Abstract Introduction QE and Asset Prices Quantifying the effects of QE Methodology Results Conclusions Bibliography

Transcription

1 Financial asset price relationships in the presence of Quantitative Easing Evidence for the transmission channels of Quantitative Easing using a multivariate VAR model Abstract The Bank of England s use of Quantitative Easing in the aftermath of the United Kingdom s financial crisis has sparked interest in the financial market impact of the policy. While the objectives of The Bank were macroeconomic in purpose, intervention in UK financial markets necessitated the formation of theory that predicted how different asset types would react to the wholesale purchase of government gilts and the resulting gilt yield reduction. This study examines the key financial assets that were intended to be affected by Quantitative Easing, establishing whether price reactions of corporate bonds, equities and the dollar/ sterling exchange rate match up to the predictions of QE s theoretical foundations. A multivariate VAR model is used on weekly data to examine the relationships between these assets, using impulse response functions, structural break analysis, and Granger causality to determine whether QE had its intended effect. This study finds that there is no strong evidence for decreased UK gilt yields having an effect on UK corporate bonds or equities, with the Bank s purchases of longer-term gilts especially being insignificant as a causal force for the yields of other assets. Furthermore this study finds evidence that QE did not reduce yields for UK gilts of shorter maturities, with significant effects only occurring at the longer end of the maturity spectrum. 1

2 Contents Abstract Introduction QE and Asset Prices Portfolio Balance Channel Signalling/Expectations Channel Liquidity Channel Credit Channel Quantifying the effects of QE Methodology Variable Selection Unit Root tests VAR model specification Cointegration Rank testing VAR with exogenous variables estimation Results Granger Causality Impulse Response Functions Structural break analysis Dummy Variable tests Dynamic Multiplier Functions Conclusions Bibliography

3 1. Introduction By the end of 2008 the global financial crisis had driven the UK financial sector into a period of extreme duress, leading the Bank of England to consider the unconventional policy of Quantitative Easing to prevent further bankruptcies and economic downturn. The intention of this policy was to dramatically increase the monetary base in the UK economy, alleviating the liquidity issues that the private banking sector was under and helping the UK to achieve its 2% inflation target. Reversing the downward trend in asset values and domestic consumption were also objectives for the Bank s Monetary Policy Committee. (Joyce et al, 2011) To serve these objectives, from March 2009 the Bank of England purchased long-term UK gilts to the value of 375 billion pounds, with additional purchases of high-rated corporate bonds and other financial assets. These purchases occurred mostly in two distinct periods, the first being between March 2009 and February 2010, and a second period of purchases between October 2011 and November During this time the Bank of England held reverse-auctions purchasing mostly government gilts of maturities between 10 and 25 years, but also a substantial amount of gilts of maturities between 5 and 10 years. In terms of affecting financial markets, the Bank of England designed its policy impact based primarily on portfolio balance theory originally proposed by Tobin. (1958) According to this theory changing asset quantities in a market impacts on its relative expected return, therefore a change in quantity of one asset, ceteris paribus, will alter its relative expected return in comparison to competing assets. In terms of the designed impact of QE, decreased market quantity in government gilts increases its price, thereby lowering its yield (interest rate) and will induce portfolio operators to switch out government gilts for other relatively more profitable assets. In effect the Bank of England intended for economic agents to rebalance their portfolios away from long-term government gilts, increasing demand and therefore the prices of other assets, as well as improving the overall liquidity of financial assets remaining available for trading. This paper has two objectives: First it intends to empirically model financial markets during the UK financial crisis, focussing on the asset types that were repeatedly cited in the Bank of England s theoretical models, and providing estimates of the nature of price relationships over the financial crisis period. The second objective is to then explore the impact of QE through examining the effects of shocks to gilt yields on equities, corporate bonds and the dollar exchange rate, determining the scale and longevity of these shocks and whether they correspond in nature to the predictions of the Bank 3

4 of England s theoretical models. The overall purpose of this is to determine whether financial markets operated during the QE period in a manner that allowed QE to work as intended. The rest of this paper is structured as follows: section 2 will include a brief theoretical introduction to the concepts and implications tied with the theory surrounding QE. The focus of this section will be the theoretical implications for QE, and a brief discussion of the expectations created by this theory on various financial assets. Section 3 will then outline other academic studies and discuss whether existing empirical findings match the expectations outlined in section 2. In section 4, this paper will go through the methodology of its own analysis of QE, describing variable selection, econometric modelling and model specification testing. Section 5 and 6 will then present the results of this analysis, and offer some conclusions on the outlook of QE intervention. 2. QE and Asset Prices The Bank of England report a range of channels through which QE can theoretically affect the economy, with some having stronger implications for financial markets than others. Given that this section is intended to be a brief overview, the discussion of these channels in this section will limit itself to the effects on financial asset values rather than describing the potential effects on the wider economy. 2.1 Portfolio Balance Channel The Portfolio Balance channel was first proposed by Tobin, and is loosely based on Keynes' Liquidity Preference model (Tobin, 1958, p.71). It is a popular theoretical concept in Keynesian monetary economics, and is recurrent discussion point in articles that analyse central banking policy (Salido, Javier and Nelson, 1971). Since the outbreak of the financial crisis in 2007, most articles that cover 'unconventional' monetary policy in some way have referred to this channel (E.g. in Inkinen et al, 2010). Theoretically the Portfolio Balance channel reflects the impact of changing asset quantities in a market on its relative expected return. A change in quantity of one asset, ceteris paribus, will alter its relative expected return in comparison to competing assets. For example, decreased quantity in one type of asset increases its price, thereby lowering its yield (interest rate) and will induce portfolio operators to switch out the affected asset for other relatively more profitable assets. In effect portfolios are rebalanced away from the asset affected by the quantity change, increasing demand and therefore the prices of other assets (Harrison, 2012). For the policy-maker this provides a lever for intervention to increase asset prices by modifying the quantity of a particular asset. For the Bank of England, the quantities of UK gilts were 4

5 chosen to be affected, the Bank s purchases drastically reducing the amount of long-term gilts available to the public, having an effect on the remaining gilt s rates of return relative to assets which were not targeted. As Tobin s theory suggested, the effects of these gilt purchases can cross several asset types, a decrease in the amount of available UK gilts causes the relative price of corporate bonds to be low in comparison, driving up demand for corporate bonds. Equities prices should also be positively affected, with investors being incentivised to sell their gilt holdings to the Bank of England and to purchase equities whose rates of return have improved relative to these gilts. The effects of the portfolio balance channel are resultantly very widespread, as almost all asset types will see their rates of return relative to UK gilts change with large-scale Bank of England intervention. In terms of the price relationships between secondary assets, i.e. the assets that are not directly affected by QE intervention but are rather affected by the changing quantities of UK gilts, portfolio balance theory suggests that no observable behaviour change should occur. QE purchases could however alter the portfolio decisions made by an economic agent when choosing between two secondary assets, corporate bonds and equities, if the reduced availability of low-risk gilts induces investors to reduce their holdings in higher-risk equities in favour of less risky corporate bonds. In this way investors would be attempting to reduce their risk profile down to a level that meets their requirements. However, conceivably since there is no dramatic change in the quantity available of either equities or corporate bonds available during the period, there should be no large scale change in price relationships between them. In addition, as high-quality corporate bonds and equities can be considered competing assets, an increase in the price of one type should coincide with a decreasing price in the other. In this way, portfolio balance theory suggests that both corporate bond and equity prices should be positively affected by decreasing gilt yields, but be negatively associated with changes to their rates of return relative to each other. 2.2 Signalling/Expectations Channel The second potential channel that QE has been expressed to work through is the so called 'Signalling channel' and the similar Expectations channel the latter of which has also been referred to as the macro/policy news channel and policy signalling effects in a Bank of England publication (Joyce et al., 2011). The Signalling Channel reflects the impact on expectations that occurs when a monetary authority makes a statement of intent about a certain macro policy. In these circumstances, individuals can be reassured or worried by the news, and alter their expectations of future asset values and yields accordingly (Kapetanios et al., 2012). This channel uses the assumption that investors are rational and forward looking, and will therefore make inferences from central bank announcements, and using this information to make market based decisions. In this way, investors will not only react to a policy made by the central bank when it is actually carried out, but also when it is initially 5

6 announced. This leads to important implication that a large part of the quantitative easing effect will be recorded in the first few days around and announcement. Many of the articles published in the last few years have argued that the expectations effect QE creates is just as important as the portfolio balance effect; and as such this theory is discussed to a great extent by the articles discussing optimal monetary policy (Bernanke et al, (2004) Adam and Billi (2004), etc.). The signalling effect is related to the expectations channel, but operates in a different way: Eggertsson and Woodford (2003) amongst other claim that if the zero-bound interest rate policy of QE is seen to be a credible commitment by the Central Bank, individual expectations of future asset performances will be revised upwards. The signalling channel is based on the assumption that private agents expect that central bank purchases to lower interest rates will induce the central bank to commit to lower interest rates later. (Otherwise the central bank would lower the value of its own bond holdings) If agents know that purchases will take place, they will also expect future rates to be lower, this causes rates to be lower today as long as the conditions of expectations theory holds. This mechanism is summarized by Clouse (2003, p.33) In this way a realistic sounding commitment made by a central bank will have ramifications before the policy measure has been enacted, and will have lingering effects well after the intervention has been concluded. For the purposes of this paper, the effects of the signalling/expectations channel should reinforce the effects of the portfolio balance channel. Apart from the general improvement in market prices across all assets that will be associated with central bank intervention, announcements of gilt purchases should encourage the same portfolio re-balancing behaviour from agents as the actual purchases themselves. Therefore this channel should not theoretically dampen any portfolio balance effects to be observed in the data. However, separating the portfolio balance channel from the effects of signalling and expectations is problematic. Given that economic agents will make portfolio decisions based from policy announcements, some portfolio rebalancing will occur before any intervention takes place, this means that results taken from the time-periods of actual purchases will potentially yield results that are less pronounced and do not truly reflect the overall market reaction. On a superficial level, this paper will conduct structural break analysis in an attempt to observe any changing price relationships that can be attributed to QE announcements rather than the actual intervention. Overall, given the mutually reinforcing nature of these channels, the intention of this paper is to at least properly capture the entirety of the portfolio balance effects and signalling effects, limiting itself by not attempting to isolate the individual channel effects 2.3 Liquidity Channel The Liquidity channel is discussed by many of the same academics who discuss the portfolio balance effect, as the two channels are often inter-connected or occur in tandem. As such it is mentioned in 6

7 official publications made by both the Federal Reserve and the Bank of England. (See Clouse, 2003 and Joyce et al., 2011). This channel covers the results of a Central bank being a significant and secure buyer of assets in a market which is suffering from market failure resulting from liquidity issues and uncertainty. The central bank provides a steady demand and thereby makes the sale of assets less costly to the seller, allowing market participants to conduct trading more frequently and with more certainty that there will be a buyer if the participant decides to trade. The central bank also provides a steady stream of excess liquidity that pervades the market, reducing or nullifying the effects illiquidity had on asset prices and yields. This channel is again covered by Tobin (1958) as well as Allen and Gale (1994), Joyce et al (2011) who discuss the channel briefly in connection with QE and the other channels. Shleifer and Vishny (2011) assert that the liquidity channel is the primary method through which QE works, and that the expectations and portfolio balance channels are only secondary in importance. For this paper, the liquidity channel could potentially have an effect on the price relationships between relatively liquid equity assets and the more illiquid government and corporate bonds. During periods of financial duress, it can be expected that economic agents will attempt to have portfolios that are relatively more liquid than under normal circumstances. Holding liquid assets allows agents to respond to changing market circumstances quicker, which is beneficial when asset markets are volatile. This paper can therefore expect there to be a higher liquidity premium associated with holding longer-term bonds and gilts relative to holding equities and more liquid debt assets. With QE intervention it could be expected that the excess liquidity injected into the economy will lessen the value of holding equities as a liquid asset and therefore lower equity prices compared to bond and gilts. A possible expectation of the liquidity channel is therefore that equity prices relative to bond and gilts prices will be negatively affected by QE intervention. 2.4 Credit Channel The credit or bank lending channel is another possible transmission mechanism for the effects of QE purchases, where the injection of liquidity by the central bank, increases the size of a bank s portfolio, inducing them to lend more at a reduced interest rate. This cheap credit theoretically improves the financial health of firms and households and supports asset prices (Joyce et al. 2011). Clouse et al. (2003) discusses this channel and while they note that due to the zero-bound on interest rates lending is unlikely to increase substantially, arguing that banks will absorb this excess liquidity in an effort to prepare for future monetary shocks, they concede that an increase in lending is likely to manifest in slightly higher asset prices. (Clouse et al 2003). Furthermore, with lower interest rates, the relative value of future dividends for equities should increase, increasing demand for such assets. In this way, the credit channel could result in a small increase in prices for equities. 7

8 3. Quantifying the effects of QE As introduced above, the intention of this paper is to isolate the effects of QE purchases from the general chaos of the financial crisis in order to determine how price relationships between different assets were affected by the Bank of England s intervention. The first objective is to determine the nature, if any, of the price relationships between the different asset types and maturities. This is intended to illustrate whether or not QE had the widespread effect it was intended to on asset types that it did not directly intervene with. Analysis to determine whether causal relationships between financial assets will be the focus of the study, with attention paid to the scale and the longevity of any causal relationships. Secondary analysis will revolve around comparisons between the same assets over different time periods, showing how price relationships change when QE purchases are either occurring or not. Conducting the same analysis over different time-periods also allows the interpretation of structural breaks and to lend some wider economic intuition to changes in price relationships. The most important aspect, as expected, is the effect of government gilt yields on other financial assets, however significant changes to price relationships between secondary assets also presents interesting evidence for portfolio balance theory. These intentions being stated, the intention of this paper is to let the data speak, so the method used is intended to impose as few restrictions or specifications as possible, and to draw conclusions from observation from the data without leaning too heavily on theory. 4. Methodology Given the novelty of QE as policy tool and the chaotic nature of the global financial crisis, there is not yet a clear consensus on how to empirically assess the effects of QE. Because of this, the current studies on the subject have used a variety of methods to quantify the effects. These range from DOLS used by Gagnon et al (2010), to a GARCH-M model utilised by Joyce et al. (2011). Vector Autoregressive or VAR models, which are very frequently used for analysis of financial market data and macroeconomic indicators, are the most commonly used by other empirical studies of QE. Notable examples include Kapetanios et al. (2012) use of three types of VAR for it s study on the macroeconomic effects, and Bridges and Thomas (2012) use of a co-integrated VAR. This paper intended to use a conventional VAR methodology, while testing for cointegration between variables in which case a Vector Error Correction Model (VECM) should be used. A VAR model 8

9 was chosen as it allows dependent variables to be specified as a function of their own past values, as well as the lagged values of other variables within the system. The particular type of VAR used in this paper is sometimes referred to as a VAR-X, or a VAR with exogenous variables, with this paper including QE intervention as exogenous dummy variables. This paper treats the Bank of England s intervention as exogenous to asset prices/yields, with the assumption that proper overall financial market function was the objective of QE intervention, not the price level/yield of any individual asset class, and therefore the Bank of England did not purchase long-term gilts in order to alter the value of any individual asset. The exact specification of this paper s VAR will be outlined in later sections, but it takes the general form: P k Y t = α + β i Y t i + γ j X t j + ε t i=1 j=0 Where Y t is a p vector of endogenous variables and X t is a k vector of exogenous variables. 4.1 Variable Selection As discussed above, this paper views that high-quality equities and corporate bonds are the most likely substitutes for government gilts for portfolio investors. Given no change to risk preferences, it can be expected that those who held gilts for their low-risk return would seek assets of a similar highquality when re-balancing their portfolios. Furthermore these assets were chosen because they are highly liquid, and would therefore be the most likely assets to be purchased by investors seeking to re-invest the money they received from selling government gilts. The dollar sterling exchange rate was included to show any effects that QE had on the exchange rate, this exchange rate was selected above others as a variable because it was less likely to exhibit the effects of Euro-area financial crisis, and would therefore capture more of the UK s QE effect. For this reason this paper examined the following assets: FTSE100 (closing price). Averaged from daily data into weekly format. Dollar to Sterling Exchange rate. Averaged from daily data into weekly format. UK government nominal spot rate gilt yields for 5, 15 and 25 year maturities. Averaged from daily data into weekly format. Corporate bond nominal spot rate gilt yields for 5, 15 and 25 year maturities. Averaged from daily data into weekly format. Equity data was taken from Datastream and Yahoo finance while the bond and gilt yields were taken directly from the Bank of England s yield curve data. Both the government nominal gilt and UK 9

10 corporate bond yields were calculated by the Bank on maturities ranging from 1 year to 30 years, with the Commercial liabilities (corporate bonds) calculated from assets tied to the LIBOR rate. The dollar exchange rate was also collected from the Bank of England s statistical database. These variables were chosen to be analysed in weekly format rather than with monthly intervals which is much more common in the literature. This is because of the relatively short window where QE purchases actually occurred, where monthly data intervals would leave less than 25 observations where purchases consistently occurred. Daily data was considered for analysis however it suffered from much larger issues with residual assumptions. Furthermore, information on the timing and scale of QE purchases are not available in daily format, meaning that it would be difficult robustly interpret daily price fluctuations as reactions to QE purchases. Weekly format was therefore chosen as a middle ground between available data and interpretable results. Data was collected in daily format from between the 1 st of January 2008 and the 29 th of December 2014, a time window which captures all of the main QE purchases, it was then converted into a weekly average. This averaging was intended to capture the weekly volatility of asset values more appropriately than simply taking the weekly closing prices and yields. This paper also included a selection of dummy variables intended to capture the effect of QE gilt purchases and also to control for exogenous shocks to individual assets. These dummies are specified as follows: 3 dummies corresponding to large shocks to individual asset markets associated with the UK financial crisis. These are accounted for in the model after tests suggested there were significant contagion effects between different asset markets during these shocks. These structural-break dummies were tested for inclusion using a LR-test in order to improve the models residual normality. 5 other non-qe structural breaks were tested for after observation of the data, but were omitted because they did not significantly improve the model. The three dummies include: o A shock taking place between 25/08/2008 and 6/10/2008 where the FTSE100 dropped significantly over a relatively short time window coinciding with financial crisis in the UK. o A shock to corporate bond yields taking place over two weeks between 17/11/2008 and 01/12/2008 where gilt yields dropped by over 67 basis points. o A shock to the dollar sterling exchange rate taking place between 28/07/2008 and 10/11/2008 where the dollar appreciated from $1.98/ to $1.49/. This is again connected with the financial crisis in the UK. 10

11 Separate from this, this paper included 6 dummy variables aimed at capturing the impact of QE purchases on the endogenous variables. These include: o Govt5purchases: A dummy variable which is value 1 in the weeks when the Bank of England were purchasing gilts with 5 years to redemption, and zero otherwise. o Govt15purchases: A dummy variable which is value 1 in the weeks when the Bank of England were purchasing gilts with 15 years to redemption, and zero otherwise. o Govt25purchases: A dummy variable which is value 1 in the weeks when the Bank of England were purchasing gilts with 25 years to redemption, and zero otherwise. The dummies for 5, 15, and 25 gilt purchases are of interest to see whether purchases of gilts of different maturities affect secondary assets more or less. For example, whether the purchases of short maturity gilts produced more of an effect on equities and corporate bonds than long-term gilt purchases. o QE1 dummy: where the value of this variable is 1 when purchases were occurring in between 2009 and 2010, and zero otherwise. Given that QE purchases occurred in two distinct bouts of intervention, this variable is included to see whether QE1 had a more significant effect than the second bout. o QE2 dummy: where the value of this variable is 1 when purchases were occurring in between 2011 and 2012, and zero otherwise. Similar to above, this dummy is included to judge the effect of the continuous intervention between 2011 and o QE all purchases: this dummy is valued 1 when any Bank of England purchases are occurring, regardless of maturity of the assets purchased or whether the purchases were part of a large period of intervention or isolated small-scale interventions. This dummy is included to encompass the entirety of the intervention s effect. 4.2 Unit Root tests This section outlines the unit root tests conducted to ensure that all variables to be used in VAR and VEC analysis are I(1) non-stationary processes. This paper utilised two of the most popular and widely used unit root tests, the Augmented Dickey-Fuller test and the Phillips-Perron test. Any contradictions between the conclusions of these two tests were checked by conducting a DFGLS test. Tests of the variables in levels returned with non-rejections of the null for all variables at at least the 5% significance level. The dollar exchange rate was the only variable where tests returned with a rejection of the null for some specifications of the ADF, however the PP tests all returned with non- 11

12 rejections at the 5% level. The tests were then repeated for the variables in first differences, which Table 1 summarises: Table 1 Variable ADF ADF ADF ADF PP PP PP (First δ = 0 δ = 0 δ = 0 No δ = 0 δ = 0 No differences) α = 0 restrictions α = 0 restrictions FTSE * * * * * * * Dollar * * * * * * * 5-year Govt * * * * * * * 15-year Govt * * * * * * * 25-year Govt * * * * * * * 5-year Corp * -98* * * * * * 15-year Corp * * * * * * * 25-year Corp * * * * * * * Note: * indicates that the null of a unit root is rejected at 1% level 4.3 VAR model specification As shown in the previous section, unit root tests determined that all relevant variables were I(1) unit root processes of various specifications. Because of this, analysis of these variables would either be conducted using a VAR model with all variables in their first differences, or if co-integration was determined to be present, then a VEC model. This paper follows the Johansen and Juselius (1993) method of cointegration testing to determine the presence of long-term relationships, with a VAR model being specified which contains no autocorrelation in the residuals, then Trace and Maxeigenvalue cointegration tests being conducted. Following this procedure, the first stage was choosing the appropriate lag order. This paper conducted both pre-estimation and post-estimation lag selection criterion using the variety of tests that are commonly used for time-series data. The following information criterion were used by this paper: 1) HQ Hannan-Quinn information Criterion 2) LogL Log-Likelihood 12

13 3) LR Sequential modified LR test statistic 4) FPE Final Prediction Error 5) AIC Akaike Information Criterion 6) SIC Schwarz Information Criterion The outputs of which are summarised below in table 2: Table 2 Lag LogL LR FPE AIC SC HQ NA 3.85e * e * e e e e-17* e e *indicates the lag order recommended by criterion. This paper follows the procedure followed by many of the studies that conduct VARs and VECs on financial data, in choosing a lag-order based on recommendations from information criterion, and then testing for serial correlation in the lags with a LM test. Selection was also made with reference to studies such as Kilian and Ivanov (2005) that test the various information criterion s robustness to small sample sizes, non-normality and the issues connected with various data intervals. As can be seen above, there is no clear consensus between the various information criteria s for a specific lag number, therefore this paper estimated VAR models lags between 1 and 8 and then tested each respective resulting model using the Lagrange Multiplier test for serial correlation in the residuals. (Presented in Johansen (1995)). The test results for a VAR(7) is summarised below: Table 3 Lags LM-Stat Probability

14 As is made clear above, VAR models of other than, 7 lags exhibit serial correlation in the residuals, because of this, and the recommendation made by the AIC and FPE, this paper selected 7 lags for its baseline model to test for cointegration. This conclusion was supplemented by the use of a Wald Lag exclusion test which tests that coefficients equal zero at a given lag. Again the recommendation from this test is a model of either 3 or 4 lags. The results of the Wald test is summarized below: Table 4 Lag AVCLOSE100 CORP5 CORP15 CORP25 DOLLAR GOVT5 GOVT15 GOVT25 Joint Lag 1 [ 00000] [ 00000] [ 00000] [ 00000] [ 00000] [ 00000] [ 00000] [ 00000] [ 00000] Lag 2 [ ] [ ] [ ] [ ] [ 01345] [ ] [ 05298] [ ] [ 1.36e-13] Lag 3 [ ] [ ] [ ] [ ] [ 08200] [ ] [ ] [ ] [ 00362] Lag 4 [ ] [ ] [ ] [ ] [ ] [ ] [ ] [ ] [ 00629] Lag 5 [ ] [ ] [ ] [ ] [ 00652] [ ] [ ] [ ] [ ] Lag 6 [ ] [ ] [ ] [ ] [ 00660] [ ] [ ] [ ] [ 00244] Lag 7 [ 04455] [ ] [ ] [ ] [ ] [ ] [ ] [ ] [ 00602] Values in parentheses [] are p-values from Wald exclusion tests An interesting note here is that it seems that the Dollar variable is the variable driving preventing lag exclusion. This corroborates with the previous section where the recommended lag order for the Dollar in unit root tests was around 7 lags. 4.5 Cointegration Rank testing Given that this paper found a VAR model with an appropriate lag order to remove serial correlation in the residuals, a Cointegration rank test was then performed to test for the nature and number of cointegrating variables. Like the unit root tests in the earlier section, this test was performed on all types of unit-root process, and used both the trace and max-eigenvalue statistics for rank determination. These results are summarised below: Table 5 14

15 Data Trend: None None Linear Linear Quadratic Test Type No Intercept Intercept Intercept Intercept Intercept No Trend No Trend No Trend Trend Trend Trace Max-Eig Critical values based on MacKinnon-Haug-Michelis (1999) Given that none of the unit root tests in the earlier section suggested that any of the variables were quadratic processes in their levels, the final column of the table can be ignored. However all of the other columns in the table above contain important implications for this study. In the 7 lags model, no unit root specification other than the linear with trend and intercept terms causes either test to determine cointegration. This paper suggests that there is therefore no cointegrating relationships in this model, given the results found in the 7-lag tests, so this paper determined to use a VAR model. The VAR model used difference variables to achieve stationarity. The next section will outline the specification and results of the VAR model. 4.6 VAR with exogenous variables estimation Information criterion, AIC and FPE recommended 4 lags for this model. LM tests for autocorrelation were conducted, with the following results: Table 6 Lags LM-Stat Probability This model demonstrations no autocorrelation in the residuals at 4 lags, so this lag level was chosen for analysis. Table 7 Component Jarque-Bera test stat Degrees of freedom Prob. FTSE year Corp year Corp

16 25-year Corp Dollar/Sterling year Govt year Govt year Govt Joint This model retains the issues of heteroscedasticity and non-normal residuals, but satisfies the stability condition to allow for forecasting. This paper decided to correct residual estimates using Newey-west standard errors. Once the 4-lag model was specified, the objective was to judge the causal relationships between the endogenous variables in the system, and to conduct tests to determine the effects, if any, of the exogenous variables. The first type of analysis conducted was the granger causality/block Wald exogeneity tests. This is followed by brief interpretation of the lagged coefficients of the endogenous variables, with Wald tests for statistically significant relationships. This is then followed by the interpretation of impulse response functions. In order to determine the effects of the exogenous QE variables, Wald tests were conducted to test for significant effects, and dynamic multiplier functions were created to demonstrate the effects of these variables on the endogenous variables in the system. After this, structural break tests were conducted in order to determine whether QE changed any of the relationship dynamics during the sample. This analysis is then followed by a brief comparison of sub-sample periods and alternative exogenous variables. 5. Results 5.1 Granger Causality Below in table 8(A) is the coefficient estimates of the endogenous variables in the system after being estimated by OLS with Newey-West standard errors. Each column refers to the dependent variable and the value in each cell is the estimated lagged coefficient. All variables in the table are in their first differences. Superscript *, **, and *** refer to the statistical significance level of the F-tests for granger causality at 10%, 5%, and 1% levels respectively. Coefficients with significance levels of 5% or 1% are shown in italics for ease of interpretation. As an example, the first column seventh row denotes the effect of 5 years to maturity corporate bond yields lagged 3-periods on the FTSE100. As can be seen by the table, the effect is strongly negative and significant at the 1% level. Intuitively, an increase in the yields of corporate bonds with 5 years to maturity causes the value of FTSE100 stocks 16

17 to decrease, suggesting a positive relationship between the price of these bonds and the price of the FTSE. The FTSE also holds a negative relationship with the dollar exchange rate, when the dollar depreciates against sterling, the value of the FTSE decreases. 5-year corporate bonds yields hold strongly significant negative relationship with the price of the FTSE lagged one period, however they also have a positive relationship with the price level of the FTSE lagged by four periods. The 5-year yields also exhibit significant relationships with their government equivalents of 5 and 15 years to maturity as well as the dollar sterling exchange rate. Both the 15-year and 25-year corporate bond yields exhibit significant positive relationships with the yields of shorter maturities of both corporate and government bonds. Interestingly, corporate bonds of all maturities have significant negative relationships with the yields of 25-year government gilts, with an increase in these yields dropping corporate yields. This suggests a negative price relationship between extremely long-term government gilts and corporate bonds, potentially due to the substitutional nature of these asset types. All three of the government yield variables have a negative relationship with the price of the FTSE to at least the 5% significance level. This suggests a positive price relationship between the two types of assets. Government gilt yields also had significant negative relationships with the yields of short-term corporate yields, lending further evidence that these two asset categories were substitutes for one another in investor portfolios. An appreciation in the dollar is associated with decreasing government gilt yields and therefore increased gilt prices, this is in keeping with the other assets in the model which all exhibit negative relationships with the dollar exchange rate. Finally, it seems that the longer maturity government gilts were significantly negatively correlated with the yields of assets of 5-years to maturity. To further demonstrate the significance of these relationships tables 8(B)-(D) show the results of granger causality and Wald exogeneity tests over the entire sample. Each cell of Table 8(B) contains the relevant P-value of the granger causality test with values under 0.05 shown in italics to signify rejections of the null hypothesis of granger non-causality. Table 8(C) contains the P-values for the F- test statistics from Wald tests on the null hypothesis that the lagged coefficients of the independent equal zero. Table 8(D) contains the same p-values but from a chi-square distribution. Once again, values that reject the null hypothesis are stylised in italics for ease of interpretation. For Table 8(B) the most interesting results are those that find the 5 and 15 year maturity corporate bonds to be exogenous, only being significantly affected at below the 10% level by the FTSE price level and 5-year government gilt yields. This corresponds with the coefficients table, where only these variables have a statistically significant effect on more than 1 lag. The 25-year corporate yields are determined to be 17

18 granger caused its government gilt equivalent as well as the 5-year government and corporate bonds at the 10% level. All other variables in the system were found to not be granger exogenous at the 5% level, with the 3 government gilt yields especially responding to their corporate equivalents. It is interesting to note that the direction of causality tends to be from corporate bond yields to government bond yields rather than the other way around. The FTSE index only seems to granger cause the shortest maturities in the model, as well as the value of the dollar against sterling, with longer maturities being unaffected by the FTSE s price level. Short term bonds and gilts seem to exhibit the most significant granger causal relationships, effecting all variables except the dollar during the financial crisis period. The Wald-test p-values largely follow the conclusions found in the granger causality tests found in Table 8(B), with the key difference being the statistical significance of the longer term government gilts. The F-test results show that both the FTSE and the 15-year corporate yields show significant relationships at the 10% significance level, while the 15-year government gilt yields also have a significant relationship with it s corporate equivalent at the 10% level. The dollar exchange rate also has more statistically significant effects on the other variables in the model according to the F- tests, having statistically significant relationships at the 5% level with the 5-year government and corporate yields as well as the 15-year government yields. The results of the Granger tests suggest that short-term corporate bonds and, to a lesser extent, equity prices governed the price level of government gilts. The economic intuition here could be that investors made the decisions to sell bonds to the Bank only in order to capitalise in the equity and corporate bond markets. The behaviour between short-term gilts and bonds appear to be more bi-directional, suggesting that those who sold gilts would have primarily bought bonds of a similar maturity or others of a short-term to maturity. 5.2 Impulse Response Functions To further illustrate this analysis, this paper uses impulse response functions to illustrate the transmission of shocks to each variable. This paper elected to use the conventional orthogonalized impulses using a Cholesky decomposition, which is a very common method. The Cholesky ordering of variables for these impulses is frequently discussed as having significant effects on the response functions, however this paper found that re-arranging the order of the variables offered no significant changes to the results in the functions below. The shocks graphed from the impulse variable is a one standard deviation innovation with the confidence intervals being set at two asymptotic standard errors. Monte Carlo computed confidence intervals were also computed, but demonstrated no different implications in significance from the standard asymptotic standard errors. The responses 18

19 were graphed to 10 periods, by which time all of the responses for all variables have died out to zero. This suggests that shocks during the sample period were of a very short term nature, with most responses dying out after around 5 periods. Fig.1.1 shows the responses of the FTSE to the impulses from the other variables in the model. Corroborating with the expectations made from the granger causality tests, the major responses come from the 5-year corporate yield, the dollar exchange rate and from the 25-year government yield. The 5-year corporate yield impulse, which can be interpreted as a positive shock of one standard deviation to the yield, results in significant negative response from the FTSE after 4 periods. Intuitively, dropping 5-year corporate bond prices causes the FTSE price level to decrease around 4 periods later. The FTSE is also negatively affected by an appreciation of the dollar against the pound, where the effect is similar in magnitude but occurs much more rapidly, with the response settling down after just 4 periods. Finally, an impulse from the 25-year government gilt yield initially causes the FTSE price level to decrease after around 3 periods, however this situation reverses itself after 6 periods where the effect is equal and opposite. The entirety of the gilt yield effect is encompassed in 7 periods. Fig.1.2 shows the responses of the 5-year corporate bond, which is only significantly affected by the FTSE100 and the 5-year government yields. An increase in the FTSE causes a rapid spike in corporate bond yields, which decays rapidly to a small but significant negative reaction. This suggests that the FTSE price level increases cause corporate bond prices to decrease initially but then increase after 1 period, suggesting that investors substitute corporate bonds for equities when the latters value increases. The 5-year government gilt causes an initially positive reaction which decays after 2 periods. The 25-year government yields seem to have a small positive relationship with the 5-year corporate yields after 7 periods, but this also decays rapidly and cannot be considered significant. Fig.1.3 shows the responses of the 15-year corporate bond yields to the other variables, with the only significant responses are to the FTSE, 5-year corporate and government yields as well as the 25 government gilt yields. Both of the government yields cause negative responses from the 15-year corporate yield, with the 5-year s effect taking the longest at 5 periods to transmit a negative effect. A conclusion here is that investors seek to replace both long-term and relatively short-term government bonds with corporate bonds over the time period in question. The strongest response comes from the yields of the 5-year corporate bonds, which have significant positive relationship with the 15-year yields, but one that decays rapidly after just two periods. A much smaller but similar effect is caused by the FTSE, again suggesting that equities were viewed as substitutes to corporate bonds over the time period. 19

20 Fig year corporate yields have large positive responses to impulses from FTSE and the other corporate yields, all of which settle after 2-3 periods. The 5-year corporate yield impulse causes a small negative response after 3 periods, which again decays rapidly. Both the 5 and 25-year government yields cause small but significant negative responses, with the 5-year impulse taking 5 weeks to manifest in a negative yield reaction. Dollar responses, shown by Fig.1.5 are significant and positive to impulses from the short term corporate bond yields, and the FTSE100, both of which settle after at most 3 weeks. The 25-year yield impulse creates a small but significant and positive reaction from the dollar exchange rate, suggesting that sterling depreciates whenever long-term corporate bond yields increase. This is the opposite of the response from 5-year government gilts, where increased yields cause sterling to appreciate. Fig.1.6 shows the responses of the 5-year government gilt, where the only significant impulses are those generated by the FTSE and the 5-year corporate bond yields. Fig.1.7 shows that positive shocks to the FTSE, 5 and 15 year corporate bond yields, and the 5-year government yields cause significant positive responses from the 15-year government yield. All of these responses settle rapidly within three weeks. Fig.1.8 finally shows the responses of the 25-year government gilt yields. Of all the variables, the 25-year gilt yields show the most significant responses to impulse shocks. Impulses from the FTSE and the 5 and 15-year corporate yields cause positive rapid initial responses, with the FTSE and 5-year impulses causing small negative effects after 2 periods. This is similar in nature to the response to the 25-year corporate bond, although the negative effect is borderline insignificant. 25-year gilt yields respond to increasing gilt yields of shorter maturities positively, but these shocks die out before 4 weeks. 20

21 Table 8a FTSE100 5-Corp 15-Corp 25-Corp Dollar 5-Govt 15-Govt 25-Govt FTSE100(-1) FTSE100(-2) FTSE100(-3) FTSE100(-4) ** *** -7.59E-05*** -4.37E E *** -7.24E-05** -6.82E-05** E E E E-05*** 00104** 7.19E E E E E E E-05** -9.98E-05*** -5.63E-05** E-05*** 1.36E E E E-05** 3.98E E-05 5-Corp(-1) *** ** *** * * 5-Corp(-2) *** ** ** *** ** 5-Corp(-3) ** * * 5-Corp(-4) *** ** *** * ** 15-Corp(-1) ** Corp(-2) Corp(-3) ** Corp(-4) Corp(-1) ** Corp(-2) * * * * 25-Corp(-3) *** Corp(-4) Dollar(-1) *** *** *** ** Dollar(-2) ** ** * Dollar(-3) Dollar(-4) *** ** * Govt(-1) *** *** *** ** ** Govt(-2) 39344* * ** 5-Govt(-3) * Govt(-4) * *** *** * *** ** *** 15-Govt(-1) ** * Govt(-2) ** ** ** ** 15-Govt(-3) ** *** 15-Govt(-4) ** Govt(-1) * Govt(-2) * ** *** *** * *** *** 21