PrefBlog

Jaksa Cvitanic, Andrei A. Kirilenko have published a paper titled High Frequency Traders and Asset Prices:

Do high frequency traders affect transaction prices? In this paper we derive distributions of transaction prices in limit order markets populated by low frequency traders (humans) before and after the entrance of a high frequency trader (machine). We find that the presence of a machine is likely to change the average transaction price, even in the absence of new information. We also find that in a market with a high frequency trader, the distribution of transaction prices has more mass around the center and thinner far tails. With a machine, mean intertrade duration decreases in proportion to the increase in the ratio of the human order arrival rates with and without the presence of the machine; trading volume goes up by the same rate. We show that the machine makes positive expected profits by “sniping” out human orders somewhat away from the front of the book. This explains the shape of the transaction price density. In fact, we show that in a special case, the faster humans submit and vary their orders, the more profits the machine makes.

They specify:

Machines are assumed to be strategic uninformed liquidity providers. They have only one advantage over the humans – the speed with which they can submit or cancel their orders. Because of this advantage, machines dominate the trading within each period by undercutting slow humans at the front of the book. This is only one of the strategies used by actual high-frequency traders in real markets, and the only one we focus on.[footnote] In the language of the industry, machines aim to “pick-off” or “snipe out” incoming human orders.

Footnote: Other known high frequency trading strategies include (i) the collection of rebates offered by exchanges for liquidity provision, (ii) cross-market arbitrage, and (iii) “spoofing”- triggering other traders to act.

The guts of the paper is:

We find that the presence of a machine is likely to change the average transaction price, even in the absence of new information. We also find that in the presence of a machine, the shape of the transaction price density remains the same in the middle, between the bid and the ask of the machine, the far tails of the density get thinner, while the parts of the tails closer to the bid and the ask of the machine get fatter. In the presence of the machine, mean intertrade duration decreases in proportion to the increase in the ratio of the human order arrival rates with and without the presence of the machine. Trading volume goes up by the same rate. In other words, if the humans submit orders ten times faster when the machine is present, intertrade duration falls and trading volume increases by a factor of ten.

Second, we compute the optimal bid and ask prices for the machine that optimizes expected profits subject to an inventory constraint. The inventory constraint prevents the machine from carrying a significant open position to the next intra-human-trade period. The optimal bid and the ask for the machine are close to being symmetric around the mean value of the human orders, with the distance from the middle value being determined by the inventory constraint – the less concerned the machine is about the size of the remaining inventory, the closer its bid and the ask prices are to each other. The expected profit of an optimizing machine is increasing in both the variance and the arrival frequency of human orders.

Our two findings are interrelated; one the one hand, an optimizing machine is able to make positive expected profits by “sniping” out human orders somewhat away from the front of the book. On the other hand, execution of the “sniping” order submission strategy results in a transaction price density with bulges near the front and thinner outer tails. In fact, in a special case, the faster humans submit and vary their orders, the more profits the machine makes.

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The conclusion of interest is:

We also find that a machine that optimizes expected profits subject to an inventory constraint submits orders that are essentially symmetric around the mean value of the human orders. The distance between the machine’s bid and ask prices increases with its concern about the size of the remaining inventory. The expected profit of an optimizing machine increases in both the variance and the arrival frequency of human orders.

Briefly mentioned on October 18 was High Frequency Trading and its Impact on Market Quality:

In this paper I examine the impact of high frequency trading (HFT) on the U.S. equities market. I analyze a unique dataset to study the strategies utilized by high frequency traders (HFTs), their profitability, and their relationship with characteristics of the overall market, including liquidity, price discovery, and volatility. The 26 HFT firms in the dataset participate in 68.5% of the dollar-volume traded. I find the following key results: (1) HFTs tend to follow a price reversal strategy driven by order imbalances, (2) HFTs earn gross trading profits of approximately $2.8 billion annually, (3) HFTs do not seem to systematically engage in a non-HFTr anticipatory trading strategy, (4) HFTs’ strategies are more correlated with each other than are non-HFTs’, (5) HFTs’ trading levels change only moderately as volatility increases, (6) HFTs add substantially to the price discovery process, (7) HFTs provide the best bid and offer quotes for a significant portion of the trading day and do so strategically so as to avoid informed traders, but provide only one-fourth as much book depth as non-HFTs, and (8) HFTs may dampen intraday volatility. These findings suggest that HFTs’ activities are not detrimental to non-HFTs and that HFT tends to improve market quality.

He provides a good discussion of pinging:

Pinging is defined by the SEC as, “an immediate-or-cancel order that can be used to search for and access all types of undisplayed liquidity, including dark pools and undisplayed order types at exchanges and ECNs. The trading center that receives an immediate-or-cancel order will execute the order immediately if it has available liquidity at or better than the limit price of the order and otherwise will immediately respond to the order with a cancelation” (SEC, January 14, 2010). The SEC goes on to clarify, “[T]here is an important distinction between using tools such as pinging orders as part of a normal search for liquidity with which to trade and using such tools to detect and trade in front of large trading interest as part of an ‘order anticipation’ trading strategy” (SEC, January 14, 2010).

Of interest is the section titled “10-Second High Frequency Trading Determinants”:

This section examines the factors that influence HFTs’ buy and sell decisions. I begin by testing a variety of potentially important variables in an ordered logistic regression analysis. The results show the importance of past returns. I carry out a logistic regression analysis distinguishing the dependent variables based on whether the HFTr is buying or selling and whether the HFTr is providing liquidity or taking liquidity. Finally, I include order imbalance in the logit analysis and find that the interaction between past order imbalance and past returns drives HFTr activity and is consistent with HFTs engaging in a short term price reversal strategy.

Also of interest is the section titled “Testing Whether High Frequency Traders Systematically Engage in Anticipatory Trading”:

In this section I test whether HFTs systematically anticipate and trade in front of non-HFTs (“anticipatory trading”) (SEC, January 14, 2010). It may be that HFTs predict and buy (sell) a stock just prior to when a non-HFTr buys (sells) the stock. If this is the case, HFTs are profiting at the expense of non-HFTs.[footnote]

Footnote: Anticipatory trading is not itself an illegal activity. It is illegal when a firm has a fiduciary obligation to its client and uses the client’s information to front run its orders. In my analysis, as HFTs are propriety trading firms, they do not have clients and so the anticipatory trading they may be conducting would likely not be illegal. Where HFT and anticipatory trading may be problematic is if market manipulation is occurring that is used to detect orders. It may be the case that “detecting” orders would fall in to the same category of behavior as that resulted in a $2.3 million fine to Trillium Brokerage Services for “layering”.

Trillium was fined for the following layering strategy: Suppose Trillium wanted to buy stock X at $20.10 but the current offer price was $20.13, Trillium would put in a hidden buy order at $20.10 and then place several limit orders to sell where the limit orders were sufficiently below the bid price to be executed. Market participants would see this new influx of sell orders, update their priors, and lower their bid and offer prices. Once the offer price went to $20.10, Trillium’s hidden order would execute and Trillium would then withdraw its sell limit orders. FINRA found this violated NASD Rules 2110, 2120, 3310, and IM-3310 (now FINRA 2010, FINRA 2020, FINRA 5210, and also part of FINRA 5210).

I don’t have any problems with what Trillium did – it’s just another example of random illegality. By me, that just shows that most traders are little girls with no conception whatsoever of fundamental value and FINRA panders to them. FINRA’s press release states … :

In concluding this settlement, Trillium and the individual respondents neither admitted nor denied the charges, but consented to the entry of FINRA’s findings.

… from which I conclude that FINRA doesn’t think it was a crime either and the whole thing was simply a case of regulatory extortion.

Of great interest is the author’s estimate of the effect of HFT on market impact:

Figure 4: Time Series of High Frequency Traders’ and Non High Frequency Traders’ Book Depth. This Figure analyzes the depth of the order book and how much depth different types of traders provide by analyzing the price impact of a 1000 share trade hitting the order book with and without different types of traders. There are three graphs. The first, Price Impact of a 1000 Share Trade, examines the total price impact a 1000 share trade would have with all available liquidity accessible. The second graph, Additional Price Impact without HFTs on the Book, depicts the additional price impact that would occur from removing HFTs’ limit orders The third graph, Additional Price Impact without non-HFTs on the Book, graphs the additional price impact from removing non-HFTs’ limit orders. The daily dollar price impact value is calculated giving equal weight to each stock. The order book data is available during 10 5-day windows. The X-axis identifies the first day in the 5-day window. That is, The observation 01-07-08 is followed by observations on January 8th, 9th, 10th, and 11th of 2008. The next observation is for April 7, 2008 and is followed by the next four consecutive trading days. To separate the 5-day windows I enter a zero-impact trade, creating the evenly spaced troughs.

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Also of interest was the effect of the short-selling ban on market participation by HFT:

Figure A-1: High Frequency Trading’s Fraction of the Market around the Short-Sale Ban. The figure shows how HFTs’ fraction of dollar-volume trading varied surrounding the September 19, 2008 SEC imposed short-sale ban on many financial stocks. In the HFT dataset, 13 stocks are in the ban. The two graphs plot HFTs’ fraction of dollar-volume traded for the banned stocks and for the unaffected stocks. The first graph reports the fraction of dollar-volume where HFTs supplied liquidity. The second reports the fraction where HFTs demanded liquidity. I normalize the banned stocks’ percent of the market in both graphs so that the affected and unaffected stocks have the same percent of the market on September 2, 2008. The two vertical lines represent the first and last day of the short-sale ban.

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In a working paper published by the Federal Reserve Bank of New York, authored by Tobias Adrian & Hao Wu and titled The Term Structure of Inflation Expectations:

We present estimates of the term structure of inflation expectations, derived from an affine model of real and nominal yield curves. The model features stochastic covariation of inflation with the real pricing kernel, enabling us to extract a time-varying inflation risk premium. We fit the model not only to yields, but also to the yields’ variance-covariance matrix, thus increasing identification power. We find that model-implied inflation expectations can differ substantially from break-even inflation rates when market volatility is high. Our model’s ability to be updated weekly makes it suitable for real-time monetary policy analysis.

They point out:

However, breakeven inflation rates of zero-coupon off-the-run curves (i.e., implied inflation) still are not pure measures of inflation expectations. This is because the absence of arbitrage implies that the difference between zero-coupon nominal and real yields can be decomposed into three components:

Breakeven Inflation = Expected Inflation + Inflation Risk Premium + Convexity

The literature commonly adjust for the convexity effect (see Elsasser and Sack, 2004). However, the adjustment of breakeven inflation for the inflation risk premium requires the estimation of a term structure model.

The paper by Brian P. Sack and Robert Elsasser is titled Treasury Inflation-Indexed Debt: A Review of the U.S. Experience. The convexity complication is explained as:

One complication with interpreting inflation compensation involves the adjustment for convexity. For a given level of the yield on a nominal security, uncertainty about future inflation increases the expected return on that security. This is a mechanical relationship that arises from the convexity of real returns in inflation—specifically, because higher inflation erodes the real return on the security at a slower rate than lower inflation boosts it (see the appendix). This point was originally made by Fischer (1975); a more recent description of the relationship between inflation compensation and future inflation can be found in McCulloch and Kochin (1998).

Although convexity tends to pull down inflation compensation relative to expected inflation, there may be an inflation risk premium that works in the opposite direction.

The methodology of Adrian & Wu is:

In this paper, we develop an affine term structure model that captures the dynamics of real and nominal yields curves, as well as the evolution of their variance-covariance matrix. This is important, as the inflation risk premium is proportional to the conditional covariance of the real pricing kernel and inflation. In order to increase the power for identifying the inflation risk premium, we match both the term structure of the yield curves, and the term structure of variances and covariances.

We find a relatively small and stable inflation risk premium. The order of magnitude of the inflation risk premium is comparable to other recent estimates in studies that use inflation protected bonds over similar sample periods, but it is smaller and less variable than estimates that use nominal bonds and inflation over longer time periods (see Buraschi and Jiltsov, 2005, and Ang, Bekaert, and Wei, 2006).

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The Federal Reserve Bank of San Francisco has published a working paper by Jens H. E. Christensen, Jose A. Lopez and Glenn D. Rudebusch titled Inflation Expectations and Risk Premiums in an Arbitrage-Free Model of Nominal and Real Bond Yields:

Differences between yields on comparable-maturity U.S. Treasury nominal and real debt, the so-called breakeven inflation (BEI) rates, are widely used indicators of inflation expectations. However, better measures of inflation expectations could be obtained by subtracting inflation risk premiums from the BEI rates. We provide such decompositions using an estimated affine arbitrage-free model of the term structure that captures the pricing of both nominal and real Treasury securities. Our empirical results suggest that long-term inflation expectations have been well anchored over the past few years, and inflation risk premiums, although volatile, have been close to zero on average.

This contradicts the results of Haubrich, et al, from the FRB-Cleveland, (paper reviewed on PrefBlog) who claimed:

The inflation risk premium on a ten-year bond varied between 38 and 60 basis points during our [1982-2008] sample period.

while the FRBNY paper by Adrian & Wu (discussed below) claimed a 0-40bp Inflation Risk Premium for 5-10 year time horizons.

The Christensen group first did a Principal Component Analysis of Treasury yields:

Researchers have typically found that three factors, often referred to as level, slope, and curvature, are sufficient to account for the time variation in the cross section of nominal Treasury yields (e.g., Litterman and Scheinkman, 1991). This characterization is supported by a principal component analysis of our weekly data set, which consists of Friday observations from January 6, 1995, to March 28, 2008, for eight maturities: three months, six months, one year, two years, three years, five years, seven years, and ten years. Indeed, as shown in Table 1, 99.9 percent of the total variation in this set of yields is accounted for by the first three principal components. Furthermore, the loadings across the eight maturities for the first component are quite uniform; thus, like a level factor, a shock to this component will change all yields by a similar amount. The second component has negative loadings for short maturities and positive loadings for long ones; thus, like a slope factor, a shock to this component will steepen or flatten the yield curve. Finally, the third component has U-shaped factor loadings as a function of maturity and is naturally interpreted as a curvature factor.

Only the first two principal components are required to explain real yields – best of all, the “slope” component is well-correlated with that of nominals:

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After developing the model, they conclude:

Finally, for our preferred specification, we subtract each model-implied expected inflation rate from the comparable-maturity model-implied BEI rate and obtain the associated inflation risk premium (IRP). At both the five- and ten-year horizons, these premiums are fairly small, as shown in Figure 5.(17) Indeed, during our sample, these inflation premiums have varied in a range around zero of about ±50 basis points.(18)

Footnote 17: This result provides some support for the argument that the gain to the U.S. Treasury from issuing TIPS bonds instead of nominal bonds may be quite limited, as argued in Sack and Elsasser (2004).

Footnote 18: Again, in theory, the sign of the inflation risk premium depends on the covariance between the real stochastic discount factor and inflation, but there are real-world considerations as well. For example, a liquidity premium for holding TIPS instead of nominal Treasury bonds would show up as a negative inflation risk premium.

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Finally, the authors conclude:

This paper estimates an arbitrage-free model with four latent factors that can capture the dynamics of both the nominal and real Treasury yield curves well and can decompose BEI rates into inflation expectations and inflation risk premiums. The model-implied measures of inflation expectations are correlated closely with survey measures, while the estimated inflation risk premiums fluctuate in fairly close range around zero. The empirical results suggest that long-term inflation expectations have been well-anchored in the period from year-end 2002 through the first quarter of 2008.

In a working paper published by the Bank for International Settlements, authored by Peter Hördahl and Oreste Tristani, titled Inflation risk premia in the US and the euro area:

We use a joint model of macroeconomic and term structure dynamics to estimate inflation risk premia in the United States and the euro area. To sharpen our estimation, we include in the information set macro data and survey data on inflation and interest rate expectations at various future horizons, as well as term structure data from both nominal and index-linked bonds. Our results show that, in both currency areas, inflation risk premia are relatively small, positive, and increasing in maturity. The cyclical dynamics of long-term inflation risk premia are mostly associated with changes in output gaps, while their high-frequency fluctuations seem to be aligned with variations in inflation. However, the cyclicality of inflation premia differs between the US and the euro area. Long term inflation premia are countercyclical in the euro area, while they are procyclical in the US.

This model is much more macro-oriented than most:

In this paper we focus on modelling and estimating the first of these two components – i.e. the inflation risk premium – in order to obtain a “cleaner” measure of investors; inflation expectations embedded in bond prices. In doing so, we try to reduce the risk that liquidity factors might distort our estimates by carefully choosing when to introduce yields on index-linked bonds in the estimations. We also include survey information on expectations, which should aid us in pinning down the dynamics of key variables in the model. Moreover, in order to understand the macroeconomic determinants of inflation risk premia we employ a joint model of macroeconomic and term structure dynamics, such that prices of real and nominal bonds are determined by the macroeconomic framework and investors’ risk characteristics. More specifically, building on Ang and Piazzesi (2003), we adopt the framework developed in Hördahl, Tristani and Vestin (2006), in which bonds are priced based on the dynamics of the short rate obtained from the solution of a linear forward-looking macro model and using an essentially a¢ ne stochastic discount factor (see Duffie and Kan, 1996; Dai and Singleton, 2000; Duffee, 2002).

They find a rather peculiar difference in the responses of EUR denominated bonds vs Treasuries to output-gap shocks:

There is however one striking di¤erence in the conditional dynamics of risk premia in the two currency areas. While we find that inflation premia always respond positively to upward inflation shocks, the response to output gap shocks di¤er between the US and the euro area. A positive output shock results in a higher inflation premium in the US, while it lowers it in the euro area. The positive relationship for the US could reflect perceptions of a higher risk of inflation surprises on the upside as the output gap widens, while the euro area result is consistent with investors becoming more willing to take on risks – including inflation risks – during booms, while they may require larger premia during recessions.

The model’s detailed results are:

Looking at the results in more detail, Figure 9 shows that a one standard deviation upward shock to the output gap (about 0.4%) in the US pushes the 10-year break-even rate up by around 15 basis points on impact. About two thirds of this e¤ect is due to a rising inflation premium, while one third corresponds to an increase in expected inflation as a result of the expansionary shock. At the 2-year horizon, the effect on the break-even rate is even larger, at around 26 basis points on impact, but now the bulk of this response is due to rising inflation expectations (16 basis points), whereas the inflation premium accounts for the remaining 10 basis points. Hence, a shock to the output gap seems to result in a parallel shift in the inflation premium, while inflation expectations react much more strongly for short horizons than long, reflecting the short- to medium-term persistence of output gap shocks. In the euro area, a positive shock to the output gap also raises expected inflation – and more so at the 2-year horizon than the 10-year horizon – but the inflation premium response is uniformly negative (Fig. 11). Moreover, as the expected inflation response declines with the horizon, the break-even response goes from being positive at the 2-year horizon to being slightly negative at 10 years.

The authors conclude, in part:

Our results show that the inflation risk premium is relatively small, positive, and increasing with the maturity, in the United States as well as in the euro area. Our estimated inflation premia vary over time as a result of changes to the state variables in the model. Specifically, in both economies the output gap and inflation are the main drivers of inflation premia. The broad movements in long-term inflation risk premia largely match those of the output gap, while more high-frequency premia fluctuations seem to be aligned with changes in the level of inflation.

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