Rijksuniversiteit Groningen, Faculty of Economics and Business
On Bubble formation in American and European equity markets
Master Thesis as partial fulfillment of the requirement for the completion of the
Master Finance Program of the Rijksuniversiteit Groningen.
Student:
Supervisor:
Jort Pestman
Prof. Dr. Roelof Salomons
(s2522519)
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On Bubble formation in American and European equity markets
Abstract
Recently western equity markets have experienced their tenth year of consecutive bull markets. American equity valuations are creeping up and have reached a CAPE of 30.23 almost double the historic average. Simultaneously debt markets are experiencing historically low yields and significant signs of overheating. Employing a GSADF test
to test for bubble formation in US and EU equity markets, two recent periods of exuberance are identified. This is partially supported by quantity data that historically characterizes bubble formation. Particularly the explosive US dynamics in 2017 are unusual seeing the continuous strong earnings and lack of exuberant sentiment during that
period. To asses if there is indeed euphoric sentiment surrounding the bubble an AR GARCH (1,1) process is employed to asses mean aversion during US business cycles. There is only limited evidence of mean aversion for the
current business cycle, leaving uncertainties regarding sentiment of current US valuation.
5 Table of contents 1. Introduction 7 2. Literature review 9 2.1 Definition of a Bubble 9 2.2 Theoretical model 10
2.3 The Price / Earnings and Price / Dividend ratio 11
2.4 Trade volume and Psychological factors 13
2.5 Issuance levels and Risk Premia in bubble formation 14
2.6 Consequences of bubble formation 15
3 Data analysis 15
3.1 Data origination and summary 16
3.2 Analysis of bubble formation 17
3.3 Discussion on the data 27
4 Method 28
4.1 Surveyance of previous works on mean reversion 29
4.2 Static mean reversion 30
4.3 Business Cycles 33
5 Results 33
6 Conclusion 38
Annex 41
7 1. Introduction
Asset bubbles have been observed as early as 1636 with the Dutch Tulip bubble. Rapid price increases led speculators to expect even more price increases, while the fundamental value of the flower did not change at the same rate. The first stock bubble was the South Sea bubble where rumors led to expectations that could not be met. Again, investors had overestimated
fundamental value and driven up the price to unrealistic levels. Many crises followed with the recent culmination in the Tech Bubble of 2000 and Housing Bubble of 2008. Financial markets seem unable to shake the symptoms of overvaluation that take hold every decade or so.
It has been more than a decade since financial markets crashed and this has been the start of a bull market of equivalent length. This is the longest streak of subsequent bull markets the Western World has ever experienced and this naturally entails worry for investors. Alongside this the most important American stock index, the S&P500, is at peak heights in terms of price. It must also be said that fundamentally, earnings have soared. However in terms of valuation the Shiller CAPE-Ratio, the cyclically adjusted measure of the Price-Earnings ratio, currently stands at 30.23. This is above the heights seen before the financial crisis of 2008 and 10 points under the heights of the tech bubble and well above its historical average of 15.6.
Aside from equity markets, debt markets may also be seeing signs of overheating. Low interest rates and directed financial stimulus for banks by central banks have created an environment that stimulates borrowing. Even more so, government bonds are directly being purchased by central banks around the world. This creates demand out of thin air and is devoid of sound market dynamics. The concern is that this has led to “yield seeking behavior” in bond markets where investors turn to lower quality corporate credit instead of government bonds to generate return1. Indeed it is not just quantity but quality that is of concern. Debt can have a disciplining effect on companies who know that they will have to repay. Cutting corporate excess and implementing systems that monitor costs is a good thing. However a large part of debt increases are initiated by already highly leveraged firms. These “leveraged loans” and declining credit ratings in general form a risk for the financial system. Lamoen, Mattheusens and Droes (2017)2 find significant
evidence of exuberance in government bond markets using a method that will also be used in this paper, that of unit root testing by Phillips, Shi, Yu (2015)3. Other commentators like the FED
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Globalization, for all the good it has brought, has created such a degree of interconnectedness that it is impossible to comprehensively grasp the precise impact policy will have. The current state of technological advancement is simply insufficient to comprehend the effects.
This hints at the core problem facing valuation in modern times and may explain why we are experiencing so many more crises than before. The line between price and value is thin.
Valuation resides in a grey area and small overstatements of expected earnings can culminate in large deviations of price from fundamental value. A misjudgment of the effects of a new policy can be further exaggerated due to psychological factors like herd behavior. The question is not if this will happen but rather when this will happen. The important task policy makers face is devising models to catch a bubble in its infancy and prevent it from escalating.
In the second section of this paper the current findings on asset bubble formation will be reviewed. Thereafter in the third section, value and quantity data will be analyzed. It will be judged if there are signs of explosive behavior in US and European markets using a recent innovation called the Generalized Supremum Augmented Dicky Fuller test. In the fourth section of this paper, a method will be detailed that examines the dynamics of sentiment. Employing an Auto Regressive model with GARCH (1,1) errors on the value function put forth by Tarlie (2017)6, the static mean reversion speed can be derived. This method can be used to derive changes in sentiment towards fundamental value. It will be used to assess if there are signs of the occurrence of mean aversion, instead of mean reversion in fundamental value. The value of mean reversion speed in the current period is compared to those in previous periods to make a
comparison. In the fifth section the results of the analysis will be presented and the sixth and last section will provide a discussion on the results.
In this thesis I expect to find a low mean reversion speed in the current US business cycle, comparable to previous business cycles characterized by mean aversion or high sentiment. This hypothesis is grounded in the high volatility observed after the run up in 2017 - 2018, being the classic element of the deflation of a bubble. Moreover valuations during that period where very high, earnings expectations may have been overstated. Casting doubt on this hypothesis however is the continuity of strong earnings, giving grounding for the increase in valuation. It may be that the S&P500 is finding a new, higher long term average valuation. Another strong omission is the distinct feeling of euphoria during that period.
The contribution of the analysis of mean reversion is that it is a quantitative measure of
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The GSADF tests reveal that European markets experienced explosive behavior in price adjusted for fundamentals in 2014 that has since died down. In other words it is likely that European markets have mean reverted since 2014. Quantity data in the EU does not seem to exhibit explosive characteristics that are significant at the 5% level. US markets have experienced explosive behavior in 2014 but also throughout 2017 and 2018. Additionally, explosive debt quantity issuance in both 2014 and 2017 strengthens this claim.
The quantitative test for euphoria (mean aversion) in business cycles successfully detects 4 of the 5 previous periods of euphoria identified by Tarlie (2017). Moreover the distinction between contractions and expansions is correctly made, seeing that contractions on average contain a far stronger mean reversion parameter than expansions. However there is no concrete evidence of euphoria (or mean aversion) in the current business cycle. The mean reversion parameter is still negative albeit marginally.
2. Literature review
2.1 Definition of a bubble
The definition of a bubble is given in a multitude of ways in the body of literature. Each definition focusses on one specific aspect it finds most important or recognizable. The most general definition of a bubble is:
A bubble is a phenomenon of rapid price increases due to the belief that one can sell the asset for more later causing the price to deviate from fundamental value, leading eventually to a sharp price depreciation.
A bubble however may not always be positive but can also be negative. If sentiment is such that earnings are expected to mis expectations there can be “undershooting” of the price. There have been papers on negative bubbles, see for instance Goetzman and Kim (2018)7.
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Today’s prices reflect all information held in past prices. Therefore agents seeking excess return in the market should invest according to fundamental value and not according to the path of past prices. Indeed this is quite the opposite from what happens during a bubble. Speculators judge whether to enter the bubble or not based on the probability of prices rising again dependent on the behavior of past prices.
When agents misjudge fundamental value, sophisticated traders will incorporate information and eliminate the bubble before it comes to fruition. Fama says that sophisticated traders will make sure stock prices are independent and priced to their intrinsic value. They will take up short positions and apply enough pressure to prices until they move back to their intrinsic value. However in Fama’s reasoning Fama raises a point to disprove his own point. As Fama (1965)8 states:
“How many sophisticated traders are needed to guarantee independence of stock prices?”
To his own question Fama states that it is impossible to find an answer. Indeed in every event of bubble formation in history there have been traders and investors who have called the inflation of prices and profited from it. The point is that there are not enough traders to correct prices due to the very nature of a bubble and the short selling constraints of every trader. Investors display imitative herd behavior, meaning that most investors will divert resources to supplying and furthering the bubble instead of preventing it. Many traders will believe in the bubble speculatively or rationality and help feed it as opposed to preventing it.
The frequency with which bubbles occur in modern times and the few traders or investors that call them, most of the time different people, shows that the exact identification of a bubble is more so luck than sophistication that leads them to their conclusions. However, the field of bubble formation prediction has made significant steps since then. In the coming sections the characterization and modelling of bubble formation will be discussed
2.2 Theoretical model
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According to Taipalus (2012)9 there are four types of models: the speculative, rational, intrinsic
and churning bubble model. The rational bubble model is the only theoretical model actively used. The other models are either specific to only one type of bubble or do not offer the
modelling component of the bubble. Blanchard and Watson propose to analyze bubbles through a simple framework: 𝑃𝑡= 𝑃𝑡𝑓+ 𝐵𝑡 𝑃𝑡𝑓 = 𝐸𝑡 [𝛴𝑛=∞𝑖=1 ( 1 1 + 𝑅1) 1 𝐷1+ ⋯ + ( 1 1 + 𝑅𝑛) 𝑛 ∗ 𝐷𝑡] or 𝑃𝑡𝑓 = 𝐸𝑡 [𝛴𝑛=∞𝑖=1 ( 1 1 + 𝑅1) 1 𝐸1+ ⋯ + ( 1 1 + 𝑅𝑛) 𝑛 ∗ 𝐸𝑡] 𝐵𝑡= 𝐸𝑡( 𝐵𝑡+1 1 + 𝑅𝑡+1 )
Price (𝑃𝑡) is the sum of fundamental value (𝑃𝑡𝑓) and a bubble component (𝐵𝑡). Fundamental value is difficult to capture. This is either proxied by the present value of all future dividends (𝐷𝑡) or earnings (𝐸𝑡), where the discount factor (𝑅𝑡) is constant. There is no convincing evidence pointing to a specific metric for fundamental value being the best. While dividend as a proxy is distorted by the payout ratio of company it yields better consideration of future expectations. On the other hand earnings are not distorted by a payout ratio but they are dependent on accounting conventions. Moreover earnings may be overly cyclical and hold no reliable guidance on future profitability . Throughout this thesis both measures will be used.
The bubble component is dependent on the expected value of the bubble in the next period. The bubble survives as long as the expectations of the bubble surviving are intact. Thus, the bubble and its existence is purely driven by sentiment. The drawback of this model is that the bubble component is not directly observable.
2.3 Price-Dividend and Price-Earnings ratio
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The current P/E ratio will be used as opposed to the Shiller CAPE due to the length of EU data.
Campbell and Shiller (1988)10 provide a theoretical case for imposing structure on the bubble
component. Philips, Wu and Yu (2011)11 use this for their analysis of bubble formation and later
incorporate this into the GSADF test explained in section 3. The following section represents their technical derivation of the link between the rational bubble model and the price dividend ratio. This is extendable to the price earnings ratio according to Shiller and Campbell (1988)10. In short they reason that earnings form the base for dividends. Earnings can be used as a proxy for fundamental value, however due to the higher cyclicality of earnings as compared to dividends Shiller and Campbell advise using the 10-year moving average of the Price-Earnings ratio. The starting point of the analysis of PWY (2011) is that price can be rewritten in terms of expectations surrounding fundamental value and future price. Then applying a logarithmic transformation and recursive substitution yields the following expressions in terms of fundamental value and the bubble component.
𝑝𝑡𝑓 =𝑘 − 𝛾 1 − 𝜌+ (1 − 𝜌) ∑ 𝜌 𝑖𝐸 𝑡𝑑𝑡+1+𝑖 ∞ 𝑖=0 𝑏𝑡= lim 𝑖→∞𝜌 𝑖𝐸 𝑡𝑝𝑡+𝑖
Where all the lower case letters p, d and r are the logarithm of their upper case counterparts and where:
𝑘 = − log(𝜌) − (1 − 𝜌) log ( 1 𝜌 − 1)
𝜌 = 1
(1 + 𝑒𝑝−𝑑̅̅̅̅̅̅)
With 𝑝 − 𝑑̅̅̅̅̅̅̅ representing the average price dividend ratio. The advantage of this model is obvious. Instead of an unobserved component the bubble component is modeled directly in the form of price expectations. Solving by forward iteration and taking expectation operators in the format seen in section 2.2 yields:
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Where the left term of the RHS is the characterization of fundamental value and the right term of the RHS is the bubble component as we are used to in the rational bubble model. The model can be summarized as:
log 𝑃𝑡− log 𝐷𝑡 = log 𝑃𝑡𝑓+ log 𝐵𝑡
𝒑𝒕 𝒅𝒕
= 𝒑𝒕𝒇+ 𝒃𝒕
This format of analysis is helpful as it represents all factors as a direct relation between price, dividend and the discount factor. Thus using only observable factors to impose structure on the bubble component. Moreover important statistical relationships regarding the volatility of the individual factors can be derived. This will be discussed in detail in section 3. The equation derived above alongside that of the price-earnings ratio will be the fundamental equation of this paper and it will be extensively examined.
The expected dynamics in case of bubble formation for the PE-ratio are guided by the previous analysis of Phillips, Shi and Yu (2015). In the run-up to a bubble the ratio will be higher than average and will exhibit explosive behavior as price rises faster than fundamental value.
However when the bubble pops the aftermath can have consequences for earnings. As these may drop faster than price the PE-ratio could experience another temporary surge until price decline catches up. The PD-ratio dynamics are at first similar to that of the PE-ratio. However as dividends are more stable than earnings the PD-ratio will experience less volatile movements than the PE-ratio in the aftermath of the bubble.
A strong point of critique to the method above lies in the transversality condition. To yield a unique solution to the model there should be one path of earnings or dividends that determines fundamental value. However as future values of these metrics are not observable, estimates are inherently uncertain. This makes the model of fundamental value inherently unreliable.
Following the reasoning of Brad Jones (2014)12, that as the measure for fundamental value is inaccurate more factors should be taken into account to provide an accurate measure, quantity data will be included on top of quality (valuation) data. This will provide a stronger base for inference. These additional factors are mentioned in the next section(s).
2.4 Trade Volume and Psychological factors
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A great deal of the development of a bubble has to do with the psychological factor of Positive Feedback. We see Positive Feedback when prices have moved higher in the past and we expect even higher prices in the future. This is what drives a bubble upwards, when fundamental value does not provide grounding for this. The result of positive feedback is that speculators trade with the idea of resale optionality. Rather than holding a stock for investment purposes they hold the stock purely because of the expectation of short term price gains.
This behavior contributes to the explosiveness of a bubble causing the stock price to be inflated. Next to this it causes frantic behavior by speculators, constantly timing when to enter and when to exit a bubble. This behavior results in higher trade volume and shortened holding periods compared to “normal” times not characterized by exuberance.
Scheinman and Xiong (2003)14 find evidence for higher trading volume preceding the collapse of a bubble. Brad Jones (2014) finds similar evidence in combination with shorter holding periods. There are many more psychological factors guiding investor behavior during episodes of bubble formation. The interested reader is referred to Shiller’s (2000) Irrational Exuberance for more examples.
2.5 Issuance levels and risk premia in bubble formation
The current monetary stance is seen by some as one of the driving forces behind the high levels of corporate debt issuance. High issuance volume has been found to be a pre-emptive symptom of a bubble by Brad Jones (2014). In agreeance Borio and Lowe (2002)15 argue that a prolonged period of financial imbalance, effectively meaning a period of too loose or too tight monetary policy, entails too rapid credit expansion and higher capital accumulation.
These views are not universal but the rationale is sound. Low interest rates and loose credit standards will grant more firms access to funds. Even those that would otherwise not have gotten access. This eventually leads to the deterioration of credit quality and heightened risks of default.
Brad Jones (2014) finds that the classical pattern running up to crises in 2000 and 2008 was an initial increase in issuance levels, then a spike in credit spreads reflecting heightened default risk and then the bubble bursting.
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Brad Jones (2014) finds evidence for increased IPO activity running up to a crisis in unison with higher SEO issuance. Along with a higher quantity of equity the quality decreases. This can be seen from a decreasing risk premium preceding the crisis. This lies in the euphoric attitude preceding a crisis. Risk is downplayed as economic conditions are assumed to be good. Classic behavior prior to crisis is the general feeling euphoria and the understatement of risk that are to come.
2.6 Consequences of bubble formation
Detecting asset bubbles is important as the health of financial markets is directly related to the real economy. Much has to do with the restriction of investment and consumption due to the fall in wealth and decline in trust and credit in an economy.
Consumption spending can be constrained due to its dependence on household wealth when a bubble pops according to Bernanke and Gertler (2000)16. Not only does wealth determine how much a consumer can spend but it also determines the ease with which a consumer spends. If a consumer has more faith in the future, due to higher wealth and thus the ability to negate setbacks the consumer will spend more freely than a consumer with no wealth and ambiguity about the future.
Another important link is the ease with which credit is issued. Bank credit constraint is highly reactive to economic circumstances. To see how this works the Kiyotaki-Moore model gives a nice representation of these dynamics. In the model a shock to the economy can be amplified by credit restrictions. In good times collateral value is high and economic prospects bright. This stimulates the issuance of credit due to low credit restrictions.
Then when there is a negative shock to the economy, for instance a decrease in asset value this shock is exaggerated due to lower collateral value and dampened economic prospects. Banks provide less capital and investment decreases.
3. Data analysis
16 3.1 Data origination and summary
European government bond yields are drawn from the ECB data warehouse. This indicator is the compiled average yield for EU countries for a 10 year maturity. For the US, the government bond yield is drawn from the FED database again for a 10 year maturity, see Annex A.1. US yields have recently reversed their path due to the decision of the FED to tighten monetary policy in December 2015, both EU and US yields are low historically. Risky Corporate bond yields for the EU are based on the ICE BofAML “Euro High Yield Effective Yield” index, non-investment grade or junk bonds. For the US they are based on the same index but for the US. For this research it would have been preferred to also include riskier investment grade bonds however this data could not be acquired. The current data was sourced from the Saint Louis FED “FRED” database. The series is duration matched with the government yield time series in the sense that the maturity of the bonds is the same. The decline tells us investors are requiring lower
premiums for default risk compared to historical yields, see Annex A.2.
These two time series will be used to create the credit spread for the EU and US throughout the period 1998 – 2018. The credit spread has historically been a good indicator of bubbles as it shoots up when credibility of companies decline and investors require a higher reward for the risk they take. Drawing from the graph in Annex A.3 clearly one can see the indicative power of credit spreads in past crisis periods.
Compilation of the dividend and earnings data for the Eurostoxx50 was an arduous process drawing from 50 firms x 20 years = 1.000 annual reports. For each year the dividend and earnings per constituent were weighted to the firm’s market value over the total market value of all firms in the index.
This was done by multiplying average shares outstanding with the average share price, or when this was unavailable the year end share price. This might cause minor discrepancies in the outcome. The year to year constituents of the EuroStoxx50 index where drawn from Siblis Research.
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Dividends have strongly recovered since the financial crisis and are trending upwards at a strong rate for both markets. All deflation for inflation is done with CPI sourced from again the St. Louis FED database.
In Annex A.6 the time series for Index value for both markets is found. Price data for the US is drawn from Shiller’s data set and price data for the EU is drawn from Reuters Eikon. There is a divergent price path between US and EU equity markets. The EuroStoxx50 has never achieved its historic level prior to the Financial Crisis. While the S&P500 is at its all-time high. Annex A.7 contains the Price / Dividend ratios of both markets and annex A.8 contains the Price / Earnings ratio of both markets.
Equity issuance data for the EU is sourced from the ECB in the form of the gross issuance (excluding buybacks) of listed shares by non-financial companies. Financial companies are excluded because the data for the US only includes non-financial companies. US data was
sourced from the data section of the website of the FED. The data was only available in quarterly series. The monthly linearly interpolated time series are shown in Annex A.9. The US graph is far smoother than the EU time series due to the linear interpolation.
Debt issuance data is based on net debt flows which is the difference between issuance and repayment of debt. The data for the EU is again drawn from the website of the ECB while the data from the US is drawn from the data section of the FED. The data reveals a striking trend. Unlike equity issuance in debt markets the EU is experiencing increasingly large amounts of debt issuance while US debt issuance levels are also high but waning. See annex A.10 for an
overview of the graphs.
3.2 Analysis of bubble formation
A statistical analysis of bubble formation will be done using the GSADF test pioneered by Philips Shi and Yu (2015). The core conceptual idea is that the valuation metrics in a bubble process are characterized by a transition from stationarity, to unit root and eventually to an explosive root. As the PD-ratio or PE-ratio adhering to fundamental value should have at most an unit root, an explosive (or greater than 1) root provides evidence for an irrational component in the valuation time series.
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Adding to this they found a long term cointegrating relationship between prices and dividends. Implying that fundamental value predicted price over the long term, providing evidence against bubble formation.
The novelty of the GSADF test compared to the standard Augmented-Dicky-Fuller test is an innovation in reaction to Evans’ (1991)18 critique of the initial test performed by Diba and
Grossman (1989). Evans stated that the usual ADF test of non-stationarity did not perform well in scenarios with multiple collapsing bubbles, unable to discern between them and heavily dependent on the starting point of the analysis.
Philips, Shi and Yu (2015) have developed a right sided (instead of left sided) rolling recursive test of the supremum value of the autoregressive parameter to overcome this problem. The rolling recursive technique is used to overcome the issue Evans (1991) put forth, namely that the test does not work for larger samples that contain multiple bubbles. Partitioning the analysis into different smaller segments, dependent on a rolling window size and testing them recursively overcomes this problem.
Testing for an explosive unit root instead of stationarity in variable yt with possible j lags,
constant µ, rolling window sizes r1, r2 and error term ε the following expression is used:
𝛥𝑦𝑡 = µ𝑟1,𝑟2+ ɸ𝑟1,𝑟2𝑦𝑡−1+ ∑ 𝛹𝑟1,𝑟2 𝑗
𝑖=1
𝛥𝑦𝑡−𝑗 + 𝜀𝑡
The right sided hypothesis is tested if the autoregressive parameter has a unit root or if the alternative holds true that there is evidence of explosive behavior:
H0: ɸ = 1
H1: ɸ < 1
The critical values of the test are generated using Monte Carlo simulation of 1000 simulations characterized by a Wiener Process. The lag count is determined by information criteria. Philips, Shi and Yu advise using the BIC or the equivalent SIC, which is set to select the lag length automatically in the test.
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While the GSADF test seems comprehensive, it may be fruitful to add an additional metric to measure the occurrence of extreme dynamics in a more simpler way. Large buildups may be non-stationary but not explosive and in this way evade detection by the GSADF test. While they may warrant further examination.
Jeremy Grantham of GMO asset management uses the rule that if real price deviates 2 standard deviations from trend there may be a bubble. However as this thesis uses metrics that reduce price by fundamental value, it may be wise to lower this deviation a bit as price is bound to more volatile alone than when accounted for by fundamentals. Therefore instead of 2 standard
deviations the 1.5 standard deviations bound will be used to indicate potential bubble formation in the metrics.
The Z-scores are standardized measures of standard deviation for each observation in a time series. They are standardized to the long run average and standard deviation of the time series. All deviations are then measured to these figures. Together the GSADF test values and the Z-scores will represent an overview of explosive behavior in the financial time series mentioned in the preceding section.
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Z-Score and GSADF test results EU
For all the bubble indicator data for the EU an overview is given of the highest standard score or autoregressive parameter value (ɸ) for a specific period. The section “recent statistic” indicates the highest value following the 2008 bubble crash. The specific time period in which the value occurs is noted
in brackets under the value. At the bottom the conclusion of the evidence is given comparing if the Z-score is above the 2 standard deviation metric and if the AR parameter is above the critical value.
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Z-Score and GSADF test results US
For all the bubble indicator data for the US an overview is given of the highest standard score or autoregressive parameter value (ɸ) for a specific period. The section “recent statistic” indicates the highest value following the 2008 bubble crash. The specific time period in which the value occurs is noted
in brackets under the value. At the bottom the conclusion of the evidence is given comparing if the Z-score is above the 2 standard deviation metric and if the AR parameter is above the critical value.
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The following section will provide the results graphically. The green lines are the actual movement of the metric examined guided by the right side y-axis. The evolution of the critical GSADF values are depicted by the red line and the movement of the GSADF test statistics are depicted by the blue line represented by the left side y-axis.
To assess the reliability of the measures used, back testing to see if they capture previous bubble periods will give an indication of the degree of accuracy they have in explaining future bubbles. The P/D ratio picks up the tech bubble, whereas the P/E ratio misses it. It may seem as if the 2008 bubble is well documented by both metrics. However they seem to pick up on the explosive
run down of the valuation metrics as opposed to their increases. This is an important
observation. Thorough observations yields that the spike in explosive behavior occurs in the aftermath of the bubble (post 2008) and it can therefore be concluded that the metrics do not pick up on this bubble when it was building up.
The EuroStoxx50 PD-ratio captures explosive behavior building up in 2014 which peaks in 2015, thereafter running down. The EuroStoxx50 PE-Ratio is relatively lacking in its ability to discern explosive periods.
Most of the explosive behavior captured by the P/E ratio is after the 2008 crisis. An
improvement might be to use the Shiller CAPE-ratio which uses the 10 year moving average earnings. The smoothed time path of dividends also seems to be an improvement.
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The S&P500 graphs both pick up on the explosive behavior in the tech bubble. Close
examination again reveals that both metrics fail to find an explosive run up prior to the 2008 crisis and rather react to the sharp downturn following these crisis. However small spikes in explosive activity can be seen for both ratio’s in the period prior to the 2008 crisis. Meaning that the S&P500 performs better than the statistics for the EuroStoxx50 in predating the crisis. After this period, the S&P500 P/D ratio is characterized by the sole explosive run up in 2017. And two smaller, not significantly (at the 5% level) explosive periods in 2014 and 2016.
Drawing from the PE-ratio 2014 and 2016 do seem to exhibit explosive characteristics as well as 2017.
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The Z-scores of the high yield spread in annex A.4 yield an interesting observation not directly observable from the un-standardized credit spreads. US credit spreads have not moved above a standard deviation of 0.85 in non-bubble periods pre-2010. However thereafter in two instances: November 2011 (+ 0.876 standard deviations) and February 2016 (+ 0.99 standard deviations) volatility exceeded this level. The same has not occurred in the EU were the pre-2010 no bubble threshold is higher at 1.20 standard deviations in 1998.
Following the GSADF test of the high yield spread in both markets, they have been characterized by an explosive run up in spreads following the aftermath of the collapse of earnings and price in 2014. While investor worry increased, this eventually subsided and there is no recent evidence of explosive behavior in credit spreads.
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Analysis of equity issuance using the Z-score method shows that current US equity issuance has surpassed the 1 standard deviation mark at which previous deviations have occurred without a crisis as a consequence, this is displayed in the table. Prior to the tech bubble the highest standard deviation was 1.65 and prior to the Financial crisis this was only 1.05 standard deviations. This metric even hit 2.326 standard deviations in de middle of 2018. This means there is a serious deviation from mean in absolute issuance volume in US equity issuance while EU markets have issuance levels that are not significantly higher compared to past volumes. However these numbers may be warranted for if economic activity and corresponding market values are also higher. The important metric to assess is therefore equity issuance volume deflated by the index of market value. Indeed where the unadjusted US equity issuance values show significant signs of explosive behavior the adjustment for market value significantly reduces the relative amount issued. The period after the 2008 crisis is characterized by a remarkably stable period of equity issuance growth where the growth is in line with market value. The only exception is sharp decline following the market downturn in the US. In US markets, in the end of 2018, there is a steep fall in equity issuance volume, signaling a significant uptick in explosiveness. This is due to the market wide pullback of equities at the end of 2018. Where the picture has drastically changed for the US, the EU has experienced smaller
adjustments due to the limited rise in equity values in that area. While 2018 is associated with a limited uptick in activity, there seem to be no worrying signs in equity issuance.
A pleasant surprise is that adjusted equity issuance data seems to have done a reasonable job predicting the 2008 crisis as opposed to the valuation metrics. Both seeing run ups in 2008.
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In 2014 and 2016 the EU experienced episodes of 2.8 and 3.0 standard deviation up ticks in absolute debt issuance volume, comparable to that of the tech bubble in 2001 of 2.85. Even more so, recently in March 2018 EU debt issuance levels broke the 3 standard deviation barrier
amounting to a never before seen upward volatility of 3.42 standard deviations. US absolute debt issuance standard deviations reached highs of 1.6 preceding the tech bubble in 1998 and 1.8 preceding the Financial crisis in 2007. Recently the US has seen higher standard deviations of 2.6 in 2015 and 2016. However this has died down in recent years. Interestingly the decrease in issuance has concurred with monetary tightening of the FED, which started in December of 2015.
However, accounting for GDP growth a different picture emerges. Accounting for GDP growth reveals that adjusted US debt issuance volume is actually falling in recent years. After the explosive behavior in 2012 there is no strong increase, rather there is an explosive decrease in debt volume accounted for GDP growth. Indeed the explosive behavior seen in the graph at the end of 2018 is the explosive decrease in US adjusted debt security issuance.
EU adjusted debt issuance experienced two run ups in issuance volume in 2012 and 2014 and more recently a small run up in 2018. However all these values fall under the critical value and cannot be characterized as truly explosive.
On the other hand adj. US debt issuance data has done a good job in predicting the 2008 crisis in contrast to the P/D and P/E ratios. EU debt issuance data seems to have a harder to time
predicting this crisis. The 2000 crisis was missed by both the EU and US adj. debt issuance metrics
27 3.3 Discussion on the data
Back testing the valuation metrics of the P/D and P/E ratio showed that while they did a decent job in forecasting the 2000 tech bubble in accordance to PSY (2015), the run up to the 2008 bubble was actually missed by these metrics. The explosive run up in the GSADF test statistic shown around 2008 is confusing at first, but it is the result of the explosive run down of the P/D metric and run up of the P/E after the bubble burst in 2008. This is because earnings dropped faster than price and price dropped faster than dividends.
However, adjusted issuance volume for both debt and equity in the US did pick up on the explosive behavior. This proves the point Brad Jones (2014) made and solidifies the position of quantity issuance data as a valuable metric for bubble formation analysis. It also shows that while bubbles fueled by exuberance in equity markets may be picked up by valuation metrics, bubbles fueled by exuberance in debt (housing) markets are better found by adjusted issuance data.
Turning to the analysis of the current period, in terms of valuation there seems to have been some weakly explosive behavior in 2014 for both markets. However only the US has
experienced explosive behavior in 2017 in terms of both the PD-ratio and PE-ratio, that has since deflated at the end of 2018. The contrast between these two periods (2014 and 2017) is that 2014 was driven by a run up and run down of earnings and 2017 to 2018 was characterized by strong and steady earnings in the US. For reference the time path of earnings for the US market has been included on the next page.
As can be judged from the graph, the drop in index value in 2014 was warranted as earnings dropped as well. However the deep decline in the last quarter of 2018 has no fundamental cause. Earnings remained in excellent condition. Therefore it may not be earnings but sentiment
towards earnings driving valuation in this specific period.
28
Statistical packages cannot handle the non-linear aspect of the dynamic element in the Kalman Filter. Martin Tarlie modeled this aspect himself, however due to time constraints replicating this is not an
option.
The strong volatility on the back of constant strong earnings is further underwritten by quantity data in the US. Equity issuance experienced an explosive fallback in issuance volume in the last quarter of 2018. For US adjusted debt issuance the run up and run down exhibits the same pattern as that of the PD and PE ratio. The question arises if we have seen the inflation and deflation of a bubble in 2017.
Drawing from an observation made by Martin Tarlie (2017), the dynamics in valuation seen in 2017 and 2018 may imply bubble formation. The factor that is preventing analysts from calling the bubble is the lack of distinct euphoria. Therefore a quantitative measure of euphoria is needed to assess whether sentiment was exuberant, is still exuberant, or has turned against markets. One such measure is the speed of mean reversion. The speed of mean reversion details the speed with which valuation returns to trend, or its mean value. Strong mean reversion implies that a deviation from trend returns to trend quickly. On the other hand mean aversion, or negative mean reversion speed implies an increasing deviation from mean value. Here higher valuation implies even higher valuation. Mean aversion has historically been followed by sharp mean reversion and the onset of volatility.
4. Method
Drawing from the statistical analysis in the previous section it can be concluded that there is significant evidence of recent explosive behavior in price in the US and a subsequent crash on the backdrop of continuously strong earnings.
Moreover adjusted quantity data underwrites this result adding to the volatility observed during this period. European markets have not experienced these dynamics. To assess how sentiment regarding valuation is driving this dynamic, an analysis will be performed to see if this bull market is different from many other bull markets in preceding periods. The concept of mean reversion detailed earlier might offer some restitution. Historically, price series have been observed to revert to the mean, meaning higher expected returns are eventually followed by lower expected returns. It will be informative to see how the time varying discount rate has behaved in this bull market.
29
The time periods will be cut up into subsections according to business cycles (along the lines of the NBER-framework). Differing dynamics along these time frames might yield information to the cause of the dynamics we are seeing. In the coming sections a surveyance of the state of mean reversion models is presented and the mean reversion model (with constant parameter) that will be used in this paper follows thereafter.
4.1 Surveyance of previous works on mean reversion
Mean reversion is a phenomenon is well addressed in economic and financial literature. Most notably Summers (1986)19 and Fama and French (1988)20 have laid the foundation for the work to come. The initial idea was that usually price equals its fundamental value. Only due to noise traders does price revert from fundamental value. This could be captured using an autoregressive model:
𝑃𝑡 = 𝑃𝑡∗+ 𝑧𝑡 𝑧𝑡 = µ + ɸ𝑧𝑡−1+ 𝜂𝑡
Where P* is the fundamental value and zt a disturbance noise. To then check for mean reversion
the deviation from mean value is examined. This is done by the following model:
𝑃𝑡 = µ + 𝑃𝑡∗+ ɸ(𝑧𝑡−1− (µ + 𝑃𝑡∗)) + 𝜂𝑡
In this model price revolves around the mean µ + P*t. The stochastic element zt-1 denotes the
deviations from this mean price which is proxied by fundamental value. A way to characterize the speed with which the price reverts back to the mean is using the “half-life” method. Which is how long it takes zt to absorb a half unit shock:
30
There are numerous other econometric models available to further identify these dynamics. For instance Gürkaynak (2008)21 proposes a Markov Switching model to model the switching
coefficients. Each switching regime is given a probability of occurring. The coefficient takes on a value according to each regime the model is in.
However the drawback of this approach is that the coefficient can only take on a discrete set of values. This limits the dynamic element in a model in the sense that it decreases the amount of time variance the variable of interest in the model can have.
Filtering the mean reversion speed from the valuation function using the signals the function yields has a continuous set of output variables. It therefore thought that when properly specified the Kalman filtering technique is superior to the Markov Switching model due to the precise estimates it can yield.
4.2 Static Mean Reversion
I make use of the model put forth by Tarlie et. al. (2017) with the simplification of a constant parameter. Instead of varying across time the model will be static, but applied to different time periods for comparative purposes.
The mean reversion speed is modeled as a function of the value function q(t) while an AR(1) process is imposed on it extract the coefficient relating previous values to future values of valuation. The expectation is to find smaller negative value to positive of this coefficient in the period surrounding 2017 – 2018. This means the value process in that period is only weakly mean reverting or even mean averting. However, as the exact time varying parameter cannot be calculated and the mean reversion speed only turns averting for a short while the metric is unlikely to become mean averting when averaged over a longer period.
The valuation function itself is based on the price in relation to a multiple of 10 year trailing earnings. The moving average of the earnings helps overcome the small sample bias we potentially face in cutting the time frame up into sub periods as fundamental value is
consequently based on a much larger previous time frame. The value function is the following:
31
Where the process is characterized by a logarithmic transformation to make it comparable over time and undo the effect of level differences. More on this transformation in the last part of this section. Fundamental value is as mentioned before, the moving average of 10 years trailing earnings adjusted by a multiple and determined by the following function:
𝐹𝑡 = 𝑏𝐸10
Where the parameter b is the conversion value relating fundamental value to price . This is an important parameter, guarding the central assumption that on average price equals fundamental value. This is base assumption when assessing mean reversion. When using the model for a sample, b can be calculated so that on average in a sample the expected value of E(q(t)) = 0 as price and fundamental value are the same. This yields the following method to calculate b:
0 = 𝐸 (ln ( 𝑃𝑡 𝑏𝐸10 )) ln 𝑏 = 𝐸 (ln 𝑃𝑡 𝐸10 )
However, this assumption that the expected value is zero is not completely guaranteed when setting the b parameter to the appropriate value. To accurately judge if this is the case it must be checked if the cost of capital is the same as the return it generates. Otherwise the valuation changes due to the discount rate being either too low or too high. Return must not exceed the opportunity cost of capital. As Cochrane (2011)22 notes, time varying discount rates have a large impact on valuation:
𝐴𝑣𝑔(𝑟) = 𝐴𝑣𝑔(𝑝)
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If the natural logarithm was not applied to the valuation function, the line about which the process oscillates would be an upwards trending line and interpretation of values would constantly be different as time progresses.
Having derived an expression for the valuation function allows us to derive the expression for static mean reversion. As mentioned before an AR(1) structure will be imposed on the equation. Furthermore there is likely to be significant autocorrelation between the error terms in this model as the change in valuation is likely to depend on past valuation. This implies that the volatility can be conditional on previous volatility. This will lead to the violation of the assumption of homoskedasticity in the error terms. As autocorrelation implies heteroskedasticity but
heteroskedasticity does not necessarily imply autocorrelation (also other causes..) it makes sense to first test and possibly adjust for autocorrelation and then test if heteroscedasticity is still present.
Preliminary standard tests would normally be employed to judge if it is necessary to carry out further examination. This test could be the Q-statistic test by Ljung & Box. However that test tends to fail in the case of longer lag order serial correlation or conditional heteroscedasticity. Therefore in the case of this model it will be worthwhile to examine the volatility of the error terms as well and including a LM test for ARCH terms to see if the error terms are indeed dependent on their squared lags.
Thereafter to check if heteroscedasticity is still present in our model (after including a GARCH process when finding evidence for autocorrelation) a white test can be performed. If there is still heteroscedasticity present in the model HAC-standard errors can be included.
Not dealing with heteroskedasticity can be a problem. Following work by Cogley and Sargent (2005)23, not taking the violation of homoscedasticity into account leads to the possibility of
spurious correlation in a model. If evidence is found of heteroskedasticity this will have to adjusted for in our model. The non-linearity of volatility is modelled well by a GARCH process. This allows for non-linearities in the volatility of the error term. When applying this process the model will be the following:
𝑑𝑞(𝑡) = 𝛾𝑞𝑡−1+ 𝜂𝑡
33
A negative value for the γ coefficient will imply mean reversion. The size of the coefficient will determine the degree to which this is present in the period. This is because preceding higher valuations are followed by lower valuations and thus returning to the mean. On the other hand a positive value for the γ coefficient will imply mean aversion. Higher valuation is followed by even higher valuation, or in the case of a negative bubble even lower valuation. Valuation then exhibit explosive tendencies and it is at these moments that bubble formation is evident in valuation.
4.3 Business cycles
Use will be made of the static mean reversion speed rather than dynamic mean reversion speed. The analysis will commence through a comparative analysis of different periods. Through this analysis different trends in time or markets may yield information to how current activity differs from past activity.
Most importantly according to Martin Tarlie there have been 5 previous instances of negative mean reversion speed (or mean aversion) throughout history. Namely: the early 1920’s, the late 1920’s, the early 1930’s, the early 1980’s, the late 1990’s and the early 2000’s. These periods may either have been periods where markets where extremely expensive or cheap. However they were all periods were the cycle of valuation perpetuated itself explosively. Knowledge of these periods will prove useful in back testing the model. If the model is able to recognize these periods as mean averting then the model is accurate.
An overview of the American business cycles since 1857 is drawn for the National Bureau of Economic Research (NBER). Comparing the speed of mean reversion in those cycles to the current cycle might be informative to what is going on. The NBER designates a contraction to be present when there are two successive periods of negative growth. When growth is positive again we are seeing an expansion.
While a comparable analysis with Europe would have been a nice novel aspect to this research the time span is too short to test for mean reversion. Even more so seeing the use of the proxy of fundamental value taking up 10 years’ worth of data before actual work can be done.
5. Results
34
The value for the b parameter is found by lnb = E( lnPt / E10). This yields an average parameter
value of b = 15.605. This is the long run average earnings multiple of the S&P500. On average, price of the index will revert to 15.605x expected earnings. Periods where valuation was above this value are positive values and periods where valuation was below this value are noted as negative values.
Then, it must hold that over the sample valuation on average the cost of capital must be the same as the return on capital ( avg(r) = avg(p)). As average return in our sample is 0.0616 and average profitability is 0.0702, earnings will have to adjusted by an adjusting factor of 0.0616 / 0.0702 = 0.876542. This results in the time path shown below. Historically there has been an enormous run up in valuation from 1980 to 2000 where valuation reached peak heights. Valuation remains within reasonable bounds around 2008. Recently valuation has been running up towards
valuation seen in 2000 and equaling the valuation seen in the “roaring twenties”.
Next the necessity of the addition of the GARCH process to the fundamental value equation is examined. The results of the tests on the AR(1) structure are shown in the table below:
Test results for Auto Correlation and Heteroskedasticity
Test Value P-Value Breusch Pagan test 59.785 0.0000 Q-statistic (5 lags) 28.577 0.0000 White Test 106.9533 0.0000 -1.2 -0.8 -0.4 0.0 0.4 0.8 1.2 90 00 10 20 30 40 50 60 70 80 90 00 10
35
The Breusch Pagan test (LM test) and Q-statistic show that there is strong evidence of serial correlation in the model. This provides evidence to support the hypothesis formed by observing the graph. The White test reveals significant evidence of heteroskedasticity. Further evidence of auto correlation is provided by the graph of the residuals of the value function:
Graph of the residuals of the adjusted value function
If the time series would have been homoscedastic the residuals would have varied within the bounds shown in the graph. However the graph shows frequent violation of these points. There is also considerable evidence of volatility clustering a classical signal of auto correlation. The GARCH process is equipped to deal with these non-linearities.
On the next page the results for the AR(1) GARCH process of the adjusted q(t) function for all US business cycles is shown.
36 Table of values for γ for different US business cycle periods
Expansions and contractions follow interchangeably and are drawn from the NBER cycle dating committee. The NBER defines a contraction as a minimum of two periods of negative growth of the economy. Regrettably some cycles, predominantly contractions, where too short to be used as regression
and these values could not be obtained.
*Significant at the 1% level ** Significant at the 5% level *** Not enough observations to estimate
Cycle Type Cycle Length Coefficient value γ
The results generated are in line with expectations, with a few notable exceptions. The average mean reversion speed during a contraction is -0.11483 while in an expansion it is -0.04319. These results are as expected. What is observed historically is that in an expansion valuation deviates from trend and only slowly reverts to the mean. While in a contraction the markets revalue companies and revert to the mean more quickly as expectations are recognized to be too good to be true. In the results there are seven instances of positive mean reversion speed, or in other words mean aversion.
Back testing reveals that four of the five historical mean aversion episodes identified by Tarlie’s Anti-Bubble model have been identified, which is a good result seeing the static nature of the model. Specifically the early 20’s, late 20’s, early 80’s and late 1990’s are successfully
identified. The model misses the episode of mean aversion in the early 30’s albeit yielding only a marginally negative parameter. The reasonable success of the back testing of episodes of mean aversion increases the accuracy of current estimates.
However, two inaccurate episodes of mean aversion are identified by the model. The model finds evidence for mean aversion during a period of expansion in the mid 1940’s and during the
contraction in 2007 – 2009. Both results are unlikely. The positive value of the autoregressive parameter in 2007-09 could be explained by the precipitous drop in earnings during this period. From the earnings graph of the S&P500 in annex A.5 on can see this sharp drop. The sudden decrease in earnings, faster than that of price, can lead to the momentary increase in valuation ratio’s as if overvaluation is present. Even while using the Shiller CAPE ratio this effect is reduced but might still be present. This might possibly be driving the mean averting process captured during that period.
Observation of the time path of valuation does not directly reveal the strongly mean aversive parameter during the expansion of 1946 – 1948. This will be treated as an anomaly and an indication that the model is not perfect and results must be interpreted with consideration. The period of interest, the current business cycle has a marginally negative and significant coefficient value of -0.025873. While this is the second lowest coefficient in the time series for periods of expansion it is still negative. However as this value is an average of the whole business cycle this value may not be telling the whole story and previously mean reverting values (in 2014) may blur the mean averting period in 2017. This reveals the drawbacks of the static mean reversion model.
38
Application of the previous method to European dividends yields non-sensical results. This is in part due to the equalization of return and profitability over time requiring enormous adjustments to the data set. The method is not informative due to the short time frame of the data set.
Therefore the comparison between European and US markets that would of have been fruitful cannot be put forth.
6. Conclusion
This thesis has analyzed the potential of bubble formation in American and European equity markets. The literature identified the P/E and P/D ratio as suitable metrics for analysis examining the dynamics of volatility surrounding valuation. The framework chosen was that of the GSADF test where explosive episodes are separated from episodes of simple unit roots or stationarity. However due to the many conditions and assumptions surrounding these metrics the addition of quantity data was advisable to strengthen the conclusions made from the P/E and P/D ratio. Back testing of the GSADF test to previous known bubble periods revealed the weakness of valuation metrics in detecting bubble formation. While the 2000 tech bubble was successfully identified, only the deflation of the 2008 bubble was caught and not the run up to the bubble. The reason being that fundamentals decreased faster than the price, meaning the P/E ratio spiked after the bubble deflated. On the other hand adjusted equity and debt issuance were able to capture this phenomenon.
Applying the GSADF test to the current period, the observation was made that US markets were characterized by recent explosive behavior in 2014-2016 and 2017-2018, the behavior in 2017 was largely supported by quantity data. Whereas European markets had experienced explosive behavior in 2014 which was only partially supported by quantity data and no signs of explosive behavior in more recent times. The explosive behavior and following strong pull back in the US in 2017 occurred on the back of continuous strong earnings. This observation provided the foundation for further research into the dynamics of valuation and the potential for mean averting dynamics in 2017 – 2018. While there is substantial evidence of a bubble forming and deflating, earnings have not given way to a reason for deflation and there is a distinct lack of euphoria. The Anti-Bubble framework was employed to analyze the changing mean reverting dynamics across time in the US. The dynamic version could not be employed therefore a static version was adopted partitioned along US business cycles. Surprisingly the static method successfully
39
Moreover the method successfully differentiated between contracting and expanding periods where the mean reverting parameter should respectively by strongly negative or marginally negative. The period of interest, the expansion from 2009 – 2018 was characterized by a marginally negative parameter. In context of previous expansions that were also negative it has the smallest negative value. However the absence of a positive parameter, knowing that
previously mean averting periods were successfully identified, does not allow the conclusion that the US market has experienced mean averting behavior in this context. Consequently the
conclusion that the US market has experienced the inflating and popping of a bubble cannot be made with sufficient evidence as earnings remain strong while there is no definitive evidence on euphoric sentiment during this period.
In the literature only limited evidence of current and European and Japanese bubble formation is available. This thesis contributes to this weak spot in the literature by confirming that there is currently no evidence of bubble formation in European markets, however there was evidence of exuberance in 2014. This thesis confirms doubt regarding valuation regarding US markets however it is not able to provide concrete evidence of the dynamics following the likely exuberant period in 2017.
While interesting results were generated, this research was impaired by data constraints. Having identified the absence of research on European and Japanese valuation of equity markets at the start of this research the aim was to fill this gap in the literature. However during the data collection periods the absence regarding data on these regions became apparent. Japanese data was virtually non-existent and quickly dropped from the research topic. Following the loss of this region the comparative and novel element of the research depended on the acquisition of European data. Still without viable and reliable sources yielding dividend or earnings data the option of manually acquiring the necessary data was the only feasible option. This induced the necessary inaccuracies into the data, however the outputs seemed realistic and that data was workable.
Another problem not foreseen at the start of this research was the methodological issues faced when using European data for mean reversion analysis purposes. Through the change of the European continent to the Euro and the relatively limited history of the union, mean reversion analysis was not feasible. This meant that the novel comparative aspect of this thesis was lost on this section of the research, which is regrettable.
40
Making aggregates of European stock indexes prior to the start of the EuroStoxx50 to proxy its value in periods earlier than 1998 could lead to more fruitful analysis of European markets. For the Japanese markets, serious inroads need to made regarding data availability. The average retail investor interested in Japanese equities faces a serious data constraint. Research could also significantly benefit from more data availability in this region. The more accurate and reliable availability of fundamental data on these index would decrease the barrier faced by financial research in relation to this geography.
However, aside from the mere availability of data, the most important area of improvement in valuation research is the method of proxying fundamental value. The current valuation metrics seem to operate well in an equity fueled bubble, when the bubble is directly fed through a hype in equities. However the fundamental value metrics perform worse was the bubble is either a housing or debt bubble. While models of bubble formation in housing markets are available in the research, they are not linked to equity movements. There is still a gap in the literature
41
ANNEX
A. 1 Graphs of EU and US government bond yields
A.2 Graph of EU and US high yield Corporate bonds
A.3 Graph of the EU and US Credit Spread 0 1 2 3 4 5 6 98 00 02 04 06 08 10 12 14 16 18
EU gov bond Yield
1 2 3 4 5 6 7 98 00 02 04 06 08 10 12 14 16 18
US Gov Bond Yield
4 6 8 10 12 14 16 18 20 22 98 00 02 04 06 08 10 12 14 16 18
US Corporate high yield
0 4 8 12 16 20 24 28 98 00 02 04 06 08 10 12 14 16 18
EU Corporate High Yield
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A.4 Z-score of the High Yield spread
A.5 Dividend and Earnings EuroStoxx 50 and S&P500
-2 -1 0 1 2 3 4 5 98 00 02 04 06 08 10 12 14 16 18
Z-Score credit spread
-2 -1 0 1 2 3 4 5 98 00 02 04 06 08 10 12 14 16 18
US Z-score Credit Spreads
43
A.6 Index Value EuroStoxx 50 and S&P 500
A.7 Price / Dividend ratio EuroStoxx 50 and S&P 500
A.8 Price / Earnings ratio EuroStoxx50 and S&P500
400 800 1,200 1,600 2,000 2,400 2,800 3,200 98 00 02 04 06 08 10 12 14 16 18 Price S&P500 20 30 40 50 60 70 80 90 100 98 00 02 04 06 08 10 12 14 16 18
Price / Dividend ratio S&P500
0 40 80 120 160 200 240 98 00 02 04 06 08 10 12 14 16 18
Price / Dividend ratio EuroStoxx 50
0 10 20 30 40 50 98 00 02 04 06 08 10 12 14 16 18
Price/ Earnings Ratio EuroStoxx 50
0 20 40 60 80 100 120 140 98 00 02 04 06 08 10 12 14 16 18
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A.9 US and EU gross equity issuance and their Z-scores
A.10 Time series EU and US debt issuance and Z-score 0 5 10 15 20 25 30 35 40 98 00 02 04 06 08 10 12 14 16 18 EU equity Issuance 20 40 60 80 100 120 140 98 00 02 04 06 08 10 12 14 16 18 US Equity Issuance -20 -10 0 10 20 30 90 92 94 96 98 00 02 04 06 08 10 12 14 16 18 EU Debt security Issuance
-2 -1 0 1 2 3 4 5 6 90 92 94 96 98 00 02 04 06 08 10 12 14 16 18 US Debt Security Issuance
-1 0 1 2 3 4 5 6 7 98 00 02 04 06 08 10 12 14 16 18
EU Equity Issuance Z-score
-2 -1 0 1 2 3 98 00 02 04 06 08 10 12 14 16 18
45 -3 -2 -1 0 1 2 3 4 98 00 02 04 06 08 10 12 14 16 18
Z-score Debt Security Issuance EU
-3 -2 -1 0 1 2 3 98 00 02 04 06 08 10 12 14 16 18
46 References
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