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The portfolio balance channel: an analysis on the impact of quantitative
easing on the US stock market
Imran Hussain Shah, Francesca Schmidt-Fischer and Issam Malki
No. 74 /18
BATH ECONOMICS RESEARCH PAPERS
Department of Economics
2
The portfolio balance channel: an analysis on the impact of quantitative
easing on the US stock market
Imran Hussain Shah1*, Francesca Schmidt-Fischer
1
and Issam Malki
2
Abstract
This paper provides empirical evidence on the pass-through of quantitative easing (QE) on
equity returns in the United States (US). The methodology mimics the programme’s impact on
investors’ required returns for financial assets through the QE portfolio balance channel. This
analysis of monetary policy involves using a VAR model, simulating a reduction in the share
of sovereign bonds as part of central bank purchases. The findings suggest that QE caused a
significant reduction in the equity risk premium (ERP) for the S&P 500. This equates to an
increase in equity prices of 9.6% and acts as evidence for an active portfolio rebalancing of
private sector individuals into risky assets following QE. The findings of the paper also suggest
that the impact of a monetary policy expansion results in varying effects, while an expansionary
policy has a stronger positive effect on equity prices with QE than without. Furthermore, we
test for the presence of structural breaks in the VAR model. Firstly, using a multiple structural
breaks approach, we find evidence of regime shifts and secondly accounting for the shifts in
the conditional mean leads to similar conclusions as found earlier.
Key words: equity risk premium, regime shifts, quantitative easing, portfolio balance channel,
equity returns.
JEL classification: E44, E51, E52, E58, G1
*Corresponding author: Imran Hussain Shah, Department of Economics, 3 East 4.27, University of Bath, Claverton
Down, Bath, BA2 7AY, United Kingdom. T: +44 (0)1225 38 5848. E-mail addresses: I.Shah@bath.ac.uk (Imran
Hussain Shah).
a Department of Economics, University of Bath, Bath, UK
2
Department of Economics and Quantitative Methods, University of Westminster, UK
3
1. Introduction
During the global financial crisis, the federal open market committee (FOMC) responded to
deteriorating conditions in financial markets and economic growth by lowering the target
federal funds rate to a range of 0% to 0.25%. With persisting slack and the policy rate at the
zero lower bound (ZLB), the Federal Reserve (Fed) subsequently embarked on unconventional
monetary policy. First signalled in Bernanke’s Jackson Hole speech in November 2008, this
measure, often referred to as quantitative easing (QE), resulted in a series of asset purchases by
the central bank. By October 2014, the cumulative purchases of mortgage-backed securities
(MBS), agency debt and longer-term treasury bonds, amounted to an expansion of the Fed’s
balance sheet to $4.5 trillion. With the aim of reducing borrowing costs faced by a range of
private individuals and companies, the channels through which QE is passed onto the real
economy are open to debate. The portfolio balance channel and its potential effectiveness in
reducing bond yields has discussed, with Hamilton and Wu (2012), Gagnon et al. (2010) and
D’Amico and King (2010) only being some examples. However, the programme’s possible
impact on equity prices is covered scarcely in academic literature and exclusively in connection
with the signalling channel of unconventional monetary policy (Kiley, 2014; Rosa, 2012).
Literature surrounding QE, such as Joyce et al. (2011), concluded that equity prices did not
react in a uniform way but in fact, the initial announcements induced a fall in prices. With the
negative responses outweighing any modest rallies, the total effect was estimated to be
approximately -3.5%. Nevertheless, the overall price increase until May 2010 amounted to
50%, evidencing some drawbacks of an event study. Most event studies carried out assign a
strong focus on government bond yields with respect to the portfolio balance channel. In fact,
Gagnon et al. (2010) assume this to be the primary channel through which large-scale asset
purchases (LSAP) function and is based on the assumption that today’s asset prices are thought
to reflect investors’ expectation on future asset shares. Gagnon et al. identified key policy
announcement days, they then analysed the response of bond yields of different maturities.
They find that QE1 announcements accumulate to a drop of 91bp in the 10-year Treasury bond
yield. Furthermore, Krishnamurthy and Vissing-Jorgensen (2011) report a similar decline of
107bp cumulatively in agency debt and the 10-year Treasury bond. However, they sustain the
move to be induced by a combination of the preferred habitat for longer-term ‘safe’ assets as
well as the signalling channel.
Empirical studies exploring the feed-through of QE via the portfolio balance channel mainly
focus on government bond yields. For example, Hamilton and Wu (2012) evaluated the impact
4
of the maturity extension programme (MEP) by modelling the impact on term structure to
outstanding Treasuries. According to Hamilton and Wu (2012), the 10-year bond yield only
decreases by 14bp, which suggests that central bank debt management to be of almost negligible
importance. This, however, is contradicted by Gagnon et al. (2010) whom findings suggest a
higher decline of 30-100bp. The latter outcome results from a model explaining the 10-year
nominal term premium through measures of net supply of government bonds to the private
sector and the business cycle. D’Amico and King (2010) suggest that a persistent shift in the
yield curve of up to 50bp -the largest effect in longer-term Treasuries resulted from the QE1
programme. Furthermore, the literature indicates that QE has an effect on lowering interest
rates, whilst evidence on the effectiveness of raising equity prices is uncertain (Kiley, 2014
2013; Rosa, 2012).
The aim of this paper is to explore the empirical evidence of an equity price impact arising from
QE, through modelling its implementation in the context of private sector portfolio shifts. Joyce
et al. (2011) describe a framework to responses on various asset prices, including equities in
the United Kingdom (UK). This paper follows the same approach as in Joyce et al., measuring
the impact of QE on stock market, however, focuses on the QE programme in the United States
(US), where the government bond market is significantly larger than that of the UK
3
. We
analyse the portfolio balance channel of QE on a variety of assets using VAR model is used to
explore the relationship between relative shares and investors’ required returns for major asset
classes. Impulse response functions (IRFs) are then computed to simulate the negative supply
shock in Treasuries held by the private sector, allowing the assessment of the portfolio balance
mechanism on expected equity returns. This modelling technique consents for the
disentanglement of the equity required rate of return and the risk-free government bond rate,
enabling an estimation of the change in equity risk premium (ERP) induced by QE, and a
subsequent translation into equity price returns. Next, a variance decomposition is conducted
to account for the effect of a shock to the share on Treasuries on the other asset classes’ shares
and returns. Since ERP is a primary component for assessing the cost of capital and asset
allocation decisions, we further investigate the impact of monetary policy before and after the
implementation of QE programs, an approach developed following the 2007-2008 financial
crisis. This is indeed an important topic to investigate since much of the existing literature does
compare the performance of monetary policy before the financial crisis. For this purpose, it is
3
Although, the overall purchases conducted by both countries were similar in size in terms of GDP: roughly 20%
of the size of the economy (Fawley and Neely, 2013).
5
necessary to assess the stability of the dynamic behaviour in the equity prices and the possibility
of the presence of policy regimes.
In this context, we assess the robustness of our findings when allowing for the conditional mean
of the VAR model to shift. This can be viewed as an extension to Joyce et al. (2012) framework
as well as an assessment of the presence of policy regimes. For this purpose, we relax the
assumption that the conditional mean of the VAR model is constant over time. Indeed, the
literature in Belke et al. (2015), and Su and Hung (2017) on QE effects suggest the possibility
of the presence of structural breaks. In this context, Belke et al. (2015) focuses on the stability
of the cointegrating vector (of the relationship between the US interest rates, German interest
rates and US/Euros exchange rates), which does not describe any conclusive results on whether
QE caused structural breaks. Su and Hung (2017) suggests the presence of structural breaks in
major stock market indices, which then incorporated to measure the effect of QE. Both studies,
however, do not consider a regime shift case and the potential changing effect of different QE
announcements. For example, Belke et al. (2015) does not find any conclusive evidence on
whether different QE programmes cause different effects, while Su and Hung (2017) assume
implicitly a homogenous effect since they capture the QE effect post breaks of the individual
indices. Second, the literature incorporating breaks in a context slightly different from that of
the present paper. This paper considers the case of possible shift in regimes in the VAR model.
Applying Qu and Perron (2007) structural breaks test on the VAR model, we find evidence that
the long run relationship between shares and returns is subject to shifts in the conditional mean.
The findings suggest that these regimes coincide with important economic and financial events
including the effect of one QE programmes. Thus, we account for these shifts to assess the
robustness of our findings based on the standard approach.
This paper is arranged as follows. Section 2 introduces a description of the economic
background behind QE with a specific focus on the portfolio balance channel. Section 3 focuses
on an interpretation of the portfolio balance channel in the context of asset allocation. In section
4 and 5 the framework employed to measure the effectiveness of QE on equity returns is
presented and discussed with regards to data and methodology. Section 6 presents the main
findings and implications and focuses on model specification and robustness of the model
including the application of Qu and Perron (2007) tests. Some concluding remarks are provided
in Section 7.
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2. Critical review and episodes in relation to QE in the US
2.1. Critical review
During normal market periods, central banks respond to fluctuations in output gaps and
deviations from the desired inflation target by managing the prevailing short-term interest rate
- the bank rate (Taylor 1993). In the wake of the financial crisis of 2007-08, the Fed reacted to
deteriorating conditions in the domestic economy by cutting the federal funds rate to its
effective ZLB. However, as the recession intensified and conventional monetary policy reached
its limit, the central bank was forced to pursue another path if it were to provide additional
stimulus. By implementing QE, a programme entailing asset purchases from the private sector,
the Fed effectively expanded its balance sheet to increase bank reserves and consequently boost
the amount of money in circulation. The aim to sustain the real economy in a recession is
achieved by lower borrowing costs to a range of private individuals and companies, ultimately
increasing nominal spending and investments (Joyce et al. 2011).
The transmission channels that enable this stimulus to influence domestic demand are strongly
debated in the literature, but the most advocated amongst central bankers is the portfolio balance
channel. Ben Bernanke (the former chairman of the Fed), revealed during a speech at the 2010
Jackson Hole conference: “I see the evidence as most favourable to the view that such
purchases work primarily through the so-called portfolio balance channel,
…
the Federal
Reserve's purchases of longer-term securities affect financial conditions by changing the
quantity and mix of financial assets held by the public”. This theory suggests that central banks
can influence the yield of an asset by changing its supply relative to that of others. In other
words, by reducing the availability of the asset in question its price increases (due to the inverse
relationship between yield and price). Furthermore, it implicitly recalibrates an investor’s
expected return on it (as higher prices lower the return an investor is hoping to receive in the
future). Depending on the degree of substitutability between the asset purchased by the central
bank and others in the market, investors will rebalance their portfolios into holding those assets
with similar features (e.g. duration and risk), in turn affecting their respective price levels too.
This aspect of the programme induces an increase in net wealth of investors, encouraging
additional spending in the real economy. In the context of QE, as operated by the Bank of
England and the Fed, the purchases of longer-dated government bonds leads investors to
substitute their portfolio shares of sovereign securities into money, corporate bonds and
equities.
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For the portfolio balance channel to be effective, the asset purchased by the central bank and
money ought not to be regarded as perfect alternatives (Tobin, 1958; Brunner and Meltzer,
1968). If this were the case, investors would abstain from reinvesting the capital received from
assets sold to the central bank and no changes to the portfolios would be made. This concept,
known as the liquidity trap or irrelevance proposition, theoretically arises if the central bank
was to buy ‘one-period’ bonds as part of QE (Eggertsson and Woodford, 2003). At the ZLB,
short-dated bonds are likely to bear no interest, which together with their limited credit risk,
makes them the closest substitutes for money. However, by purchasing longer-dated bonds, a
central bank can avoid a pure money-injecting effect, encouraging the working of the portfolio
balance effect (Bowdler and Raida, 2012).
The mechanism behind the portfolio balance channel, assuming imperfect substitutability, has
commonly been attributed to two possible effects in the literature, namely the preferred habitat
and the duration risk. The preferred habitat effect stems from certain investors’ preference as
to which type of assets to hold in terms of maturity. Institutional investors and pension funds
for example, may favour holding a large share of long-dated assets to match their liabilities’
maturity. Given the strong demand for these bonds, asset purchases by the central bank
therefore induce a scarcity effect in that particular yield curve segment, depressing yields and
pushing up their prices. Riskier assets with similar maturity are also likely to be affected as
portfolios reallocate towards them in search of returns. Because the price effect is dependent
on maturities comprised in the QE programme, this effect is often referred to as the local supply
effect (Joyce et al., 2012). Duration risk, or interest rate risk, on the other hand, is a concept
incorporated in the price of a bond through its term premium. It is a measure of compensation
afforded to investors on account of their inherent aversion towards the risk of having to hold
longer maturity assets. Purchases by the central bank, however, reduce the average duration of
the bonds held by the private sector and may herewith reduce the term premium in the market.
Investors that wish to hold on to a certain amount of risk are ready to pay a higher price for that
particular bond or shift their portfolios into riskier assets such as corporate bonds or equities
(Bowdler and Raida, 2012).
2.2. Episodes of QE
The financial crisis of 2008-2009 forced the monetary policy target rate to its effective lower
bound in the US and consequently the Fed was obliged to adopt unconventional monetary
policies. Following the financial crisis, the Fed not only lowered the target rate from 1.0% to
0.25% but also implemented a more unconventional approach to monetary policy called QE.
8
Dudley (2010) illustrated that the primary aim of the QE was to reduce long-run interest rates
in order to stimulate economic activity.
The Fed announced its QE1 program on 25 November 2008 and completed it on March 2010
in order to reduce mortgage discount rates and raise the credit supply for house purchases (Da
Costa, 2011; Olsen, 2014). Fawley and Neely (2013) stated that the objective of QE1 was to
purchase the liabilities of housing association mortgage-backed securities (MBSs) and
government-sponsored enterprises (GSE). The Fed announced it was to purchases $600 billion
in total, with $100 billion of GSEs and $500 billion of MBSs. The QE1 program increased
further in March 2009, when the Fed announced it was to buy another $750 billion of MBSs
and $175 billion of the GSEs. The QE1 program ended on the 31 March 2010 and subsequently
the Fed observed gains in the financial markets and decided to keep interest rates between 0
and 0.25% (Stroebel and Taylor, 2012).
The Fed launched its QE2 program on 3 November 2010 and completed it on 30 June 2011.
The aim of the QE2 program was to reduce unemployment and lower inflation and furthermore
would involve reinvesting payments from its holding in long-term bonds retaining a face value
of $2.054 trillion (Fawley and Neely 2013; Krishnamurthy and Vissing-Jørgensen, 2011).
Initially, the Fed purchased $600 billion of long-run US Treasuries until the second quarter of
2011 and continued the programme with $75 billion of purchases monthly, however with a
regular assessment of the pace and the magnitude of the program. In September 2011 after
completion of QE2, the Fed announced the maturity extension program known as Operation
Twist after the US economy experienced a substantial government shutdown due to reaching
the debt ceiling, higher unemployment, the Eurozone sovereign debt problems resurfacing and
a lower US credit rating (Bowley, 2011; Olsen, 2014). The objective of the maturity extension
program was to extend the average maturity of its holdings of securities by decreasing the long-
run interest rates and pushing up the short-run interest rates (Swanson et al., 2011). Moreover,
the Fed also reinvested the principal payments from MBSs and agencies into MBSs instead of
into Treasuries. The focus of this maturity extension program was to push long-term interest
rates down and short-term rates up. The program continued until 20 June 2012 and involved
monthly purchases and sales of $45 billion of Treasury securities.
The Fed then announced the beginning of QE3 on the 13th September 2012 while the maturity
extension program was also continued. The program was to boost economic growth as well as
to ensure that inflation was within target. Initially, the program started with monthly purchases
of MBSs to the amount of $40 billion along with $45 billion of longer-term US Treasuries until
9
there was an improvement in unemployment levels. This made QE3 quite different from QE1
and QE2, because the end of the program would be determined by “goal achievement” rather
than by a given date – thereby gaining the nickname “QE-Infinity”. Simultaneously with the
still ongoing maturity extension program, the joint effect was to put downward pressure on
long-term interest rates, support the housing markets and ensure comprehensive financial
circumstances were more accommodative. QE3 had no exogenous ending date.
3. Unconventional monetary policy in theory: the portfolio balance model
This section highlights the theoretical concepts that give rise to QE’s portfolio balance channel.
The economic framework on which it is built upon is referred to as the mean-variance model
and was originally by Tobin (1958). In this model, the representative agent maximises their
excepted utility from end-of-period wealth by setting the share of wealth allocated to each
asset to . Subject to an initial wealth constraint and asset supplies, the investor therefore
formally faces the problem:
(1)
where the basic model as outlined above, generates the following necessary condition for a
maximum
4
:
(2)
where is the expected excess asset returns over a benchmark (usually a numeraire
asset), is the coefficient of constant relative risk aversion (CRRA) and is the variance-
covariance matrix of the assets’ expected returns.
Following the approach of Engel and Frankel (1984), risk aversion and the covariance matrix
are assumed to be constant over time. When proceeding with these assumptions, the expected
excess returns are amongst other things determined by the covariance matrix of asset returns
that can be interpreted as substitutability between two assets. In other words, when varying the
relative stock of two assets, the resulting change in expected excess return will be determined
by the magnitude of the covariance. Additionally, the expected excess return depends on the
investor’s potential inability to allocate the wealth maximising weight due to, for example,
limited supply or regulatory restrictions. This results in the investor requiring a compensation
in form of an expected excess return on an alternative asset to willingly holding it. However,
4
See Fraser and Groenewold (2001) for derivation.
10
policy makers can, as pointed out earlier manipulate the required rate of return by influencing
the shares of assets outstanding. When the Fed adopted QE, it was designed to drive the yield
on sovereign bonds so low that investors would rebalance their assets away from risk-free
government bonds into higher-yielding, riskier assets (Joyce et al., 2011).
However, an application of the VAR model to the abovementioned theory would require
expected excess returns to be observable. In order to grasp the effect of QE on the required rate
of return as an endogenous variable, the investor is therefore assumed to have rational
expectations here forth. Hence the difference between excess returns and expected excess
returns is determined only by a random estimation error.
(3)
where and .
Combining equation 2 and 3 and by adding a constant term , the basic model can be rewritten
as follows
5
:
(4)
where the vector of excess returns is specifed as a linear combination of asset shares in the
portfolio , with weights proportional to the variance-covariance matrix of the assets’ excess
returns and the degree of relative risk aversion (Fraser and Groenewold 2001).
The portfolio balance model as described above, makes a number of over-simplified
assumptions: one of them being that the covariance matrix and risk aversion are time invariant.
It seems unlikely that these aspects would not be affected during times of financial or economic
turmoil (Yellen, 2011). Furthermore, it substantially simplifies on the variables affecting
expected asset returns, not capturing the influence of business cycles, portfolio performance,
etc. Nevertheless, this analysis applies this approach at the basis of a VAR model in which the
co-movements between expected excess returns and asset shares can be portrayed, allowing for
an understanding of the effect of QE on the US stock market.
5
See Frankel and Engel (1984) for derivation.
11
4. Data description and preliminary statistics
The monthly data applied in this analysis
6
examines the effect of the Federal Reserve Bank of
St. Louis’ QE policy on the US asset prices. It consists of end-of-month realized yearly returns,
asset shares and dividend yields spanning from January 1984 to January 2017. As part of the
portfolio rebalancing channel, four major asset classes are assumed to be available for
investment: equities, investment grade corporate bonds, Treasury bonds and money. The latter
takes the role of a numeraire asset and is represented by the US measure of broad money (M2).
This analysis employs the S&P 500 total return index for equities. The total return index tracks
both capital gains and aggregates any cash distributions (for example dividends), which are
then reinvested into the index. It therefore indicates a more precise representation of return to
an investor than the price index. Similarly, total return indices are employed for corporate and
government bonds, represented by the Barclays investment-grade corporate bond and US
Treasury total return index respectively. Here the total return index serves a similar function to
that of the S&P 500, where price variations are captured along with any coupon payments.
The total return indices above enter the analysis as excess return over money. For this purpose,
the target federal funds rate, serving as a proxy for the return on the numeraire asset, is
subtracted from the year-on-year (yoy) return of the indices. The upper target rate is here used
in order to portray the Fed’s current policy stance. It is worth noticing that this analysis employs
yearly returns. As the return on an investment, the yield, is usually expressed annually, it
herewith avoids any issues with annualising lower frequency outcomes. In fact, it circumvents
the implicit assumption that annualising the change in monthly returns induces a recurrent
shock of the same magnitude each month of the year.
Table 1 below indicates the relevant summary statistics for these calculations and reports the
return on money i.e. the Fed funds target rate, over the sample investigated. At this point, it is
again emphasised that due to the rational expectation assumption, the excess returns can be
understood as expected excess returns.
6
All the information is obtained from Thomson Reuter’s Datastream.
12
Table 1: Excess returns and money return summary statistics
Mean
Standard
Deviation
Maximum
Minimum
Kurtosis
Skewness
JB
P-value
Excess Return on Equities
8.2%
16.2%
53.4%
-43.6%
0.5
-0.6
0.00
Excess Return on Corp. Bonds
6.8%
10.2%
62.8%
-15.7%
5.1
1.5
0.00
Excess Return on Sov. Bonds
5.2%
7.8%
40.3%
-10.0%
3.6
1.4
0.00
Return on Money
4.0%
2.9%
11.4%
0.3%
-1.0
0.2
0.00
The entries of the Table 1 confirm that riskier assets are characterised by a higher average
return, and as expected also present a higher volatility (standard deviation). It can be observed
though that the Barclays bond indices’ maximum observation seems over-estimated. This can
probably be attributed to initial complications, for example pricing, during the first years after
inception of the total return indices. In fact, since establishment of the index in 1973 until
approximately 1984, the year-on-year returns experience some enormous swings, reaching
extreme levels of even 166% on corporate bonds. Consequently, we have used data starts from
1984 and excludes observations of the chaotic volatility resulting from the enormous swings
prior to January 1984 for this analysis.
The asset shares of the individual asset classes are computed as percentage of the total market
value over the same sample. The market value of the bonds and equities is defined as their
market capitalization, calculated by multiplying the price of an asset by its outstanding
securities. For the numeraire asset, however, the value of broad money enters the analysis as a
representation of the market value. The latter is a measure of money supply including narrow
money as well as savings deposits, money market mutual funds plus other short-term time
deposits.
Fig. 1. Financial market indicators development from 1984-2017
13
Fig. 1 shows the asset shares where the black, red and orange solid lines (black, grey and light
grey when viewed in grey scale) correspond to S&P 500, the sovereign bonds, and corporative
bonds respectively and the black dotted line displays M2. In line with the findings of Joyce et
al. (2012), Fig.1 illustrates a strong opposite relationship between equities and broad money.
Interestingly, the share of equities and particularly Treasuries, increased significantly in the
midst of the financial crisis and thereafter. For equities, this effect is possibly mainly due to
capital gains, keeping in mind that the market value index is a function of share prices amongst
others. For Treasuries, in contrast, this development is most likely to be indorsed to an increase
in issuance to match the purchases of the Fed.
0%
10%
20%
30%
40%
50%
60%
70%
1984
1985
1986
1987
1988
1989
1990
1991
1992
1993
1994
1995
1996
1997
1998
1999
2000
2001
2002
2003
2004
2005
2006
2007
2008
2009
2010
2011
2012
2013
2014
2015
2016
2017
M2 S&P 500 Sov. Bonds Corp Bonds
14
Fig. 2. Total Treasury securities outstanding and QE
As Fig. 2 depicts, the issuance of Treasuries picked up significantly in the middle of 2008 from
$9.5 trillion to approximately $20 trillion in October of 2016, showing a more than doubling of
the government bond market over the duration of the global financial crisis and QE programme.
Considering that the purchases by the Fed only comprised $1.6 trillion of Treasury securities,
this implies a substantial expansion in the market value and probably explains the increase of
the share in government bonds as shown in Fig. 1.
5. Estimation methodology
This section emphasis entirely on the effects of the QE programme on the equity market in the
US. As mentioned in the introduction, this is done by assessing the effect of the portfolio
balance channel via a VAR model. This consents for an examination of the relationship among
the relevant variables and their autoregressive components, which are carefully selected in the
context of the QE transmission channel. IRFs can then quantify the time path of a reduction in
the availability of government bonds, i.e. a negative shock to the share in US Treasuries, on the
other exogenous variables. Further analysis allows for an understanding of what implications
the outcomes from the IRFs have on the US equity markets. A variance decomposition is then
conducted to determine the relative significance of a QE shock to the share in government bonds
in explaining the variability on the other variables in the model. Furthermore, we investigate
0
5
10
15
20
1973
1975
1977
1979
1981
1983
1985
1987
1989
1991
1993
1995
1997
1999
2001
2003
2005
2007
2009
2011
2013
2015
2017
Start of QE Total Treasury Securities Outstanding (in trillion $)
15
the validity of our findings when permitting for the conditional mean of the VAR model to
shift.
5.1. The VAR model: A portfolio balance channel and stock market
We estimate a VAR to analyse the portfolio balance approach on a variety of assets to
investigate the impact of monetary policy on both asset shares and excess returns. The
parameters are estimated for multi equations by OLS. Our VAR ( take the following reduced-
form:
(5)
where is a vector of endogenous random variables, is the fixed vector of intercepts
is the vector of exogenous random variables and are fixed coefficient matrices, and is
vector of errors with time invariant covariance. The vector includes of investment-grade
corporate bonds, government bonds and equities, where money enters the model as the
numeraire asset. Moreover, this paper contains exogenous variables intended to detain the
business cycle. For this purpose, the annual growth rate of industrial production (IP) and a
measure of inflation are thought to be applicable. Assuming these variables to be
predetermined, while is a strong assumption as it prevents inflation and economic growth to be
affected by the endogenous interest rates. In the context of QE and bearing in mind that the
Fed’s mandate explicitly targets price levels, inflation will therefore be excluded from the
analysis.
An IRF analyses changes in one variable’s error term and assesses the feed-through to the other
variables in the system. In VAR models, changes in a variable enter the analysis as nonzero
errors. In this context the nonzero element of is connected with a change to the share of
government (sovereign) bonds. The autoregressive property of the VAR then ensures that this
change will be carried forward to the other endogenous variables in the periods to come, but
problems with explanation of IRFs could arise if the error terms are correlated. In fact, the
variance-covariance matrix is non-diagonal, meaning that an exogenous shock to variable
is simultaneously associated with a shock to any other endogenous variable
7
. Because this
analysis is interested in dividing the impact of a shock to the share in government bonds, the
VAR can be rewritten such that the shock to a certain variable is uncorrelated to the others and
therefore the only innovation affecting the system. An application of identification restriction
7
See Table T1 in the Appendix
16
is the Cholesky decomposition. This essentially pre-multiplies the left-hand side of the equation
by the inverse of a lower triangular matrix , comprising the standard deviations of . This
results is a diagonal variance-covariance matrix .
(6)
where A is equal to:
Formally this restriction is computed by setting zero-restrictions on for . The
transformation reflects that a shock to variable has no contemporaneous effect on the other
variables , but rather exhibits a recursive behaviour. This implies that the first variable in
the VAR is only affected contemporaneously by the shock to itself, while the second variable
is affected by the shocks to the first variable and the shock to itself, etc. Given this importance
of the relative ordering of variables within the matrix, one problem with this procedure is that
an appropriate ordering cannot be determined by statistical methods. It is therefore subjectively
selected which variables are most endogenous, relative to what the economic background of
the model implies.
When studying the portfolio rebalancing effect, it is presumed that the asset shares are the most
exogenous followed by the returns. Within the first group the following order is assigned to the
variables: equities, investment grade bonds and government bonds. Returns, in contrast, are
arranged as government bonds first, investment grade bonds second and equities last. The
restriction may be motivated as follows: the shares are the variables affected by QE purchases
and may therefore be the only ones that have potential impact on all others. The other variables,
are by ordering subsequently less exogenous and are simultaneously assumed not to respond to
the monetary policy shock in the same month, suggesting a slower feed-through. It is herewith
suggested that investors with relatively risk-free portfolios, such as pension funds and insurance
companies, will shift into slightly riskier assets, such as corporate bonds and equities to meet
return requirements (Joyce et al., 2017). The prices of these assets are affected correspondingly.
5.2. The expected excess return and the equity risk premium
17
The model captures the change in expected excess return on the various asset classes induced
by the central bank’s programme. At this point, it is worth emphasising again that in the
framework of this analysis the expected excess return is understood as required rate of return
and is not to be confused with actual price returns. Although the resulting fluctuations in
expected excess return from the IRFs to bonds can be understood as a revision to their yield,
the interpretation for equities, however, is not quite as straight-forward. The equity required
rate of return () is defined as the sum of the risk-free government bond yield () and the
equity risk premium () and expresses the compensation investors involve for bearing the
additional risk from holding this asset.
Following the Capital Asset Pricing Model (CAPM) introduced by Sharpe (1964):
(7)
In order to put the results from the VAR into context and grasp the price effect of QE on the
stock market, the analysis by Joyce et al. (2012) attempts the conversion of their IRF results
into equity returns by using a dividend discount model. This paper proposes a different,
although similar approach to deriving price returns. This is done by disentangling the IRF’s
resulting shock to equities’ required return into its components, the ERP and the risk-free rate.
Following Equation 7, this analysis deducts the change in expected sovereign bond yields from
the change in excepted equity excess return resulting from the IRF. The resulting difference in
expected ERP, is thereafter interpreted to a respective change in the price level given the historic
relationship between ERP and equity prices as follows.
5.3. The impact of QE on equity price returns
The historical ERP can be derived by the dividend yield method, also known as the Gordon
growth model (Gordon and Sharpio, 1956). The theory suggests that the excess return of a stock
can be calculated by incorporating the dividend yield to a constant dividend growth rate.
(8)
is the dividend yield (dividend expressed as percentage of current price of the stock index)
and constant dividend growth rate. Rearranging the above and substituting equation
7 into it, the ERP can be calculated as follows:
(9)
18
At this point, an assumption requires to be made on how long-term dividend growth is defined.
Herewith, the latter is set equal to the yoy dividend growth of the sample average (8.5%). Due
to long-term dividend growth being constant, changes in the ERP are therefore solely induced
by changes in the risk-free rate and the dividend yield prevailing in time t. The advantages of
this approach is its intuitive nature. However, it relies on a perpetuity assumption and is
therefore sensible to which one is adopted.
The ERP is a key factor in deciding how much wealth an investor is willing to attribute to this
specific asset class. On the basis that the value of an asset is determined by the present value of
excepted cash flow and discounted back to estimate a current price level, the risk-free rate and
ERP play a crucial role. The risk aversion of an investor herewith determines how much their
is willing to pay for a certain asset – the higher the perception of risk, the higher its price and
consequently the lower the willingness to pay for the same set of expected cash flows (Brealey
et al. 2008).
Fig. 3. Historical equity risk premium and price index
Fig. 3 clearly suggests an inverse relationship between the calculated ERP and the price index.
This association can also be confirmed by the regression outlined below (Neely et al. 2015).
(10)
In this way, a conclusion on how changes in the ERP induced by QE, alter yoy equity price
returns () for the S&P 500, can be drawn. The 1% change in ERP is scaled to the purchases
conducted by the Fed for a more accurate estimation. Because stock indices are usually quoted
in price returns, applying the price index rather than the total return index, circumvents the
0
500
1000
1500
2000
2500
9%
10%
11%
12%
13%
14%
1984
1986
1988
1990
1992
1994
1996
1998
2000
2002
2004
2006
2008
2010
2012
2014
2016
ERP (Lhs) S&P 500 Price Index (Rhs)
19
drawback of having to disentangle the return in terms of capital gains from other cash
distributions (Brealey et al. 2008).
5.4. Regime shifts and stability of the VAR(p) model
We also investigate the stability of the VAR model and examine whether there exist regimes
consistent with economic or financial events that may prompt monetary policy regimes in the
US. In the previous exercise, we assumed constant conditional mean in the VAR, which seemed
to exhibit residuals spikes that may lead to regime shifts. accounted for the effect of announcing
implementing monetary policy, which is captured by a dummy variable specific to the
announcement date. Thus, is, we relax the assumption of constant conditional mean in the VAR
and allow the system to shift. However, does not capture the effect of the policy itself on the
VAR model and its parameters. In other words, we aim to test for the presence of structural
breaks on the VAR, which may indicate indicating a response of the model’s parameters to
economic and financial changes. in in monetary policy. In order to test for the presence of such
these shifts, we test for the presence of monetary policy regimes in the VAR model.
We implement Qu and Perron (2007) (QP, henceforth) test to identify structural breaks in a
multivariate context. QP introduced a multiple structural breaks test that can be applied to
multivariate regressions and considers a very general model. This test is an extension of the
previously developed by Bai and Perron (1998, 2003) that considers the null hypothesis of l
breaks versus the alternative of l+1 breaks for linear (univariate) regression. In our case, we
deal with a VAR model that is characterized by stationary long run relationships, and thus, QP
can be a suitable test to identify break dates in the system. QP suggest a range of test statistics,
which includes: the
T
LRsup
, the sequential test and the double maximum tests. The
T
LRsup
formally defined as:
Tm1TTm1T
m
,...,
1
bobdbT L
~
logT
ˆ
,...,T
ˆ
L
ˆ
log2L
~
logT,...,TL
ˆ
log2
up
,n,n,p,mLRsup
s
(11)
Where m is the maximum number of breaks found,
m
TT ˆ
,...,
ˆ
1
are the Quasi Maximum
Likelihood Estimator estimates of dates (partitions) using the partitions defined in
m
,...,
1
and
is the trimming rate or minimum distance between each partition. Testing
the changes can be done sequentially. Formally, the test statistic can be written as:
lTljjT
lj
TTTlrTTTTlrllSEQ
j
ˆ
,...,
ˆˆ
,...,
ˆ
,,
ˆ
,...,
ˆ
supmax\1 111
11 ,
(12)
20
where:
111, ˆˆˆˆˆˆ
; jjjjjjj TTTTTT
.
First, we estimate breaks over the sample period endogenously. Within the VAR, we allow for
all the coefficients in the conditional mean to change. Subsequently, we are able to analyse the
VAR properties for every identified regime.
6. Empirical analysis
6.1. Model specification: unit root tests and VAR (p)
In the context of the VAR model, failure to demonstrate stationarity would lead shocks to the
system, not only to be persistent through time, but also to propagate. We analysis the time series
properties of the variables by using the unit root tests that include the extension of the M class
tests analysed in Ng and Perron (2001) and the feasible point optimal statistic of Elliot et al.
(1996). Hence, the data is tested for the null hypothesis of a unit root at level with constant. The
resulting test-statistics exceed the critical value (in absolute terms), rejecting the null hypothesis
of the excess returns having a unit root. Table 2 indicates that all asset returns and shares are
found to be stationary at level.
Table 2. Unit root test results
DF-GLS
PP
MZa
MZt
MSB
MPT
Excess Return on Equities
-3.42**
-4.50**
-31.21**
-3.94**
0.13**
0.83**
Excess Return on Corp. Bonds
-3.54**
-4.17**
-10.27**
-2.24**
0.21**
2.48**
Excess Return on Sov. Bonds
-3.56**
-3.84**
-26.73**
-3.62**
0.14**
1.04**
Share of Equities (YOY%)
-2.86**
- 3.92**
-16.60**
-2.86**
0.17*
1.54**
Share of Corp. Bonds (YOY%)
-3.29**
-3.66**
-30.92*
-3.93**
0.12*
0.80**
Share of Sov. Bonds (YOY%)
-3.54**
-3.11**
-15.26**
-2.70**
0.18*
1.85**
Note: ** indicate the level of significance at 5%. The unit root tests with structural breaks in essentially trend-
stationary series, namely, (MZt) Elliott-Rothenberg-Stock, (MZa) Ng-Perron (MSB) Silvestre-Kim-Perron, SKP-
MZT Silvestre-Kim-Perron and PP- Z Phillips-Perron.
We estimated the VAR model by using monthly data on a sample from 1984M1 to 2017M1. It
is commonly known that the results of a VAR analysis are sensitive to the lag-length selected.
In order to construct accurate IRF, it is hence crucial to account for this (Eadie et al., 1971).
The number of lags has been set using Akaike’s information criterion (AIC), the Schwarz
criterion (SBIC) and Hannan-Quinn criterion (HQ) refer to a VAR model with 2 lags reported
in the Appendix Table T2. To check for autocorrelation of the residuals, we plotted the residual
21
autocorrelations and estimated the Lagrange Multiplier (LM) test
8
. The result derived from the
LM test did not confirm autocorrelation and come to the same conclusion as the correlograms
reported in the Appendix Fig. F1. Finally, to check the VAR(2) stability, Table T2 in the
Appendix depicts that no root lies outside the unit circle, which confirms stability (Lütkepohl,
2013). These results are an important confirmation that the selected lag-length for the model is
appropriate, and it is therefore considered as adequate to proceed with structural analysis of the
IRFs and variance decomposition.
6.2. The impulse response functions
We employ an impulse responses analysis to study the response of excess returns and asset
shares to the shock of sovereign share. This latter is assumed to take three forms. First, we
consider the form when the relationship is governed by a constant conditional mean. This form
refers to the situation when the response of excess returns and asset shares to the shock of
sovereign share is constant and the same over time. We relax the assumption of constant
conditional mean and allow for the possibility of structural breaks and regime shifts. In this
context, shocks of sovereign shares might prompt different responses from excess returns and
excess shares due to shifts in the conditional mean of the model. The sovereign share can be
interpreted as response to economic and financial events such as the QE shock, namely a
negative reduction in the share of sovereign bonds available to the markets.
Fig. 4 shows the IRFs the red dashed lines show a one standard error 95% confidence band
around the estimates of the coefficients of the IRFs. Fig. 4a-4c shows the responses of returns
for a one-standard deviation fall in the share of sovereign (QE shock). The QE shocks (share of
sovereign falls) have, as expected, a positive and highly significant effect on the equities
returns, the corporate return and the sovereign return. Our findings are consistent with those of
Fratzscher et al. (2013), who highlight the positive impact unconventional monetary policy has
on the expected excess returns in the US. These findings are also in line with the view that
suggest the typical response of the stock market to the Fed’s announcement, results in a rise in
excess returns when the policy is expansionary and vice versa. This is due to the positive effect
of an expansionary policy on investors’ expectations.
The share of US government bonds decreases meaningfully at inception of the central bank’s
intervention, slowly returning back to its original value, showing a gradual fading off of the
shock reported in the Fig. 4d-4f. This is in line with the theory that central bank purchases
8
See Table T3 in the Appendix.
22
decrease the available supply of bonds to be purchased. Whilst the share of investment grade
bonds does not seem to be affected by the programme at all, equities shares strangely also
experience a decline. Although, this result is not compatible with the portfolio balance theory,
it is consistent with the findings of Joyce et al (2012) and might reflect the strong inverse
relationship in shares of equities to broad money over the sample. However, both corporate
bonds and equities exhibit an insignificant IRF, suggesting the unimportance of this shock to
these shares. Moreover, it can be noticed that the effect from a reduction in governments bonds
abates only very slowly in all variables. In fact, an alteration of relative asset shares triggers a
portfolio rebalancing into riskier assets, whilst adjusting the expectation of future returns down.
This is reflected as a decline in bond yields of similar magnitude for both government and
investment grade securities, as well as a shrinking of the required rate of return on equities.
Whilst the initial reaction to a one standard deviation shock leads to a decline in sovereign and
corporate bonds yields of 1% and 2% respectively, it is already reverted to half the size after 8
months. Nevertheless, the government bond yield seems to reduction at a faster pace that the
required return on equities.
Fig. 4. Expected excess returns and asset shares responses to fall in sovereign share
Form 1: Constant conditional mean
23
6.3. Variance decomposition
In addition, Table 4 shows the variance decomposition of shares and returns, which highly
supports our initial findings. We notice that, simultaneously, the role of QE in explaining
expected excess returns is important in the short run. The monetary policy shock accounts for
sizable components of the variation in the sovereign (21%), the corporate (16%) and equity
returns (4%). In contrast, sovereign shocks explain only 0.44% and 1.47% of the variation of
equity and corporate shares respectively. This is in line with the corresponding results of
impulse responses analysis. Because QE play a rather import role in excess returns.
Table 4. Variance decomposition to shock of QE
Period
Eq_share
Corps_share
Sov_share
Sov_return
Corps_return
Eq_return
1
0.00
0.00
33.54
16.96
11.29
1.18
2
0.18
0.21
30.45
18.32
12.99
2.02
4
0.39
0.34
27.28
18.98
14.08
2.55
6
0.45
0.45
25.21
19.34
14.57
2.91
8
0.46
0.60
21.66
19.65
14.89
3.35
10
0.44
0.73
21.41
19.94
15.11
3.61
12
0.42
0.85
19.95
20.19
15.26
3.78
16
0.37
0.97
16.77
20.61
15.41
3.90
20
0.35
1.09
14.00
20.90
15.47
3.97
24
0.36
1.21
13.88
21.09
15.49
4.01
28
0.41
1.34
09.88
21.21
15.52
4.03
30
0.44
1.47
09.10
21.25
15.53
4.04
6.4. The equity risk premium and equity price returns
As pointed out in the methodology, the ERP can be calculated as the difference between the
equity yield and the risk–free rate (see equation 7) and herewith suggests a gradual response in
the ERP. The results from this simulation of a one standard deviation show are translated to a
decline in the share of Treasuries ranging from approximately $850 billion to $1.4 trillion using
the month of inception of the three QE programmes. In order to grasp a more precise estimation,
24
this value is then multiplied by the ratio of the actual size of the Treasury market to the market
value of the Barclays Treasury index
9
. The resulting value is then used to scale the three QE
programmes. We computed the ERP by using impulse responses and scaling as explained in
the Appendix Table T5. Fig. 5 depicts that the unconventional monetary policy shocks impact
the ERP negatively, where an average reduction in the ERP of 0.23% can be observed for each
of the three programmes after 12 months. It implies that the changes in the ERP have a negative
effect on the returns of the S&P 500 and this leads to a decrease in the amounts of cash invested
in riskier assets such as stocks. The findings are qualitatively similar to that of Poshakwale and
Chandorkar (2016) and Bredin et al. (2007) for the equity market.
Fig. 5. Equity risk premium implied from impulse response functions
The range of estimates found can be plotted into price returns by the computed historical ERP.
The result shows that a 1% rise in the ERP from one period to the other corresponds to a 4.14%
price reduction of the S&P 500
10
. Alternatively, a reduction in the ERP suggests a positive
impact on annualised equity returns. This is consistent with the evidence from Fig.3, where a
clear inverse relationship between these two variables is revealed.
9
See Table T5 in the Appendix.
10
See Table T6 in the Appendix
25
The potential impact on equity prices is estimated, where the ERP reaches its minimum after
18 months. This occurs in order to allow the market to fully price in the shock, rather than just
considering the instant impact and foregoing a potential slower feed-through of QE to equity
markets. In the Table 5 the yearly equity price return contributions from each of the QE
programmes is exhibited.
Table 5. Estimated impact of QE on yearly S&P 500 returns
Response in S&P 500 price index
QE 1 ($300 bn)
1.9%
QE 2 ($600 bn)
3.7%
QE 3 ($755 bn)
4.0%
Cumulative rise
9.6%
With the last programme being the most effective in raising equity prices, the evidence suggests
only a minor difference in effect between the QE2 and QE3. Overall, the portfolio balance
effect induced by QE seems to have successfully contributed to a boost in equity prices by 9.6%
over the duration of the programme. The findings of this paper are in line with recent literature
that finds a positive relationship between monetary policy expansion and stock market
(Laopodis, 2013; Liu and Asako, 2013; Poshakwale and Chandorkar, 2016).
Furthermore, we explore the response of the ERP to monetary policy shocks before and after
the introduction of QE. For this purpose, we divide the sample into two groups, with the pre-
QE sample running from January 1984 to November 2008 and the post-QE sample from
December 2008 until January 2017. Table 6 indicates the response of the ERPs of the sovereign
shares, with and without QE. We can see that the ERPs respond negatively to the monetary
policy shocks before and after QE. However, there is a sizeable difference between the
responses of the ERPs to expansionary monetary policy shocks over the two periods. This is in
line with the findings of Karras (2013) that the effectiveness of monetary policy shocks
decreases with their magnitude.
Table 6. Equity risk premium implied from impulse response functions before and after
QE
Before QE
After QE
ERP
ERP
ERP QE1
ERP QE2
ERP QE3
26
1
-0.75%
-0.63%
-0.38%
-0.71%
-0.79%
2
-0.60%
-0.03%
-0.02%
-0.03%
-0.03%
3
-0.52%
-0.02%
-0.01%
-0.02%
-0.02%
4
-0.42%
-0.09%
-0.05%
-0.10%
-0.11%
5
-0.35%
-0.13%
-0.08%
-0.15%
-0.17%
6
-0.30%
-0.19%
-0.11%
-0.21%
-0.23%
7
-0.25%
-0.23%
-0.14%
-0.27%
-0.29%
8
-0.21%
-0.26%
-0.16%
-0.30%
-0.33%
9
-0.18%
-0.27%
-0.16%
-0.31%
-0.34%
10
-0.15%
-0.27%
-0.16%
-0.30%
-0.33%
11
-0.13%
-0.25%
-0.15%
-0.29%
-0.32%
12
-0.11%
-0.23%
-0.14%
-0.26%
-0.29%
Average
-0.33%
-0.22%
-0.13%
-0.25%
-0.27%
Finally, we further examine the impact on annual S&P 500 returns after QE in order to compare
it without QE. Table 7 reports that individual and cumulative rises in the S&P 500 returns are
about 13% after QE, which is significantly higher than returns without QE. One possible
explanation for the size asymmetric response is that during QE, the Fed purchased high quality
fixed income securities provided by central bank reserves hence effectively replacing relatively
illiquid money with liquid cash reserves. This led to a fall in both short and long-term bond
yields so leading to higher excess equity returns.
Table 7. Estimated impact of QE on yearly S&P 500 returns after QE
Response in S&P 500 Price Index
After QE
QE 1 ($300 bn)
2.60%
QE 2 ($600 bn)
4.94%
QE 3 ($755 bn)
5.46%
Cumulative Rise
13.0%
6.5. Empirical evidence of regime Shifts
The estimated break dates are reported in Table 8 below. The value of the SupLR test reports
an estimated value of 600.16, which is greater than the 1% critical value. The WDmax and SEQ
tests confirm that the number of breaks identified is the same as the maximum number allowed
(e.g. 3 breaks allowed). The dates identified coincide with the post QE in one occasion
including the QE in 2008, which is estimated as the final break. The first and second break
27
coincide with the post market crash in 1987 and post Asian financial crisis in 1998, respectively.
Thus, the break dates we estimated using the QP approach do not cover all the QE
announcements, but captures key events.
This is typical when using structural break tests that identify breaks endogenously using
computational algorithms as argued by Crafts and Mills (2017). In the context of QP test, this
could be due to the nature of the procedure and algorithm implemented to identify the breaks.
First, the QP approach allows for common breaks in the system, which is its strength and at the
same time a restricting feature. This latter imposes a common date of the occurrence of shifts
in regimes on all the equations in the system, which does not necessarily reflect the true break
date in each equation of the system. Second, as argued by Crafts and Mills (2017), the properties
of this class of structural break tests in dynamic systems is yet to be fully established, which
may explain failing to identify the exact date. Nonetheless, given the stationarity property of
our data, the break dates may be useful as a guide to approximate the effect of regime shifts in
the VAR model.
Table 8. Structural Breaks Test Results
Qu-Perron Procedure
Tests
Statistics
SupLR
600.16*
WDmax
255.55*
Seq (2/1)
185.62*
Seq (3/2)
223.54*
Estimated Breaks
Break Dates
95% C.I.
November 1989
(October 1989, December 1989)
October 2000
(September 2000, November 2000)
October 2009
(September 2009, November 2009)
Notes: * denotes significance at 1%. SupLR tests the null of no breaks versus the alternative of 3 breaks. WDmax
tests the null of no breaks against the alternative of unknown number of changes up to 3 breaks. Seq (2/1) tests the
null of 1 break against the alternative of 2 breaks. Seq (3/2) tests the null of 2 break against the alternative of 3
breaks.
Accounting for these shifts in regimes, we can identify the impulse responses specific in each
regime. Unlike the first exercise, where the VAR model is assumed to have a constant
conditional mean (and consequently the responses are constant over the sample), when
accounting for the shifts in the conditional of the VAR model we identify relatively different
responses to fall in sovereign share. Figs. 6, 7, 8 and 9 depict these responses for regimes 1, 2,
3 and 4 respectively.
Fig. 6. Expected excess returns and asset shares responses to fall in sovereign share
28
Form 3- regime 1 (1984m1-1989m11)
Fig. 7. Expected excess returns and asset shares responses to fall in sovereign share
Form 3- regime 2 (1988m12-2000m10)
29
Fig. 8. Expected excess returns and asset shares responses to fall in sovereign share
From 3-regime 3 (2000m11-2009m10)
30
Fig. 9. Expected excess returns and asset shares responses to fall in sovereign share
Form 3-regime 4 (2009m11-2017m01)
According to the IRFs, accounting for regime shifts does leads to different behaviour across
regimes. For example, returns and share series exhibit a highly persistent behaviour during
regimes 1 to 3, which shows that the stock market transmitted shocks are persistent over time
(e.g. do not die off over the time horizon). Moreover, this also suggests that the level of and
31
return on shares behave in a similar manner in these regimes. In terms of the magnitude and
sign, regimes 1 and 2 (Fig. 7 and 8) display higher persistence, while regime 3 (Fig. 8) seems
to have a relatively stable dynamic before exhibiting a tendency to persist over time. In addition,
the responses of the returns to monetary shocks are negligible for regime 3. This could be
because regime 3 covers some part of QE1. Regime 4, as depicted in Fig. 9, shows similar
patterns to those in Fig. 4a-4c. Regime 4 represents the period where the shifts in the stock
market can be viewed as driven by various QE announcement. The shocks in equity, corporate
and sovereign returns decline quickly and die off eventually. In contrast, equity and sovereign
shares show a slow return to the long run, while corporate shares exhibit a quick recovery from
a negative shock. The overall observation from this empirical exercise is that the regimes that
coincide with QE programmes (including regime 4) respond consistently to them, while
regimes coinciding with other economic and financial events (such as regimes 1 and 2) do not.
This suggests that unconventional monetary policy is successful in achieving the aims of the
Fed.
7. Conclusion
The results provide evidence for a direct effect of QE induced by the portfolio balance channel
on returns of sovereign bonds, in addition riskier assets such as corporate bonds and equities.
Our estimates formally support to the widespread belief that QE in the US has a substantial
positive influence on equity prices. The findings suggest that QE shocks induce negative
impacts on the ERP and leads to higher S&P 500 returns. Interestingly, equity returns appear
to evidence a slower pace of adjustment and therefore a slower reversal of price reaction than
US Treasuries, demonstrating a slower feedthrough of the portfolio balance channel to riskier
assets. Particularly remarkable though, is the finding that QE effectively increased equity prices
by 9.6%, mainly due to a lowering of the ERP. This demonstrates that the portfolio balance
channel has a direct impact on equities’ rate of return in excess of that on sovereign bond yields.
The price increase described therefore solely stems from a readjustment of the equity yield
through the risk premium. Moreover, our empirical findings indicate that before and after the
implementation of QE, the monetary policy shocks have a negative effect on the ERPs of the
aggregate market. However, a negative response of the ERP leads to higher returns of the S&P
500 with QE. The empirical evidence provided in the paper sheds light on the equity market’s
size asymmetric response to the Fed’s policy with and without QE.
Moreover, while much of the literature assume – either implicitly or explicitly – that the
conditional mean of the VAR model is constant over the sample, we find evidence that the VAR
32
specification of relax this assumption and assess the stability of the relationship between
government bonds, investment-grade corporate bonds and equities is not stable of the sample,
three breaks have been identified that include key economic events. This has various
implication on policy. First, the dynamics of the market is found to be unstable and may lead
to different policy regimes. In the context of our findings, the long run relationship was not
driven only by QE programmes. Second these policy regimes are described by different events
and different policy implementation approaches. Whiles the first two regimes are characterised
by traditional approach to monetary policy, Regime 4 is consistent with the emergence of QE
and the unconventional policy approach. Third, crises pre-2007 have significant impact on the
balance portfolio channel. According to our findings, pre- QE regimes experienced persistent
shocks, while the regime that coincide with the QE programmes exhibit quick recovery in most
cases. This may indicate the effectiveness of QE in reducing the uncertainty in the market as
opposed to traditional monetary policy intervention.
Therefore, the results of this paper suggest that QE can improve financial market liquidity. Our
conclusion is that QE has played an important role in conducting monetary policy in the US in
much the way that was anticipated and intended. In a world with highly interconnected capital
markets, QE is likely to have contributed to a portfolio reallocation and re-pricing of financial
securities on a global level (Fratzscher et al., 2012). Even though the empirical findings of this
paper are unlikely to have captured the full effects of QE and its exact consequences on equity
returns, the portfolio balance channel nevertheless proves to be a powerful in reducing the
required rate of return on a range of assets displaying different risk profiles.
33
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Appendix
Fig. F1. Residual Test for Autocorrelation Correlograms (2 Std. Error Bounds)
-.8
-.4
.0
.4
.8
2 4 6 8 10 12
Cor (EQ_SHAR E,EQ_SHARE(-i))
-.8
-.4
.0
.4
.8
2 4 6 8 10 12
Cor (EQ_SHAR E,CORPS_SHARE( -i))
-.8
-.4
.0
.4
.8
2 4 6 8 10 12
Cor (EQ_SHAR E,SOV_SHARE(-i))
-.8
-.4
.0
.4
.8
2 4 6 8 10 12
Cor (EQ_SHAR E,SOV_RETURN (-i) )
-.8
-.4
.0
.4
.8
2 4 6 8 10 12
Cor (EQ_SHAR E,CORPS_RETU RN (-i) )
-.8
-.4
.0
.4
.8
2 4 6 8 10 12
Cor (EQ_SHAR E,EQ_RETURN (- i))
-.8
-.4
.0
.4
.8
2 4 6 8 10 12
Cor (CO RPS_SHARE,EQ_SHARE( -i))
-.8
-.4
.0
.4
.8
2 4 6 8 10 12
Cor (CO RPS_SHARE,COR PS_SHARE(- i))
-.8
-.4
.0
.4
.8
2 4 6 8 10 12
Cor (CO RPS_SHARE,SOV_SHARE(- i))
-.8
-.4
.0
.4
.8
2 4 6 8 10 12
Cor (CO RPS_SHARE,SOV_RETUR N( -i))
-.8
-.4
.0
.4
.8
2 4 6 8 10 12
Cor (CO RPS_SHARE,COR PS_RETUR N( -i))
-.8
-.4
.0
.4
.8
2 4 6 8 10 12
Cor (CO RPS_SHARE,EQ_RETU RN (-i) )
-.8
-.4
.0
.4
.8
2 4 6 8 10 12
Cor (SOV_SHARE,EQ_SHAR E(-i))
-.8
-.4
.0
.4
.8
2 4 6 8 10 12
Cor (SOV_SHARE,CO RPS_SHARE(- i))
-.8
-.4
.0
.4
.8
2 4 6 8 10 12
Cor (SOV_SHARE,SOV_SHARE(- i))
-.8
-.4
.0
.4
.8
2 4 6 8 10 12
Cor (SOV_SHARE,SOV_RETU RN( -i))
-.8
-.4
.0
.4
.8
2 4 6 8 10 12
Cor (SOV_SHARE,CO RPS_RETUR N( -i))
-.8
-.4
.0
.4
.8
2 4 6 8 10 12
Cor (SOV_SHARE,EQ_R ETURN (-i) )
-.8
-.4
.0
.4
.8
2 4 6 8 10 12
Cor (SOV_RETU RN ,EQ_SHARE(-i) )
-.8
-.4
.0
.4
.8
2 4 6 8 10 12
Cor (SOV_RETU RN ,CORPS_SHAR E(-i))
-.8
-.4
.0
.4
.8
2 4 6 8 10 12
Cor (SOV_RETU RN ,SOV_SHARE(-i))
-.8
-.4
.0
.4
.8
2 4 6 8 10 12
Cor (SOV_RETU RN ,SOV_RETURN (-i) )
-.8
-.4
.0
.4
.8
2 4 6 8 10 12
Cor (SOV_RETU RN ,CORPS_R ETURN (-i) )
-.8
-.4
.0
.4
.8
2 4 6 8 10 12
Cor (SOV_RETU RN ,EQ_RETUR N(- i))
-.8
-.4
.0
.4
.8
2 4 6 8 10 12
Cor (CO RPS_RETU RN,EQ_SH ARE(-i))
-.8
-.4
.0
.4
.8
2 4 6 8 10 12
Cor (CO RPS_RETU RN,C ORPS_SHAR E(-i))
-.8
-.4
.0
.4
.8
2 4 6 8 10 12
Cor (CO RPS_RETU RN,SOV_SHAR E(-i))
-.8
-.4
.0
.4
.8
2 4 6 8 10 12
Cor (CO RPS_RETU RN,SOV_R ETURN (-i) )
-.8
-.4
.0
.4
.8
2 4 6 8 10 12
Cor (CO RPS_RETU RN,C ORPS_R ETURN (-i) )
-.8
-.4
.0
.4
.8
2 4 6 8 10 12
Cor (CO RPS_RETU RN,EQ_R ETUR N(- i))
-.8
-.4
.0
.4
.8
2 4 6 8 10 12
Cor (EQ_R ETURN ,EQ_SHARE(- i))
-.8
-.4
.0
.4
.8
2 4 6 8 10 12
Cor (EQ_R ETURN ,COR PS_SHARE(-i) )
-.8
-.4
.0
.4
.8
2 4 6 8 10 12
Cor (EQ_R ETURN ,SOV_SHARE(-i) )
-.8
-.4
.0
.4
.8
2 4 6 8 10 12
Cor (EQ_R ETURN ,SOV_RETUR N(- i))
-.8
-.4
.0
.4
.8
2 4 6 8 10 12
Cor (EQ_R ETURN ,COR PS_RETUR N(- i))
-.8
-.4
.0
.4
.8
2 4 6 8 10 12
Cor (EQ_R ETURN ,EQ_RETUR N( -i))
Autocorrelations with 2 Std.Err. Bounds
Table T1. Variance-Covariance matrix of the VAR model*
Sh. of
Equities
Sh. of Corp.
Bonds
Sh. of Sov.
Bonds
ER on Sov.
Bond
ER on Corp.
Bonds
ER on Equities
Sh. of Equities
0.87
-0.12
-0.24
-0.14
0.30
3.65
Sh. of Corp. Bonds
-0.12
0.03
0.03
0.15
0.15
-0.44
Sh. of Sov. Bonds
-0.24
0.03
0.10
0.25
0.14
-0.86
ER on Sov. Bonds
-0.14
0.15
0.25
7.14
7.92
1.35
ER on Corp. Bonds
0.30
0.15
0.14
7.92
11.77
5.39
ER on Equities
3.65
-0.44
-0.86
1.35
5.39
38.71
*Note (1): ‘Share’ abbreviated as ‘Sh.’ and excess return as ‘ER’
Table T2. VAR stability condition and Lag-Length Criteria
VAR without Dummy
Root (Maximum)
0.9933
38
SC (Selected Lag)
-39.58 (2)**
HQ (Selected Lag)
-39.84 (2) **
AIC (Selected Lag)
-40.08 (2) **
*Note (1): ** 5% significance level
Table T3. Residual test for autocorrelation LM test for VAR
LM Test Statistic
P-Value
Lag 1
39.46
0.32
Lag2
Lag 3
30.28
77.19
0.73
0.01
Table T4. Jarque-Bera test for univariate normality
Norm (1)
Skewness
Kurtosis
Excess Return on Equities
199.86***
1.02***
6.59***
Excess Return on Corp. Bonds
978.86***
0.97***
11.93***
Excess Return on Sov. Bonds
157.5***
0.52***
6.51***
Share of Equities
6.89**
-0.23
3.60**
Share of Corp. Bonds
667.05***
-0.39***
10.51***
Share of Sov. Bonds
5.76*
-0.11
3.66**
Joint
2015.94***
Table T5. Scaling of one standard deviation IRFs to size of QE programmes
Start of
Purchases
Barclays
Market Value*
Treasury Securities
Outstanding*
Ratio
One Stdev*
Scaling
QE 1 ($300 bn)
Mar-2009
3080
11126
3.61
866
0.10
QE 2 ($600 bn)
Nov-2010
5211
13861
2.66
1168
0.19
QE 3 ($755 bn)
Sep-2012
6067
16066
2.65
1386
0.21
Source: Thomson Reuter’s Datastream, Fawley & Neely (2012)
*Note (1): Values in Billions of US Dollar $
Table T6. Regression output from Equation 10
Variable
Coefficient
Std. Error
t-Statistic
P-Value
39
-4.14
0.12
-34.91
0.00
0.07
0.01
18.06
0.00
0.75
Equation E1: The Log-Likelihood Ratio
T = number of observations
m = number of parameters in each equation
= determinant of the residual’s covariance matrix (restricted and unrestricted)
q = degrees of freedom of Chi-Square distribution
Source: Chi-Square Distribution Table, Lütkepohl (2013)
