The Sound of Many Funds Rebalancing


 Gregory Palmer
 9 months ago
 Views:
Transcription
1 The Sound of Many Funds Rebalancing Alex Chinco and Vyacheslav Fos December 5, 2017 Abstract This paper proposes that long rebalancing cascades generate noise in financial markets. There are two components to our analysis. First, to show that long rebalancing cascades can generate noise, we analyze a randomnetworks model where it s possible to predict whether a particular stock s demand will be affected by a long rebalancing cascade but not how the stock s demand will be affected due to computational complexity. Then, to show that long rebalancing cascades actually do generate noise in realworld financial markets, we study the endofday holdings of exchangetraded funds (ETFs). We demonstrate the existence of long ETF rebalancing cascades, and we document evidence of market participants treating the resulting demand shocks as noise. Taken together, these two components suggest that noise can be an externality imposed by a collection of funds following simple rebalancing rules and not just the result of individual investors who each behave randomly. JEL Classification. G02, G12, G14 Keywords. Noise, Indexing, Thresholds We thank Kerry Back, Nick Barberis, Zahi BenDavid, James Choi, Tony Cookson, Xavier Gabaix, Itay Goldstein, Sam Hartzmark, Ralph Koijen, Pete Kyle, Chris Parsons, and Jeff Pontiff as well as seminar participants at CalTech, Colorado, Illinois, Maryland, Yale, the Young Scholars Finance Consortium, the FINRA MarketStructure Conference, the SFS Calvalcade, the Conference on the Econometrics of Financial Markets, and the Helsinki Behavioral Finance Conference for extremely helpful comments and suggestions. Current Version: University of Illinois at UrbanaChampaign, College of Business; Boston College, Carroll School of Management; 1
2 1 Introduction Noise makes financial markets possible but also makes them imperfect (Black, 1985). Imagine you re a trader who s just discovered that stock Z is underpriced. In a market without noise, there s no way for you to take advantage of this discovery. The moment you try to buy a share, other traders will immediately realize that you must have uncovered some good news. And, you won t find anyone willing to sell at the old price (Milgrom and Stokey, 1982). Noise pulls the rug out from under this notrade theorem. In a market with noise, someone is always trying to buy or sell stock Z for erratic nonfundamental reasons. So, when you try to buy a share, it won t raise too many eyebrows. Because your buy order could just be some more random noise, other traders won t immediately realize that you must have uncovered some good news. The existence of this plausible cover story allows you to both trade on and profit from your discovery. But, where exactly does this allimportant noise come from? Who generates it? And, what are their erratic nonfundamental reasons for trading? The standard answer to these two questions is that i) noise comes from individual investors, and ii) their demand looks erratic and unrelated to fundamentals because individual investors are just plain bad traders. These are the standard answers for a reason. Not only do individual investors suffer from all sorts of behavioral biases when they trade (Barberis and Thaler, 2003) but they also trade far too often (Barber and Odean, 2000). So, individual investors clearly generate noise. But, are they the only source? It seems unlikely. The role of individual investors in financial markets has steadily declined over the past few decades. To give one representative statistic, individual investors held 47.9% of all U.S. equity in 1980, but that percentage was down to only 21.5% in 2007 (French, 2008). Yet, we haven t seen a corresponding drop in trading volume. Motivated by this logical gap, we propose another noisegenerating mechanism: long rebalancing cascades (stock A s price jumps, which causes a fund to buy stock A and sell stock B, which causes a second fund to sell stock B and buy stock C, which causes... ). There are two parts to our analysis. First, we analyze a randomnetworks model to show how long rebalancing cascades can generate noise. Then, to show that long rebalancing cascades actually do generate noise in realworld financial markets, we study the endofday holdings of exchangetraded funds (ETFs). Theoretical Model. Our hypothesis that noise comes from long rebalancing cas 2
3 cades was sparked by a second trend that s shaped financial markets over the past few decades, the rise of indexlinked investing (Wurgler, 2010). At the same time as individual investors were shrinking in importance, passive investing indexing was becoming popular as an alternative to active investment management, while active managers... were becoming more indexlike in their investing (Stambaugh, 2014). In fact, the number of indexes now exceeds the number of U.S. stocks. 1 Most of these new indexlike funds were not created in Jack Bogle s image, however. Many include stocks based on custom criteria, such as having low volatility or high dividends, 1 and involve thresholdbased portfolio rules. For example, the PowerShares S&P 500 LowVolatility ETF [SPLV] tracks the quintile of S&P 500 stocks with the lowest volatility. We say that this fund uses a thresholdbased rule because an arbitrarily small change in a stock s volatility can move it from 101st to 100th place on the lowvolatility leaderboard. When this happens, the lowvolatility ETF has to exit its position in one stock and build a new position in another. This rebalancing activity will affect both the stock being added to as well as the stock being deleted from the lowvolatility index in equalbutopposite ways. For example, due to the additional buying pressure, the price of the stock being added will rise while the price of the stock being deleted will fall. So, because there are so many of these indexlike funds tracking so many different thresholdbased benchmarks, a small change in stock A s price can cause some fund to buy stock A and sell stock B, which can then cause a second fund following a different index to sell stock B and buy stock C, which can then cause... We use a randomnetworks model to theoretically study how this sort of alternating buysellbuysell sequence might result in apparently random demand shocks (a.k.a., noise) even though the individual funds are following simple deterministic rebalancing rules. Each node in the network corresponds to a stock. And, two nodes are connected with an edge, not if the corresponding stocks both belong to the same benchmark index, but rather if a change in one of the stock s characteristics would cause it to swap places with the other stock in some fund s benchmark index. Thus, a node with many edges corresponds to a stock that s on the cusp of a rebalancing threshold for many different funds. The model explains how, even if it s possible to compute the likelihood that stock Z will be affected by a long rebalancing cascade that starts with an initial shock to stock A, it can still be computationally intractable to predict the direction, buy? or sell?, of the resulting demand shock. 1 Bloomberg. 5/12/2017. There Are Now More Indexes Than Stocks. 3
4 Economists have long had the intuition that apparent randomness might just be the result of computational complexity. For instance, way back in 1921 John Maynard Keynes pointed out that, although the population of France isn t random, whether or not this number happens to be an even or odd number at any given instant may as well be. Yet, in the past, this intuition has remained just that an intuition. The goal of analyzing this randomnetworks model is to describe precisely why it s computationally intractable to predict how a long rebalancing cascade will affect the demand for stock Z in as transparent a way as possible. The goal is to give a concrete foundation for this longheld intuition, making it possible to identify other situations where the same logic applies. Rebalancing Cascades. After describing how long rebalancing cascades can transform simple deterministic rules into apparently random demand shocks, we next give empirical evidence that this transformation actually takes place in the realworld. With this goal in mind, we first pick both i) a particular group of funds following thresholdbased strategies and ii) a set of initial shocks. Then, we show that, in the wake of these initial shocks, it s possible to compute which stock Zs are most likely to be hit by a long rebalancing cascade involving this group of funds but not the direction of the resulting demand shock. For our particular group of funds, we study ETFs. This might seem like an odd choice at first. If you ask a random person on the street to name an ETF, you re probably going to get The SPDR S&P 500 ETF [SPY] for an answer. But, while this is the oldest and most wellknown ETF, it is no longer representative of the industry as a whole. The vast majority of ETFs now track niche selfdefined indexes. A recent article in the Financial Times described how Exxon Mobile was held by ETFs following numerous thresholdbased indexes like active beta, momentum, dividend growth, deep value, quality, and total earnings. 2 And, more and more people are talking about how ETF rebalancing can influence trading in individual stocks. 3 We get data on each ETF s endofday portfolio holdings from XpressFeed. This data covers every trading day from January 2010 to December We restrict our sample to include only those ETFs that rebalance their positions daily think about the PowerShares S&P 500 LowVolatility ETF rather than the SPDR S&P 500 ETF. To be sure, these ETFs are smaller than the broad marketindex funds, but their rebalancing activity can still affect the underlying stocks because they tend 2 Financial Times. 10/7/2017. On The Perverse Economic Effects Created by ETFs. 3 Bloomberg. 4/10/2015. Tail Can Wag Dog When ETFs Influence Single Stocks, Goldman Says. 4
5 to do their trading during the final 20 or 30 minutes of the trading day. 4 It s also important to emphasize that we net out changes in ETF holdings due to creations and redemptions, which are executed as inkind transfers for tax reasons (Madhavan, 2016) and so can t generate the distortions that underpin long rebalancing cascades. Then, for our set of initial shocks, we use M&A announcements, referring to the target of the announcement as stock A. This data comes from Thomson Financial. M&A deals are a natural choice for the initial shocks because, in the words of Andrade et al. (2001), a profusion of event studies has demonstrated that mergers seem to create shareholder value, with most of the gains accruing to the target company. While M&A targets are certainly not random, the exact date of the announcement (Tuesday, Wednesday, or Thursday?) effectively is. Here s how we structure our empirical tests. Following the announcement of each stock A as an M&A target, we collect the set of stock Zs that are unrelated to stock A. For a stock Z to be unrelated to a particular stock A, it has to be twice removed in the network of ETF holdings at the time of the M&A announcement. It can t have been recently held by any ETF that also recently held stock A. And, it can t have been held by any ETF that also held a stock that was held by another ETF that held stock A. The chain has to be A B C Z or longer. Note that, because there are smartbeta ETFs focusing on largecap, value, and industryspecific benchmarks, this twiceremoved criteria implies that the set of stock Zs doesn t share wellknown characteristics such as size, booktomarket, or industry with the stock A. The randomnetworks model we study suggests that, all else equal, a stock that is on the cusp of more funds respective rebalancing thresholds will be more likely to be hit by a long rebalancing cascade. So, we split each set of stock Zs into two subsets: those with an abovemedian number of neighboring stocks, which are on the cusp of many different ETFs rebalancing thresholds, and those with a belowmedian number, which aren t. Consistent with our economic story, we find that ETF rebalancing volume grows by 169% more for the abovemedian group of stock Zs than for the belowmedian group in the 5 days immediately following an M&A announcement. But, we also find that this percentage increase in ETF order flow is no more likely to be made up of buy orders than of sell orders. In other words, we document that it s possible to predict which stock Zs are most likely to be affected by a long ETF rebalancing cascade but not the direction of the resulting demand shock. Demand Noise. Finally, after showing that long ETF rebalancing cascades are 4 Wall Street Journal. 5/27/2015. StockMarket Traders Pile In at the Close. 5
6 equally likely to result in buy and sell orders for stock Z from a statistical perspective, we conclude our analysis by giving supporting evidence that market participants also treat the demand shocks coming from long ETF rebalancing cascades as noise. Specifically, we find that abovemedian subset of stock Zs tends to have higher liquidity than the belowmedian subset. This result is consistent with a model where the abovemedian stock Zs has higher demandnoise volatility. 1.1 Related Literature This paper connects to three main strands of literature. Noise. The problem we study is motivated by the central role that noise plays in assetpricing theory. Noise plays a starring role in your favorite informationbased asset pricing (Grossman and Stiglitz, 1980; Hellwig, 1980; Admati, 1985; Kyle, 1985) or limitstoarbitrage model (Shleifer and Summers, 1990; Shleifer and Vishny, 1997; Gromb and Vayanos, 2010). This paper proposes an explanation for noise that does not rely on individual investors behaving randomly. Indexing. Our proposed explanation then connects our paper to the literature on index inclusion (Wurgler, 2010). These papers can be classified into two broad groups. The first group studies the predictable effects of stock A s inclusion in an index for stock A itself. For instance, Chang et al. (2014) shows that getting added to the Russell 2000 results in a price increase. For other examples involving ETFs, see BenDavid et al. (2016), Brown et al. (2016), and Israeli et al. (2017). The second group studies the predictable change in the correlation between the behavior of stocks A and B after stock A gets added to an index that stock B already belongs to. For instance, Barberis et al. (2005) shows that a stock s beta with the S&P 500 jumps sharply after it gets added to the index. For other wellknown examples, see Greenwood and Thesmar (2011), Vayanos and Woolley (2013), and Anton and Polk (2014). In contrast to these papers, we focus on the unpredictable consequences of stock A s index inclusion for an unrelated stock Z as highlighted in Figure 1. Thresholds. And, this explanation implies that noise can be an externality imposed by funds following many different thresholdbased rebalancing rules, which further connects our analysis to work studying simple financial decision rules. While we focus on ETFs, our central insight also applies to quantitative hedge funds following strategies like value and momentum (Khandani and Lo, 2007; Lou and Polk, 2013) and pension funds with strict portfolio mandates (Pennacchi and Rastad, 2011). Many 6
7 Amplification: Comovement: Demand Noise: (this paper) A buy A buy A buy A buy B buy B sell B sell C buy C buy Z sell Z buy Figure 1: How This Paper Is Different. There is an existing literature on indexlinked investing. Papers in this literature fall into two broad groups. The first group studies how supplementary trading due to index inclusion can amplify initial shocks to stock A (Row 1). The second group of papers studies how stock A s returns suddenly move a lot more like stock B s returns whenever stock A and stock B happen to belong to the same index (Row 2). By contrast, this paper focuses on the unpredictable consequences of stock A s index inclusion, not for stock A or stock B, but for a seemingly unrelated stock Z (Rows 3 and 4). of these funds use strict portfolio rules with the form: Buy the top 30% and sell the bottom 30% of stocks when sorting on X. More generally, people use thresholdbased rules to make all sorts of financial decisions (Gabaix, 2014). The existing literature measures the cost of using an overly simple rule in terms of losses in expected utility. Whereas, we look at how simple decision rules can affect demand volatility. 2 Theoretical Model This section introduces a randomnetworks model where stocks (the nodes) are connected to one another via fund rebalancing rules (the edges). In the model, an initial shock to a randomly selected stock A has the potential to trigger a long rebalancing cascade if there are many different funds following many different rebalancing rules. The model is designed to explain why predicting the effect of a long rebalancing cascade on the demand for any particular stock Z is computationally infeasible, making the resulting demand shock seem like noise. 2.1 Model Setup Here s how the randomnetworks model is set up. Nodes, Edges, and Neighbors. Consider a market with S 1 stocks indexed by s {1,..., S} def = S. Each of these stocks will correspond to a node in our network. In the analysis below, we will often look at the limiting case as the market gets infinitely 7
8 large, S. We will often refer to arbitrary stocks A, B, C,..., s, s,..., Z S when describing properties of the network. In addition to the S stocks, this market also contains a large collection of funds following a diverse collection of rebalancing rules equivalently, tracking a diverse collection of benchmark indexes. These rebalancing rules will define the edges in our network. Two nodes will be connected with an edge, not if the corresponding stocks are held by the same fund, but rather if a shock to one of the stocks would cause some fund to swap out its position in that stock for a new position in the other. If stock s and stock s share an edge, then we will call them neighbors. A node with many neighbors corresponds to a stock on the cusp of many funds rebalancing thresholds. def We use N s to denote stock s s neighbors and N s = N s to denote the size of this set. All neighbors are not created equal, though. To illustrate, consider the situation where stock s and stock s are the 2001st and 2000th largest stocks in the Russell universe. On one hand, a positive shock to stock A has the potential to move it from 2001st to 2000th position in the Russell ecosystem, which would force any fund tracking the Russell 2000 to swap its existing position in stock B for a new position in stock s. But, on the other hand, if stock s dropped from 2001st to 2002nd position, then these same funds wouldn t have to change a thing. With this asymmetry in mind, we use directed edges. If a negative shock to stock s would cause some funds to sell stock s and buy stock s, then we will draw an arrow from stock s to stock s. Whereas, if a positive shock to stock s would cause some fund to buy stock s and sell stock s, then we will draw an arrow from stock s to stock s. An arrow will always point towards the stock that realizes a positive shock. This distinction divides each stock s collection of neighbors into two different subsets. If s N + s, then there is an arrow pointing from stock s to stock s. This means that either a negative shock to stock s or a positive shock to stock s would cause some fund to dump its position in stock s and build a new position in stock s. We refer to this set as stock s s positive neighbors. Conversely, if s N s, then there is an arrow pointing from stock s to stock s. This means that either a positive shock to stock s or a negative shock to stock s would cause some fund to dump its position in stock s and build a new position in stock s. We refer to this set as stock s s negative neighbors. Clearly, if stock s is a positive neighbor to stock s, then stock s is a negative neighbor to stock s. Figure 2 gives some smallscale examples of this network structure. Degree Distribution. We want our randomnetworks model to capture the idea that 8
9 B C A N + A N A N A Figure 2: Nodes, Edges, and Neighbors. Nodes denote the same 3 stocks (A, B, and C) in various network configurations. Table reports number of neighbors for stock A in each configuration. There is an arrow from stock A to stock B if a negative shock to stock A would result in a positive shock to stock B or a positive shock to stock B would result in a negative shock to stock A. If there is an arrow from stock B to stock A, then stock B is a positive neighbors to stock A, B N + A. If there is an arrow from stock A to stock B, then stock B is a negative neighbor to stock A, B N A. long rebalancing cascades are possible if there are many funds following many different trading strategies. In this setting, nodes in the network will be densely connected to one another via a large number of edges. Ideally, there would be a single parameter that controls how dense these connections are i.e., a single parameter that controls how likely it is that two stocks are on the cusp of some fund s rebalancing rule. A natural way to do this is to study a family of random networks whose edges have been assigned according to some probabilistic rule. Then, a single parameter can control the likelihood that an edge connects any randomly selected ordered pair of stocks. We will assume that i) there is an arrow from stock s to stock s with probability κ/s for some parameter 0 κ < log(s) and that ii) the presence or absence of an arrow between any two stocks will be independent of the presence or absence of any other arrow. Given these two assumptions, the number of positive and negative neighbors for each stock s will obey a Poisson distribution as S : N ± s Poisson(κ) (1) See Appendix A for details. Again, this statistical rule is helpful because it means that market connectedness can be summarized using a single parameter: κ = E[N ± s ] (2) If κ 0, then the market is fragmented; the typical stock will tend to have very few neighbors. By contrast, if κ 0, then the market is densely connected. State Variables. We ve just seen how stocks in the model are connected to one 9
10 another via a network formed by various funds respective rebalancing rules. But, what we really want to know is: How do these connections propagate shocks through the market from one stock to the next? So, we need to introduce a set of state variables to keep track of how each stock has been affected by the network. X A s (t) { 1, 0, + 1} denote the current state of stock s following an initial shock to stock A at time t = 1. If X A s (t) = +1, then a rebalancing cascade has caused some fund to build a new position in stock s. Whereas, if X A s (t) = 1, then the opposite outcome has taken place, and a rebalancing cascade has caused some fund to exit its position in stock s. We will use the convention that all S stocks start out in their original state at time t = 0: Let X A s (0) = 0 for all s {1,..., S} (3) Then, at time t = 1, we assume that nature randomly selects one of the S stocks in the market and changes its state. We will refer to this randomly selected initial stock as stock A and assume that the initial shock is positive without loss of generality: X A A (1) = X A A (1) X A A (0) = +1 (4) Updating Rule. To see whether the state of stock s at time t will be affected by a rebalancing cascade that started with an initial shock to stock A at time t = 1, we first identify the subset of stock s s neighbors which realized shocks with the appropriate sign at time (t 1): U + def A s (t) = { s N s + X A s (t 1) < 0, s / U A s (t 1) } (5a) U def A s (t) = { s Ns X A s (t 1) > 0, s / U + A s (t 1) } (5b) Recall that a fund s rebalancing decision will have equalbuyopposite effects on the stock being added to and the stock being removed from its portfolio. So, U + A s (t) represents the set of positive neighbors to stock s which realized negative shocks at time (t 1); whereas, U A s (t) represents the set of negative neighbors to stock s which realized positive shocks at time (t 1). The additional restrictions that s / U A s (t 1) and s / U + A s (t 1) in Equations (5a) and (5b) prevent a time (t 2) shock to stock s from affecting stock s at time (t 1) and then immediately rebounding back again to affect stock s at time t. Without this additional restriction, a rebalancing cascade would not have a welldefined direction. Finally, we use U A s (t) def = U + A s (t) U A s (t) to denote the combined set containing both kinds of recently updated neighbors for stock s at time t and assume U A s (1) = U A s (0) = 0 for all s S as initial conditions. 10
11 Then, following an initial shock to stock A at time t = 1, we compute the state of each stock s at times t 2 as follows: U A s (t) def = sign [ s U A s (t) X A s (t 1) ] (6a) X A s (t) = sign[x A s (t 1) U A s (t)] (6b) The state of stock s can change in 3 different ways at time t in response to an initial shock to stock A at time t = 1. First, stock s can realize a negative shock, X A s (t) 0, if most of its recently updated neighbors just realized positive shocks, U A s (t) = +1. This is what happens when several of stock s s neighbors get added to various benchmark indexes at stock s s expense. Second, stock s can realize a positive shock, X A s (t) 0, if most of its recently updated neighbors just realized negative shocks, U A s (t) = 1. This is what happens when stock s gets added to several funds benchmark indexes. And third, stock s might realize no shock at all, X A s (t) = 0, if the positive and negative shocks to its recently updated neighbors exactly cancel each other out, U A s (t) = 0. Color Coding. If stock s N s +, then we will draw an arrow from stock s to stock s in our diagrams, s s. But, there are two ways that this edge could transmit a shock. Stock s could be positively affected by a negative shock to stock s, or stock s could be negatively affected by a positive shock to stock s. We use colors to distinguish between these two possibilities, using the convention that edges in a cascade will always have a different color than the stock that initiated the rebalancing decision. We will represent cases where a negative shock to stock s causes some fund to sell stock s and buy stock s as s s. By contrast, we will represent cases where a positive shock to stock s causes the same fund to buy stock s and sell stock s as s s. Discussion. At this point, we re done describing the model s setup. But, before moving on to the model s analysis, it s worth pausing for a moment to talk about two important details. The first is that the model doesn t include a constrained optimization problem, which is unusual for theoretical models in economics. Economists usually apply network theory by adding a network structure to an existing assetpricing model and showing that this additional structure distorts how agents were previously solving their original constrained optimization problem (e.g., see Duffie et al., 2009; Ozsoylev and Walden, 2011; Atkeson et al., 2015). But, we re trying to make a different kind of point. We re trying to show that long rebalancing cascades can qualitatively change the 11
12 A B C A B C A B C A B C A B C X A A (t) X B A (t) X C A (t) t = 0 t = 1 t = 2 t = 3 t = Figure 3: Feedback Effects. An example rebalancing cascade on a network with 3 stocks. An arrow from stock B to stock A means that stock B is positive neighbor for stock A, B N + A. A node is colored blue if X A s(t) = +1; it s colored red if X A s (t) = 1; and, it s colored black if X s,a (t) = 0. At time t = 0, all 3 stocks start out with unchanged fundamentals, X A s (0) = 0 for all s {A, B, C}. At time t = 1, stock A realizes a positive shock, X A A (1) = +1, which is denotes by a blue star. This initial shock causes a fund to rebalance its position at time t = 2, buying stock A and selling stock B so that X A B (2) = 1. This secondary shock causes another fund to rebalance its position at time t = 3, selling stock B and buying stock C so that X A C (3) = +1. Finally, this tertiary shock causes one last fund to rebalance its position at time t = 4, buying stock C and selling stock A so that X A A (4) = 1. kind of constrained optimization problem that agents have to solve by introducing noise. More is different. And, the goal of the model is to show why. How is it that long cascades are able to turn simple deterministic rebalancing rules into apparently random demand shocks? This is a question about how stocks in the model are connected to one another not about any particular optimization problem agents are solving. So, we ve structured our model accordingly. The second important detail is that our model allows for feedback effects as illustrated in Figure 3. An initial positive shock to stock A might force a sizebased fund to buy stock A and sell stock B, which might force a momentumbased fund to sell stock B and buy stock C, which might force a volatilitybased fund to buy stock C and sell stock A, bringing the cascade full circle. Feedback effects are going to play a central role in the analysis below. But, it is crucial to point out that this loop stops once it returns to stock A. The updating rule in Equation (6a) implies that stock B s state will remain unchanged so long as X A A (t) = 0, which in turn implies that a rebalancing cascade can last no more than T def = (S + 1) periods. We ve made infinite feedback loops off limits to make our theoretical analysis more straightforward. But, rebalancing cascades would 12
13 clearly be more complex if they contained infinite feedback loops. So, if anything, this assumption that we ve made for analytical tractability works against us. 2.2 Likelihood We want to show that, while it s possible to compute which stocks are most likely to be hit by a long rebalancing cascade, it s computationally infeasible to predict the direction of this impact. So, in this subsection, we start by characterizing the probability that a particular stock will be hit by a long rebalancing cascade. Cascade Inclusion. Let I A s denote an indicator variable for whether the state of stock s S would ever be affected by a rebalancing cascade that starts with stock A: def ] I A s = max (7) t T [ 1{ XA s(t) 0} If I A s = 1, then we will say that stock s was included in the cascade started by an initial shock to stock A. Whereas, if I A s = 0, then the state of stock s would remain at X A s (t) = 0 for the entire duration of a rebalancing cascade starting with stock A. Note that stock A, which realized the initial shock, is always included in any resulting cascade, I A A = 1, since X A A (1) = +1 by construction. And, this fact remains true even if the state of stock A eventually returns to X A A (T ) = 0 due to some later feedback effect, just as we saw happen in Figure 3. We then use the variable L A [1, S] to denote the length of the rebalancing cascade that would be triggered by an initial shock to a randomly selected stock A at time t = 1: def L A = S s=1 I A s (8) The average rebalancing cascade has to have a length of at least E[L A ] = 1, and this can only occur if initial shocks never ever cause any funds to rebalance. Similarly, the average rebalancing cascade can have a length of no more than E[L A ] = S, and this can only occur if an initial shock to an stock always results in a rebalancing cascade that includes every stock in the market. Percolation Threshold. The length of the typical rebalancing cascade that would be set off by an initial shock to a randomly selected stock A changes dramatically as market connectivity crosses a critical threshold of κ = 1. This point is called a percolation threshold in the randomnetworks literature (Bollobás, 2001). Proposition 2.2 (Percolation Threshold). The expected cascade length in a large 13
14 20 E[L s ] κ λ κ Figure 4: Percolation Threshold, Below. xaxis: expected number of positive/negative neighbors for each stock in the network, κ. y axis: expected cascade length, E[L s ], as given by Equation (9). Dashed line: percolation threshold at κ = 1. : sample averages in 1000 simulations of a random network with 5000 nodes. Figure 5: Percolation Threshold, Above. xaxis: expected number of positive/negative neighbors for each stock, κ. yaxis: expected fraction of stocks included in a cascade, λ, as given by solution to Equation (10). Dashed line: κ = 1. : sample averages in 1000 simulations of a random network with 5000 nodes. market is given by lim E[L A] = S 1 1 κ if κ [0, 1) if κ > 1 (9) Let λ def = lim S E[L A /S] denote the fraction of stocks involved in an average cascade. If κ > 1, then λ satisfies the equation λ = 1 e κ λ (10) Figure 4 plots the expected cascade length, E[L A ], as a function of overall market connectivity, κ. It shows that increasing the number of neighbors per stock increases the expected cascade length. If the typical stock has less than 2 neighbors, one positive and one negative, then at some point this chain reaction will peter out i.e., cascades will have finite length. This is the region in Figure 4 to the left of κ = 1. If the expected cascade length is finite, then each individual rebalancing cascade will include an infinitesimal fraction of the countably infinite number of stocks in the market as S. This corresponds to the line at λ = 0 for all κ < 1 in Figure 5. But, as soon as the expected cascade length becomes infinite for κ > 1, the typical rebalancing cascade will then impact a finite fraction of this infinitely large market. And, as a result, Figure 5 shows that λ > 0 as soon as as κ > 1. Likelihood of Impact. We can use the result in Proposition 2.2 to make predictions about which stocks are most likely to be hit by a long rebalancing cascade. Bayes rule tells us that, conditional on an overall level of market connectivity, the probability 14
15 stock s with N s ± neighbors will be involved in a cascade is given by: Pr[I A s = 1 N ± s, κ] Pr[N ± s I A s = 1, κ] E[I A s κ] (11) This brings us to the following corollary, which states that stocks with more neighbors are more likely to be impacted by a long rebalancing cascade. Corollary 2.2 (Likelihood of Impact). The probability that a randomly selected stock s will be included in a rebalancing cascade that starts with an initial shock to a randomly selected stock A at time t = 1 is increasing in its number of positive/negative neighbors: N ± s E[I A s N ± s, κ] > 0 (12) Thus, to sum up, long rebalancing cascades occur in densely connected markets with κ > 1, and stocks with more neighbors are more likely to be affected by these cascades. 2.3 Direction We ve seen how to predict which stocks are more likely to be hit by long rebalancing cascades. So, now let s investigate why it s so hard to predict how these long rebalancing cascades will affect the demand for each stock. Direction of Effect. Let D A s denote the final state of stock s at the conclusion of a rebalancing cascade that started with stock A: def D A s = X A s (T ) (13) Recall that the final data T = S + 1. If D A s = +1, then the net effect of the rebalancing cascade on the demand for stock s was positive. If D A s = 1, then the net effect was negative. And, if D A s = 0, then either stock s wasn t involved in the cascade or there was a feedback loop that canceled out any initial effect that the cascade had, just as diagrammed in Figure 3. Whether vs. How. Before getting to the math, let s first build some intuition for what we want to prove. Take a look at Figure 6. Both panels display cascades unfolding on 4 different networks. The nodes and edges are just as described in Subsection 2.1. The thick edges denote the rebalancing decisions that were made in response to an initial positive shock to stock A, which is represented by the large blue star. The gray shaded edges denote the potential rebalancing decisions that were not triggered by this initial shock to shock A. We are interested in how each of the 4 cascades eventually affects the demand 15
16 for stock Z, which will be represented by the color of the large square. A large blue square will denote a positive impact on stock Z, D A Z = +1; whereas, a large red square will denote a negative impact on stock Z, D A Z = 1. Panel (a, left) does not report how each edge was involved in the rebalancing cascade or how stock Z was eventually affected. Panel (b, right) does. We ve omitted the arrows representing the direction of each edge to avoid visual clutter, so now s s denotes a negative shock to stock s causing some fund to sell stock s and buy stock s while s s denotes exact same transaction triggered by a positive shock to stock s. Looking at the left panel, you can easily tell whether stock Z will be involved in each of the 4 cascades. In all but the bottomright network, there is a clear path from the large blue star denoting stock A to the large black square denoting stock Z. But, while it s easy to trace out this path, which immediately reveals whether stock Z will be hit by the rebalancing cascade, there s no easy way to predict how stock Z will be effected by looking at the left panel. There s nothing in the left panel that would make you think that the upperleft network should result in a positive shock to stock Z, D A Z = +1. The only way to figure this out is by pressing play and seeing how the cascade unfolds. This is what we want to show mathematically. Root of the Problem. The source of the computational complexity lies in the facts that i) rebalancing cascades have an alternating buysellbuysell structure and ii) they follow thresholdbased rules. These two facts imply that evaluating how a long rebalancing cascade involving L A stocks will affect the demand for stock Z is equivalent to evaluating the output of a logical circuit with L gates. Tiny changes in the finegrained structure of a logical circuit can flip the sign of its output. So, predicting how a long rebalancing cascade will impact stock Z means keeping track of every minute detail of how the cascade unfolds. There are no shortcuts. This is the root of the problem. To illustrate, imagine that stock A realizes a positive shock at time t = 1 and there s an alternating buysellbuysellbuy path from stock A to stock Z that would result in a positive shock to stock Z, ˆDA Z = +1, if it were the only branch of the cascade. But, suppose that stock A also has another neighbor that doesn t sit on this branch, which means that there might be another way for the initial shock to propagate through the network and affect stock Z. Depending on how this second branch of the cascade unfolds, it could either reinforce or interfere with the original path and alter your original guess of D A Z = +1. This is the situation outlined in the dashed box at the top of Figure 7. 16
17 (a) Whether? (b) How? Figure 6: Whether vs. How. Both panels display the same 4 rebalancing cascades unfolding on the same collection of 4 random networks. Nodes and edges are as described in Section 2.1; however, we ve omitted the arrows representing the direction of each edge to avoid visual clutter. Thick edges denote rebalancing decisions made in response to an initial positive shock to stock A, which is represented by a large blue star. Gray shaded edges denote potential rebalancing decisions that were not involved in the rebalancing cascade. Stock Z in each network is represented by the large square. We are interested in how each rebalancing cascade will affect the demand for stock Z, and we represent this outcome with by the color of the large square in the right panel. Blue denotes a positive impact, D A Z = +1; whereas, red denotes a negative impact Z, D A Z = 1. Panel (a, left) does not report how each edge was involved in the rebalancing cascade. Panel (b, right) does. s s denotes a negative shock to stock s causing some fund to sell stock s and buy stock s; whereas, s s denotes the same event triggered by a positive shock to stock s. While it was easy to figure out whether stock Z is involved in each cascade by inspecting the left panel, there s simply no way to predict how stock Z will be effected i.e., is the large square in the right panel blue or red? without actually calculating how the entire cascade plays out. 17
18 ?? A Z Case 0: Case 1: Case 2: Case 3: Case 4: Figure 7: Root of the Problem. Dashed box shows situation where stock A, which has N + A = 2 positive neighbors, realizes a positive shock and one of those neighbors is involved in an alternating buysellbuysellbuy path from stock A to stock Z that would result in a positive shock to stock Z, ˆD A Z = +1, if it were the only branch of the cascade. Remaining panels, labeled Case 0,..., 4, show various ways that stock A s second positive neighbor might be involved in the rebalancing cascade, too. The rebalancing cascade s effect on stock Z will be positive unless this second path reconnects with the first path in exactly 2 steps. This example illustrates how, to predict how a long rebalancing cascade will affect the demand for stock Z, you have to keep track precise details about the cascade s global structure. 18
19 The remaining panels show various ways that this second branch might unfold. If the second branch of the cascade never reconnects as in Case 0, then your original guess of ˆD A Z = +1 will be correct. And, if this second branch reconnects in 1, 3, or 4 steps, then your original guess will also be correct. But, if the second branch happens to reconnect in exactly 2 steps, then your original guess will be wrong. This subtle change in the details of how the alternative branch of the cascade unfolded made the difference between the rebalancing cascade having a positive effect on stock Z and the rebalancing cascade have no effect on stock Z at all. Thus, predicting how a long rebalancing cascade will affect the demand for some stock Z is complex because you have to keep track of the cascade s global structure. To figure out how stock Z will be affected by a long rebalancing cascade, you have to check every detail of how the entire cascade unfolds. Computational Complexity. The proposition below encapsulates this basic insight. Proposition 2.3 (Computational Complexity). Suppose that there is alternating buysellbuysell path of rebalancing decisions from stock A to stock Z that would result in a demand shock of ˆDA Z to stock Z if it were the only branch in the cascade. If κ > 1 and at least 2 stocks on this path have 3 or more neighbors, then not only is determining whether D A Z = ˆD A Z an NPcomplete problem but Pr[D A Z = d ˆD A Z ] = Pr[D A Z = d] for each d { 1, 0, 1} with high probability as κ. What this result is saying is that, in a market with many funds following many different rebalancing rules, figuring out how one particular branch of a long rebalancing cascade affects the demand for stock Z doesn t tell you anything about the net effect of the entire rebalancing cascade on the demand for stock Z. So, even if you know that stock Z will be affected by a long rebalancing cascade, you may as well just flip a coin when it comes to predicting how stock Z will be affected. Note that NP completeness is a statement about how fast the difficulty of a problem grows as its size increases. So, saying that determining whether D A Z = ˆD A Z is NPcomplete problem means that this problem gets really hard really fast as the number of stocks grows large S. See Appendix A for details. Densely Connected. There are 3 important details about this result that are worth emphasizing. The first is that rebalancing cascades are only hard to predict in a densely connected market with κ > 1. If κ [0, 1), then the number of stocks in any secondary branch of the cascade that links stock A and stock Z will tend to be finite. So, the difficulty of figuring out whether this secondary chain will change 19
20 ˆD A Z will be capped as the market grows large, S. Corollary 2.3a (Densely Connected). Determining whether D A Z = ˆD A Z is not an NPcomplete problem when κ [0, 1). Alternating Pattern. The second important detail is that rebalancing cascades are only hard to predict if they involve an alternating sequence of buy and sell orders. In a world where a positive shock to one stock can only ever result in a positive shock another stock, predicting how stock Z will be affected by a long rebalancing cascade starting with stock A is equivalent to predicting whether stock Z will be affected because all stocks will be affected in the exact same way. Thus, the alternating buysellbuysell nature of portfolio rebalancing rules plays a key role in the result. Corollary 2.3b (Alternating Pattern). Determining whether D A Z = ˆD A Z is not an NPcomplete problem in a market with onedirection shocks. ThresholdBased Rules. The third and final important detail is that rebalancing cascades are only hard to predict if they involve thresholdbased rules. To see why this is the case, just imagine changing the updating rule defined in Equation (6) to something that did not involve a threshold. For example, suppose that the update to stock s at time t is the average the shocks to its recently updated neighbors and this update altered the state of stock s by θ (0, 1): Ũ A s (t) def 1 = s U A s (t) U A s (t) X A s (t 1) (14a) X A s (t) = θ { X A s (t 1) ŨA s(t) } (14b) In this sort of market, longer chains will have smaller effects on the demand for stock Z in the same way that an AR(1) process s impulseresponse function will be weaker at longer horizons. As a result, you could get a pretty good estimate of how a long rebalancing cascade starting with stock A would affect the demand for stock Z by checking the directions of the shortest paths from stock A to stock Z. Corollary 2.3c (ThresholdBased Rules). Determining whether D A Z = ˆD A Z is not an NPcomplete problem in a market without thresholdbased rebalancing rules. 3 Rebalancing Cascades The previous section explained how a long cascade might theoretically be able to transform a collection of simple deterministic rebalancing rules into random demand 20
21 shocks. This section gives empirical evidence that the transformation actually does take place in realworld financial markets. To do this, we focus on a particular group of funds following thresholdbased strategies and study the rebalancing cascades that emerge following a set of initial shocks. Then, we show that, while it s possible to compute which stocks are most likely to be hit by each cascade, it s not possible to predict the direction of the resulting demand shock. 3.1 Group of Funds We choose exchangetraded funds (ETFs) as our particular group of funds following thresholdbased strategies. Benchmark Variety. There are 3 reasons for this choice. The first is that we need a large group of funds following a very heterogeneous collection of trading strategies. Prior to January 2008, ETFs all looked like the SPDR S&P 500 ETF [SPY] in that they all tracked some sort of preexisting market index, like the S&P 500. But, in early 2008, the SEC changed its guidelines so that an ETF could track its own selfdefined benchmark. After this change, Invesco PowerShares was free to create an ETF tracking the returns of the quintile of S&P 500 stocks with the lowest historical volatility even though there was no preexisting lowvolatility S&P 500 index. All Invesco had to do was promise to announce the identities and weights involved in the benchmark one day in advance. Now, there are more ETFs than stocks. 5 From ProShares we have CLIX (100% long internet retailers and 50% short bricksandmortar U.S. retailers) and EMTY (which just bets against bricksandmortar retailers)... meanwhile from EventShares, we have policyfactor ETFs... like... GOP (full of oil drillers, gun manufacturers, and so on that would benefit from Republican policies) and DEMS (with companies that should do well under Democrats, such as cleanenergy companies). There is also an ETF called TAXR that invests in companies poised to benefit most from a successful attempt to pass a tax reform bill. 6 The sheer number and variety of these socalled smartbeta ETFs has become something of a hotbutton issue of late. To be sure, niche funds tend to be smaller. But, even the rebalancing activity of small ETFs can affect a stock s fundamentals because ETFs do all of their rebalancing during the final 20 to 30 minutes of the trading day. Manager Discretion. The second reason for this choice is that ETF managers have 5 Bloomberg. 5/16/2017. Mutual Funds Ate the Stock Market. Now ETFs Are Doing It. 6 Financial Times. 11/21/2017. A ROSE by any other ticker symbol... 21
22 less ability to deviate from their stated benchmark than mutualfund or hedgefund managers. This is due to the underlying structure of the ETF market (Madhavan, 2016; BenDavid et al., 2017). The company running an ETF (a.k.a., its sponsor ) has an obligation to create or redeem shares of the ETF at the endofday market value of its stated benchmark. If an ETF s price is higher than the endofday market value of its benchmark, then an arbitrageur can sell shares of the ETF back to its sponsor and use the proceeds to buy shares of the underlying assets in the benchmark index. Conversely, if an ETF s price is lower than the endofday market value of its benchmark, then an arbitrageur can sell shares of the assets in the benchmark and use the proceeds to buy shares of the ETF from its sponsor. Thus, ETF managers will always hold a basket of securities that closely mirrors the endofday market value of their stated benchmark. Following this logic through to it s natural conclusion, if arbitrageurs are constantly asking an ETF sponsor to create or redeem lots of shares, then the sponsor must be losing lots of money. So, just like you d expect, creations and redemptions are only a small fraction of daily trading volume for ETFs, and these trades involve less than 0.5% percent of ETFs net assets (Investment Company Institute, 2015). Instead, ETF trading volume primarily comes from managers rebalancing activity just prior to market close. This endofday trading is how ETF sponsors make sure that there is very little difference between the market value of their endofday holdings and the market value of their stated benchmark. An ETF manager who does the bulk of his rebalancing right at market close will incur higher trading costs. But, the typical investor in a smartbeta ETF is not looking for a cheap way to buy and hold a broad market portfolio. ETF investors traded $20 trillion worth of shares last year even though ETFs only have $2.5 trillion in assets. That s 800% asset turnover, which is about 3times more than stocks. 7 An investor interested in holding a smartbeta ETF is looking for quick access to a very targeted position. He d rather the ETF manager have slightly higher trading costs and be much more faithful to his stated benchmark. For a niche ETF, the additional trading costs incurred by the endofday trading are nothing compared to the costs associated with replicating the entire position from scratch. Data Availability. The third and final reason for choosing ETFs is data availability. Other papers in the ETF literature, such as BenDavid et al. (2016), impute daily portfolio positions from endofquarter financial statements. But, we are interested 7 Bloomberg. 3/3/ Ways Passive Investing Is Actually Quite Active. 22
Steve Keen s Dynamic Model of the economy.
Steve Keen s Dynamic Model of the economy. Introduction This article is a nonmathematical description of the dynamic economic modeling methods developed by Steve Keen. In a number of papers and articles
More informationBinary Options Trading Strategies How to Become a Successful Trader?
Binary Options Trading Strategies or How to Become a Successful Trader? Brought to You by: 1. Successful Binary Options Trading Strategy Successful binary options traders approach the market with three
More informationMA 1125 Lecture 05  Measures of Spread. Wednesday, September 6, Objectives: Introduce variance, standard deviation, range.
MA 115 Lecture 05  Measures of Spread Wednesday, September 6, 017 Objectives: Introduce variance, standard deviation, range. 1. Measures of Spread In Lecture 04, we looked at several measures of central
More informationFTS Real Time Project: Smart Beta Investing
FTS Real Time Project: Smart Beta Investing Summary Smart beta strategies are a class of investment strategies based on company fundamentals. In this project, you will Learn what these strategies are Construct
More informationExploiting the Inefficiencies of Leveraged ETFs
Exploiting the Inefficiencies of Leveraged ETFs [Editor s Note: Here at WCI we try to keep things as simple as possible, most of the time. Not today though. Today we re going to be discussing leveraged
More information3 Price Action Signals to Compliment ANY Approach to ANY Market
3 Price Action Signals to Compliment ANY Approach to ANY Market Introduction: It is important to start this report by being clear that these signals and tactics for using Price Action are meant to compliment
More informationUnderstanding ETF Liquidity
Understanding ETF Liquidity 2 Understanding the exchangetraded fund (ETF) life cycle Despite the tremendous growth of the ETF market over the last decade, many investors struggle to understand the mechanics
More informationProblem Set 1 Due in class, week 1
Business 35150 John H. Cochrane Problem Set 1 Due in class, week 1 Do the readings, as specified in the syllabus. Answer the following problems. Note: in this and following problem sets, make sure to answer
More informationBest Reply Behavior. Michael Peters. December 27, 2013
Best Reply Behavior Michael Peters December 27, 2013 1 Introduction So far, we have concentrated on individual optimization. This unified way of thinking about individual behavior makes it possible to
More informationCorporate Finance, Module 21: Option Valuation. Practice Problems. (The attached PDF file has better formatting.) Updated: July 7, 2005
Corporate Finance, Module 21: Option Valuation Practice Problems (The attached PDF file has better formatting.) Updated: July 7, 2005 {This posting has more information than is needed for the corporate
More informationReal Estate Private Equity Case Study 3 Opportunistic PreSold Apartment Development: Waterfall Returns Schedule, Part 1: Tier 1 IRRs and Cash Flows
Real Estate Private Equity Case Study 3 Opportunistic PreSold Apartment Development: Waterfall Returns Schedule, Part 1: Tier 1 IRRs and Cash Flows Welcome to the next lesson in this Real Estate Private
More informationUsing Fractals to Improve Currency Risk Management Strategies
Using Fractals to Improve Currency Risk Management Strategies Michael K. Lauren Operational Analysis Section Defence Technology Agency New Zealand m.lauren@dta.mil.nz Dr_Michael_Lauren@hotmail.com Abstract
More informationCharacterization of the Optimum
ECO 317 Economics of Uncertainty Fall Term 2009 Notes for lectures 5. Portfolio Allocation with One Riskless, One Risky Asset Characterization of the Optimum Consider a riskaverse, expectedutilitymaximizing
More informationEvaluating Performance
Evaluating Performance Evaluating Performance Choosing investments is just the beginning of your work as an investor. As time goes by, you ll need to monitor the performance of these investments to see
More informationIf you are over age 50, you get another $5,500 in catchup contributions. Are you taking advantage of that additional amount?
Let s start this off with the obvious. I am not a certified financial planner. I am not a certified investment counselor. Anything I know about investing, I ve learned by making mistakes, not by taking
More informationSome Characteristics of Data
Some Characteristics of Data Not all data is the same, and depending on some characteristics of a particular dataset, there are some limitations as to what can and cannot be done with that data. Some key
More informationA SpreadsheetLiterate NonStatistician s Guide to the BetaGeometric Model
A SpreadsheetLiterate NonStatistician s Guide to the BetaGeometric Model Peter S Fader wwwpetefadercom Bruce G S Hardie wwwbrucehardiecom December 2014 1 Introduction The betageometric (BG) distribution
More informationAnalysing the ISMPPC Model
University College Dublin, Advanced Macroeconomics Notes, 2015 (Karl Whelan) Page 1 Analysing the ISMPPC Model In the previous set of notes, we introduced the ISMPPC model. We will move on now to examining
More informationModule 3: Factor Models
Module 3: Factor Models (BUSFIN 4221  Investments) Andrei S. Gonçalves 1 1 Finance Department The Ohio State University Fall 2016 1 Module 1  The Demand for Capital 2 Module 1  The Supply of Capital
More informationGetting started with WinBUGS
1 Getting started with WinBUGS James B. Elsner and Thomas H. Jagger Department of Geography, Florida State University Some material for this tutorial was taken from http://www.unt.edu/rss/class/rich/5840/session1.doc
More informationThe Determinants of Bank Mergers: A Revealed Preference Analysis
The Determinants of Bank Mergers: A Revealed Preference Analysis Oktay Akkus Department of Economics University of Chicago Ali Hortacsu Department of Economics University of Chicago VERY Preliminary Draft:
More informationChapter 1 Microeconomics of Consumer Theory
Chapter Microeconomics of Consumer Theory The two broad categories of decisionmakers in an economy are consumers and firms. Each individual in each of these groups makes its decisions in order to achieve
More informationReinforcement Learning. Slides based on those used in Berkeley's AI class taught by Dan Klein
Reinforcement Learning Slides based on those used in Berkeley's AI class taught by Dan Klein Reinforcement Learning Basic idea: Receive feedback in the form of rewards Agent s utility is defined by the
More informationShort Selling Stocks For Large And Fast Profits. By Jack Carter
Short Selling Stocks For Large And Fast Profits By Jack Carter 2017 Disclaimer: No financial advice is given or implied. Publisher is not registered investment advisor or stockbroker. Information provided
More informationCopyright by Profits Run, Inc. Published by: Profits Run, Inc Beck Rd Unit F1. Wixom, MI
DISCLAIMER: Stock, forex, futures, and options trading is not appropriate for everyone. There is a substantial risk of loss associated with trading these markets. Losses can and will occur. No system or
More informationThe Kelly Criterion. How To Manage Your Money When You Have an Edge
The Kelly Criterion How To Manage Your Money When You Have an Edge The First Model You play a sequence of games If you win a game, you win W dollars for each dollar bet If you lose, you lose your bet For
More informationMaturity, Indebtedness and Default Risk 1
Maturity, Indebtedness and Default Risk 1 Satyajit Chatterjee Burcu Eyigungor Federal Reserve Bank of Philadelphia February 15, 2008 1 Corresponding Author: Satyajit Chatterjee, Research Dept., 10 Independence
More informationFIN FINANCIAL INSTRUMENTS SPRING 2008
FIN40008 FINANCIAL INSTRUMENTS SPRING 2008 The Greeks Introduction We have studied how to price an option using the BlackScholes formula. Now we wish to consider how the option price changes, either
More informationChapter 19 Optimal Fiscal Policy
Chapter 19 Optimal Fiscal Policy We now proceed to study optimal fiscal policy. We should make clear at the outset what we mean by this. In general, fiscal policy entails the government choosing its spending
More informationAutomated Options Trading Using Machine Learning
1 Automated Options Trading Using Machine Learning Peter Anselmo and Karen Hovsepian and Carlos Ulibarri and Michael Kozloski Department of Management, New Mexico Tech, Socorro, NM 87801, U.S.A. We summarize
More informationDaily Stock Returns: Momentum, Reversal, or Both. Steven D. Dolvin * and Mark K. Pyles **
Daily Stock Returns: Momentum, Reversal, or Both Steven D. Dolvin * and Mark K. Pyles ** * Butler University ** College of Charleston Abstract Much attention has been given to the momentum and reversal
More informationCopyright by Profits Run, Inc. Published by: Profits Run, Inc Beck Rd Unit F1. Wixom, MI
DISCLAIMER: Stock, forex, futures, and options trading is not appropriate for everyone. There is a substantial risk of loss associated with trading these markets. Losses can and will occur. No system or
More informationBenedetto De Martino, John P. O Doherty, Debajyoti Ray, Peter Bossaerts, and Colin Camerer
Neuron, Volume 79 Supplemental Information In the Mind of the Market: Theory of Mind Biases Value Computation during Financial Bubbles Benedetto De Martino, John P. O Doherty, Debajyoti Ray, Peter Bossaerts,
More informationThis presentation is part of a three part series.
As a club treasurer, you ll have certain tasks you ll be performing each month to keep your clubs financial records. In tonights presentation, we ll cover the basics of how you should perform these. Monthly
More informationCopyright 2011 Pearson Education, Inc. Publishing as AddisonWesley.
Appendix: Statistics in Action Part I Financial Time Series 1. These data show the effects of stock splits. If you investigate further, you ll find that most of these splits (such as in May 1970) are 3for1
More informationSolving dynamic portfolio choice problems by recursing on optimized portfolio weights or on the value function?
DOI 0.007/s0640069073z ORIGINAL PAPER Solving dynamic portfolio choice problems by recursing on optimized portfolio weights or on the value function? Jules H. van Binsbergen Michael W. Brandt Received:
More informationThe Zero Lower Bound
The Zero Lower Bound Eric Sims University of Notre Dame Spring 4 Introduction In the standard New Keynesian model, monetary policy is often described by an interest rate rule (e.g. a Taylor rule) that
More informationA Statistical Analysis to Predict Financial Distress
J. Service Science & Management, 010, 3, 309335 doi:10.436/jssm.010.33038 Published Online September 010 (http://www.scirp.org/journal/jssm) 309 Nicolas Emanuel Monti, Roberto Mariano Garcia Department
More information1. A is a decision support tool that uses a treelike graph or model of decisions and their possible consequences, including chance event outcomes,
1. A is a decision support tool that uses a treelike graph or model of decisions and their possible consequences, including chance event outcomes, resource costs, and utility. A) Decision tree B) Graphs
More informationHandout 4: Deterministic Systems and the Shortest Path Problem
SEEM 3470: Dynamic Optimization and Applications 2013 14 Second Term Handout 4: Deterministic Systems and the Shortest Path Problem Instructor: Shiqian Ma January 27, 2014 Suggested Reading: Bertsekas
More informationMultifactor rulesbased portfolios portfolios
JENNIFER BENDER is a managing director at State Street Global Advisors in Boston, MA. jennifer_bender@ssga.com TAIE WANG is a vice president at State Street Global Advisors in Hong Kong. taie_wang@ssga.com
More information18. Forwards and Futures
18. Forwards and Futures This is the first of a series of three lectures intended to bring the money view into contact with the finance view of the world. We are going to talk first about interest rate
More informationEfficiency and Herd Behavior in a Signalling Market. Jeffrey Gao
Efficiency and Herd Behavior in a Signalling Market Jeffrey Gao ABSTRACT This paper extends a model of herd behavior developed by Bikhchandani and Sharma (000) to establish conditions for varying levels
More informationLECTURE 2: MULTIPERIOD MODELS AND TREES
LECTURE 2: MULTIPERIOD MODELS AND TREES 1. Introduction Oneperiod models, which were the subject of Lecture 1, are of limited usefulness in the pricing and hedging of derivative securities. In realworld
More informationData Analysis. BCF106 Fundamentals of Cost Analysis
Data Analysis BCF106 Fundamentals of Cost Analysis June 009 Chapter 5 Data Analysis 5.0 Introduction... 3 5.1 Terminology... 3 5. Measures of Central Tendency... 5 5.3 Measures of Dispersion... 7 5.4 Frequency
More informationReinforcement Learning
Reinforcement Learning Basic idea: Receive feedback in the form of rewards Agent s utility is defined by the reward function Must (learn to) act so as to maximize expected rewards Grid World The agent
More informationFinance 197. Simple Onetime Interest
Finance 197 Finance We have to work with money every day. While balancing your checkbook or calculating your monthly expenditures on espresso requires only arithmetic, when we start saving, planning for
More informationPRE CONFERENCE WORKSHOP 3
PRE CONFERENCE WORKSHOP 3 Stress testing operational risk for capital planning and capital adequacy PART 2: Monday, March 18th, 2013, New York Presenter: Alexander Cavallo, NORTHERN TRUST 1 Disclaimer
More informationSIMPLE SCAN FOR STOCKS: FINDING BUY AND SELL SIGNALS
: The Simple Scan is The Wizard s easiest tool for investing in stocks. If you re new to investing or only have a little experience, the Simple Scan is ideal for you. This tutorial will cover how to find
More informationUnitofRisk Ratios A New Way to Assess Alpha
CHAPTER 5 UnitofRisk Ratios A New Way to Assess Alpha The ultimate goal of the Protean Strategy and of every investor should be to maximize return per UnitofRisk (UoR). Doing this necessitates the right
More informationCOMPLETE CURRENCY TRADER. How To Time Forex Trades Perfectly: Increase Your Win Ratio & Profit Consistently
How To Time Forex Trades Perfectly: Increase Your Win Ratio & Profit Consistently CONTENTS Why You Should Be Listening To Me? 2 Billionaire Hedge Fund Manager s Greatest Secret Revealed 3 Individual Currency
More informationChapter 15: Dynamic Programming
Chapter 15: Dynamic Programming Dynamic programming is a general approach to making a sequence of interrelated decisions in an optimum way. While we can describe the general characteristics, the details
More informationThe Assumption(s) of Normality
The Assumption(s) of Normality Copyright 2000, 2011, 2016, J. Toby Mordkoff This is very complicated, so I ll provide two versions. At a minimum, you should know the short one. It would be great if you
More informationThe BaumolTobin and the Tobin MeanVariance Models of the Demand
Appendix 1 to chapter 19 A p p e n d i x t o c h a p t e r An Overview of the Financial System 1 The BaumolTobin and the Tobin MeanVariance Models of the Demand for Money The BaumolTobin Model of Transactions
More information10 AGGREGATE SUPPLY AND AGGREGATE DEMAND* Chapt er. Key Concepts. Aggregate Supply1
Chapt er 10 AGGREGATE SUPPLY AND AGGREGATE DEMAND* Aggregate Supply1 Key Concepts The aggregate supply/aggregate demand model is used to determine how real GDP and the price level are determined and why
More informationA Motivating Case Study
Testing Monte Carlo Risk Projections Geoff Considine, Ph.D. Quantext, Inc. Copyright Quantext, Inc. 2005 1 Introduction If you have used or read articles about Monte Carlo portfolio planning tools, you
More informationInflation Targeting and Revisions to Inflation Data: A Case Study with PCE Inflation * Calvin Price July 2011
Inflation Targeting and Revisions to Inflation Data: A Case Study with PCE Inflation * Calvin Price July 2011 Introduction Central banks around the world have come to recognize the importance of maintaining
More informationDeterministic Dynamic Programming
Deterministic Dynamic Programming Dynamic programming is a technique that can be used to solve many optimization problems. In most applications, dynamic programming obtains solutions by working backward
More informationMutual Funds through the Lens of Active Share
Mutual Funds through the Lens of Active Share John Bogle, founder of The Vanguard Group, is famous for his opinion that index funds are unequivocally the best way to invest. Indeed, over the last decade,
More informationGlobal and National Macroeconometric Modelling: A Longrun Structural Approach Overview on Macroeconometric Modelling Yongcheol Shin Leeds University
Global and National Macroeconometric Modelling: A Longrun Structural Approach Overview on Macroeconometric Modelling Yongcheol Shin Leeds University Business School Seminars at University of Cape Town
More informationLectures 13 and 14: Fixed Exchange Rates
Christiano 362, Winter 2003 February 21 Lectures 13 and 14: Fixed Exchange Rates 1. Fixed versus flexible exchange rates: overview. Over time, and in different places, countries have adopted a fixed exchange
More informationSTATISTICAL ANALYSIS OF HIGH FREQUENCY FINANCIAL TIME SERIES: INDIVIDUAL AND COLLECTIVE STOCK DYNAMICS
Erasmus Mundus Master in Complex Systems STATISTICAL ANALYSIS OF HIGH FREQUENCY FINANCIAL TIME SERIES: INDIVIDUAL AND COLLECTIVE STOCK DYNAMICS June 25, 2012 Esteban Guevara Hidalgo esteban guevarah@yahoo.es
More informationVanguard ETFs. A comprehensive guide for financial advisers
Vanguard ETFs A comprehensive guide for financial advisers Contents Introduction to ETFs 4 What are ETFs? 4 How do they work? 4 What are the benefits of Vanguard ETFs? 5 Buying and selling ETFs 6 Market
More informationBachelor Thesis Finance
Bachelor Thesis Finance What is the influence of the FED and ECB announcements in recent years on the eurodollar exchange rate and does the state of the economy affect this influence? Lieke van der Horst
More informationQuestions for Review. CHAPTER 16 Understanding Consumer Behavior
CHPTER 16 Understanding Consumer ehavior Questions for Review 1. First, Keynes conjectured that the marginal propensity to consume the amount consumed out of an additional dollar of income is between zero
More information1 Asset Pricing: Bonds vs Stocks
Asset Pricing: Bonds vs Stocks The historical data on financial asset returns show that one dollar invested in the Dow Jones yields 6 times more than one dollar invested in U.S. Treasury bonds. The return
More informationThis presentation is part of a three part series.
As a club treasurer, you ll have certain tasks you ll be performing each month to keep your clubs financial records. In tonight s presentation, we ll cover the basics of how you should perform these. Monthly
More informationSharpe Ratio over investment Horizon
Sharpe Ratio over investment Horizon Ziemowit Bednarek, Pratish Patel and Cyrus Ramezani December 8, 2014 ABSTRACT Both building blocks of the Sharpe ratio the expected return and the expected volatility
More informationIEO Sector Weights. Price Chart
December 02, 2016 ISHARES US OILGAS EXPLORATION PRODUCTN (IEO) $65.87 Risk: High Zacks ETF Rank 3  Hold 3 Fund Type Issuer Energy  Exploration BLACKROCK IEO Sector Weights Benchmark Index DJ US SELECT
More informationMathematics in Finance
Mathematics in Finance Robert Almgren University of Chicago Program on Financial Mathematics MAA Short Course San Antonio, Texas January 1112, 1999 1 Robert Almgren 1/99 Mathematics in Finance 2 1. Pricing
More informationHUR ST Cycle Trader. Identify the Most Explosive, Highly Profitable Trades in THIS Market! AVAILABLE FOR THE FIRST TIME ANYWHERE!
AVAILABLE FOR THE FIRST TIME ANYWHERE! NEW HUR ST Cycle Trader Based on the work of J.M. Hurst Identify the Most Explosive, Highly Profitable Trades in THIS Market! The Most Influential Discovery of My
More informationLYXOR ANSWER TO THE CONSULTATION PAPER "ESMA'S GUIDELINES ON ETFS AND OTHER UCITS ISSUES"
Friday 30 March, 2012 LYXOR ANSWER TO THE CONSULTATION PAPER "ESMA'S GUIDELINES ON ETFS AND OTHER UCITS ISSUES" Lyxor Asset Management ( Lyxor ) is an asset management company regulated in France according
More informationPricing & Risk Management of Synthetic CDOs
Pricing & Risk Management of Synthetic CDOs Jaffar Hussain* j.hussain@alahli.com September 2006 Abstract The purpose of this paper is to analyze the risks of synthetic CDO structures and their sensitivity
More informationIntroduction to Bond Markets
1 Introduction to Bond Markets 1.1 Bonds A bond is a securitized form of loan. The buyer of a bond lends the issuer an initial price P in return for a predetermined sequence of payments. These payments
More informationHidden Costs in Index Tracking
WINTON CAPITAL MANAGEMENT Research Brief January 2014 (revised July 2014) Hidden Costs in Index Tracking Introduction Buying an index tracker is seen as a cheap and easy way to get exposure to stock markets.
More informationIterated Dominance and Nash Equilibrium
Chapter 11 Iterated Dominance and Nash Equilibrium In the previous chapter we examined simultaneous move games in which each player had a dominant strategy; the Prisoner s Dilemma game was one example.
More informationIlliquidity Contagion and Liquidity Crashes
Illiquidity Contagion and Liquidity Crashes Giovanni Cespa and Thierry Foucault SoFiE Conference Giovanni Cespa and Thierry Foucault () Illiquidity Contagion and Liquidity Crashes SoFiE Conference 1 /
More informationOnline Appendix. Revisiting the Effect of Household Size on Consumption Over the LifeCycle. Not intended for publication.
Online Appendix Revisiting the Effect of Household Size on Consumption Over the LifeCycle Not intended for publication Alexander Bick Arizona State University Sekyu Choi Universitat Autònoma de Barcelona,
More informationTRADE FOREX WITH BINARY OPTIONS NADEX.COM
TRADE FOREX WITH BINARY OPTIONS NADEX.COM CONTENTS A WORLD OF OPPORTUNITY Forex Opportunity Without the Forex Risk BINARY OPTIONS To Be or Not To Be? That s a Binary Question Who Sets a Binary Option's
More informationThe best mutual funds: DFA or Vanguard? Print
The best mutual funds: DFA or Vanguard? Print Written by Paul Merriman Monday, 12 June 2006 We have been teaching investors how to use Vanguard and Dimensional Fund Advisors funds for more than a decade.
More informationPrice Action Breakdown. Exclusive Price Action Trading Approach to Financial Markets. by Laurentiu Damir
Price Action Breakdown Exclusive Price Action Trading Approach to Financial Markets by Laurentiu Damir Copyright 2016 Laurentiu Damir All Rights Reserved. This ebook is copyright protected. No part of
More informationThe Binomial and Geometric Distributions. Chapter 8
The Binomial and Geometric Distributions Chapter 8 8.1 The Binomial Distribution A binomial experiment is statistical experiment that has the following properties: The experiment consists of n repeated
More informationHow Much Profits You Should Expect from Trading Forex
How Much Profits You Should Expect from Trading Roman Sadowski Trading forex is full of misconceptions indeed. Many novice s come into trading forex through very smart marketing techniques. These techniques
More informationProblem Set # Public Economics
Problem Set #3 14.41 Public Economics DUE: October 29, 2010 1 Social Security DIscuss the validity of the following claims about Social Security. Determine whether each claim is True or False and present
More informationExtraction capacity and the optimal order of extraction. By: Stephen P. Holland
Extraction capacity and the optimal order of extraction By: Stephen P. Holland Holland, Stephen P. (2003) Extraction Capacity and the Optimal Order of Extraction, Journal of Environmental Economics and
More informationMark Twain: It ain t what you don t know that gets you into trouble. It s what you know for sure that just ain t so.
DEBUNKING THE TAIL RISK HEDGING SALES PITCH By Arun S Muralidhar, Sriram Lakshminarayanan and Harish Neelakandan 1 Mark Twain: It ain t what you don t know that gets you into trouble. It s what you know
More informationExpectation Exercises.
Expectation Exercises. Pages Problems 0 2,4,5,7 (you don t need to use trees, if you don t want to but they might help!), 9,5 373 5 (you ll need to head to this page: http://phet.colorado.edu/sims/plinkoprobability/plinkoprobability_en.html)
More informationLet s remember the steps for the optimum asset mix using the EF:
The concept of efficient frontier is one of the undisputed pillars of the current investment practice. First defined in 1952 by Harry Markowitz, it helped shift our focus from the performance of individual
More information5.1 Personal Probability
5. Probability Value Page 1 5.1 Personal Probability Although we think probability is something that is confined to math class, in the form of personal probability it is something we use to make decisions
More informationMVE051/MSG Lecture 7
MVE051/MSG810 2017 Lecture 7 Petter Mostad Chalmers November 20, 2017 The purpose of collecting and analyzing data Purpose: To build and select models for parts of the real world (which can be used for
More informationThe Fallacy behind Investor versus Fund Returns (and why DALBAR is dead wrong)
The Fallacy behind Investor versus Fund Returns (and why DALBAR is dead wrong) July 19, 2016 by Michael Edesess It has become accepted, conventional wisdom that investors underperform their investments
More informationModeling FixedIncome Securities and Interest Rate Options
jarr_fm.qxd 5/16/02 4:49 PM Page iii Modeling FixedIncome Securities and Interest Rate Options SECOND EDITION Robert A. Jarrow Stanford Economics and Finance An Imprint of Stanford University Press Stanford,
More informationThe purpose of this paper is to briefly review some key tools used in the. The Basics of Performance Reporting An Investor s Guide
Briefing The Basics of Performance Reporting An Investor s Guide Performance reporting is a critical part of any investment program. Accurate, timely information can help investors better evaluate the
More informationMARKET EFFICIENCY & MUTUAL FUNDS
MARKET EFFICIENCY & MUTUAL FUNDS Topics: Market Efficiency Random Walks Different Forms of Market Efficiency Investing in Mutual Funds Introduction to mutual funds Evaluating mutual fund performance Evaluating
More informationLeveraged ETFs. Where is the Missing Performance? EQUITY MARKETS JULY 26, Equity Products
EQUITY MARKETS Leveraged ETFs Where is the Missing Performance? JULY 26, 2012 Richard Co Executive Director Equity Products 3129303227 Richard.co@cmegroup.com John W. Labuszewski Managing Director Research
More informationH EDGING CALLABLE BONDS S WAPS WITH C REDIT D EFAULT. Abstract
H EDGING CALLABLE BONDS WITH C REDIT D EFAULT S WAPS JanFrederik Mai XAIA Investment GmbH Sonnenstraße 19, 8331 München, Germany janfrederik.mai@xaia.com Date: July 24, 215 Abstract The cash flows of
More informationI. The ProfitMaximizing Firm
University of PacificEconomics 53 Lecture Notes #7 I. The ProfitMaximizing Firm Starting with this chapter we will begin to examine the behavior of the firm. As you may recall firms purchase (demand)
More informationPath dependence. Federico Frattini. Advanced Applied Economics
Path dependence Federico Frattini Advanced Applied Economics Scott E. Page (2006) Path dependence, Quarterly Journal of Political Science, 2006, 1, 87115. Basic notion a small initial advantage or a few
More informationTrading Diary Manual. Introduction
Trading Diary Manual Introduction Welcome, and congratulations! You ve made a wise choice by purchasing this software, and if you commit to using it regularly and consistently you will not be able but
More informationKnowing EXACTLY When to Sell Your Stocks
Knowing EXACTLY When to Sell Your Stocks Buying stocks is fun. There are so many sources you can go to for great ideas. As investors, we re drawn to stocks that have exciting stories. We expend vast amounts
More information