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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ghariton
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Re: Risk = ??

Post by ghariton »

LadyGeek wrote:
ghariton wrote:I've been speculating for a while that three-factor models -- volatility, skewness and kurtosis -- give more insight into security valuation than the more traditional approaches.
I'm confused on your terminology.

The "three-factor models" I'm thinking of, aka Fama and French three-factor model use regression analysis to curve-fit past performance. Goodness of fit (R^2) is the corresponding metric. (See: Fama-French three-factor model analysis)

volatility, skewness and kurtosis are the 2nd (some associate volatility with variance), 3rd, and 4th moments of a probability distribution. See: Moment (mathematics)
A three-factor model is any model that tries to explain expected returns in terms of three factors. It is usually specified in terms of a linear equation of the sort

Y = A + B(1)*X(1) + B(2)*X(2) + B(3) *X(3)

although there is no strong theoretical reason that it be linear. The B's are usually estimated by running a multiple regression, using historic data.

Fama and French have suggested that one of the variables be volatility (either relative to the market, i.e. beta, or on its own, i.e. variance), value (e.g. price/book ratio) and size of company. Some others suggest a four-factor model, where there would be an X(4) measuring momentum. But other measures can be reasonable candidates for the three (or four) factors.

I would continue to use volatility as X(1), but I would use the expected skewness of returns as X(2) and expected kurtosis as X(3). As usual, since we don't have measures of expected skewness and kurtosis, we would probably use historic data to calculate the first four moments of the distribution of expected returns.

In this formulation, B(2) would be the price of positive skew, reflecting the empirical observation that many people like the possibility of large wins even if of low probability (e.g. lottery tickets, IPOs) and are willing to pay for it, by accepting a lower expected return (or equivalently by bidding up the price). Similarly B(3) would be the price of kurtosis or fat tails, i.e. the possibility that very rare events are in fact not that infrequent. Most people would accept a slightly lower expected return, or equivalently pay a higher price, to avoid "fat tails", (e.g. hedging with options -- now the price includes the premium of the option).

The regression analysis would attempt to estimate just how much people in aggregate are willing to pay for positive skewness, or to avoid fat tails. If a successful model could be developed, it could be used to "value" securities and to detect which ones are mispriced -- the philosopher's stone of investment analysis :wink:.

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Re: Risk = ??

Post by newguy »

ghariton wrote:The regression analysis would attempt to estimate just how much people in aggregate are willing to pay for positive skewness, or to avoid fat tails. If a successful model could be developed, it could be used to "value" securities and to detect which ones are mispriced -- the philosopher's stone of investment analysis
First of all I'd like to know what kurtosis adds to variance. THey seem to be the same thing with a higher power.

How would you use it to value securities? In FF they regress against returns. I think you're looking at a different way to do VaR. It might add something in that case if say abnormal skewness tended to persist for a while.

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Re: Risk = ??

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newguy wrote:First of all I'd like to know what kurtosis adds to variance. THey seem to be the same thing with a higher power.
They are two independent characteristics of any probability distribution. For a given mean and a given variance (or other measure of volatility), a distribution with high kurtosis has more probability of "tail" or extreme events, and lower probability of events around the mean. You can see this by superimposing pictures of the "Student's t" distribution with the same mean and variance, but different degrees of freedom n. For large n, this looks like a Gaussian distribution. As n gets smaller, the tails get bigger and the central spike gets "sharper". My understanding is that a lot of financial modelling these days assumes a Student's t with n = 4 (moderate kurtosis) or n = 2 (high kurtosis). (Of course, there are many distributions other than Student's t that have higher kurtosis than the Gaussian.)

A major failing of the financial models used before 2008 is that almost all of them assumed a Gaussian distribution, or at least a low kurtosis, and hence underestimated the probability of tail events.
How would you use it to value securities? In FF they regress against returns. I think you're looking at a different way to do VaR. It might add something in that case if say abnormal skewness tended to persist for a while.
In FF they regress returns against three factors -- volatility, value (price/book) and size. I'm suggesting regressing returns against volatility, skewness and kurtosis of the distribution of returns of that security (or portfolio). Just change the independent variables in the regression.

Again, skewness, kurtosis and volatility are all independent attributes. A security might have the same mean, volatility and skewness but higher or lower kurtosis. I.e. there may be more extreme events than "normal" for an investment of that volatility, and when they do occur, they might be skewed toward large gains.

I try not to think about VaR, as I find it a very misleading measure.

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Re: Risk = ??

Post by IdOp »

newguy wrote:First of all I'd like to know what kurtosis adds to variance. THey seem to be the same thing with a higher power.
To add to ghariton's reply, since

x2 > x4, when x < 1

but

x2 < x4, when x > 1

then kurtosis, as compared to variance, might be intuitively expected to be more sensitive to parts of the distribution away from the mean than near the mean.
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Re: Risk = ??

Post by newguy »

Well I played around and kurtosis does seem to be quite different from variance even if somewhat positively correlated.

My problem with building a regression model is that in normal FF it compares returns to returns. I'm just not sure comparing a statistic to a return would make much sense. At least VaR tries to predict volatility from volatility. However looking at some charts, it seems to relate a little bit.

Here's scatterplots of rolling SPY monthly returns with the 3 stats.
monthly.png
monthly.png (9.47 KiB) Viewed 4137 times
And yearly
yearly.png
yearly.png (10.98 KiB) Viewed 4137 times
Interesting how skew and kurtosis correlation went negative at longer time frames.

I think a machine learning algo is better suited to make predictions from that stuff. It can do things like find clusters of points where they may have predictive ability. Note that the graphs are points for both return and a stat at the end of the day, it's not making predictions, for that you'd need something like VaR using some kind of GARCH. ie, predict the volatility then get the expected return.

newguy

add:code

Code: Select all

library(quantmod)
library(e1071)#libraries used

getSymbols(c("SPY"), src='yahoo', from="1993-01-29")#dnld data
spy.logr <- log(dailyReturn(SPY[,"SPY.Adjusted"])+1)  #log returns
period <- 21 # about monthly
spy.retn <- rollapply(spy.logr, period, sum, by=period, align="right")
spy.var <- rollapply(spy.logr, period, var, by=period, align="right")
spy.skew <- rollapply(spy.logr, period, skewness,by=period, align="right")
spy.kurt <- rollapply(spy.logr, period, kurtosis, by=period, align="right")
plot.fit<-function(x,y){
  plot(coredata(spy.retn)~coredata(x), xlab=y, ylab="log returns")
  abline(fit <- lm(spy.retn~x), col = "red")
  legend("top", bty="n", legend=paste("R2 =", 
         format(summary(fit)$adj.r.squared, digits=2)))
}
par(mfrow=c(1,3)) #3 graphs per line
plot.fit(spy.var,"variance")
plot.fit(spy.skew,"skew")
plot.fit(spy.kurt,"kurtosis")
Last edited by newguy on 11 Sep 2013 14:02, edited 1 time in total.
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Re: Risk = ??

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Re: Risk = ??

Post by LadyGeek »

It all goes back to the predictability of the data. Take a look at finiki: Risk and return - finiki, the Canadian financial Wiki (I'm the primary author)

The Portfolio diversification section contains a VaR analysis. 2008 unexpectedly (pun intended) threw the analysis out the window. If you want to see how the VaR analysis was done, download the Excel file. The analysis depends on the accuracy of the asset correlations.

To investors who are having problems following the math- don't worry about it. It's more important to understand the concepts described in the finiki article.
Last edited by LadyGeek on 10 Sep 2013 19:02, edited 1 time in total.
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Re: Risk = ??

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LadyGeek wrote:It all goes back to the predictability of the data.....If you want to see how the VaR analysis was done
That's not really a prediction, or what I'd call VaR. VaR is usually done using something like GARCH for the next day's volatility. It assumes that historical volatility has some predictive power of future volatility, declining over time. Here's the first google link I got, but it looks good.

http://www.portfolioprobe.com/2013/08/2 ... stimators/

Notice that the GARCH model is wrong on the next day's volatility <5% of the time, which is what was asked for.

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Re: Risk = ??

Post by parvus »

ghariton wrote:I try not to think about VaR, as I find it a very misleading measure.
5% of the time?
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Re: Risk = ??

Post by ghariton »

parvus wrote:
ghariton wrote:I try not to think about VaR, as I find it a very misleading measure.
5% of the time?
If your time horizon is one day, yes. My investing horizon -- or even my average holding time -- tends to be a bit longer.

The other problem is that VaR tells you a threshold loss that will be met or exceeded a certain percentage of the time. It does not tell you how big your average loss is, given that you hit the threshold.

More generally, I hate one-number summary statistics. They conceal detail that is often essential. By contrast, of course, CEOs with their very short attention spans love such summary statistics.

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Re: Risk = ??

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Ah yes, the CEOs swanning about, before the screen goes black. :wink:
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Re: Risk = ??

Post by LadyGeek »

newguy wrote:...VaR is usually done using something like GARCH for the next day's volatility. It assumes that historical volatility has some predictive power of future volatility, declining over time. Here's the first google link I got, but it looks good.
http://www.portfolioprobe.com/2013/08/2 ... stimators/

Notice that the GARCH model is wrong on the next day's volatility <5% of the time, which is what was asked for. newguy
I've encountered GARCH before, but never really understood it. Thanks to my MegaEmployer, I have an online subscription to some excellent finance texts (they think I'm using this site for engineering :wink: ). From my favourite finance author, Frank J. Fabozzi:
Fabozzi wrote:Forecasting Yield Volatility
...the yield volatility, as measured by the standard deviation, can vary based on the time period selected and the number of observations. Now we turn to the issue of forecasting yield volatility. There are several methods.

Equally Weighted Average Method...

Weighted Average Method...

ARCH Method and Variants
A times series characteristic of financial assets suggests that a period of high volatility is followed by a period of high volatility. Furthermore, a period of relative stability in returns appears to be followed by a period that can be characterized in the same way. This suggests that volatility today may depend upon recent prior volatility. This can be modeled and used to forecast volatility.

The statistical model used to estimate this time series property of volatility is called an autoregressive conditional heteroscedasticity model or ARCH model. Here “conditional” means that the value of the variance depends on or is conditional on the value of the random variable. “Heteroscedasticity” means that the variance is not equal for all values of the random variable.
From what I understand above, the models assume a similar future based on past performance. The full text shows periods of performance using "t-1" which hints at recent performance (vs. "t - n" periods). I could be wrong, but that's what I see.

Attribution: Frank J. Fabozzi; Steven V. Man, "Introduction to Fixed Income Analytics: Relative Value Analysis, Risk Measures, and Valuation," Second Edition, October 12, 2010, ISBN 978-0-470-57213-9, accessed 10-Sep-13, Safari Books Online.
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Re: Risk = ??

Post by parvus »

George and I once got into a discussion, years ago, about heteroscedasticity (thanks to my misspelling). I interpreted it simply as moving correlations/covariances.
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Re: Risk = ??

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LadyGeek wrote:From what I understand above, the models assume a similar future based on past performance.
That's essentially right. It's the future of volatility though, not returns. It also tries to model the behaviour of volatility which is heteroskedastic, ie. the volatility spikes and decays back to a mean at some rate. Look at a graph of volatility and you'll see this.
vol.png
vol.png (7.32 KiB) Viewed 4036 times
VaR is usually just a confidence interval around the returns taken from terms fitted to the series using GARCH (or some variant of it) .
var.png
var.png (8.87 KiB) Viewed 4036 times
You can also see how often it goes out of bounds by fitting on previous data and then doing a forecast 1 day at a time for some new data using the previous fitted behaviour.
exceed.png
The red dots are where the daily loss was greater than expected 95% of the time.

Here's the code to add to the previous stuff where I'll go add the code

Code: Select all

library(rugarch)
gspec <- ugarchspec(mean.model=list(armaOrder=c(0,0)), distribution="std")
gfit <- ugarchfit(gspec, spy.logr)
par(mfrow = c(2,1))
plot(gfit, which = 2)
plot(gfit, which = 3)
groll <- ugarchroll(gspec, spy.logr,refit.window = "moving")
plot(groll, which = 4)
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Re: Risk = ??

Post by ghariton »

A person's risk aversion varies with stress levels:
Financial markets may be more vulnerable to traders' stress levels than previously thought, according to a scientific study which found that high levels of the stress hormone cortisol can induce risk aversion.

The findings, which turns on its head the assumption that traders appetite for risk-taking remains constant throughout market up and downs, suggests stress could in fact make them more cautious, exacerbating financial crises just at a time when risk-taking is needed to support crashing markets.

In a study of City of London traders and of the effect of cortisol on behaviour, researchers led by Dr John Coates - a former Goldman Sachs and Deutsche Bank derivatives trader turned neuroscientist - said this tendency towards caution could be an "under-appreciated" cause of market instability.

<snip>

"Traders, risk managers, and central banks cannot hope to manage risk if they do not understand that the drivers of risk taking lurk deep in our bodies," Coates said. "Risk managers who fail to understand this will have as little success."
I think the lesson applies to individual investors as well. Be careful if you are trading when you are under stress, either because of financial markets or for personal reasons. Wait until you have calmed down.

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Re: Risk = ??

Post by mcbar »

I wonder if it follows, then, that an absence of stress leads to excessive risk taking, the type of over-exuberance that tends to precede market bubbles.
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Re: Risk = ??

Post by parvus »

I wonder sometimes about the definition of risk, and today I was wondering again. I have some scary investments -- in the sense that I don't know whether they will work out or not. Some have, some not.

I was commenting to a friend, a Depression-era child, that over the past decade I've made $7 for every $1 that I lost. But that $1 loss is the most significant for her. She is still grateful to me that, as her courier (I was really nothing more), I went to Merrill Lynch's offices on University Ave. and handed over a cheque to purchase 8% Canadas. That was 20 years ago. No chance of loss, plus a reasonable income.

It worked out -- for her.

With that anchor, I'm not going to convince her that the equity risk premium pays off -- over longer holding periods.

This makes me doubtful that the orthodox ETF/index contingent really understands risk -- or at least has the stomach for it. They get caught up in the minutiae of currency hedging and tracking error, and thus want the lowest-cost market risk, without thinking through whether market risk is something that they really want to bear at all.

I say this after having rebalanced my portfolio. I had to ask, what risks am I willing to choose. I admit to being opportunistic and speculative (which makes me perfect for CAPM and different risk appetites, although I'm not terribly a rational investor).
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Re: Risk = ??

Post by ghariton »

parvus wrote:This makes me doubtful that the orthodox ETF/index contingent really understands risk -- or at least has the stomach for it.
And then you get the folk who experienced the downside of risk all too vividly during 2008-2009, got very scared, and have spent the last five years on the sidelines. They have lost an opportunity to gain.

For those who like to define risk in terms of the possibility of loss, rather than in terms of volatility, how do they define loss? Is it against a benchmark of zero, or is it against a benchmark of average market return (the index, if I dare use that word)? Just because an opportunity lost seems more intangible than a negative sign in front of your change in position, doesn't mean that it is any less real.

To try to make that a bit more intuitive, think of a world of inflation running at 5% and nominal returns on say the S&P 500 averaging 10%. If one's goal is to avoid or minimize losses, one might be tempted to put one's money in a HISA at 3%. But that merely guarantees a loss, both against the S&P 500 and against one's purchasing power. In other words, nominal dollars are not a good benchmark against which to measure loss, an consequently risk.

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Re: Risk = ??

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parvus wrote:This makes me doubtful that the orthodox ETF/index contingent really understands risk -- or at least has the stomach for it. They get caught up in the minutiae of currency hedging and tracking error, and thus want the lowest-cost market risk, without thinking through whether market risk is something that they really want to bear at all.
This has nothing to do with "the orthodox ETF/index contingent" specifically. This forum has many posters who analyse individual stocks and who also get caught up in all sorts of related minutiae, etc., thus ignoring the forest for the trees.

You need a financial plan before you invest. A crucial aspect of that plan is risk, including your ability, willingness and/or need to take it. Deal with that issue first. That's usually the hardest part. Then design your portfolio, be it indexed or not, accordingly.
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Re: Risk = ??

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Bylo Selhi wrote: You need a financial plan before you invest. A crucial aspect of that plan is risk, including your ability, willingness and/or need to take it. Deal with that issue first. That's usually the hardest part. Then design your portfolio, be it indexed or not, accordingly.
:thumbsup: :thumbsup:
Actually the hardest part is sticking to your plan.
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Re: Risk = ??

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Bylo Selhi wrote:This has nothing to do with "the orthodox ETF/index contingent" specifically. This forum has many posters who analyse individual stocks and who also get caught up in all sorts of related minutiae, etc., thus ignoring the forest for the trees.
I don't doubt that at all. My Depression-era friend suffers not from CRRA (constant relative risk aversion in the jargon of CAPM) but absolute risk aversion.

If I have put things too starkly, as the orthodox ETF/index contingent, it's only because that's the way we conceptualize markets: as benchmarks. When folks ask for advice here, they generally talk about ETFs/index funds and what they should allocate among the given choices. They seem to be focused on cost.

Now, in rebalancing my portfolio -- I don't do it very often, perhaps every three years -- I was intrigued by how well my mutual funds did versus my ETFs. I would have expected the ETFs to do better. They didn't. So I have some difficult decisions to make because I was hoping to rebalance more into ETFs.

That got me into wondering. Take it as you will. I realized I had a much stronger "gambling" instinct than I had thought. Not "shoot out the lights or swing for the fences." I was willing (well, with some data) to deviate from the benchmarks.

But I have a value bias.
You need a financial plan before you invest. A crucial aspect of that plan is risk, including your ability, willingness and/or need to take it. Deal with that issue first. That's usually the hardest part. Then design your portfolio, be it indexed or not, accordingly.
[/quote][/quote]
Yes, of course. A financial plan is crucial for beginners. Then comes the investment policy statement -- when they've got their debts and liabilities under control.

Beyond that, I'm not sure a cookie-cutter 40% bonds, 60% equities portfolio works, whether it's ETFs or some other investments that can be comparable to a recognized benchmark.

The financial plan, presumably, is to pay down debt, as quickly as possible and free up money for saving -- assuming the lifecycle approach, such that rational people borrow young, earn in their middle years, and accumulate enough to have the same level of consumption in their retirement: i.e., income smoothing. Nice theory. Got the Nobel Prize. Not sure it actually describes (nor actuates) people's real behaviour.

Investing, depending on risk tolerance, may not be the best way to achieve income/consumption smoothing.

Yet, we take our lights from conventional benchmarks and plug them into the most readily available ETFs/index funds.

That assumes a degree of risk beyond employment income risk. For what purpose? To replace income? Not likely, since there is no duration match, and there is more volatility in investment income than there is in employment income.

So what is the investment purpose? The lifecycle hypothesis? Speculation? Something different?

From a lifecycle perspective, I would suggest just buy the market and forget about it. If it underperforms your wages, oh well. If it outperforms, bonus!
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Re: Risk = ??

Post by Flaccidsteele »

With regards to the title of the thread. Only speaking for myself, the definition of risk depends on the individual. If an individual has a lack of knowledge around a particular type of investment, then for them, it is risky. Vice versa.
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Re: Risk = ??

Post by ghariton »

Flaccidsteele wrote: the definition of risk depends on the individual.
True in a world of knowledgeable investors and lots of good data. Risk is indeed multidimensional, and different dimensions have different importance for different people. For example, some may worry more about relatively infrequent losses that are very large. Others might worry more about smaller but more frequent losses. Yet others may worry more about losses that occur when they are already under financial stress, e.g. losses during a downturn.

And of course there are different views on the definition of "loss", as I mentioned upthread. For some, a loss is a reduction in the number printed at the bottom of their monthly statement, i.e. a reduction in nominal dollars. For others (like me) a loss is a reduction in purchasing power, i.e. falling behind inflation. For yet others a loss is doing worse than a benchmark, e.g. a pension fund which has mounting liabilities as well as assets. Finally, there is the concept of lost opportunities, so that a loss might be underperformance of a broad index, e.g. the S&P 500 or the Russell 2000.

Unfortunately, all of this is too difficult for most people -- they don't have the knowledge or patience, they are not used to thinking in abstractions, etc. So the financial community, aided and abetted by the academics, has invented a set of summary measures that are supposed to be useful in a vast range of situations. They are better than nothing. But the popular ones all suffer from a fatal flaw IMO -- they all rely on past experience and historic data. And as the regulator insists on mutual fund peddlers telling us: The past is not necessarily a good guide to the future. The regulators insist on this disclaimer for returns. But it applies just as much to risks.

So what to do? I pay little or no attention to historic variances, betas and correlations, or indeed to historic data in general. Rather I try to peer into the future, however imperfectly: In what kind of markets is a company operating? What competition does it face? Are its products essential or nice-to-have? How is technology affecting its business? What will be the impact of more globalization? And so on.

Or you can do as I did: Decide that this is all too much work, and purchase broad passively-managed index funds. We don't know which companies will do well over time, but we do know that the share of national income that is going to capital (as opposed to labor) is growing, and I want a piece of that.

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Re: Risk = ??

Post by Norbert Schlenker »

parvus wrote:I'm not sure a cookie-cutter 40% bonds, 60% equities portfolio works, whether it's ETFs or some other investments that can be comparable to a recognized benchmark... and accumulate enough to have the same level of consumption in their retirement: i.e., income smoothing. Nice theory. Got the Nobel Prize. Not sure it actually describes (nor actuates) people's real behaviour.

Investing, depending on risk tolerance, may not be the best way to achieve income/consumption smoothing...

From a lifecycle perspective, I would suggest just buy the market and forget about it. If it underperforms your wages, oh well. If it outperforms, bonus!
This seems a bit of a ramble, at the end of which you suggest the conventional wisdom anyway. I can't tell if you think the income smoothing goal is right, or even right just for you. You seem to have put a lot of thought into it and, when push comes to shove, gone with "Whatever!".

FWIW, I think the income smoothing - more accurately comsumption smoothing - approach is broad brush correct. IMHO wildly varying consumption patterns are not of benefit emotionally. But then I'm an ant, not a grasshopper and, while I believe that I share that trait with many other FWF members, there are many grasshoppers in the world for whom this doesn't hold. Humans are adaptable though, so if you think you'll be happy to die in your workboots, or can go from making a good income and blowing it all and then some to living in a trailer back in the woods on OAS+GIS+CPP, without emotional upset, then there's no need to worry about saving or investing.
ghariton wrote:...different views on the definition of "loss"...
To add yet another view, an inability to meet one's obligations as they come due. How to heat a dwelling after retirement at the low end, how to pay the staff on the yacht at the top end. It's tempting to view the second as froth and frivolity but, if that's what you're used to being able to do, giving it up might be a pretty painful process.
Nothing can protect people who want to buy the Brooklyn Bridge.
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NormR
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Re: Risk = ??

Post by NormR »

Norbert Schlenker wrote:IMHO wildly varying consumption patterns are not of benefit emotionally.
I think it depends on the scale you're thinking about. I doubt that most people are keen on living it up for a few years and then losing everything.

However, living high off the hog every day reduces the pleasure of occasional luxuries. Who wants to eat premium steak every day? It's much better have one on occasion. In some cases it might be wise to vary consumption patterns - while maintaining the capability not to have to.
Last edited by NormR on 16 Mar 2014 23:11, edited 1 time in total.
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