Valuation-based market timing with PE10 can improve returns?

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NoRoboGuy
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Postby NoRoboGuy » Thu Jun 02, 2011 12:27 pm

I read the paper. My initial reaction to any 100+ year study is that 'in the long run we are all dead.'

The working use of this concept for most investors (not endowments) is to look at the PE10 during 15 or 20 year periods - http://www.multpl.com/ - I did not find any constant range you can always count on. That is, the range from one 20 year period does not appear to me to be related to the next period.

Also, while one can point to extreme periods such as 1929, one can also point to 'overvalued' periods such as 2003-2007 and 2009-2011 when you would have 'lost out' on big gains if you had a light or non-existent equity allocation, not to mention you would not have known when the 'top' was that time.

Finally, I did not find in the paper where it details the 50/50 approach. Since it is the basis of comparison for the thesis, is it not meaningful to know whether the 50/50 allocation is rebalanced daily, weekly, annually, or bi-annually?

Bottom line is the 'relative value' of using PE10 does not appear to be constant in any working way for me - maybe I am just not smart enough to 'get it' - good thing I am a passive investor. :wink:

At the risk of sounding redundant...past performance is no indication of future results.

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Postby yobria » Thu Jun 02, 2011 1:07 pm

bob90245 wrote:I beg to disagree regarding P/E10 patterns stop working. It's like saying we will never experience a tech bubble like the late 1990's again. Maybe not while the current crop of investors have fresh memories. But maybe the generation of investors that come after us.


I have two questions for you regarding that:

1. How certain do you think it is another PE/10 identifiable stock bubble like the tech bubble will happen over the next 30 years?

2. If such a PE/10 identifiable bubble does occur, how confidently will you exploit it? Scale of 1-10, with 10 being "Next PE/10 bubble, I'm going to mortgage the house, leverage everything I have and use options and futures to make a killing." With 1 being "I might tweak my asset allocation a bit, but you can only identify such bubbles in hindsight, and you never know when they're going to end."

Nick

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Postby yobria » Thu Jun 02, 2011 1:12 pm

dupe post

letsgobobby
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Postby letsgobobby » Thu Jun 02, 2011 1:43 pm

yobria wrote:
bob90245 wrote:I beg to disagree regarding P/E10 patterns stop working. It's like saying we will never experience a tech bubble like the late 1990's again. Maybe not while the current crop of investors have fresh memories. But maybe the generation of investors that come after us.


I have two questions for you regarding that:

1. How certain do you think it is another PE/10 identifiable stock bubble like the tech bubble will happen over the next 30 years?

2. If such a PE/10 identifiable bubble does occur, how confidently will you exploit it? Scale of 1-10, with 10 being "Next PE/10 bubble, I'm going to mortgage the house, leverage everything I have and use options and futures to make a killing." With 1 being "I might tweak my asset allocation a bit, but you can only identify such bubbles in hindsight, and you never know when they're going to end."

Nick


my answers:

1. I think the extreme valuations of 1929, 1965, 1974, 1981, 2000, and 2009 come along often enough to be acted on at least "once or twice" per investing career. I've been investing x 15 years and already had 2 such opportunities (late 90s, and late 2008-early 2009). that's often enough to be of measurable utility.

2. next time PE10 is 5, if I am under the age of 50, I would answer "9". I never use options/futures so I can't say 10. But I would use borrowed money (from a mortgage) and be 100% stocks. next time PE10 is 40, I will be no more than 20% stocks.

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Postby bob90245 » Thu Jun 02, 2011 2:12 pm

yobria wrote:
bob90245 wrote:I beg to disagree regarding P/E10 patterns stop working. It's like saying we will never experience a tech bubble like the late 1990's again. Maybe not while the current crop of investors have fresh memories. But maybe the generation of investors that come after us.

I have two questions for you regarding that:

1. How certain do you think it is another PE/10 identifiable stock bubble like the tech bubble will happen over the next 30 years?

My opinion is that the odds of another PE/10 identifiable stock bubble like the tech bubble happening over the next 30 years is very low. Prior to the tech bubble of the 1990's, there was the "tronic" bubble of the 1960's and ended with the Nifty 50 bubble of the early 1970's. So there was a 20-year gap between the 1970's and the 1990's until the arrival of a new crop of "New Era" stock investors who never lived through the prior bubbles. Maybe we should all be looking forward to the next bubble to occur after 2035. :D

yobria wrote:2. If such a PE/10 identifiable bubble does occur, how confidently will you exploit it?

Well if I'm a true Boglehead, I would be strictly adhering to the cannonical age-in-bonds guideline. :wink: Besides which, when said bubble arrives 30 years hence, I'll be 30 years older, retired and no longer have the need to "exploit" such "opportunities". :lol:
Ignore the market noise. Keep to your rebalancing schedule whether that is semi-annual, annual or trigger bands.

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Postby letsgobobby » Thu Jun 02, 2011 11:14 pm

wellmoneyed wrote:I tried to read the entire thread - I'll admit to a little skimming. :D

One thing I did not see brought up is the dependence of PE10 as a "constant". Historically some number being high and some number being low.

Looking forward I can see some game changing technology (Artificial Intelligence, Robotics). It seems like you could make a reasonable case for PE being shifted up permanently or at least for a long time if new technology fundamentally alters our average growth rate. If this is true, then it seems like this strategy would end with growth going off the charts and you sitting on the sidelines waiting (forever) for PE's to come back down.


this could be. it highlights why any valuation based tactical allocation should be utilized only at extreme valuations, and not in 'cliff' form.

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Postby Roy » Fri Jun 03, 2011 6:40 am

letsgobobby wrote:it highlights why any valuation based tactical allocation should be utilized only at extreme valuations, and not in 'cliff' form.


Agreed. This is perhaps the best use of the metric, if one could stomach the implementation—a huge "if" regardless of what many think in calmer moments. And even hypothetically, if investing solely on these valuations, I would not advise being out of stocks entirely at any PE, or all-in. So, even if one got frightened when "irrational exuberance" was proclaimed, one would still have held some stocks to take advantage of the three great years that followed. And at the March lows, one would still have held a position in bonds. But there would always be factors to consider besides just the PE that would affect implementation.

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grayfox
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Postby grayfox » Fri Jun 03, 2011 9:14 am

In my opinion, what is missing is sound theory behind all this P/E10 stuff.

It is observed that S&P 500 smoothed earnings yield (P/E10) varies over time. You would like to find a way to exploit those variations to become richer than Croesus. I guess the generally idea is that the stock market mean reverts--when it is high, it gets pulled lower; when it is low it gets pulled higher.

However, it think that references to mean reversion amounts hand waving. First of all, looking at P/E10 for the past 20 years. It looks to me like either 1. the mean has moved up higher, or 2. the mean reversion mechanism has broken completely. How could it be above the so-called mean for 20+ years if there is supposed to be this mean reversion force acting on the market?

For this to be good science, you need to
1. have some theory about what exactly drives P/E10.
2. employ logical thinking about how to make use of the theory, and
3. empirical evidence that the theory holds.

What I see is being done starting first assume some vague notion of mean reversion then #2. come up with strategy to exploit mean reversion to make money and then #3. use empirical evidence to backtest the strategy. I think backtesting strategies without a sound theory is likely to produce data-mined results.

The theory part is almost completely lacking. What is it that drives P/E10? Why does it vary so widely over time? If it mean reverts, what mean does it revert to?

The only guy who has even addressed this that I know about is Ed Easterling of Crestmont Research, whose theory is that earnings yield is driven by inflation or stable prices. Stable prices means high P/E. Unstable prices, either deflation or high inflation means low P/E. But I've read his book and articles and don't find him convincing at all.

So right now, why is P/E10=23.2 and not 10? Why should anyone expect to earnings yield to be lower in the future? Why not higher?

:?: What is the logical theory about what drives earning yield, i.e. P/E10? :?:
Last edited by grayfox on Fri Jun 03, 2011 9:23 am, edited 2 times in total.

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Postby SP-diceman » Fri Jun 03, 2011 9:19 am

yobria wrote:
bob90245 wrote:I beg to disagree regarding P/E10 patterns stop working. It's like saying we will never experience a tech bubble like the late 1990's again. Maybe not while the current crop of investors have fresh memories. But maybe the generation of investors that come after us.


I have two questions for you regarding that:

1. How certain do you think it is another PE/10 identifiable stock bubble like the tech bubble will happen over the next 30 years?

2. If such a PE/10 identifiable bubble does occur, how confidently will you exploit it? Scale of 1-10, with 10 being "Next PE/10 bubble, I'm going to mortgage the house, leverage everything I have and use options and futures to make a killing." With 1 being "I might tweak my asset allocation a bit, but you can only identify such bubbles in hindsight, and you never know when they're going to end."

Nick


100%, you don’t think human nature has changed do you?
You don’t even need a stock market, they did it with tulips in the 1600’s.

(lets not forget, we just had a housing bubble, I don’t consider tech the “last” bubble)

I think “identifiable” and “exploit” are poor word choices.
“Exploit” makes it sound like you are supposed to short the bubble.
(its hard to believe after a massive stock run-up reducing equity holdings is walking into a risky casino)
“Identify” makes it sound like you need to explain it.

All that’s really being discussed here is degree.
Remember that a 50/50 Boglehead, after a tremendous stock run up
sells equity. (he calls it rebalancing)
After a tremendous bear market a Boglehead buys equity. (he calls it rebalancing)
(notice he identifies/exploits nothing, you don’t really need to)

For all those who ask: How come no one exploits this? How come a fund hasn’t been created?
I don’t really think its anything new.
If you and I have a million cash and the market experiences a 65% decline.
You say you’re going in 50/50 and I say I’m going in 100%, I’m expected to have a higher
return since I took more risk.

There’s nothing new in the concept if you leave equities you could miss a bull market,
if you’re in equities you can be caught in a decline.
The same questions always apply, your age, your need to take risk, years to retirement.

To my view, if your 2 years from retirement and PE10 is low and you go 100% equity,
you have other problems.


Thanks
SP-diceman

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Postby richard » Fri Jun 03, 2011 9:25 am

grayfox wrote:In my opinion, what is missing is sound theory behind all this P/E10 stuff.

The theory is that the less you pay for earnings, the higher your returns.

Think of high quality long-term bonds. If you buy and hold a bond yielding 5%, your return will by higher than buying and holding a bond yielding 2%.

We're trying to buy the 5% stock rather than the 2% stock. If we could estimate future earnings (and therefore earnings yield, since we know today's price), we would be close to being able to do this.

The problem is that we don't know what earnings will be in the future, we have to estimate. Earnings tend to grow on a long-term trend path (2%-3% real), but with a lot of noise (they bounce around this trend). PE10 smooths the numbers so that you're seeing long-term trend rather than short-term noise.

Note that p/e mean reverts. The odds of the market p/e being lower than 0 or higher than 100 are essentially zero.

There are problems with all this, but that's the basic theory.

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Postby grayfox » Fri Jun 03, 2011 9:45 am

richard wrote:
grayfox wrote:In my opinion, what is missing is sound theory behind all this P/E10 stuff.

The theory is that the less you pay for earnings, the higher your returns.

Think of high quality long-term bonds. If you buy and hold a bond yielding 5%, your return will by higher than buying and holding a bond yielding 2%.

We're trying to buy the 5% stock rather than the 2% stock. If we could estimate future earnings (and therefore earnings yield, since we know today's price), we would be close to being able to do this.

The problem is that we don't know what earnings will be in the future, we have to estimate. Earnings tend to grow on a long-term trend path (2%-3% real), but with a lot of noise (they bounce around this trend). PE10 smooths the numbers so that you're seeing long-term trend rather than short-term noise.

Note that p/e mean reverts. The odds of the market p/e being lower than 0 or higher than 100 are essentially zero.

There are problems with all this, but that's the basic theory.


Sorry, that doesn't answer the question. Of course higher yields mean higher expected returns. That's well known. Even the B&H Bogleheads are expecting lower returns with higher P/E10, but they're not trying to market time with P/E10.

What the market timing strategy is trying to do is exploit movements in P/E10 to get higher returns than B&H. If earnings yield is low today, it will be high in the future so just wait until it is higher. The strategy counts on P/E10 in the future being lower than today. This vague notion that it mean reverts. Hand waving.

:?: But my question is why is P/E10 today 23.2? Why not 10? Why not 30? What drives P/E10? Nobody has tried to answer that, except Easterling.

Today the 30-year TIP yields 1.77% and E10/P is 4.2%.
Suppose in the future 30 year real interest rate is 0.5% In that case, E10/P = 2% would still provide an equity premium. That would be P/E10=50.

Why couldn't P/E10 go up to 50 over the next decade and stay there for the rest of your lifetime?

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Postby letsgobobby » Fri Jun 03, 2011 11:26 am

One answer would be that it never has. If it does, one would have missed out on stellar returns, but betting on something that has never happened seems unwise.

In answer to your other question (about 20 years of elevated PE10), I reply, "markets can remain irrational longer than you can remain solvent." Therefore one cannot bet the farm on this approach. Having said that, the volatility-adjusted return of the stock market from the mid-90s through 2008 was quite horrible. miraculously, once PE10 dropped well below its long term average (of 16) in early 2009 (it was 10.5 in mid-March), returns since that time have been, well, awesome.

This approach does demand a great deal of patience, as well as tolerance for huge tracking error. It seems this may be why extreme PE10s still exist: psychology (what Bogle called the 'speculative factor') doesn't change. People become too optimistic and too pessimistic about future earnings, allowing an enterprising investor to take advantage.

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Postby richard » Fri Jun 03, 2011 11:43 am

grayfox wrote::?: But my question is why is P/E10 today 23.2? Why not 10? Why not 30? What drives P/E10? Nobody has tried to answer that, except Easterling.

It's 23 because investors believe current prices are reasonable in light of current conditions, including future growth and available alternatives.

If that's your question, there is no good answer. There is no generally accepted pricing model.

grayfox wrote:Why couldn't P/E10 go up to 50 over the next decade and stay there for the rest of your lifetime?

There's no logical reason it couldn't. It's not likely to.

PE10 of 50 for an extended period would most likely imply a high degree of confidence in the future. High confidence would likely be associated with real interest rates above 2%, in which case it would be safer to buy bonds, in which case PE10 would go down.

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Postby Rodc » Fri Jun 03, 2011 11:51 am

First of all, looking at P/E10 for the past 20 years. It looks to me like either 1. the mean has moved up higher, or 2. the mean reversion mechanism has broken completely. How could it be above the so-called mean for 20+ years if there is supposed to be this mean reversion force acting on the market?


So called secular bull and bear markets tend to last ~20 years.

Looking at the full history of data, P/E10 shows about the same thing: it predicts (more technically correlates) with returns best out around 20 years, much smaller correlation at 10 years, very little correlation for less than 10 years. (note really this is only a handful of independent points so could be noise driven). So this very slow mean reversion (if it exists at all, could be noise) is nothing new to the past 20 years: it is standard market behavior.

May well be psychological: it takes a new generation to have a new outlook. Who knows?

Note that government policy plays a role: look at the last few years and how monetary policy and desire to pump up the markets work. Other times when market are screaming, policy is to tighten up. Look at the fed policy to revive the housing markets, look at the 90s tech boom, look at the 70s and trying to break inflation and the fall out effects on the stock market.

Lots of feedback mechanisms (short term towards bubbles, longer term to counter bubble, and the reverse when things go south). Of course these feedback mechanism work at cross purposes so the effects can be slow and irregular. So, tons of noise.

But the points you raise are important. P/E10 can never be anything more than a very crude measure. It is not often that P/E10 gives a clear signal, if ever (sure in hindsight it does).
We live a world with knowledge of the future markets has less than one significant figure. And people will still and always demand answers to three significant digits.

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Postby grayfox » Fri Jun 03, 2011 1:45 pm

Well here is my suggestion. Put all the backtesting of P/E10 strategies on the back burner. Instead, try to explain what drives valuations like P/E10.

At this point, I don't think it's understood well enough to make any kind of forecast of future valuations. That, for instance, at 23.2 today we should all lighten up on stocks because it will be below the mean in a few years.

For starters, just come up with some logical theory to explain the past history of valuation. Is it driven by inflation, like Easterling thinks, or are there other factors? Do valuations follow 20-year secular cycles. If so, why?

:arrow: Without some sound theoretical basis, there is really no way to know that some superior results of a strategy aren't just random results that won't repeat in the future.

Also, if there was a sound theory behind this, you should be able to answer many questions, for example:

1. Does P/E10 mean revert?
2. If so, to what value does it revert to?
3. Can the mean value be calculated as a precise or approx number? Is it constant over time? Does it even exist?

4. Why has the observed sample mean P/E10 been about 15? Why not 5 or 25?
5. Why has the sample mean increased to 16.4 over the past 20 years? Why doesn't the sample mean converge with more months of data?

6. Why was P/E10 7 in 1982 and 40 in 2000?
7. Can these extreme values be explained by economic factors, like inflation rate, interests rates, gdp growth, employment rate, etc.?

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Postby letsgobobby » Fri Jun 03, 2011 2:24 pm

you might as well ask those questions about the risk-reward profile of any asset class. Do stocks outperform bonds? Will they always? Why? By how much? Why not by more? less?

PE10, like PE, is a rough measure of the price the entire investing community is willing to pay for a dollar of earnings - that's it. If you don't think the value people are willing to pay for an asset varies widely over many years for many factors, then why has housing fallen by 1/3 in the last 5 years? Same asset, different price, and radically so.

I could provide answers to your questions but that would be beside the point. You seem to want only a traditional economics explanation for the phenomenon and exclude, a priori, a behavioral finance explanation.

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Postby DP » Fri Jun 03, 2011 2:42 pm

Grayfox,
The theory is that there is a tendency to revert to the mean. What drives this is human nature and the behavior of crowds, presumably driven to extremes by greed and fear. Because human nature is pretty constant such behavior can be expected to repeat in the future. This is a theory, not a law like gravity that happens in a defined and predictable way. A sound theory does not guarantee an answer to all your questions.

While I agree a trading strategy should always have some theoretical basis, it is not necessary to have all the answers to make a simple trading strategy. Simple models that take advantage of specific factors, such as mean reversion, trend, valuation, have been shown to work over reasonable lengths of time. There is no guarantee that they will continue to work in the future (the same can be said for buy and hold). A more thorough answer would probably have to come from someone with more time on their hands and better schooled in the field of behavioral finance.

Don

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Postby yobria » Fri Jun 03, 2011 2:52 pm

SP-diceman wrote:100%, you don’t think human nature has changed do you?
You don’t even need a stock market, they did it with tulips in the 1600’s.

(lets not forget, we just had a housing bubble, I don’t consider tech the “last” bubble)

I think “identifiable” and “exploit” are poor word choices.
“Exploit” makes it sound like you are supposed to short the bubble.
(its hard to believe after a massive stock run-up reducing equity holdings is walking into a risky casino)
“Identify” makes it sound like you need to explain it.


If you take "identifiable" and "exploitable" off the table, all we're arguing about is whether, with hindsight, some future price pattern will resemble a bubble.

And of course we'll be able to find those in future decades. But who cares? If you can't identify and exploit it at the time, it's irrelevant. And isn't the whole point of the PE/10 to identify and exploit?

Nick

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Postby letsgobobby » Fri Jun 03, 2011 2:56 pm

when there is evidence that some have consistently exploited this specific opportunity, what would persuade doubters that it is more than luck? Could anything?

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Postby yobria » Fri Jun 03, 2011 3:12 pm

letsgobobby wrote:when there is evidence that some have consistently exploited this specific opportunity, what would persuade doubters that it is more than luck? Could anything?


Being educated people, we begin with the null hypothesis: The big free lunch you think you discovered probably isn't really going to make you rich.

Want to reject the null hypothesis? Simply post your next 20 trades here, and we can determine statistically if you method works. Same as any scientific experiment.

Nick

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Postby floydtime » Fri Jun 03, 2011 3:19 pm

grayfox wrote::?: But my question is why is P/E10 today 23.2? Why not 10? Why not 30? What drives P/E10? Nobody has tried to answer that, except Easterling.


Mr. Bogle has stated in no uncertain terms (and proven, imo) that Speculation drives P/E. Nothing more, nothing less.

In other words, two basic things drive a stock's price...

1 - what the company earns (the cold, hard, "show me the money" data).
2 - speculation about what the company will earn in the future (P/E ratio).

EDIT - Note that the speculation portion (P/E), certainly for the market as a whole, is for all intents and purposes, RANDOM.

p.s. - what an interesting thread!
Last edited by floydtime on Fri Jun 03, 2011 3:47 pm, edited 3 times in total.
"Do not value money for any more nor any less than its worth; it is a good servant but a bad master" - Alexandre Dumas

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Postby Dick Purcell » Fri Jun 03, 2011 3:24 pm

I’m just, y’know, an investor.

I want to govern my (a) cash flows and (b) asset allocations for best result probabilities for my particular $$ resources and future $$ needs and goals, y’know?

I think it’s reasonable to expect that higher current PE10 portends likelihood of lower returns in next few years, and lower portends higher. So if history tends to confirm that, I wanna incorporate that in what I do now in cash flow and asset allocation. I think the way to do that is incorporate, in my stocks return-rate-probability estimates, a history-based slope relationship of next-few-years expected-return-rates to current PE10, for Monte application to compare alternatives and make prudent current cash flow and allocation decision for my $$ plan and goals.

Anything you theorists can reveal to help me would sure help me. Right now I’m a-gonna use PE10 because I have a source for it, but If you researchers find I should be using PE9 and can give me a source, please let me know. Same with how many years ahead for the expected return rate to be affected by current PE10, and the slope of that relationship – please let me know anything your research reveals that can help me refine my approach.

Meantime, I‘ll stay focused on assessing, comparing, and selecting for my particular $$ plan and future $$ needs and goals, y’know.

Dick Purcell

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Postby gulliver » Fri Jun 03, 2011 3:41 pm

sounds like hocus to me

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Postby letsgobobby » Fri Jun 03, 2011 3:48 pm

yobria wrote:
letsgobobby wrote:when there is evidence that some have consistently exploited this specific opportunity, what would persuade doubters that it is more than luck? Could anything?


Being educated people, we begin with the null hypothesis: The big free lunch you think you discovered probably isn't really going to make you rich.

Want to reject the null hypothesis? Simply post your next 20 trades here, and we can determine statistically if you method works. Same as any scientific experiment.

Nick


strawman. I don't trade, and you know that this approach does not advocate trading.

I posted at fatwallet in real time from 2007-present. The posts stand, unedited. Of course I don't expect you to read 213 pages (neither would I) but if you want to see 'trades' (shifts in asset allocation) posted in advance, the data is there for you to examine. I'm 'psychtobe' in the thread.

http://www.fatwallet.com/forums/finance/708018/

Those 'trades' as you call them permitted me excellent returns with minimal volatility through one of the greatest financial crises we've seen. I am comfortable with that outcome. I only need one or two of those in a career to make a career.

Right now, with PE10 23, it suggests lower-than-median 20 year returns for the S&P500, but not to such a degree that it's obvious how much to act on it. My recommendation is that between PE10 of, say, 12 and 25, most people should do nothing. Me, I've drifted down from a recent high of 57% to 53% because of PE10. Hardly radical. Doubt your portfolio has done anything different. If stocks continue swooning, in addition to rebalancing, I'll maybe over-rebalance a little. This is a (very) long term strategy. I'm 37. I can literally wait 40 years to (hopefully) be right. I had to wait 13 years (from 1996 to 2009) to be right last time!

example:

rated: posted: Mar. 3, 2007 @ 9:11p

that's not bold. 3 digits is bold. Bob Prechter said sub-1000 on the DJIA in 1995. He was wrong of course, and if DJIA ever sees sub-1000 again the world has very serious problems.

But sub-10,000? That's nothing. retesting the Oct 02/Mar 03 lows would not be unheard of. Think 7500. Would be a great buying opportunity. Would probably reflect serious deterioration in the housing market and significant mortgage default/foreclosure activity, concomitant with continued dollar devaluation. The end of US treasury purchases by Chinese and Japanese central banks with subsequent bond declines would be the final straw.

to eventually:

rated: posted: Mar. 28, 2009 @ 10:10a

Earnings are relevant because they have always been relevant. The points you make are valid, but they have also been valid at every other point in the history of markets; earnings go up and down, thus the reason for using 10 year average earnings rather than 12 month trailing or 12 month projected or any other. Your personal belief that we are undergoing a sea change in consumption and earnings eerily echoes the (your words) cliched "this time it's different" mantra. I don't believe it is different this time. I am not aware of any other time period in any major world stock market in the last 100 years or so when the following 3 conditions were met:
1. market down > 50% from its peak;
2. P/E10 < long-term average;
3. forward 15 year real returns including dividends and inflation, less than long term averages.

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Postby yobria » Fri Jun 03, 2011 4:50 pm

letsgobobby wrote:strawman. I don't trade, and you know that this approach does not advocate trading.


Sure it does, you change your AA based on PE/10 (in some cases, I believe you said, borrowing money and betting everything you have). So post those trades.

letsgobobby wrote:Those 'trades' as you call them permitted me excellent returns with minimal volatility through one of the greatest financial crises we've seen. I am comfortable with that outcome. I only need one or two of those in a career to make a career.


Oh yes - every anonymous person on the internet made millions trading stocks, don't you know that. ;) . But how about posting those trades here real time going forward.

letsgobobby wrote:I'm 37. I can literally wait 40 years to (hopefully) be right. I had to wait 13 years (from 1996 to 2009) to be right last time!


Sounds like this trading strategy doesn't signal that often. Perhaps we'll never have enough points to disprove the null hypothesis.

But next few times that big free lunch pops up - the one that you can see, but the geniuses at the hedge funds can't - be sure and post your AA change here, and we can track the results.

Nick

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Postby letsgobobby » Fri Jun 03, 2011 5:19 pm

Nick, As long as you are prepared to wait up to 20 years, I will try to oblige your request. Cheers -

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Postby Rodc » Fri Jun 03, 2011 7:04 pm

Why has the observed sample mean P/E10 been about 15? Why not 5 or 25?


At P/E (or P/E10) of 5 the earnings yield is 20%. Unless bond yields are very high that is going to look mighty attractive. May take folks a little time to overcome the fear that got yield so high, but eventually that yield will be too high to resist and dollars will flow back into stocks, raising P/E (P/E10, etc.)

Likewise, at a P/E (P/E10) level of 25 the earnings yield on stocks is only 4%, and unless bond yields are extremely low that will not be attractive for long. The complement of P/E10 of 5 is probably more like P/E10 of 30 or 35, or an earnings yield of 3% or so. On a risky investment, 3% is likely to start to look lousy even with low bond yields. As soon as something wakes people up from the euphoria of a rising market they will snap out of it and start taking profits, and down comes the market.

The average earnings yield is a little over 6% (no surprise this agrees with the long term real annualized return of stocks). Compare that to about 2% for intermediate treasuries. Then compare risk. I think it would be very surprising to find the long term average P/E (P/E10) way off from an earnings yield of 6% if treasuries are yielding 2% long term.

Now could the true underlying "mean P/E10" be 10% different, 20% different? Sure, plenty of noise in this system. More likely there is no mean, but rather even if somehow you could strip off speculation and emotional driven noise there is a balance between what safe assets are yielding and what risky assets are yielding. That balance is what you might expect from "mean reversion": people need some expected extra return for taking on risk, but they don't generally need a ton before the reward causes them to bite.

Personally I don't think you need a lot of fancy theory to see roughly why things are more or less the way they are. Unfortunately there is too much noise to do much with it most of the time.
We live a world with knowledge of the future markets has less than one significant figure. And people will still and always demand answers to three significant digits.

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Postby SP-diceman » Fri Jun 03, 2011 8:33 pm

yobria wrote:
SP-diceman wrote:100%, you don’t think human nature has changed do you?
You don’t even need a stock market, they did it with tulips in the 1600’s.

(lets not forget, we just had a housing bubble, I don’t consider tech the “last” bubble)

I think “identifiable” and “exploit” are poor word choices.
“Exploit” makes it sound like you are supposed to short the bubble.
(its hard to believe after a massive stock run-up reducing equity holdings is walking into a risky casino)
“Identify” makes it sound like you need to explain it.


If you take "identifiable" and "exploitable" off the table, all we're arguing about is whether, with hindsight, some future price pattern will resemble a bubble.

And of course we'll be able to find those in future decades. But who cares? If you can't identify and exploit it at the time, it's irrelevant. And isn't the whole point of the PE/10 to identify and exploit?


No.
You don’t identify and exploit bubbles, you leave them.
(remember, at high prices your selling equities)

To be honest I’m not even sure what the tech bubble has to do with anything,
we are talking about diversified equity holdings not sector concentrations.



Thanks
SP-diceman

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Postby fredflinstone » Sat Jun 04, 2011 9:50 am

Thanks, everyone, for your responses. I have read a lot of criticisms of Prof. Pfau's study. Some are reasonable. Others are pretty ridiculous. In any case, I still have not read anything that causes me to question Professor Pfau's basic results. In a nutshell, I believe that Prof.' Pfau's paper shows that (a) valuations matter, and (b) it is possible to improve risk-adjusted returns by taking into account equity valuations.

Jack Bogle himself has advocated "gentle market timing" and "tactical asset allocation" when valuations are extreme. It is abundantly clear that valuation-based market timing does not violate Mr. Bogle's teachings. See:

viewtopic.php?t=29534&start=0&postdays=0&postorder=asc&highlight=

(See also Larry Swedroe's comments in the thread above. Very interesting.)

I don't accept the premise that the "Stay the Course" philosophy precludes valuation-based market-timing. To my mind, "Stay the Course" simply means writing an IPS and sticking to it. If my IPS tells me to reduce equity allocation if PE10 reaches say 40, then Staying the Course means I should reduce equity allocation at a PE of 40. At least that's how I see it.

I'm not making any final changes yet. I will let this percolate a bit more. I am, however, going to begin working on a revised (draft) IPS that takes into account age, TIP yields, and PE10.

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Postby letsgobobby » Sat Jun 04, 2011 1:27 pm

some think any claims to have successfully done this are all bluster. ok, I don't expect anyone to believe any old internet poster, even if the data is all right there.

These are 3 NY Times articles that I read at the market nadir that made the same claim. They were simple, and to the point. It was hard to buy from October 2008 to late February 2009.... but it was the right thing to do. It didn't take psychic ability to time this market. It just took guts. The data was right there, in the Times, for all to see. Stocks had not been that 'cheap' in many, many years. Buying value had always paid off. It was likely, though not guaranteed, to pay off again. Worth a flyer:

http://economix.blogs.nytimes.com/2009/ ... p-e-ratio/

http://economix.blogs.nytimes.com/2009/ ... ent-cheap/

http://economix.blogs.nytimes.com/2008/ ... re-stocks/

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Postby floydtime » Sat Jun 04, 2011 10:32 pm

Apologies if this was already posted, but is there a place (or symbol?) where one can always go view the "current" Shiller PE10?
"Do not value money for any more nor any less than its worth; it is a good servant but a bad master" - Alexandre Dumas

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Postby Pres » Sat Jun 04, 2011 10:43 pm

floydtime wrote:Apologies if this was already posted, but is there a place (or symbol?) where one can always go view the "current" Shiller PE10?

Yes, here:
http://www.multpl.com/

Shiller's own data is updated monthly, I think:
www.econ.yale.edu/~shiller/data/ie_data.xls

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Postby yobria » Sun Jun 05, 2011 12:52 am

SP-diceman wrote:No.
You don’t identify and exploit bubbles, you leave them.


Um, before you leave them, you must identify them. And far more profitable to exploit them than just avoiding them (if you really believe in the system).

SP-diceman wrote:To be honest I’m not even sure what the tech bubble has to do with anything,
we are talking about diversified equity holdings not sector concentrations.


Oh, fine by me. The tech bubble is the example PE/10 believers used in this thread to show their trading system works. I certainly didn't bring it up.

Nick

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Postby BlueEars » Sun Jun 05, 2011 12:35 pm

DP wrote:Grayfox,
The theory is that there is a tendency to revert to the mean. What drives this is human nature and the behavior of crowds, presumably driven to extremes by greed and fear. Because human nature is pretty constant such behavior can be expected to repeat in the future. This is a theory, not a law like gravity that happens in a defined and predictable way. A sound theory does not guarantee an answer to all your questions.

While I agree a trading strategy should always have some theoretical basis, it is not necessary to have all the answers to make a simple trading strategy. Simple models that take advantage of specific factors, such as mean reversion, trend, valuation, have been shown to work over reasonable lengths of time. There is no guarantee that they will continue to work in the future (the same can be said for buy and hold). A more thorough answer would probably have to come from someone with more time on their hands and better schooled in the field of behavioral finance.

Don

When we look at physics we see very successful models which work in a limited way. Newton's laws are great for everyday things. Then you need Special and General Relativity to get at more esoteric phenomena. The Standard Model is very precise but has trouble with gravity. Etc, etc.

So in physics models have their limitations. In the stock market we have lots of questionable models. Underlying that is the impossibility of classical physics, quantum physics, or any known physics predicting future events outside of mathematically known limitations (like the N-body problem).

Still I kind of like some trend analysis :). It doesn't know the future any better then valuation based investing. One could combine trend analysis with valuation models -- I really think there is something there.

Or there is the old stand by of buy-hold if you don't like that stuff. Pick your poison :).

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Postby cjking » Sun Jun 05, 2011 1:27 pm

yobria wrote:Um, before you leave them, you must identify them. And far more profitable to exploit them than just avoiding them (if you really believe in the system).


Please explain how you would make the level of profits you envision in your phrase "far more profitable" by exploiting a bubble, if it were possible to know one existed? For example, let's suppose it's the year 2000 and a time traveler has told you that the IRR from selling one 40th of an S&P 500 portfolio in each of the next 40 years is going to be an unimpressive 2% real. Other than selling your equities and investing in something more attractive, maybe property yielding 4%, or bonds yielding 2% real thus giving you the same return with less risk, how can you exploit the time traveler's information?

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Postby SP-diceman » Sun Jun 05, 2011 2:08 pm

yobria wrote:
SP-diceman wrote:No.
You don’t identify and exploit bubbles, you leave them.


Um, before you leave them, you must identify them. And far more profitable to exploit them than just avoiding them (if you really believe in the system).

SP-diceman wrote:To be honest I’m not even sure what the tech bubble has to do with anything,
we are talking about diversified equity holdings not sector concentrations.


Oh, fine by me. The tech bubble is the example PE/10 believers used in this thread to show their trading system works. I certainly didn't bring it up.

Nick


A Boglehead reduces equity after large market run-ups. (rebalance)
A Boglehead increases equity after large sell offs. (rebalance)

He didn’t identify anything.
The same thing happens here.

The boglehead has no clue when he reduces equity if it was “the” top.
He has no clue when he increases equity if its “the” bottom.
He’s simply following his plan.

The PE10’er is doing the same.
He reduces risk as equity increases, and
increases risk as equity decreases.

You can change your equity without “calling” tops/bottoms or “exploiting” something.
(Bogleheads do it all the time)

If you want to call something that causes you to adjust your equity a:
“Secret Technical Indicator”

I have no problem with it, but you would need to call a Bogleheads account balance a:
“Secret technical Indicator”.


Thanks
SP-diceman

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Postby yobria » Sun Jun 05, 2011 10:21 pm

cjking wrote:
yobria wrote:Um, before you leave them, you must identify them. And far more profitable to exploit them than just avoiding them (if you really believe in the system).


Please explain how you would make the level of profits you envision in your phrase "far more profitable" by exploiting a bubble, if it were possible to know one existed? For example, let's suppose it's the year 2000 and a time traveler has told you that the IRR from selling one 40th of an S&P 500 portfolio in each of the next 40 years is going to be an unimpressive 2% real.


As a practical matter, if you were really certain of this, you could enter into a long term options contract, exactly as Warren Buffett did a few years ago. Call your local investment bank.

But - 40 years? Way too long a time period for a bubble.

Shiller used a 10 year period in his famous declaration in 1996 that, due to valuations, the stock market should be avoided for the next decade.

He was just as confident then as our PE/10 posters on this board are today.

Oops.

Nick

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Postby letsgobobby » Sun Jun 05, 2011 11:16 pm

yobria wrote:
Shiller used a 10 year period in his famous declaration in 1996 that, due to valuations, the stock market should be avoided for the next decade.

He was just as confident then as our PE/10 posters on this board are today.

Oops.

Nick


Not so fast. In 2008-09, stocks returned to 1996 levels. Stocks returned only their dividends for 12 years. It was a great time to be in gold, bonds, small caps, foreign stocks - anything, but the S&P500. He was very, very right, indeed. There is no doubt this approach requires patience and fortitude.
Last edited by letsgobobby on Sun Jun 05, 2011 11:18 pm, edited 1 time in total.

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Postby yobria » Sun Jun 05, 2011 11:18 pm

letsgobobby wrote:
yobria wrote:
Shiller used a 10 year period in his famous declaration in 1996 that, due to valuations, the stock market should be avoided for the next decade.

He was just as confident then as our PE/10 posters on this board are today.

Oops.

Nick


Not so fast. In 2008-09, stocks returned to 1996 levels.


Now I'm no math whiz, but it doesn't quite seem that 10 year stock prediction made in Jan, 1996 could include the years 2008-09.

Nick

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Postby letsgobobby » Sun Jun 05, 2011 11:19 pm

I edited my post to reflect the patience required for this approach. Not every investor will have it.

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Postby yobria » Sun Jun 05, 2011 11:36 pm

SP-diceman wrote:A Boglehead reduces equity after large market run-ups. (rebalance)
A Boglehead increases equity after large sell offs. (rebalance)

He didn’t identify anything.
The same thing happens here.

The boglehead has no clue when he reduces equity if it was “the” top.
He has no clue when he increases equity if its “the” bottom.
He’s simply following his plan.

The PE10’er is doing the same.
He reduces risk as equity increases, and
increases risk as equity decreases.

You can change your equity without “calling” tops/bottoms or “exploiting” something.
(Bogleheads do it all the time)

If you want to call something that causes you to adjust your equity a:
“Secret Technical Indicator”

I have no problem with it, but you would need to call a Bogleheads account balance a:
“Secret technical Indicator”.


Thanks
SP-diceman


These comments show a lack of understanding of the basic principles of investing and asset allocation.

Rebalancing when stocks rise is a means of returning to your target risk/return profile.

Using a trading scheme based on the PE/10 to try to guess when stocks are under or overvalued - when you're right but the Wall Street pros that set the prices are wrong - is a completely different concept.

It's the difference between considering yourself an average golfer, and thinking you can beat Tiger Woods.

The problem is, stocks have a PE of 5 or 10 or 30 for a reason. For example, last time stocks had really low P/Es (30 years ago), bonds were yielding something like 15%. Not the best time to dump bonds.

Just because mechanical market timing "follows a plan" like buy/hold/rebalance doesn't make it a legitimate strategy.

Nick

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Postby cjking » Mon Jun 06, 2011 7:27 am

yobria wrote:
cjking wrote:
yobria wrote:Um, before you leave them, you must identify them. And far more profitable to exploit them than just avoiding them (if you really believe in the system).


Please explain how you would make the level of profits you envision in your phrase "far more profitable" by exploiting a bubble, if it were possible to know one existed? For example, let's suppose it's the year 2000 and a time traveler has told you that the IRR from selling one 40th of an S&P 500 portfolio in each of the next 40 years is going to be an unimpressive 2% real.


As a practical matter, if you were really certain of this, you could enter into a long term options contract, exactly as Warren Buffett did a few years ago. Call your local investment bank.

As a practical matter, there is no option that will allow me to exploit this information. Nor will an investment bank be interested in creating a custom-derivative for my few hundred K.

PE10 predictiveness, even though accurate and valuable, cannot be exploited for speculative gain. It is nevertheless a market inefficiency, which might disappear, now that so much attention is being paid to it. If it does disappear, that won't necessarily end its value for all purposes, nor would that necessarily be harmful to someone who uses it as a trigger for varying asset allocation.


But - 40 years? Way too long a time period for a bubble.

You have a valid point, that the metaphor of a bubble implys sudden or rapid deflation at some point. I simply use it as shorthand for a period of "overvaluation" by which I mean when an asset is unusually unattractive relative to others, or its own history. A "bubble" (by my definition) doesn't have to have rapid or sudden deflations, though it usually will. The 2000 bubble does seem to be an exception, unwinding more slowly than previous bubbles, and a IPS that takes valuations into account must cope with this scenario.
Shiller used a 10 year period in his famous declaration in 1996 that, due to valuations, the stock market should be avoided for the next decade.

He was just as confident then as our PE/10 posters on this board are today.

Oops.

Nick

I agree that making fixed length predictions of any length is not a good way to use PE10. That, and anything that allows you to make speculative profits, aren't what it does well. (Edit: after consulting his data, I would say that the sort of prediction he should have made, in for example June 1996, was that the long-term expected real return on equities was between 3% and 4%. What that should mean for any particular person's allocation to equities might depend on their circumstances and strategy, and possibly on expected returns for alternative assets.)

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Postby SP-diceman » Mon Jun 06, 2011 10:04 am

yobria wrote:These comments show a lack of understanding of the basic principles of investing and asset allocation.

Tell me about understanding, a few posts ago PE10 was a divining rod used to identify
sector bubbles for exploitation.
(though I don’t think we nailed down if futures or puts should be used)
yobria wrote:Rebalancing when stocks rise is a means of returning to your target risk/return profile.

Yes, yes don’t stop at “rebalance” tell me how he rebalances.
Doesn’t he sell equity after a market rise?
Doesn’t he buy equity after a market fall?
(wow just like the PE10’er)

Since you spoke of understanding, let me see if understand you.
When a Boglehead reduces equity after market run-ups, he’s being “smart, safe, conservative”
When a PE10’er reduces equity after market run-ups he’s entering a dangerous, risky, casino.
When a Boglehead increases equity after market sell-offs, he’s being “smart, safe, conservative”
When a PE10’er increases equity after market sell-offs, he’s entering a dangerous, risky, casino.

A very, very interesting take on the situation.

yobria wrote:It's the difference between considering yourself an average golfer, and thinking you can beat Tiger Woods.

Wow, is that misguided.
Bogleheads beat professionals all the time.
Its not about being smarter than wallstreet.
Its about having a plan, diversification, low costs.
Its about reducing risk after market run-up’s and increasing risk after market sell off.
Probably 90% of what a PE10’er is doing.

Thanks
SP-diceman

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Postby dmcmahon » Mon Jun 06, 2011 10:08 am

Rodc wrote:At P/E (or P/E10) of 5 the earnings yield is 20%. Unless bond yields are very high that is going to look mighty attractive. May take folks a little time to overcome the fear that got yield so high, but eventually that yield will be too high to resist and dollars will flow back into stocks, raising P/E (P/E10, etc.)

Likewise, at a P/E (P/E10) level of 25 the earnings yield on stocks is only 4%, and unless bond yields are extremely low that will not be attractive for long.


And what about when stocks are at P/E10 of 25+, while at the same time bond yields are 3% (10-year) ranging to 4.2% (30-year)? In other words, when both stocks and bonds are equally unattractive?

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Postby yobria » Mon Jun 06, 2011 10:15 am

cjking wrote:As a practical matter, there is no option that will allow me to exploit this information. Nor will an investment bank be interested in creating a custom-derivative for my few hundred K.


If you really can produce that time machine (ie a 100% certainty of a result over 40 years), I'm sure you can raise plenty of investment capital.

cjking wrote:PE10 predictiveness, even though accurate and valuable, cannot be exploited for speculative gain. It is nevertheless a market inefficiency, which might disappear, now that so much attention is being paid to it.


Right, problem is you don't have that time machine. What you have is a vague pattern, that may take decades to emerge again, that doesn't work in other countries, and that may or may not work in the US going forward. So you really don't have much.

Heck, I can create one of those: Australia has outperformed Italy over the past century. So I predict that over the next 50 years, this will continue. If the pattern holds, that is.

Nick

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Postby cjking » Mon Jun 06, 2011 10:56 am

yobria wrote:
cjking wrote:As a practical matter, there is no option that will allow me to exploit this information. Nor will an investment bank be interested in creating a custom-derivative for my few hundred K.


If you really can produce that time machine (ie a 100% certainty of a result over 40 years), I'm sure you can raise plenty of investment capital.


The point of the "time machine" example was merely to get you to agree that accurate predictions are not necessarily exploitable by retail investor for speculative profits.

I believe there has been some recent theoretical work done that explains why even institutions may not be able to correct mispriced markets - I forget the details, but I think it was covered in threads on market efficiency in the past year or two. Books like "Wall Street Revalued" and "The Myth of the Rational Market" may also help in this regard.
[/quote]

cjking wrote:PE10 predictiveness, even though accurate and valuable, cannot be exploited for speculative gain. It is nevertheless a market inefficiency, which might disappear, now that so much attention is being paid to it.


Right, problem is you don't have that time machine. What you have is a vague pattern, that may take decades to emerge again, that doesn't work in other countries, and that may or may not work in the US going forward. So you really don't have much.
[/quote]

This paragraph is a series of assertions, none of which I agree with, backed by no reasoning at all. (Edit: OK I'm posting quickly because I have to go, I agree that I don't have a time machine. All I have is a very good predictor, on average, over the long term,of equity returns. )

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Postby letsgobobby » Mon Jun 06, 2011 11:19 am

yobria wrote:
cjking wrote:As a practical matter, there is no option that will allow me to exploit this information. Nor will an investment bank be interested in creating a custom-derivative for my few hundred K.


If you really can produce that time machine (ie a 100% certainty of a result over 40 years), I'm sure you can raise plenty of investment capital.

cjking wrote:PE10 predictiveness, even though accurate and valuable, cannot be exploited for speculative gain. It is nevertheless a market inefficiency, which might disappear, now that so much attention is being paid to it.


Right, problem is you don't have that time machine. What you have is a vague pattern, that may take decades to emerge again, that doesn't work in other countries, and that may or may not work in the US going forward. So you really don't have much.

Heck, I can create one of those: Australia has outperformed Italy over the past century. So I predict that over the next 50 years, this will continue. If the pattern holds, that is.

Nick


then, you had exactly the same percentage stocks in 1999 (PE10 40) as 2009 (PE10 10)? I just have a hard time seeing how that makes any sense.

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Postby fredflinstone » Mon Jun 06, 2011 12:18 pm

letsgobobby wrote:
yobria wrote:
cjking wrote:As a practical matter, there is no option that will allow me to exploit this information. Nor will an investment bank be interested in creating a custom-derivative for my few hundred K.


If you really can produce that time machine (ie a 100% certainty of a result over 40 years), I'm sure you can raise plenty of investment capital.

cjking wrote:PE10 predictiveness, even though accurate and valuable, cannot be exploited for speculative gain. It is nevertheless a market inefficiency, which might disappear, now that so much attention is being paid to it.


Right, problem is you don't have that time machine. What you have is a vague pattern, that may take decades to emerge again, that doesn't work in other countries, and that may or may not work in the US going forward. So you really don't have much.

Heck, I can create one of those: Australia has outperformed Italy over the past century. So I predict that over the next 50 years, this will continue. If the pattern holds, that is.

Nick


then, you had exactly the same percentage stocks in 1999 (PE10 40) as 2009 (PE10 10)? I just have a hard time seeing how that makes any sense.


I agree with letsgobobby. I don't think it makes sense to ignore valuations. First, taking into account valuation is common sense and, second, doing so is supported by 140 years of empirical data (per Pfau's paper).

I'm starting to draft a revised IPS. the formula I am tinkering with determines the percent in equities based on three factors: age, PE10, and the 5-year TIPS real yield:

min(100,(max(10,(144-(1.25*AGE)-(2*PE10)-(15*TIPS)))))

in the equation above, % equities can never be higher than 100 and never can be lower than 10. Keep in mind that I am somewhat more risk-averse than most investors and my need for growth is fairly low. Here are some sample values:

Code: Select all

PE10   age   TIPS     % equity
10     20       0           99
15     20       0           89
20     20       0           79
25     20       0           69
30     20       0           59
35     20       0           49
40     20       0           39   
      
10     40       0           74
15     40       0           64
20     40       0           54
25     40       0           44
30     40       0           34
35     40       0           24
40     40       0           14
      
10     60       0           49
15     60       0           39
20     60       0           29
25     60       0           19
30     60       0           10
35     60       0           10
40     60       0           10


any constructive criticism is welcome.

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Postby novastepp » Mon Jun 06, 2011 12:47 pm

Is there any way to determine how far the mean reversion will be? So someone following this approach looks at where we are today and says that the mean will revert...but how far?
The means are never static because data is added every day, so do you just assume reversion to a new PE10 number everyday, even if the change is minimal?
And who's to say the mean isn't going to creep upward or downward? Do you trend the trend?

Just inquiring, thanks.

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Postby Mel Lindauer » Mon Jun 06, 2011 1:11 pm

fredflinstone wrote:I'm starting to draft a revised IPS. the formula I am tinkering with determines the percent in equities based on three factors: age, PE10, and the 5-year TIPS real yield:

min(100,(max(10,(144-(1.25*AGE)-(2*PE10)-(15*TIPS)))))

in the equation above, % equities can never be higher than 100 and never can be lower than 10. Keep in mind that I am somewhat more risk-averse than most investors and my need for growth is fairly low. Here are some sample values:

Code: Select all

PE10   age   TIPS     % equity
10     20       0           99
15     20       0           89
20     20       0           79
25     20       0           69
30     20       0           59
35     20       0           49
40     20       0           39   
      
10     40       0           74
15     40       0           64
20     40       0           54
25     40       0           44
30     40       0           34
35     40       0           24
40     40       0           14
      
10     60       0           49
15     60       0           39
20     60       0           29
25     60       0           19
30     60       0           10
35     60       0           10
40     60       0           10


any constructive criticism is welcome.


I notice that your formula would never have an investor in TIPS, even at 60, right before retirement. I don't think that makes sense. Look at all the great TIPS returns you would have missed.
Best Regards - Mel | | Semper Fi


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