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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Post by deaddog »

George$ wrote:
I guess I don't buy that as a solution. I don't see 'volatility' as a loss. I see selling below the buy price as a loss.

For the long term investor like myself (I am not a short term speculator), I cannot contemplate a 'stop loss' order - which if executed guarantees a loss. I don't sell on market volatility. I do sell to realize gains or because I have lost confidence in the company itself, in its fundamentals (and not on what the market thinks about it).

Just my two cents.
Are you saying that going into any investment you don't know what your risk is? Or is it 100%. You are willing to lose all your money if the investment doesn't go the way you think it might.

Have the fundamentals of any company in the market changed. When were you aware of the change and how has the price of that stock reacted to the change.

My experience has been that the price reacts long before the fundamental change is realized by the investing public.

Even if the long-term buy and hold strategy will show a better return in the long run (whatever that is). The fact that your investment could go to zero because the fundamentals change is too much risk for me.
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Post by Lado »

For me, ulcer index as developed by Peter Martin works best as a measure of risk. Volatility just doesn't cut it as a measure of risk.


From Wikipedia:

The Ulcer Index is a stock market risk measure or technical analysis indicator devised by Peter Martin in 1987, and published by him and Byron McCann in their 1989 book The Investors Guide to Fidelity Funds. It's designed as a measure of volatility, but only volatility in the downward direction, i.e. the amount of drawdown or retracement occurring over a period.

Other volatility measures like standard deviation treat up and down movement equally, but a trader doesn't mind upward movement, it's the downside that causes stress and stomach ulcers that the index's name suggests.
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Post by gummy »

Lado wrote:For me, ulcer index as developed by Peter Martin works best as a measure of risk. Volatility just doesn't cut it as a measure of risk.
I love the Ulcer Index, if for no other reason ... because of its name. :lol:
The neat thing about this index is that it has a numerical value as opposed to "drawdown" which don't
... unless you calculate an "average" drawdown which is akin to calculating an average square of drawdown (like that Ulcer thing).

It's sorta like a definition of "risk" which involves one's personal aversion to loss (hence cannot be calculated for a given asset) or a definition which incorporates an investor's tolerance to volatility or their inability to meet their financial goals.

Although risk = standard deviation was the norm, I reckon it's less acceptable these days.

However, tho' it sounds more reasonable, I don't like risk = uncertainty, either.
I can imagine an outfit that guarantees a sequence of annual returns for the next umpteen years, if you invest in their whatzit assets.
The sequence of returns may have a large standard deviation.
But the future returns are known. There is no uncertainty.
Volatile, yes ... but risky?

I have my own preference for a "risk" definition (involving historical returns, inflation, asset allocations for a portfolio, rebalancing period and Monte Carlo simulations), but it'll never catch on because it's much too complicated.

Come to think of it, mebbe standard deviation is good 'cause it's easy. :?
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Post by Lado »

To illustrate by means of an example, look at the US models (no not supermodels with weird outfits that nobody buys) on my site here.

At the top of the page is a table with the compound annual growth rate, ulcer index and maximum drawdown. If you scroll down the page you will see equity curves for each of the models. The model with the highest CAGR is not one that I personally use due to the high maximum drawdown. Instead I have my $US invested as per the QLD/IEF model since it has a very acceptable annual return (45.3%), a low ulcer index (3.7% versus 5.7% for a buy-and-hold strategy) and an acceptable maximum drawdown (13.4%). The QLD/PSQ model is also acceptable for my risk profile.

The QLD/QID model has the highest CAGR of 90.5% but I can't handle the maximum drawdown of 31.1%.

If you want to know what QLD, IEF, QID and the other ETF symbols represent, please scroll to the bottom of the page.
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Post by DanielCarrera »

Standard deviation measures uncertainty, but for people who think of risk as the "probability of loss", the standard deviation is still a very useful measure. If returns have a normal distribution[1] then saying "the standard deviation is X" is equivalent to saying that there is a 26% chance that you will suffer a loss worse than X. That sounds a lot like a "probability of loss" to me.

[1] There is evidence that returns are not normal, but my basic point remains true.
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Post by Studebaker Hawk »

Lado wrote:maximum drawdown.
Isn't maximum drawdown yet to be experienced? How optimized is your system to the data you have, ie, how many variables and how many times did you adjust them? Did you reserve any data for out of sample testing?

Isn't it possible that the model with the acceptable maximum drawdown (13.4%) will have the highest drawdown in the future and the model with the highest maximum drawdown (31.1%) will have the lowest drawdown in the future?

Why maximum drawdown and not geometric standard deviation?

Since it's likely that you'll experience a drawdown that exceeds your test drawdowns or your recent drawdowns, have you looked at money management techniques to help keep you in the game? Van Tharp comes to mind.

How correlated are your different models? If they aren't, then why not use Kelly betting with diversification of uncorrelated models to reduce the volatility? Why not use half Kelly?

Best of luck (and don't leave your whole wad/winnings on the table).
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Post by Lado »

Maximum drawdown in my table refers to the maximum drawdown to date.

Certainly there is correlation between the models given that they all do the same thing when a long signal is generated (i.e. the US models buy QLD). The best model is a matter of personal preference so I list them all rather than just the one(s) that fit my profile.

I personally prefer to consider maximum drawdown for each model because we all look at our portfolio values and take into consideration how much the current portfolio value is below a previous peak (at least I think that's we all do).
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Post by George$ »

deaddog wrote:Are you saying that going into any investment you don't know what your risk is? Or is it 100%. You are willing to lose all your money if the investment doesn't go the way you think it might.
Over my 40+ years of investing I have been 100% wiped out in individual stock holdings at least six times. But I've also hit some home runs and my overall gains far exceed my losses.

Don't forget that the most you can lose on the downside in an individual investment is 100% (assuming no leveraging or shorts) - but you can make much much more than 100% on the upside. (Even at today's depressed values my MSFT holdings represent an 800% gain on the original average purchase price.)

About risk. Excepting with hindsight I don't think I ever fully understand the risk I'm taking in the market. :roll:

Buffett has defined risk = 'nature of being in certain kinds of businesses and from not knowing what you are doing'
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Post by deaddog »

George$ wrote: Over my 40+ years of investing I have been 100% wiped out in individual stock holdings at least six times. But I've also hit some home runs and my overall gains far exceed my losses.

Don't forget that the most you can lose on the downside in an individual investment is 100% (assuming no leveraging or shorts) - but you can make much much more than 100% on the upside. (Even at today's depressed values my MSFT holdings represent an 800% gain on the original average purchase price.)

About risk. Excepting with hindsight I don't think I ever fully understand the risk I'm taking in the market. :roll:

Buffett has defined risk = 'nature of being in certain kinds of businesses and from not knowing what you are doing'




Sounds like my story. You didn’t mention the ones that went way up then crashed. NT anyone.

I define risk as the amount I’m prepared to lose on any trade. I don’t like to risk more than 2% of my capital on any one trade.
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Post by DanielCarrera »

ghariton wrote: And yet, here we are forty years later, all implicitly assuming that the world follows a Gaussian distribution. I include the people who post here. When was the last time one of you used a median or a mid-mean, rather than an arithmetic or (shudder) geometric mean to describe return on investment over a multi-year period?
I hope this isn't a stupid question, but what's wrong with the geometric mean? If my investment returns 30% for 9 years in a row and -100% the 10th year, the arithmetic mean is 17% which sounds pretty good, and the median is 30% which sounds even better, but the reality is that I lost everything and only the geometric mean captures that ( (1.3*1.3*1.3...*0)^0.1 = 0 ).
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Post by Shakespeare »

In essence, the geometric mean considers only the start and end dates, and ignores the path between.
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Post by DanielCarrera »

Shakespeare wrote:In essence, the geometric mean considers only the start and end dates, and ignores the path between.
Ok, fair enough. What would you recommend instead? In my example, the median and the arithmetic mean both give absurd answers.
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Post by Shakespeare »

I was taught that the median is the most robust measurement. Error can be estimated by the probable deviation [the median of the absolute value of the deviations from the median].
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Post by DanielCarrera »

Shakespeare wrote:I was taught that the median is the most robust measurement. Error can be estimated by the probable deviation [the median of the absolute value of the deviations from the median].
Well, median is certainly robust in the sense that it is less affected by outliers and it is usually considered a better indication of the "typical" result. But in a world where returns compound, outliers can matter a lot. In my example, we would agree that the typical return is 30%, but you stil lost all your money.
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Post by lilbit »

Georges, thank you for your candid post about being wiped out six times in your 40 + years of investing. You have given a relative newcomer like myself HOPE!! (I know, hope is not a strategy - but I think you understand what I mean.)
Thank you for your encouragement. I have been on a steep learning curve, since I started DIY investing in 2005! :wink:
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Post by ghariton »

gummy wrote:I can imagine an outfit that guarantees a sequence of annual returns for the next umpteen years, if you invest in their whatzit assets.
The sequence of returns may have a large standard deviation.
But the future returns are known. There is no uncertainty.
Volatile, yes ... but risky?
Nice sleight of hand. :wink:

The return in your example may vary from year to year, but for any given year, it is jnown in advance. Hence for any given year it isn't volatile. It follows that the net present value of income folows is known with certainty and hence so is the price I would pay. IOW the price is known with certainty, both now, and at every future point in time. So where's the volatility?
Come to think of it, mebbe standard deviation is good 'cause it's easy. :?
I personally don't like the standard deviation because it's meaningful only when the tails of the distribution are not too fat. ISTM that the Gaussian )or lognormal) are terrible models to use for financial returns. I'd rather try to think of the entire expected distribution of returns, if I can figure it out, or anyway concentrate on the tails rather than the middle.

There's a lot more randomness out there -- the tails are much fatter -- than most people believe.

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Post by DanielCarrera »

ghariton wrote: I personally don't like the standard deviation because it's meaningful only when the tails of the distribution are not too fat. ISTM that the Gaussian )or lognormal) are terrible models to use for financial returns. I'd rather try to think of the entire expected distribution of returns, if I can figure it out, or anyway concentrate on the tails rather than the middle.

There's a lot more randomness out there -- the tails are much fatter -- than most people believe.
What would you pick instead of standard deviation? Also, what would you pick in terms of median/mean? See my example earlier where median andd arithmetic mean give abusrd answers.
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Post by George$ »

A good lengthy discussion of recent investment risk and VaR (Value at Risk) in particular
Risk Mismanagement by JOE NOCERA - NY Times, Jan 4, 2008

A bit from near the end of the article ...
At the height of the bubble, there was so much money to be made that any firm that pulled back because it was nervous about risk would forsake huge short-term gains and lose out to less cautious rivals. The fact that VaR didn’t measure the possibility of an extreme event was a blessing to the executives. It made black swans all the easier to ignore. All the incentives — profits, compensation, glory, even job security — went in the direction of taking on more and more risk, even if you half suspected it would end badly. After all, it would end badly for everyone else too. As the former Citigroup chief executive Charles Prince famously put it, “As long as the music is playing, you’ve got to get up and dance.” Or, as John Maynard Keynes once wrote, a “sound banker” is one who, “when he is ruined, is ruined in a conventional and orthodox way.”

MAYBE IT WOULD HAVE been different if the people in charge had a better understanding of risk. Maybe it would have helped if Wall Street hadn’t turned VaR into something it was never meant to be. “If we stick with the Dennis Weatherstone example,” Ethan Berman says, “he recognized that he didn’t have the transparency into risk that he needed to make a judgment. VaR gave him that, and he and his managers could make judgments. To me, that is how it should work. The role of VaR is as one input into that process. It is healthy for the head of the firm to have that kind of information. But people need to have incentives to give him that information.”
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Post by sydney2 »

RISK IS SOMETIMES VERY.....Stupid....stupid....

How could anyone buy into Nortel after the reverse split they did a few years ago. I watched with amazement.

To watch and see Nortel reverse split from somewhere in the 2 or 3 dollar range up to $15.00 and then watch as investors continued to buy it...only to see it crumble and do what it had alrady done, go down to nothing:shock: :shock:
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Post by kcowan »

sydney2 wrote:...only to see it crumble and do what it had alrady done, go down to nothing:shock: :shock:
They were probably following their brokers directions...
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Post by deaddog »

George$ wrote:A good lengthy discussion of recent investment risk and VaR (Value at Risk) in particular
Risk Mismanagement by JOE NOCERA - NY Times, Jan 4, 2008
One part I agree with (My bolds.)
Indeed, Ethan Berman, the chief executive of RiskMetrics (and no relation to Gregg Berman), told me that one of VaR’s flaws, which only became obvious in this crisis, is that it didn’t measure liquidity risk — and of course a liquidity crisis is exactly what we’re in the middle of right now. One reason nobody seems to know how to deal with this kind of crisis is because nobody envisioned it.

In a crisis, Brown, the risk manager at AQR, said, “you want to know who can kill you and whether or not they will and who you can kill if necessary. You need to have an emergency backup plan that assumes everyone is out to get you. In peacetime, you think about other people’s intentions. In wartime, only their capabilities matter. VaR is a peacetime statistic.”
Most Finacial Plans don't have any way to define risk nor do they have an emergency backup plan.
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Post by George$ »

From Pimco
Tail Risk Management: Why Investors Should Be Chasing Their Tails
and a bit from the link ....
Q: What is “tail risk?”

Bhansali: Tail risk can be defined as the risk posed by events that are relatively rare, but that can have substantial impact on a portfolio. These rare events can cause outsized gains or losses for investors. We are most concerned with the tail risks that can severely damage portfolios.

Tail risk refers to the risk of potential investment outcomes on the edges of statistical return distributions. In a typical bell curve, the tallest areas near the center represent the more likely outcomes. The “tails” are where the bell curve tapers down toward the edges. Of course, there are both left tails and right tails, but having a long-term view requires special attention to the avoidance of catastrophic losses, or left tails. Because real markets don’t neatly follow the bell curve, underestimating the likelihood and severity of events on the tails can result in extreme losses.

Traditional risk management and pricing tools often underestimate the frequency and severity of these left tail events and, by extension, their detrimental effect on returns. Investors who fail to account for tail risk will likely eventually suffer, as recent events have demonstrated, and long-term returns may fail to meet their investment objectives.
....
....

So, we find that nearly all tail risks that matter for typical investment portfolios are systemic risks in which everyone desires liquidity, but nobody is willing to provide it. By their very nature, these are macro risks because they have a very high correlation with monetary policy. So, while tail risks can be very distinct in their origins, they all tend to share the same macro risk impact on investment portfolios. This concept is important when considering how to hedge against tail risks.
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Post by tidal »

George$ wrote:A good lengthy discussion of recent investment risk and VaR (Value at Risk) in particular
Risk Mismanagement by JOE NOCERA - NY Times, Jan 4, 2008
Woefully Misleading Piece on Value at Risk in New York Times
The piece so badly misses the basics about VaR that it is hard to take it seriously, although many no doubt will.

The article mentions that VaR models (along with a lot of other risk measurement tools, such as the Black-Scholes options pricing model) assumes that asset prices follow a "normal" distribution, or the classical bell curve. That sort of distribution is also known as Gaussian.

But it is well known that financial assets do not exhibit normal distributions. And NO WHERE, not once, does the article mention this fundamentally important fact...

Let us turn the mike over to the Financial Times' John Dizard:

As is customary, the risk managers were well-prepared for the previous war. For 20 years numerate investors have been complaining about measurements of portfolio risk that use the Gaussian distribution, or bell curve. Every four or five years, they are told, their portfolios suffer from a once-in-50-years event. Something is off here....

A once-in-10-years-comet- wiping-out-the-dinosaurs disaster is a problem for the investor, not the manager-mammal who collects his compensation annually, in cash, thank you. He has what they call a "résumé put", not a term you will find in offering memoranda, and nine years of bonuses....

All this makes life easy for the financial journalist, since once you've been through one cycle, you can just dust off your old commentary.

But Nocera makes NO mention, zero, zip, nada, of how the models misrepresent the nature of risk. He does use the expressoins "kurtosis" and "fat tails" but does not explain what they mean. He merely tells us that VaR measures the risk of what happens 99% of the time, and what happens in that remaining 1% could be catastrophic. That in fact understates the flaws of VaR. The 99% measurement is inaccurate too...

Reliance on VaR and other tools based on the assumption of normal distributions leads to grotesque under-estimation of risk. As Paul De Grauwe, Leonardo Iania, and Pablo Rovira Kaltwasser pointed out in "How Abnormal Was the Stock Market in October 2008?":
We selected the six largest daily percentage changes in the Dow Jones Industrial Average during October, and asked the question of how frequent these changes occur assuming that, as is commonly done in finance models, these events are normally distributed. The results are truly astonishing. There were two daily changes of more than 10% during the month. With a standard deviation of daily changes of 1.032% (computed over the period 1971-2008) movements of such a magnitude can occur only once every 73 to 603 trillion billion years. Since our universe, according to most physicists, exists a mere 20 billion years we, finance theorists, would have had to wait for another trillion universes before one such change could be observed. Yet it happened twice during the same month. A truly miraculous event. The other four changes during the same month of October have a somewhat higher frequency, but surely we did not expect these to happen in our lifetimes.
...

So Nocera, by failing to dig deeply enough, winds up defending a failed orthodoxy. I suspect we are going to see a lot of that sort of thing in 2009.
good article... worth the read... also germane to your more recent post on fat tails. thx.
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Post by George$ »

From today's Globe and Mail Report on Business, easy read, highly recommended --
Value Investing reveals the risk behind diversification - by George Athanassakos
..and a bit ....
A fundamental tenet of modern portfolio theory is the notion of diversification. Rather than holding one or a few stocks, investors instead should hold a large basket of stocks.

A strategy that attempts to outperform the market based on stock picking - in other words, selecting stocks that seem to be underpriced - will lead to a poorly diversified portfolio and risk for which there will be no reward. According to the theory, diversification helps investors minimize risk and, so doing, avoid losses.

The notion of diversification, however, assumes that risk can be measured. Events over the past two years have cast doubt on how risk should be measured and have forced many believers in modern portfolio theory to reassess their models and risk metrics. They have come to realize that risk depends on too many (known and unknown) variables to be accurately measured.

Surprisingly, this realization is not new. As early as 1930, John Maynard Keynes had indicated that uncertainty and risk could not be quantified and measured. Unfortunately for Mr. Keynes, English clergyman and mathematician Thomas Bayes had a different opinion of risk, that risk could be quantified and measured by a probability distribution, and his views prevailed over those of Mr. Keynes and dominated modern finance theory. It is thus Rev. Bayes whom investors can thank for the importance of diversification in modern portfolio theory.
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Post by WishingWealth »

As a reference: http://www.riskglossary.com/

WW
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