CAPE in the Context of Real Rates & Inflation, 1880-2018

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SimpleGift
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CAPE in the Context of Real Rates & Inflation, 1880-2018

Post by SimpleGift » Tue Mar 13, 2018 9:09 am

Like many perhaps, my vague notion has been that low interest rates lead to high stock valuations, and vice versa. From the classic discount model, index fund investors are paying for the net present value of the stock market's future earnings and cash flows. If interest rate expectations are low, investors are more willing to pay a higher multiple today in exchange for the more valuable future cash flows — and vice versa.

According to this traditional model, we should then expect that the lower the interest rate, the higher the CAPE value* in a continuous inverse relationship. The actual empirical evidence, however, presents a somewhat different historical relationship between CAPE and interest rates, which this post explores.

*CAPE, the Shiller P/E, or P/E 10 ratio, is a valuation measure usually applied to the U.S. S&P 500 equity market. It is defined as the market price divided by the moving average of the trailing ten years of earnings, adjusted for inflation.

REAL RATES & INFLATION: Since interest rates are made up of a real yield and an inflation component, we can look at each of these separately first, to observe their past impact upon CAPE values. In the two charts below, U.S. monthly 10-year real Treasury yields and trailing 12-month inflation rates are sorted in rank order, from lowest to highest, with their associated CAPE values.
  • Image
    NOTE: Horizontal axis is not linear. Real yield = nominal yield - 12-month trailing inflation.

    Image
    NOTE: Horizontal axis is not linear. Inflation = 12-month trailing rate.
    Source: Shiller Data
Far from being linear and monotonic (continuously increasing or decreasing), stock market valuations have tended to be highest when real rates are in the 2%-4% range and when inflation is in the 1%-3% range — and they fall off rather quickly on both sides of these two intervals. In addition, the relative impact of these two variables on CAPE values has been roughly equal in magnitude.

COMBINED IMPACTS: By integrating the real yield and inflation data, Research Affiliates in a 2017 paper developed a continuous function that describes CAPE values for any given level of real yield and inflation. This two-dimensional model was applied to both U.S. stocks since 1880 (at left below) and developed-market international stocks since 1972 (at right). In their model, the combination of real yields and inflation produced R^2 values over 50%, explaining over half of the variation in CAPE values.

Again, this combined model shows the highest CAPE values occurring when real rates were in the 2%-4% range and inflation was 1%-3%. Contrary to popular belief, reductions in real yields or inflation below these ranges did not boost stock valuations.
DISCUSSION: The key takeaway for me is that we've been close to the "sweet spot" for high equity valuations for quite a few years, with moderate real interest rates and inflation. A sustained rise in either one of these would likely be a shock to P/E multiples.

One caution: In a recent thread, we saw that CAPE values are not a stationary time series and — beyond real rates and inflation — investors are willing to pay different amounts for the same dollar of earnings in different eras. Thus the shape of the "topographic CAPE maps" above may remain constant, but the CAPE values of the contour lines seem bound to shift in different time periods.

Other thoughts?
Cordially, Todd

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Re: CAPE in the Context of Real Rates & Inflation, 1880-2018

Post by lazyday » Tue Mar 13, 2018 10:22 am

Historically, there has not been a strong relationship
between interest rates and valuations for real assets, and while inflation has impacted stock market
P/Es, the impact has been modest for smaller changes in inflation. Using the model that Jeremy
Grantham and I built years ago for explaining the Shiller P/E of the US stock market over time, an
increase in inflation to around 2.5% would actually cause the valuation of the stock market to increase,
not decrease. When we built the original “Investor Comfort” model in the late 1990s, I solved for the
market’s ideal level of inflation. It turned out to be 2.5% – any deviation from that level, whether up or
down, caused the market to trade at a lower valuation.
Ben Inker
GMO Quarterly Letter
December 14, 2017

Elsewhere, if I recall correctly, Grantham may have gone into more detail on the investor comfort model, updating it to include more variables.

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siamond
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Re: CAPE in the Context of Real Rates & Inflation, 1880-2018

Post by siamond » Tue Mar 13, 2018 2:37 pm

The trouble is:
- nominal interest rates (or yields) are interesting, as they have been a pretty good model for expected nominal returns for bonds.
- 1/CAPE values are interesting, as they have been a fairly decent model for expected real returns for stocks.
- but... there is no half decent way to compute expected inflation (please don't tell me that the common wisdom of TIPS investors represents greater wisdom than a complete shot in the dark! plus TIPS are fairly new anyway)
- so... we often end up using the trailing past 12 months of inflation (or some moving average) to convert a nominal interest rate in a real interest rate, not having any better idea.
- and... empirically, real interest rates computed in such a way proved to be a really POOR model for expected real returns for bonds. Simply because a past moving average of inflation is a very poor way to try to compute expected inflation.

I'm afraid that those considerations introduce such much noise in the charts computed by the OP that we may not be able to get anything useful out of them. Which is unfortunate, as this is a good question!

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Re: CAPE in the Context of Real Rates & Inflation, 1880-2018

Post by SimpleGift » Tue Mar 13, 2018 3:33 pm

siamond wrote:
Tue Mar 13, 2018 2:37 pm
- but... there is no half decent way to compute expected inflation (please don't tell me that the common wisdom of TIPS investors represents greater wisdom than a complete shot in the dark! plus TIPS are fairly new anyway)
- so... we often end up using the trailing past 12 months of inflation (or some moving average) to convert a nominal interest rate in a real interest rate, not having any better idea.
Agree, deriving real rates from nominal yields and trailing inflation data is not the best — and is only due to the absence of other good options. In the OP charts, I used trailing 12-month inflation to get real rates, while Arnott et. al. used 36-month trailing inflation for the real rates in their "CAPE topographic charts" above. Both produced similar results.

Just to add: My interest in the OP analysis was not to be forecasting expected returns for stocks, but rather to reinforce the point that macroeconomic conditions (especially real rates and inflation) have a large impact on stock valuations. Too often, Forum posters compare CAPE values across time, without conditioning the values for different real interest rate and inflation environments. Different times can mean very different "normal" CAPE values. A long-held peeve!
Cordially, Todd

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Re: CAPE in the Context of Real Rates & Inflation, 1880-2018

Post by gmaynardkrebs » Tue Mar 13, 2018 3:51 pm

I think it might be because very low real rates predict a loss in confidence in the future growth potential. In other words, if low real interest rates signal that something bad is up ahead for the economy (ie, lack of investable opportunities, which we may be seeing now with all the buybacks), one might reasonably assume that future corporate dividends, earnings and earnings growth, and cash flows to investors will not just go on willy-nilly as they have before. I've always thought that was a flaw in the Gordon equation, that it just took low interest rates as a number to use for discounting future cash flows, without looking at what the number was signalling about the likelihood of achieving the cash flows going ahead, in the presumably more dire economic environment in which future earnings/dividends/cash flows would have to be generated.

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Re: CAPE in the Context of Real Rates & Inflation, 1880-2018

Post by siamond » Tue Mar 13, 2018 5:55 pm

SimpleGift wrote:
Tue Mar 13, 2018 3:33 pm
My interest in the OP analysis was not to be forecasting expected returns for stocks, but rather to reinforce the point that macroeconomic conditions (especially real rates and inflation) have a large impact on stock valuations. Too often, Forum posters compare CAPE values across time, without conditioning the values for different real interest rate and inflation environments. Different times can mean very different "normal" CAPE values. A long-held peeve!
Yes, I understand. I didn't mean to overly focus on expected returns, just to emphasize that the comparison you ran used numbers related to different time frames. And... I don't how to do any better, and probably would have done something similar. :wink:

I've been wondering about this topic for a long time as well, while being actually quite skeptical about the premise that real interest rates have a truly significant impact on stock valuations. I am skeptical for a very simple reason. Bond returns and stock returns did NOT display a negative correlation, they had a roughly null (or slightly positive) correlation. This just doesn't jive with the premise. As to inflation, it did negatively correlate with stock (real) returns, albeit weakly. So... I am not too sure your pet peeve is entirely justified, to be honest. But it's a really good question.

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Re: CAPE in the Context of Real Rates & Inflation, 1880-2018

Post by Tyler9000 » Tue Mar 13, 2018 6:16 pm

SimpleGift wrote:
Tue Mar 13, 2018 3:33 pm
Just to add: My interest in the OP analysis was not to be forecasting expected returns for stocks, but rather to reinforce the point that macroeconomic conditions (especially real rates and inflation) have a large impact on stock valuations. Too often, Forum posters compare CAPE values across time, without conditioning the values for different real interest rate and inflation environments. Different times can mean very different "normal" CAPE values. A long-held peeve!
Well said, and very interesting. There are very few immutable constants in the universe, and it makes sense that a fixed "normal" CAPE value probably did not make the cut.

:sharebeer

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Re: CAPE in the Context of Real Rates & Inflation, 1880-2018

Post by siamond » Tue Mar 13, 2018 6:44 pm

SimpleGift wrote:
Tue Mar 13, 2018 9:09 am
By integrating the real yield and inflation data, Research Affiliates in a 2017 paper developed a continuous function that describes CAPE values for any given level of real yield and inflation. This two-dimensional model was applied to both U.S. stocks since 1880 (at left below) and developed-market international stocks since 1972 (at right). In their model, the combination of real yields and inflation produced R^2 values over 50%, explaining over half of the variation in CAPE values.
Didn't notice the reference to this new article from Research Affiliates. Will read, and quite possibly re-run the numbers, as the result seems quite surprising... Thanks for sharing!

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Re: CAPE in the Context of Real Rates & Inflation, 1880-2018

Post by SimpleGift » Tue Mar 13, 2018 6:49 pm

siamond wrote:
Tue Mar 13, 2018 5:55 pm
I've been wondering about this topic for a long time as well, while being actually quite skeptical about the premise that real interest rates have a truly significant impact on stock valuations. I am skeptical for a very simple reason. Bond returns and stock returns did NOT display a negative correlation, they had a roughly null (or slightly positive) correlation. This just doesn't jive with the premise. As to inflation, it did negatively correlate with stock (real) returns, albeit weakly. So... I am not too sure your pet peeve is entirely justified, to be honest. But it's a really good question.
With the data already in a spreadsheet, I ran 10-year rolling correlations between the Shiller CAPE values and both inflation and the estimated real rates. In the first chart below it appears that, with the exception of the Great Depression and the Great Recession, CAPE and inflation have been fairly consistently negatively correlated over the last century (low inflation = high CAPE and vice versa).
But when running the same analysis on CAPE and estimated real rates, it's hard to see any consistent correlation (chart below). If anything CAPE has perhaps been more positively correlated with real rates than negatively over the last century.
Keep in mind we're correlating inflation and real rates to stock valuations here, not stock returns.
Last edited by SimpleGift on Tue Mar 13, 2018 6:52 pm, edited 1 time in total.
Cordially, Todd

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Re: CAPE in the Context of Real Rates & Inflation, 1880-2018

Post by gmaynardkrebs » Tue Mar 13, 2018 6:52 pm

siamond wrote:
Tue Mar 13, 2018 5:55 pm
SimpleGift wrote:
Tue Mar 13, 2018 3:33 pm
My interest in the OP analysis was not to be forecasting expected returns for stocks, but rather to reinforce the point that macroeconomic conditions (especially real rates and inflation) have a large impact on stock valuations. Too often, Forum posters compare CAPE values across time, without conditioning the values for different real interest rate and inflation environments. Different times can mean very different "normal" CAPE values. A long-held peeve!
Yes, I understand. I didn't mean to overly focus on expected returns, just to emphasize that the comparison you ran used numbers related to different time frames. And... I don't how to do any better, and probably would have done something similar. :wink:

I've been wondering about this topic for a long time as well, while being actually quite skeptical about the premise that real interest rates have a truly significant impact on stock valuations. I am skeptical for a very simple reason. Bond returns and stock returns did NOT display a negative correlation, they had a roughly null (or slightly positive) correlation. This just doesn't jive with the premise. As to inflation, it did negatively correlate with stock (real) returns, albeit weakly. So... I am not too sure your pet peeve is entirely justified, to be honest. But it's a really good question.
I would argue that real interest rates should have a significant impact on stock valuations logically and mathematically. When they don't, this suggests that a countervailing force is at work. The question to me is, what is that countervailing force? Is it irrational exuberance? Animal spirits? QE? Thoughts, anyone?

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Re: CAPE in the Context of Real Rates & Inflation, 1880-2018

Post by siamond » Tue Mar 13, 2018 8:55 pm

SimpleGift wrote:
Tue Mar 13, 2018 6:49 pm
In the first chart below it appears that, with the exception of the Great Depression and the Great Recession, CAPE and inflation have been fairly consistently negatively correlated over the last century (low inflation = high CAPE and vice versa).
[...]
But when running the same analysis on CAPE and estimated real rates, it's hard to see any consistent correlation (chart below). If anything CAPE has perhaps been more positively correlated with real rates than negatively over the last century.
[...]
Keep in mind we're correlating inflation and real rates to stock valuations here, not stock returns.
Cool, I was going to do something like that, but you were faster! Yes, I understand, your point was about valuations and interest rates, but people typically use those metrics as a proxy for expected returns, hence my (admittedly approximate / cutting corners) reasoning in the previous post. Let me take a bit of time, and play with numbers as well. You certainly raised yet another intriguing topic!

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Re: CAPE in the Context of Real Rates & Inflation, 1880-2018

Post by Angst » Tue Mar 13, 2018 9:43 pm

siamond wrote:
Tue Mar 13, 2018 8:55 pm
SimpleGift wrote:
Tue Mar 13, 2018 6:49 pm
In the first chart below it appears that, with the exception of the Great Depression and the Great Recession, CAPE and inflation have been fairly consistently negatively correlated over the last century (low inflation = high CAPE and vice versa).
[...]
But when running the same analysis on CAPE and estimated real rates, it's hard to see any consistent correlation (chart below). If anything CAPE has perhaps been more positively correlated with real rates than negatively over the last century.
[...]
Keep in mind we're correlating inflation and real rates to stock valuations here, not stock returns.
Cool, I was going to do something like that, but you were faster! Yes, I understand, your point was about valuations and interest rates, but people typically use those metrics as a proxy for expected returns, hence my (admittedly approximate / cutting corners) reasoning in the previous post. Let me take a bit of time, and play with numbers as well. You certainly raised yet another intriguing topic!
One of the things I enjoy in particular at this website is when there's a thread that piques siamond's interest. Thank you both to siamond and SimpleGift! I'll probably just lurk about in the background while the two of you, and others, sort things out here. Interesting stuff. :)

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Re: CAPE in the Context of Real Rates & Inflation, 1880-2018

Post by Pelerus » Wed Mar 14, 2018 11:34 am

To echo gmaynardkrebs, here is my best guess for why we don’t see a more linear relationship (i.e. highest CAPEs at the lowest interest/inflation rates and lowest CAPEs at the highest interest/inflation rates).

The lowest interest & inflation rates tend to be associated with weaker economic conditions, characterized by low velocity of money (hence low inflation) and accommodative monetary policy/low demand for money (hence low interest rates).

Weaker economic conditions are in turn associated with lower stock valuations for fundamental reasons - that is, the magnitude of future cash flows is in doubt. Consequently, even if those future cash flows are discounted to present value at a lower rate, the present value still decreases since the lower discounting factor is overwhelmed by the lower future value factor.

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Re: CAPE in the Context of Real Rates & Inflation, 1880-2018

Post by SimpleGift » Wed Mar 14, 2018 11:49 am

gmaynardkrebs wrote:
Tue Mar 13, 2018 3:51 pm
I think it might be because very low real rates predict a loss in confidence in the future growth potential. In other words, if low real interest rates signal that something bad is up ahead for the economy (ie, lack of investable opportunities, which we may be seeing now with all the buybacks), one might reasonably assume that future corporate dividends, earnings and earnings growth, and cash flows to investors will not just go on willy-nilly as they have before.
This is similar to the view expressed in Research Affiliates' paper summarized in the OP — and my biggest takeaway from the paper. Once real rates and inflation move beyond their moderate "sweet spot" (either lower or higher), markets have higher uncertainty about future prices and growth. Thus it's not necessarily the absolute level of real rates or inflation causing valuations to fall, but the uncertainty — as interest rate and inflation volatility rise, the discount rate rises, reducing stock valuation multiples.
Cordially, Todd

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Re: CAPE in the Context of Real Rates & Inflation, 1880-2018

Post by Castanea_d. » Wed Mar 14, 2018 12:16 pm

Very interesting analysis and discussion; thank you for raising this issue.

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Re: CAPE in the Context of Real Rates & Inflation, 1880-2018

Post by TJSI » Wed Mar 14, 2018 6:36 pm

In answer to gmaynarkrebs question, I believe the best candidate for high valuations are buybacks. They are buying pressure for sure and unless they illicit a negative reaction are going to increase price.

Interest rates also play an important role. If interest rates continue to rise, bonds will again become a competitive source of income and serve as a competitor of stocks for investor money.

If buybacks are cut back at some time, we are likely to see a significant drop in valuations.

TJSI

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Re: CAPE in the Context of Real Rates & Inflation, 1880-2018

Post by siamond » Wed Mar 14, 2018 10:38 pm

SimpleGift wrote:
Tue Mar 13, 2018 9:09 am
By integrating the real yield and inflation data, Research Affiliates in a 2017 paper developed a continuous function that describes CAPE values for any given level of real yield and inflation. This two-dimensional model was applied to both U.S. stocks since 1880 (at left below) and developed-market international stocks since 1972 (at right). In their model, the combination of real yields and inflation produced R^2 values over 50%, explaining over half of the variation in CAPE values.
I skimmed through the paper. Can't claim I understand everything, but a few things struck me.

First, their goal is essentially to develop some sort of improved short-term forecast (polite way to say market timing), focusing on a model which constrains the CAPE assessment by market conditions (e.g. current interest rate, past 36 months of inflation) to improve the short-term forecasting power of CAPE (which is, as we know, totally ineffective for short-term horizons). Ok, well, good luck with that, I don't need to run the numbers to know that speculative forces will totally dwarf any such rationalization of market conditions.

Next, they readily acknowledge that the 'CAPE conditioning' model is useless beyond a three years horizon. Because inflation and real interest rates are basically unpredictable by then (indeed!). And they recommend to come back to the regular CAPE for such purpose.

Another thing is that their out-of-sample testing is VERY limited. Instead of testing each of the individual countries for which they have the numbers, they put them in an aggregate ('developed countries') and ran ONE test, over a few decades. This test happens to have some similarities with the US result, and they declared victory. Excuse me? That is not serious out-of-sample testing. They also seem to make the classic mistake of relying on ex post (hindsight) linear regressions without testing them in a purely ex ante (foresight) context. Which is a polite way to say 'data mining alert'.

Methodology issues aside, even if we make a giant leap of faith about this study, I am struggling with its relevance. Personally, I have zero interest in short-term forecasts (an exercise in foolishness). My interest in CAPE and interest rates (or yields) is about expected returns (in the statistical/probabilistic sense) for a 10+ years horizon, essentially for financial planning reasons. For which their model has zero applicability. So... what's the point? What am I missing? :shock:

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Re: CAPE in the Context of Real Rates & Inflation, 1880-2018

Post by SimpleGift » Wed Mar 14, 2018 11:43 pm

siamond wrote:
Wed Mar 14, 2018 10:38 pm
Methodology issues aside, even if we make a giant leap of faith about this study, I am struggling with its relevance. Personally, I have zero interest in short-term forecasts (an exercise in foolishness). My interest in CAPE and interest rates (or yields) is about expected returns (in the statistical/probabilistic sense) for a 10+ years horizon, essentially for financial planning reasons. For which their model has zero applicability. So... what's the point? What am I missing?
The OP and this thread are only focused on the historical relationship between CAPE values and macroeconomic variables (specifically real rates and inflation) — and that's the part that was referenced in Arnott et al's paper. Beyond their CAPE/rates/inflation model, their paper doesn't have much more to contribute to this discussion, as best I can tell.

The balance of their paper I can agree with you about — they seem to be trying to make too much hay from their model, using it to try to improve the short-term forecasting of stock returns, and even suggesting that their CAPE contours maps are "mean reversion targets" in various interest rate environments. Since the OP and this thread don't have anything to do with forecasting future returns, I just ignored the rest of their paper and considered it superfluous to the discussion topic at hand.

The relevance of their CAPE/rates/inflation model?
  • 1) As also shown by the two univariate analyses in the OP (the two colored charts), there has not historically been a continuous inverse relationship between CAPE values and real rates or inflation, contrary to the classic discount model.

    2) Rather, CAPE values have tended to be highest when real rates are in the 2%-4% range, and inflation is 1%-3% — and CAPE has fallen off rather quickly on both sides of these two intervals, both higher and lower.

    3) In the U.S., we've been at or near this historical "sweet spot" for high equity valuations for quite a few years.

    4) A sustained rise in either real rates or inflation (and higher inflation may be the more threatening today) would likely be a shock to current CAPE multiples and cause the market to trade at lower valuations.
Cordially, Todd

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Re: CAPE in the Context of Real Rates & Inflation, 1880-2018

Post by siamond » Fri Mar 16, 2018 8:38 am

Thanks for the clarification, SimpleGift.

What makes me a bit itchy is that, if some sort of relation is indeed established between current CAPE values and macroeconomic factors (e.g. interest rate), some people might jump to the conclusion "ah, ok, the current valuation is actually kind of 'normal' given those macroeconomic factors, so I have no reason to be especially worried about the coming decade". And well, this doesn't appear to be true, as the mid/long-term expected returns do NOT appear to be impacted by such macroeconomic factors. And those expected returns look pretty dismal. SimpleGift, I know this is NOT what you were saying, but this is what I fear some people might get out of this.

Anyhoo, I think we need a bit more analysis first. I still didn't run the monthly numbers as I am planning to, but will do this week-end.

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Re: CAPE in the Context of Real Rates & Inflation, 1880-2018

Post by lazyday » Fri Mar 16, 2018 9:29 am

More on the "investor comfort" model
Ben Inker and I designed a simple model 15 years ago to explain the shifts in P/E levels of the S&P 500. Recently we updated it. Our model does not attempt to justify the P/E levels as logical or deserved, nor does it attempt to predict future prices. It just shows what has tended to be the market’s typical response over the years to major market factors. By far, the two most important of these are profit margins, the higher the better, and inflation, where stable and lower is better, except not too low.
Then there’s inflation, which the market hates despite a history of stocks proving that their fundamentals are robust in the longer term in passing inflation through to consumers. Stocks, unlike bonds, are clearly real assets, so inflation should not matter. But in real life, when inflation first appears or accelerates, there is an immediate, coincident negative effect on P/E multiples.
This model for sure seems to say that for 92 years, at least, the market has with remarkable consistency been a coincident indicator of superficially appealing variables that in a strict economic sense have been inappropriate, and that have caused spectacular and unnecessary market volatility.
https://www.barrons.com/articles/granth ... 1501794059

Exhibit 2: https://si.wsj.net/public/resources/ima ... 165817.jpg

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Re: CAPE in the Context of Real Rates & Inflation, 1880-2018

Post by SimpleGift » Fri Mar 16, 2018 11:17 am

siamond wrote:
Fri Mar 16, 2018 8:38 am
What makes me a bit itchy is that, if some sort of relation is indeed established between current CAPE values and macroeconomic factors (e.g. interest rate), some people might jump to the conclusion "ah, ok, the current valuation is actually kind of 'normal' given those macroeconomic factors, so I have no reason to be especially worried about the coming decade".
Would just point out that, even with Research Affiliate's super-duper, two-dimensional Gaussian model, real interest rates and inflation only explained about one-half of the historical variation in CAPE values (R^2 = 0.51). So the other half of the variability is due to other factors — including investor behavior, e.g., animal spirits, irrational exuberance or pessimism.

To your point, my sense is there's obviously been what statisticians would call a "location shift" in CAPE values since about 1990 (chart below). Much of this shift toward higher P/Es can no doubt be attributed to the dramatic decline in real interest rates and inflation of the last three decades, in accordance with the classic discount model.
  • Image
    Note: The full data series is divided into four 35-year periods, with their means in red.
    Source: Shiller Data
But the degree to which this shift is also due to changing investor behavior (their willingness to pay more for a dollar of U.S. companies' earning than in previous eras) is uncertain. No doubt it's been a factor, but how much? Will these investor preferences persist in the decades to come? In the end, I'm more comfortable talking about the impacts of real rates and inflation on CAPE values than trying to predict future investor behavior and preferences!
Last edited by SimpleGift on Fri Mar 16, 2018 11:48 am, edited 1 time in total.
Cordially, Todd

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Re: CAPE in the Context of Real Rates & Inflation, 1880-2018

Post by gmaynardkrebs » Fri Mar 16, 2018 11:44 am

SimpleGift wrote:
Fri Mar 16, 2018 11:17 am
'''But the degree to which this shift is also due to changing investor behavior (their willingness to pay more for a dollar of U.S. companies' earning than in previous eras) is uncertain. Certainly it's been a factor, but how much? Will these investor preferences persist in the decades to come? In the end, I'm more comfortable talking about the impacts of real rates and inflation on CAPE values than trying to predict future investor behavior and preferences!
Can one separate investors' "willingness to pay more for a dollar of U.S. companies' earning than in previous eras" from low real rates, low inflation, and high CAPE?

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Re: CAPE in the Context of Real Rates & Inflation, 1880-2018

Post by SimpleGift » Fri Mar 16, 2018 12:17 pm

gmaynardkrebs wrote:
Fri Mar 16, 2018 11:44 am
SimpleGift wrote:
Fri Mar 16, 2018 11:17 am
'''But the degree to which this shift is also due to changing investor behavior (their willingness to pay more for a dollar of U.S. companies' earnings than in previous eras) is uncertain. Certainly it's been a factor, but how much? Will these investor preferences persist in the decades to come? In the end, I'm more comfortable talking about the impacts of real rates and inflation on CAPE values than trying to predict future investor behavior and preferences!
Can one separate investors' "willingness to pay more for a dollar of U.S. companies' earnings than in previous eras" from low real rates, low inflation, and high CAPE?
I was making a distinction between a) investors responding to low real rates and inflation by paying a higher multiple today in exchange for the more valuable future cash flows (the classic discount model), and b) investors worldwide subjectively believing that large-cap U.S. companies are just superior today (esp. tech firms) and deserving of a valuation premium.

One is rational economic decision-making in the face of lower rates, while the other is subjective investor behavior based on U.S. companies' recent profit margins, brand names, global reputations, etc. Both are involved in the higher CAPE values for U.S. stocks since 1990, I believe — but not sure how one might separate their impacts.
Cordially, Todd

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Re: CAPE in the Context of Real Rates & Inflation, 1880-2018

Post by gmaynardkrebs » Fri Mar 16, 2018 1:26 pm

SimpleGift wrote:
Fri Mar 16, 2018 12:17 pm
gmaynardkrebs wrote:
Fri Mar 16, 2018 11:44 am
SimpleGift wrote:
Fri Mar 16, 2018 11:17 am
'''But the degree to which this shift is also due to changing investor behavior (their willingness to pay more for a dollar of U.S. companies' earnings than in previous eras) is uncertain. Certainly it's been a factor, but how much? Will these investor preferences persist in the decades to come? In the end, I'm more comfortable talking about the impacts of real rates and inflation on CAPE values than trying to predict future investor behavior and preferences!
Can one separate investors' "willingness to pay more for a dollar of U.S. companies' earnings than in previous eras" from low real rates, low inflation, and high CAPE?
I was making a distinction between a) investors responding to low real rates and inflation by paying a higher multiple today in exchange for the more valuable future cash flows (the classic discount model), and b) investors worldwide subjectively believing that large-cap U.S. companies are just superior today (esp. tech firms) and deserving of a valuation premium.

One is rational economic decision-making in the face of lower rates, while the other is subjective investor behavior based on U.S. companies' recent profit margins, brand names, global reputations, etc. Both are involved in the higher CAPE values for U.S. stocks since 1990, I believe — but not sure how one might separate their impacts.
I could see how one could draw such a distinction conceptually, but I can't see how one could reliably test, verify, or quantify it. In which case, the distinction is meaningless in practice. Perhaps that is what you are saying?

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Re: CAPE in the Context of Real Rates & Inflation, 1880-2018

Post by SimpleGift » Fri Mar 16, 2018 1:40 pm

gmaynardkrebs wrote:
Fri Mar 16, 2018 1:26 pm
I could see how one could draw such a distinction conceptually, but I can't see how one could reliably test, verify, or quantify it. In which case, the distinction is meaningless in practice. Perhaps that is what you are saying?
Well, the Research Affiliate's model in the OP suggests that real interest rates and inflation have explained about 50% of the historical variation in CAPE values — leaving the other half explained by factors beyond the macroeconomics, including subjective investor behavior. So this might be a place to start in breaking down the recent drivers of higher CAPE valuations.
Cordially, Todd

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Re: CAPE in the Context of Real Rates & Inflation, 1880-2018

Post by learning_head » Fri Mar 16, 2018 1:55 pm

Fascinating analysis, SimpleGift! Thank you!

I am unclear about this though...
SimpleGift wrote:
Wed Mar 14, 2018 11:43 pm
... CAPE values have tended to be highest when real rates are in the 2%-4% range, and inflation is 1%-3% — and CAPE has fallen off rather quickly on both sides of these two intervals, both higher and lower.
...
In the U.S., we've been at or near this historical "sweet spot" for high equity valuations for quite a few years.
Looking at the last "quite a few years", it does not look to me like we have been in that sweet spot...

For inflation, we seem to be lower than 2% in 2013-2016 span and only just entered 2%-4% zone consistently in 2017 (according to monthly numbers from this site)

Code: Select all

2013 	1.6 	2.0 	1.5 	1.1 	1.4 	1.8 	2.0 	1.5 	1.2 	1.0 	1.2 	1.5 	1.5
2014 	1.6 	1.1 	1.5 	2.0 	2.1 	2.1 	2.0 	1.7 	1.7 	1.7 	1.3 	0.8 	1.6
2015 	-0.1 	0.0 	-0.1 	-0.2 	0.0 	0.1 	0.2 	0.2 	0.0 	0.2 	0.5 	0.7 	0.1
2016 	1.4 	1.0 	0.9 	1.1 	1.0 	1.0 	0.8 	1.1 	1.5 	1.6 	1.7 	2.1 	1.3

2017 	2.5 	2.7 	2.4 	2.2 	1.9 	1.6 	1.7 	1.9 	2.2 	2.0 	2.2 	2.1 	2.1
For real-interest rate, we are even further out from the 1-3%. Last time we were in the sweet spot, it was 2011 when I look at that graph. This is based on a 5-year real interest rate though - is that the issue?

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Re: CAPE in the Context of Real Rates & Inflation, 1880-2018

Post by SimpleGift » Fri Mar 16, 2018 2:43 pm

learning_head wrote:
Fri Mar 16, 2018 1:55 pm
This is based on a 5-year real interest rate though - is that the issue?
Yes, I should have been more specific about "quite a few years." CAPE values in the U.S. first went above 20 in 1993 and, except for 2009 during the Great Recession, have not been below that level since then — so we have about 25 years of elevated CAPE values, consistently above their historical range.

During that 25-year period, real interest rates have averaged 1.9% and annual inflation has averaged 2.3% — both of which are at or near the "sweet spot" for highest CAPE values identified in Research Affiliate's historical model in the OP.
Cordially, Todd

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Re: CAPE in the Context of Real Rates & Inflation, 1880-2018

Post by gmaynardkrebs » Fri Mar 16, 2018 2:55 pm

Do you think CAPE has ceased to be predictive? I think it was only accounting for 38% of the future valuation when it was proposed by Shiller? After the numbers you give (ie., 25 years of elevated CAPE values, consistently above their historical range), I wonder it we are at the infamous "permanently high plateau" of CAPE values.

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Re: CAPE in the Context of Real Rates & Inflation, 1880-2018

Post by SimpleGift » Fri Mar 16, 2018 3:11 pm

gmaynardkrebs wrote:
Fri Mar 16, 2018 2:55 pm
Do you think CAPE has ceased to be predictive? I think it was only accounting for 38% of the future valuation when it was proposed by Shiller? After the numbers you give (ie., 25 years of elevated CAPE values, consistently above their historical range), I wonder it we are at the infamous "permanently high plateau" of CAPE values.
It's certainly possible — as long as real interest rates and inflation stay in a moderate range (say 1%-3%), and U.S. tech companies remain the darlings of investors worldwide, there's no reason CAPE values couldn't stay elevated in the U.S. for years to come.

Since there's no pre-ordained value at which stocks are destined to trade, "reversion to the mean" is not a certain destiny. That said, if either inflation or real rates experience a sustained rise in the years ahead, I'd expect to see CAPE values decline and stocks to trade at lower valuations. Just my two cents.
Cordially, Todd

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Re: CAPE in the Context of Real Rates & Inflation, 1880-2018

Post by lazyday » Fri Mar 16, 2018 11:11 pm

Someone let me know that Barron's direct link doesn't work without a subscription. Sorry about that. To read the article, google the title:
Grantham: Why Are Stock Market Prices So High?
and then click to it from the search results.

On why equities have been so expensive for the last 20 years:
behaviorally it is absolutely not a new era. It is precisely – to a 0.90 correlation – the same ole same ole. The peaks of 1929 and 1965 delivered favorable margins and inflation inputs but for a very short while in both cases. In contrast, the period of 1997 to 2017 has delivered to investors their preferred conditions almost the entire time, with only two very quick time-outs for market breaks. Can the market really be this easy to explain? Well, it has been for 92 years!

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Re: CAPE in the Context of Real Rates & Inflation, 1880-2018

Post by Jeff Albertson » Thu Mar 22, 2018 3:33 pm

The current Economist Buttonwood column also references a paper from Research Affiliates, "CAPE Fear: why CAPE Naysayers are Wrong".
Image
America’s ratio is 32.8, whereas Canada is trading on a CAPE of 20. Germany is on 19 and Britain on 14. All are trading near their historical averages; in contrast, Wall Street is at double its usual level.
https://www.economist.com/news/finance- ... overvalued

https://www.researchaffiliates.com/en_u ... wrong.html

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Re: CAPE in the Context of Real Rates & Inflation, 1880-2018

Post by siamond » Tue Apr 03, 2018 10:37 pm

SimpleGift wrote:
Tue Mar 13, 2018 9:09 am
REAL RATES & INFLATION: Since interest rates are made up of a real yield and an inflation component, we can look at each of these separately first, to observe their past impact upon CAPE values. In the two charts below, U.S. monthly 10-year real Treasury yields and trailing 12-month inflation rates are sorted in rank order, from lowest to highest, with their associated CAPE values.
Sorry, I did play with such numbers a week ago, then I totally forgot to post about it... I used the monthly numbers from multpl.com.

One thing I wanted to do was to check if there was a start date sensitivity to the hypothesis, and also to check if some specific time periods have an oversized effect on the charts SimpleGift provided. First off, I ran some general stats with various starting points. Note that I used the current conditions, i.e. current interest rate and current inflation rate (nominal and real), then I looked at inflation averaged over a period of time (36 months, 12 months).

Image

A pretty constant result is that the real interest rate is fully decorrelated from Shiller PE (aka CAPE). For the inflation, averaging it or not doesn't really change the picture. But the correlation numbers change quite dramatically, depending on the starting point. So I started to ponder what would a chart displaying correlation of some of those metrics with Shiller PE would look like when using rolling periods of 30 years. And well, this is rather messy, to say the least.

Image

Note how all those curves tend to go to zero for recent 30-years periods (i.e. ending in 2015+), when the high inflation/interest period post oil crisis is no longer included in the rolling period.

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Re: CAPE in the Context of Real Rates & Inflation, 1880-2018

Post by siamond » Tue Apr 03, 2018 10:54 pm

Then I reproduced charts similar to what SimpleGift provided in the OP, sorted by interest rate or inflation rate, Shiller PE on the vertical axis, with the inflection at both ends. And I started to play with the starting date (1900+, 1950+, 1970+, 1988+).

For the (real) interest rate, things fell apart very quickly, and I'll skip the details. Even the 1950+ chart proved unsatisfying, with just a few years in the mid-80s providing a small inflection at the end of the graph. Between this observation and the complete lack of correlation with Shiller PE, I think we can put the real interest rate aside, and forget about the hypothesis in this respect.

Now inflation resisted much better to my tests. Here is the 1950+ chart, using the inflation averaged over 12 months, as an example. 1970+ is fairly similar. And even 1988+, to my surprise, worked ok-ish, although inflation has been quite successfully tamed in the past 30 years. Still, the last chart is quite flattened, and I am not too sure what we can infer from the current inflation rate (in 2017/18).

Image

Image

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Re: CAPE in the Context of Real Rates & Inflation, 1880-2018

Post by siamond » Tue Apr 03, 2018 11:17 pm

Finally, I started to think that we may read too much from those sorted charts with monthly observations. It just takes a couple of years to provide 20+ data points on such a chart and create an inflection point. Let's simply come back to a basic side-to-side comparison between the trajectory of Shiller-PE and the trajectory of the inflation, and let's use our brain's ability to identify apparent patterns. Click on the image for a larger display.

Image

Now let's squint a bit. Personally, what I see is the following:
- when the inflation rate was high, Shiller PE seemed fairly consistently low
- when the inflation rate was moderate, pretty much anything could happen to Shiller PE (low, high, moderate)
- in the past 30 years, inflation was very tame, and PE went all over the place.

Then let's come back to the real interest rate. About this one, I don't know if you can notice anything interesting, but... I can't.

Image

Bottomline... In my humble opinion, those past observations, metrics and charts do not seem to tell us much about the current situation in 2017/18. Inflation is tame, interest rates are low, and... the Shiller PE simply has a life of its own.

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Re: CAPE in the Context of Real Rates & Inflation, 1880-2018

Post by Top99% » Wed Apr 04, 2018 8:03 am

siamond wrote:
Tue Apr 03, 2018 11:17 pm
Bottomline... In my humble opinion, those past observations, metrics and charts do not seem to tell us much about the current situation in 2017/18. Inflation is tame, interest rates are low, and... the Shiller PE simply has a life of its own.
Simplegift- Thanks for starting a great thread. My own theory is recency bias is at partly at work here. Many of us came of age in the 70s - 90s when nominal interest rates where in in the 15 to 5% range. We have been expecting a return to the range we view as "normal" and after waiting for nearly a decade now are losing patience and chasing anything with yield and driving up valuations accordingly. The first victims were RIETs and high dividend stocks. If interest rates did return to what we deem normal we would flock back to bonds and CDs in a hurry. Of course as others have implied nobody knows nothing when it comes to what is a "normal" nominal or real interest rate in today's globalized world.
My view from under the bridge down by the river.
Adapt or perish

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Re: CAPE in the Context of Real Rates & Inflation, 1880-2018

Post by 1nv35t » Wed Apr 04, 2018 8:24 am

... taxation also has some bearing

Image

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Re: CAPE in the Context of Real Rates & Inflation, 1880-2018

Post by gmaynardkrebs » Wed Apr 04, 2018 8:34 am

If the fed credibly raised it inflation target to 4%, which would temper the possible recency bias I think, what would happen to TIPS prices? Equity prices? I'm pretty sure it would negatively impact prices for existing nominal bonds, but that's the easy one.

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Re: CAPE in the Context of Real Rates & Inflation, 1880-2018

Post by garlandwhizzer » Wed Apr 04, 2018 1:08 pm

This is a very interesting discussion between two of the most enlightened minds on the Forum, Simplegift and Siamond. I'll throw in a few simple observations, sort of the Cliff's Notes version.

First, if inflation rises in a persistent fashion future corporate profits streams are discounted by the expected difference between real and nominal returns over a given time period. 10 dollars nominal becomes 7 dollars real in 5 years, hence rational investors are not willing to pay as much for 10 dollars of current corporate profits and they also discount the level of expected future profit growth by the impact of expected inflation. Therefore PEs are expected to fall and real returns to suffer when inflation gets cranked up. If inflation rates stabilize in a reasonable area, say 2% - 3.5%, this historically does not happen on an ongoing basis. The problem arises in a serious way only when inflation becomes a self-perpetuating a wage-price spiral which happened in 70s and 80s when PE levels fell eventually below 8. We are a long way from that now.

Second, if real interest rates rise beyond a certain point, especially somewhere around 1.5% - 2% real, they become an very attractive alternative to the volatility of stocks. Currently Treasury intermediate rates and TIPS of any duration are less than 1% better than inflation. This is not a big problem now but if real rates continue to rise, and certainly if they exceed aggregate corporate profit growth, PEs are likely to decline significantly as money flows from stocks to bonds.

IMO, neither of these issues requires action now. Bear markets are usually associated with an economic recession and there are no hints on the horizon of such a thing now in the US or globally. The crystal ball for the future remains, as Larry says, opaque.

Garland Whizzer

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