Redefining risk

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Don Lawson
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Post by Don Lawson »

Wow, what a lively discussion of risk. There are many very intelligent people on this forum.

What started my thought of 100% equity portfolio through retirement was an article I read by Paul Merriman and I'm hoping some of you can help me dissect this a little.

Full Disclosure: I am not currently implementing any of these strategies because I am 30+ years away from needing retirement income.

Here is a link to the article: (Apparently I'm too new to post the link to the .pdf file but google "Paul Merriman Distributions .pdf"

Paul examines different withdrawal strategies during the 40 year period of 1970-2010. He starts off with 1mm dollars and using various allocations he examines: 4% flexible and inflation adjusted rate, 5% flexible and inflation adjusted rate, and a 6% flexible and inflation adjusted rate.

His portfolios are constructed using DFA funds and he is including a 1% management fee and trading expenses.

What strikes me immediately is the difference between the S&P 500 w/ dividends portfolio and the 100% global equity portfolio. Asset allocation within equities makes a huge difference! It's not just about equity to fixed income ratio.

In a 100% equity portfolio (SP500 including dividends) using a 5% withdrawal rate that is adjusted every year based on the CPI, your money is gone before your 22nd year.

In a 100% equity portfolio (globally diversified) using a 5% withdrawal rate that is adjusted every year based on the CPI, your million dollars not only lasts the full 40 years, but you still have 34 million in your portfolio in 2010.

What a stark difference. It is also interesting to note that no equity allocation below 50% survived the 5% fixed (CPI adjusted) withdrawal plan for the entire 40 years.
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Don Lawson
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Post by Don Lawson »

pkcrafter wrote:
Loss of principal is a risk: loss of purchasing power is also a risk. Dismissing the first definition and only looking at the second seems to me to be rather short-sighted.


Paul
Isn't loss of principal a risk only because you are losing purchasing power?
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Don Lawson
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Post by Don Lawson »

What is also interesting to me from the Merriman article is that using a 100% global equity portfolio and a flexible withdrawal plan, 4% really is greater than 6%.

After the 40 year period using 4% withdrawal rate every year you would receive a cumulative $17mm and using a 6% withdrawal rate you would receive a cumulative $14mm. Of course most of the excess distributions are back end heavy but a 4% withdrawal rate caught up to a 6% withdrawal rate after 17 years. Also, with the 4% rate you have a significantly larger portfolio to pass on to heirs.
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nisiprius
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Post by nisiprius »

Don Lawson wrote:In a 100% equity portfolio (SP500 including dividends) using a 5% withdrawal rate that is adjusted every year based on the CPI, your money is gone before your 22nd year.

In a 100% equity portfolio (globally diversified) using a 5% withdrawal rate that is adjusted every year based on the CPI, your million dollars not only lasts the full 40 years, but you still have 34 million in your portfolio in 2010.
That's because 5% is high.

The characteristic of conservative investments is that they're predictable. There's a low but fairly well-defined amount they can provide; draw less than that and the chance of failure is low, draw more than that and the chance of failure is high. Risky investments, by virtue of being less predictable, are less certain to fail at higher withdrawal rates. So, to make risky investments look good, simply pick a higher withdrawal rate, and the chances of failure will decline the more of the risky investment you include.

To see this clearly, use reductio ad absurdam: run Monte Carlo simulations on portfolios assuming a 100% withdrawal rate and portfolios consisting of varying amounts of stocks, bonds, and lottery tickets. You will quickly deduce that given that withdrawal rate, the safest portfolio--the one with the highest success rate--is 100% lottery tickets.

If you want to try this sort of thing and play fair, you should try to forget every study you've ever seen, and start by deciding what you think, for planning purposes, is an appropriate failure rate, one that is satisfactory to you with your own risk tolerance, before considering anything else. If I handed you a pair of dice at age 65 and said "Roll them. If they come up snake-eyes you will be destitute at age 80, otherwise you will have a comfortable retirement," would you roll them? If not, then you want a failure rate of less than 3%.

If ask what is the largest safe withdrawal rate having first defined "safe" to mean "a failure rate of 3% or less," what I've seen in every study I've looked at, is that the withdrawal rate is almost independent of portfolio composition. It's always around 3-3.5%. Adding stocks doesn't enable you to safely withdraw more. What it does do is to increase your average final value, i.e. it doesn't help you but it helps your heirs.

Try it yourself using Vanguard's nest egg retirement calculator.

The Merriman paper--the link seems to be at http://www.merriman.com/PDFs/Distributions.pdf --that isn't even a statistical study, it's one specific time period. What can I say but, "Great, now we know what works best if we happen to be starting in 1970?"
Last edited by nisiprius on Wed Aug 24, 2011 11:02 am, edited 1 time in total.
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Post by pkcrafter »

Don Lawson wrote:What is also interesting to me from the Merriman article is that using a 100% global equity portfolio and a flexible withdrawal plan, 4% really is greater than 6%.

After the 40 year period using 4% withdrawal rate every year you would receive a cumulative $17mm and using a 6% withdrawal rate you would receive a cumulative $14mm. Of course most of the excess distributions are back end heavy but a 4% withdrawal rate caught up to a 6% withdrawal rate after 17 years. Also, with the 4% rate you have a significantly larger portfolio to pass on to heirs.
Don, here you have completely dismissed risk as if it did not exist. The reality of risk is that you may not end up with 17mm, in fact you could end up with far less.

See John Norstad's classic article. You can skim the article and just look at the chart at the bottom of the page to understand possible returns.

http://homepage.mac.com/j.norstad/finan ... -time.html
While the basic argument that the standard deviations of the annualized returns decrease as the time horizon increases is true, it is also misleading, and it fatally misses the point, because for an investor concerned with the value of his portfolio at the end of a period of time, it is the total return that matters, not the annualized return. Because of the effects of compounding, the standard deviation of the total return actually increases with time horizon. Thus, if we use the traditional measure of uncertainty as the standard deviation of return over the time period in question, uncertainty increases with time.

Paul
When times are good, investors tend to forget about risk and focus on opportunity. When times are bad, investors tend to forget about opportunity and focus on risk.
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Don Lawson
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Post by Don Lawson »

nisiprius wrote:That's because 5% is high.

The characteristic of conservative investments is that they're predictable. There's a low but fairly well-defined amount they can provide; draw less than that and the chance of failure is low, draw more than that and the chance of failure is high. Risky investments, by virtue of being less predictable, are less certain to fail at higher withdrawal rates. So, to make risky investments look good, simply pick a higher withdrawal rate, and the chances of failure will decline the more of the risky investment you include.

To see this clearly, use reductio ad absurdam: run Monte Carlo simulations on portfolios assuming a 100% withdrawal rate and portfolios consisting of varying amounts of stocks, bonds, and lottery tickets. You will quickly deduce that given that withdrawal rate, the safest portfolio--the one with the highest success rate--is 100% lottery tickets.

If you want to try this sort of thing and play fair, you should try to forget every study you've ever seen, and start by deciding what you think, for planning purposes, is an appropriate failure rate, one that is satisfactory to you with your own risk tolerance, before considering anything else. If I handed you a pair of dice at age 65 and said "Roll them. If they come up snake-eyes you will be destitute at age 80, otherwise you will have a comfortable retirement," would you roll them? If not, then you want a failure rate of less than 3%.

If ask what is the largest safe withdrawal rate having first defined "safe" to mean "a failure rate of 3% or less," what I've seen in every study I've looked at, is that the withdrawal rate is almost independent of portfolio composition. It's always around 3-3.5%. Adding stocks doesn't enable you to safely withdraw more. What it does do is to increase your average final value, i.e. it doesn't help you but it helps your heirs.
Fantastic perspective and I think by far the best post on this thread. Re-framing the question as you do makes a lot of sense.

I haven't seen that vanguard tool so thank you.

One thing that I notice with all the Monte Carlo Simulations is that with what we know now (fama-french three factor model) that we still use the SP 500, or in the case of the vanguard calculator the Wilshire 5000 (US market cap weighted index).

How much different would the numbers look if a truly diversified US/International, small value tilted portfolio was used? For the time period 1970-2010, I would guess the difference is significant.
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Don Lawson
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Post by Don Lawson »

pkcrafter wrote:
Don, here you have completely dismissed risk as if it did not exist. The reality of risk is that you may not end up with 17mm, in fact you could end up with far less.

See John Norstad's classic article. You can skim the article and just look at the chart at the bottom of the page to understand possible returns.
While the basic argument that the standard deviations of the annualized returns decrease as the time horizon increases is true, it is also misleading, and it fatally misses the point, because for an investor concerned with the value of his portfolio at the end of a period of time, it is the total return that matters, not the annualized return. Because of the effects of compounding, the standard deviation of the total return actually increases with time horizon. Thus, if we use the traditional measure of uncertainty as the standard deviation of return over the time period in question, uncertainty increases with time.

Paul
I see your point and it is a good one. But like I mentioned before, why are we just using S&P 500 data? Is it because other good data doesn't exist. To me, that's like saying your fixed income can be accurately represented by Australian government bonds.
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Post by jln »

nisiprius wrote:That's because 5% is high.
Yes. The optimal portfolio to hold in retirement very much depends on the inflation-adjusted withdrawal rate.

In Asset Allocation and Portfolio Survival, I ran a large number of Monte Carlo simulations to investigate this problem. (Nearly 12 billion simulated months in various scenarios - this took about 6 hours of computer time back in 1999 on an ancient iMac!)

Define the "optimal portfolio" to be the one that maximizes the 30-year survival rate with constant inflation-adjusted ("real") withdrawals. Here's the results in a nutshell:

3% real withdrawal rate: Max survival rate = 98%. Quite a few portfolios work to get 98% survival. All of them contain at least 20% cash, at least 20% stocks, and at most 40% bonds. Example: 30/20/50 stocks/bonds/cash.

4% real withdrawal rate: Max survival rate = 88%. Again, several portfolios reach 88%. All of them contain at most 10% cash, between 20% and 40% bonds, and at least 60% stocks. Example: 60/30/10 stocks/bonds/cash.

5% real withdrawal rate: Max survival rate = 75%. The optimal portfolios all contain at least 90% stocks. Example: 90/5/5 stocks/bonds/cash.

6% real withdrawal rate: Max survival rate = 63%. The optimal portfolio is 100% stocks.

7% real withdrawal rate: Max survival rate = 51%. The optimal portfolio is 100% stocks.

These results pretty much agree with common sense if you think about it for a minute.

One size does not fit all. More conservative investors might prefer a 3% real withdrawal rate, which requires sacrificing to save significantly more when working. More aggressive investors might prefer a 5% real withdrawal rate, which requires much less saving when working, especially if they can afford to and are willing to reduce their withdrawal rates if times get bad. Moderate or average investors might prefer a 4% real withdrawal rate. It looks like 6% and 7% real withdrawal rates are very risky.

Note that none of these withdrawal rates are totally "safe" (as in "SWR"). They all have a chance of failure over 30 years. None of them is a free lunch - they all have significant downsides.

The only 100% "safe" withdrawal rate would be the current real yield on TIPS. Unfortunately, thanks to the lousy economy, I believe that current real yields on some TIPS are actually negative.

A 100% stock portfolio would be appropriate only for a very aggressive investor with a very high tolerance for risk. For all others, holding bonds and cash in addition to stocks is optimal.

For more details see the paper. It has all the data and funky 3D surface graphs.

What are the most important things you can do to help this picture? Number 1: Keep costs low, low, low. For example, the difference between expenses of 0.2% and 1.0% is huge. Number 2: Diversify, diversify, diversify. For example, adding foreign stocks would improve the numbers a bit. I investigate these topics further in More Portfolio Survival Studies.

By the way, in terms of "protecting against inflation", stocks have pretty much no correlation with inflation (-0.03), while cash (short US Treasuries) has a pretty high correlation (0.41). Of course, stocks have a much higher expected return than cash, and that matters too. TIPS, of course, are the best inflation hedge - it's part of the name, after all!

Before Richard and/or Rodc object, I beg you to ignore the exact numbers presented above. It would be best to read this post looking through a bowl of jello. Just look at the patterns and general ideas. E.g., it looks like 3% is pretty safe, even if it's not 100% safe. The often-cited 4% looks OK, but is far from perfectly safe. 5% looks rather risky, and 6% and 7% are too risky for just about everyone. The lower the withdrawal rate, the more conservative the optimal portfolio. The more you can save when working, the more secure you can be in retirement with a lower withdrawal rate and a more conservative portfolio (duh!). The only absolutely 100% safe portfolio is 100% TIPS. There ain't no such thing as a free lunch (TANSTAAFL). Keep costs super-low. Diversify. These are the lessons I took away from this exercise.

John Norstad

p.s. A kitten update: They've doubled in weight already - over 4 lbs each! Still as cute and as sweet as they could possibly be. Here's a recent picture, with Aladdin on the left and her sister Ziggy on the right:

Image
Last edited by jln on Fri Nov 04, 2011 7:54 am, edited 1 time in total.
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Post by jln »

thewatcher wrote:The risk thing is very time-dependent with equities and reduces the longer you hold them.
[ride-hobby-horse]
Not true. Time does not necessarily ameliorate risk. See Risk and Time.
[/ride-hobby-horse]

John Norstad
Last edited by jln on Fri Nov 04, 2011 7:55 am, edited 1 time in total.
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Post by jln »

Sigh. I really should avoid this, but I can't help myself.
Dick Purcell wrote: My Bodie textbook has 10^9 repetitions of the label "risk" that are inconsistent with those definitions you quoted. These 10^9 misuses of the word refer only to return-rate standard deviation. Nothing about wealth, or value, or whether it matters in people's welfare.

Does not address $. Does not address when $ may be needed.
Not true. Total return rate standard deviation is equivalent to standard deviation of end-of-period wealth, over any time horizon. (Because of compounding, over long time horizons one needs to take logs to make standard deviations even make sense, but we'll ignore that here.) Bodie is very well aware of this, and his textbook has good explanations of all of this.
Doesn't even pass the grade school test of common sense. Measures deviation without specifying what is deviated from. According to this pinhead use of the term, a 10%-mean investment with 2% standard deviation has the same "risk" as a 1%-mean investment with 2% standard deviation.
Not true. Deviation is from the mean, as usual. Investors care about both expected return (the mean total return) and the risk (as measured by standard deviation of total returns). They like expected return. They dislike risk. All rational investors prefer 10% mean 2% sd to 1% mean 2% sd. Bodie is very well aware of this, and his textbook has good explanations of all of this.
If those guys want to babble to each other this way, up in their ivory tower, that's their privilege. But we have 100 million Americans down on earth whose futures depend on this stuff. We need investment educators who can speak purpose-focused common sense in people-ese. I nominate Professor Taylor.
Professors Taylor and Bodie have no disagreement. Neither babble. Their only difference is that Bodie explains the formal models behind the common sense of Taylor. Their main conclusions and advice for we mere mortals down here on earth are essentially the same.

John Norstad
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Post by Dick Purcell »

John –

You certainly should have avoided it.

It makes me sad to reply. In describing and clarifying the investment environment, in most respects the Bodie book and the university investment education taught with it are very good. And at the math, and at explaining it, you are marvelous.

But in investment selection, and in communication, for the 99% of us who are individual investors and whose world it shapes, the Bodie book and its university investment education are dreadful, irresponsible. And when you dispute my points exposing this problem, you misrepresent my points so blatantly it's hard to believe your misrepresentatiions are not intentional. That is very offensive. Please stop that.

1. Your first assertion is nonsense.

Return-rate standard deviation does not consider wealth.

For assessing real risk for a real person’s investment plan, with dollar additions and withdrawals along the way and future dollar needs and goals, return-rate standard deviation is nothing more than one of many essential pieces of raw material for further analysis.

2. Your second assertion misses the point. Ivory tower “investment education” drowns us all in the absurd notion that risk is measured by standard deviation ALONE. Regardless of mean. Did you misrepresent my point on purpose, or just not understand it?

3. Your third assertion is sad. If you can’t detect the keep-it-simple purpose-focused common sense of Taylor from the ocean of ivory-tower-ese in the Bodie book that dominates “investment education” . . .

Here in my Bodie book:

>> The table of contents is ten large fine-print pages, listing 27 chapters containing over 350 sections, some with numerous subsections.

>> The glossary is 13 large fine-print pages with definitions of 550 terms.

>> The index is 20 large fine-print pages listing 2700-odd topics.

>> There are over a thousand of those large fine-print pages.

>> It appears to me, from sampling, that the book has over three-quarters of a million words, and many hundreds of Greeky formulations and symbols. Sorry for failing to give you an exact count – at my age I don’t have enough years left to count them.

What is all of this about??

Well, I’ve suffered a lot of hours with my head buried in this massive book, looking for how to assess, compare, and seek best investments in terms of Taylor’s definition of risk. I can’t find it.

To do this, of course, we’d have to apply probabilistic return rates in each of the series of years or other periods of the investor’s cash flow plan, which plan will typically have cash flow additions and withdrawals in the various years or other periods along the way. There will of course be the mighty effects of compounding. We’d need to incorporate estimated effects of fees, taxes, inflation.

Through this kind of analysis, we can show assessments and comparisons of investments in terms of probabilities for what the investor is investing for, will need, and understandsnet real dollars for his future needs and goals.

This we could teach and do using Monte Carlo simulation. (Of course, we’d want to explore and present variations in assumptions, as I’m sure Rodc and Magellan would insist.) We could present graphs of probabilities for net real dollar results for the investor’s future needs and goals. We could present graphic comparisons of investments this way, to inform the investor so he can judge what’s best for his needs, goals, and priorities.

This would fit the definition of risk from Taylor.

As far as I can see, it is nowhere in that massive Bodie book. As one part of my search, I combed the entire 2700 items in the 20 pages of the index, looking for suggestions of it. Could not find it.

If you can find it in that Bodie book, please let me know.

For the university investment education pouring out of our universities and shaping the investment world of 100 million individual investors, most facing serious risk of inadequate future finances, this would be responsible teaching of investment probabilities. Probabilities for the financial purpose!

Drowning us all in oceans of misleadingly-labeled ivory tower mathematical abstractions is not.

Dick Purcell
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Post by bobcat2 »

jln writes.
Define the "optimal portfolio" to be the one that maximizes the 30-year survival rate with constant inflation-adjusted ("real") withdrawals.
There is a fundamental problem with the above definition of an “optimal retirement portfolio”. Namely it mismeasures risk.

There are two dimensions to risk.
(1) Probability of failure
(2) Magnitude of failure

Risk is the product of those two dimensions.
Risk = (Probability of failure) x (Magnitude of failure)

The approach jln uses completely ignores the magnitude of failure dimension of risk. Retirement portfolios for a given WR heavily weighted to stocks often give lower failure rates (probability of failure) than bond weighted portfolios, but the stock failures are sometimes spectacular and occur early in the retirement period (magnitude of failure).

Consider two portfolios and the same WR over a 30-year retirement horizon. One portfolio is weighted toward stocks (say 70/30). The other portfolio is weighted toward bonds (say 40/60).

At the given WR the failure rate for the stock weighted portfolio is 3% and the failure rate for the bond weighted portfolio is 5%.

But none of the bond weighted portfolio failures occur in the first 25 years of the retirement horizon. OTOH half of the stock weighted portfolio failures occur in the first 15 years of the retirement horizon. To completely ignore this second aspect of the risks of the two portfolios is incorrect. It is quite likely that a measure that incorporates both dimensions of risk would conclude that the bond weighted portfolio is superior to the stock weighted portfolio.

In other words simply relying on the probability of loss dimension of risk often results in recommending portfolios that are too aggressive, because it ignores the greater potential magnitude of loss such portfolios entail. This doesn’t mean that Monte Carlo analysis that looks only at probability of failure should be abandoned when looking at retirement portfolios, but rather that such analysis needs to be accompanied by additional analysis that considers the magnitude of failure.

Richard Fullmer has an easy to read paper on this - Mismeasurement of risk in financial planning
Link to paper - http://www.plansponsor.com/uploadfiles/Russell.pdf

Here is an excerpt of a short article by Fullmer and Zvi Bodie on the nature of risk that addresses this problem with an brief example.
The following are four examples of misleading statements found repeatedly on investor education sites:...

example (3.) This tool computes the “probability of success” for your financial plan and should guide your investment decision making. This is a dangerous half-truth that confuses the science of probability measurement with the science of risk measurement. The probability of anything is never a complete measure of its risk. Risk measurement is concerned not only with the probability of events but also with the consequences of those events. Using the probability of success as a risk measure can mislead investors into using an overly aggressive investment portfolio, because the severity of the downside goes unaccounted for.
Link to article. http://www.bu.edu/phpbin/news-cms/news/ ... 4&id=55461

BobK
In finance risk is defined as uncertainty that is consequential (nontrivial). | The two main methods of dealing with financial risk are the matching of assets to goals & diversifying.
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Dick Purcell
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Post by Dick Purcell »

BobK --

Having bickered with you in the past, I take great pleasure in agreeing with you here.

Back in the thread of months ago where Taylor stated his definition of risk, Magician refined the definition by making exactly the point you make here. Risk has both probability and badness dimensions.

Here too, I'd want to put greatest effort into informing the investor. In completing the kind of risk assessment you call for, some math types might be tempted to multiply the various magnitudes of shortfall by their probabilities and come up with a single number for "total risk."I'd rather inform the investor of the spectrum of magnitude-probability slices or increments. Maybe for the investor, when he sees that, he thinks about it and concludes that down to minus X, shortfall is only "bad" -- but below X is "terrible."

Dick Purcell
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Post by bobcat2 »

Hi Dick,

Here is a quote from Taylor Larimore last summer where he gives his favorite definition of risk.
Taylor Larimore wrote:Bogleheads:

This is my favorite definition of "investment risk":

"The probability of not reaching our goal."
So either Taylor has quietly changed his definition of risk after I criticized his definition in the thread last summer, or you are inaccurately quoting him. If he has changed his mind, it's good to see that his definition of risk is now more in line with that of Zvi Bodie's definition of risk. A point Lbill noted in last year's thread.

Link to thread.
http://www.bogleheads.org/forum/viewtop ... lor#772391

BobK
In finance risk is defined as uncertainty that is consequential (nontrivial). | The two main methods of dealing with financial risk are the matching of assets to goals & diversifying.
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Post by Ben24 »

Applying genuinely long term charts and expected those type of results in any 10-15 year time period is risky.
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Post by magician »

bobcat2 wrote:There are two dimensions to risk.
(1) Probability of failure
(2) Magnitude of failure

Risk is the product of those two dimensions.
Risk = (Probability of failure) x (Magnitude of failure)
Suppose that you owe a loan shark $1,000 tomorrow, and your portfolio is worth $990 today. (This particular loan shark won't take less than his due; he'll break your legs if you're short by $1 or $999.)

The probability-of-failure dimension is easy to measure: you might get the extra $10 and you might not. The magnitude-of-failure is easy as well, but less intuitive: it's 0 if you get at least $10 by tomorrow and +∞ if you get less than $10 by tomorrow.

Sometimes, even when it's easy, it's not so easy.
Simplify the complicated side; don't complify the simplicated side.
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Post by magician »

Ben24 wrote:Applying genuinely long term charts and expected those type of results in any 10-15 year time period is risky.
Whatever that means.

;)
Simplify the complicated side; don't complify the simplicated side.
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Post by Dick Purcell »

Awwwww, BobK.

You ended our time of agreement so quickly. But I did enjoy agreeing with you, if only for minutes.

(In the thread that I remember where Taylor offered his definition of risk, as I remember it both Magician and Dbr offered wise refinements which Taylor agreed to. Sorry if I failed to remember and cite a contribution you made.)

But now to your ending our agreement, which you achieve by citing a shocking report of an alleged “Bodie with a responsible view of investment risk.”

If your Bodie has a responsible view of investment risk, he ought to demand the immediate purging of all copies of the Bodie textbook filling the heads of our youth and financial advisors with the misconceptions of risk and portfolio selection taught by drowning them in the likes of this illustration, taken from that Bodie book's website:

[img]<table><tr><td><a%20href="https://picasaweb.google.com/lh/photo/1 ... tr></table>[/img]

See that Rf over at horizontal axis = zero? That Rf means risk-free rate, and it’s located at horizontal axis zero because the Bodie behind this book thinks and teaches that risk is “standard deviation (%).”

Standard deviation of what? From the “(%)” and the sizes of the numbers along the axes, you can detect that this is a graph of percent return rate for the individual year. So according to this thing, risk is standard deviation of percent return rate for the individual year.

See that upper-left curve? It’s curving up because it has what this Bodie book calls “risk aversion” – that is, aversion to return-rate standard deviation. That curve reflects an equation called a “utility function.”

See that point C? According to the Bodie behind this book, that is the optimal portfolio. It's chosen by the utility function equation, at the point where that equation's curve meets the reddish straight line.

But wait! What about the investor? What about probabilities and risk for his investment purpose? His purpose is meeting (or exceeding) his future dollar needs and goals, multiple years ahead. In that pursuit, he is investing and will invest dollars, now and in some years ahead. Where is all that?

Sorry. No consideration is given here to the investor’s future dollar needs and goals, or probability of meeting them, or probabilities and magnitudes of potential shortfall. Or how many dollars he invests or when.

This graph does not address the investor’s financial resources or needs and goals at all. Gives zero consideration to dollars.

This graph does not select an investment for an investor – it selects an investment for an equation! – that “utility function.”

This graph – indeed, the whole ocean of stuff in the Bodie book about choosing a "best portfolio" – is not designed for the interests of investors. It’s designed for the interests of professors!

This kind of nonsense enables academics to stay up in their ivory towers and have fun selecting investments for equations instead of people. They don’t have to come down to earth, where 100 million investors have their feet on the ground. In the world of this Bodie book, professors don’t have to address the financial resources and future needs and goals of actual people.

This book should be titled Investor-Free Investing.

Can your Bodie, who according to your reporting has a responsible view of risk, put an immediate end to teaching of this nonsense? This stuff threatens the financial futures of most Americans.

This kind of !#$%&!! is the principal opponent of the wisdom of John Bogle. It is the principal reason the great majority of American investors are confused and misled into the financial industry fleece machine. Stop it!

Dick Purcell
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Post by thewatcher »

jln wrote;
[ride-hobby-horse]
Not true. Time does not necessarily ameliorate risk. See Risk and Time.
[/ride-hobby-horse]
Your article, specifically the bar chart at the end of it, confirms that risk is reduced with time. After the entire period you have calculated the chance of having less than if the monay were kept in the bank as 1.26SD below the median. However, after a very short period of time, less than a year for example, the chance of such loss will approximate to 50%. So it's pretty clear that the risk of loss, defined by you as vs money-in-bank, decreases with time.

No-one is suggesting risk goes away altogether or that the spread of end results doesn't widen with time. But risk of loss does decrease.

TW
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Post by VictoriaF »

Dick Purcell wrote:Magician --

But I need my Bodie book. It plays a leading role in my novel.

Dick Purcell
Is the title of the novel "Ivory Tower"?

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Post by Dick Purcell »

Victoria –

That would sure be an appropriate title. The Ivory Tower certainly plays a lead role, so much like the role of the Bodie book it’s hard to tell them apart.

I tried to check with Beatrice, who is writing the story, but of course she has to stay on the move and impossible to locate. There are a lotta people who don’t want this stuff exposed, and it isn’t just academics who have built their careers teaching this stuff and writing about it. The financial industry just loves this ivory tower stuff, feeds on it you could say. It confuses people so badly they turn to the financial industry for (heh heh) “help.”

What the financial industry loves most about this stuff from the ivory tower is its use of the fear-word risk to label return-rate standard deviation for the individual year, and its teaching people to base investment selection on their fear of that short-term "risk." That diverts people’s attention from their future needs and goals, to focus instead on their fear for the individual year, where they cannot see where they’re likely to be going – and cannot see the terrible long-term costs of financial industry fees.

Beatrice will put some of her draft chapters on a secret website, for me and our fellow investigators of this scandal to get an advance sense of how she is telling the story. While most of what she's telling is what we’re discovering about this scandal, which is just shocking, she's also telling a little of what is happening to us as we work to expose this scandal, which is pretty scary too. She may have some of it up and ready for our first peek next week. Then I can check and answer your question on her latest thinking for the title.

While I don’t know Beatrice’s latest thinking for the title, I know what she calls the process that ivory tower “investment education” enables the financial industry to do to most investors. She calls it “spook and fleece.” She has a marvelous example of ivory-tower-endorsed software for execution of the spook and fleece.

While the story she's writing is technically a novel, tragically most of it is true. If Beatrice tells this story right, what she’s writing could do a lot to expose the ivory tower investment-selection nonsense and help a lot more of our fellow Americans see the light of John Bogle’s wisdom.

Dick Purcell
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Post by Don Lawson »

When running monte carlo simulations, is it true that each year/month/days returns for a given asset class are completely independent of each other?

I know if you are rolling dice, obviously each roll is completely independent of the one before or after (ie: you roll three 6's in a row, your next roll still has a 1 in 6 chance of being a 6)

With markets, if you have returns of 20% one year, are next years results statistically dependent in any way on the previous years returns? This may be a very basic concept but I just don't know the answer.

Also, do numbers change in monte carlo simulations change much if weeks or days are used instead of months?
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Post by bobcat2 »

With markets, if you have returns of 20% one year, are next years results statistically dependent in any way on the previous years returns?
Yes stock market returns are somewhat dependent, but probably not the way you think they are.

If the stock market has a move much larger than average in one period in either direction it is more likely than usual to have a big move in either direction in the next period. The converse is also true. An extremely small move in either direction compared to the average move is more likely than usual to be followed by another extremely small move in either direction. This phenomena is most pronounced in relatively high frequency trading data that is daily or higher, but it is also somewhat observed at lower frequency monthly data and even a little bit at low frequency annual data.

Mandlebrot was the first researcher to note this feature of financial return data over 50 years ago. Today we refer to this attribute of financial return data as volatility clustering.

BobK
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Post by magician »

Don Lawson wrote:When running monte carlo simulations, is it true that each year/month/days returns for a given asset class are completely independent of each other?

I know if you are rolling dice, obviously each roll is completely independent of the one before or after (ie: you roll three 6's in a row, your next roll still has a 1 in 6 chance of being a 6)
If the die is fair. ;)
Don Lawson wrote:With markets, if you have returns of 20% one year, are next years results statistically dependent in any way on the previous years returns? This may be a very basic concept but I just don't know the answer.
Some (most?) probably exhibit some serial correlation; some probably don't.
bobcat2 wrote:If the stock market has a move much larger than average in one period in either direction it is more likely than usual to have a big move in either direction in the next period. The converse is also true. An extremely small move in either direction compared to the average move is more likely than usual to be followed by another extremely small move in either direction. This phenomena is most pronounced in relatively high frequency trading data that is daily or higher, but it is also somewhat observed at lower frequency monthly data and even a little bit at low frequency annual data.

Mandlebrot was the first researcher to note this feature of financial return data over 50 years ago. Today we refer to this attribute of financial return data as volatility clustering.
This is another interesting example of a serial dependence phenomenon.
Don Lawson wrote:Also, do numbers change in monte carlo simulations change much if weeks or days are used instead of months?
Yes. Daily returns are much noisier than weekly returns or monthly returns. If you use daily data to get the statistics for your Monte Carlo simulation, you will likely find that the volatility is higher and correlations lower than if you use monthly data to get the statistics.
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Re: Redefining risk

Post by swaption »

Don Lawson wrote:Most long-term investors have an incorrect view of risk. They define risk as a loss of principal when the real risk to a long-term investor is the loss of purchasing power over time.

With this in mind, all asset classes BUT equities are extremely risky. Equities are the only asset class with a lengthy track record of overcoming this risk. When long-term investors add cash, gold, and even bonds to their portfolio they are hurting their chances of overcoming this risk. And frankly, I'm surprised how easily people lose sight of this.
I think you have an assymetric view of risk. There may be a higher liklihood that you lose purchasing power with assets other than equities, but there is a far higher risk that equities result in an extreme adverse outcome, and investors generally give this far greater weight. For example, the potential for equities to result in purchasing power of 10% relative to the current value cannot be eliminated from the realm of possibilities. So long-term invesotrs are potntially faced with some risk of more modest purchasing power during retirment, or the remote risk of being poor.

Someone shuffles a deck of cards. Offers you 10:1 odds on your life savings if he picks any card other than an ace. I say most people (with ample life savings) don't take that bet. That's risk aversion. It's not just about probability and outcomes. People would rather live a modest retirement than risk losing everything.
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Post by nisiprius »

Don Lawson wrote:With markets, if you have returns of 20% one year, are next years results statistically dependent in any way on the previous years returns? This may be a very basic concept but I just don't know the answer.
Oddly enough, I personally believed up until 2006 or 2007 or so that the returns for, say, the S&P 500, or for midcap mutual funds, or whatever, must have some year-to-year correlation. It was just so obvious. After all, we (think we) see "bull" and "bear" markets that last many years, if the last two years have both been good isn't that starting to look like a "track record?"

I don't have the figures at hand, but at some point I started to wonder about this. So I got out an Excel spreadsheet and entered the annual returns for the S&P for a long period of time--probably back to 1926--in one column, and offset it by one year in the next column. That is, the line for "1950" had the 1950 annual total return in the first column and the 1951 annual total return in the second column.

And I had Excel compute the correlation coefficient. You could have knocked me over with a feather.

It was so darn-all close to zero as made no difference.

People keep saying the academics find "momentum" over short periods and "reversion to the mean" over long ones that one year is exactly the period of time over which no correlation exists...
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Post by nisiprius »

You can try it yourself. This is the data, from 1926 to 2004, out of the 2005 SBBI yearbook. It's annual total returns for "large company stocks," which is the S&P 500 starting from 1977 or so, the S&P 90 before then.

I just tried it again. Excel calculates the correlation coefficient--between one year and the next, over that time period--as 0.054.

11.62%
37.49%
43.61%
-8.42%
-24.90%
-43.34%
-8.19%
53.99%
1.44%
47.67%
33.92%
-35.03%
31.12%
-0.41%
-9.78%
-11.59%
20.34%
25.90%
19.75%
36.44%
-8.07%
5.71%
5.50%
18.79%
31.71%
24.02%
18.37%
-0.99%
52.62%
31.56%
6.56%
-10.78%
43.36%
11.96%
47.00%
26.89%
-8.73%
22.80%
16.48%
12.45%
-10.06%
23.98%
11.06%
-8.50%
4.01%
14.31%
18.98%
-14.66%
-26.47%
37.20%
23.84%
-7.18%
6.56%
18.44%
32.42%
-4.91%
21.41%
22.51%
6.27%
32.16%
18.47%
5.23%
16.81%
31.49%
-3.17%
30.55%
7.67%
9.99%
1.31%
37.43%
23.07%
33.36%
28.58%
21.04%
-9.11%
-11.88%
-22.10%
28.70%
10.87%

P. S. I'm not at all sure that it's valid because I'm not at all sure that consecutive annual returns of the S&P index qualify as "independent random samples form a normal distribution," but for what it's worth a chart from an ancient copy of Biometrika Tables says that for a sample of 100, and a measured correlation 0.05 in a sample, the "5% confidence limits" on the population correlation coefficient -0.14 to +0.25. And since we have only 78 points it would be wider than that. In other words, not only is the correlation low, it could be zero.
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Post by bobcat2 »

Hi Nisi,

You wrote.
People keep saying the academics find "momentum" over short periods and "reversion to the mean" over long ones that one year is exactly the period of time over which no correlation exists...
Academic studies of the properties of returns usually use daily data or data of even higher frequency. Occasionally they use monthly data. Annual data are hardly ever used. Even if there is momentum or reversion to the mean I would not expect it to show up in low frequency annual data. That would make for easy stock market pickings if it did show up, and in that case even Gene Fama would disavow efficient markets.:lol:

BTW the distribution of stock market returns changes with the frequency of the return data. Low frequency annual data appear to be well characterized by the log normal distribution. Hourly return data and return data of even higher frequencies are not remotely characterized by the log normal distribution.

Return data rarely display any autocorrelation whatever the frequency (although this may not be true for very high frequency data such as minutes or seconds), so I am not surprised that you didn't find any first order autocorrelation in your annual return data.

Autocorrelation in the squares of the returns, OTOH, nearly always shows up in return data, although it may not show up in low frequency annual data. Why don't you square your return data and estimate the correlation coefficient between one year and the next on that? If it does show up that means there is volatility clustering even in the annual return data and that annual volatility (SD) is most likely mean reverting rather than constant.

BobK

PS - While autocorrelation in the squares of annual return data may not be significant, I can practically guarantee that it would be significant if you were using monthly or higher frequency return data.
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Post by Dick Purcell »

Don, BobK, Magician, Nisi –

On your topic of time intervals of the data and how it may affect things such as serial correlation and/or mean reversion, you guys are on a very interesting topic. Some other threads have raised ghosts of interesting effects for multi-year time horizons.

In Wade’s extensive research on SWR and related topics, he’s reported that compared to Monte Carlo simulations with random walk, no serial correlation, his rolling 30-year sequences of history show less dispersion of 30-year results. While there are serious deficiencies in the rolling-sequences approach, the difference in dispersion of 30-year results is enough that Wade has expressed concern about what it means. First guess would be that there is negative serial correlation that the random-walk Monte is missing. But as Nisi points out, the data don’t show such correlation one year to the next. ?????

In another thread, Cjking observed the same effect that concerns Wade. Cjking described his way to adjust his Monte Carlo wth a mean-reversion component to reduce dispersion of long-term results, to better match the less-than-random-walk dispersions of long-term results in the market history.

Others objected (including John Norstad and me, in harmony!) on grounds of terribly inadequate long-term-sequence historical data. All of this was based on Shiller data from 1870 forward, which yields only four separate 30-year sequences. Also, it was reported that the effect of reduced dispersions of longer-term results (compared to Monte random walk) appeared in history of the USA but not other nations.

Still, in the US market history, the effect is quite dramatic, as I will illustrate in a minute.

We were working with market data that reflected an individual-year-return-rate standard deviation of 18.

Verde reported analysis showing that for simulation of 30-year investment, if your only concern is the probabilities for the final result, the individual-year return-rate standard deviation should be shrunk from the 18 down to 9.3!

John made a comparable test for ten-year investments and found that if your only concern is final result, the appropriate individual-year standard deviation is only about 80% of the single year standard deviation of 18, which is about 14.4.

To try to generalize these results, in that other thread I produced a graph that should not be used but is I think interesting and informative to look at. I applied a "decay factor" to standard deviation for the individual year, wherein the decay is greater for longer investment time horizons. I set the decay so it fits the single-year 18 and Verde's 30-year 9.3 -- and voila! the same decay just about hit John's 10 year SD of 14.4 (it hit 14.7)

Here is the graph, for viewing -- but not for use, for reasons repeated below the graph. The vertical axis label SDS means standard deviation shrunken. That's standard deviation for the individual year, each year through the time horizon.

[img]<table><tr><td><a%20href="https://picasaweb.google.com/lh/photo/J ... tr></table>[/img]

Here is what this graph says: IF you disregard the strong advice not to use it, and you are investing a sum for Y years and care only about final-result probabilities – go out the horizontal axis to your time horizon Y, up to the curve, then straight left to the vertical axis. In your Monte sims, use that SDS as the SD for the individual year.

Why not use this graph:

1. The SD shrinkage shown in the graph is based on woefully, disastrously inadequate statistical evidence.

2. While the shrinkage can be seen in US history, other nations do not show it.

3. in view of the uncertain uncertainties about the future, it is especially imprudent to apply something that dramatically reduces uncertainties based on such flimsy evidence.

Still – look at that SD shrinkage! Verrry dramatic!

Dick Purcell
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Post by jln »

bobcat2 wrote:The approach jln uses completely ignores the magnitude of failure dimension of risk.
The points you make in general are excellent, and I make them too in other contexts. For example, people talk about risk as "the probability of failure to meet a goal". But as you explained, this is bogus. If my goal is a million dollars, missing it by $1 is meaningless, but missing it by half a million dollars is a very big deal. So magnitudes of shortfall are very important. It seems like a minor change, but we need to make both nouns in the statement plural: "the probabilities of failures to meet a goal". In technical terms, we need to look at the entire probability distribution of possible outcomes, not just a single point in that distribution.

But when talking about failure rates in retirement, the picture changes a bit, because you can't lose more than everything. Magnitudes of loss below $0 are meaningless. So talking about probability of failure in this context is more meaningful. It's basically addressing the biggest fear of retirees: "Will my money last?".

You talk about the issue of when your money runs out. E.g., in my 3% real withdrawal rate example, my simulations came up with a max success rate of 88% over 30 years. This doesn't give the full picture. What's the success rate over 10 years, or 20 years, or 25 years, or 40 years? That matters. I do address this issue in one of my papers, but I didn't talk about it in my post above.

John Norstad
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Post by jln »

Dick Purcell wrote: For assessing real risk for a real person’s investment plan, with dollar additions and withdrawals along the way and future dollar needs and goals, return-rate standard deviation is nothing more than one of many essential pieces of raw material for further analysis.
Yes, dollar additions and withdrawals along the way complicate the picture a great deal compared to the relatively simple scenario of a single lump sum investment. There's a great deal of research about this in the ivory tower literature. There's not much about this in the typical MBA textbooks because the math is just too hard for the typical MBA student's tiny little brain. But I assure you that return-rate standard deviation continues to play a central role in those kinds of studies. By the way, Bodie has written papers in this area that are quite interesting.

I'm currently trying to do some of my own work in this area. It's really hard but quite interesting. If I ever manage to make sense of what I'm up to, I'll probably write it up.

John Norstad
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Post by jln »

Dick Purcell wrote:This graph does not select an investment for an investor – it selects an investment for an equation! – that “utility function.”
As an investor, consider the following two statements:

1. All else being equal, I like having more money. If someone offered me $100 with no strings attached, I'd take it.

2. Although I like getting more money, I value getting a single extra dollar more when I'm poor than when I'm rich. If I only have $1 to my name, getting one more dollar is very important. If I already have $1 million dollars, getting an extra one is nice, but not such a big deal.

Utility theory is based on only these two assumptions. If we want a way to measure an investor's risk preferences, we need some kind of equation to make that measurement. Without any way to measure this, all we can do is rather meaningless hand-waving.

Are some investors more conservative than others, with what we call a "higher aversion to risk"? When we talk about investing, is this something that's important to consider? If so, I think it's not controversial to say that we need a way to measure it. That's what utility functions do. There's nothing nefarious or mysterious going on here.

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Post by bobcat2 »

jln writes.
But when talking about failure rates in retirement, the picture changes a bit, because you can't lose more than everything. Magnitudes of loss below $0 are meaningless. So talking about probability of failure in this context is more meaningful. It's basically addressing the biggest fear of retirees: "Will my money last?".
I disagree. In one case to keep your money from running out in retirement you need to cut your spending by 50% per year in the last 20 years of a retirement planning horizon of 30 years. In the other case you need to cut your spending by 5% in the last 3 years of retirement to keep from running out. That is a huge difference. I am assuming no one is going to keep spending at the same rate if more than half of their portfolio is depleted say 7 years into a 30 year planning horizon. There may be people that foolish, but I am assuming most people adjust their spending to avoid destitution in retirement if the plan goes awry.

It seems to me the most straightforward way to assess magnitude of loss is to multiply the real amount of failure per year by the number of failed years for each failure.

So if your targeted real withdrawal amount is $30,000/year, multiply that amount by the number of failed years. This is the amount of total shortfall for each failure.

To get a number for total risk that takes both probability and magnitude into account multiply the average shortfall for each strategy by the probability of shortfall for that strategy.

BobK
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Post by jln »

thewatcher wrote:Your article, specifically the bar chart at the end of it, confirms that risk is reduced with time. After the entire period you have calculated the chance of having less than if the monay were kept in the bank as 1.26SD below the median. However, after a very short period of time, less than a year for example, the chance of such loss will approximate to 50%. So it's pretty clear that the risk of loss, defined by you as vs money-in-bank, decreases with time.
The mistake here is your definition of risk as "probability of loss", as we've discussed at length here in this thread, and as I discuss at length in the article. You have to also consider the magnitudes of the possible losses. We need to talk about "probabilities of losses" over the entire probability distribution.

John Norstad
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Re: Redefining risk

Post by peter71 »

Don Lawson wrote:Most long-term investors have an incorrect view of risk. They define risk as a loss of principal when the real risk to a long-term investor is the loss of purchasing power over time.

With this in mind, all asset classes BUT equities are extremely risky. Equities are the only asset class with a lengthy track record of overcoming this risk. When long-term investors add cash, gold, and even bonds to their portfolio they are hurting their chances of overcoming this risk. And frankly, I'm surprised how easily people lose sight of this.
Hi Don,

There are probably as many definitions of risk as there are definitions of "bad investment outcomes," perhaps even more, inasmuch as technical definitions often cover a myriad of "unexpectedly good investment outcomes" too. So I think your original post, like several other posts in this thread, is overstated.

Having said that, I do think there are lots of people out there who've been 100% stocks for several decades and are doing just fine (so far). I even know one who's done something not entirely different from what Malkiel might have advised in the early 70's: i.e., throw a bunch of darts at the financial pages, buy a bunch of stocks, ignore all stock, asset allocation, rebalancing and math noise for the next 40 years . . . I think it's worked ok for him, but it's kind of hard to tell as he has absolutely zero interest in talking about investing strategies. :D

Best,
Pete
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Post by Dick Purcell »

BobK –

I agree with the direction you are pointing, that there’s more to it than just (a) fix the number of years, at say 30, then (b) calculate the probability of failure. As you suggest, if two portfolios have the same probability of failure, the more aggressive one will have more probability of failing by more.

But instead of calculating magnitude of failure, it may be more relevant to express the difference in probabilities of failing earlier – which I think you suggested in an earlier post. Of two portfolios with the same failure rate for 30 years, the more aggressive portfolio will have greater probability of failing earlier, say year 22.

If we show Fred that at the end of 30 years, at age 90, in one portfolio he may be penniless and owe $40,000, and in the other portfolio he may be penniless and owe $2 million, he may say either way I’m out of money and harassed by bankers visiting me in my new home under the 6th Street bridge. What’s the difference?

But if you show him that in the more aggressive portfolio, he has more risk of running out of money much earlier, say in year 22, that is more likely to win his attention, and should. Lots of folks will remain alive physically and mentally past 22 years but never make it to year 30.

So I propose: Don’t first fix the years at 30 or whatever, and try to express the magnitudes of failure. Instead, just do the probability analysis in a way that shows failure probability for each year. Fred will see that for two portfolios that have the same failure rate for 30 years, the more aggressive has greater probabilities of leaving him penniless earlier, while he's more likely to be alive and aware of the horrors of his pennilessness.

Dick Purcell
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Post by jln »

bobcat2 wrote:I disagree. In one case to keep your money from running out in retirement you need to cut your spending by 50% per year in the last 20 years of a retirement planning horizon of 30 years. In the other case you need to cut your spending by 5% in the last 3 years of retirement to keep from running out. That is a huge difference. I am assuming no one is going to keep spending at the same rate if more than half of their portfolio is depleted say 7 years into a 30 year planning horizon. There may be people that foolish, but I am assuming most people adjust their spending to avoid destitution in retirement if the plan goes awry.
An excellent point. One does not have to commit to a fixed real withdrawal rate. If you are able and willing to live on less, you can plan based on that assumption. But one downside to this idea is that it really only works for retirees who have accumulated significant wealth and have quite a bit more saved than what they need for basic living expenses. "Golly, Martha, the market hasn't been doing so well this year - I guess we'll have to forget about that second vacation home for a while." This is a small minority of people, I think. In the real world, most retirees live very modestly and really need their income, and don't have that many optional expenses that they can eliminate if times get bad.

Modeling this is difficult. For any such strategy, in order to look at optimal asset allocations, I think that what you want to do is maximize the expected utility of total consumption over the time period in question. Or something like that.

Annuities are another major option we haven't discussed - buying insurance against those nasty probabilities of failure. Modeling that is hard too. I think that these kinds of studies make annuities look rather attractive, at least for supporting critical floor living expenses (avoiding the "cat food" scenarios). And they support much higher income levels than the so-called "safe" withdrawal strategies we've been talking about here. But there are downsides too, and in any case this is another story beyond what we've been discussing so far.

By the way, the aforementioned Zvi Bodie has done quite a bit of research and writing in these areas over his career.
It seems to me the most straightforward way to assess magnitude of loss is to multiply the real amount of failure per year by the number of failed years for each failure.
Interesting idea. Straightforward, but too overly simplified, I suspect.

Here's an example of a kind of graph I've played with based on these kinds of Monte Carlo simulations. It shows age in retirement on the X-axis and probability of failure on the Y-axis for one modeled portfolio and withdrawal rate. This kind of thing is more useful than just looking at the single point at 30 years into retirement.

Image

Maybe the area under the curve is the kind of measurement of "risk" that you're talking about? Or something like that? I just pulled this idea out of thin air - there's probably something stupid about it. On thing wrong is that if you extend the X-axis to infinity, the curve asymptotically approaches 100%, and the area under it is infinite. That's always true for these kind of simulations, with any withdrawal rate and and any mix of risky investments. (You'd need to support your withdrawals with risk-free TIPS to make this not true.) The curve always has this elongated S-shape starting at 0% and going all the way up asymptotically to 100%.

Suppose we did this and got, say, a 70% probability of failure at age 150. Who cares? Nobody lives that long. So it seems to me that actuarial probabilities of death at each age should play a prominent role in any equation that tries to measure the relative riskiness of various strategies.

The bottom line is when you think about all these issues all at once it gets very complicated very quickly. The only way to attack this kind of complexity is to start by making lots of unrealistic simplifying assumptions, such as: We'll start by looking only at a fixed 30 year horizon, assuming we're going to die exactly on that date in the future. We'll assume that we don't buy any annuities. We'll assume a fixed real withdrawal rate. We'll assume a fixed asset allocation with rebalancing throughout the time period. Those assumptions are all unrealistic, of course, but one can still learn interesting and useful things from the simple experiments based on these assumptions.

This is a very fun discussion. Thanks, bobcat2!

John Norstad
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Dick Purcell
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Post by Dick Purcell »

John --

That graph of yours is exactly what I was proposing in my post just above. Compare two portfolios that way, failure probability by year, and show that to the investor. You are informing the investor to make the choice.

But please don't let the ivory tower types keep your wonderful graph up in the tower and try to go from that to some mathematical notion of total risk that nobody understands. Their job is not to create math, it's to inform the investor, which your graph does wonderfully well.

Terrific graph! On behalf of the hundred million of us down here on the ground, thanks!

Dick Purcell
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Post by Dick Purcell »

John –

Your defense of the ivory tower boys’ selection of peoples’ investments via utility function represents the notion that the ivory tower boys are a superior species, can translate people into equations, and should be making investment selections for those dumb peasants down on the ground.

NONONONONONONONONONO ! ! !

The ivory tower boys have shown themselves to be wholly unqualified for that job – or at least Bodie has – by expressing people’s utility in terms of return-rate standard deviation for the individual year instead of financial results for investors’ future needs and goals. Just look at his Bodian nonsense:

[img]<table><tr><td><a%20href="https://picasaweb.google.com/lh/photo/K ... tr></table>[/img]

If those boys way up in that ivory tower had just a modicum of responsibility, they would realize that instead of creating oceans of inscrutable math, their responsibility is to provide the rest of us tools for comparing alternatives in terms of probabilities for the purpose we are investing for and understand – net real dollars for our future needs and goals.

Then we will make the choices, thanks.

Dick Purcell
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Post by bobcat2 »

Hi John,

Let's take an example of how my calculation would work. The real withdrawal amount is $30,000 per year for 30 years.

Portfolio A is 70/30.
Portfolio B is 30/70.

Portfolio A at a given withdrawal rate has a failure rate of 4%
Portfolio B at the same withdrawal rate has a failure rate of 6%.

Total Risk = (prob of failure) x (avg shortfall)

Here is Portfolio A's total risk value.
Total Risk Portfolio A = .04 x $190,000 = $7,600

Here is Portfolio B's total risk value.
Total Risk for Portfolio B = .06 x $100,000 = $6,000

Portfolio B is less risky because it avoids the big losses in the early years that sometimes devastate Portfolio A. For example 50% stock market decline in first 3 years of retirement.

I don't see why one wouldn't include the above numbers as well as your graphs when discussing the results. I would start with the above numbers and then the graphs would show why Portfolio A is riskier (higher total risk score), despite a lower failure rate.

You wrote.
One does not have to commit to a fixed real withdrawal rate. If you are able and willing to live on less, you can plan based on that assumption. But one downside to this idea is that it really only works for retirees who have accumulated significant wealth and have quite a bit more saved than what they need for basic living expenses. "Golly, Martha, the market hasn't been doing so well this year - I guess we'll have to forget about that second vacation home for a while." This is a small minority of people, I think. In the real world, most retirees live very modestly and really need their income, and don't have that many optional expenses that they can eliminate if times get bad.
Taking on stock market risk does not solve this problem. Stock market risk may manifest itself in the form of zero or negative real stock market returns over a long period of time, such as the last 12 years of US stock returns, and then the retiree is in much worse shape. What happens to the retiree who 'needs' 60% or more of his assets in stocks and their associated high 'expected' returns in retirement to meet his goal, and the stock market declines 40% or more in the first few years of retirement. This is the problem with simply looking at the prob of failure -it favors risky investments by ignoring magnitude of failure. If someone 'needs' 50% or more in stocks during retirement and acts on that basis, there is a significant probability that he will fall very far short of his 'needs' in retirement.

BobK

PS - The rains of Irene started here in the DC area about an hour ago. I am not sure how long I'll be on the internet today.:cry:
In finance risk is defined as uncertainty that is consequential (nontrivial). | The two main methods of dealing with financial risk are the matching of assets to goals & diversifying.
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Post by nisiprius »

bobcat2 wrote:Hi Nisi,

You wrote.
People keep saying the academics find "momentum" over short periods and "reversion to the mean" over long ones that one year is exactly the period of time over which no correlation exists...
Academic studies of the properties of returns usually use daily data or data of even higher frequency. Occasionally they use monthly data. Annual data are hardly ever used. Even if there is momentum or reversion to the mean I would not expect it to show up in low frequency annual data. That would make for easy stock market pickings if it did show up, and in that case even Gene Fama would disavow efficient markets.:lol:

...Autocorrelation in the squares of the returns, OTOH, nearly always shows up in return data, although it may not show up in low frequency annual data. Why don't you square your return data and estimate the correlation coefficient between one year and the next on that? If it does show up that means there is volatility clustering even in the annual return data and that annual volatility (SD) is most likely mean reverting rather than constant.

BobK
It turns out to be -0.089. I.e. none.

-0.025 if I cube it. -0.080 if I take the fourth power. What the heck, -0.055 if I take the tenth power. I'd appreciate it if someone would check my work, by the way... I'm just using the square of the percentage return. Did you mean for me to add one, then square, then subtract one?

I'm (obviously) not even trying to be sophisticated about this. But I think looking at serial correlations between annual returns is worth doing, even if you and the academics already know there isn't any, and here's why.

Supposed authorities claim to see "secular bulls" and "secular bears" that are so objectively clear that they can mark the start and finish points and calculate durations and take averages. Thus, we are told, the three secular bears of the twentieth century lasted 171, 237, and 165 months, and as of 2010 the "fourth cycle that is unfolding" had lasted 108 months.

Given the common interpretation of stock returns as a series of bull markets and bear markets that are said to last much longer than one year, I think the average naïve investor would be surprised to find there's no correlation between one year's return and the next. It leads me personally to wonder whether "bull markets" and "bear markets" actually have any more reality to them than the constellations in the sky.

I wish I could read Japanese. I'll bet I could find Japanese financial columnists in 1995 saying--with appropriate weaseling, of course--"don't worry, the average Japanese bear market has only lasted 76.15 months, and we're 63.25 months into this one."

Of course, from, I dunno, 1870 to 1930, you did have a situation where the entire stock market could be manipulated by very small numbers of very big investors, and perhaps there was more meaning to it then; back then, "bulls" didn't necessarily mean people who thought the market would go up, it meant people who intended to make it go up.

Studies or no studies, DFA or no DFA, I am skeptical about momentum in general for the simple reason that probably 99.9% of all stock market investors have always believed there is momentum. Hard to believe that the market is so inefficient that it doesn't allow for it. Has DFA really found something with their computers that a century of technical analysts, informed by human pattern recognition could have missed?
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Dick Purcell
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Post by Dick Purcell »

John –

You claim that assessing result probabilities for real people’s cash flow plans, with additions and withdrawals along the way, is terribly difficult math, far beyond the tiny brains you sneeringly attribute to MBAs. Your claim is (a) dead wrong. It is also (b) so reeking of the ivory tower boys’ erroneous notion that they are a superior species, and so lacking in sense of responsibility to the investing public, it makes my toes hurt.

To make your claim valid, state it this way: For ivory tower types seeking stuff to publish about, and seeking to make it appear they are doing something, and totally unaware of their responsibility to the investing public , the math can be made to appear hard.

For the math, try this little two-step, using Monte Carlo:

1. Lay out a year-by year projection of the investor’s cash flow investment plan and goals, additions or withdrawals in various years, just as one of your “tiny-brained MBAs” or other peasants down on the ground commonly does in Excel

2. Run your simulation so each run proceeds year by year, in three steps for each year: withdrawal, random return rate, addition.

That’s the math.

(Oops! I almost forgot that Rodc and Magellan may be inspecting this post. Run it with various assumptions, to reveal sensitivities of results to those assumptions.)

The communication job is still ahead – present your simulation results in investment-comparison graphs carefully designed to inform the investor. That’s the purpose of the math, remember? But the presentation is another subject. Here I wanted to give you the math.

Strange that in that Bodie book, there are ¾ million words, hundreds of Greeky things, 2700-odd items in the index – but nothing about the little two-step above or any method for assessing result probabilities for real people’s dollar plans and goals. But of course, that’s not strange at all -- his textbook is not designed for the interests of investors – it’s designed for the interests of the financial industry and professors.

How about we chuck that book and give those tiny-brained MBAs and the rest of us peasants ten pages on (a) the two-step above, (b) refinements for including fees-taxes-inflation, and (c) suggestions for turning the output into investor-communication graphs?

Dick Purcell
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Post by jln »

Dick Purcell wrote:Just look at his Bodian nonsense:

U = E(r) - 0.5*A*sigma^2

If those boys way up in that ivory tower had just a modicum of responsibility, they would realize that instead of creating oceans of inscrutable math, their responsibility is to provide the rest of us tools for comparing alternatives in terms of probabilities for the purpose we are investing for and understand – net real dollars for our future needs and goals.
That equation is one the most fundamental in financial economics. It's not "Bodian" - it goes all the way back to Harry Markowitz in the 1950s. It says that investors like expected return (E(r)), and they dislike volatility as measured by variance (sigma^2). The relationship is linear. The coefficient of relative risk aversion A measures the rate at which an individual investor is willing to trade off one against the other.

Some may find such a simple equation inscrutable ("I hated math in school!"). I liked math in school and find it simple and profound. I mean, come on, it's just algebra - there's not even any calculus involved!

It's precise purpose, in your own words, is to "compare alternatives" for achieving "net real dollars for our future needs and goals". There is no other purpose.

The equation is for lump sum investments and applies over any time horizon. As I mentioned, deriving similar equations that accommodate periodic additions and/or withdrawals is more complicated.

Monte Carlo simulations are interesting, but closed-form solutions to these problems are much more interesting and useful.

In any case, as I mentioned, that equation turns out to be critically important when working with periodic addition/withdrawal problems. I'm working on such a problem now involving asset allocation "glide paths", and I'm using that equation in a critical way. The insights I'm getting are much more important and interesting than what you can get with Monte Carlo methods alone, although I'm finding that the two approaches often complement each other in a nice way.
the ivory tower boys’ ... so lacking in sense of responsibility to the investing public.
You need to realize that the main concern of the academics ("ivory tower boys") is to understand how the world works, not a sense of responsibility to the investing public. Their models and theories often require math that the public mostly cannot understand. So be it. This is a characteristic of all scientific disciplines, not just financial economics.

Should academics in general be more socially responsible and make a greater attempt to educate the public about their disciplines? Probably. Does this mean that they should never do math, build models, or write textbooks for students about their formal work? No.

If Bodie's textbook were intended for a general audience, your "investing public", it would indeed be absurd. But it was never intended for that audience. To criticize it from that point of view is not fair.

If a nuclear physicist publishes a textbook on nuclear power reactions, it will inevitably be filled with equations and math that the general consumer of electricity has no hope of understanding, but are important to engineers who design and work in nuclear power plants. It such a physicist being irresponsible to the electricity-consuming public? Of course not. Why hold finance professors to a different standard?

John Norstad
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Post by jln »

Hi back, Bobcat.

I think that the right way to come up with a single number to measure the risk of outliving your money would be to multiply failure probabilities at each age times the probability of still being alive at that age, then sum them up. This single number would be the true "probability of failure", I think.

So, for example, a failure probability of 10% at age 75 would be weighted much more heavily than the same failure probability at age 95, because your chances of still being alive at 75 are much higher than at 95.

Note that the probability of failure curve slopes upwards as age increases, from 0% to 100%, but the probability of still being alive curve slopes downwards as age increases, from 100% to 0%. Multiplying the two together and adding them up is what we'd do.

I have a vague recollection of seeing this kind of work somewhere, but I don't remember where.

It would be quite interesting to redo my Monte Carlo experiments this way, to see what asset allocations at various withdrawal rates minimize this better "probability of failure" number rather than the "probability of failure at 30 years." Would the results be dramatically different? I don't think so, but I don't know. Perhaps I'll dig up some actuarial mortality tables and try doing this some day.

John Norstad
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Post by bobcat2 »

Hi again John,

Your approach would be interesting, but it would be different than what I am proposing. Let me illustrate my approach with a trivial example.

I have a 70/30 portfolio with a real WR of 4%, a real withdrawal of $30,000 per year, and a 30 year retirement horizon. In this trivial example I only run 100 MC simulations. There are 3 failed runs and thus a failure rate of 3%.

The first failure occurs after 12 years.
So the shortfall for that failure is (30-12)*$30,000 = $540,000

I do the same type of calculation for the other 2 failures.

Shortfall 2 occurs after 27 years so the 2nd shortfall is $90,000.

Shortfall 3 occurs after 22 years so the 3rd shortfall is $240,000.

Thus the average shortfall of the 3 failures is $290,000.


Total risk = (failure rate) x (avg shortfall per failure)

and in this example
Total risk = (.03) x ($290,000) =$8,700

The difference between my trivial example and a real example would be the number of MC simulations, which in reality would be in the several thousands rather than 100. Therefore, the number of shortfalls would be in the hundreds rather than three.

BobK
In finance risk is defined as uncertainty that is consequential (nontrivial). | The two main methods of dealing with financial risk are the matching of assets to goals & diversifying.
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Post by jln »

bobcat2 wrote:Taking on stock market risk does not solve this problem. Stock market risk may manifest itself in the form of zero or negative real stock market returns over a long period of time, such as the last 12 years of US stock returns, and then the retiree is in much worse shape. What happens to the retiree who 'needs' 60% or more of his assets in stocks and their associated high 'expected' returns in retirement to meet his goal, and the stock market declines 40% or more in the first few years of retirement. This is the problem with simply looking at the prob of failure -it favors risky investments by ignoring magnitude of failure. If someone 'needs' 50% or more in stocks during retirement and acts on that basis, there is a significant probability that he will fall very far short of his 'needs' in retirement.
Agreed, and that's what my results showed. At the higher withdrawal rates, the optimal portfolios have more stocks, but at the cost of a much higher failure rate. At the lower withdrawal rates, the optimal portfolios have mostly bonds and cash, with the benefit of a much lower failure rate.

So why don't people just use the lower withdrawal rates? One reason is because you have to save tons more when working to save up enough money to do this. For example, to support the same dollar withdrawals, a withdrawal rate of 3% requires saving 33% more every month than does a withdrawal rate of 4%, and it requires saving twice as much every month than does a withdrawal rate of 6%. So the tradeoff is between the standard of living and level of savings when working and the standard of living and risk of outliving your money when retired. Not everyone wants to or is able to make this tradeoff in the same way. In any case, what you're doing is trading off consumption today against consumption tomorrow - this isn't rocket science, it's just what saving for the future is all about.

Another big downside of the lower withdrawal rates is that you tend to die with a huge portfolio. That's money you earned and saved but never had a chance to spend on anything. For most people this is not an optimal solution to the lifetime spending/saving problem.

At the most conservative end of the spectrum (the limiting case), the failure rate is 0% at any age, the withdrawal rate is the real return on TIPS, the portfolio is 100% TIPS, you have to save a huge portion of your income when working, and you die with an enormous pile of unspent money. It's an option, but I don't think it's the option that most people would prefer.

Using your entire portfolio to purchase an annuity is another conservative option. You get a much higher withdrawal rates than with the TIPS strategy, and you get a failure rate of 0% at any age, with one big difference: You die with nothing left.

That's another tradeoff you can make - you can use part of your portfolio to buy an annuity at some age, and keep some of it to invest and spend. This seems to me like an attractive compromise. Many people have investigated this and written about it.

So you're right - stocks don't solve the problem. Nothing really "solves" the problem - it's all about tradeoffs with different strokes for different folks, as usual. I don't see a disagreement here.

John Norstad
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Post by Dick Purcell »

John –

I’m looking for something to agree on in your last post addressing selected quotes from me. You've given me one! – your saying that the purpose of the ivory tower boys is to understand how the world works. Love it! In describing and teaching how the investment world works – hold your chair – I think that Bodie book and what the boys have done and are doing is fine. In fact, terrific!

The problem is that they stray from that into dreaming up ways for them to sit up in the ivory tower and make people’s investment selections. There they are a menace to the public. That’s where the rest of your sentence, where you say the boys have “not a sense of responsibility to the investing public,” is obviously most true.

Exhibit A is that goofy utility function you cited. Are you claiming that you see nothing wrong with leading people to choose investments based on a bit of mathematics that doesn’t even address the investment purpose?

Nothing about the dollars and years of the investor’s future needs and goals? Nothing about the dollars and years of investment to get there?

C’mon. I can’t believe you accept that.

I wonder where in the world the boys in the ivory tower find their new recruits. Where do they find kids smart enough to do the math, but so lacking in responsibility and common sense they swallow the teaching of investment selection according to that utility curve?

+++++

You’re right that there are different audiences – 100 million investors facing perilous financial futures, and some boys up high who want to write about utility functions. As they say, different books for different folks.

But surely some of the boys up there are aware that what they claim to be “investment education” for a special elite (them) is drowning the investment environment of the entire investing public. Check the outline of the investment section of required training for CFPs, who number upwards of 60,000 guiding the investing public, and you’ll find a summary of the table of contents of the Bodie book. You know, Treynor ratio and such.

If one of the ivory tower boys gets a twinge of responsibility to the investing public, he could visit the CFP Board and advise them to toss out their echo of the Bodie book, switch the training to focus on pursuing investors’ best interests – result probabilities for the investor’s future financial needs and goals.

That would sure help us common folk a lot more than another paper on utility function math.

You’re right that responsibility for the terrible current investment education situation is broader than the Bodie book. We might ask why, despite the fact the 99% of America’s investors are individuals, the leaders of our universities have surrendered teaching of investment to the financial-industry-friendly business schools, from which the stuff in the Bodie book floods the entire nation.

Dick Purcell
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Post by bobcat2 »

Hi again John,

Here is where there is a disagreement with your results.
4% real withdrawal rate: Max survival rate = 88%. Again, several portfolios reach 88%. All of them contain at most 10% cash, between 20% and 40% bonds, and at least 60% stocks. Example: 60/30/10 stocks/bonds/cash.
I suspect that if the total risk measure is used, which also incorporates magnitude of loss as well as a failure rate, there is way too much equity in these portfolios (60% or more). I suspect that the safest portfolios at the withdrawal rate range of 3.5% to 4.5% would have far more bonds and far fewer stocks once magnitude of shortfalls is also accounted for. At 60% or more equities a 50% stock decline in the early years of retirement will decimate the portfolio.

There is a caveat here. Right now with interest rates so low and stock investing so risky, and economic growth so shaky, there are no good solutions. This analysis is based on more normal conditions. If things stay the way they are for an extended period, I'm afraid the best solution is to postpone retirement, save at a higher rate before retirement, and scale down retirement plans. :cry:

BobK
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Post by magellan »

bobcat2 wrote:Hi again John,

Here is where there is a disagreement with your results.
4% real withdrawal rate: Max survival rate = 88%. Again, several portfolios reach 88%. All of them contain at most 10% cash, between 20% and 40% bonds, and at least 60% stocks. Example: 60/30/10 stocks/bonds/cash.
I suspect that if the total risk measure is used, which also incorporates magnitude of loss as well as a failure rate, there is way too much equity in these portfolios (60% or more). I suspect that the safest portfolios at the withdrawal rate range of 3.5% to 4.5% would have far more bonds and far fewer stocks once magnitude of shortfalls is also accounted for.
My MC retirement planner implements something very much like this. It's an output called the 'Average Spending Shortfall' and is shown as a percentage just under the probability of success. Using the planner's default inputs with a few changes and looking at this output value nicely demonstrates your point above.

To see it for yourself, run the planner and change the following

1) current age to 65
2) Taxable Portfolio Value to $1,000,000
3) Spending Policy to Stable
4) annual retirement spending to $40,000

Next, set the investing style to Aggressive and run the planner and note the results. For comparison, set the investing style to Moderate and run the planner again.

Here's the description of Average Spending Shortfall from the planner documentation:
Along with probability of success, another important output is the size of the shortfall for those simulation iterations where the plan failed (ran out of money). A plan with a reasonably high probability of success that usually fails in the early years may be less robust than a plan with a lower probability of success that usually fails near the end of the plan. The Average Spending Shortfall shows the average percent of total planned retirement spending that couldn’t be funded in those simulation iterations that failed. For example, consider a retirement plan with level spending planned for 40 years. Further, assume that when the retirement plan fails, on average it fails in simulation year 30. Such a plan would have an average spending shortfall of 25%. This is because on average 1/4 of the retirement plan’s spending wouldn’t get funded in those iterations that failed. Note that for a plan with a 90% probability of success, 90% of the iterations had no shortfall at all. The shortfall depicted by the average spending shortfall only applies to the iterations where the plan failed (eg 10% of iterations in the case of a 90% probability plan). For an example of how a plan’s inputs can affect the magnitude of the spending shortfall, run a plan with an “aggressive” investing style, then rerun it with a “risk averse” style and notice the change in average spending shortfall.
If you'd rather not run the test yourself, I'll give it away. The result of the two runs with these inputs shows a steady 84% prob of success, but the aggressive portfolio has a 24% average spending shortfall, while the moderate one shows a 16% avg shortfall.

Jim
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Post by bobcat2 »

Hi Jim,

You wrote.
Along with probability of success, another important output is the size of the shortfall for those simulation iterations where the plan failed (ran out of money). A plan with a reasonably high probability of success that usually fails in the early years may be less robust than a plan with a lower probability of success that usually fails near the end of the plan. The Average Spending Shortfall shows the average percent of total planned retirement spending that couldn’t be funded in those simulation iterations that failed.
So yes - your results and approach are very much in line with what I have been talking about. The only thing I am adding to what you have already done is taking the product of the two risk dimensions to get a composite value for total risk.

Irene has knocked me offline for a couple of hours and the peak of the storm is still hours away. I doubt if I will be posting much in the next 36 hours.

BobK
In finance risk is defined as uncertainty that is consequential (nontrivial). | The two main methods of dealing with financial risk are the matching of assets to goals & diversifying.
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