Risk = ??

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

Post by gummy » 26 Aug 2005 11:48

If you accept the definition:
Risk = Standard Deviation
then what do you think it's supposed to measure?

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Post by ghariton » 26 Aug 2005 13:52

Risk is a measure of uncertainty, in my opinion. It has a negative connotation for some people, but not for me. It just indicates that the unexpected might happen.

If I want the negative version, I specify "risk of loss". Then it is clear I am focussing on only "bad" outcomes.

In some situations, the two concepts lead to the same ranking of situations. This happens when the probability distribution underlying the outcomes is symmetric. Then I don't need to worry about any ambiguity.

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Post by Shakespeare » 26 Aug 2005 14:33

Risk is a measure of uncertainty, in my opinion. It has a negative connotation for some people, but not for me. It just indicates that the unexpected might happen.
Several of us come from a physical science background, and are reasonably comfortable with that interpretation - despite it's imprecision. :wink:
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Post by pustertahler » 26 Aug 2005 16:50

I accept the definition that risk = standard deviation, just becouse so far std dv is the best fit to what risk is in finance: the possiblity that we have less than the amount of money we need exactly when we need it.

If we agree this is a good definition of risk, then a risk measure should be a function of too many variables:

- the amount of money we have: if we have much more than needed, a high loss, though we don't like it, will be less dramatic
- time: a 20% drop of my portfolio when I'm 40 years old is different from when I'm 80 (therefore the 110 - age = stock% formula)
- semivariace: down is bad, up is good
- outliers: std dev tends to forget big unusual returns and we know that if you're out of the market in those 2 or 3 big days it can make the difference.

Then yes, risk is a measure of uncertainty, and std dev is the best we have so far, but we have to keep looking for something better.

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Post by Shakespeare » 26 Aug 2005 16:58

std dev tends to forget big unusual returns
Standard deviation is more sensitive to outliers than the more robust alternative, probable deviation.
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Post by DenisD » 26 Aug 2005 17:47

Maybe risk can be measured by the Ulcer Index. The name is appropriate any way! :wink:
Ulcer Index (UI) is a method for measuring investment risk that addresses the real concerns of investors, unlike the widely used standard deviation of return (SD). It is a measure of the depth and duration of drawdowns in prices from earlier highs.
Ignore the references to market timing.

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Re: Risk = ??

Post by jiHymas » 26 Aug 2005 22:11

gummy wrote:If you accept the definition:
Risk = Standard Deviation
then what do you think it's supposed to measure?
Standard deviation measures all sorts of useful things: the pretensions of analysts who call themselves quants after slapping a few columns of data on a spreadsheet; the innumeracy of advisors who quote the implications of their wild-ass guesses to countless decimal places of precision; the degree of desperation amongst academics who have to publish something, no matter what; and the gullibility of the investors who desperately want some assurance that somebody understands this stuff better than they do.

Sadly, it doesn't measure risk. Risk is the chance that an investor's portfolio will materially underperform its objectives. The easiest way to reduce risk is to lower the objectives.

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Re: Risk = ??

Post by DanH » 27 Aug 2005 09:13

jiHymas wrote:Risk is the chance that an investor's portfolio will materially underperform its objectives. The easiest way to reduce risk is to lower the objectives.
What if 'risk free' alternatives (i.e. GICs, gov't bonds) only guarantee a return that is materially below one's objectives? Using your definition, don't equities actually have less risk than GICs and bonds - i.e. equities would have a chance > 0% of achieving stated objectives while GICs/bonds would have a chance = 0% of achieving objectives.

How's that for twisting your logic? ;)

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Re: Risk = ??

Post by Springbok » 27 Aug 2005 09:33

jiHymas wrote:
Sadly, it doesn't measure risk. Risk is the chance that an investor's portfolio will materially underperform its objectives. The easiest way to reduce risk is to lower the objectives.
Each component of the portfolio would presumably have it's own risk . Wouldn't some number need to be assigned to this risk, so that the overall risk can be estimated?

Lets say I have $300k in my portfolio. $100k is in a GOC 5yr bond, $100k is in a stock - say CIBC (CM) and the other $100k is in an income trust - say Enerplus (ERF.UN).

How do I measure the risk of this portfolio?

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Re: Risk = ??

Post by jiHymas » 27 Aug 2005 10:14

DanH wrote:
jiHymas wrote:Risk is the chance that an investor's portfolio will materially underperform its objectives. The easiest way to reduce risk is to lower the objectives.
What if 'risk free' alternatives (i.e. GICs, gov't bonds) only guarantee a return that is materially below one's objectives? Using your definition, don't equities actually have less risk than GICs and bonds - i.e. equities would have a chance > 0% of achieving stated objectives while GICs/bonds would have a chance = 0% of achieving objectives.

How's that for twisting your logic? ;)
It's not twisting it at all. Your analysis is absolutely correct.

An easier example is a portfolio set up to make the balloon payment on a favourable mortgage in five years time. The 'risk-free' portfolio is a 5-year Canada Strip with a principle value not less than the amount of the balloon payment.

Such a portfolio would be much more risky it its objective was to pay next week's grocery bill, or to provide for retirement income.
Springbok wrote: Lets say I have $300k in my portfolio. $100k is in a GOC 5yr bond, $100k is in a stock - say CIBC (CM) and the other $100k is in an income trust - say Enerplus (ERF.UN).

How do I measure the risk of this portfolio?
What are the portfolio objectives? "Risk" is a meaningful term only when both assets and liabilities are measured.

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Re: Risk = ??

Post by Springbok » 27 Aug 2005 10:21

jiHymas wrote:
Springbok wrote: Lets say I have $300k in my portfolio. $100k is in a GOC 5yr bond, $100k is in a stock - say CIBC (CM) and the other $100k is in an income trust - say Enerplus (ERF.UN).

How do I measure the risk of this portfolio?
What are the portfolio objectives? "Risk" is a meaningful term only when both assets and liabilities are measured.
Answer a question with a question?

Take any objective - I don't care about the actual number - Just how would you put numbers against the components of the portfolio so this portfoli's risk can be compared with that of a different portfolio - say an all GOC bond portfolio.

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Re: Risk = ??

Post by nadreck » 27 Aug 2005 14:05

gummy wrote:If you accept the definition:
Risk = Standard Deviation
then what do you think it's supposed to measure?
Risk is not equal to standard deviation

Risk is the probability of a particular outcome or the correct combination of probabilities of the individual quantum events that need to occur for the given outcome to happen.

Standard deviation measures past performance of one single metric of any possible subject of analysis it is not at all related to the probability of future outcomes/development of that subject of analysis.

If I am gambling on a roll of the dice and I am weighing the 'risk' of 7 coming up, it is in no way related to the standard deviation of the last few throws, but on the fact that there are 6 out of 36 possible combinations of dice that give you that outcome and any specific physics of irregularities in the surfaces and weight distribution within the dice. Any relationship to a small sequence of throws historically is random.

To cary that analogy to analizing an individual stock, commodity or even market index I can only say that probability of any particular outcome of any of these in the future can not in anyway be related to measuring a partly randomly assessed metric and calculate standard deviation on a series of those measures. Any relationship between that and their future performance is largely coincidental.
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Re: Risk = ??

Post by jiHymas » 27 Aug 2005 15:43

Springbok wrote:
jiHymas wrote:
Springbok wrote: Lets say I have $300k in my portfolio. $100k is in a GOC 5yr bond, $100k is in a stock - say CIBC (CM) and the other $100k is in an income trust - say Enerplus (ERF.UN).

How do I measure the risk of this portfolio?
What are the portfolio objectives? "Risk" is a meaningful term only when both assets and liabilities are measured.
Answer a question with a question?
Sure. Risk is a complicated subject.
Springbok wrote:Take any objective - I don't care about the actual number - Just how would you put numbers against the components of the portfolio so this portfoli's risk can be compared with that of a different portfolio - say an all GOC bond portfolio.
OK. We'll assume that this portfolio is set up to fund retirement income and that the target retirement date is 20 years from today.

Please note than in the analysis below, I am just guessing at the numbers.

First the bond. Five year GOC bonds are projected to have a real yield of 1% through the piece, so in twenty years that portfion of the portfolio is projected to have a real value of $122M. The risks are, essentially, inflation and deflation. So we'll make a wild guess that the actual real value has a probability distribution of $90 (5%) $100 (5%) $110 (20%) $120 (40%) $130 (20%) $140 (10%)

Next, CM. Mature Blue Chip (with some nicks in it!) in a mature industry. So our base expectation is that it will grow with the rest of the economy at 2% pa. Base Scenario makes it worth $149 in 20 years. Risks are that they'll blow themselves up, lose market share to an upstart, or get better at what they do. Wild guess of returns distribution is $50 (5%) $75 (5%) $100 (10%) $125 (20%) $150 (50%) $175 (10%).

Next, Enerplus. Commodity Fad Fund. But its got nice reserves of a finite and valuable resource, so our base expectation will be $175. Risks are that oil gets cheap, they run out, they get taxed or nationalized, or that oil gets expensive. Wild guess of returns distribution: $25 (5%) $50 (5%) $75 (10%) $100 (10%) $125 (10%) $150 (10%) $175 (20%) $200 (20%) $225 (10%)

You could replace these returns distributions with some explicitly based on historical standard deviations if you wanted to. You might be a little embarrassed if the client starts asking nozy questions, like "Why?", though.

Now, do a Monte Carlo analysis on your returns distributions and come up with a histogram of expected portfolio end-value. For each dollar value on the histogram, determine the annual payments of a life annuity purchased with those funds. Maybe you come up with something like: $10,000 (15%) $15,000 (20%) $20,000 (30%) $25,000 (20%) $30,000 (15%). If your portfolio objective is to get an annual income of $15,000 (2005 dollars) from the portfolio, then your risk is a 15% chance of not making it. Too much risk? Buy investments with a narrower return distribution. Or lower your expectations. Or both. Come up with a plan based on inputs you're comfortable with that lead to the result that's best for you.

*********************************

You may not like the returns distributions I've projected above. That's fine. Put in your own. That's the whole point. The assumptions are right there in front of everybody and may be adjusted, updated and tinkered with to one's heart's content.

The approach could be refined, obviously. Maybe you don't want to do a straight Monte Carlo analysis, but link things in some way ... a 5-year GOC end value of $90 implies hyper-inflation, so whenever we pick that result, we'll boost the commodity up a bit.

Or perhaps we can do some explicit top-down analysis. There's a 10% chance of H5N1 wiping out 15% of the world's population in five years time. What does that scenario do to the returns distributions? Figure it out and add another level to your Monte Carlo analysis.

And note that any criticism of this approach on the grounds that there are too many wild guesses is completely invalid. They're simply more explicit, require more thought than the other wild guesses involved in forecasting and don't claim to be "risk". They claim to be returns distributions quantifying the forecasting error. "Risk" is the chance your retirement will not occur as planned.

***************************************************

Further to my response to DanH: If you have a portfolio valued at $1 and your portfolio objective is to have $1,000,000 by next Tuesday, then your least risky investment is a lottery ticket. I would expect a competent advisor to (i) tell the client the risk of failure is overwhelming (ii) try to convince the client that a greater chance of success is possible if the portfolio objective is changed slightly to having $1.05 in one year and (iii) buy the lottery ticket if the client insists on maintaining his portfolio objective while being fully informed of the risk.

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Post by martingale » 27 Aug 2005 20:22

For the record, I think "everyone is right" here.

The inherent risk of a security or a portfolio is its standard deviation. This measure of risk is useful when you want to compare the returns on two different securities: If they have the same expected return, but one has a lower risk, the one with the lower risk is clearly better. When you want to compare two different securities or equities or portfolios, explain why bonds are "less risky" than equities, or whatever, then this is the right definition of risk for your conversation. This is a technical term of economics and finance not to be confused with the ordinary English meaning of "risk".

The risk that someone will not meet their financial objectives, that they will live too long, or not long enough, or that they will be stricken by a crippling disease, or that they will be unemployed, etc., are all risks that people care very much about, lose sleep over, and which are not ordinarily described as or thought of as standard deviations. This is the sort of risk people have in mind when they say, "You are 80% in equities? Wow, that is risky". These kinds of risks are not volatilities, and so not standard deviations. This is a non-technical use of the word risk in ordinary English and it is better described as "your chances", or in the technical language of statistics, they are likelihoods or probabilities.

So, "what is the definition of risk" is a question without enough qualification: The risk of what? The risk inherent in a return of a security? Or the risk of some particular event coming to pass?
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Post by nadreck » 27 Aug 2005 22:48

martingale wrote:The inherent risk of a security or a portfolio is its standard deviation. This measure of risk is useful when you want to compare the returns on two different securities: If they have the same expected return, but one has a lower risk, the one with the lower risk is clearly better. When you want to compare two different securities or equities or portfolios, explain why bonds are "less risky" than equities, or whatever, then this is the right definition of risk for your conversation. This is a technical term of economics and finance not to be confused with the ordinary English meaning of "risk".
However it still presumes that the risk that is being measured is one that applies to the future and there is nothing to suggest that the future standard deviation (or future probable returns) are related to the historical measures available now. If I compare say Adobe's 'risk' by this with the 'risk' of the Nasdaq as a whole over certain periods I would probably see Adobe as a less risky investment than the index, I don't think that makes any sense since there are far more possible scenarios where Adobe drops significantly in value (no matter how good an individual company it is) than the index as a whole, though there are some sector considerations that could take the Naz down more than Adobe in some circumstances.
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Post by jiHymas » 27 Aug 2005 23:08

martingale wrote:The inherent risk of a security or a portfolio is its standard deviation.
...
This is a technical term of economics and finance not to be confused with the ordinary English meaning of "risk".
Well, fine. You can say it's a defined term, full stop, and you'll hear a lot of agreement. Hey, you can define black as White, if you like, without going to jail. It's a free country.

But if I've got a five-year obligation I want to immunize (as in my mortgage example above), I simply fail to understand any argument that says a five-year strip is not the lowest risk instrument around.

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Post by gummy » 28 Aug 2005 04:11

Once upon a time (in another forum-world) we talked 'bout risk and the discussion was quite interesting :)

What I find difficult to understand, when advisors speak to a poor-joe client, is using the word "risk" to mean something foreign to the client's financial vocabulary ... yet (I guess) it happens, no?

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Post by martingale » 28 Aug 2005 04:51

jiHymas wrote:But if I've got a five-year obligation I want to immunize (as in my mortgage example above), I simply fail to understand any argument that says a five-year strip is not the lowest risk instrument around.
To be properly qualified you should rephrase that:
If I've got a five-year obligation a five-year strip has the lowest risk of failing to meet that obligation.
or to put it in technically correct terminology:
If I've got a five-year obligation a five-year strip has the lowest likelihood of failing to meet that obligation.
In other words the word "risk" in your statement should attach to the concept "fail to meet obligation" rather than the concept "five year strip". The inherent risk of a five year strip does not change depending on its use!

The general problem here is that in ordinary English usage the word "risk" typically means "likelihood of failure", whereas in technical usage risk describes the volatility of a likelihood. There is no ordinary usage term that is equivalent to the technical definition of risk as volatility.

Again, it is my opinion that everybody is right here, they are just using slightly different vocabularies. The word "risk" is getting used in two different ways. According to each vocabulary, what is being said makes a lot of sense. The confusion arises when the different definitions of the word "risk" are conflated with one another and people sloppily mix the technical and non-technical usages of it in one paragraph.
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Post by Springbok » 28 Aug 2005 07:34

gummy wrote: What I find difficult to understand, when advisors speak to a poor-joe client, is using the word "risk" to mean something foreign to the client's financial vocabulary ... yet (I guess) it happens, no?
Right! The term "risk" is used loosely and if risk=std dev, then the word "risk" in this context should be given a different name.

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Re: Risk = ??

Post by Springbok » 28 Aug 2005 07:44

jiHymas wrote: And note that any criticism of this approach on the grounds that there are too many wild guesses is completely invalid. They're simply more explicit, require more thought than the other wild guesses involved in forecasting and don't claim to be "risk". They claim to be returns distributions quantifying the forecasting error. "Risk" is the chance your retirement will not occur as planned.
The approach reminds me of those decision making tools (grid analysis?)

Useful tools that make you think through all the aspects, but often come out the way you want becuase of the weighting you choose.

Guessing the future is difficult.

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Post by treetops » 28 Aug 2005 13:01

My definition:

Risk is the probability and consequence of being wrong. It must include both. Case-in-point: Nuclear power. Very low probability of being wrong. Not such a small consequence of being wrong, though.

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Post by treetops » 28 Aug 2005 13:03

The poll needs a 4th category : "both of the above"

P

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Post by jiHymas » 28 Aug 2005 23:56

martingale wrote:The inherent risk of a five year strip does not change depending on its use!
Well, now we have hit on the crux of the matter, haven't we?

I claim that a five-year-strip, or any other financial instrument has no inherent risk, any more than a hammer has an intrinsic value as a tool.

I claim that you can no more make up a valid universal and orderly progression of risk from bills through bonds to equities than you can come up with a universal ranking for a hammer, a screwdriver and a wrench.

Risk is a term to be defined and measured for the assets relative to the associated liabilities - for the tool relative to the job - even if determining the nature of those liabilities is a difficult project. Double-entry bookkeeping is everywhere, from finance to philosophy ("'Take what you like and pay for it' says God")

When you look at standard deviation of raw returns, you are implicitly benchmarking against cash, which is a useful exercise only if you are running a money market fund. There is no more intrinisic validity to such a ranking than that for one produced in any other frame of reference.
Springbok wrote: The approach reminds me of those decision making tools (grid analysis?)

Useful tools that make you think through all the aspects, but often come out the way you want becuase of the weighting you choose.
Garbage In Garbage Out is just as applicable today as it ever was - perhaps more so, now that we all have an entire 1960's-era computer department on our desks.

Hidden assumptions are everywhere and one can quite often be surprised at their implications.

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Post by treetops » 29 Aug 2005 00:10

The inherent risk of a five year strip does not change depending on its use!
Mais non. The risk inherent in a 5-year strip is VERY MUCH different when used in a diversified investment plan versus 100% strips as an extreme example. Then, that difference is magnified by the risk tolerance of the investor - i.e. what they can afford to lose, rather than what they think they can afford to lose

Probability and Consequence...hey, isn't that a Bronte novel? :roll:

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Post by martingale » 29 Aug 2005 02:52

I hope you do see that there are two conflated vocabularies here. There is the technical vocabulary of economics in which "risk" has a precise technical definition. Railing against that is something like complaining to physicists that you don't particularly like their definition of "force" because it doesn't fit very well into the sentence "I hate being forced to learn vocabulary".

There isn't any lay term that means precisely what "risk" means in the technical vocabulary. It is a word with an exact mathematical definition, just as in physics the word "force" is defined by a set of equations. It's unfortunate that some people use technical jargon to try and brow beat "poor joes" into parting with their money; but at the same time, it's senseless to rail against the technical vocabulary in general simply because it doesn't exactly match ordinary English usage. No technical vocabulary ever will. The technical vocabulary exists because, using it, it is possible to have a more precise, more concise discussion, when you are among people who have learned it.

Everyone here agrees on the underlying concepts. We all agree that the probability of failure depends on both the problem and the proposed solution. We all agree that some securities are more volatile than others (even if we can't agree on how to measure it). The only disagreement here is whether one should use the technical definition of "risk" as specified in countless first year economics text books, or the lay definition of risk understood by every English speaker. My answer is that it depends on the context, and that you should try, as much as possible, to work out which vocabulary someone is using when you read their statements.

When I said the inherent risk of a security doesn't change I was clearly using the technical definition of risk, and it's practically a tautological statement. When treetops "refuted" that statement he did so by re-interpreting my statement using the non-technical definition of risk. That does nothing to advance understanding; conflating the definitions simply results in confusion.

Rail against the technical vocabulary if you like. While you're at it you might as well head down to New Orleans and see if you can beat back the sea with a stick. I am not sure what you hope to accomplish.
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