Risk = ??

[novice]

An interesting approach to managing risk... perhaps familiar to Martingale?


http://www.scoop.co.nz/stories/HL0510/S00272.htm/

n

[George$]

On the Nature of Risk 53-page pdf file of powerpoint.

Some interesting charts!

[George$]

A short article on What is Risk?

Typically, risk is defined as the degree of uncertainty associated with the return of an asset. Yet risk comes in many shapes and sizes, and the financial community has found a dizzying number of methods to quantify and develop techniques to attempt to keep it at bay. What follows is a short discussion of the varying types of risk as well as ways to measure risk on the whole.

[Bylo Selhi]

From the recent The Future of Life-Cycle Saving & Investing conference, Rethinking Your Investment Risk

Living standard risk – the variability of your living standard—and portfolio risk—the variability of the return on your investments—sound similar. But they aren’t. You can have a very risky portfolio, but a very safe living standard...

Financial Mindbenders
· The Poor Should Invest in Riskier Assets than the Rich
· The Old Should Invest in Riskier Assets than the Young
· Stocks are Riskier the Longer You Hold Them
· Lifestyle Funds Entail Major Living Standard Risk

P.S. It's worth spending some time to look at the other materials from the conference.

[Maciek]

From the recent The Future of Life-Cycle Saving & Investing conference, Rethinking Your Investment Risk

Living standard risk – the variability of your living standard—and portfolio risk—the variability of the return on your investments—sound similar. But they aren’t. You can have a very risky portfolio, but a very safe living standard...

Financial Mindbenders
· The Poor Should Invest in Riskier Assets than the Rich
· The Old Should Invest in Riskier Assets than the Young
· Stocks are Riskier the Longer You Hold Them
· Lifestyle Funds Entail Major Living Standard Risk

P.S. It's worth spending some time to look at the other materials from the conference.

Is there a formal paper to go with that Kotlikoff article, or is that all there is available?

[Bylo Selhi]

Is there a formal paper to go with that Kotlikoff article, or is that all there is available?

That was from a presentation he gave at the cited conference. A Google search indicates the same item appeared in the Nov06 issue of Consumer Reports Money Advisor.

Kotlikoff has also collaborated with Scott Burns on two retirement-planning related books, one here and the other still in the works as well as a series of columns mentioned here.

And if you still want more, there's always his page at BU.

[Maciek]

And if you still want more, there's always his page at BU.

Great topics, thanks.

[George$]

the "What Is Risk?"topic is being discussed over at Vanguard Diehard

In part from this link ....

24. you could write a whole book on this subject
larry swedroe| 01-11-07 | 07:13 AM

Risk is many things when it comes to not meeting financial goals, and it goes beyond investments--like can have a great investment plan, but you die earlier than expected, or are disabled, and don't have insurance, so your "investment" plan fails. A good risk management plan integrates an investment plan into a well-thought-out estate, tax and insurance plan.

Having said that, risk also differs from uncertainty. Risk is where can measure odds (like with dice or expected life) while uncertainty we don't know odds--investing is uncertainty, not risk.

Having said that we can talk about risks in terms of things like SD which is often used as THE measure (mistakenly--because it only is meaningful if distribution is normal or near normal). IF not, as is the case with many investment (junk bonds, hedge funds, VC, etc) you need to also consider skewness and kurtosis (fat tails)

And then you have all the other types of risks like geopolitical risks, etc.

But to me perhaps the most important way to think about risk is what are the odds (or best estimate of the odds) of failing to achieve your financial goal. You want IMO to create a plan that does that with the least amount of risk because for most people beyond a certain level the marginal utility of wealth is low relative to the negative utility of a loss of wealth that might occur if you take more risk.

Hope that is helpful

29. From Bogle's "Common Sense on Mutual Funds"
TimDex| 01-11-07 | 09:41 AM

For me, the best definition of risk is a simple one -- which I found (and marked heavily) in Bogle's "Common Sense."

It's on page 14, and he is quoting a comment from Laurence Siegel in an article by Peter Bernstein (odd how that name keeps coming up isn't it?):

"Risk is not short-term volatility, for the long-term investor can afford to ignore that. Rather, because there is no predestined rate of return, only an expected one that may not be realized, the risk is the possibility that, in the long run, stock returns will be terrible."

Bogle follows by noting that these comments are a "healthy reminder," but that the central message remains the same, that focusing on the long-term is still far superior to the short-term.

Tim

32. #27 got the answer right
focus| 01-11-07 | 10:24 AM]

From Merton and Bodie's Finance textbook:
Uncertainty exists whenever one does not know for sure what will happen in the future. Risk is uncertainty that "matters" because it affects people's welfare. Thus, uncertainty is a necessary, but not sufficient, condition for risk. Every risky situation is uncertain, but there can be uncertainty without risk.

Well it looks to me like this question has already been considered and answered by some very smart people (Bodie and Merton) so there need not really be any confusion about it.

The best thing to do woud be to find a copy of that FInance textbook and study it. Then perhaps open it up for discussion, rather than everyone just making up their own definitions off the top of their heads.

[Bylo Selhi]

Philospher Of Risk

Author and high-powered investment adviser Peter Bernstein holds forth on low rates, rising volatility, and the surprising reliability of equities...

How do you define risk?
The definition is not mine, but I like it. It's from Elroy Dimson at the London Business School: Risk means more things can happen than will happen.

That means you don't know the limits of what can happen, but you still have to make decisions. So you manage risks by comparing them to potential returns, and through diversification.

Remember, just because more things can happen than will happen doesn't mean bad things will happen. The outcome can be better than you expect. Maybe a stock I own will triple...

[mudLark]

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

A very interesting thread, yet again confirming we have very smart people contributing to this forum.

ISTM that within the context asked the simple mathematical answer to gummy's question is "...standard deviation is a measure of volatility:" as described here. But, it also STM the more we collectively understand, the more we are forced to acknowledge the possibility that the only constant (K) in the universe is the one in chaos. Therefore, acceptance of this definition may ignore the "risk" of "uncertaintly", introduced because of the ever present and unpredictable influence of K.

Does this mean the more we believe that everything is ultimately chaotic (perilous and uncertain), the more we risk not believing in anything with absolute certainty And, if so, what are the risks

[George$]

In reading about Berkshire's annual meeting in the May 21, 2007 Calgary Herald I find the following (with my emphasis):

Q: What are your thoughts on tracking volatility in an attempt to measure risk?

Buffett: "Volatility does not measure risk. Beta, which is a measure of volatility, is nice and mathematical, and wrong. Past volatility does not measure the risk of investing now.
Risk comes from the nature of being in certain kinds of businesses and from not knowing what you're doing."

Munger: "We've come to realize that very smart people can do very dumb things, and we've tried to learn who, so we can avoid them."

And on the same exchange as reported at Morningstar's Vanguard Diehards

A shareholder from Los Angeles referred to the fact that many people talk about "sigmas" (the standard deviations of price changes) and equate volatility with risk. He asked why a rational person would substitute the opinions of the public (as reflected in volatility caused by mass decisions) for one's own measurement of the inherent risk of a company.

Buffett: The measurement of volatility: it's nice, it's mathematical, and wrong. Volatility is not risk. Those who have written about risk don't know how to measure risk. Past volatility does not measure risk. When farm prices crashed, [farm price] volatility went up, but a farm priced at $600 per acre that was formerly $2,000 per acre isn't riskier because it's more volatile. [Measures like] beta let people who teach finance use the math they've learned. That's nonsense. Risk comes from not knowing what you're doing. Dexter Shoes was a terrible mistake-I was wrong about the business, but not because shoe prices were volatile. If you understand the business you own, you're not taking risk. Volatility is useful for people who want a career in teaching. I cannot recall a case where we lost a lot of money due to volatility. The whole concept of volatility as a measure of risk has developed in my lifetime and isn't any use to us.

Munger: Finance taught in business schools is about 50% twaddle. We early recognized that very smart people do very dumb things. We wanted to figure out when and why.and who, so we could avoid them.

[kcowan]

So far we love the volatility in our AAPL shares. I guess there is good volatility and bad volatility

[martingale]

Suppose you wanted to immunize yourself against the ups and downs of the stock market. One way you could do this is to establish a fund that would smooth out the returns. In bad years the fund would top up the return you earn, and in good years you'd top up the fund with the extra return. You would then experience the return on your investment as being relatively constant, due to the presence of the fund.

One way to define risk is to say that it is proportional to the amount of money it would take to create such a fund, whether or not you actually create the fund. You can imagine hiring an actuary to help you work out how big this fund should be, and call that cost the risk you are taking.

A little bit of math (that any actuary can do) and some simplifying assumptions (like, you are only going to immnize against 99% or 99.9% of outcomes rather than 100%) will show that the cost of such a fund is proportional to the standard deviation of the returns. Therefore, if the size/cost of that immunizing fund is proportional to the risk you are taking, so is the standard deviation of returns.

You would include BOTH the ups and the downs in that calculation because you do need the ups to top the fund up when values rise, so your measure of risk needs to include not just the excess losses, but also the excess gains. You want the full variance, not the negatives-only semi-variance.

That, more or less, is why ordinary volatility is a good measure of risk. It is proportional to the cost of immunizing yourself from the variations.

Caveats: Unlike typical actuarial problems like insuring someone's life or insuring against bad weather it's hard to know whether the historical economic data we've got will be any use in the future, so you may have to guess at what the volatility will be going forward, rather than calculating it from the past values. Second, the market may not be normally distributed so the size of the fund may be under-estimated (and the risk understated). Nevertheless, it's not a bad starting point.

p.s., you could also immunize yourself by purchasing derivatives, and the cost of those derivatives would again be proportional to the standard deviation of returns--except in the extremes, where the normal distribution approximpation breaks down, and real world options pricing diverges from what the volatility measure predicts.

[ghariton]

it's hard to know whether the historical economic data we've got will be any use in the future, so you may have to guess at what the volatility will be going forward, rather than calculating it from the past values.

Yes. But that is not an argument against using volatility as a measure of risk. Rather, it is an arguemnt against (or perhaps using caution in)nusing past experience to forecast the future. If volatility is the right concept (and I think it is), then we can make our best guesses about its expected value in future, using historic values as just one input.

Second, the market may not be normally distributed so the size of the fund may be under-estimated (and the risk understated). Nevertheless, it's not a bad starting point.

Yes again. But here the trap is to believe that the variance (or standard deviation) is the only measure of volatility available. There are many others, some of which work quite well, even when the underlying distribution isn't Gaussian.

Elsewhere, someone cited the old chestnut that there is a difference between uncertainty and risk. Risk is applicable when you can estimate the probabilities of various outcomes, while certainty is the state of one's ignorance when even the probabilities of outcomes are unknown (a distinction first introduced by Frank Knight, as I recall.)

But if one is a Bayesian, as I am, there are no situations where one cannot estimate the probabilities of various outcomes. All probabilities are to be interpreted subjectively, and as long as you have a view on a subject, you hold it with a certain degree of confidence, which is quantifiable.

Georges

[gummy]

I suspect that most investors find Standard Deviation = Volatility = [s]Uncertainty[/s] a worthwhile concept. (I do.)

My objection is with the use of the word "risk" which is (for the ordinary Joe) associated with loss.

I'd like to propose another financial term:
A stock is said to be Sensational if its average monthly return over the previous 12 months is less than some market index.

There are variations, like S&P-sensational, etc.

As a matter of interest, most of the stocks I hold are TSX-sensational.

[martingale]

If you want to object to the use of the word "risk" to describe volatility in the stock market you necessarily also have to object to the use of the word "risk" in insurance policies against bad weather, illness, or death. It's the same definition of risk. In both cases, risk is measured as the cost of the fund necessary to immunize against the volatility.

In the case of insurance your premiums, and everyone else's, represents the annuitized cost of the fund required to immunize the insurance company against the risk (plus a little profit). In the case of investing no-one ever actually constructs such a fund, but if they did, the principle is exactly the same, and you could imagine paying into an annuitized fund that immunizes you against the risk of investing. Of course, in the case of investing it's likely that the price of the annuity would be nearly exactly equal to the difference between the return on stocks and the risk-free asset, less the costs of managing the fund, so no-one does that. In theory, though, they could.

You might well object to the entire financial industry's use of the word "risk" and say that it is different than the lay-person's understanding of risk. It is true that as a technical term from finance "risk" has a more specific definition. It's also true, though, that if you want to involve yourself in managing your own finances, reading financial literature, and so on, that you ought to familiarize yourself with jargon terms such as "risk", "duration", "option", or "preferred" that means something slightly different than their every-day use.

Your insurance policy does not claim to immunize you against ALL risk, just the specific risks listed in your policy. Similarly, a fund established to eliminate the impact of volatility on your return would not immunize you you against ALL risk from investing--only from "market risk". Beyond the "market risk" that is measured adequately by volatility there is the idiosyncratic risk of investing in any particular firm, inflation risks, currency risks, and the risk of an extraordinary event such as war or natural disaster that devestates the financial system, and so on.

So I think "risk" is the right word, but it needs to be qualified, it is "market risk" that volatility measures, and there are additional risks beyond market risk that an investor typically bears.

[gummy]

In the Webster definition of "risk" which I gave above, the words "loss" or "injury" or "hazard" or "peril" occur.
Using the word "risk" when considering these events is fine (with me).

To use "risk" to mean the cost of "immunizing against volatility" seems too far out in left field (for me).

If your returns oscuillated between -10% and +10% and I were blessed with returns 20% higher than yours (from +10% to +30%)
the cost to us of "immunizing against volatility" would be the same.

But, in my opinion, it's a stretch of the (non-financial) imagination to suggest that our "risk" is the same.

Of course, financial gurus can define anything they like and arrange arguments to show that their definition is [s]meaningful[/s] [s]valid[/s] useful.

I really like the one that goes:
"Scientists at WDL have labelled the major consituent of the moon as green cheese."
Then I could confidentlhy claim that ... uh, the moon is made of green cheese.
All you have to do is read up on the chemical constituents of this stuff.

[Gus]

In oil exploration economic modelling, risk and and uncertainty are strictly defined and are distinct concepts. Uncertainty means the statistical range of sizes (or values) of the field that you hope to find; it's a quantitative expression of the geological prospect model. Risk is the chance that the model is fatally flawed and that you will drill a dry hole. Both factors are quantifiable; uncertainty as a (usually) truncated lognormal distribution and risk as a probability.

This definition of risk is not very useful when applied to the financial market as whole, since a total loss is only possible in the event of a global catastrophe, the likes of which history has never seen. However, it would be more useful on the level of an individual stock or portfolio. It should be possible to estimate the probability of your uncertainty model of, say, Enron's future stock price is completely and catastrophically wrong and that you will suffer a total loss due to the fraud that was never part of your investment model.

If you want to object to the use of the word "risk" to describe volatility in the stock market you necessarily also have to object to the use of the word "risk" in insurance policies against bad weather, illness, or death. It's the same definition of risk. In both cases, risk is measured as the cost of the fund necessary to immunize against the volatility.

It's futile to ask the financial or insurance industry to change the language that they use, but I share Gummy's concern that the word "risk" has been hijacked to mean "volatility" without leaving a word to fill the lexical hole that "risk" fills for the financially unwashed. For, example, in insurance "risk" could have been used for the probability that a claim will be made and "uncertainty" or some such word used for an estimate of how big the claim might be. When I ask my insurance agent what risks are covered, I don't expect her to discuss "the cost of the fund necessary to immunize against the volatility".

[gummy]

... without leaving a word to fill the lexical hole that "risk" fills for the financially unwashed.

Aah, I wish I had said that!

[kcowan]

I guess I am more thinking of basic principles than mathematics. For investors, risk is the probability that their expectations will not be met. But as has been mentioned, it is really the probability that their targets are missed below not above.

And once the targets has been exceeded, then it is the cumulative target not regression to the mean. IOW if my target in 2006 was 7% growth but I made 30%, then my target for 2007 is 7% on top of my Dec. 31 2006 base. Whereas, with regression to the mean, a loss in 2007 of 12% would keep me "on plan" of 7% p.a. compounded.

So I am really lying to myself if I say that 7% p.a. is my real objective. Because I will be upset with the 12% decline needed in 2007 to regress to the mean. Also I should be equally upset about the 30% year because it was so volatile and not anticipated. In fact, if I am truly committed to my 7% p.a. plan, I should be taking corrective actions to get rid of the outlyers that caused that volatility.

So we seem to be dealing with psychology rather than mathematics.

(In a prior life, I ran a $3 billion annual plan. The executives wanted to impose a measure of forecast accuracy on the sales division because it had become a corporate standard for the executives. I fought against it and won by illustrating that we depended on people exceeding their targets to compensate for those that miss. Had we imposed the measure, sales forces would put orders in the drawer in order to have flexibility to make their forecasts. But some would fail to make their targets and, as a company, our result would be worse because we would at best make our corporate targets only when all sales divisions made their targets - an impossibility.)

So my advice is the beware the one sided probability distribution!

[martingale]

There is a difference between "risk" and "measure of risk".

Your Webster's definition is telling you a risk is the chance of something unpleasant happening, like, losing your money on the stock market. But how much risk is that? Websters doesn't tell you how to measure it. To measure risk you need the tools of modern finance.

The measure of risk is the cost of the insurance premium you have to pay to compensate the unpleasant event if it happens. In other words (by some mathematics) it's proportional to volatility.

The unpleasant event you are hoping to compensate is associated with some probability distribution. The first and second moments of that distribution (the expected return and volatility) are enough information for an actuary to tell you how much it will cost to compensate the risk if it happens. You seem pre-occupied with the third moment, the asymmetry of the risk, for some reason that I don't understand: You don't usually need the third moment of the distribution to predict how much it will cost to insure against it; or rather, the assymmetry will have a smaller impact on the cost of insurance than the volatility will.

If you've accepted the mean as a viable measure of return, it seems to me that you are then pretty much forced to accept volatility as risk.

If you want to complain about the inappropriate use of moments of the probability distribution we can have an interesting conversation about whether the mean return is what you should be using. Why are you using mean returns?

The average investors is NOT in the position of an actuary: We don't play the game enough times to be guaranteed the long-run return in the long run. For example, if a loss of capital would be a catastrophe for you, you may not really be comforted by the notion that it'll only happen 0.5% of the time--any risk at all may be unacceptable to you. So, volatility as risk may be great for a pension fund with a virtually unlimited time horizon, but a poor measure for someone who has a 10-15 year investing horizon.

In that case you may say sure, it's a good measure of risk for a pension fund, but a poor measure of risk for me: I'm concerned about the return I might earn in the short run, and the maximum loss I could face in the short run, and not interested in the long run at all. You would, then, reject both the mean return and volatility as sensible measures of investment return and investment risk. You could, for example, decide that you want to use the minimum return achieved over the last 10 years as your measure of return, and the maximum loss ever observed as your risk. This is all very arbitrary, but we're looking at the short-run, where uncertainty looms large, so possibly we can't do any better.

(The point hiding in there is if you are going to exclude the up-side surprises from your risk measure, what business do you have including those up-side surprises in your return?)

In any case, in the long run, the mean is a sensible measure of return, and volatility is a sensible measure of risk. One tells you how much, in the long run, you will earn; the other tells you how much you would have to pay an insurer to avoid the fluctuations along the way.

[NormR]

Suppose you wanted to immunize yourself against the ups and downs of the stock market. ...

Or you could buy T-Bills.

[Gus]

This is all very arbitrary, but we're looking at the short-run, where uncertainty looms large, so possibly we can't do any better.

(The point hiding in there is if you are going to exclude the up-side surprises from your risk measure, what business do you have including those up-side surprises in your return?)

In any case, in the long run, the mean is a sensible measure of return, and volatility is a sensible measure of risk. One tells you how much, in the long run, you will earn; the other tells you how much you would have to pay an insurer to avoid the fluctuations along the way.

In the business models I have run, the up-side surprises are (or should be) present in the long tails of the lognormal distributions of outcomes. The arithmetic mean of the distribution incorporates the up-side appropriately. In the case of the oil exploration projects (where the chance of failure is often greater than 50%), it is far better to use a risked as opposed to an unrisked mean (of the barrels expected or the dollar value of the field) if you need a single number, ceteris paribus, to rank the prospect against others. (The risked mean being the mean of the uncertainty distribution multiplied by the probability of success.)

It's true that we often focus asymmetrically on the downside when looking at uncertainty or volatility. That's a definite psychological bias because most of us anticipate being able to cope quite nicely should our investments exceed our expectations. ( This conservative bias can lead to missed investment opportunities, admittedly. A manager I once worked for used to threaten his geologists with firing if we found a field bigger than the 1 in 100 (P99) case on our probability distributions. An emptier threat than this has never been uttered.)

I realize that you don't have your advisor hat on when you engage in these discussions but I hope you understand that, for many of your clients, their understanding of the word risk, at least when used quantitatively, is a dimensionless number between zero and one.

[martingale]

In the business models I have run, the up-side surprises are (or should be) present in the long tails of the lognormal distributions of outcomes.

Yes, as they should be. I do agree with most of your post.

I do want to point out that a business and an individual are in very different circumstances from a risk analysis perspective.

A business should act in the interests of its shareholders. The shareholders hold a diversified portfolio of companies and are not particularly harmed if an individual business goes bankrupt. An individual investor saving for retirement, though, only has one life to live, and if they screw it up, they're just screwed.

So, for example, a business should ALWAYS take a bet that has a 1/10 chance of paying off 1000% but a 9/10 chance of bankrupting the business, whereas, an individual investor never should take such a chance. Shareholders who own bits of many thousands of businesses will win that bet often enough for it to be worthwhile. The individual only gets one chance, and a 9/10 chance of bankruptcy is a catastrophe.

This is why older investors should almost always hold a large portfolio of bonds, even though you can prove that a high percentage of times holding all stock would do better. The tiny probability of short-run catastrophe cannot be diversified away, so it makes the whole scenario unacceptable despite the great expected return. In essence, an investor to some extent has to maximize their minimum return, whereas a business is aiming to maximize it's mean return.

[NormR]

So, for example, a business should ALWAYS take a bet that has a 1/10 chance of paying off 1000% but a 9/10 chance of bankrupting the business, whereas, an individual investor never should take such a chance. Shareholders who own bits of many thousands of businesses will win that bet often enough for it to be worthwhile. The individual only gets one chance, and a 9/10 chance of bankruptcy is a catastrophe.

Sounds like 'Enron' thinking to me. Have you factored jail time into your equation?