Forecasting Return and Spillover with GARCH


Spillover Effect on the Stock Market and Bond Prices in Relation with GARCH


This study examines the spillover effect between bond and stock markets in the U.S. using GARCH. The finding of a unidirectional spillover flow from bonds to stocks in the U.S. is discussed in the light of new marketplace variables that have been introduced into the markets in the previous decade. These variables include the rise of HFT, algorithm-driven trading, and central banking interventionism via unconventional monetary policy. The effect on forecasting volatility, price and return of asset classes, studied through the lens of other commodity price movement and volatility—such as oil and gold markets—creates a compelling picture for why GARCH models may need to be reworked to incorporate new data regarding the new ways in which the 21st century marketplace is using technology and central bank interventionism to shape market movements and market outcomes.

Table of Contents


1 Introduction 4

1.1 Why this research is important 4

1.2 What this paper examines 6

1.3 The most important findings and contributions this study makes to existing literature 7

2 Literature Review 11

3 Hypothesis Development 19

3.1 Spillover as a Result of Unconventional Monetary Policy 19

3.2 Low-Vol Complacency 20

3.3 Spillover is Unidirectional 21

3.4 Algorithm-Driven Trading and Market Movement 22

4 Data and Methodology 23

5 Findings 27

6 Analysis 37

7 Conclusion 47

References 49



1 Introduction


Globalization has substantially altered the working dynamics of markets of both developed and emerging nations. Sakthivel, Bodke and Kamaiah (2012) note that as a result of globalization, the spillover effect has become far more commonplace than what once used to be the case, for “world financial markets and economics are increasingly integrated due to free flow capital and international trade” (p. 253). This phenomenon has been seen most recently in the spillover effect of the 2008 housing bubble crisis in the U.S., which was quickly felt across sectors both domestically and internationally and served as an indication of the interconnectedness of modern markets and economies in the 21st century. Understanding spillover among equities and bonds along with other commodities, such as oil and gold, can play a significant role in how to forecast volatility and better manage funds, such as those responsible for guaranteeing pensions for workers in the not-too-distant future.

1.1 Why this research is important

Research in the spillover effect between the stock and bond markets is important because each represents one of the major asset classes for investors. According to Dean et al. (2010), there a number of theories which may explain the relationship between equities and bonds—the asset substitution hypothesis, the financial contagion hypothesis, the news specificity hypothesis, the news decomposition hypothesis, and the asymmetric price adjustment hypothesis. In short, the two asset classes are more or less seen as two sides of a negatively correlating coin. However, with the introduction of QE (quantitative easing) in the U.S., the relationship has seemingly altered, especially with respect to volatility, as a rebalancing towards both US and non-US assets was triggered with QE1 through 3 (Fratzscher, Lo Duca, Straub, 2016). The CBOE Volatility Index US:VIX on a two-year chart shows an ever-dwindling sense of volatility or risk in the market.


Figure 1. Two-year chart for VIX.


Source: CBOE Volatility Index (2017)


Park and Um (2016) likewise highlight the spillover effect of unconventional monetary policy in the US on bond markets and note that a mere mention of “news” of unconventional monetary policy in the US is enough to trigger a short-term spillover in the bond market in Korea. Short-term hedges in gold during such swings have been found by Baur and Lucey (2010) to be effective in protecting a portfolio from headline-driven spillover between equities and bond markets. But for forecasting the spillover effects, today’s GARCH models may need to take into consideration a rapidly changing market culture—namely, one that is driven by algorithms which have been blamed both for flash crashes and for melt-ups in recent years, along with the “existence of pure contagion” (Jayech, 2016, p. 631; Kirilenko, Kyle, Samadi and Tuzun, 2017). The velocity of volatility, the absence of liquidity (save for that provided by central banks), counter party risk, sovereign debt, risk parity, and overall fundamentals (AMZN is trading currently at a substantially elevated P/E of 250 and is one of a handful of stocks driving the overall market), are all signs of a market that has changed dynamically in just the past decade (Snider, 2014). In short, both QE and the rise of machines in trading have introduced new dynamics into the market that traditional GARCH models may not effectively factor into their equations. The result is that while some models may serve as better predictors of market movement, there remains a lack of fundamental understanding of spillover in relation to institutional forces.

This raises the question: Has the duel-engine of algorithm-driven trading and the central bankers’ policy of QE (bond purchases) created an irrational spillover effect between the stock and bond markets that has, as one result, crushed volatility to all-time historic lows? Has marketplace complacency taken hold because of an 8-years-long impression that the central banks will indeed do “whatever it takes” to backstop markets—as Draghi stated in 2012 with regard to the ECB’s role in maintaining the integrity of the European marketplace (Draghi, 2012). The VIX used to rise and fall much more frequently than it does today, as the chart above shows.

1.2 What this paper examines

This paper will examine volatility in the light of spillover between equities and bonds to more deeply understand the present day markets and what can be inferred from them. To assess this relationship, 20-year charts spanning from 1997 to 2017 will be used.

Equities offer investors ownership in a company; in times when the economy is booming, ownership of stocks can be financially rewarding. Bonds offer investors the opportunity for fixed income through interest; when the economy is stagnating or slowing down, investors can turn to bonds as a kind of safe haven. Oil as a commodity is often seen as an indicator of overall market sentiment, while the price of gold is commonly viewed as a hedge or safe haven in times of economic uncertainty. As more investors seek one or the other, prices go up—the basis of a supply-and-demand market economy. In the case of the bond market, higher bond prices produce lower yield. When unconventional monetary policy (such as the preservation of low interest rates over a significant amount of time, which can substantially distort markets) becomes conventional the world over, an unknown mechanism has entered into the dynamic and old formulas must be considered anew.

1.3 The most important findings and contributions this study makes to existing literature

This paper contributes to the existing body of literature examining monetary policy and asset price volatility—particularly to the work by Bernanke and Gertler (2000), which found that “it is desirable for central banks to focus on underlying inflationary pressures” (p. 17). One of the Fed’s aims over recent years has been to achieve 2% inflation. The pursuit of this aim should be factored into modern economic theory as it has had and will go on to have a substantial effect on economic forces. As Benford et al. (2009) show, “the aim of quantitative easing is to inject money into the economy in order to revive nominal spending” (p. 91). However, after eight years of QE, the inflation target is still as of yet unachieved, just as it was during the economic crisis of thirty years ago (Llewellyn, Nieto, Huertas and Enoch, 1992). Heller (2017) describes the current situation as one of “monetary mischief” brought about by central bank tampering that has inordinately inflated asset prices, decoupled markets from fundamentals, and created an “everything bubble” that Dowd and Hutchinson (2017) describe as the result of the “biggest monetary experiment ever” and the path towards what could quite possibly turn out to be “the biggest ever collapse” (p. 306). With this in mind, a fund manager of state and local pensions may be forgiven for bringing in a 0.6% return in 2016 when the assumed rate is more than 5% (Aubry, Crawford and Munnell, 2017)—market forces are increasingly entering into unknown territory and few managers have the tools to respond to what is more and more resembling a “wild west” type of economy, driven by AI, central planning and headlines instead of fundamentals.

It is necessary to add to the existing literature because of the present climate in which many financial managers find themselves today. As the recent report on pension funds by Aubry et al. (2017) has shown, there is a high degree of difference between the assumed rate of return for many funds and the actual rate of return. Indeed, the figure below indicates how poorly pension funds have performed when the economy experiences a downturn (notably following the dotcom bubble and the housing bubble).


Should spillover effect between asset classes with respect to a new GARCH model prove an effective indicator of future outcome, fund managers could be better situated to prepare for crisis situations and save their funds from collapse by reducing risk while simultaneously achieving a higher rate of return. The present case of negative cash flows as a percentage of market assets for state and local pension plans indicates that such an indicator could be a boon to fund managers.


However, considering the price of the bond market and the flattening curve (recently inverted in China), the question could be asked as to whether or not fund managers are already attempting to reduce risk to a level that supersedes any hope of return comparable to what is needed over an extended period of time. That question must surely be saved for future research as it is beyond the scope of this present paper.

In the following chapter, a literature review as well as a theoretical framework is provided, with two hypotheses described that will be tested according to the methodology explained in chapter 3. Findings are provided in chapter 4 and analyzed in chapter 5.


2 Literature Review

The findings of Gencer and Musoglu (2014) show that examining the relationship between equities and bonds with respect to gold and GARCH can reveal a suitable course of action for fund managers in adverse economic times. Their study provides empirical findings which “depict gold as a unique asset to reduce the portfolio risk especially in times of adverse market conditions” (Gencer and Musoglu, 2014, p. 705). This is precisely that type of indicator that can be helpful for fund managers facing the current economic uncertainties, which the flattening yield curve in the U.S. indicates is a reality. Coupled with present-day political and social issues (a threat of nuclear wars on multiple fronts a distinct possibility as sanctions against Russia are set in place and provocations towards North Korea and China continue to be ratcheted up), destabilizing economic conditions are ever present across multiple spectrums (negative rates in Japan, central bank balance sheet expansion from East to West, debt at unsustainable levels). Against this backdrop, Gencer and Musoglu (2014) analyzed seven year data logs of gold and bond prices alongside Turkey’s stock market index BIST 100 and calculated returns according to the following formula:

“Rt 1 = log(Pt 1) – log(Pt)

where, Rt 1, denotes return, Pt and Pt 1 represent price at time t and price at time t 1, respectively” (p. 707). The formula showed that “gold investments generate the highest return at the lowest risk, measured in terms of standard deviation, while bond returns are very slightly negative, and stocks are the riskiest investments with considerably lower returns and higher unconditional volatility compared to gold. It can be seen that gold and bond returns are skewed to the right whereas BIST100 returns are skewed to the left” (Gencer and Musoglu, 2014, p. 707). The table presents these findings in detail.


Source: Gencer and Musoglu (2014)

This skew indicates that by taking an approach to safe havens as spillover from one asset class to another gets underway may be an acceptable practice. Gencer and Musoglu (2014) explain:

The current volatility of bond returns are the most affected by own past volatility, while the current volatility of stocks is the least affected. In terms of cross conditional volatility terms, the results reveal that there is a bi-directional volatility transmission between gold and stocks. The past volatility in gold returns negatively affects the current volatility in stocks, while the volatility transmission is positive from stocks to gold. For the gold-bonds model, the cross coefficients delineate a uni-directional volatility transmission from gold to bonds which is negative. The results of the diagnostic tests based on standardized residuals depict no serial correlation and no remaining ARCH effects, reifying the BEKK-GARCH (1, 1) model adequate to capture the dynamics of volatility spillover between the series (p. 708-709).


Source: Gencer and Musoglu (2014)

The study by Gencer and Musgolu (2014) is helpful in shaping the hypotheses of this current study, which bases its theoretical framework in the concept expressed by both the study by Gencer and Musoglu (2014) and the view expressed by Heller (2017) which specifically targets Fed policy and its 2% inflation target rate, described as likely to result in “a massive erosion of the value of the dollar” (p. 247). The combination of policy and correlation between asset classes with regard to GARCH may be taken as the cumulative expression of a marketplace that is entirely consumed with how central bank interventions will be interpreted and acted upon by market players. In the year 2017, central banking intervention is a fact, as Draghi, Yellen and many other central bank players have shown. How the average fund manager is meant to obtain the assumed rate of return for his fund in an environment that is anything but normal (judging by historical guidelines) remains a particular problem—and a practical problem as well (seeing as how pension plans are dependent upon the assumed rate of return being a consistent average over 5 years) (Aubry, Crawfor and Munnell, 2017). The study by Eser and Schwaab (2013) is also essential in the formulation of this theoretical framework, as it examines the impact on yield of asset purchases by Draghi’s ECB and its Securities Markets Programme. The findings show that, not surprisingly, “bond yield volatility is lower on intervention days for most SMP countries, due to less extreme movements occurring when the Eurosystem is active as a buyer” (Eser and Schwaab, 2013, p. 1). What this reveals is that when the market knows that there is a buyer of bonds, volatility collapses. The sense in today’s market, if one judges from the VIX at all-time lows, is that the central banks will continue to be buyers of assets even while the Fed hints at reducing its book and Draghi hints at tapering. The studies by Neuenirch (2012) and Rosa (2016) confirm as much, among others, and help serve as the basis for this study’s hypotheses, which are discussed in the next chapter.

The measure of these hypotheses may be taken by analyzing GARCH charts of stock and bond markets along with gold (as an assumed safe haven) and oil (as an indicator of overall market movement). A potential “wrench” that could be thrown into this mix might be the rise of crypto-currencies, such as Bitcoin (BTC), Bitcoin Cash (BCC), Ethereum (ETH) and myriad others. The rise of crypto-currencies is relatively new and could be indicative of yet another bubble or of a market weary of markets that are manipulated on several fronts, where price discovery is next to impossible. Evaluating GARCH models with assets against BTC, BCC or ETH could be relevant for a future study and several researchers have already undertaken steps in this direction, including Katsiampa (2017), Cermak (2017) and Wang and Vergne (2017). The rise of cryptocurrency in and of itself may be interpreted as a signal that abnormal volatility changes in the marketplace as a result of unconventional monetary policy are causing investors to seek assets that out of the hands of central banking control. Such a movement in market sentiment may also act as an indicator of future fluctuations, especially if political, economic and social turmoil continue to build (Blundell-Wignell, 2014). Measuring the spillover between stocks and bonds in the light of this development could yield some potentially useful financial analysis relevant to forecasting—especially where assumptions about the market are concerned.

There is also significant pressure from sector forces on spillover, as industries struggle within splintering socio-political climates that impact economics on a global scale. The chemicals industry, like other sectors, is dependent upon both “economic growth overseas” and commodity prices that can impact “economic growth in the US” (Muir, 2016, p. 5). In addition, governmental policies and changes can impact the industry, as is seen in South America, where various “region’s development policies that privilege industrialization as the route to economic growth” are currently being implemented, as in the Sinos Valley of Brazil (Schreiber et al., 2016, p. 58). For the chemicals industry, the policies of governments and political situations are a direct impact. For instance, recent regulations in the US regarding toxic waste emissions have compelled companies within the chemicals industry to reduce their levels of waste, boost their adherence to corporate social responsibility policies, and change the way they interact with the environment—all of which impacts the industry’s cost-savings balance (Muir, 2016, p. 44). Another example is that of government farm programs and policies, which bear a direct impact on the fertilizer market, a substantial segment of the chemicals industry (Muir, 2016, p. 57). As Muir (2016) notes, the chemicals industry “is subject to a large number of state and federal laws and regulations involving public health, worker safety, and environmental protection”—all of which are fiercely debated in the public forum during election cycles, as legislators, pundits, lobbyists and politicians attempt to influence the political issues and governmental regulations that impact businesses and communities.

Likewise, the growth of consumer pressure adds to the demand for product, and where there is demand there is foreseeable upside. The chemicals industry thus benefits from demand-side support in regions where government policies help to shore up agricultural investment and/or industrialization, both of which provide a market for the chemicals industry. As consumer pressure wanes, so too does the demand in each of these markets, which drives the global economy towards recession and negatively impacts the ability of the chemicals industry to produce sales. At the same time, as technology develops and innovation leads to the production of new consumer goods, the chemicals industry can be placed in a growth position by benefiting from the innovative resurgence of the technologies market (Schreiber et al., 2016, p. 59). All of this has an impact on volatility.

Bentes (2015) examines volatility in gold returns using the GARCH, IGARCH and FIGARCH frameworks and provides new evidence suggesting that the FIGARCH (1, d, 1) model is the best method of capturing linear dependence in the conditional variance of gold returns. Also, for forecasting gold returns volatility, this same model appears to be most effective when compared to other GARCH models. The finding of this study, however, can be compared to the findings of the study by Kristjanpoller and Minutolo (2015) who use considerably more variables as inputs in assessing the volatility of gold returns. Their study shows that a hybrid ANN (Artificial Neural Network) GARCH model is capable of forecasting gold price volatility in both spot and futures indexes. The ANN-GARCH model presented by the researchers is found to reduce the mean average percent of error by 25% when the model is used with EUR/USD, YEN/USD exchange rates as inputs along with the DJI and the FTSE stock indexes, and the oil price return. The implications of the model being more effective when these inputs are provided suggests that the volatility of gold returns is more accurately predicted when that asset class is weighed in comparison with other asset classes as well as FX. The dominating idea here is that no asset class volatility can be or should be predicted wholly as though it existed in an isolated sphere and was not impacted by spillover even in subtle or undetectable ways.

A third approach to hedging is identified by Arouri, Lahiani and Nguyen (2015) who assess Chinese stocks and recommend hedging a portfolio with gold after their study, using VAR-GARCH and five competing multivariate GARCH specifications. The researchers found that significant return and volatility cross effects can be forecasted using this model as opposed to others. Using their model, they concluded that gold could be viewed as a hedge for Chinese stocks and a safe haven during economic crises. The researchers found the VAR-GARCH as the best model for forecasting volatility spillover when examining spillover among these assets.

These three studies represent the diverse opinions, options and ways to view GARCH and spillover within the realm of asset classes and economic instability. Though there are myriad others, as shall be discussed in more detail in the following chapter, these studies typify the trends in spillover research. The fact that each study in this small sample surveys a handful of variables, each different from the other, before recommending their own favored or preferred GARCH model indicates that the variables which are viewed are, it cannot be understated, significant in the final analysis.


3 Hypothesis Development

The hypotheses of this dissertation are based on theories of spillover found in the relevant literature. Because the various studies all have their own approach to the subject of GARCH modeling and offer different results, the aim of this study is to provide a general understanding of how GARCH modeling might be advanced in the future according to new variables impacting the volatility of the marketplace today. Several studies find that spillover between markets is impacted by

3.1 Spillover as a Result of Unconventional Monetary Policy

The focus of the first hypothesis is on the impact of unconventional monetary policy on spillover between the bond and stock markets. Numerous studies have identified unconventional monetary policy, most recently seen in the form of quantitative easing (QE) in the U.S., as having an effect on markets (Kuttner, 2001; Rigobon, 2003; Bohl, Siklos and Werner, 2007; Neuenirch, 2012; Rogers, Scotti and Wright, 2014; Rosa, 2012; Rosa, 2016; Lombardi, Siklos and Amand, 2017). The role of central banks in the past few decades has seen changes in market phenomenon—from alterations in interest rates to effects in the bond and stock markets. The theory generated by Lombardi et al. (2017) rests upon the common equation assumed by most researchers regarding spillover—namely, that


where the change in return on an underlying is related to monetary policy surprises. Lombardi et al. (2017) note that “given the relative size and significance of the US financial system to the global financial system, US monetary policy surprises are the source of spillover effects” in their theoretical framework (p. 4). Several other studies support that framework, however, including the work of Rosa (2016) which finds that speeches by Fed Chair Yellen have a direct impact on the volatility of asset prices in a way that cannot be conceived as normal. Likewise, Rogers et al. (2014) find that unconventional monetary policy as utilized by the US Fed, the BOE, the ECB and the BOJ have impacted equity markets, bond markets and exchange rates. Their study indicates, moreover, that spillover from the US throughout the global marketplace is a much stronger unidirectional flow than spillover form the global marketplace to the US markets. Rogers et al. (2014) show that unconventional monetary policy correlates with yield curve development in recent years—and so for these reasons the first hypothesis of this study is the following:

H1: The spillover effect in the US equities and bond markets is a direct result of central banking intervention.

3.2 Low-Vol Complacency

The theory that volatility in the markets is artificially low as a result of market complacency has been put forward by some researchers as well. Van Dijk, Lumsdaine and Van Der Wel (2016) have shown that US markets anticipate Fed meetings, demonstrating a remarkable effect on volatility with regard to them. Auinger (2015) has shown that declines in implied volatility acts as a signal of market complacency—and when these signals are read in conjunction with central banking telegraphing their own signals to the market—whether it is an intention to raise rates, keep rates low, continue active buying of debt or taper buying and reduce the books—the market acts in response. Low implied volatility and an historically low VIX indicate that something far more serious is happening in the markets than what may meet the eye from traditional GARCH models (Basher and Sadorsky, 2016). With volatility at all-time lows and complacency firmly embedded in the market as a result of years of unconventional monetary policy that underscores a general desire by central banks to do, as Draghi has stated, whatever it takes to keep investments safe, markets may be less susceptible to certain variables that ordinarily would be impactful in normal conditions.

H2. Volatility is low because the market is complacent in its belief that central banks must and will intervene.

3.3 Spillover is Unidirectional

The theory for this hypothesis stems from the findings of Zhang, Zhang, Wang and Zhang (2014) who have shown that in the US, spillover flows from the bond market to the stock market and not vice-versa. Yavas and Rezayat (2016) have also focused on the unidirectional flow of spillover, signaling that the phenomenon is meaningful when interpreted in the light of monetary policy. The relevance of this finding, in the light of unconventional monetary intervention, lies in the fact that the Fed has been a consistent buyer of bonds, which in turn leads to spillover into the stock market.

The importance of evaluating this theory using GARCH is that if spillover is indeed unidirectional and correlative with central bank intervention, the impact on stock futures forecasting would be significantly dependent upon what steps it is expected that the Fed will take. If a reduction of the books becomes an apparent step in policy and a return to normal monetary policy is expected, a serious pullback in equities could be the result of a tapering effect in the bond market. With QE at an end, the relationship between stock and bond prices in the past few years could tell something about the overall market sentiment.

H3. Spillover from bonds to stocks is a result of QE.

3.4 Algorithm-Driven Trading and Market Movement

The theory for this hypothesis is found in the work of a number of researchers, including Gsell (2008) and Hendershott and Riordan (2013). Their studies focus on the impact that algorithmic trading has on the market and how this new technological innovation is driving more and more traders to make adjustments to their strategies. One of the main reasons for this is that the algorithms are designed to make automatic trades whenever the right signals are interpreted by the machines using them. Avis, Chang and Wu (2017) have also raised issues about algorithmic-trading and its connection to volume and volatility in their study on extreme price movements in the age of higher algorithmic trading. Goldstein, Kumar and Graves (2014) likewise study the relationship between algorithms and trading, though their focus also extends to high-frequency trading, which is another variable that might be impactful on market movement. Similarly, as Ricci (2014) notes, an HFT will use algorithmic trading “in multiple assets” while it seeks out statistical arbitrage opportunities and acts aggressively via the submission of market orders” (p. 1). This indicates that algorithmic-trading is a significant variable that should be assessed in the light of spillover movements.

H4. Algorithmic-trading is an important variable in assessing the movement direction of spillover and volatility.



4 Data and Methodology

The method chosen to test the hypotheses of this study is to analyze the GARCH charts obtained via the Volatility Institute of the Leonard N. Stern School of Business at NYU. The V-Lab contains a multitude of GARCH graphs that allow for a substantial analysis of stock and bond markets of the past 20 years. By analyzing these graphs in conjunction with oil and gold commodity prices over the same time period, it is expected that a pattern will emerge, which can be viewed in the light of emerging institutional forces (QE, HFT, and algorithm-driven trading floors) and which can assist in understanding the variables that could be factored into producing a new GARCH model.

Bi-directional spillover in any case has already been identified (along with unidirectional spillover) in each of the G7 countries, according to the study by Zhang, Zhang, Wang and Zhang (2014), with the U.S. showing unidirectional spillover from the bond to the equity markets. This study assumes the same approach, with emphasis on the causality-in-variance test constructed by Hafner and Herwatz (2006) using the Lagrange multiplier (LM) principle. The LM principle has demonstrated robustness as Hafner and Herwatz (2006) have shown, especially with regard to leptokurtic innovations, while allowing that distortion is a possibility when lead and lag order is concerned in CCF tests. The following table demonstrates the return of equity and bond indices, Re = return of equities and Rb = return of bond indices.


Table 2. Descriptive statistics for Re, Rb of Western markets.


Source: Zhang et al. (2014)

Prior to construction of their GARCH model, Zhang et al. (2014) test the autoregressive conditional heteroskedasticity (ARCH) effects of Re and Rb using the LM model and find evident ARCH effect with a lag of 1 in every instance.


Table 3. LM Test for ARCH.


Source: Zhang et al. (2014)


Volatility between equities and bonds was estimated as shown in Table 4 and the unidirectional spillover from the bond to the equities market shown in Table 5.

Table 4. Univariate GARCH (1,1)


Table 5. Causality-in-variance test results.


Source: Zhang et al. (2014)

As Zhang et al (2014) note, the LM-GARCH model indicates unidirectional spillover from bonds to stocks in the U.S.—why that should be so is not discussed but an examination of further GARCH narratives, in bull and bear markets, could reveal possible stories to explain this movement. As the researchers state, “taking the subprime crisis and sovereign debt crisis into account, our emperical result has significant, meaningful and practical implications” (Zhang et al., 2014, p. 214). Thus, the hint is that unconventional monetary policy may have something to do with it.

However, assessing any single variable, such as how central bank intervention has impacted volatility in the marketplace or altered the spillover effect, is not possible as a result of this precursory analysis. The aim of this methodology is merely to make initial headway into a complex schematic that acknowledges variable interconnectedness within a matrix that is continuously shifting in today’s global markets.

The hypotheses to be assessed are:

H1: The spillover effect in the US equities and bond markets is a direct result of

central banking intervention.

H2. Volatility is low because the market is complacent in its belief that central

banks must and will intervene.

H3. Spillover from bonds to stocks is a result of QE.

H4. Algorithmic-trading is an important variable in assessing the movement

direction of spillover and volatility.


Acknowledging that the scope of this study is broader than its feasibility is practical, the hypotheses described above may still be examined in the light of GARCH graphs and comparisons, with a survey of market forces to help provide a possible gateway to a new formula for forecasting asset spillover, return and volatility.


5 Findings

The GARCH chart for the S&P 500 from Aug 1997 to Aug 2017 reveals correlation between dwindling volatility and a higher index price beginning most dramatically in 2010 when volatility hit a 10% low after peaking at 70% during the height of the economic crisis of 2008. Low and steady volatility from 2004 to 2007 correlated with a steady rise in index price, following the dotcom bubble implosion and the collapse of Enron at the turn of the 21st century—a time period marked by much sharper terms of volatility increase and decrease and a wider range of volatility overall from the time period 1997 to 2003. The S&P index increased in price over the first half of this same time period (1997-2000) and then began a pullback that lasted until 2003 when volatility stayed well below 20% and hovered in the low teens for nearly four years. The price of the S&P appreciated over this stretch before collapsing in 2008 when volatility spiked more than 400% within a matter of months.

Volatility highs coincided with index price decline in 2009 but following that there was no correlation between volatility and index price, which rose steadily from 2009 onwards. The only difference between pre-2009 index price and GARCH volatility and post-2009 is the existence of QE.

Figure 4. S&P 500 1997-2017 GARCH.


Source: V-Lab (2017a)


The central bank intervention from Dec. 2008 to March 2010 known as QE1 occurred following this parabolic rise in volatility in 2009 (and collapse in equity prices), and saw the purchase of hundreds of billions of dollars worth of MBS. QE1 was followed by QE2, 3 and 4—which will be discussed in more detail in the following chapter. The bond purchases of QE resulted in evident spillover, just as the study by Zhang et al. (2014) indicated.

The volatility summary table for the S&P 500 is shown below.

Table 6. Volatility summary table S&P 500.

Compared to the Barclays bond index US Agg. Credit AA GARCH chart, the correlation between bond prices and volatility is less pronounced. In 2008, there is the same sharp rise in volatility followed by the same descent in volatility in late 2009-2010—at which time bond prices in the index also rise—but they seemingly track volatility since 2010. Spillover from the S&P into the bond market can be discerned in terms of negative correlation. With the rise in the S&P index, the price of bonds fell until 2000, when a bear market began to emerge in equities and a bull market in bonds got underway, going until the latter half of 2003. This bull in the bond market was marked by a steady by wide rang in volatility. The bull market reversed and entered into bearish territory just as the bulls began to return to the S&P in 2003—again marking a moment of negative correlation.

Figure 5. Barclays US Agg. Credit AA GARCH volatility graph.


Source: V-Lab (2017b)

With an average monthly volatility of 1.97%, the bond market presents less risk than the stock market over the same time period, though the returns are far less rewarding, too. An analysis of what this signifies in terms of forecasting may depend upon the variables that are used in the evaluation matrix, which will be discussed in more detail in the next chapter as well.

Table 7. Volatility summary Barclays US Agg. Credit AA.


Looking at Randgold Resources Ltd GARCH volatility, it is again apparent that the price of gold was not seriously impacted until the 2008 crisis, whereupon it increased exponentially. Volatility was at its peak, moreover from 1998 to 1999 but the price of gold was not dramatically impacted, though it did rise over the course of the next ten years. However, the return of Randgold’s stock has stabilized along with its volatility which has not increased above 80% since 2009.

Figure 6. Randgold Resources Ltd GARCH volatility graph.


Source: V-Lab (2017c)

Table 8. Volatility summary Randgold Resources Ltd.


The return on Randgold is lower than the return on bonds, which is lower than the return on the S&P. Unidirectional spillover from the bond market to the stock market has thus resulted in the greatest returns in the stock market while safe haven markets have produced the lowest returns (negative returns overall) over the same time period. The complacency in the market is apparently fueled by the expectation of central bank intervention.

The oil market saw the commodity’s price peak with the 2008 bubble and decline ever since, the biggest drops coming with sharp peaks in volatility in 2008-2009 and 2014-2016. The WTI GARCH chart below in Figure 7 shows the relationship between volatility and price decline but also indicates a broader range in return with significant volatility as traders score big on swings.

Figure 7. GSCI WTI crude oil index GARXCH volatility graph.


Source: V-Lab (2017d)

The return in oil has been significant following the bear run 2014 to 2016 but the oil market has failed to rise above resistance set prior to the inflated prices that resulted from foreign policy initiatives Saudi oil pressure on the price. Market sentiment as interpreted by the oil market is indicative of a none-too-confident outlook, which weighs on the bond/stock markets and their underlying fundamentals.


Table 9: Volatility summary GSCI WTI



The oil price paints a different picture of the global economy because it puts actual pressure on nations to adjust to sales accordingly, as can be seen everywhere from Russia to the Middle East. Even in the U.S. fracking is only possible when the oil price hits a specific target—otherwise it is simply not profitable. With oil being used in so much production, the price of oil tells a significant story about economic issues and economic fundamentals—a story that is simply not being told by the equities market, which is receiving all the spillover from the bond market.

A look at one of the stock market’s biggest winners in the past two years, when the price of oil has stagnated at less than half its peak pre-bubble price, shows AMZN at the height of its historic value.

Figure 8. Inc GARCH volatility graph


Source: V-Lab (2017e).

Amazon’s tremendous bull run has coincided with the onset of QE and indicates the spillover effect from bonds to stocks in the U.S. Its significant increase in price in just the last two years with the end of QE4 raises questions about the company’s fundamentals and the role of banks in corporate bond buying as well as algorithm trading. The collapse in return with the substantial reduction in volatility correlating with the increase in asset price suggests that this company is one of the main drivers of the equity market for good or for ill.

Table 10. Volatility summary AMZN.


AMZN’s return is nearly right in line with the return of the S&P 500 and its volatility is highest in its early years, the late 1990s and early 2000s. AMZN’s bull run is somewhat matched by TSLA’s great bull run of the past 4 years. Bears in gold have likewise been rewarded over the same stretch of time, indicating that the spillover from bonds to equities has come also at the expense of safe haven buyers and gold hedgers. TSLA’s catapult in underlying price value has been nothing short of magnificent, especially when one considers the very considerable cash burn the company has been undergoing throughout this same time period.

Figure 9. Tesla Inc GARCH volatility graph


Source: V-Lab (2017f).

Tesla’s volatility has spiked less since mid-2014 and its price gains have increased while returns have remained relatively stable. Tesla’s volatility may return in the coming months as its cash burn continues at a significant rate. However, along with AMZN, Facebook, Google and Apple, Tesla is one of the dominant players in the market, driving equities and ETFs to all-time highs.

Table 11. Volatility summary TSLA


Tesla’s return is higher than the S&P 500 but so too is its volatility. The opposite is the case with AAPL. Its return is in line with the S&P and its volatility is much nearer the index’s than TSLA’s.

Figure 10. Apple Inc GARCH volatility graph.


Source: V-Lab (2017g)

Table 12. Volatility summary AAPL.


The incredible bull market enjoyed by AAPL since the 2008 crisis is one of the greatest indicators of how equities have benefitted from bond market spillover inspired by QE’s launch in the post-2008 crisis period. Volatility in AAPL has steadily decreased as the stock’s price has steadily increased. The almost perfect correlation suggests that the unidirectional spillover effect must include central banking variables along with algorithm impacts to explain this movement in greater detail.

The bull market rally of the stock markets since 2008 correlates with the collapse in bond market yield and the bear market in gold (a traditional safe haven, which enjoyed a terrific bull market until 2012-2013, wherein bears took over and brought the price of the asset back down to 1250 where it currently sits today.


6 Analysis

Hypotheses tested and displayed in the findings in the previous chapter show the following:

H1: The spillover effect in the US equities and bond markets is a direct result of

central banking intervention.

Spillover is unidirectional, flowing from bonds to stocks over the duration of the Fed’s QE (2008-2013) and even following as the BOJ and ECB continue their own versions of bond-buying policy. The unidirectional flow is signified in the downward volatility trend and the movement of the bond market juxtaposed with the movement in the S&P 500 as well as individual stocks.

H2. Volatility is low because the market is complacent in its belief that central

banks must and will intervene.

With central bank intervention highly publicized and apparent in bond-purchasing, it can only be surmised that the low-vol complacency within the markets, as seen in the GARCH graphs of the bond index, the S&P index, the oil index and the individual stocks, is the direct result of markets waiting for central banks to cease their intervention policies.

H3. Spillover from bonds to stocks is a result of QE.

While this spillover is unidirectional, there may be more to it than the variable of QE can indicate, as the unidirectional flow is not only an effect of unconventional monetary policy but also the outcome of market movement generated by myriad other factors, from fund management assessment to algorithmic-driven trading.

H4. Algorithmic-trading is an important variable in assessing the movement

direction of spillover and volatility.

This variable is complex to assess from the limited data obtained through the GARCH graphs discussed in the previous chapter. While there does appear to be a connection between the rise of algorithmic-driven trading and a collapse in volatility, the spillover effect may have less to do with this variable than with other factors already discussed.

Spillover from bonds to stocks can be seen to be unidirectional throughout the period of QE commenced by the Federal Reserve in 2008 to 2013. However, the BOJ picked up where the Fed left off with its purchasing of debt in the Japanese market and the ECB had done as much in Europe since the Fed ended QE. As has been shown by prior studies, there is significant spillover from world markets to US markets so the same process can essentially be understood to still be in continuation. For all intents and purposes, the era of QE is still in effect with only rumors of balance sheet unwinding and tapering making headlines and momentarily driving algorithms, though not substantially as the GARCH graphs indicate for oil, gas, stocks and bonds.

One consideration to make when analyzing the GARCH graphs and the spillover effect is the impact of interest rates, as it is the interest rate that sets in motion the bond market on the most fundamental level. The Vasicek model is a model used in finance for understanding the development or movement of interest rates. The model is based on one single factor or source of market risk but it is useful in evaluating the pricing of derivatives or interest rates. Developed in 1977 by Oldrich Vasicek, the model also has a function in stochastic charting (Vasicek, 1977). Vasicek himself characterized it as an equilibrium within the term structure.

The formula for the model is and shows that stochastic differential equation gives place to the instant interest rate. It is the parameter of the standard deviation that allows for volatility to be determined (James, Webber, 2000).

Vasicek (1977) notes that a number of assumptions are at play in this formula—such as the idea that spot interest “follows a diffusion process” and that it is on the spot rate that “discount bond” prices are dependent; the final assumption that “the market is efficient” (p. 177) is perhaps the most dangerous one—or the one that applies least in today’s market of dark pools, high-frequency traders, spoofing, and market manipulation. One must have a sense of how different today’s market is from Vasicek’s of nearly forty years ago. The mathematics may not have changed, but the assumptions need to be updated.

The context for which the model was created was the notion that interest rates cannot go up or down forever and will in the long run, or over time, proceed within a limited range. There is a “drift factor” along with the long-term equilibrium parameter that is meant to serve as the bar to which interest rates return—but in today’s world of “artificially low” interest rates, this bar may be subject to further examination, even if the interest rate stays at a constant, non-fluctuating state. What Vasicek did not foresee in his model is the real possibility of negative interest rates, as we have today in Europe. However, a different model—the Cox-Ingersoll-Ross model, along with others like the Black-Karsinski model, have attempted to take this deficiency into consideration, by noting that the drift factor takes over for the evolution of the rate as it nears zero and thus the rate drifts higher back in the direction of its natural equilibrium. But of course this model assumes that the natural equilibrium is attainable because it also is based on the same assumption as Vasicek’s—namely that the market is efficient. Is today’s market efficient? The GARCH graphs would indicate that the market is in a rather unusual state, one that is uncharacteristically calm, yet not without an awareness of inherent risk.

Bauwens, Laurent and Rombouts (2006) put the questions most succinctly in their study of multivariate GARCH models: “Is the volatility of a market leading the volatility of other markets? Is the volatility of an asset transmitted to another asset directly (through its conditional variance) or indirectly (through its conditional covariances)? Does a shock on a market increase the volatility on another market, and by how much? Is the impact the same for negative and positive shocks of the same amplitude?” (p. 79). The purpose of the GARCH is to relate asset prices to factors—however, in the past 10 years, significant changes have come to the marketplace that have altered traditional thinking about how markets operate. Those changes are manifested in equities and bond markets and in commodity prices, such as oil and gold. There is immense uncertainty in the markets even as all-time highs are hit in the DOW, the S&P 500, while oil stagnates under $50 a barrel and gold hovers at its 200 DMA. The new factors that have been introduced include technology and central banking interventionism particularly in the form of unconventional monetary policy. How does a pricing model react to these factors? This study has shown through it analysis of the GARCH graphs in the previous chapter that these factors should be incorporated in a new GARCH approach to better understand the relationship between central banking intervention, algorithm-driven trading, and uncertainty regarding underlying fundamentals, the need to hedge, and the need to buy safe haven assets.

With regard to algorithm-driven trading, an examination of flash crashes over the past few years can suggest that this factor should also play a part in how volatility is forecasted in the future. As Borch (2017) notes, flash crashes themselves need to be studied more, as they themselves mark new terrain in the equities market and should be seen as a new factor in volatility fluctuations: “the Flash Crash of 6 May 2010 has an interesting status in discussions of high-frequency trading, i.e. fully automated, superfast computerized trading: it is invoked both as an important illustration of how this field of algorithmic trading operates and, more often, as an example of how fully automated trading algorithms are prone to run amok in unanticipated frenzy” (p. 350). Algo-financial markets are here to stay and are generating massive movements in the marketplace at times when liquidity, headlines, and time of day are all variables that make an impact on the phenomenon. As Zook and Grote (2016) observe, the role of HFT is game-changing in the global marketplace: “Enormous investments have been made in creating transmission technologies and optimizing computer architectures, all in an effort to shave milliseconds of order travel time (or latency) within and between markets. We show that as a result of the built spatial configuration of capital markets, “public” is no longer synonymous with “equal” information. High-frequency trading increases information inequalities between market participants” (p. 121).

Evaluating the spillover effect between bonds and equities with respect to GARCH is only half of the solution in terms of identifying an accurate forecasting model. Another aspect of the solution that is far more complex to identify is the issue of which variables to use as inputs in the forecasting formula. Just as a model of the earth may be presented which is geocentric, heliocentric, spherical or flat and—though they all differ—can be used as both a navigational tool and an explanatory method of assessing the movement of the stars within a specific spectrum, the GARCH models offer a singular view of market force dynamics capable of forecasting within a limited range. However, to suggest that any one such model is best or most efficient is a highly risky activity which is really only possible through a narrowing of the lens on the field of economic data.

Risk aversion is another issue that should be considered, especially in the light of the charts analyzed in chapter 4 and the need of fund managers to secure return for the sake of the future. Safeguarding against risk is a practice that an investor engages in and that determines market activity when there is a choice between two investments of equal return: an investor focused on risk aversion will act on the option that offers the least risk to the investor. One possible measure of risk aversion is the Arrow-Pratt measure, which is also called the coefficient of absolute risk aversion (Pratt, 1964) and this measure could be a variable that is considered among fund managers today. In portfolio theory, risk aversion is assessed by the degree of marginal benefit that an investor would need in order to assume even more risk. In today’s marketplace, economic variables are being redefined by the banks and the technology used by trading firms: risk is unknown at any one moment—and if one studies VIX or GARCH volatility, the expectation in the marketplace is that there is very little awareness of risk whatsoever. The markets are complacent to a high degree, to judge from the S&P 500 GARCH graph, or any of the equities assessed in the previous chapter.

Measuring risk aversion is important to financial decision making because one’s aversion for risk will determine the nature of one’s investments. Riskier investments tend to produce greater returns, but they also pose the greatest risk of failure; less risky investments typically ensure minimal to modest or set returns, which may not help to grow an investor’s wealth substantially but will essentially provide little cause for concern of losing one’s investment. One’s risk aversion can help to signify whether one taking too risky positions in a portfolio or if one can stand to branch out of safer investments to seek higher yield.

Nonetheless, the expected return that a fund manager might have for a portfolio is the most difficult input to estimate because there are myriad variables that can and will impact the market, especially in today’s algorithm-driven, Fed-defining market. Finding a risk-free rate and beta are much simpler to estimate as beta is based on past history and a risk-free rate is based on expected interest—but this variables will not always help a fund manager to meet the assumed rate of return needed for his fund. The problem emerges, then, that rates are being suppressed by the Fed for a reason other than bringing stability to the marketplace. How a measure of volatility in such a case can help a fund manager make decisions may not be enough to protect the portfolio. Market performance is, after all, tremendously complex, and making projections or forecasting movement in the short or long-term scenario is something that analysts attempt—but to some degree there is a limitation to the value of these forecasts. A model is only as good as its inputs, and the research of this study indicates that more inputs are needed to properly forecast volatility and return in this new marketplace.

The question that remains is whether real inflation is running higher than reported. The present market state has been described as an “everything bubble”—with housing prices soaring above their initial bubble peaks in 2007-2008 in several cities across the country; with the stock market continually surging to all-time highs; and with medical expenses and educational expenses continuing to increase. With bond yields at all-time lows, it may be only a matter of time before buyers begin demanding a higher rate of return—at which point the Fed may be obliged to raise rates, even if only by another 25 basis points.

The robustness of this study is in the development of a sense of how markets will react to these questions and how a GARCH model may be modified to account for these reactions. Because the old normal has been replaced by the new normal of unconventional monetary policy, a new way of modeling may indeed be needed. The recommendations of this study are for a renewed examination of volatility in relation to spillover in the light of QE, algorithmic trading, and market expectations regarding tapering and the likelihood of rates rising anytime soon.

With an average monthly volatility of 1.97%, the bond market presents less risk than the stock market over the same time period, though the returns are far less rewarding, too. As was reported in the previous chapter, an analysis of what this signifies in terms of forecasting may depend upon the variables that are used in the evaluation matrix. The variables that could indicate a proper risk/reward ratio for fund managers will need to incorporate underlying variables. Predicting movements on the marketplace based on what has transpired since 2008 would be to accept these movements as normal, rational or natural, when it can be argued that they are anything but. Forecasting for volatility and return in such a climate as this is one that can be very dangerous and risky to one’s fund or portfolio. How to proceed from here requires careful evaluation of more than just volatility indexes—it requires a complete understanding of how the markets are being manipulated and why spillover is wholly unidirectional in the U.S. yet bidirectional in other countries, such as Japan or Italy. What is happening in these marketplaces to make the spillover effect two-way instead of one-way?

Foreign markets are also a place to look as they impact currency exchanges, the price of oil, and options for hedging. Hedging would not be recommendable in a foreign market whose assets are appreciating, as Canada’s did in from 2000 to 20009. Canada’s S&P/TSX Composite index soared by more than 20% during the first decade of the 21st century. The foreign market significantly outperformed, for example, the US market because of the strengthening of the Canadian dollar against the US dollar. In other words, as the US dollar weakened, investments in overseas markets became a sound investment during this time period as there was less risk. A hedge against a sudden shift in this dynamic may have been appropriate so as to limit what risk there was, but in terms of identifying strategic assets set for appreciation and hedging against identifiable assets set for depreciation, this becomes a case where no hedge for depreciation is necessary because the depreciation is all in the domestic market and not in the foreign exchange currency market.

Another way to look at is to monitor the dynamic of today’s currency wars, as China seeks to export deflation (Noble and Widau, 2014; Eichengreen, Park and Shin, 2017), negative interest rates are introduced in various countries (such as in Japan) (Honda, Kuroki and Tachibana, 2013), and helicopter money drops are discussed in a variety of forums (Turner, 2016). Such a situation becomes more complex as instability increases on a global scale (measured via social and political unrest—though this unrest would not seem to correlate with the GARCH graphs pertaining to the S&P; still the rise in the gold index and the price of bonds could indicate some expression of this unrest in the marketplace). The same fundamental logic does apply in any case: in markets where the currency is strengthening, the FX rate risk would not require hedging unless one was concerned about limiting risk on every level. As deflation and stagnation/stagflation become realities, the move into bonds and the seeking of yields in equities may continue to push markets higher, while hedging in gold may increase at the same time. Oil may stay in the $45-$50 range for a number of years to come unless some breakout in price is motivated by an alignment of sellers (the last such alignment saw Saudi Arabia conspiring with the US to crush the Russian economy—that for now at least appears to have failed). With FX that is falling through devaluation as has been the case with the Chinese Yuan, the need for a hedge becomes palpable, just as it does in any market where risk is ascertained—thus the rise in the gold index as seen in Figure 6. If business in a foreign country necessitates holding the currency for any amount of time, or if the assets and commodities within that country are suffering from deflation, the hedge should be utilized. If inflation is in effect, however, in that particular country, the hedge in this particular case would not be recommended as the point per this instance is to move risk off and in the situation where the country is experiencing inflation, no hedge would be necessary.

With oil below $50, the global marketplace is uncertain; so too with political fallout—sanctions posed against Russia will impact Germany and the EU; Brexit did impact currency movement. The dollar’s dominance throughout the world is likewise being tested by an alliance of forces stretching from Russia to China to Iran. The rise of cryptocurrencies is also saying something to markets and this variable can be seen in the low volume of the equities market in the past 5 years. The sabre-rattling of the U.S. towards NK and vice-versa is a cause of alarm, especially as threats make headlines and headlines drive algorithms, which drive markets. The role of the Fed in all of this remains uncertain, as questions still remain about whether rates will rise or whether the Fed will continue to suppress, as growth expectations in the economy have not been met.

Credit default swaps are another item that must be assessed, as they play a substantial part of balance sheets and market activity. A credit default swap is used to mitigate the risk associated with credit exposure. As with any other type of derivative it is a type of insurance and the purpose of buying credit default swaps is to hedge the risk of default on the credit. They are sold for a premium, just like an option, and the seller offers this type of insurance as a revenue stream. In the housing bubble, credit default swaps played a large part in the crisis, as hedge fund manager Dr. Michael Burry showed with his strategy of purchasing credit default swaps from firms willing to sell him insurance on toxic debt, which they believed to be AAA-rated and which Burry knew to be completely toxic: Burry had calculated that a slight increase in mortgage defaults would create a tidal wave of bundles of debt crashing in value and he fully expected this increase to occur. By the time the defaults started increasing, a full-blown panic occurred and the credit default swaps that were purchased by Burry became very expensive and very hard to get: Burry’s investment paid off very handsomely to say the least, as Lewis (2015) has shown. For Burry, credit default swaps were a way for his fund to take advantage of a disproportionate amount of bad loans bundled and sold to investors under misleading ratings applications. By purchasing credit default swaps at knock-down prices before they were really in demand and thus beating other firms to the punch (firms who were actually investing in the toxic debt bundled as AAA-rated packages), Burry was able to make a considerable return on investment that netted his fund billions when he sold his swaps once they were in high demand and bringing in a higher price.

Credit default swaps can be used to transfer credit risk associated with corporate debt, mortgage-backed securities, municipal bonds and emerging market bonds. The seller of the insurance is paid a premium and for the premium assumes the risk of default or other credit event that might negatively impact the holder of the credit.

Credit default swaps would be a beneficial financial instrument to utilize in the case of an entity seeking to reduce its exposure to credit risk. Just like purchasing options on an underlying security in case of a market downturn can be an alternative to selling the security outright and provide protection against the risk of loss for a specified amount of time at a specified premium, a credit default swap provides the owner of a security or bond with protection against default, should the bond or mortgage for whatever reason be downgraded by ratings agencies, lose its value as the result of a credit event, or be defaulted on by the borrower. Thus, credit default swaps can serve as a hedge.

In this situational environment, the GARCH can only be as effective a tool as the inputs that go to define it. If recent trends are to be realized over a significant amount of time in the coming future, the spillover from bonds to stocks in the U.S. could continue—but at some point, the spillover should cease, especially if hyper-inflation becomes the next crisis to hit the marketplace the world over. In such an environment, forecasting volatility will be an uneven exercise, as the market will be fluctuating between machine-driven trading and human-driven trading when the machines are shut down because of abnormal marketplace activity. Basing a forecasting model on past activity without these variables in place or an understanding of how past activity has been brought about by unconventional activity in different spheres is a recipe for unexpected losses over time—or at least for lower returns than are required for a fund to continue to offer the kind of promises to pensioners and investors that have been traditionally been promised in more normalized times.


7 Conclusion

The findings of this study indicate that unconventional monetary policy is evident in terms of its impact in GARCH models of equities and bond prices. Technological factors are also a key variable that should be measured in future analysis. The rise of the HFT, algorithmic-driven trading is also impactful on market movements, and when coupled with market complacency as a result of Fed intervention, the markets appear to be overly ripe for a correction that is likely to come as soon as central banking policy returns to a more normative stance. This suggests that in order for adequate forecasting models to be effective in the new normal of economic environments, where conditions are dictated by central banks and telegraphing all the signaling that algorithm-driven markets care to assess, a more prudent model should be developed that can properly assess the expected outcomes of the main major variables’ effect on market prices.

This study has shown that GARCH can be an effective model when it is measuring movement spillover using a few variables at a time. When, however, a slew of variables enter into the picture, it is more difficult to calculate the effect. The position that forecasters might prefer to take in the light of these new changes in the marketplace may be to consider how central banking policy is shaping things, how the markets are trending and what the trends are indicating. Successful fund managers like Paul Singer have been very vocal in recent months and years about unconventional monetary policy and its distorting effects on the market. How this will play out when the Fed begins to unwind its balance sheet remains to be seen. Hedging with safe havens like gold or silver may be a suitable practice, but will the unidirectional spillover from bonds to stocks remain intact if the Fed does begin to normalize rates? Or might the spillover effect turn into a mass exodus from the equities market into the bond market as investors seek protection from rising volatility. If the VIX has been artificially suppressed along with the interest rates, it may stand to reason that volatility could return with a bang if the central banks begin their unwind. If this occurs and algorithmic-driven trading takes hold of a swift market movement and turns a collapse into a rout, the markets could quickly become too messy to be trusted to the machines. In such an environment a GARCH model may not be the most appropriate tool to use.

In such an environment, certain assumptions about the world must be made, just as financial statement analysts will make when applying GAAP principles to their assessment of business performance, model, strategy and risk. What is the world up to and how will it impact the company’s overall aim towards profitability? If a return to sound monetary policy occurs, a return to market fundamentals may also be on the horizon. This would suggest that only for the time being is GARCH a tool that might be better used when the markets return to something resembling authenticity, where price discovery is undertaken, and markets work without the influence of centralized forces seeking to maintain some degree of volume. The suppression of volatility as seen in the GARCH graphs for stock and bond markets ever since the rise of QE is the biggest indicator that market forces are not what they once were. Coupled with the knowledge of a distinctly human element gone missing from the marketplace transactions, replaced by algorithmic-driven trading, the equities and bond markets can be seen as something of an experiment, wherein there is no way of knowing just what will happen until the actions of the Fed become clear. Only then will forecasting spillover and volatility be a useful tool for investing and developing a trading strategy.



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