(d) Quantitative empirical evidence
1743 Professor Putnins also provided his own quantitative empirical analysis.
1744 He gave evidence that a large number of empirical studies have analysed how prices respond to trading and have quantified price impact functions. It is said that these studies consistently find support for the notion that trades have price impact, with buying causing prices to increase and vice versa. Such empirical studies have established various empirical features of price impact. For example, larger trades both in absolute volume and as a proportion of daily volume have larger price impact but at a diminishing rate, price impacts have temporary and permanent components consistent with market microstructure theory, and price impacts are larger in smaller and less liquid securities but nevertheless present in even the largest and most liquid securities, including large capitalisation stocks and foreign exchange markets. By "diminishing rate", Professor Putnins meant that the impact of each additional unit of volume in a given direction is smaller than the previous unit; for example, if buying a volume X pushes the price up an amount Y, buying twice as much (a volume of 2X) pushes the price up less than twice as much (more than Y but less than 2Y).
1745 Professor Putnins also said that the empirical support for the notion that trading impacts prices is so consistent and widely accepted that recent empirical work on price impact has now turned its attention to precisely characterising the functional form of price impact curves, i.e. how much price changes in response to trades of different volume. Moreover, apparently several studies in this line of research have found that when the right functional forms are used, price impact curves of many different assets seem to consistently follow a universal price impact curve. Professor Putnins says that this suggests that the way trading impacts prices in different markets and different securities is governed by the same statistical rules and a common theoretical basis. I would say now that in my view that assertion was overly ambitious. Moreover, I would note that the empirical literature, such as it exists, did not directly deal with the Bank Bill Market and its complexity. I am not here dealing with the simplicity of a market for trading in widgets.
1746 Generally, according to Professor Putnins, the consensus in the empirical academic literature is that trades cause price impact and that this is a phenomenon that holds in a large number of different markets and securities. But notwithstanding this so called "consensus", Professor Putnins nevertheless found it necessary to conduct and did conduct his own empirical analysis of how trading on the Bank Bill Market affects the prices/yields of Prime Bank Bills and the BBSW. The main conclusions he drew from his empirical analysis were as follows:
(a) There is very strong evidence (a high level of statistical significance, at a confidence level exceeding 99%) that trading on the Bank Bill Market impacts both the yields of Prime Bank Bills and the level of the BBSW.
(b) It is very likely that buying on the Bank Bill Market pushes yields/BBSW down and selling on the Bank Bill Market pushes yields/BBSW up.
(c) In addition to the very strong statistical significance, the magnitudes of the price impacts (effects of trading on both Prime Bank Bill yields and the BBSW) are material in magnitude, even in response to fairly small volumes of buying or selling.
(d) Price impacts are found consistently for a number of different model specifications and alternative assumptions, indicating that the evidence is robust and not particularly sensitive to the specific choice of model or assumptions.
(e) The nature of price impacts (functional form and characteristics) on the Bank Bill Market is similar to price impacts in a large number of other markets (other asset classes and other countries), suggesting that the Bank Bill Market conforms to the standard theoretical mechanisms and statistical properties that he referred to.
1747 Professor Putnins gave evidence that the overall approach to analysing how trading on the Bank Bill Market affects the prices/yields of Prime Bank Bills and the level of the BBSW is to estimate regressions of changes in yields/BBSW on measures of the net "signed" volume of buys and sells (buy volume minus sell volume). These regressions use the trading data to measure the typical (average or expected) change in Prime Bank Bill yields/BBSW for a given volume of buying or selling. Apparently, this approach is common in the empirical market microstructure literature. The regression coefficient estimates are used to test whether trading has an impact on yields/BBSW, if so what is the nature of that impact (magnitude, shape, characteristics), plot price impact curves, and ultimately arrive at a calibrated price impact model that can be used to estimate impacts of specific trading activity.
1748 In the first step, estimating the signed volume of trading (also known as the "order imbalance", i.e. the difference between buying and selling volumes), Professor Putnins used the "bulk volume classification" (BVC) approach (see Easley D, Lopez de Prado M and O'Hara M "Discerning Information from Trade Data" (2016) 120 Journal of Financial Economics 269). He used this approach so he said for two reasons: (a) it is well suited to the nature of the trading data for the Bank Bill Market, which is only reliable at daily levels of aggregation, and (b) it provides improvements over older methods (such as the Lee-Ready algorithm) that focus on the "aggressor side" of trading to classify buying and selling. Professor Putnins said that the advantages of the BVC over "aggressor side" approaches are particularly relevant in this setting where the objective is to estimate the price impact of trading.
1749 Let me explain why Professor Putnins did not use the Lee-Ready algorithm, and the reasons are not unimportant. In the data available to him, the time stamps were unreliable, the putative sequence of trades did not necessarily reflect the sequence in which they occurred, there was little information on quotes, and several individual trades could have been aggregated into one printed trade. These issues made it unrealistic to do a tick-by-tick analysis and thus apply other trade classification procedures such as the Lee-Ready algorithm, but according to Professor Putnins they did not limit the ability to work with daily aggregates. The empirical market microstructure literature provided tools for working at either level of granularity being tick-by-tick data or clock-time aggregated data, such as the trading data for the Bank Bill Market.
1750 In the second step, estimating the price impact regressions, Professor Putnins controlled for a number of factors that could affect changes in yields/BBSW, including past changes (accounting for temporary price impacts and reversals), day-of-the-week effects, and day-of-the-month effects including effects around the transition from one maturity bucket to the next. He also tested for differences between three tenors (1 month, 3 month and 6 month), differences between the impacts of buying and selling, and different functional forms for how yields/BBSW respond to trading. According to Professor Putnins his results indicate the following:
(a) There is negative serial correlation in yield changes similar to many other markets, meaning that an increase in yields on one day is likely to be followed by a partial reversal (a decrease in yields) the following day. This tendency for reversals indicates the presence of temporary price impacts. He said that reversals and negative serial correlation can be caused by, inter-alia, market manipulation.
(b) There is intra-week and intra-month seasonality in yield changes, including effects around maturity bucket boundaries, confirming the need for these control variables.
(c) The three tenors differ significantly in their levels of liquidity, with the three-month being the most liquid, followed by the one-month, and then the six-month.
(d) There is no evidence of asymmetry in the impact of buys compared to sells. For this reason, Professor Putnins considered symmetric price impact functions.
(e) There is a very high correlation (0.96) between daily changes in volume-weighted average yields at which Prime Bank Bills are traded and daily changes in the level of the BBSW for the respective tenor. Professor Putnins said that the very high correlation indicates that the BBSW closely mirrors the yields at which trades occur on the Bank Bill Market in the respective tenor, consistent with the design of the BBSW rate setting mechanism. This result also suggests that if trading affects Prime Bank Bill yields, it is also likely to affect the BBSW through its effect on BBSW panellists' views and submissions to AFMA.
(f) In all models, the coefficients of signed trading volume (irrespective of the functional form) are highly statistically significant indicating, so Professor Putnins said, very strong evidence (greater than 99% confidence level) that trading on the Bank Bill Market impacts both the yields of Prime Bank Bills and the level of the BBSW. Professor Putnins said that this is a highly robust result. Specifically, buying on the Bank Bill Market pushes yields/BBSW down and selling on the Bank Bill Market pushes yields/BBSW up.
(g) The net trading activity of Bank Bill Market participants is responsible for a considerable fraction of the daily variation in Prime Bank Bill yields. When signed volume is added to the regression models, R-squared values increase considerably, and the final calibrated models explain 63% to 75% of the daily variation in Prime Bank Bill yields and the BBSW.
(h) Price impacts in the Bank Bill Market, that is, effects of trading on both Prime Bank Bill yields and the BBSW, can be well fitted to a power law model with exponent 0.6. The model is represented by the following equation:
The power exponent (lower case delta) is 0.6. The upper case delta r term with the t subscript represents daily changes in Prime Bank Bill yields. V (with superscript SIGNED and subscript t) is signed volume, sign(.) is the sign operator, |. | is the absolute value operator, and C (as a function of t) is a set of control variables. This exponent is very similar to that found in the empirical price impact literature of around 1/2 to 2/3 (0.5 to 0.67) in a large number of different markets. Professor Putnins said that this finding suggests that the nature of price impact on the Bank Bill Market is similar to price impact in a large number of other markets (other asset classes, other countries). Square-root impact laws have been used in industry models of price impact functions and various price impact studies. Exponents around 2/3 have been documented. According to Professor Putnins this result indicates that price impacts in the Bank Bill Market conform to the standard theory and statistical properties that have become widely accepted in the market microstructure literature.
(i) Professor Putnins said that the price impact curves indicate that in addition to the very strong statistical significance, the price impacts, that is, effects of trading on both Prime Bank Bill yields and the BBSW, are material, even in response to fairly small volumes of buys or sells.
1751 Let me elaborate further on some aspects of the methodology. First let me deal with the preliminary but important question of trade classification.
1752 Professor Putnins gave the following evidence.
1753 He applied the "bulk volume classification" (BVC) technique of Easley, Lopez de Prado, and O'Hara (2016) to estimate the percentage of buy and sell order flow (trading volume) on each day in each tenor. The "signed order flow" is then calculated as the buy percentage multiplied by the volume traded that day in that tenor minus the sell percentage multiplied by the volume traded that day in that tenor.
1754 Easley, Lopez de Prado, and O'Hara (2016) developed this method to discern the direction and quantum of trading intentions from market data so as to identify within a given period of time (e.g. one day) whether there was an imbalance between buyers and sellers and if so how large that imbalance was. "Buy" and "sell" order flow refers to those orders for which the trader has some underlying reason or intention to buy or sell the security (respectively) other than simply accommodating, or providing liquidity to, the imbalance between buy and sell order flow of other market participants. Examples of buy/sell order flow include buying or selling by a trader that believes the security is under-priced or over-priced, buying or selling to satisfy short-term funding needs, buying or selling to hedge risks or exposures, and buying or selling to influence the price.
1755 According to Professor Putnins, this task of discerning trading intentions from data is related to the idea of identifying which side of a trade (the buyer or the seller) was the aggressor (the active order that executed against a resting quote), insomuch as traders with strong intentions to buy or sell might more often be on the aggressor side of a trade, but not necessarily. Suppose a buyer has some fundamental reason for wanting to buy the security (e.g. a belief that it is under-priced). Instead of hitting the prevailing offer quote in the market and becoming the aggressor side of the trade, the trader may instead post an order to buy at its own bid in a specific volume (a limit order). When that order is hit by the seller, the buyer is on the non-aggressor side of the trade. To continue to buy via limit orders, the trader has to repeatedly post at its bid or at higher prices, meaning that prices are forced up (or prevented from declining) by the buyer even though the active side of the trade is the seller.
1756 It is now necessary to descend further into Professor Putnins' equations, the question of signed volumes and BVC. Why is this so? Well, one of the principal challenges to Professor Putnins' evidence concerns the problem of circularity which is manifested by considering equations (1), (2), (3) and (4) that I will set out in a moment. Let me first explain equations (1), (2) and (3). Equations (1) and (2) are used to construct equation (3). The output of equation (3) is then used as one of the inputs to equation (4).
1757 Let r (subscripts i,t) be the volume-weighted average yield at which Prime Bank Bills in tenor i are traded on day t, and V (subscripts i,t) be the volume (principal, in $100 million) of tenor i Prime Bank Bills traded on day t. The estimated buy volume in tenor i on day t (following Easley, Lopez de Prado, and O'Hara (2016)) is given by equation (1):
where T(.) is the cumulative distribution function (CDF) of student's t-distribution with df degrees of freedom, r (subscripts i,t) minus r (subscripts i,t-1) is the change from day t - 1 to day t in the yield at which Prime Bank Bills in tenor i are traded (in basis points), and lower case sigma (subscript delta r) is the standard deviation of daily yield changes. Following Easley, Lopez de Prado, and O'Hara (2016), Professor Putnins used df = 0.25 to account for fat tails in the data. Because Prime Bank Bills were traded in terms of yield rather than price, and yields were inversely related to prices, he switched the expressions for V (with superscript BUY, and subscripts i,t) and V (with superscript SELL, and subscripts i,t) (relative to Easley, Lopez de Prado, and O'Hara (2016) who worked with prices) to account for the fact that if buying pushed prices up, it pushed yields down, and vice versa.
1758 Similarly, the estimated sell volume in tenor i on day t is given by equation (2):
and the signed volume of the tenor-day (the "order flow imbalance", measured in units of $100 million of principal) is given by equation (3):
1759 Now let me turn to Professor Putnins' method of empirical analysis in more detail. The primary objective of his analysis was to quantify the magnitude of the impact of trading on the Bank Bill Market, because according to him the direction of the impact was already well-established by theory (microeconomic analysis and market microstructure theory) as well as previous empirical studies. That is, buying tends to increase prices and selling tends to decrease prices. According to Professor Putnins, the magnitudes of price impacts (the sensitivity of prices to a given volume of buying or selling) are a function of market-specific factors such as liquidity and therefore have to be estimated for the Bank Bill Market.
1760 To quantify the effects of trading on the Bank Bill Market or the "price impact" of trading, starting with the effect on the yields of Prime Bank Bills, Professor Putnins used an approach that he said was standard in the empirical market microstructure literature. The approach is to estimate regressions of yield changes (the equivalent of price changes or realised returns in securities that are traded with reference to price rather than yield) on measures of the volume of purchases/sales ("buys"/ "sells") or the imbalance between buying and selling. For securities that trade in terms of yield, VWAY is the analogue of the volume-weighted average price (VWAP), which is a commonly used measure of the price at which trades occur when aggregating a number of trades through time.
1761 For each tenor i on each day t, Professor Putnins estimated the signed volume of trading (also known as the "order imbalance"), denoted V (with superscript SIGNED and subscripts i,t). This measure indicates the volume of buying, net of the volume of selling. It is positive when there is more buying than selling and negative when there is more selling than buying. He also measured the change in the yields at which Prime Bank Bills traded on the Bank Bill Market by taking the difference between the volume-weighted average yield (VWAY) of trades in Prime Bank Bills of tenor i on day t and the VWAY of trades in Prime Bank Bills of tenor i on day t - 1 (the previous trading day).
1762 An alternative measure of the yields quoted for Prime Bank Bills during the BBSW Rate Set Window is the level at which the BBSW for the tenor i sets that day t. Professor Putnins also measured the daily changes in the BBSW for each tenor.
1763 The basic form of the price impact regressions (estimated separately for each tenor and therefore suppressing tenor subscripts, i, from here onwards) is given by equation (4):
.
1764 C (as a function of t) is a vector of control variables including: (a) lagged yield changes (upper case delta r term with the t-1 subscript) to absorb first-order serial correlation that could arise from reversals after yields are temporarily dislocated from their equilibrium levels; (b) a set of day-of-the-week dummy variables to account for any intra-week seasonality; and (c) a set of day-of-the-month dummy variables to account for any intra-month seasonality and in particular transition effects when going from one maturity bucket to the next (late to early instruments or early to late instruments). Factors that affect Prime Bank Bill yields but are not included in the model are captured in the error term (lower case epsilon as a function of t). Professor Putnins modified the basic form of the price impact regressions in various ways that he explained to test specific effects and to introduce non-linearity in price impacts.
1765 To begin with, Professor Putnins regressed yield changes (uppercase delta r term with the t subscript) on only the control variables to investigate autocorrelation, seasonality, and maturity bucket transition effects. He reported the results in Table B.1, which I have not thought it necessary to reproduce in these reasons given my principal conclusions on this entire analysis that I will explain later.
1766 Professor Putnins' overall approach was to take Westpac's trading on each of the contravention dates, feed it through the calibrated price impact model to obtain an estimate of the effect of that trading on Prime Bank Bill yields and the BBSW and quantify the error bounds on the estimate using standard statistical techniques. On his approach the estimated impacts with error bounds provided evidence on the magnitude of Westpac's impact (if any) and the degree of confidence (statistical likelihood) that one could have in those estimated impacts.
1767 The first step is to calculate Westpac's signed (directional) trading volume each day, which Professor Putnins did using two different approaches. The first approach takes the difference between Westpac's volume of buys represented by V (superscript BUY, and subscripts WBC,i,t) and its volume of sells represented by V (superscript SELL and subscripts WBC,i,t) in a given tenor on a given date, to give you the signed volumes represented by V (superscript SIGNED, and subscripts WBC,i,t). The signed volumes, V (superscript SIGNED, and subscripts i,t) in the price impact models measure order flow with respect to trading intentions, not just the aggressor side of trades. This approach to calculating Westpac's signed volumes accounts for the possibility that some of Westpac's trading could be undertaken for the purpose of providing liquidity (by acting as a market maker) and some of Westpac's trading is undertaken for other reasons involving intentions to buy or sell, such as beliefs about whether Prime Bank Bills are over- or under-priced, managing funding and short-term liquidity needs, hedging risks, and managing exposure. In this approach, the amount of volume associated with market making is approximated by the roundtrip volume (volume of buys that are accompanied by sells within the same tenor and day). Accordingly, only the non-roundtrip (that is, directional) volume contributes to Westpac's signed volumes. Professor Putnins said that it is likely that roundtrip volume is associated with market making activity and non-roundtrip volume with trading for other reasons and he therefore referred to this approach as the "likely approach".
1768 Professor Putnins said that the reason that roundtrip volume approximates the trading associated with market making is that typically market making involves holding positions for only a short period of time and actively managing inventory positions towards zero. Such trading generates approximately equal volumes of buying and selling, and a high proportion of roundtrip volume within a trading day. Professor Putnins said that the characteristics of Westpac's trading activity indicate that on the contravention dates it is likely that most of Westpac's trading was undertaken for reasons other than market making because on many days Westpac's trading is 100% non-roundtrip (all buying or all selling).
1769 The second approach, referred to by Professor Putnins as the "conservative approach", counts only one-half of Westpac's signed directional volume (after removing the roundtrip volume). The motivation for this approach is that on average and in aggregate, one-half of trading volume (counting both buy volume and sell volume) is on the aggressor side of the trade. It is said that this approach is conservative in that it is likely to underestimate the volume traded by Westpac for purposes other than market making (volume where there was an intention to buy or sell, which is what is used in the signed volume and consequently the price impact models), and therefore underestimate Westpac's impact on Prime Bank Bill yields and the BBSW. For example, on the majority of days, where Westpac is trading entirely in one direction (only buying or only selling a given tenor) and therefore (so Professor Putnins says) it is unlikely that much (if any) of Westpac's trades are due to market making, only half of its volume is attributed as arising from an intention to buy or sell for non-market making reasons. It is said that estimates from the conservative approach should therefore be viewed as a lower bound on the estimated impact of Westpac's trading.
1770 Table C.1 of Professor Putnins' report tabulated the estimated impacts of Westpac's trading on particular dates. Now it is obvious that the Table does not of itself show trading for a manipulative purpose, nor establishes any "artificial price" as such. It is only purporting to show the effect or likely effect of trades. Let me explain some features of the Table. Lower case r (subscripts i,t) is the volume-weighted average yield at which Prime Bank Bills of the given tenor were traded on the Bank Bill Market on the given date. BBSW (subscripts i,t) is the rate at which the BBSW set for the given tenor on the given date. Westpac direction specifies whether Westpac was a net buyer or net seller in the given tenor on the given date. Westpac volume in direction identifies the volume (in $mil) traded by Westpac in the direction given by Westpac direction (it is the volume of their sales when they are net selling and the volume of their purchases when they are net buying). Westpac signed volume is the directional net volume (in $mil) traded by Westpac (volume of buys minus volume of sells). This is the value used as V (superscript SIGNED, and subscripts WBC,i,t) in the likely approach (as I have explained). Directionality is the percentage of Westpac's total volume (buy volume plus sell volume) that is in the direction given by Westpac direction. As noted previously, Directionality shows that on the majority of days, Westpac traded entirely in one direction (only buying or only selling a given tenor).
1771 I have considered it appropriate to set out the entirety of Table C.1 in these reasons. As is apparent from other parts of my reasons, ASIC's dominant purpose analysis has only been made out on the trading days of 6 April 2010, 20 May 2010 and 1 and 6 December 2010. Accordingly, strictly speaking in terms of the contravention dates I need only consider the question of effect or likely effect on the said four dates. But just in case others take a different view, it is appropriate to set out the quantitative analysis in respect of all contravention dates. But I should also say now, more generally, that whatever the date, I have not found Professor Putnins' model and approach to be that persuasive, as I will explain shortly. So even for the said four dates, the results produced in Table C.1 are of little assistance. But I accept the possibility that others may take a different approach and so I have reproduced Table C.1 below.
1772 By way of explanation, Professor Putnins provided the following note to Table C.1, albeit with minor amendments to two of the values that I have made:
This table reports the estimated effects of Westpac's trading on the BBM on particular dates. The estimates are obtained from the fitted price impacts of the signed volume traded by Westpac (the "Likely Approach") and half of the signed volume traded by Westpac (the "Conservative Approach") using the calibrated price impact model described in Appendix B. Ref. refers to the Schedule Number and Item Number (separated by a dot) from the ASIC Amended Pleading. r (subscripts i, t) is the volume-weighted average yield at which PBBs of the given tenor were traded on the BBM on the given date. BBSW (subscripts i, t) is the rate at which the BBSW set for the given tenor on the given date. Westpac direction specifies whether Westpac was a net buyer or net seller in the given tenor on the given date. Westpac volume in direction identifies the volume (in $mil) traded by Westpac in the direction given by Westpac direction (it is the volume of their sales when they are net selling and the volume of their purchases when they are net buying). Westpac signed volume is the directional net volume (in $mil) traded by Westpac (volume of buys minus volume of sells). Directionality is the percentage of Westpac's total volume (buy volume plus sell volume) that is in the direction given by Westpac direction. Likely effect on r (subscripts i, t) and Likely effect on BBSW (subscripts i, t) are the point estimates of how r (subscripts i, t) and BBSW (subscripts i, t) (respectively) are impacted by Westpac's trading in the given tenor on the given date, using the Likely Approach and the calibrated price impact model (measured in basis points, bps). Effect bounds provides a 99% confidence interval for the effect of Westpac's trading on r (subscripts i, t) and BBSW (subscripts i, t), accounting for both statistical error on estimates within the calibrated price impact model, and variation between the Likely and Conservative Approaches. Effect confidence provides a categorical description of the impact of Westpac's trading on r (subscripts i, t) and BBSW (subscripts i, t) and the statistical confidence in that estimate. It takes one of five categories. The two categories corresponding to the strongest evidence are "Material Increase, Very Likely" and "Material Decrease, Very Likely". An effect is classified in one of these first two categories if, using the Conservative Approach, the absolute estimated effect is greater than 1bp with statistical confidence exceeding 99%. The next two categories by strength of evidence are "Material Increase, Likely" and "Material Decrease, Likely". An effect that is not classified in either of the first two categories is classified in one of the next two categories if, using the Likely Approach, the absolute estimated effect is greater than 0.5bp with statistical confidence exceeding 90%. Effects that do not satisfy any of the previous four categories are assigned to the fifth category, "Marginal or insignificant", indicating the absence of strong evidence for Material impacts.
1773 At this point it is now appropriate to consider the evidence given by Mr Bishop. Mr Bishop considered that the econometric analysis presented by Professor Putnins was flawed and could not be relied upon. I should say that I tend to agree, as I will elaborate on later.
1774 Mr Bishop said that traded volumes alone did not reveal whether pressures on yields were in a particular direction as a result of a party seeking to either buy or sell Prime Bank Bills. He said that in reality there were two sides to every trade and every trade had both a buyer and a seller. Mr Bishop pointed out that Professor Putnins, seemingly to avoid this problem, used the BVC method to classify daily volumes as buy or sell volumes based on the change in yield compared to the previous day. Professor Putnins used this to estimate the percentage of buy and sell order flow on each day and for each tenor. In particular, Professor Putnins designated volumes traded as "sell volumes" if the yield increased from the previous day, and designated them as "buy volumes" if the yield decreased from the previous day. The calculated signed order flow ("net volume") was the buy percentage multiplied by the volume traded for that day and tenor minus the sell percentage multiplied by the volume traded for that day and tenor.
1775 But Mr Bishop said that by using the change in yield as the dependent variable, and by using volumes based on the BVC as the independent variable, Professor Putnins estimated a model that was circular. I agree. Now Professor Putnins relied on Easley, Lopez de Prado and O'Hara (2016) to estimate the impact of volumes, classified using the BVC, on the change in the Prime Bank Bill yield (for 1, 3 and 6 month tenors respectively), but Mr Bishop said that the Easley, Lopez de Prado, and O'Hara (2016) equation (6) used a measure of the difference between the best buy and sell price (i.e. the spread) as the dependent variable, not the change in yield compared to the previous day. This is well apparent from p 282 of that article which stipulated:
Mr Bishop said that as a result it was not subject to the same circularity problem as Professor Putnins' model. In relation to Easley, Lopez de Prado and O'Hara (2016), Professor Putnins appeared to rely on equation (6) from that article. But in Professor Putnins' own work, the supposedly independent variable (the net buy or sell volume) was itself a function of the dependent variable (the change in yield), and so the change in yield was effectively explained in terms of the change in yield.
1776 Again, I agree with Mr Bishop's analysis. In equation (4) that I have set out earlier, it is well apparent that the independent variable (V, superscript SIGNED, subscript t) with the beta co-efficient is being used to, inter-alia, explain the dependent variable (the delta r term, subscript t), which is the change in yield. But the independent variable is itself sourced from equation (3), which is itself derived from equations (1) and (2), as I have set out above. But if you analyse equations (1) and (2), they themselves use as inputs changes in yield. Following this all through, the independent variable in equation (4) is used to explain the dependent variable in circumstances where the independent variable itself is ultimately derived from the dependent variable. This is a plain vanilla example of circularity, and in my view not only in terms of directionality but also in having some impact on magnitude as I will shortly explain.
1777 Mr Bishop also said that Professor Putnins' models using volume weighted average Prime Bank Bill yields and BBSW were essentially the same. He said that Professor Putnins either used the change in the volume weighted average Prime Bank Bill yields to estimate "net volume" and then used this to estimate changes in volume weighted average Prime Bank Bill yields, or Professor Putnins used the change in BBSW to estimate "net volume" and then used this to estimate the change in BBSW. Mr Bishop said that both of these approaches were circular. Again, I agree.
1778 Now Professor Putnins argued that circularity was only relevant to the direction of the relationship. He claimed that theory and empirical evidence strongly supported assuming that demand-driven trades increase prices and supply-driven trades reduce prices. But Mr Bishop considered that the circularity in Professor Putnins' approach rendered the analysis not only unreliable for estimating the direction of trading on prices but also the magnitude of the relationship between Prime Bank Bill volumes traded and price changes. That is, circularity was a problem for the whole analysis. In elaboration, Mr Bishop said the following.
1779 He gave a simple example of how circularity affects the magnitude of the measured relationship as well as the direction. Consider a variable for daily rainfall ("y"). Then assume the generation of a new variable, which is ten times daily rainfall ("x"). If one regresses y on x, one will obtain a highly statistical significant relationship with a coefficient of ten. The relationship being estimated is y = 10x. The circularity not only guarantees a statistically significant result but also determines the coefficient of ten. Now Mr Bishop said that Professor Putnins used a more complicated transformation of the daily change in Prime Bank Bill yields and BBSW than that described for rainfall, but he said that this more complex transformation did not change the essence of what Professor Putnins' results purported to show and the assumed transformation still determined the results. In particular, his approach transformed the daily change in yields using a t-distribution, multiplied the transformed variable by the daily total volumes traded and, in his preferred model, raised the resulting variable to an exponent of 0.6. He said that the only way in which anything other than the daily change in yields entered into the volume variable was through multiplication by the actual volumes traded in the day.
1780 But Mr Bishop contended that Professor Putnins' approach allocated more of actual volumes to "buy" trades on days on which the price increased (yield decreased) by a greater extent and allocated more of total volumes to "sell" trades on days on which the prices decreased (yield increased) to a greater extent. He said that this generated a correlation between yield changes and signed volumes, which were defined as buy trades minus sell trades.
1781 Mr Bishop said that the total volume affected the magnitude of the measured coefficient, so that, if, for example, Prime Bank Bill volumes were ten times as large for the same yield changes, or if they were measured in billions of dollars rather than millions of dollars, the estimated coefficient would change. The chosen transformation also affected the estimates. Mr Bishop said that the fact that the coefficient could change depending on the total volumes used as an input rendered Professor Putnins' approach an unreliable method to measure the magnitude of effects because they also depended on the arbitrary transformation used. Now Professor Putnins claimed that other relevant studies were subject to the same circularity. But as Mr Bishop pointed out, Professor Putnins used the change in yield not only to determine the direction of a trade as "buy" or "sell" but also the quantity of the trade that was "buy" or "sell". But only one paper cited by Professor Putnins appeared to carry out the same regression as him (Chakrabarty B, Pascual R and Shkilko A, "Evaluating Trade Classification Algorithms: Bulk Volume Classification versus the Tick Rule and the Lee-Ready Algorithm" (2015) 25 Journal of Financial Markets 52). But as Mr Bishop said, this is only one of the many regressions they performed and the purpose was not to make any inferences from the regression but to compare different ways of computing the "order imbalance" by evaluating different trade classification algorithms. As the authors clearly explain, at least on my understanding of this paper, they compared the BVC approach with the trade-based tick rule and the apparently popular Lee-Ready algorithm and ultimately concluded that the latter approaches gave higher accuracy for signing both volume and order imbalances.
1782 In summary, according to Mr Bishop, the estimated coefficient, that is the magnitude, reflected the circularity in the model in which change in yield was regressed on a transformation of change in yield. As he said, the assumed form of the relationship determined the size of the effect, and so the circularity determined not only the direction of the finding but also the size of the measured finding. I must say that I agree with Mr Bishop.
1783 As Mr Bishop pointed out, the main problem with circularity was that it produced no new evidence to solve the problem because the results followed directly from what was assumed. Mr Bishop also gave evidence that there were other conceptual limitations with Professor Putnins' econometric analysis, in addition to the circularity in the model, that it is now convenient to also deal with.
1784 First, Professor Putnins' analysis did not examine whether Westpac's observed trading deviated from commercially rational behaviour. Professor Putnins assumed that either 100 per cent or 50 per cent (on a "conservative" basis) of volumes were artificial and then attempted to estimate the impact of those volumes on Prime Bank Bill yields and BBSW.
1785 Professor Putnins assumed that all of Westpac's actual net volumes (actual Westpac buy trades minus actual Westpac sell trades) were intentional "buy" volumes for those days it was alleged to have acted to influence Prime Bank Bill yields downwards and assumed that all of Westpac's net volumes were intentional "sell" volumes for those days on which Westpac was alleged to have influenced Prime Bank Bill yields and BBSW upwards as opposed to trading undertaken to provide liquidity to other market participants. This was based on the assumption that liquidity trades would cancel each other out on the same day. That is, Professor Putnins' assumed that there would be an equal volume of buy and sell trades for liquidity provision in a day. Mr Bishop said that although this may have been broadly true over time, it was very unlikely that buy and sell trades for liquidity provision would exactly offset each other on each and every day, and that there were legitimate commercial rationales to trade other than providing liquidity.
1786 Further, on a "conservative" approach, Professor Putnins assumed that 50 per cent of Westpac volumes for the alleged manipulation days involved active buying or selling. But Mr Bishop said that this assumption was arbitrary.
1787 Further, Professor Putnins did not investigate whether the relevant net buy or sell volumes (even if correctly classified) were traded for a manipulative purpose as opposed to one or more commercially rational purposes. As a result, according to Mr Bishop, Professor Putnins did not show what increment, if any, of volumes were for the purpose of manipulation, and so could not establish what the effects or likely effects of that increment of volumes were on Prime Bank Bill yields and BBSW.
1788 Second, a further conceptual issue with Professor Putnins' econometric analysis was that, even if circularity did not exist, the model did not take into account factors other than volumes traded in the Bank Bill Market that could influence Prime Bank Bill yields and BBSW, such as the expected RBA cash rate between the purchase date and maturity date, the cost and availability of international wholesale funding, and the credit risk of Prime Banks.
1789 According to Mr Bishop, by excluding important drivers of Prime Bank Bill yields from the econometric model, Professor Putnins risked over-estimating the effect of the included variables, notably "net volumes". Such a deficiency is known as omitted variable bias.
1790 Third, Professor Putnins did not know the timing of Prime Bank Bill trades. This was because the time stamp on the Prime Bank Bill trades in the broker data that Professor Putnins analysed was not reliable. The Prime Bank Bill trades used in Professor Putnins' analysis could have been, for example, at 10.05 am. Professor Putnins could not therefore have come to a reliable conclusion that the volumes that were traded had an impact when BBSW observations were meant to take place.
1791 Fourth, Professor Putnins calibrated a model for market-wide estimated "net volumes" and then used a different volume measure, Westpac actual net volumes, as an input. Mr Bishop said that this was inappropriate given that the model was designed to estimate the effect of market-wide volumes (estimated using the BVC) rather than Westpac actual net volumes (measured as actual Westpac buy trades minus actual Westpac sell trades). Westpac's actual net volumes could be much higher than the estimated market wide "net volumes".
1792 Mr Bishop produced a table, which I have reproduced below but slightly re-ordered, showing for each of the alleged contravention dates the relevant tenor, the market wide "net volumes" for that tenor obtained using Professor Putnins' econometric model and Westpac's actual net volumes. Professor Putnins used the Westpac net volumes as an input into the market wide model to estimate the impact of Westpac's trading on Prime Bank Bill yields and BBSW. Mr Bishop's table also shows the actual total volumes traded in the Bank Bill Market on each of these dates.
Inconsistency between market-wide estimated "net volume" and actual net volume
Trade date Tenor Market-wide "net volume" ($m) Westpac actual net volume ($m) Total volume ($m)
06 Apr 2010 1 182.1 1,622 1,622
06 Apr 2010 3 -483.5 1,020 1,400
30 Apr 2010 1 -526.1 980 1,380
20 May 2010 1 -85.4 710 710
10 Jun 2010 3 -359.7 -360 1,590
20 Sep 2010 1 69.5 1,180 1,180
20 Sep 2010 3 99.4 250 430
22 Sep 2010 3 -318.5 500 1,310
01 Dec 2010 3 980.3 2,770 3,090
06 Dec 2010 3 60.6 3,030 3,030
01 Mar 2011 3 283.6 1,390 2,240
04 Mar 2011 3 -890.6 2,720 3,150
01 Jun 2011 3 125.2 260 500
06 Jun 2011 3 -209.9 620 1,540
09 Jun 2011 3 -226.6 -1,470 2,130
06 Jun 2012 3 -1452.6 3,060 3,500