chisey,

So how can a long term index investor profit from thinking about distributions other than the normal distribution? This seems to me a classic case in which intellectual effort DOESN'T pay off, in that, e.g., the possibility that the S&P could theoretically increase more than 100% in a year but can only lose 100% is well, pretty theoretical.

Best,
Pete

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Re: Risk vs uncertainty

Post by chisey » Fri Dec 30, 2011 12:08 pm

peter71 wrote:Hi Again Chisey,

So how can a long term index investor profit from thinking about distributions other than the normal distribution? This seems to me a classic case in which intellectual effort DOESN'T pay off, in that, e.g., the possibility that the S&P could theoretically increase more than 100% in a year but can only lose 100% is well, pretty theoretical.

Best,
Pete
Well, realizing that he can't fully count on the normal distribution is the most important lesson. Investment returns have much fatter tails so risk and reward can't fully be described using the normal distribution.

That doesn't mean one can't use standard deviation as a way to compare the volatility of different portfolios, and higher volatility can be associated with certain kinds of risks. There is utility there . . . one just can't take it as the only measure of risk, or assume that one can ascribe specific probabilities of loss based on a normal distribution. If anything, fully realizing that we can't use the normal distribution to its fullest extent ought to make more careful and conservative investors out of all of us, so I think that in itself is pretty useful info.

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Re: Risk vs uncertainty

Post by GregLee » Fri Dec 30, 2011 12:12 pm

kontango wrote:Even if returns are not normally distributed (which they aren't), ...
Relevant to the distribution of returns:
Note that a normally-distributed variable has a symmetric distribution about its mean. Quantities that grow exponentially, such as prices, incomes or populations, are often skewed to the right, and hence may be better described by other distributions, such as the log-normal distribution or Pareto distribution.
http://en.wikipedia.org/wiki/Normal_distribution
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Re: Risk vs uncertainty

Post by LadyGeek » Fri Dec 30, 2011 12:32 pm

For those mathematically inclined, our Canadia sister site Financial Webring Forum hosts an archive of tutorials from forum member Gummy. He does a comparison of normal vs. log-normal distributions of the S&P 500 index here (3 part series).

Back to risk vs. uncertainty....
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Re: Risk vs uncertainty

Post by peter71 » Fri Dec 30, 2011 12:41 pm

Hi Greg,

So the practical take-home of right-skewness is that investors in the S&P should assume there's a significantly better chance of outsized positive returns than would be suggested by the normal curve (which suggests that a return of over 67.23% for the S&P 500 next year is a highly improbable "3 SD" event (specifically, one with only a 0.15% chance of happening). Do you think investors would benefit by estimating the chances of such a spectacular year differently?

Best,
Pete

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Why standard deviation?

Post by jln » Fri Dec 30, 2011 12:48 pm

There's some compelling math behind the common practice of using standard deviation as a measure of the informal notion of "risk," at least in contexts compatible with the exposition that follows.

Define a risk averse investor to be any investor who has the following two properties:

1. No matter how much money he has, the investor would always be happy to have another dollar. This property is called non-satiation.

2. The more money he has, the less important it becomes to the investor to have one more dollar. For example, if he only has $1 to start with, getting another $1 is more important than it would be if he has $1 million to start with. This property is called decreasing marginal utility of wealth.

Note that this definition does not use the notion of standard deviation or any other statistical concepts. It's quite simple. It seems clear that nearly all investors are "risk-averse" in this sense.

We need one more definition. An investment I1 is defined to be more efficient than an investment I2 if all risk averse investors (in the sense defined above) prefer I1 to I2.

With these two quite reasonable definitions, we can prove the following theorem:

Suppose I1 and I2 are two investments with lognormally distributed returns, with instantaneous yearly expected returns alpha1 and alpha2 and standard deviations of instantaneous yearly returns sigma1 and sigma2 respectively. Then I1 is more efficient than I2 if and only if:

alpha1 >= alpha2 and sigma1 <= sigma2

with strict inequality holding in at least one of the inequalities. This result holds for all time horizons and initial levels of wealth.

This theorem from mathematical finance is at the heart of all those efficient frontier graphs. In more-or-less plain English, it tells us that risk-averse investors like expected return (they want to increase it) and they dislike standard deviation (they want to decrease it).

Put another way, if we think informally of "return" as something we like (and would like to increase all else being equal), and if we think informally of "risk" as something we dislike (and would like to decrease all else being equal), then in the context of comparing competing feasible lognormally distributed investment alternatives, the theorem tells us that standard deviation is the proper way to measure "risk".

Don't worry about the notion of "instantaneous return" in this theorem. I won't define that here. It's a technical detail. It's OK for our purposes as an approximation to think of the more familiar "simply compounded yearly return".

The theorem holds for all time horizons. Contra Dick, there's nothing special about short time horizons.

Note the two big assumptions in the theorem. First, investors are risk-averse. This seems more than reasonable. Second, the two investments are lognormally distributed. That's a bit more controversial, but still not unreasonable as a first-order rough approximation to how most "normal" investments behave.

For a proof see Theorem 4.2 on page 20 of An Introduction to Portfolio Theory.

With best wishes to all of my fellow risk-averse investors for a very happy and prosperous new year, I remain faithfully yours,

John Norstad

p.s. I have no comment on the original topic of "risk" versus "uncertainty". That's philosophy and above my pay grade. My remarks here are much more modest. They are just about math facts, which is an area where I can sometimes manage to muddle through and have at least some confidence that I actually know what I'm talking about.
Last edited by jln on Fri Dec 30, 2011 5:17 pm, edited 1 time in total.

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Re: Risk vs uncertainty

Post by chisey » Fri Dec 30, 2011 12:55 pm

chisey wrote: Well, realizing that he can't fully count on the normal distribution is the most important lesson. Investment returns have much fatter tails so risk and reward can't fully be described using the normal distribution..
Let me add to my own comments here.

Theoretically, investment returns must be right-skewed since the possible values can go to positive infinity but are capped on the low end at -100%. I suspect, though I am not well enough read on the literature to say with confidence, that there are long periods of time during which investment returns are somewhat normal. That is to say, you can probably count on them centering around a mean return, with most periods being relatively close and fewer periods straying further from this mean. So maybe it's correct that much of the time a normal distribution is a reasonable fit for returns of volatile assets.

But what is killer in risky investments are exceptional events-- macro changes to the environment which could be sudden or gradual-- that cause improbable (under the normal assumption) returns. The thing is, these sorts of things are not that exceptional. They are irregular and unpredictable but not especially rare. Obviously it's these things that are the main cause of normality going out the window, and we can't pretend them away and just use the normal in our expectations.

The S&P 500 provides a really easy example of this. The long term std dev of annual returns is somewhere around 16-18%, and the long term mean is around 10-11%. That means 95% of the time we should see returns between -25% and +45%. But there were 8 years between 1928 and 2010 where the return was out of these bounds . . . about 10% of the time, or twice as often as normality would predict. 5 of those times the departure was on the low side, which is of critical importance when you think about risk. There is no analytical distribution that fits stock returns, as far as I know . . . though people have tried the Cauchy distribution and others.

So when one thinks about volatility and especially loss, one may assume that most of the time, returns have a bell-ish shape around the mean. But one cannot make more detailed assumptions than that, and one should especially not believe that extreme returns are as improbable as normality predicts.

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Re: Risk vs uncertainty

Post by peter71 » Fri Dec 30, 2011 1:06 pm

Hi Chisey,

Agreed that it's a little off, but moneychimp puts the SD at 18.9 rather than 16-18, so some of those 8 outsized years might drop out?

http://www.moneychimp.com/articles/rand ... orizon.htm

Of course, arguably the entire enterprise of trying to forecast based on any past distributions alone is crazy given changes in the system (though I think that cuts both ways in that, while it's often and correctly noted that markets can behave irrationally due to human emotions like panic and euphoria, humans and the computers they program to trade for them can also (perhaps stubbornly, perhaps wrongly!) decide that a market that's moved 3 or 4 SD's in a year is "due for a reversal."

Best,
Pete

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Re: Risk vs uncertainty

Post by chisey » Fri Dec 30, 2011 1:16 pm

peter71 wrote:Hi Chisey,

Agreed that it's a little off, but moneychimp puts the SD at 18.9 rather than 16-18, so some of those 8 outsized years might drop out?

http://www.moneychimp.com/articles/rand ... orizon.htm

Of course, arguably the entire enterprise of trying to forecast based on any past distributions alone is crazy given changes in the system (though I think that cuts both ways in that, while it's often and correctly noted that markets can behave irrationally due to human emotions like panic and euphoria, humans and the computers they program to trade for them can also (perhaps stubbornly, perhaps wrongly!) decide that a market that's moved 3 or 4 SD's in a year is "due for a reversal."

Best,
Pete
Yep, and unfortunately the measurement depends on the source and timeframe, which just goes to show how hard it really is to expect things to fall nicely into such an elegant distribution. The fact is we really don't have that much data. We don't even know what the mean should be, yet we try to build return probabilities around it.

My points in all this are: (1) it is foolish to use a normal distribution to estimate the probability of a big loss in volatile markets. We should not expect most markets to be normal, and even if we did the parameters cannot be particularly well-estimated; and (2) it's okay to use standard deviation as a tool to help you assess volatility-associated risks-- just don't assume a probability distribution is available to help you assign a particularly accurate likelihood of loss based on this standard deviation.

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Re: Risk vs uncertainty

Post by magician » Fri Dec 30, 2011 3:46 pm

nisiprius wrote:For example, when you hear that the founders of LTCM called what happened a "ten-sigma event," how do you interpret that statement?
I interpret it as nonsense. The author, undoubtedly, simply wanted to convey that it was extremely unlikely, and chose to use a term he didn't understand fully, not unlike authors who say that something grows "exponentially" when they want to convey that it's growing really, really fast (without realizing that exponential growth can be really, really slow).
nisiprius wrote:Notice that the author did not say "But obviously the market was not following a normal distribution." The author interpreted LTCM's founds to mean, and I believe the founders did mean, that the market conditions of 1998 had only a one-septillionth chance of occurring.
Of course not, because the author didn't understand the terms he was using.
nisiprius wrote:I'll bet you could ask a hundred students "What is the probability of the return of an investment falling within two standard deviations of the mean," and eighty of them would say "95%."
I'll bet if you asked 100 of my students you wouldn't get 80 answering that way (or even 50), but I'll concede that you're probably correct if you asked 100 of somebody else's students. ;)
nisiprius wrote:Frankly, I think I might, too, if I weren't in a situation where I was being forced to be careful.
I'll report you to your statistics prof; maybe it's not too late to lower your grade. What was his name, again?
nisiprius wrote:And of course, don't forget that normality is not an unreasonable assumption if we know a priori that the thing we are looking at is the sum of many independent random variables--the central limit theorem applies. One of the huge and often ignored differences between financial application of statistics, and their use in science or manufacturing, is that in the later cases there really are many, practical, real-world situations where we know enough about the underlying characteristics of a system that we can say that it's reasonable to assume a sum of independent variables.
Exactly why we teach students to use tables of normal distributions for analyzing portfolios.
nisiprius wrote:My statistics prof said that lack of independence was a far more common and more serious problem than lack of normality. We see this in real life in e.g. fault-tree calculations that don't allow properly for common causes, like "independent" engines whose fuel lines are not independently routed.
He's right, and I like your fault-tree analogy. (In my risk analysis work I've done a fair number of calculations for reliability and MTBF; it's especially difficult to explain to managers why the calculation isn't simply P1 × P2 × . . . × Pn.)
Simplify the complicated side; don't complify the simplicated side.

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Re: Risk vs uncertainty

Post by magician » Fri Dec 30, 2011 3:51 pm

SP-diceman wrote:If I make a large bet on a coin toss the odds can be calculated exactly. (50/50)
If the coin is fair.

(Please don't say that you assume that the coin is fair, for then you're not calculating the probabilities, you're merely assuming the probabilities.)

Suppose that, before you made that large bet, the coin had been tossed five times and all five times it came up heads. If you were offered 1:1 odds on the next toss, would you bet on heads, or tails? Why?
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Re: Risk vs uncertainty

Post by magician » Fri Dec 30, 2011 3:54 pm

peter71 wrote:I teach stats to social scientists and I can assure you I'm part of the problem in the sense that I just don't teach students much beyond normal distribution and the fact that it often doesn't hold (plus I also cover skewness and kurtosis). Thinking back to what I was myself taught in Prob Stats 101 in the math department, I can't recall even being taught about skewness and kurtosis (though with the popularization of black swan talk and power law talk by Taleb and Gladwell I suspect those concepts are now covered).
The CFA curriculum now focuses exclusively on normal distributions (though they do mention skewness and (excess) kurtosis); they used to discuss more general probability distributions. I find their new focus to be a step backward. (Similarly for their dropping of Macaulay duration from the curriculum; please don't get me started.)
Simplify the complicated side; don't complify the simplicated side.

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Re: Risk vs uncertainty

Post by Dick Purcell » Fri Dec 30, 2011 4:19 pm

John Norstad –

I was trying to avoid addressing it, but you’ve forced us into it: it is not only the financial industry that benefits from the misleading labeling of standard deviation as “risk” – ivory tower theorists benefit too.

And you demonstrated it with steps toward utility-free utility theory!

++++++++

My Uncle Silas was a farmer in Vermont. Never finished high school.

But he had common sense. He knew that the utility of his investments was the dollars they provided, when required for his needs and goals. And he knew that depended not only on what investment he picked but also how much he invested and when.

He used to hire kids who were working their way through the university. One day one of those kids came in and tried to explain to Uncle Silas something about utility theory. Uncle Silas let that kid keep his job cleaning the chicken coop but told him never to enter the farmhouse again.

Uncle Silas told me “That young fellah (Vermont, you know) tried to tell me he could pick the best investment for me without considering how much I invest or when, or what future results I will need and when! The nut!!

“Instead, he’d measure my aversion to standard deviants!”

++++++++

John, what we should be doing is our best to estimate and communicate what investments offer and how they compare in result probabilities for the particular investor’s dollar plan and future needs and goals. That’s the investor’s purpose, and that's what he is most likely to understand.

I’ll grant you that utility theory can have marginal utility, for folks who just can’t or won’t understand the most clearly presented dollar-result-probability options. But to make utility theory value positive in investor guidance, the utility theorists are going to have to toss out the present stuff and address investment utility – dollar results for an investor’s dollar plan and future dollar needs and goals. And to apply it, they are going to have to come down from the tower and learn about the particular investor’s present and projected financial means and needs.

All this fancy stuff about choosing best investments for people through analyses that aren’t built on the person’s dollar plans and goals, but instead presented with the deceptive labels “risk” and “expected return” or just “return,” are irresponsible diversions from the purpose, serving the interests of the financial industry and the theorists to the detriment of the investing public.

Dick Purcell

PS – Your essay does not at all justify the mislabeling of standard deviation as risk. Standard deviation does not measure adversity!! It doesn’t even measure what it deviates from!! It can instead more honestly be labeled standard deviation. Or if you must deviate from calling it what it is, label it uncertainty.

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Re: Risk vs uncertainty

Post by GregLee » Fri Dec 30, 2011 4:40 pm

peter71 wrote:Hi Greg,

So the practical take-home of right-skewness is that investors in the S&P should assume there's a significantly better chance of outsized positive returns than would be suggested by the normal curve (which suggests that a return of over 67.23% for the S&P 500 next year is a highly improbable "3 SD" event (specifically, one with only a 0.15% chance of happening). Do you think investors would benefit by estimating the chances of such a spectacular year differently?
Hi Peter,
I don't know that they should assume that, and I don't know whether they would benefit.
Greg, retired 8/10.

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Re: Risk vs uncertainty

Post by SP-diceman » Fri Dec 30, 2011 9:13 pm

magician wrote:
SP-diceman wrote:If I make a large bet on a coin toss the odds can be calculated exactly. (50/50)
If the coin is fair.

(Please don't say that you assume that the coin is fair, for then you're not calculating the probabilities, you're merely assuming the probabilities.)

Suppose that, before you made that large bet, the coin had been tossed five times and all five times it came up heads. If you were offered 1:1 odds on the next toss, would you bet on heads, or tails? Why?
Is having a team of scientists examine the coin now part of the game?
Now we have to define fair?

I would consider the coin being fair part of the uncertainty.
Theoretically a fair coin (after “testing”) can become “un-fair” just depending on how its handled.

I would bet tails simply because it satisfies my human weakness to spot what’s “due.”
Theoretically there is no “correct” pick so I may as well choose the one that makes me feel good,
it wont change my 50/50 odds.

Even though it doesn’t change the odds, I would consider knowing the previous flips a different game.
With no information I may have just picked heads because of how we phrase it
heads/tails just picking the first.

Probably the emotionally safest way would be to flip my own coin to tell me what to bet.
(fair or not)

For the record I don’t believe “fair” matters in one bet.
Lets say you had a coin that always comes out tails, now my decision would make it a 50/50 chance.
(much like 2 boxes, one has a gift inside, pick one)

A “fair” coin typically relates to a sequence of bets.


Thanks
SP-diceman

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