The failure of valuation predictions

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Johno
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Re: The failure of valuation predictions

Post by Johno »

larryswedroe wrote:Homer
the problem is that when financial economists state the term expected return they mean that it's just the mean of a wide potential dispersion. It's the investors who make the mistake of treating it with precision that isn't meant to be.
Larry
I agree. By standard definitions saying 'the expected return is 4%' does not say anything whatsoever about the variability of return. Those who interpret that statement to necessarily imply a tight clustering around 4% are the ones making a mistake. I think it really comes down to what was said above: understanding statistics or not. Interpreting an expected return of X as meaning the realized return will be close to X, predicting the future as in a crystal ball, is a basic misunderstanding of, outright refusal to try to understand it sometimes seems, statistical concepts.
edge
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Re: The failure of valuation predictions

Post by edge »

Um, just because a point falls within a normal distribution does not make the distribution normal. Sort of a weird statement.
larryswedroe wrote:edge

actually only at short horizons are markets not LOG normally distributed--they cannot be normally distributed. at longer horizons like even a year they are pretty log normally distributed

Also as others have noted,-- MCS can easily account for non normal distributions

And finally the three largest drops in the last 45 years, all about 50% or more are all in the "normal" distribution, in the left tail of that log normal distribution

Given those facts IMO your statement doesn't hold up
Larry
Quark
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Re: The failure of valuation predictions

Post by Quark »

Johno wrote:
larryswedroe wrote:Homer
the problem is that when financial economists state the term expected return they mean that it's just the mean of a wide potential dispersion. It's the investors who make the mistake of treating it with precision that isn't meant to be.
Larry
I agree. By standard definitions saying 'the expected return is 4%' does not say anything whatsoever about the variability of return. Those who interpret that statement to necessarily imply a tight clustering around 4% are the ones making a mistake. I think it really comes down to what was said above: understanding statistics or not. Interpreting an expected return of X as meaning the realized return will be close to X, predicting the future as in a crystal ball, is a basic misunderstanding of, outright refusal to try to understand it sometimes seems, statistical concepts.
Just knowing that it's wrong "to necessarily imply a tight clustering around 4%" doesn't tell you if the expected range is, for example, 3% to 5% or -16% to 24%. That would seem a useful bit of information.

We frequently see forecasts to one or more decimal places. That would imply a range of less than +/- one percentage point.

See the prior posts by Rodc and others in this thread making the same point.
Rodc
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Re: The failure of valuation predictions

Post by Rodc »

Right. If I have some reason to believe I have a particular distribution, say Gaussian for fun, and I have 100 samples I can fit a curve to those samples and use that curve to generate 10,000 samples some of which will be outside the range of what I measured.
Just to expand a bit. If in this case I fit a Gaussian, but in reality the distribution is Cauchy, my sim might do an ok job of estimating the central tendency of the resulting distribution from years of investing. But if I want something like the withdrawal rate that results in a 97% chance of not running out of money the answer will be very optimistic.

On the other hand, if I fit a Cauchy distribution and reality is Gaussian (or lognormal) my answer will be very pessimistic.

So depending on what you want to know, one has to be very careful regarding the inputs.

In general our ability to even set the most basic inputs like expected mean are very limited and so the value of Monte Carlo sim is often limited to making nice looking graphs and selling people investment products.

As a homework assignment, given 100 samples of annual real returns with a mean of 7% and a standard deviation of 20%, what might the actual mean of the randomly sampled distribution be (say with a 95% confidence interval)? Or perhaps better put, what is the standard deviation of the error in the sample mean vs the actual mean? Make whatever simplifying assumption you like to make the problem tractable. Given this answer, what is the value of a Monte Carlo simulation that uses this mean?
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.
Johno
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Re: The failure of valuation predictions

Post by Johno »

Quark wrote:
Johno wrote:
larryswedroe wrote:Homer
the problem is that when financial economists state the term expected return they mean that it's just the mean of a wide potential dispersion. It's the investors who make the mistake of treating it with precision that isn't meant to be.
Larry
I agree. By standard definitions saying 'the expected return is 4%' does not say anything whatsoever about the variability of return. Those who interpret that statement to necessarily imply a tight clustering around 4% are the ones making a mistake. I think it really comes down to what was said above: understanding statistics or not. Interpreting an expected return of X as meaning the realized return will be close to X, predicting the future as in a crystal ball, is a basic misunderstanding of, outright refusal to try to understand it sometimes seems, statistical concepts.
1. Just knowing that it's wrong "to necessarily imply a tight clustering around 4%" doesn't tell you if the expected range is, for example, 3% to 5% or -16% to 24%. That would seem a useful bit of information.

2. We frequently see forecasts to one or more decimal places. That would imply a range of less than +/- one percentage point.
I think this response just repeats the basic problem. Expected return by standard definition means the midpoint of the distribution of future outcomes and isn't intended to say anything about the range. OTOH there is no standard concept of an 'expected range'. So again the problem in many cases is that the person stating his or her estimate of the expected return is speaking in standard statistical terms, but some of the audience doesn't understand those terms.

A random variable has an expected value and a variance. It's fair for you to say you'd like to know an estimate of the variance, but not reasonable to try to redefine expected value as also including variance, and say it's automatically illegitimate or misleading to just quote an expected value. Only if the reader misunderstands what it means.

And for example for stocks there's fundamental reason earnings yield 1/PE[x] would tend to indicate expected return. It's the same relationship qualitatively, though not as tight a relationship quantitatively, that makes us think yield of risky bonds is related to their expected return, and more so still for low risk bonds. But 1/PE[x] gives no direct information about variance of future return. By your logic we would not discuss one separate topic, what does earnings yield tell us about the expected value, because it doesn't tell us much about *another topic*, the variance. That doesn't make sense to me.

2. Again this statement is full of potential confusion. Some people here vociferously insist that 'forecast' and 'expected return' are the same thing but in serious financial economic literature or discussion they simply aren't. When somebody on CNBC says the S&P will finish the year at 2150 I would agree there's an implication that they believe it will be close to that, and the implication of closeness is a bit stronger still if they say 2125, weaker if they say '2100, maybe 2200'. But in financial economic literature if a writer says a certain method yields an expected return of 3.6% and another method gives 4.1%, neither number is implying anything about the variance in realized return. And in that case it's just confusing to say 'both methods come up with an expected return of 4%'. The reader can see that varying methods yield different estimates and make of that difference what they will for their own purposes. They don't need to have it censored 'for their own safety' as 'both give 4%'.
larryswedroe
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Re: The failure of valuation predictions

Post by larryswedroe »

Rod

I think most people would say that events like the oil embargo of 73-74, the Asian Contagion of 1998, the events around 911 and the financial crisis were all "black swans"--highly significant events that were basically not forecasted.

Now that doesn't mean we could not have a much bigger event, but the Great Depression is in the data and during that event the market crashed about 85% if memory serves

Larry
Rodc
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Re: The failure of valuation predictions

Post by Rodc »

larryswedroe wrote:Rod

I think most people would say that events like the oil embargo of 73-74, the Asian Contagion of 1998, the events around 911 and the financial crisis were all "black swans"--highly significant events that were basically not forecasted.

Now that doesn't mean we could not have a much bigger event, but the Great Depression is in the data and during that event the market crashed about 85% if memory serves

Larry
Hi Larry,

That may be. I suppose it is just a matter of the definition one wants to use.

Something like 2008 was indeed not well forecast and the timing not forecast at all. So in that sense it was indeed a great surprise.

But on the other hand, I think most understand that a 50% market crash is to be expected to come out of the blue at least a couple/few times in an investing lifetime, so while the specifics were a surprise the fact that market crashes happen was not in general a surprise.
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.
Quark
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Re: The failure of valuation predictions

Post by Quark »

Johno wrote:I think this response just repeats the basic problem. Expected return by standard definition means the midpoint of the distribution of future outcomes and isn't intended to say anything about the range. OTOH there is no standard concept of an 'expected range'. So again the problem in many cases is that the person stating his or her estimate of the expected return is speaking in standard statistical terms, but some of the audience doesn't understand those terms.
Expected return (or expected value) is the probability weighted sum of the possible outcomes. For example, a 1% chance of 1,000,000 and a 99% chance 1 has an expected value of approximately 10,000, which is not the midpoint.

http://www.investopedia.com/walkthrough ... eturn.aspx or http://ci.columbia.edu/ci/premba_test/c ... /s6_3.html

You certainly can report expected return without more, but without an indication of variance, just the expected return number is not nearly as useful. If you have the data to calculate expected return, you should be able to come up with some measure of dispersion. Reporting within one or two standard deviations is pretty common.

For what it's worth, if you google "expected return formula" (or at least if I do it), most links also cover the formula for variance.
sk.dolcevita
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Re: The failure of valuation predictions

Post by sk.dolcevita »

Rodc wrote:
Right. If I have some reason to believe I have a particular distribution, say Gaussian for fun, and I have 100 samples I can fit a curve to those samples and use that curve to generate 10,000 samples some of which will be outside the range of what I measured.
Just to expand a bit. If in this case I fit a Gaussian, but in reality the distribution is Cauchy, my sim might do an ok job of estimating the central tendency of the resulting distribution from years of investing. But if I want something like the withdrawal rate that results in a 97% chance of not running out of money the answer will be very optimistic.

On the other hand, if I fit a Cauchy distribution and reality is Gaussian (or lognormal) my answer will be very pessimistic.

So depending on what you want to know, one has to be very careful regarding the inputs.

In general our ability to even set the most basic inputs like expected mean are very limited and so the value of Monte Carlo sim is often limited to making nice looking graphs and selling people investment products.

As a homework assignment, given 100 samples of annual real returns with a mean of 7% and a standard deviation of 20%, what might the actual mean of the randomly sampled distribution be (say with a 95% confidence interval)? Or perhaps better put, what is the standard deviation of the error in the sample mean vs the actual mean? Make whatever simplifying assumption you like to make the problem tractable. Given this answer, what is the value of a Monte Carlo simulation that uses this mean?
You don't necessarily need to use Gaussian or Cauchy, or such distribution for MCS. One could use the actual empirical data of historical returns to draw samples from. Of course, the question remains how closely does the empirically observed distribution approximate the true population (i.e. how stationary it is) . But one got to start somewhere - it is futile to hunt for perfection. The key is to understand well, really well, the limit of one's analysis and to not give in to siren song of mathematical/numerical precision (false).
Rodc
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Re: The failure of valuation predictions

Post by Rodc »

The key is to understand well, really well, the limit of one's analysis and to not give in to siren song of mathematical/numerical precision
That is certainly true.

Unfortunately the limits of Monte Carlo simulations are such that in general they are not all that useful in this context, IMHO.

FWIW: I strongly encourage one to go through the exercise I suggested to gain a better understanding the limits of MC.
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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JoMoney
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Re: The failure of valuation predictions

Post by JoMoney »

The key is to understand well, really well, the limit of one's analysis and to not give in to siren song of mathematical/numerical precision
What this amounts to though, as Rodc already implied, is your results are just a "subjective probability" needlessly ran through a mathematical exercise. It's already known it lacks precision, fails the basic axioms of probability, and will be skewed to your subjective weightings.
"To achieve satisfactory investment results is easier than most people realize; to achieve superior results is harder than it looks." - Benjamin Graham
larryswedroe
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Re: The failure of valuation predictions

Post by larryswedroe »

Rod completely agree and we explicitly warn clients/investors to EXPECT randomly several more of these in their lifetimes making it critical that they don't take more risk than they have the ability, willingness or need to take. And showing them the bottom 5% of MCS results is a good way to do that IMO. In other words, battles are won in the preparatory phase, not on the battlefield itself. Forewarned is forearmed.
My point was simply to show that these massive drops are already in the runs of MCS even if you just used historical data



Best wishes
Larry
lack_ey
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Re: The failure of valuation predictions

Post by lack_ey »

JoMoney wrote:
The key is to understand well, really well, the limit of one's analysis and to not give in to siren song of mathematical/numerical precision
What this amounts to though, as Rodc already implied, is your results are just a "subjective probability" needlessly ran through a mathematical exercise. It's already known it lacks precision, fails the basic axioms of probability, and will be skewed to your subjective weightings.
I'm not seeing in which sense you mean that the axioms of probability are being violated. Which one and how?

We don't know the actual probabilities of different events, so we have estimates for those. Different people disagree on what the best estimates might be. Step 3: ??? Step 4: axiom violated?
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JoMoney
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Re: The failure of valuation predictions

Post by JoMoney »

lack_ey wrote:
JoMoney wrote:
The key is to understand well, really well, the limit of one's analysis and to not give in to siren song of mathematical/numerical precision
What this amounts to though, as Rodc already implied, is your results are just a "subjective probability" needlessly ran through a mathematical exercise. It's already known it lacks precision, fails the basic axioms of probability, and will be skewed to your subjective weightings.
I'm not seeing in which sense you mean that the axioms of probability are being violated. Which one and how?

We don't know the actual probabilities of different events, so we have estimates for those. Different people disagree on what the best estimates might be. Step 3: ??? Step 4: axiom violated?
The one I think most obvious, Second axiom, "...if you cannot precisely define the whole sample space, then the probability of any subset cannot be defined either"
"To achieve satisfactory investment results is easier than most people realize; to achieve superior results is harder than it looks." - Benjamin Graham
lack_ey
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Re: The failure of valuation predictions

Post by lack_ey »

JoMoney wrote:
lack_ey wrote:
JoMoney wrote:
The key is to understand well, really well, the limit of one's analysis and to not give in to siren song of mathematical/numerical precision
What this amounts to though, as Rodc already implied, is your results are just a "subjective probability" needlessly ran through a mathematical exercise. It's already known it lacks precision, fails the basic axioms of probability, and will be skewed to your subjective weightings.
I'm not seeing in which sense you mean that the axioms of probability are being violated. Which one and how?

We don't know the actual probabilities of different events, so we have estimates for those. Different people disagree on what the best estimates might be. Step 3: ??? Step 4: axiom violated?
The one I think most obvious, Second axiom, "...if you cannot precisely define the whole sample space, then the probability of any subset cannot be defined either"
For whatever you're interested in, the sample space is just the set of all possible outcomes. If looking at the return of an asset in the next year in percentage, all the numbers between -100% and infinity. Where's the problem mathematically?
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JoMoney
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Re: The failure of valuation predictions

Post by JoMoney »

The problem is your prior knowledge of "all possible outcomes". If the limits you propose are being somewhere between losing everything and infinite gain, and weighting it all equally, you're not going to get anything out of the result, other than your prior assertion that anything and everything was possible.
Typically people run these scenarios estimating it as being bound by either their subjective belief or inferring that the future can't be different from the limits of the past, which is empirically proven wrong over and over again.
"To achieve satisfactory investment results is easier than most people realize; to achieve superior results is harder than it looks." - Benjamin Graham
lack_ey
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Re: The failure of valuation predictions

Post by lack_ey »

JoMoney wrote:The problem is your prior knowledge of "all possible outcomes". If the limits you propose are being somewhere between losing everything and infinite gain, and weighting it all equally, you're not going to get anything out of the result, other than your prior assertion that anything and everything was possible.
Typically people run these scenarios estimating it as being bound by either their subjective belief or inferring that the future can't be different from the limits of the past, which is empirically proven wrong over and over again.
I'm just telling you that the set of all possible outcomes is definitely kosher from the mathematical perspective. You were making a precise argument about the mathematics getting broken, "the axioms of probability [] being violated." No, we can actually "precisely define the whole sample space." Were this not the case, then the math would break down or would need to be relaxed.

We look at a set of subsets of the sample space (events). Each has a certain probability. Nobody said that different events occur with equal likelihood, like returns between -80% and -50% being as likely as returns between -10% and 20%. And nobody said that we actually know what the probabilities are. As I said, people will disagree about what those probabilities are. That's life. Most all of our models of real life are wrong, just to different degrees.

I don't suggest that people assume the future can't be different from the limits of the past, and in general I would recommend methods that attempt to be more consistent with the past where possible (it's not all subjective) and that square with knowledge about the world.
cottonseed1
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Re: The failure of valuation predictions

Post by cottonseed1 »

We have gone on for 3 pages debating the merits of this model or that, how the output of the model should be stated interpreted etc. I think Charlie Munger sums it up in 4 sentences.
Charlie Munger wrote:"People have always had this craving to have someone tell them the future. Long ago, kings would hire people to read sheep guts. There's always been a market for people who pretend to know the future. Listening to today's forecasters is just as crazy as when the king hired the guy to look at the sheep guts."
Rodc
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Re: The failure of valuation predictions

Post by Rodc »

And showing them the bottom 5% of MCS results is a good way to do that IMO. In other words, battles are won in the preparatory phase, not on the battlefield itself.
Hi Larry,

As I have heard in general, not specific to investing (I think it was a General talking about battle plans), the value is not in the details of the plan but in going through the planning process.

In this case one should not believe that specific value attached to the 5th percentile answer (for example a SWR of precisely 4.2%), but it is very valuable to get someone to understand that 8% is hugely optimistic and that 4%(ish) would be more prudent, and they may need to adjust. Could be one uses a MC sim, historical data or whatever.

Rod
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.
larryswedroe
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Re: The failure of valuation predictions

Post by larryswedroe »

Rod
Again we are in complete agreement, in fact I always explain that outcomes of MCS are NOT the odds, we don't know the exact odds. They are only our best ESTIMATES of the odds and one should treat them as such. In addition one should have plan B's already decided on, the actions you will take if the left tails do show up so that your portfolio will not fail.

Best wishes
Larry
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baw703916
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Re: The failure of valuation predictions

Post by baw703916 »

cottonseed1 wrote:We have gone on for 3 pages debating the merits of this model or that, how the output of the model should be stated interpreted etc. I think Charlie Munger sums it up in 4 sentences.
Charlie Munger wrote:"People have always had this craving to have someone tell them the future. Long ago, kings would hire people to read sheep guts. There's always been a market for people who pretend to know the future. Listening to today's forecasters is just as crazy as when the king hired the guy to look at the sheep guts."
I agree that it's hard to know the future. But you still need to do financial planning. Simply disparaging attempts to forecast future returns doesn't offer any guide as to how much should be saved for retirement/college/whatever or how it should be allocated. You have to do something, based on some criterion, however suspect that criterion might be.
Most of my posts assume no behavioral errors.
sk.dolcevita
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Re: The failure of valuation predictions

Post by sk.dolcevita »

baw703916 wrote:
cottonseed1 wrote:We have gone on for 3 pages debating the merits of this model or that, how the output of the model should be stated interpreted etc. I think Charlie Munger sums it up in 4 sentences.
Charlie Munger wrote:"People have always had this craving to have someone tell them the future. Long ago, kings would hire people to read sheep guts. There's always been a market for people who pretend to know the future. Listening to today's forecasters is just as crazy as when the king hired the guy to look at the sheep guts."
I agree that it's hard to know the future. But you still need to do financial planning. Simply disparaging attempts to forecast future returns doesn't offer any guide as to how much should be saved for retirement/college/whatever or how it should be allocated. You have to do something, based on some criterion, however suspect that criterion might be.
Correct. Dare I say this kind of Boglehead ideological purity is as dangerous as the siren song of mathematical precision I mentioned above?

IMHO, it would be silly to not to learn from past, however, imperfect that process may be. BTW, statisticians (at least good ones) recognize the limit of their inquiry. Quoting George Box - "All models are wrong but some are useful." (https://en.wikipedia.org/wiki/All_models_are_wrong).
Johno
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Re: The failure of valuation predictions

Post by Johno »

Quark wrote:
Johno wrote:I think this response just repeats the basic problem. Expected return by standard definition means the midpoint of the distribution of future outcomes and isn't intended to say anything about the range. OTOH there is no standard concept of an 'expected range'. So again the problem in many cases is that the person stating his or her estimate of the expected return is speaking in standard statistical terms, but some of the audience doesn't understand those terms.
Expected return (or expected value) is the probability weighted sum of the possible outcomes. For example, a 1% chance of 1,000,000 and a 99% chance 1 has an expected value of approximately 10,000, which is not the midpoint.

You certainly can report expected return without more, but without an indication of variance, just the expected return number is not nearly as useful. If you have the data to calculate expected return, you should be able to come up with some measure of dispersion. Reporting within one or two standard deviations is pretty common.

For what it's worth, if you google "expected return formula" (or at least if I do it), most links also cover the formula for variance.
It's descending into semantics if one is going to nitpick at 'midpoint' v probability weighted averaged. Midpoint in the sense that if the distribution were cut out of a sheet of wood, that's where you'd pick it up and it would balance.

The bigger point is this conflation of expected value and variance. Yes they are often discussed together, yes it's nice to have an estimate for both. But they are different and one is not somehow inherently invalid without the other. I see a lot of comments on a lot of threads IMO display inability to or refusal to distinguish between the two, as in making the erroneous inference of a small variance from the fact that only an expected value is quoted or that it might be quoted in .1's of a %. Again, there are methods to derive an expected value for the return of stocks, for example dividend yield and growth based on fundamental trends, or earnings yield, which have a fundamental basis, but which don't give any indication of variance. Likewise short term variance is fairly predictable via VIX or GARCH but those methods say nothing directly about short term expected return. It's entirely artificial in my view to criticize a method of analyzing one thing because it's not also a method of analyzing something else.

I really think a lot of the comments against expected return estimates come down too either or both of:
1) basic lack of conceptual understanding of statistics
2) not liking the fact that fundamental estimates of expected return tend to come out distressingly low nowadays
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Re: The failure of valuation predictions

Post by Rodc »

I really think a lot of the comments against expected return estimates come down too either or both of:
1) basic lack of conceptual understanding of statistics
2) not liking the fact that fundamental estimates of expected return tend to come out distressingly low nowadays
Interestingly enough, I would suggest those pointing out that one needs to understand the quality of the estimates in order to sensibly use them are the one that likely have the best conceptual understanding of statistics.

I for one am not concerned about whether the estimate are low or not.
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.
cottonseed1
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Re: The failure of valuation predictions

Post by cottonseed1 »

baw703916 wrote: I agree that it's hard to know the future. But you still need to do financial planning. Simply disparaging attempts to forecast future returns doesn't offer any guide as to how much should be saved for retirement/college/whatever or how it should be allocated. You have to do something, based on some criterion, however suspect that criterion might be.
This reminds me of a story. A poker player is playing in his local game. His friend walks up to him and says, "You know there is cheating going on in that game." The player responds, "Yes I know that, but it is the only game in town!"

I think a useful analogy to this problem is how an outfielder catches a fly ball. Baseball players aren't doing physics equations in order to calculate where fly balls will land. In fact, studies have shown that when standing still outfielders are surprisingly poor at predicting where balls when land. In order to catch a fly ball they follow a simple heuristic: 1) Fixate one's gaze on the ball 2) start running 3) adjust one's speed so that the angle of the gaze remains constant 4) catch the ball

Obviously, investing is not physics and calculating a where a fly ball will land is far simpler than predicting the outcome of markets. In order to maintain a reasonable sense of accuracy with expected returns the confidence interval has to be so wide that it is not providing very much actionable information. This would be akin to telling an outfielder that you are confident a fly ball is going to land in the outfield, probably somewhere in left field. What you are telling him may be factually correct, but it is not very useful.

With saving for retirement I think most reasonable people behave like the outfielder. They make a very rough estimate of savings rate/returns or withdrawal/spending rate needed to sustain their retirement. They start saving/investing in a diversified portfolio that minimizes cost and adjust accordingly. If they are smart they realize that the consequences from under saving/overspending are more severe than over saving/under spending. When it doubt they err on the side of having too much rather than too little.

I think this is a particularly wise way to go about things. You listen to less noise/BS. You don't have to discern which forecast/forecasters are better than others. And you get to focus on the variables in which you have control i.e your saving/spending rate, frictional cost etc. This type of thinking is simple, yet effective. It certainly doesn't make for very sophisticated white paper, which is why you do not see much of it from the investment industry.
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