Risk = ??

Asset allocation, risk, diversification and rebalancing. Pros/cons of hiring a financial advisor. Seeking advice on your portfolio?

If Risk = Standard Deviation, then

Poll ended at 05 Sep 2005 11:48

Risk is a probability of a loss
2
11%
Risk is a measure of uncertainty
12
63%
None of the above
5
26%
 
Total votes: 19

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deaddog
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Re: Risk = ??

Post by deaddog » 31 May 2011 19:50

NormR wrote:
But if I take too much risk, can I get superior returns? Time to get a few lotto tickets. :wink:
Yabut you gotta define too much risk. :?

At least with a lotto or any other game of chance you have defined your risk. It's either/or.
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Re: Risk = ??

Post by George$ » 27 Jun 2011 17:40

An interesting article
Does Lower Risk Mean Higher Returns?
By Samuel Lee | 06-27-11 | and some text from it
Many investors have been making up for low yields by taking on more risk, whether it's by dipping into lower-quality bonds or holding more dividend-paying stocks. Exchange-traded fund sponsors have been busy launching products touting even higher payouts or more-exotic asset classes, including obscure oddities such as master limited partnerships, business-development companies, and bank loans. By seeking higher yields and greater risk, investors are likely setting themselves up for lower risk-adjusted returns and possibly worse absolute returns than if they had stood pat. Blame the strange relationship between risk and return.

High Volatility, Low Returns

Researchers have discovered a kink in the traditional risk-reward relationship. Professors Andrew Ang, Robert Hodrick, Yuhang Xing, and Xiaoyan Zhang discovered that the most volatile stocks have underperformed the least volatile stocks globally, both on absolute and risk-adjusted bases. The effect can't be explained by known risk factors such as size, value, momentum, and liquidity. Similarly, in the past four decades, the most distressed (and therefore most volatile) bonds have either lost money or underperformed investment-grade bonds on an absolute basis.

Who are these investors gleefully torching their money? Some blame investors who crave lottery-like securities, which, over the long run, lose money but have a small chance of paying out big. Others focus on wildly overoptimistic investors who push up the price of stocks that are hard to value--the winner's curse writ large. Investors should be careful when dipping their toes into the riskiest segment of any asset class, as they usually offer low risk-adjusted returns. An elegant model proposed by two researchers may tell us why.
The original academic paper that this seems to come from.
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Re: Risk = ??

Post by Peculiar_Investor » 27 Jun 2011 23:01

In the linked article from above, this chart,

Image

would seem to indicate that BBB and BA rated corporate bonds have a better risk adjusted return that A rated bonds. Am I interpreting the chart correctly?
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Re: Risk = ??

Post by George$ » 18 Sep 2011 08:23

Just came across this 2010 article - with some interesting observations

Risk, Return, and Reality Revisited - June 30, 2010•Posted by: Charles Lewis Sizemore, CFA

includes the well known fact ....
If investment returns really do follow a normal distribution pattern [as portfolio models assume], then the 1987 crash never should have happened—literally not once in over 1 billion years. The problem is that the stock market is full of “once every billion years” days, even though we have only about 80 to 100 years’ worth of reliable data. So, what does that actually mean? Suffice it to say, the returns of the stock market are not normally distributed. This means that mainstream investment tools are flawed.
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Re: Risk = ??

Post by ghariton » 18 Sep 2011 22:49

George$ wrote:
If investment returns really do follow a normal distribution pattern [as portfolio models assume], ...
Some of us have been saying for many years that distributions of investment returns have fatter tails than a Gaussian distribution would indicate.

For example, I quote from Analysis of Financial Time Series by Ruey Tsey, a textbook aimed at MBA students and published in 2002 (page 12):
Recent studies of stock returns tend to use scale mixture or finite mixture of normal distributions.... Cauchy distribution has fatter tails than the finite mixture of normal, which in turn has fatter tails than the standard normal.
Your colleague John Hull uses a Student's t distribution with four degrees of freedom (again yielding fatter tails than a Gaussian). The late Benoit Mandelbrot was recommending fractals thirty years ago. John Tukey was recommending that analysts avoid assuming a Gaussian distribution fifty years ago.

In passing I note that the assumption of fat tails is inconsistent with the use of the arithmetic mean (much less the geometric mean) as an estimate of the average return, or the variance when thinking about volatility. And yet, how many people on this forum and elsewhere still use the arithmetic or geometric mean when thinking about returns? How many people have moved beyond the variance when thinking about volatility? (How many people think about volatility at all?)

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Re: Risk = ??

Post by Rickson9 » 19 Sep 2011 00:21

Speaking for myself, I prefer more volatility than less and more frequent market turmoil as implied by fat tail distributions. However that may be a function of my age, personality and goals.
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Re: Risk = ??

Post by George$ » 20 Sep 2011 08:25

ghariton wrote:....
How many people have moved beyond the variance when thinking about volatility? (How many people think about volatility at all?)

George
Very true. The administrators at my institution who oversee the pension plan still use volatility, gaussian variance as a measure of their investment risk!! :?
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Re: Risk = ??

Post by George$ » 21 Sep 2011 08:28

ghariton wrote:.... John Tukey was recommending that analysts avoid assuming a Gaussian distribution fifty years ago. .....
George
George, thank you for this reference. I'm embarassed to admit I never heard of Tukey until now. I gather his book "Exploratory Data Analysis" is a classic. It sounds like you are familiar with it. How practical and useful is it? (Should I find a copy?) It is a pricey item - $85 for a paperback copy.
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Re: Risk = ??

Post by Shakespeare » 21 Sep 2011 08:43

I'm embarassed to admit I never heard of Tukey until now.
I used to work with the Fast Fourier Transform (FFT), which uses the Cooley-Tukey algortithm.
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Re: Risk = ??

Post by ghariton » 21 Sep 2011 17:46

George$ wrote:I never heard of Tukey until now. I gather his book "Exploratory Data Analysis" is a classic.
John Tukey was my graduate student adviser. Although EDA (as it is fondly known to his followers) came out years after I had graduated, I worked on some of it. Coincidentally, I think that it is a great book. :wink:

It was explicitly written for practitioners, although I think that theoreticians would also benefit from it. As such it is radically different from the typical statistics textbook, and to my mind is much more useful. But two cautions

(1) The approach is unorthodox and indeed I remember a senior professor at U of Toronto turning livid with rage at the very mention of Tukey's name

(2) Tukey was brilliant, but not the world's best communicator. The book follows his own thought patterns and you have to be ready to go along for the ride.

I would be pleased to lend you my copy by mail, but this is one book I do want returned eventually. Please PM me if you are interested.

George
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Re: Risk = ??

Post by George$ » 22 Sep 2011 13:03

ghariton wrote: ...I would be pleased to lend you my copy by mail, but this is one book I do want returned eventually. Please PM me if you are interested.

George
Thank you very much for the kind offer. To be honest I have a stack of at least 20 books in my study at home that I mean to read. Thus I should not add your special copy of EDA at this time. Let me hold a rain check. (Also the cost is not that egregious that I cannot afford to buy it.) -- I do like the sound of it. I value and am inclined to unconventional individuals (e.g. Feynman and Einstein were unconventional).

At present my university responsibilities are still all consuming and thus free time is very limited. But I am "retiring" at the end of this academic year and then I hope to "catch up". That's the hope. :roll:
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Re: Risk = ??

Post by deaddog » 23 Sep 2011 00:18

Most of our so-called reasoning consists of finding arguments for going on believing as we already do.( J.H. Robinson)

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Re: Risk = ??

Post by ghariton » 23 Sep 2011 11:59

Here is an alternative approach to measuring risk: Ask people what they think.

GARP is an association of financial risk managers, with its own designation (look like CFA wannabes). I find their stuff much more interesting than CFIA, but that reflects my personal interests. Anyway, they survey their members and massage the results into a risk index. Methodology and latest results are available here.
Key Findings
• The Risk Index jumped more than 2.5 points to 110.5 in Q2, closing in on the historical
high reached in Q3 2010.
• Concern about an economic slowdown, unresolved sovereign debt issues in the US and
abroad, and questions about banking fundamentals all contributed to the uptick in risk
perceptions.
• The lack of sustained job growth, impact of an expanding trade deficit, stubbornly high
consumer debt levels and anemic growth in GDP were identified as US macro-economic
indicators to watch closely.
• Looking ahead to Q3, risk managers appear most concerned about Eurozone instability,
the practical implications of a US sovereign debt crisis, ineffective US monetary policy
initiatives, and the current and long-term implications of US dollar weakness. On the
bright side, the perceived impact of geopolitical tensions eased significantly.
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Re: Risk = ??

Post by George$ » 27 Sep 2011 10:52

A recent and easy-to-read article by our colleague Norm

Risky business
So what does all this talk of betas and CAPM mean for you as an investor? In short, that you should eschew both very risky investments and very safe investments because people tend to overpay for both. Lotto-ticket type stocks are loved too much (think of the sexy allure of technology start-ups and junior mining companies), while guarantees are too highly valued (think of the hidden high fees in guaranteed income type products). As a result, taking the middle way with a moderate amount of risk appears to hit the sweet spot in many financial markets. Indeed, moderation appears to boost both returns and well-being more generally.
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Re: Risk = ??

Post by Bylo Selhi » 04 Nov 2011 10:12

Posted at Bogleheads: Beware The Long Tail - Science News
Scientists from a range of fields have been poring over financial data, finding some curious patterns in the process.

These patterns suggest that standard economic models based on the notion of equilibrium — markets will fluctuate but then settle down like the surface of a still pond — may not capture the whole story. Freak events may be a normal part of long-term economic behavior. If that’s true, then the mathematical methods guiding Wall Street’s estimation of risk are seriously flawed, offering a dangerous false sense of security...
You'd think that after being shat upon by black swans for a century or more and research by the likes of Mandelbrot and Fama over the past 50-some years economists would finally, um, repeal Gauss' bell, but you'd be wrong:
The Gaussian bell’s roots in finance go back to work by French mathematician Louis Bachelier, who modeled changes in share prices in the early 1900s. Bachelier recognized that some of his model’s assumptions were flawed, including the premise that the probability of extreme events is vanishingly small (he reportedly called such events “contaminators”). Yet these assumptions were preserved in later models, including the Black-Scholes formula, which underlies much of Wall Street’s estimation of risk.

But when it comes to financial data, a growing body of research suggests that outliers can be more like babies than bathwater. Such events may still be very rare; Stanley says that the probability that stocks would crash as they did on Black Monday in 1987 was “as close as you can come to never.” Yet Black Monday still happened. And while much of finance does behave within the bounds of a normal distribution, ignoring the rare, large events doesn’t capture reality...

Instead of dismissing such tails because they don’t fit the models, researchers might need to rework the models because they don’t fit the data, Stanley and others argue. “The model should really be driven by the data,” he says. “For a physicist, there are no outliers. If I saw a glass of water float up in the air, we’d have to re-examine the law of gravity.”...
Sedulously eschew obfuscatory hyperverbosity and prolixity.

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Re: Risk = ??

Post by Shakespeare » 04 Nov 2011 10:38

If I saw a glass of water float up in the air, we’d have to re-examine the law of gravity.”
Or statistical mechanics and entropy. A homework problem might be calculating the probability of a pencil jumping 1 cm in the air because all the atoms happen to be moving in the same direction. This calculation involves some very large factorials, and gives a number that is larger than astronomical - say, 1 in 10100 or something like that.
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Re: Risk = ??

Post by IdOp » 04 Nov 2011 15:12

Even in physics, though, there seem to be those who would make a career out of solving quadratic Hamiltonians (which on the quantum side of things are more or less closely related to Gaussian functions).

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Re: Risk = ??

Post by George$ » 29 Dec 2011 09:25

Some more recent discussion at Boggleheads on the basic but easy to confuse topic of "risk vs uncertainty"

Sample of text ...
For real risk, return-rate standard deviation and any additional return-rate uncertainty are only essential raw materials to be applied along with others in further analysis.

Calling return-rate standard deviation “risk” has the perverse effect that as the typical investor moves along the frontier to portfolios labeled as least in “risk,” she increases her real risk.

That mislabeling is also wonderful for the actively-managed-fund financial industry. It helps misfocus investors’ attention on their short-term fears for the individual year, where they cannot see the terrible long-term cost of high active-fund fees.

Please! With all your expertise and influence, you can help fight this terrible pair of labels of deception.

Dick Purcell
and
Larry, I believe you're using Frank Knight's* definitions of "risk" and "uncertainty." A recent thread commented on the issue of the public misunderstanding words like "expected" in financial writing, and I think there's a potential similar issue here. I would say that as you use them they are almost technical terms. Looking them up at http://www.m-w.com it is interesting to note the dictionary meanings of "risk" include only the negative aspects. The dictionary does not capture "risk" in the sense of standard deviation, of fluctuation either way, of volatility. And the definitions of risk use alarming words suggesting a serious matter: injury, hazard, peril:

.............

Synonyms for "risk" are listed as "hazard, imminence, menace, peril, pitfall, danger, threat, trouble."

Synonyms for "uncertain" are listed as "capricious, changeable, changeful, flickery, fluctuating, fluid, inconsistent, inconstant, mercurial, mutable, skittish, temperamental, fickle, unpredictable, unsettled, unstable, unsteady, variable, volatile."

In fact, it almost seems to me as if the common definitions for "risk" and "uncertainty" are almost swapped around from the meanings given to them by Knight. The dictionary's "risk" means rare, catastrophic. The dictionary's definition of "uncertain" means vague, variable, wishy-washy. At any rate, the important distinction you and Knight wished to capture is certainly not captured by the ordinary meaning of the two words Knight chose to use.

*Frank Knight, 1885-1972, was a University of Chicago economist who wrote an influential book, Risk, Uncertainty, and Profit, available online here.
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Re: Risk = ??

Post by ghariton » 20 Feb 2012 03:10

I've been reading Multi-moment Asset Allocation and Pricing Models, a book of essays edited by Emmanuel Jurczenko and Bertrand Maillet.

As we know, the mean-variance description of asset returns, and the CAPM model that flows logically from that description, are inadequate. What I didn't know is that there is a sizable literature that tries to explain asset prices in terms of four factors instead of just two (no, not Fama and French, which I've always thought of as ad hoc). Instead of looking at just expected return and variance (or similar measures of volatility) as the only two factors predicting price, this approach looks at expected return, variance, skewness and kurtosis. The hypothesis is that, in addition to the effects of expected returns (good) and volatility (bad), investors are willing to pay more for assets whose returns are skewed positively (good) and less for assets whose returns have fat tails (bad).

The mathematics are difficult, which is why we don't see these models applied in practice, I guess. (One practitioner is quoted as saying that he has had enough difficulty explaining the CAPM to clients; forget anything more complicated.) And empirical tests are still in early stages. Still, I'm very intrigued by the approach.

Among other things, it would make sense (for me at least) of some of the results on risk that Norm R and others have been finding -- that for common stock, experienced returns can actually fall with increasing beta, at least within moderate ranges. If Norm's sample of high-beta shares is, as a side effect, also picking up shares with positive skewness, then we would expect investors to bid up the prices for these (and so accept lower expected returns). This approach also would explain why people are willing to buy lottery tickets, accepting a negative expected return as the "price" for a very skewed return.

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Re: Risk = ??

Post by deaddog » 20 Feb 2012 11:53

ghariton wrote: This approach also would explain why people are willing to buy lottery tickets, accepting a negative expected return as the "price" for a very skewed return.

George
When people play the Lotto they know and accept the risk going in. I’m willing to risk one dollar to gain up to whatever the jack pot is. If I lose the dollar that’s the risk.
The thing is that once the draw is over you don’t have a choice.

When you make an investment you know there is risk involved and you may or may not quantify your risk. Usually you are not planning on risking 100% of your investment like you do when you buy a lotto ticket. However with most investments there is no time limit.(Options give you a time limit) There is no time when the game is over and you can choose to play again and risk more money or stand aside.

As an investor you have to decide when to end the game. If an investment loses money you can choose when to get out. It’s your choice and that’s where the emotions get involved. If you don’t have a point where you decide to cut losses you haven’t really accepted the risk. If you haven’t accepted the risk you will rationalize why you should hold the investment even if it continues to go against you.

You can have a model that works 95% of the time but if you don’t have a plan to deal with the other 5% you haven’t accepted the risk. You can measure risk to the Nth degree but if you can still lose all your money by doing nothing what good is it?
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Re: Risk = ??

Post by adrian2 » 20 Feb 2012 12:21

deaddog wrote:You can have a model that works 95% of the time but if you don’t have a plan to deal with the other 5% you haven’t accepted the risk. You can measure risk to the Nth degree but if you can still lose all your money by doing nothing what good is it?
You may think you have dealt with 100.000% of the risk but that's an illusion. Samples of what I'm pretty sure you have no protection against:
- you forgetting to put in place stop orders (e.g., sickness, old age forgetfulness etc) and/or your broker's system breaking down
- your holdings gapping down through your stops
- stock markets being suspended indefinitely
- communists taking over and nationalizing all private property
- a madmen pulling the trigger on atomic bombs
- an asteroid hitting the Earth
- etc.
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Re: Risk = ??

Post by NormR » 20 Feb 2012 12:28

ghariton wrote:I've been reading Multi-moment Asset Allocation and Pricing Models, a book of essays edited by Emmanuel Jurczenko and Bertrand Maillet.

As we know, the mean-variance description of asset returns, and the CAPM model that flows logically from that description, are inadequate. What I didn't know is that there is a sizable literature that tries to explain asset prices in terms of four factors instead of just two (no, not Fama and French, which I've always thought of as ad hoc). Instead of looking at just expected return and variance (or similar measures of volatility) as the only two factors predicting price, this approach looks at expected return, variance, skewness and kurtosis.
When you first mentioned 4 factors, I assumed adding momentum to FF's 3 factors. Also a popular thing to do. ;)

I don't remember off the top of my head, but how stable are skewness and kurtosis? That is, is the past a good guide to the future for these items?

Also, if one goes to where the math is hard, why not opt for semi-var instead of var? Perhaps that makes it too hard?
ghariton wrote:Among other things, it would make sense (for me at least) of some of the results on risk that Norm R and others have been finding -- that for common stock, experienced returns can actually fall with increasing beta, at least within moderate ranges. If Norm's sample of high-beta shares is, as a side effect, also picking up shares with positive skewness, then we would expect investors to bid up the prices for these (and so accept lower expected returns). This approach also would explain why people are willing to buy lottery tickets, accepting a negative expected return as the "price" for a very skewed return.
Isn't that just putting a behavioural argument into math speak? It doesn't really explain why. (Mind you, why problems seem to get all meta quick. ;) ) The core issue of people overly liking the lotto/guaranteed things remains. It also doesn't indicate if people are good at calibrating/valuing skewed bets which seems rather doubtful based on studies from the world of lottos.

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Re: Risk = ??

Post by deaddog » 20 Feb 2012 13:02

adrian2 wrote:
You may think you have dealt with 100.000% of the risk but that's an illusion. Samples of what I'm pretty sure you have no protection against:
- you forgetting to put in place stop orders (e.g., sickness, old age forgetfulness etc) and/or your broker's system breaking down
- your holdings gapping down through your stops
- stock markets being suspended indefinitely
- communists taking over and nationalizing all private property
- a madmen pulling the trigger on atomic bombs
- an asteroid hitting the Earth
- etc.
I have considered and accepted the majority of those risks and have a plan in place to deal with them. I can only control what I do.

Which is my point, know your risks and have a plan in place to deal with them. Measuring your risk without a method of dealing with it is a waste of time.
Most of our so-called reasoning consists of finding arguments for going on believing as we already do.( J.H. Robinson)

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Re: Risk = ??

Post by Jungle » 20 Feb 2012 15:21

Would it be correct to say a mix of 20% cdn gov bonds and 80% equity should beat (or match) the returns of 100% equity over a long term ?

For example, the chart here http://www.finiki.org/wiki/Portfolio...d_Construction shows the mixture of 80% equity/20% bonds beat 100% equity! (1972-2008)

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Re: Risk = ??

Post by NormR » 20 Feb 2012 15:30

Jungle wrote:Would it be correct to say a mix of 20% cdn gov bonds and 80% equity should beat (or match) the returns of 100% equity over a long term ?

For example, the chart here http://www.finiki.org/wiki/Portfolio...d_Construction shows the mixture of 80% equity/20% bonds beat 100% equity! (1972-2008)
Not necessarily.

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