You, Too, Can Predict Stock Market Returns

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SimpleGift
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Re: You, Too, Can Predict Stock Market Returns

Post by SimpleGift » Sat Mar 31, 2012 9:17 pm

Rodc wrote:Long term returns going forward are "predicted" by current dividend yield. If we are in a recession or coming out of one, and companies cut dividends, well that is the way it will always be.

Does that really make sense?
Rodc, looking at the recent "Great Recession," it looks like dividends-per-share were raised above the long-term growth trend in the optimism before the downturn — and then when the cuts came, dividends were simply returned back to about their average long-term growth trend. Not sure if this is true for other major recessions, but it would seem to make sense in the course of the normal business cycle.

It's also important to remember that the output from the Gordon Equation is only a rough estimate — and refining it beyond a single, whole integer is probably way too much precision!

Image
Note: Dividends-per-share includes the effects of stock buybacks. See Hussman commentary upthread.
Source: Political Calculations
Last edited by SimpleGift on Sat Mar 31, 2012 11:02 pm, edited 1 time in total.
Cordially, Todd

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camontgo
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Re: You, Too, Can Predict Stock Market Returns

Post by camontgo » Sat Mar 31, 2012 11:01 pm

There is a recent free publication from the CFA Institute which has a collection of papers on the future of the Equity Risk Premium.

The collection is available here:

http://www.cfainstitute.org/learning/pr ... emium.aspx

It is a great read with a wide range of perspectives. Authors include Cliff Asness, Bob Arnott, Roger Ibbotson, Antti Ilmanen, Jeremy Siegel, and many others.

My favorite paper is from Dimson, Marsh, and Staunton. They break things down with the following equation, which is a little more detailed than the Gordon Growth Model:

Image

D/P = Dividend Yield
Delta S = Repurchases net of dilution due to new issues
i = inflation
g = real growth
Delta PE = return due to change in PE ratio over holding period

Bogle uses a very similar decomposition the "Occam's Razor" section of Common Sense.

Of course, as the authors emphasize, this equation is an identity not an assumption. Any view of future stock returns can be mapped into the equation. Nevertheless, I think it is interesting to build up an estimate of expected return from the individual terms. In Common Sense, Bogle calls the process a "reasoned consideration of future returns".

Dimson, Marsh, and Staunton make the following estimates:

Dividend Yield: 1.8%
Repurchase Yield Net of Dilution: 0.2%
Inflation: 2.4%
Real Growth: 2.6%
PE change: 0%

So, expected return is around 7%....which isn't too different from the OP's estimate using the Gordon Growth Model.
"Essentially, all models are wrong, but some are useful." - George E. P Box

SheebaElwood
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Re: Half a brain vs. a full brain.

Post by SheebaElwood » Sun Apr 01, 2012 7:10 am

FinanceFun wrote:
SheebaElwood wrote:
Taylor Larimore wrote:
Anyone with half a brain knows that one can time the market with valuation.
That may be true for those with "half a brain." Investment authorities with a "full brain" say this about market timing:

"I've said, 'Stay-the-course' a thousand times, and I meant it every time." (Jack Bogle in Common Sense on Mutual Funds
Here's an excerpt from a book from John Bogle. You may have heard of him. He's the founder of Vanguard.

p.105: That the dividend yield as 2000 began was at an all-time low of just 1% and the PE at a near record high of 32 times earnings together explain why the average return on stocks in the current decade is at present running at an annual rate of less than 1%.

p. 237: "But, in late 1999, concerned about the (obviously) speculative level of stock prices, I reduced my equities to about 35% of assets, thereby increasing my bond position to about 65%."


"You can't time the market" really should be read as "It can be done, and done quite EASILY, however, odds are, YOU'RE not going to understand things like PE ratios, so don't bother. It's buy and hold for people like you."

For people with basic grasp of the stock market, timing is the way to go.

You Should Have Timed the Market
http://online.wsj.com/article/SB1000142 ... nalfinance
This is a foolish interpretation of what was said. To argue that reversion to the mean is more likely to have a larger impact the further from the mean you stray, is accurate and logical. To then extrapolate that and claim you can time the market - is absurd. In your example, why wouldn't you have gotten out of equities at 25 PE? 30? How much gain would you have left on the table if you sold at 25PE? And if you waited to the peak at 40 PE, how did you predict the continued multiple expansion?

It's easy to pretend to be smart in hindsight. But the simple fact is that you cannot tell me where equities will be 1 week, 1 year, or 1 decade from now. Nor can you tell me what the earnings multiple will be. How then can you claim to be able to time the market.... ???

Back to your example, the strategy of rebalancing should have been providing exit points all along the multiple expansion timeline. At 30 or 40... Or frankly anything north of 20, COULD be seen as a good time to trim your AA of stocks on a reversion to the mean basis. No one here would lambaste you for taking 10-15% stocks and move into bonds based on the principles of reversion to the mean. It's not ivory tower purist, but certainly viable.

My favorite quote on financial markets "the market can stay irrational, longer then I can stay solvent"

If you do have the ability to time the market, or talk to the dead, walk on water, fly... Then I expect you will shortly be a billionaire, and you can report back to us when that happens.

When the market PE is 2 standard deviations above the average, sell.
When the market PE is 2 standard deviations below the average, buy.

FinanceFun
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Re: You, Too, Can Predict Stock Market Returns

Post by FinanceFun » Sun Apr 01, 2012 7:23 am

camontgo wrote:There is a recent free publication from the CFA Institute which has a collection of papers on the future of the Equity Risk Premium.

The collection is available here:

http://www.cfainstitute.org/learning/pr ... emium.aspx

It is a great read with a wide range of perspectives. Authors include Cliff Asness, Bob Arnott, Roger Ibbotson, Antti Ilmanen, Jeremy Siegel, and many others.

My favorite paper is from Dimson, Marsh, and Staunton. They break things down with the following equation, which is a little more detailed than the Gordon Growth Model:

Image

D/P = Dividend Yield
Delta S = Repurchases net of dilution due to new issues
i = inflation
g = real growth
Delta PE = return due to change in PE ratio over holding period

Bogle uses a very similar decomposition the "Occam's Razor" section of Common Sense.

Of course, as the authors emphasize, this equation is an identity not an assumption. Any view of future stock returns can be mapped into the equation. Nevertheless, I think it is interesting to build up an estimate of expected return from the individual terms. In Common Sense, Bogle calls the process a "reasoned consideration of future returns".

Dimson, Marsh, and Staunton make the following estimates:

Dividend Yield: 1.8%
Repurchase Yield Net of Dilution: 0.2%
Inflation: 2.4%
Real Growth: 2.6%
PE change: 0%

So, expected return is around 7%....which isn't too different from the OP's estimate using the Gordon Growth Model.
Another fantastic equation. I wonder if we could calculate delta PE using reversion to the mean over a specified period? Current PE is ~14. Historical mean is 16. Can we assume that over the next ten years we will revert to the mean and add that into your expected returns equation?

I also like that buy backs are NET, as many companies who have buy backs don't materially impact their float.

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Re: Half a brain vs. a full brain.

Post by FinanceFun » Sun Apr 01, 2012 7:27 am

SheebaElwood wrote: When the market PE is 2 standard deviations above the average, sell.
When the market PE is 2 standard deviations below the average, buy.
How is this materially different then Rebalancing?

Hint: it isn't... Although, I would recommend a "lighter" trigger. 2 SD's is a big move. There are a lot more opportunities to capture gains and lower volatility using a rule of delta in deviation from target AA. In my case, I use 5%. 10% is just as viable. This would function similar to your 2 SD rule, but would be hit more frequently.

Another approach would be to use rebalancing for your target AA, AND tilt your AA ~10% based on your 2 SD rule. Let's you capture the frequent rebalance opportunities, and large moves in the market based on reversion to the mean. I think most here would be fine with an approach like this. Still...it isn't market timing.

Rodc
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Re: You, Too, Can Predict Stock Market Returns

Post by Rodc » Sun Apr 01, 2012 9:54 am

It's also important to remember that the output from the Gordon Equation is only a rough estimate — and refining it beyond a single, whole integer is probably way too much precision!
I agree completely.

As I have often noted, with 100 years of annual returns, and very optimistic assumptions, we can only estimate the true mean of annual returns to about +/- 2% (ie stdev of the error in the estimate of mean of the distribution is 2%). What I mean is, suppose we have a fair coin, and we estimate the distribution of heads and tails from 100 tosses - our estimate will most likely be off just by random luck as we most likely will not get 50 heads and tails. In a similar fashion 100 years of returns will give us the mean of what happened, but most likely won't give us the mean of the distribution of returns we should use going forward. And that is under wildly optimistic assumptions and ignoring that even if we do get the mean of the distribution correct we (like in the coin toss example) won't get that mean due to random luck.

All those considerations infect the terms in the Gordon equation (and similar) as well.

Using P/E10, Gordon equation, etc, we might be able to say things like, well we might expect market returns to be below average, around average, and above average with slightly better than a 50/50 chance of being correct, thinking we can say anything stronger is IMHO a fantasy.

Even a single digit of precision seems out of reach, both on historical grounds (know anyone who has done so consistently?) and on the basis of a simple statistical analysis of the information content of the available market data.
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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Re: Half a brain vs. a full brain.

Post by Rodc » Sun Apr 01, 2012 9:56 am

FinanceFun wrote:
SheebaElwood wrote: When the market PE is 2 standard deviations above the average, sell.
When the market PE is 2 standard deviations below the average, buy.
How is this materially different then Rebalancing?

Hint: it isn't... Although, I would recommend a "lighter" trigger. 2 SD's is a big move. There are a lot more opportunities to capture gains and lower volatility using a rule of delta in deviation from target AA. In my case, I use 5%. 10% is just as viable. This would function similar to your 2 SD rule, but would be hit more frequently.

Another approach would be to use rebalancing for your target AA, AND tilt your AA ~10% based on your 2 SD rule. Let's you capture the frequent rebalance opportunities, and large moves in the market based on reversion to the mean. I think most here would be fine with an approach like this. Still...it isn't market timing.
The difference is in how much you buy or sell. In rebalancing you typically move a few percent here or there. In full on market timing you make big bold moves. Could be all the way up to moving between 100% stocks and 100% bonds.
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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SimpleGift
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Re: You, Too, Can Predict Stock Market Returns

Post by SimpleGift » Sun Apr 01, 2012 11:33 am

Rodc wrote:
It's also important to remember that the output from the Gordon Equation is only a rough estimate — and refining it beyond a single, whole integer is probably way too much precision!
As I have often noted, with 100 years of annual returns, and very optimistic assumptions, we can only estimate the true mean of annual returns to about +/- 2% (ie stdev of the error in the estimate of mean of the distribution is 2%). What I mean is, suppose we have a fair coin, and we estimate the distribution of heads and tails from 100 tosses - our estimate will most likely be off just by random luck as we most likely will not get 50 heads and tails. In a similar fashion 100 years of returns will give us the mean of what happened, but most likely won't give us the mean of the distribution of returns we should use going forward. And that is under wildly optimistic assumptions and ignoring that even if we do get the mean of the distribution correct we (like in the coin toss example) won't get that mean due to random luck.

All those considerations infect the terms in the Gordon equation (and similar) as well.
Thanks, Rodc. This is the most clear and cogent explanation I've ever seen for those of us who are "statistics-challenged". :wink:
Cordially, Todd

TJSI
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Re: You, Too, Can Predict Stock Market Returns

Post by TJSI » Mon Apr 02, 2012 8:18 pm

Rick Ferri has suggested that foreign earnings growth should be included in the earnings growth component of the Gordon Model. It is often stated that foreign earnings are "sequested" due to a repatriation tax. If this is the case, then perhaps foreign earnings can't be included in the earnings growth estimate. Since dividends are paid out of cash certainly the tax effect of accessing foreign earnings would be included in any decision on dividend payouts. Maybe the foreign earnings addition need to be scaled back to reflect the repatriation tax.

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Re: You, Too, Can Predict Stock Market Returns

Post by Rodc » Tue Apr 03, 2012 8:40 am

Simplegift wrote:
Rodc wrote:Long term returns going forward are "predicted" by current dividend yield. If we are in a recession or coming out of one, and companies cut dividends, well that is the way it will always be.

Does that really make sense?
Rodc, looking at the recent "Great Recession," it looks like dividends-per-share were raised above the long-term growth trend in the optimism before the downturn — and then when the cuts came, dividends were simply returned back to about their average long-term growth trend. Not sure if this is true for other major recessions, but it would seem to make sense in the course of the normal business cycle.

It's also important to remember that the output from the Gordon Equation is only a rough estimate — and refining it beyond a single, whole integer is probably way too much precision!

Image
Note: Dividends-per-share includes the effects of stock buybacks. See Hussman commentary upthread.
Source: Political Calculations
Those three cases are interesting. Seems that current dividend yields at least at the short to mid term were anti-predictors of dividend growth.

This might imply that like past earnings are better predictors of future earning if you average over 10 years or so.

The Gordon equation framed that way would then be pretty close to: The future will be the past. Not too helpful.
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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Re: You, Too, Can Predict Stock Market Returns

Post by Lauretta » Sun Apr 15, 2018 9:39 am

SimpleGift wrote:
Fri Mar 30, 2012 10:02 am
In a recent thread on the equity premium, William Bernstein gently chided us for relying so much on historical data and reminded us of the simple formula for determining long-term expected equity returns — variously called the Gordon equation, the Gordon discounted dividend model or the constant growth dividend model. John Bogle also uses this simplified formula when he periodically opines on expected stock market returns (here with current nominal numbers):

Stock Market Returns (6.5%) = Current Dividend Yield (2%) + HIstorical Growth Rate of Dividends/Earnings (4.5%)

This made me curious if anyone had ever backtested the Gordon Model against long-term equity market returns to see if indeed it had any predictive power. A Google search turned up two interesting papers by Foerster and Sapp, one from 2006 that backtested the model against Shiller's database of dividends and equity returns from 1871 to 2005, and another from 2005 that examined the dividends and returns over 120 years from the Bank of Montreal, the longest dividend paying company in North America.

RESULTS: In both studies, they found that the Gordon discounted dividend model worked well at explaining actual equity prices that occurred 30 years in the future. When interviewed and asked if the model had predictive power, Dr. Foerster said, “On the whole it does,” says Foerster. “The deviations are consistent with times when investors are either overly optimistic or pessimistic.” Any thoughts to share?

Image
Source: Dividends and Stock Valuations
I know this is an old thread but just wondering how this model takes buybacks into account (in the light of the most recent thread on Swedroe)
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SimpleGift
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Re: You, Too, Can Predict Stock Market Returns

Post by SimpleGift » Sun Apr 15, 2018 10:00 am

Lauretta wrote:
Sun Apr 15, 2018 9:39 am
I know this is an old thread but just wondering how this model takes buybacks into account (in the light of the most recent thread on Swedroe)
Hi Lauretta,

Yes, you've stumbled on an old thread from 6 years ago, discussing a paper that backtested the Gordon Equation, to see how well it would have predicted stock returns in the past. I would say it's been superseded by this paper, which may be of interest to you:
This recent paper examines three models of stock returns (including the Gordon Equation), accounting for share buybacks.

EDIT: I see now this is the same paper being discussed in the Swedroe thread you reference. It must be a popular paper!
Cordially, Todd

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Re: You, Too, Can Predict Stock Market Returns

Post by AtlasShrugged? » Mon Apr 16, 2018 6:56 am

This might be a dumb question, but I will ask it anyway.
Thus, if you tally these items, you get:

2.0% Inflation
2.5% Real earnings growth from US sales
1.0% Real earnings from overseas sales
2.5% Dividend yield including buyback yield

That's an 8.0% sustainable return from equity, and it's 7% if you don't buy my excess overseas earnings adjustment.
Is a fair interpretation of Mr. Ferri's post that real returns are (2.5% Real earnings growth from US sales + 1.0% Real earnings from overseas sales + 2.5% Dividend yield including buyback yield) - 2.0% Inflation ? That would imply a real return of 4%. Am I right in my interpretation?
“If you don't know, the thing to do is not to get scared, but to learn.”

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Taylor Larimore
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Re: You, Too, Can Predict Stock Market Returns

Post by Taylor Larimore » Mon Apr 16, 2018 7:54 am

Bogleheads:

Approximately 10% is the average return (7% after inflation) for the S&P 500 since its inception back in 1928. Total Bond had an average return of about 5% (2% after inflation).

Personally, I make no attempt to forecast stock and bond market returns.

Suggestion:

* Spend less than you earn.

* Start saving 10% or more, early and regularly.

Result: A financially comfortable retirement.

Best wishes.
Taylor
"Simplicity is the master key to financial success." -- Jack Bogle

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