Market Impact, Informational Efficiency, and the Value of Liquidity

A worry many people have about HFT is that it raises market impact costs for large institutional traders. Trading algorithms that explicitly anticipate order flow do exist, but does that mean an outright ban on HFT would reduce trading costs? It’s hard to know the answer to that question, but it may be helpful to consider how instruments receive added value from financial markets.

Ecosystems on secondary markets appear to be completely zero-sum. This is kind of obvious when you only consider first order effects; if a short term trader buys low and sells high, then the money they made has to come from their counterparties somehow. By this logic, if one type of trader consistently makes money, then they are doing so directly at the expense of the rest of the market. This view makes less sense when markets are sufficiently mature.

Well-developed markets with widespread participation offer traders liquidity and the expectation of continued liquidity. That liquidity is worth something. For long-term traders, a liquid marketplace makes it easy to find a partner to trade with. Imagine, for example, how much you would save when selling your home if you didn’t need a broker to find buyers. Liquidity also raises the value of assets themselves; in essence, something is worth more to you if you know that you can readily sell it later. How much more though? If a prospective buyer knew a home could be later sold without paying a 3% broker fee, then maybe they’d consider bidding 1% higher for it. In financial markets, the classic example of this phenomenon is the premium that on-the-run treasuries command in comparison to those that are off-the-run: A 30-year bond with only 10 years left until maturity generally trades at a lower price than a freshly issued 10-year bond, even though the two bonds should make payments that are effectively identical. The reason suspected for this discount is that the fresh 10-year is more actively traded and easier to sell if desired.

Liquidity Provides Option-Value

One way to think of liquidity’s worth is to consider an analogy with put options. A put option offers its owner the ability to sell an asset in the future at a pre-determined price. Liquidity offers the owner of an asset the ability to sell in the future at the prevailing market price, whatever that may be. That difference is important – but even though the “option” associated with liquidity has an “exercise price” that floats with the market price, it is still worth something. Consider that investors pay their brokers for guaranteed executions at (or worse than) the market price. Or consider the existence of trade-at-settlement products, where one party will pay another in order to guarantee an execution at the day’s settlement price (a measure of market price). A liquid security thus has an embedded put option that should increase its value. [1] Options, of course, increase in value when volatility rises. The price of liquidity appears to do the same, for instance on p.42 of this paper, you can see that the on-the-run premium tends to be higher during times of high volatility. [2] [3] [4]

Market Impact

The cost of liquidity is generally divided into 2 components: the bid-ask spread and market impact. The spread is a measure of how much market-makers need to be compensated for the risk of trading with a counterparty large enough to move the price. Market impact is the change in price that occurs after a trade. Since large traders often split their transactions into many small child orders, market impact means that the latter part of these orders are executed at a less favorable price. Very roughly speaking, small traders are expected to have the bid-ask spread as their primary transaction cost and large traders are expected to have market impact as theirs. One common view is that these large traders are “informed” and their favorable information is why market-makers lose money when trading with them. Here’s a widely cited paper by Fox, Glosten, and Rauterberg of Columbia:

There are three primary kinds of private information, which we will label, respectively, inside information, announcement information, and fundamental value information…

Whatever the source of an informed trader’s private information, the liquidity provider will be subject to adverse selection and lose money when it buys at the bid from informed sellers or sells at the offer to informed buyers. As long as there are enough uninformed traders willing to suffer the inevitable expected trading losses of always buying at the offer and selling at the bid, however, the liquidity provider can break even. There simply needs to be a large enough spread between the bid and offer that the losses accrued by transacting with informed traders are offset by the profits accrued from transacting with uninformed investors… [p22 of pdf]

[T]hese informed traders buy when their superior estimate of share value suggests that a stock is underpriced and sell when it indicates a stock is overpriced, their activities make share prices more accurate. [p34 of pdf]

This is a nice story, and I think it is largely reflective of the nature of markets. There’s good reason to think that large traders will often possess valuable information; if you’re going to trade large size, then you have the resources to spend on insightful analysis. And, conversely, if you have the resources to spend on insightful analysis, then you may as well trade large size. There’s some evidence that, in aggregate, managers tend to trade enough size so that their costs balance out their expected profit. [5] This is akin to the type of market efficiency that Cliff Asness and John Liew advance:

[I]t seems like whenever we have found instances of individuals or firms that seem to have something so special (you never really know for sure, of course), the more certain we are that they are on to something, the more likely it is that either they are not taking money or they take out so much in either compensation or fees that investors are left with what seems like a pretty normal expected rate of return. (Any abnormally wonderful rate of return for risk can be rendered normal or worse with a sufficiently high fee.)

Also, it is most certainly the case that with sloppy trading you can easily throw away any expected return premium — whatever its source — that might exist around these strategies by paying too much to execute them

Some Traders Have High Market Impact but Little Valuable Information

But, as with many nice stories, the story of “toxic traders” as “informed” traders seems incomplete. Are there any participants which are generally considered “uninformed”, trade large size, and have high costs from market impact? Most obvious are index funds. [6] [7] When stocks are expected to be incorporated into an index like the S&P 500, their prices rise in anticipation. And stock prices tend to fall when they are expected to be deleted from a popular index. Because these price moves occur before the actual changes in indexes are made, funds that strictly follow an index will trade shares only after prices change, costing them money. [8] Some portion of these anticipatory price moves revert after the actual index changes are finalized (and large funds have completed their rebalancing) – which means that at least part of this expense is not in exchange for something of value, such as the added liquidity that index constituents enjoy. This effect is different from the “invisible scalp” that worries some commentators. That “scalp” concerns the deviation of a fund from its index benchmark, while we’re discussing underperformance of the actual index. Antti Petajisto has estimated this underperformance as costing investors in popular indexes at least a fifth of a percent per year, by no means a trivial sum. [9]

Price Inelasticity

If index investors really are uninformed, why should their trades (or anticipated trades) move the market price at all? The standard adverse selection model would say that less aggressively priced orders in the order book are from market makers requiring compensation for the risk of being run over by large, informed traders. If that model were complete, an informational change would be the only reason a price should ever move. This view is a vestige of the Efficient Market Hypothesis (EMH). In reality, prices move in response to changes in supply and demand, even if those changes aren’t related to any new information. Consider a really simple model, where traders each have their own point estimate for the “intrinsic value” of a stock. Unless everybody has the same estimate, when somebody buys more stock than traders with the lowest estimate are willing to sell, the market price will rise. This is another way to think of an order book. [10] The EMH idea that traders without any information should not be able to significantly move prices is like saying that there are trillions of dollars of undeployed capital backed by first-rate analysis just waiting for stocks to move a few basis points before trading them. That description doesn’t sound like reality, but who knows, perhaps if algorithms continue to take over our markets it could become true in the distant future.

Order Anticipation

Because market impact is such an important force in our markets, detecting institutional order flow could be very lucrative. Market makers moving their quotes out of the way of suspected order flow is order anticipation. Trading in the direction of suspected order flow is also order anticipation, though some label it “front-running”. In public discourse lately, there’s been some tendency to claim that order anticipation is fundamentally the domain of HFT. This is clearly wrong. The connection between stock index changes and anticipatory price moves has a time scale of days, and has been a measurable effect for decades. Similarly, there was suspicion recently that Pershing Square’s toehold purchase of Allergan shares suffered from order anticipation. Again, these price moves occurred over the scale of days, and as can be seen in an analysis by Betton, Eckbo, and Throburn, there is nothing new about toehold purchases exhibiting large price impact. [11] It’s hard to know how much of this impact is due to anticipatory trading or just supply and demand. Separating these two effects is particularly difficult because herding among traders is common and arguably a form of order anticipation itself. Traders’ tendency to make similar decisions simultaneously (herding) has an important influence on market impact, as discussed (among other things) in a wonderful empirical study by  Zarinelli, Treccani, Farmer, and Lillo. It’s also hard to dismiss order anticipation as unhealthy for markets. If liquidity providers were not able to price the risk of their counterparty being part of a takeover attempt, trading could become extremely disorderly.

Information Rents

Traders’ analyses help security prices on public capital markets reflect their real-world values. And market impact is arguably the primary mechanism that connects the information from research with asset prices. [12] At the same time, if market impact costs were too high (from order anticipation, lack of liquidity, or otherwise), nobody rational would bother to trade.

Joe Stiglitz is worried that order anticipation ‘steals’ information rents from research important to economic efficiency. And, also that automated pattern recognition could start a wasteful arms race between computerized order anticipators and fundamental traders trying to avoid them:

[T]he informed, knowing that there are those who are trying to extract information from observing (directly or indirectly) their actions, will go to great lengths to make it difficult for others to extract such information. But these actions to reduce information disclosure are costly. And, of course, these actions induce the flash traders to invest still more to figure out how to de-encrypt what has been encrypted.

If, as we have suggested, the process of encryption and de-encryption is socially wasteful — worse than a zero sum game — then competition among firms to be the best de-encryptor is also socially wasteful. Indeed, flash traders may have incentives to add noise to the market to disadvantage rivals, to make their de-encryption task more difficult. Recognizing that it is a zero sum game, one looks for strategies that disadvantage rivals and raise their costs. But of course, they are doing the same.

I have some sympathy with what he’s saying here, but perhaps his analogy of encryption offers some additional insight. Loosely speaking, encryption is cheap and decryption is very challenging. If there’s sufficient background noise in which to camouflage an “encryptor’s” signal, then probably there isn’t much a “decryptor” can do to find that signal. Obviously, we can conceive of legal or market structures that would tilt the balance of power completely towards the “decryption” camp – like if the law required traders to announce their intentions before taking action. But, for common market structures, I suspect that it isn’t too hard to be almost “maximally” encrypted, that is, to have one’s orders disguised to the point where investing more in encryption isn’t going to measurably affect their detectability. I’m not claiming that everybody is this careful; there are plenty of examples of sloppy trading. But my intuition is that currently the majority of market impact comes from price inelasticity, not order anticipation. That said, I think it’s worthwhile to consider whether there are palatable market structures that allow orders to be better concealed.

Market Manipulation

To quote (again), Matt Levine’s excellent description of manipulation:

Generally it is allowed, encouraged even, for a big market participant to hide its intentions. It is manipulation for a market participant to affirmatively mislead people about its intentions. The space between those two things is very narrow indeed.

When traders are allowed to affirmatively mislead the market about their intentions, then the space of possible “encryption” schemes becomes extremely large and complex. That complexity would make it hard for institutions to reach the “maximally encrypted” state we discussed. With manipulation allowed, Stiglitz’s vision of battles between encryptors and decryptors who “add noise to the market” would be very much “worse than a zero sum game.” Spoofing, which has new laws specifically targetting it, is probably a minor nuissance in comparison to other noise-adding manipulation. Momentum-ignition concerns me much more than spoofing, particularly the sort where very large quantities are traded in order to temporarily cause a supply (or demand) shock as well as fool order anticipators. Again, these order anticipators are not just liquidity-seeking HFTs, but also include execution algorithms, institutional “herding” [13], momentum strategies, human click-traders, and market makers forced to pull their quotes on one side while on the other side quoting more aggressively to exit their bleeding positions.

What does momentum-ignition look like? The allegations that Optiver “banged the close” on energy futures may be characteristic. Optiver appears to have been a market-maker on CME trade-at-settlement (TAS) products, used by participants desiring guaranteed trades at the settlement price. These participants, which may pay for this guarantee, include oil ETFs (Table 2, p45 of pdf). Optiver allegedly then “hedged” their position by trading very aggressively in a short period of time, distorting the settlement price with a program they called the “Hammer.” [14] This allowed them to effectively buy futures near the market price and sell them to their TAS counterparties at the distorted price. [15]

This scheme is indicative of momentum-ignition’s required features: a high-impact mechanism to enter a position and a low-impact mechanism to exit it. [16] I suspect that momentum-ignition is especially easy to spot when it involves a market-making service to a counterparty (or client) which guarantees a benchmark. [17] Matt Levine described another such scheme involving auctions in the equity market. My guess is that when manipulation distorts an important benchmark like the closing price of stocks, or the settlement price of crude oil (gasoline and heating oil too), somebody will probably notice. [18]

Momentum-ignition is prohibited in US equities, as described in this 2010 SEC Concept Release (p17), before Dodd-Frank was law. But spoofing (which the Concept Release states is a type of momentum-ignition) is now punishable with multi-decade jail sentences. I won’t argue that market manipulators should go to jail for life, but I think it’s nice when the law treats offenses similarly if they’re of similar character.

Not everybody has a problem with momentum-ignition though. Here’s Izabella Kaminska on the “concentration” of trading to maximize market impact in the FX scandal [19]:

“Concentration” tactics are normal practice for the industry. It’s the equivalent of creating economies of scale and then choosing the moment to transact so that the depth of the market, and it’s likely impact on the price, is most beneficial to you. It’s called skillful execution.

In some sense, that’s what trading is about

The HFT Controversy

When people criticize HFT, I wonder if what they really dislike is manipulative trading. I don’t know of any reason to think that manipulation is more common among HFTs than other traders. If so, many criticisms about HFT requiring institutional traders to make wasteful technology investments are misdirected. Large institutions’ transaction costs pre-date automated trading and are a natural feature of markets. Computer programs, even when they trade aggressively, can cheaply contribute to liquidity, adding real value to assets. Instead of banishing computers from our markets, society would be better served if we spent more time evaluating the harmfulness of specific behaviors. With clear, consistent definitions of manipulation and good enforcement, perhaps we can convince the public that our markets are safe.


[1] This phenomenon might appear to not add any value to an asset when it’s a shortable security. If a buyer is willing to pay a bit extra because they think the asset will be easier to sell in the future due to the liquidity “put option,” then a short-seller should be willing to accept a lower price because of the similarly embedded “call option.” There’s no reason to think these effects are equal and opposite though; a security’s short interest is usually a small fraction of its overall float.

[2] You might be especially interested in making sure financial assets are liquid if you’re naturally a seller of them. Companies that make use of capital markets (through bond or public stock offerings) would certainly fall into this category. So do governments. Here’s FRBNY’s president, William Dudley addressing the relative illiquidity of TIPS bonds in 2009:

[I]t may make sense to structure the TIPS program in a way that would help reduce the illiquidity premium associated with TIPS relative to on-the-run nominal Treasuries. Some of the current illiquidity premium is likely to shrink as financial markets stabilize. However, further improvements may require a change in either the structure of the TIPS program or the secondary market trading environment.

[3] Francis Longstaff estimated an upper-bound on the value of liquidity by comparing it to a lookback option. An omniscient investor can sell a holding at its peak, but only if its market is completely liquid. If the market were completely illiquid, then the investor can’t sell at all. So a lookback option, which would offer the investor the right to sell at the absolute peak in a given time period, gives an upper-bound on liquidity’s value. In practice, of course, there are caveats:

  1. Returns aren’t normally-distributed.
  2. An investor may not have a pre-specified timeframe. And this lookback option would have infinite value if it were over an infinite time interval – not a very tight upper bound. On a side note, bizarrely,  options like this actually exist in the real world.
  3. An omniscient investor might choose to sell a holding below its peak for other reasons (like taxes, personal reasons, or because when you know everything, there’s probably a better way to deploy capital).
  4. Omniscience doesn’t exist. And if it did, I feel like markets wouldn’t make any sense.

If you’re interested in methods to price the value of liquidity, here’s a review by Aswath Damodaran.

[4] Proprietary traders as a whole make much more money when volatility is high. Those increased profits could be partly due to the higher value of liquidity and a commensurate rise in demand for it. The entire financial sector is in some sense engaged in the business of selling option-value. One view of banks is that they make money via shorting liquidity: by holding assets (particularly fixed income) to maturity and riding out fluctuations in market value, they are rewarded with a small profit. And one argument against strict mark-to-market accounting is that it doesn’t properly encapsulate this aspect of banking. Another perspective is that when banks have shorted “too much” liquidity and the price of that liquidity has risen (i.e. volatility has gone up and the “option-value” component of liquidity is expensive), they tend to rely on governments and central banks to sell them additional liquidity cheaply in order to survive. If you consider this government backstop to be an unfair subsidy, then asking banks to mark their balance sheets to market makes more sense. I always find this connection between the two “types” of liquidity (the kind provided by central banks and the kind traders use every day) both self-evident and surprising.

[5] This is the so-called fair pricing condition. See for instance this analysis by Waelbroeck and Gomes. They used a dataset of institutional transactions with (most) “cash flow” trades separately marked. “Cash flow” trades are due to client inflows and outflows which are (probably) not reflective of fund managers’ decisions. When they exclude these “cash flow” trades, they find that, on average, returns are quite close to transaction costs for different portfolio managers (figure 4, p23). They also find costs and returns are roughly in balance for transactions of different sizes (figures 12a and 12b, p41).

[6] At least, it’s a common view that index investors piggy-back on the pricing provided by active traders and do not have any valuable information. Maybe this is an over-simplification though; some index investors could buy when they predict future index buying. In that case, would they mind overpaying slightly for something that has psychological value (like index inclusion)?

Here’s Slack CEO Stewart Butterfield on investors being potentially willing to pay a premium to bolster the perceptions surrounding their investment:

You have to choose some numbers… One billion is better than $800 million because it’s the psychological threshold for potential customers, employees, and the press.


[I]t increases the value of our stock and can allow potential employees to take our offers, and it reinforces the perception for our larger customers that we’ll be around for the long haul.

[7] The Waelbroeck and Gomes analysis in [5] gives us another example of “uninformed” traders who still pay market impact costs, if you consider “cash flow” transactions to lack informational value:

The peak impact of cash flows is statistically indistinguishable from that of other metaorders and both are indistinguishable from 1.5 times the estimated shortfall.

Their analysis also finds that “cash flow” trades’ market impact has a tendency to revert to the pre-trade price (or even past it). So these transactions have market impact expenses, but also appear to have zero (or negative) long-term alpha.

[8] Some funds are more careful and will deviate from indexes a bit in order to avoid paying some of this impact expense.

[9] I suppose this hidden cost, if real, is one way that index investors are charged by the market for piggy-backing on others’ price discovery.

[10] Many of these “orders” will not be on any exchange’s order book. But they’re somewhere in traders’ minds, which makes them like hidden orders (some people call them “latent orders”).

[11] They anaylzed thousands of public control bids from 1980-2002, a few hundred of which were accompanied by toehold purchases. The charts on p28 show significant pre-announcement price movement.

[12] Of course the price of a security can jump discontinuously in response to new information, on little to no volume. But security prices move continuously during the day, and presumably these price changes have informational value. And, when prices change discontinuously at the open, very often they do so in an auction with heavy volume. I’d imagine that, whenever a price change is accompanied by substantial trading, market impact plays an important role in price discovery. This could explain price volatility appearing lower across the weekend than during trading hours.

[13] Momentum-ignition could profit from “herding” in ways like a manipulator inducing panic, triggering stop orders, or causing forced liquidations.

[14] In reference to a similar case in the FX market, Matt Levine predicted:

Of course there will be emails – there are always emails

One issue with enforcing a ban on momentum ignition (or other market manipulation) is that, in order to prove it, knowledge of a trader’s intent is required. But I guess there are always going to be manipulators who describe their schemes over email, or just call their strategy to bang the close “the Hammer.”

[15] It appears Optiver did a bit more than that, allegedly another division used their foreknowledge of the price-hammering in other ways. From an internal company email (p54):

Nick has made a tidy profit on his trading, close to $100k I expect. But I consider the way In which he did it to be both deceitful, and reckless…

They will tell you of course that they have noticed (after we told them), that when someone sells TAS’s, the future often go down during the settlement…

Since our colleagues in Amsterdam know that we are going to do the dirty work, they simply trade their futures before hand, and make a big profit on them.

[16] The possibility that markets could allow asymmetric, profitable impact is counterintuitive. Writing about the FX rigging case, Matt Levine explains why this is confusing:

Let’s say that the chat room traders are selling euros to customers at the fix, so they want a high fix. They want to buy a lot of euros in the few minutes right before the fix, to push the price up…

Banks could further their manipulation by buying from outside banks, selling to outside banks, or doing neither. This should make you suspicious. All of those things can’t work equally well! If buying from other banks would push the price up, or down, then selling to them should push the price down, or up. The fact that the chat room traders sometimes did one, and sometimes the other, means that they hadn’t found a reliable cheat, a way to take the risk out of their trading. It means in some sense that their manipulation didn’t work. I mean, it worked fine. But there’s a reason you “cnt teach that.” It makes no sense!

Potentially, what these alleged manipulators did was increase their own position when they suspected that their counterparty bank would hedge in a low-impact fashion. When that was the case, the alleged manipulators could do their high-impact trading while their counterparty, on the opposite side, would do low-impact trading. When they suspected a rival bank would trade in a high-impact fashion, they might do the opposite. I’m not saying they were successful at this, but our markets may well allow a high-impact entrance and a low-impact exit, in contradiction with a sort of efficiency. Jim Gatheral calls this type of market efficiency, which renders manipulation impossible, a “no-dynamic-arbitrage principle.”

It would be great if we could design a market where this principle is reality. But I kind of suspect it’s impossible. Maybe the closest we can get is to de-anonymize market data long after the sensitive information it contains is stale. That would allow private-sector analysts to uncover manipulation, as well as offer victims the opportunity to see how it damages them.

[17] Finding a low-impact exit is probably also much easier for market-makers guaranteeing a benchmark price.

[18] It appears that NYMEX grew concerned about Optiver’s activity after just a few weeks.

[19] Different markets have different norms. I don’t know if pushing around the price is acceptable in FX markets, but it appears that regulators may want harsh penalties for any guilty banks.

2 thoughts on “Market Impact, Informational Efficiency, and the Value of Liquidity

  1. Jeffrey

    Another great article. An even more extreme example of uninformed size traders are leveraged ETF’s. In order to keep the same level of leverage, they are required to buy near the close if the market moves up or sell if the market moves down.. in high volatility environments, these can be very large orders, the size and direction of which are deterministic (and potentially anticipated by the market as a whole, leading to significant negative alpha for the ETF’s orders).


    1. Kipp Rogers Post author

      Thanks for pointing out this great example.

      For anyone who is interested:

      An intro to the topic from Joe Light at the WSJ, with quotes from Marco Avellaneda.

      Kid Dynamite talks about a specific example and the use of large Market-On-Close orders.

      This study examines the behavior of large-cap equity index ETFs. Figure 3 on p41 of the pdf has an estimate of the ratio of leveraged ETF rebalancing volume to total volume. On a few days this ratio is around 50%.



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