The Time Horizon of Price Responses to Quantitative Easing

Transcription

1 The Time Horizon of Price Responses to Quantitative Easing Harry Mamaysky May 20, 2016 Abstract Studies of how central bank quantitative easing (QE) policies affect asset prices typically look for effects either on the day, or within one or two days, of the QE announcement. Implicit in this methodology is the assumption that QE impacts different asset classes over an identical and short time horizon. To the contrary, we present strong evidence that QE announcements by the Federal Reserve, the European Central Bank, and the Bank of England impact the prices of different asset classes at different and often longer horizons. By restricting attention to a very short time window around QE announcements, the literature likely understates the effects of QE on asset classes that are less bond-like, which in turn leads to inappropriate conclusions about the effects of QE in securities markets. We show that while QE affects fixed income and currency markets over a short time horizon, it also has large effects on equity, volatility and credit markets when measured over a longer time period. Columbia Business School, hm2646@columbia.edu. The majority of this work was completed when Mamaysky worked in the Risk division of Citigroup. I thank Christopher Neely for valuable comments.

2 1 Introduction Since the financial crisis of 2008 and early-2009, central banks around the world have conducted monetary policy in large part via large scale asset purchases (LSAPs), also known as quantitative easing (QE). The effect of these on fixed income markets has received much attention with the general conclusion being that it has been large and immediate. QE effects on less bond-like markets, such as equities and implied volatilities, have received less attention, probably because the effects were found to be small. A general feature of this literature has been to look for QE effects in very short time periods, either intraday or in one to two days following QE announcements, with the implicit assumption being that because central bank policy announcements are very public and well-followed events, all impacted markets should incorporate the price implications of such announcements almost instantaneously. In this paper we present empirical evidence that this assumption and the focus on short-term effects that it engenders both lead to a mis-measurement of the effects of QE. In the traditional macro-finance story, QE works its way into prices through three main channels: liquidity, signaling, and portfolio balance. 1 The key question for us is whether the effect that each channel exerts on prices operates instantaneously or with a lag. This question has received little, if any, attention in the existing literature, and yet it is crucial for the proper identification of the effects of QE. We appeal to the asset pricing and market microstructure literatures to argue that capital constraints and informational frictions imply that each of these three channels is likely to affect certain asset classes with a lag. Therefore even a widely known event such as a central bank policy announcement may take time to get impounded into the price of some assets. In fact, central bank QE policies following the crisis provide a rare natural experiment in how markets process complex, though very public, data. When a central bank replaces long-term, illiquid securities with reserves, it drives down liquidity premia in the market. Lenders should then make riskier loans as the easy money from owning safe but illiquid securities is no longer available. Securities, such as MBS and agency debt, which were directly targeted by the Federal Reserve should have had large and 1 The names and subtleties of meaning vary slightly from author to author: liquidity, signaling, and portfolio balance (Gagnon et al. (2011a) and Neely (2012)); signaling, scarcity, and duration (D Amico et al. (2012)); signaling, duration, liquidity, safety, prepayment and default risk, and inflation (Krishnamurthy and Vissing- Jorgensen (2011)); preferred habitat (Modigliani and Sutch (1966,1967), Vayanos and Vila (2009)); among others. 1

3 immediate price moves, while less liquid credit instruments should be impacted over time as lenders take on additional credit risk. Likewise when a central bank credibly signals to the market its commitment to maintain accommodative short rates for a long period of time, discount rates fall and fixed income security prices rise. However the effect on asset classes with greater cash flow variability is ambiguous because of the endogeneity in the central bank s decision it chooses to maintain low rates because economic, and hence cash flow, prospects are poor, which should in turn help economic and cash flow prospects. If the central bank s assessment is a surprise, it may take investors some time to understand how other investors will interpret these two conflicting factors. The portfolio balance (or scarcity) channel encompasses either rational reallocation decisions as the supply of certain assets is reduced by the central bank, or a preferred habitat (or clientele) effect where natural holders of a given asset class are forced into another asset class because the risk-adjusted returns on the former are not sufficiently attractive. Either way, the effect of central bank buying is to force market participants to deviate from their pre-buying asset allocations. For example, pension funds which may have been content to hold riskless securities at a certain yield, may be forced to compensate in credit spreads for loss in riskless yield and thus buy riskier securities in order to meet return targets. As spreads tighten, asset allocation funds which may have been content with a conservative corporate bond to stock mix, may now be forced more into stocks. Due to a multitude of market and organizational frictions limited liquidity, decision making by consensus among multiple senior managers it is unlikely that such portfolio flows can take place quickly. The propagation of portfolio allocations from less to more risky assets therefore takes time. Each of these three effects liquidity, signaling, and portfolio balance takes time to fully work its way into all asset prices. For assets directly targeted by QE or those that are close and obvious substitutes, the effects of QE announcements should be instantaneous. For those securities where the impact relies on the workings of market mechanisms, the effect can take longer to show up. But if such effects can be anticipated, why don t agile market participants, such as hedge funds, step in and accelerate the process? To some extent, they do. However it is likely that hedge funds and similar actors do not have enough capital to make this process take place over the one or two-day window of most QE event studies. Furthermore, the ultimate direction of these effects for example the impact of signaling on cash flow risky securities is actually not a priori obvious, and market participants will need some time to settle into an equilibrium expectation for the direction of the effect. 2

4 There is a large literature on why arbitrageurs face various constraints that leave them unable to fully exploit pricing discrepancies that arise in markets (Shleifer and Vishny (1997) is a classic paper, and Gromb and Vayanos (2010) offer a current overview). Such constraints are likely to be binding when the quantity of assets subject to pricing discrepancies is particularly large, as was the case with QE. Therefore it is possible that there wasn t enough arbitrage capital in the market to sufficiently expedite the propagation of QE into risky asset classes over a one or two day time horizon, even if such effects were broadly anticipated. Though the underlying mechanism is likely different, it is interesting to note that the leadlag effects identifies by Lo and MacKinlay (1990) have a direct analogue in our analysis: one security reacts first, another related security reacts to the same news but with a lag. Lo and MacKinlay find that large stocks tend to lead small stocks in the same industry: presumably important news that affects a given sector of the economy is first reflected in large companies because analysts write their reports about these companies first and is only later reflected in the prices of similar, but smaller companies. Stocks and bonds are equally well followed by the Wall Street analyst community, but bonds are much more obviously impacted by QE, so there may be another type of lead-lag effect across the obviously versus less-obviously impacted (as opposed to large versus small) dimension. The Hong and Stein (1999) behavioral theory for momentum has implications for how QE announcements are incorporated into prices of less bond-like securities. Assume that the effect of surprise QE announcements on cash flow risky securities is not obvious at first but will ultimately be seen by analysts as supportive to asset prices this is analogous to the slowly released public information in the Hong and Stein model. The under-reaction to news by shortsighted news watchers in our case market analysts who are unable to come to an immediate conclusion about QE effects on less bond-like securities leaves profitable trading opportunities for momentum traders who then enter the market, leading to short-term momentum and longterm overshooting of fundamental value. Perhaps he had in mind something similar to this when David Tepper, a well-known hedge fund manager, said: So that s definitely sort of going to be a push-up to markets... Generally speaking, markets will go up, [because] my basic belief has been when you have large (quantitative easing), markets go up. 2 Short-term momentum implies that QE effects on stocks, implied volatilities, and credit (the 2 Tepper: No taper for long time to push up stocks, CNBC, Tuesday, October 15, cnbc.com/id/

5 cash flow risky securities) must occur over a longer time frame than one or two days after the policy announcement. Recent work by Greenwood, Hanson, and Liao (2016) shows how these three themes interact in a multi-asset market hit by a supply shock: Frictions, in the form of partially segmented markets with slow moving capital, impede the transmission of a supply shock in the primary market to prices in the secondary market; price dynamics in such a setting are characterized both by lead-lag effects, as well as short-term momentum with longer-run reversals. The key assumption generating such effects is that specialists in a particular market (for example, Treasury investors) react to Treasury supply shocks very quickly, but transmission of those shocks to a secondary market (for example, credit) needs to happen via capital flows from generalists, which occurs slowly. This description very closely matches what may have occurred during QE, as the targeted markets reacted very quickly, but slow capital flows caused secondary markets to react with a lag. Our empirical work relies heavily on Fawley and Neely (2013), who identify important QE announcements by the Federal Reserve (Fed), the European Central Bank (ECB), and the Bank of England from early 2008 to late For the most part, these announcements represented ever increasing amounts of quantitative easing; so our expectation is that the prices of targeted and related securities would rise as a consequence. 3 Using the Fawley and Neely announcements, we first verify the results of prior studies that over a short time window around QE announcements one day before and one day after the event QE effects are large for fixed income markets and currencies, and are small for equities and implied volatilities. Furthermore, we show that similar effects to those found for Fed announcements in US markets apply for ECB and Bank of England announcements in European and UK markets respectively. We bootstrap announcement dates to verify the statistical significance of these results. We then extend the horizon over which we calculate QE effects up to 21 business days after the policy announcement. By looking for the post-event horizon over which a given security s QE response is most statistically significant, we identify a security s natural response horizon to quantitative easing. We adjust our inference procedure for this selection criterion to insure that these maximally significant post-event horizons are indeed statistically meaningful. We show that even asset classes for example, US and European credit indexes with a significant one day response to QE may have maximal response horizons that are longer. 3 See the discussion in Tables 1A, 1B, and 1C in the Fawley and Neely paper. Consideration of QE withdrawal would not begin until 2013, a time period which is not covered in our analysis. The term QE announcement, as used in this paper, will therefore imply an increase in accommodation via quantitative easing programs. 4

6 We demonstrate that the horizon of central bank policy effects involves two time scales: the one or two-day time scale of the existing literature applies to currencies and relatively riskless, fixed income instruments, many of which were directly targeted by central banks; and a longer time scale of between 5 to 20 business days following central bank announcements over which QE affected cash flow risky securities such as stocks, equity implied volatilities (vols), and credit products. Over these longer time horizons, QE effects on spreads, equities, and equity vols are economically very large. In the US, UK, and Europe stock returns that are directly attributable to QE announcements are between 10% to 40%. QE announcements contributed to drops in implied volatilities between 30 and 70 points, and contributed to a tightening of investment grade (high yield) spreads of between 45 (370) and 140 (540) basis points. These effects are far larger than those identified in the extant event studies because these have not focused on the appropriate response horizons for this set of securities. The existing literature s mis-measurement of the effects of QE on risky asset prices may have caused policy makers to underestimate the effects their decisions have had in markets. The rest of the paper proceeds as follows. Section 2 is a brief survey of the literature on QE. Section 3 discusses the data set. Section 4 presents the methodology of the event study, and results for security performance over a subset of event horizons across the three different central banks. Section 5 presents the results of a bootstrap analysis to determine the time horizon at which announcement effects on a given security are maximally significant. Section 5.3 shows the maximal response time horizons aggregated by asset class. Section 6 uses a regression analysis to check the robustness of the previous results. Section 7 concludes. All tables and figures are contained in the Appendix. 2 Literature Review A voluminous literature is devoted to the market and economic effects of central bank policy. The majority of recent work on policy responses to the financial crisis focuses on either the real economic effects of central bank policy, or on its impact on fixed income markets in a short time window. Much less attention is paid to the effects on other markets (e.g. equities) or to the time horizon over which different asset classes are impacted. Stock and Flow Effects. This literature estimates the relationship between the amount of 5

7 debt that exists in various maturity buckets, or in aggregate, and how this debt is priced. If such a relationship exists, then central banks can affect long-term interest rates by targeting the outstanding stock of debt in the appropriate maturity bucket. D Amico et al. (2012) discuss three channels via which LSAP policies might affect asset prices: (1) signaling (or expectations), (2) scarcity, and (3) duration. The authors calculate the fraction of Treasuries within given maturity buckets that are held by private investors, as well as a normalized measure of aggregate duration in the Treasury market. Using pre-crisis data from December 2002 until October 2008, they show that both the scarcity (measured as the fraction of private ownership) and duration effects are positive (i.e. more private ownership or more duration risk lead to higher rates) and significant. They then show that these effects are nearly as large for the term premium component of nominal rates as for the rates themselves and thus argue that the transmission mechanism goes through the scarcity and duration channels rather than through a signaling effect. Decomposition of the nominal term premium into a real and inflation component shows that the scarcity and duration effects operate mostly through the real term premium. Using the out-of-sample scarcity and duration sensitivities, the paper estimates that the effect of LSAP I (QE1) on 5-10yr Treasuries was 35 basis points (23 from scarcity and 12 from duration), and the effect of LSAP II (QE2) was 45 basis points (35 from scarcity and 10 from duration). Other papers include D Amico and King (2013), Krishnamurthy and Vissing-Jorgensen (2012), and Gagnon et al. (2011a) which is also an event study. Estimates of the effects of individual LSAP programs on intermediate maturity Treasuries tend to be in the range of basis points. Greenwood and Vayanos (2012) and Modigliani and Sutch (1966,1967) look at how the amount outstanding and composition of government debt affect prices, though not in a QE context. Warnock and Warnock (2009) study the effect of international capital flows on Treasury pricing. Event Studies. Other papers analyze the effects of LSAPs by looking at price responses either intraday or in 1 or 2-day windows around policy announcements. Swanson (2011) looks at the effect from the 1961 Operation Twist conducted by the Fed and the Treasury. Gagnon et al. (2011a) study the Fed s LSAP policies through early 2010 (QE1). Krishnamurthy and Vissing- Jorgensen (2011) use an event study methodology to look at behavior of rates and spreads in response to QE1 and QE2 Fed announcements. Neely (2012) studies Fed quantitative easing announcements from late-2008 to early-2009 (QE1) and documents that QE1 announcements 6

8 (measured in one-day windows) had a large, negative effect on US and foreign long-term bond yields, had a negligible effect on overnight rates in the US and internationally, and had a negative effect on the US dollar. Bauer and Neely (2013) study the effects of the Fed s QE1 on the term structure of government yields in the US, Canada, Australia, Germany, and Japan. Event studies typically find larger effects than the stock and flow literature, with estimates of Treasury and MBS yield impacts between 70 and 150 basis points (with the largest effect being 180 basis points for ten-year US inflation protected yields from QE1). Another key finding is that the security class that is being targeted by QE has an important effect on which yields are impacted, with Treasury bond purchases affecting Treasury and agency yields, 4 and MBS purchases affecting credit sensitive products. Equities and Currencies. Bernanke and Kuttner (2005) find that a 25 basis point unexpected fall in Fed funds rate translates to a 1% increase in stock indexes. Stehn and Weisberger (2013) confirm this finding, and also show that an unexpected 25 basis point fall in the ten-year Treasury leads to a 1% increase in S&P500 in a one hour window around the Federal Open Market Committee (FOMC) announcement. Hooper, Slok, and Luzzetti (2013) document that QE3 had a significant (at the 85% level) and positive effect of 2% 4% on US and international stock markets over a seven day window centered on the announcement date. Neely (2012) argues that a positive correlation between real stock and bond returns implies a substitution effect where a reduction in supply of Treasuries pushes investors into stocks thereby raising the valuation of the latter. In a very interesting study and one whose results share a similar flavor to ours in that central bank policy has a very large effect on equity prices Lucca and Moench (2012) document that from 1994 to 2011, 80% of the US equity premium has occured in the 24-hour window before FOMC announcements. They also document that pre-fomc returns are higher in periods of easing (i.e. during recessions) than in period of contraction. Among several explanations for this anomaly, they cite the possibility that investors are rationally inattentive, that is they allocate limited computational resources to the most pressing task at hand, and therefore only begin to focus on Fed policy immediately prior to the actual announcements. Glick and Leduc (2013), an event study focused on half-hour windows around Fed LSAP announcements, documents that these have had a negative effect on the trade-weighted US 4 For example, see the discussion of events surrounding the August 10, 2010 Federal Open Market Committee (FOMC) announcement in D Amico et al. (2012). They find that Treasury maturities directly targeted by Fed purchases experienced larger price moves than Treasuries with similar, but longer, maturities that were not targeted. 7

9 dollar. Rosa (2012) uses Financial Times (FT) articles before and after Fed QE announcements to identify the surprise component of the announcement, and shows that the effects of these surprises on asset prices (in 5 minutes pre- and 25 minutes post-event windows) are similar in magnitude to the effects of unanticipated cuts in the Fed funds target rate. Rosa finds that an unanticipated dovish Fed QE announcement results in a half-hour decline in five-year Treasury yields of 9 basis points, a stock price increase of 0.9%, and a depreciation of the US dollar of about 1% versus other major currencies. In the UK, Rosa finds an unanticipated dovish QE announcement raises gilt prices, causes the British pound to deteriorate against other currencies, but does not have an effect of stock prices. Real Economic Effects. Previous research (Bernanke (2011) and Chung, Laforte, Reifschneider, and Williams (2012)) suggests that a 25 basis point change in the ten-year Treasury rate is associated with a 100 basis point change in the fed funds rate. Rudebusch (2010) finds that a basis point change in long-term interest rates has four times the effect on output as a basis point change in short-term interest rates. These results suggest a 100 basis point effect on long-term rates (consistent with estimates from event studies) yields economic effects similar to a 400 basis point rate cut. However, the real economic effects of QE have been estimated to be small. Chen, Curdia, and Ferrero (2011) study the effects of QE2 s $600 billion in Treasury purchases on GDP and inflation. In their model simulations, QE2 leads to a persistent increase in the level of GDP of less than half a percentage point and to a very small increase in inflation. Williams (2012) and Chung et al. (2012) report that, using the Federal Reserve Board s largescale macroeconomic model, the effect of QE2 was to lower unemployment by 0.3 percent, to raise GDP by less than half a percentage point, and to raise inflation by 20 basis points. They estimate that the combined effects of QE1 and QE2 ($2,325 billion of purchases) may have lowered unemployment by one and a half percentage points. Fuhrer and Olivei (2011) report that several models suggest a two-year effect on GDP growth rates of two- to four-times the size of an immediate reduction in ten-year Treasury rates (i.e. 100 bps in ten-year rates translates to a 2 4% increase in GDP over two years). They also report that a one percent increase in GDP growth above trend for one quarter leads to a one eighth percentage point drop in unemployment. Using these relationships, they estimate that QE2 s potential 20-30bps effect on ten-year rates led to a two year increase in GDP of % and a drop in the unemployment rate of %. 8

10 3 Data Table 1 lists the QE announcements under consideration for the Fed, ECB, and Bank of England. These events are from Fawley and Neely (2013), which also contains a detailed discussion of the timeline of the economic events that led to these central bank responses. Events are further classified into event subgroups (e.g. QE1, QE2, Twist, and QE3 for the Fed). We use the Fawley and Neely abbreviations for sub-groupings throughout, though our main results on time horizons are aggregated across all subgroups. For the Fed, we reclassified August 10, 2010 as belonging to QE2 rather than QE1 as in their paper, and otherwise made no changes to the Fawley and Neely classification or date selection. There were nine ECB events, eleven Bank of England events, and twenty Fed events. For each central bank, we define a set of domestic securities to study, ranging from fixed income to currency to equity and volatility markets. 5 For equities and currencies, we report continuously compounded returns excluding dividends and carry differentials. 6 For fixed income and volatility markets, we report changes in yield and implied volatilities, respectively, excluding coupon payments. The returns or price changes of the securities under consideration are then decomposed into their event and non-event window performance, and aggregated within subgroups and over the entire sample. We define our sample period for each central bank as starting two business days prior to the first event in Table 1 and ending twenty one business days after the final event date. These dates are chosen to accommodate the pre- and post-event windows that will be discussed later. 7 Tables 2, 3, and 4 summarize the securities set and the performance of those securities over the entire sample period. All price data are from Bloomberg. 4 Event Study Methodology Rather than using one or two day windows around quantitative easing announcements, we focus on event windows of variable lengths, parametrized by the number of business days prior to 5 We can also study the transmission effects of central bank policies on foreign markets, but this takes us too far from the main point of this paper. 6 Outside of a sharp spike during the equity sell-off of late-2008, dividend yields were roughly constant during the sample period, therefore including dividends will not impact our results on decomposing equity returns into QE and non-qe windows. 7 We exclude weekends and local market holidays (for European securities, UK and German holidays are used). Holiday calendars are obtained from the RQuantLib package in R. 9

11 (Npre = {1, 2}) 8 and after (Npost = {0,..., 21}) an event. 9 Gaps between event windows are classified as non-event windows. The sample periods for the Fed, ECB, and Bank of England are defined as the first event date minus max(npre) and the last event date plus max(npost). Each event window is associated with three dates: the window start date, the event date, and the window end date (though some of these may be the same, for example the event date may also be the window end date). Furthermore event windows are defined to be non-overlapping. Figure 1 summarizes the methodology. Should consecutive event windows overlap, the following rules are used to resolve the situation: (1) if a start date of a window is before the event date of the prior window, set the start date to the prior event date, and (2) if an end date occurs after the start date of the following window, set the end date to the following start date. Note that this classification scheme matters for allocating performance to specific announcements (e.g. whether a given day s return is part of event window 1 or 2), but will have no effect on the overall security performance over all event windows in the sample (i.e. since performance is aggregated across all of the non-overlapping event windows). For example, for the first Fed QE event in our sample, Tuesday, November 25, 2008, the window with Npre = 1 and Npost = 0 would run from day end on Monday, November 24 to day end of Tuesday, November 25, and the window with Npre = 2 and Npost = 3 would run from day end Friday, November 21 to day end of Monday, December 1 (November 27, 2008 was Thanksgiving). However, there is another QE event on Monday, December 1, 2008 whose event window starts on Wednesday, November 26, which results in an overlap. rule described above therefore yields two event windows, one from Friday, November 21 to Wednesday, November 26, and another from Wednesday, November 26 to Thursday, December 4. This procedure decomposes the time period of an event study into two, non-overlapping sets: event and non-event days. Adding up the price response of a security over these two sets will yield the total change in the security price over the entire event study. 10 The We will refer to the sum of security returns or changes in level in all the event windows as the aggregate response of the security to QE announcements. Letting r i (time 1, time 2 ) denote the return or change in 8 Lucca and Moench (2012) suggest that an anticipatory reaction by the market has been a general feature of Fed monetary policy announcements since Therefore we allow for the possibility of a response starting two days prior to the announcement. 9 In a slight abuse of notation we will use Npre and Npost to refer to either the set of all possible pre- and post-event windows, or to a specific window choice. The usage will always be clear from the context. 10 Our use of continuously compounded returns makes everything additive. 10

12 level of security i from day time 1 to time 2 the aggregate response is defined by AG i (Npre, Npost) r i (W indowstart e, W indowend e ), (1) e Events where if event e occurs on day t, we will typically have W indowstart e = t Npre and W indowend e = t + Npost except when successive event windows overlap, in which case the rules described above will be used. Note that the aggregate response is a function of the window size. Later when we look for the maximally significant response, this will involve searching over Npost {0,..., 21} such that the associated AG i (Npre, Npost) has a p-value furthest away from 0.5. This is discussed in Section 5. The aggregate response over the full sample is simply AG i (all) r i (Start of Sample, End of Sample). 4.1 Inner Bootstrap To understand whether responses around announcement dates are in any sense unusual, we compare them to responses around randomly drawn dates from our sample period (shown in Tables 2, 3, and 4). For example, for the Fed (see Table 1) QE announcements consist of twenty events, across four groups: QE1, QE2, Twist, and QE3. To bootstrap security performance, we randomly pick without replacement twenty dates over the sample period. These dates can include both the QE and non-qe dates and must fall on or after (before) the first (last) QE announcement date. The dates are then sorted and classified into the event subgroups, thereby preserving temporal order (in the sense that the first eight events are always called QE1, the next seven are called QE2, and so on). This generates one draw of returns for each security for a given N pre, N post window. Running this procedure 2500 times generates a benchmark distribution of returns for each security in each event window. For each security i and for Npre = 1, 2, we compare AG i (Npre, Npost) to this distribution to generate a collection of one-sided p-values indexed by Npost: {p i,npre 0, p i,npre 1,..., p i,npre 21 }, though we suppress the superscript in our discussions. The procedure is repeated for ECB and Bank of England announcements. These p-values are computed in each subgroup (e.g. QE1, QE2, Twist, QE3 for the Fed) and over the whole sample. We refer to this as the inner bootstrap to differentiate it from the outer bootstrap that is 11

13 discussed in Section 5.1, and which is used to account for selection bias in finding the post-event time horizon with the most significant price response. We use one-sided p-values because the hypothesis we are interested in testing is whether QE announcements (see Footnote 3) did or did not meaningfully raise security prices over a given time horizon. 4.2 Potential Bias Because the QE events in Fawley and Neely (2013) were identified after the fact, it is possible that these particular events were chosen because they resulted in large price moves, which therefore made people believe that these were important central bank announcements. However, it is also possible that certain announcements that shaped the market s expectation about central bank policy and therefore had price effects were not identified by Fawley and Neely. It is hard to know which of these effects dominates, or whether they tend to cancel out. 4.3 Results Table 5 shows the change or return in the US securities set in response to Fed QE announcements in a window with Npre = 1 and Npost = 1, which is the event window most similar to the existing literature. Each row shows the changes/returns for a given security for a particular subset of events (e.g. QE1). The bottom two rows show the response aggregated across all event subgroups, as well as the response in the non-event windows (see Figure 1). The sum of the response over event and non-event windows adds up to the aggregate change in the entire sample period that is shown in Table 2 and therefore represents the decomposition of security returns/changes into those occurring around Fed QE announcements and those occurring outside of these windows. One-sided p-values, computed using the bootstrap methodology described in Section 4.1, are shown in parentheses. For example, 2-day windows around Fed QE events represent a total of 40 days (see the days column) and the non-event windows represent 998 days, for a sample total of 1038 days. In two-day windows around QE events, the S&P 500 index fell 3.4% continuously compounded, and increased 64.3% in the remainder of the sample for a full sample return of 60.9%. The p-value of 0.26 for the S&P500 response to QE announcements means that 26% of all randomly drawn dates resulted in returns lower than 3.4% suggesting that two-day S&P500 returns 12

14 around QE announcements are not particularly unusual relative to any other 20 day period in the sample. On the other hand, we see that five-year Treasury yields fell basis points around Fed QE events, rose 4.5 basis points in the non-event windows (for a full sample fall of basis points), and the p-value on the QE response is 0.00 suggesting that it is highly significant. Tables 6 and 7 show the analogous data for ECB and Bank of England QE announcements. It is interesting to note that in Europe, German Bund yields reacted to QE by rising, rather than falling as Treasury and UK gilt yields did. This is likely because the Fed and the Bank of England targeted their domestic bond markets with their QE policies, whereas in Europe the ECB targeted tight credit conditions for its banking sector, as well as its fragile peripheral sovereign debt markets. Therefore QE policies in Europe, when they worked, served to alleviate market stress, a consequence of which was that Bunds sold off. Indeed, Bunds rallied meaningfully in the overall sample as ten-year Bund yields fell in non-event windows, but rose 58.6 basis points in two-day windows around ECB QE announcements. Because the focus of much of the ECB QE response was meant to address market concerns about credit worthiness of peripheral countries, we would expect to see large responses of sovereign credit spreads. As Table 6 shows, sovereign spreads of Italy, Spain, and Portugal (as proxied by the CDS market) tightened quickly and significantly in response to the Securities Market Programme (SMP) and outright monetary transactions (OMT) announcements We document a large negative response from the front WTI futures contract (Oil) to Fed QE announcements suggesting a short-term negative signal about the state of the economy, though this effect tends towards zero over a longer post-event horizon. This is one reason why QE announcements have an ambiguous short-term effect on cash flow risky securities: this negative signal interacts with the positive effects of easier monetary policy in a non-obvious way. Other notable features of the data include: a lack of two-day response of either 3 month T-bills or Bubills in Germany suggesting that the zero interest rate bound was already in place at the time that QE started; the large negative effect on the dollar and pound; the large positive effect on the euro (again arising out of a lessening of Euro-crisis risk); a large and significant tightening in the US investment grade CDS index, in the European investment grade and high yield CDS indexes, though not in US high yield CDS, which saw a small but not significant widening; and the lack of a meaningful implied equity vol response (for VIX, VSTOXX, and 13

15 VFTSE), 11 though there was a large fall in VFTSE when we look at 2-day before and 1-day after windows. Generally, we find results consistent with the existing literature, which also tends to focus on very short windows around QE announcement dates. 12 Notice that in short time windows, we do not find meaningful equity or equity volatility effects from QE announcements. 5 Maximally Significant Event Horizon To understand the time horizon over which QE announcements have the most pronounced effect on a given security, we ask over which post-event horizon is that security s price response to QE most significant. This methodology is cause agnostic, in the sense that it does not rely on any specific mechanism underlying the delayed response to QE. By finding the time horizon over which a given security s response to QE announcements is least likely to have been caused simply by chance which may or may not be the one or two day window around QE announcements that is typical in existing studies we are able to measure the most likely price effect of QE on that security. For Npre = {1, 2}, this involves finding the Npost {0, 1, 3,..., 19, 21} 13 which yields an inner bootstrap p-value furthest away from 0.5. We refer to this as Npost, the maximal event horizon. Unfortunately this methodology sometimes resulted in different bootstrap runs yielding different answers. For example, if the two post-event horizons with the highest p-values were one and eleven days after the event, with Npost = 1 having a p-value of 0.9 and Npost = 11 having p-value of 0.89 therefore suggesting one-day after the event as the maximal horizon a different run of the bootstrap could reverse the ranking if the respective p-values were 0.89 and 0.9. To make the maximal event horizon more robust across different bootstrap runs, we changed our definition to average p-values over three adjacent horizons, assigning the middle N post as the maximal one, i.e. Npost would be maximal if the average p-value from Npost 2, Npost, Npost + 2 was the furthest away from 0.5 across all choices of Npost. We found this procedure to be extremely robust across different bootstrap runs. 11 VIX, VSTOXX, and VFTSE are, respectively, indexes for near-term implied volatilities for the S&P500, Euro Stoxx 50, and FTSE 100 stock market indexes. 12 Results are available for all Npre Npost combinations but are not included to save space, and can be obtained from the author upon request. 13 We look at odd-numbered horizons to conserve computational time this does not impact the results. 14

16 Let us refer to this average p-value as the maximal p-value, and let us write it as p. Then Npost = arg max Npost=1,...,19 (p Npost 2 + p Npost + p Npost+2 )/3 0.5, p = (p Npost 2 + p Npost + p Npost +2)/3 (2) where p N is the inner bootstrap p-value generated for each post-event horizon as described in Section 4.1, with the i and N pre superscripts suppressed to avoid clutter. To reiterate: we are not after the time-horizon following the event over which the aggregate response is the largest rather we are after the time-horizon over which the aggregate response is most statistically atypical. Once we find the latter, we can then measure the former. 5.1 Outer Bootstrap It is clear that p is biased away from 0.5 by the selection criterion therefore inferences based on p would overstate the significance of our results. To account for this bias, we perform an outer bootstrap where we sample maximal p-values from our selection procedure under the null hypothesis that the QE event dates are, in fact, randomly chosen. Say the inner bootstrap generates 2500 draws of security returns/changes for each {N pre, N post} pair. For each draw of the outer bootstrap, we will select without replacement a number of dates corresponding to the number of events in our sample (e.g. twenty for the case of Fed QE) following the procedure of Section 4.1. We will then compute the aggregate security returns/changes for this set of randomly drawn dates for each {Npre, Npost} pair. For a given Npre we will compute the percentage of the inner bootstrap draws at each value of Npost which are smaller than the outer bootstrap return/change. This yields N post p-values, out of which we select the one which is furthest from 0.5 using the averaging methodology from equation (2). Repeating the outer bootstrap M times will give us M draws of this maximal p-value. Note that throughout the outer bootstrap draws, the inner bootstrap draws remain fixed. This greatly reduces the dimensionality of the outer bootstrap (otherwise each of the M outer bootstrap draws would have to resample the full 2500 inner bootstrap draws). Our procedure should produce the correct inference assuming the inner bootstrap produces a sufficiently sampled set of random returns. Given an Npre, let us label the the maximal p-value draws from the outer bootstrap as as p (m) for m 1,..., M. Then the outer bootstrap p-value which adjusts for the selection 15

17 criterion is given by p O M m=1 1[ p (m) < p ]. (3) M In our analysis we set M = Results Figures 2, 3, and 4 show the cumulative price response (change or return) of each security over all Fed, ECB, and Bank of England QE announcements. The x-axis shows N post, the post-event horizon (in days) over which a given cumulative response is calculated. The blue line shows cumulative responses for Npre = 1 and the red, dashed line shows the cumulative responses for N pre = 2. Two circles around a point indicate that the response is statistically significant at the 10% level (using a one-sided p-value obtained via the methodology in Section 4.1), and three circles around a point indicate the response is significant at the 5% level. Though it is unusual, in some cases (e.g. oil and gold around Fed announcements) the sign of the maximal effect changes depending on the Npost horizon (see Figure 2). Tables 8, 9, and 10 show summary data from the charts. For each security, for both 1-day before (Npre = 1, left columns) and 2-day before (Npre = 2, right columns) windows, we show the time horizon Npost over which the cumulative security response to QE announcements achieves its maximal p-value p (computed using the methodology in equation (2)). The outer bootstrap p-value p O, from equation (3), which adjusts for the selection criterion, is also shown. The right-most column in the tables show the cumulative response of the security over the entire sample window, and matches the value given in Tables 2, 3, and 4 which summarize the data. For example, Table 8 shows that for S&P500 the 1-day prior to announcement window that has the maximal p-value is 13 days after the event (Figure 5 details the S&P500 response). This window, with Npre = 1 and Npost = 13 has a p-value of 0.767, an outer p-value of 0.610, and the continuous return of S&P500 in these 14 business day windows around Fed QE announcements was 24.9%, i.e. AG SP 500 (1, 13) from (1) is 24.9% and AG SP 500 (all) = 60.88%. The maximal p-value of for windows with Npre = 2 occurs at Npost = 13; it has an outer p-value of In these 15 day windows around Fed QE announcements, the S&P500 index is up 39.77%. This compares to a price change of 60.88% over the entire sample window. These 15 day windows around Fed QE announcements therefore represent two thirds (39.77/60.88) of the 16

18 S&P500 price change from late-2008 to early-2013, suggesting that Fed QE announcements may have had a large impact on stock prices. This stands in stark contrast to the two-day window (Npre = 1 and Npost = 1) results shown in Table 5 of S&P500 being down 3.4%. Furthermore, the outer p-value of suggests that this response was significant at the 13% level when adjusting for selection bias. Stocks and Volatilities In the US, S&P500 and VIX react to Fed QE announcements at a maximally significant lag of 13 days. Aggregate responses of both are large, and significant when looking at Npre = 2. In the 2-day prior to event windows, the S&P500 is up 39.77% (out of total 60.88% full sample return) and VIX is down points (out of total point drop in the full sample). As Figure 2 shows, both responses grow as the event horizon increases. Perhaps because the market perceived QE as being particularly beneficial for financials, the effect on the financial sector ETF, XLF, is maximal on day 5 after the announcement. The Npre = 2, Npost = 5 price response is 54.64% vs 56.67% for the entire sample with p O = 95%, and Figure 2 suggests this response was persistent. In Europe, the maximal horizon for the Euro Stoxx 50 Index (see Figure 6) and VSTOXX is 15 days for both 1- and 2-day prior to event windows. All effects are extraordinarily large and significant, with p-values close to 1 and 0 respectively and outer p-values all significant at 8% or better. For Euro Stoxx 50, the aggregate response is a gain of roughly 32% around ECB QE announcements versus a fall of 35.5% in the full sample for a differential between the event and non-event windows of 67.5%! For the VSTOXX volatility index in the event windows we see a drop of approximately 70 vol points, versus a drop of 8 points in the overall sample, representing a large difference of approximately 60 points. The UK results have maximal event horizons 5 days after the event for the FTSE 100 index (see Figure 7) and 13 days for VFTSE. Stock and vol aggregate responses are large and significant (except for FTSE day prior to the event), with the majority (or more in the case of VFTSE) of the full sample change occurring in the event windows. 17

19 Rates and Currencies The maximal post-event response window is 1 day for five-, ten-, and thirty-year Treasuries (and 9 days for thirty-year Treasuries with a 2-day pre-event window). The 10 year and 30 year inflation breakeven (i.e. the difference in yields between nominal and inflation protected treasuries) maximal response horizon is 1 day (17 in the case of 30 year break-evens though early responses are also significant as can be seen in Figure 2). The dollar experiences a large drop (of either 7.12% for Npre = 1 or 15.54% for Npre = 2) with a response horizon of 1 days. The size of the responses is large and significant (for Npre = 2) as has been documented in prior work. In Europe, the maximal response horizon for ten- and thirty-year German Bunds (yields rise between 60 and 100 basis points) is 1 day post the event. For the euro (a 5% rise) the maximal horizon is 13 days post the event, though the response is not significant. Both 3 month T-bills and German Bubills have a somewhat longer maximal response horizon of 7 11 days, though the effect on T-bills is small. It is not clear why Bubills had a delayed response relative to Bunds. In the UK, the maximal response window for one-year gilts is 1 day, for ten-year gilts is 7 days, and for thirty-year gilts is 1 (Npre = 1) or 13 (Npre = 11) days. Breakeven maximal responses happen over 5 7 days post the event. And the maximal effect on the pound, a highly significant 9.73% 13.64% fall similar to the dollar s response to Fed QE, happens over a 1 3 day post-event window. Credit Spreads In the US, the maximal horizon is 1 5 days for the investment grade index and a stock-like 9 13 days for the high yield CDS index (though the response is not significant for high yield: for example with Npre = 1, the basis points is very large, but with p O = not significant, which shows the ability of the bootstrap to differentiate between large and atypical). As Figure 2 shows, the size of the response grows as the event horizon increases (almost monotonically over the full 21-day post-event period considered). This behavior is qualitatively closer to the equity and equity vol response, which also increases roughly monotonically with the event horizon, and is different from the behavior of rates, where the response attenuates with the passage of time. In Europe, the maximal response horizon for both the European investment grade and high yield CDS indexes is days, with large and significant effects. The European CDS indexes 18

20 have a similar, monotonic response to ECB QE announcements as do the Euro Stoxx 50 and VS- TOXX indexes. The sovereign CDS spreads of Italy, Spain, and Portugal mostly have maximal response horizons of either 1 or 3 days, with very large and highly significant effects reflecting the fact that much of the ECB QE directly targeted peripheral bond markets. In the UK, there is no direct credit market proxy. UK sovereign CDS widened at a maximal response horizon of 7 days post Bank of England QE announcements, however the effect was short-lived, not persistent (close to zero for Npost = 21 as Figure 4 shows), and not significant. 5.3 Maximal Response by Asset Class Figures 8 and 9 summarize our results on maximal response horizons. We divide all securities in our study into six asset classes: rates, currencies, inflation markets (i.e. break-evens), commodities, credit, and equities (which also contains implied vols). The charts show the maximal response horizon Npost (in days after the event) for each asset class on the x-axis with the outer bootstrap p-value p O on the y-axis. Only those securities with results at the 15% level or better are shown (i.e. ones where there is no evidence of a significant maximal response are excluded). There are two charts, one for Npre = 1 and one for Npre = 2. The more bond-like securities (such as fixed income and currencies) tend to have shorter maximal response horizons relative to the less bond-like securities (credit, proxied by CDS spreads, and equities along with implied vols). Tables 11 and 12 make this observation explicit by calculating the average post-event maximal horizon within each asset class at the 10% and 15% level of significance. Securities whose maximal horizons are not statistically significant are not included in the tables. The results argue strongly that bond-like securities have much lower maximal response horizons, of 1 to 3 days, versus credit at 4 to 6 days, and equities and equity implied vols of 10 to 14 days. 5.4 Interpretation The evidence suggests that those markets (Treasuries, gilts, sovereign spreads) that were directly targeted by central banks experienced the effects of QE announcement immediately. Because currencies respond so directly to funding rates, QE effects on currencies were also largely immediate. 19