Thursday, November 4, 2021

Making Sure "Number Go Up"

Source
Fake it till you make it is the way Silicon Valley works these days, as exemplified by Theranos, Uber, WeWork and many other role models. It is certainly the case with cryptocurrencies. Would you believe that an NFT of this image was worth $532M? How about nearly $1.1B? Most numbers that are quoted about cryptocurrencies are fake, in the sense that they are manipulated in order to fool the press, and thereby buy time until they become "too big to fail".

The credulous press reports make it look like the cryptocurrency market is much bigger and much more successful that it really is, further inflating the bubble. Below the fold, I provide a set of examples of the techniques that are used to fuel the mania.

Wash Trades

In regulated markets, wash trading is illegal, but the whole point of cryptocurrencies is to evade annoying regulations like this that prevent market manipulation. Nick Baker's An NFT Just Sold for $532 Million, But Didn’t Really Sell at All dissects a blatant example:
Source
The process started Thursday at 6:13 p.m. New York time, when someone using an Ethereum address beginning with 0xef76 transferred the CryptoPunk to an address starting with 0x8e39.

About an hour and a half later, 0x8e39 sold the NFT to an address starting with 0x9b5a for 124,457 Ether -- equal to $532 million -- all of it borrowed from three sources, primarily Compound.

To pay for the trade, the buyer shipped the Ether tokens to the CryptoPunk’s smart contract, which transferred them to the seller -- normal stuff, a buyer settling up with a seller. But the seller then sent the 124,457 Ether back to the buyer, who repaid the loans.

And then the last step: the avatar was given back to the original address, 0xef76, and offered up for sale again for 250,000 Ether, or more than $1 billion.
How prevalent is wash trading at cryptocurrency exchanges? The top three results I got from Google are all papers from this year.

First, Wash trading at cryptocurrency exchanges by Guénolé Le Pennec, Ingo Fiedler and Lennart Ante:
Suspicious volume of >90% is detected for most investigated exchanges.
...
Cryptocurrency exchanges allegedly use wash trading to falsely signal their liquidity. We monitored twelve exchanges for metrics of web traffic and for their administered user funds. The exchanges were clustered in three distinct groups based on previous findings: (1) accurately-reporting exchanges, (2) exchanges that engaged in wash trading, (3) exchanges with mixed evidence of wash trading. A comparison of the reported to the predicted trading volume, calibrated on the accurately-reporting exchanges, suggests that group 2 exchanges exaggerate their true volume by a factor of 25 to 50, and exchanges of group 3 by a factor of 1.25 to 33.
Second, Crypto Wash Trading by Lin William Cong, Xi Li, Ke Tang and Yang Yang:
We introduce systematic tests exploiting robust statistical and behavioral patterns in trading to detect fake transactions on 29 cryptocurrency exchanges. Regulated exchanges feature patterns consistently observed in financial markets and nature; abnormal first-significant-digit distributions, size rounding, and transaction tail distributions on unregulated exchanges reveal rampant manipulations unlikely driven by strategy or exchange heterogeneity. We quantify the wash trading on each unregulated exchange, which averaged over 70% of the reported volume. We further document how these fabricated volumes (trillions of dollars annually) improve exchange ranking, temporarily distort prices, and relate to exchange characteristics (e.g., age and userbase), market conditions, and regulation.
Third, Detecting and Quantifying Wash Trading on Decentralized Cryptocurrency Exchanges by Friedhelm Victor and Andrea Marie Weintraud:
Cryptoassets such as cryptocurrencies and tokens are increasingly traded on decentralized exchanges. The advantage for users is that the funds are not in custody of a centralized external entity. However, these exchanges are prone to manipulative behavior. In this paper, we illustrate how wash trading activity can be identified on two of the first popular limit order book-based decentralized exchanges on the Ethereum blockchain, IDEX and EtherDelta. We identify a lower bound of accounts and trading structures that meet the legal definitions of wash trading, discovering that they are responsible for a wash trading volume in equivalent of 159 million U.S. Dollars. While self-trades and two-account structures are predominant, complex forms also occur. We quantify these activities, finding that on both exchanges, more than 30% of all traded tokens have been subject to wash trading activity. On EtherDelta, 10% of the tokens have almost exclusively been wash traded.
It looks like wash trading is quite a problem, which would make rankings of exchanges and volume numbers highly inflated, not to mention prices.

Pumps-and-Dumps

Three years ago Tao Li et al published a detailed analysis entitled Cryptocurrency Pump-and-Dump Schemes concluding that:
Pump-and-dump schemes (P&Ds) are pervasive in the cryptocurrency market. We find that P&Ds lead to short-term bubbles featuring dramatic increases in prices, volume, and volatility. Prices peak within minutes and quick reversals follow. The evidence we document, including price run-ups before P&Ds start, implies significant wealth transfers between insiders and outsiders. ... Using a difference-in-differences approach, we provide causal evidence that P&Ds are detrimental to the liquidity and price of cryptocurrencies.
Source
They were pervasive then and they still are now. For example, David Gerard documents one on 16th December 2020 that took BTC to a new high over $20K:
We saw about 300 million Tethers being lined up on Binance and Huobi in the week previously. These were then deployed en masse.

You can see the pump starting at 13:38 UTC on 16 December. BTC was $20,420.00 on Coinbase at 13:45 UTC. Notice the very long candles, as bots set to sell at $20,000 sell directly into the pump.
...
A series of peaks followed, as the pumpers competed with bagholders finally taking their chance to cash out — including $21,323,97 at 21:54 UTC 16 December, $22,000.00 precisely at 2:42 UTC 17 December, and the peak as I write this, $23,750.00 precisely at 17:08 UTC 17 December.

This was exactly three years after the previous high of $19,783.06 on 17 December 2017.
And another pump on 6th October:
Someone bought 1.6 billion dollars’ worth of bitcoins in one lump on Wednesday 6 October in under five minutes, between 13:11 and 13:16 UTC. This pumped the Bitcoin price from about $50,000 to about $55,000.
Of course, they didn’t use dollars to buy the bitcoins — they used tethers to buy the coins on Binance, tethers that had been freshly created and deployed to the exchange a few days earlier.
Source
And another on 15th October:
There was a similar tether-fueled pump, to a new all-time high, just before the CFTC settlement came out on 15 October. This pump continued for a few more days.

This new all-time high was followed by a flash-crash to below $10,000 on some exchanges. Bitfinex’ed blames trading bots being shut off. [Twitter] This also suggests that the un-pumped price of Bitcoin would be far lower than the present price in tethers.

When the price dipped from its unfeasibly-pumped peak, multiple major crypto exchanges coincidentally had simultaneous downtime.
Do these simultaneous outages look suspicious or not?

Transaction Rate

Source
The press claim that Bitcoin is widely used because it processes around 270K transactions/day. But Igor Makarov and Antoinette Schoar write:
90% of transaction volume on the Bitcoin blockchain is not tied to economically meaningful activities but is the byproduct of the Bitcoin protocol design as well as the preference of many participants for anonymity ... exchanges play a central role in the Bitcoin system. They explain 75% of real Bitcoin volume
So it is really only processing around 27K "economically meaningful" transactions/day. And 75% of those are transactions between exchanges, so only 2.5% of the "transactions" are real blockchain-based transfers involving individuials. That's less than 5 per minute.

Trading Volume

Source
Naively, the press multiplies the inflated transaction rate by the inflated "price" resulting from the latest wash trades or pumps to claim that the value of Bitcoins' daily transactions is around $5B. Doing so involves valuing the 90% of the not "economically meaningful" transactions like the meaningful ones. So this number is inflated by a factor of around 10.


Source
This inflation is obvious if we look at the trading volume on major exchanges, which is currently in the region of $400M/day. Thus it represents around 8% of the claimed trading volume of Bitcoin. Interestingly, this approximately matches Makarov and Schoar's 75% of 10% of $5B as the exchange-based "trading volume" on the blockchain.


Market Cap

Source
Similarly, the press claim that the "market cap" of Bitcoin is once again approaching a trillion dollars (as much at Tesla!) is arrived at by naively multiplying the inflated "price" by the number of Bitcoins that have been mined.

Back in January when Bitcoin's inflated "price" was only around $35K, Jemima Kelly took this claim to the woodshed in No, bitcoin is not “the ninth-most-valuable asset in the world”:
if you take the all-time-high of $37,751 and multiply that by the bitcoin supply (roughly 18.6m) you get to just over $665bn. And, if that were accurate and representative and if you could calculate bitcoin’s value in this way, that would place it just below Tesla and Alibaba in terms of its “market value”. (On Wednesday!)

The only problem is, as you might have already guessed, that’s not accurate or representative and you cannot calculate bitcoin’s value in that way.
Kelly points out that the whole idea of a "market cap" for a totally speculative asset is just wrong:
working out its “market cap” is a non-starter. As some of you might remember, it was originally designed to be a currency that could be used to buy actual things! And although it fails to meet all the criteria that would make it a currency, it does have one thing in common with it: its price is underpinned by sheer faith. The difference being that with fiat currencies, that faith is effectively placed in the governments of the nation states who issue them, whereas for bitcoin, the faith is placed in . . . the hope that other people will keep having the faith.
But even if it weren't, the number multiplying the "price" is just wrong too:
although 18.6m bitcoins have indeed been mined, far fewer can actually be said to be “in circulation” in any meaningful way.

For a start, it is estimated that about 20 per cent of bitcoins have been lost in various ways, never to be recovered. Then there are the so-called “whales” that hold most of the bitcoin, whose dominance of the market has risen in recent months. The top 2.8 per cent of bitcoin addresses now control 95 per cent of the supply (including many that haven’t moved any bitcoin for the past half-decade), and more than 63 per cent of the bitcoin supply hasn’t been moved for the past year, according to recent estimates.

What all this means is that real liquidity — the actual available supply of bitcoin — is very low indeed.
Which means that:
the idea that you can get out of your bitcoin position at any time and the market will stay intact is frankly a nonsense. And that’s why the bitcoin religion’s “HODL” mantra is so important to be upheld, of course.

Because if people start to sell, bad things might happen! And they sometimes do. The excellent crypto critic Trolly McTrollface ... pointed out on Twitter that on Saturday a sale of just 150 bitcoin resulted in a 10 per cent drop in the price.

Tether

Source
Finally, it is important to note that the press reports "prices" in USD but the vast majority of trading in cryptocurrencies, as shown in the graph, is not in USD but in stablecoins, primarily Tether.

Is 1 USDT really the equivalent of 1 USD? Originally, Tether claimed that it has 1 USD in a bank account for every 1 USDT it issued, but that claim was abandoned a long time ago. There has never been an audit to determine what, exactly, is backing Tether.

Zeke Faux's Anyone Seen Tether’s Billions? is the latest in a series of exhaustive attempts to answer that question. He saw:
a document showing a detailed account of Tether Holdings’ reserves. It said they include billions of dollars of short-term loans to large Chinese companies—something money-market funds avoid. And that was before one of the country’s largest property developers, China Evergrande Group, started to collapse. I also learned that Tether had lent billions of dollars more to other crypto companies, with Bitcoin as collateral. One of them is Celsius Network Ltd., a giant quasi-bank for cryptocurrency investors, its founder Alex Mashinsky told me
Clearly, much of the backing is in "commercial paper", i.e. debts owed by other companies. Some of the companies are apparently Chinese real estate developers, desperate for credit. Some is Bitcoin and other cryptocurrencies as collateral for loans to cryptocurrency exchanges. David Gerard is suspicious:
There is no reason to assume the tethers sent to Binance in early October were not just sent as a loan and then the loan accounted as the backing reserve, i.e., Tether sending tethers to a crypto exchange for free — because, as the CFTC settlement notes, Tether has routinely done precisely that, for years. And the Bloomberg story confirms that they still do this in 2021.
Source
As the graph shows, the issuance of USDT and the "price" of BTC are completely correlated. This is the "magic money pump" I outlined inStablecoins. Newly issued USDT sent to an exchange will almost certainly be quickly used to buy cryptocurrency. This pumps the price of cryptocurrencies, including those forming part of Tether's reserve. This allows Tether to issue more USDT, which can be sent to an exchange, used to buy cryptocurrency, which pumps the price, which ... Rinse and repeat.

20 comments:

David. said...

I linked before to Stephen Diehl's work, It is time to do it again. In The Intellectual Incoherence of Cryptoassets he analyses four possible models for cryptocurrencies:

- monetary instruments or currencies
- commodities
- securities contracts.
- art

and finds them all wanting:

"Tis a very strange phenomenon that we as a civilization are allocating so much time, effort, energy and CO2 emissions towards an initiative seemingly backed only by a set of loosely-overlapping narratives that nobody can agree on. ... Crypto on the other hand is a seemingly intellectually circular product that cannot justify its existence in terms of anything but appeals to the political. Crypto seemingly exists simply to trade more crypto on purely ideological purposes attached only to several seemingly incoherent stories."

Go read the whole thing. Tip of the hat to Jemima Kelly.

David. said...

Miami returns to its roots, using the "drug dealer's algorithm" - the first one's free. Liam J. Kelly reports that Miami Will Start Giving Some of Its Residents Free Bitcoin: Mayor Suarez.

David. said...

Prof. Carol Alexander has a series of must-read blog posts that explain the shenanigans behind "number go up":

- Tether Props up Toxic Crypto Carousel
- Tether and Bitcoin Ponzi Ecosystem Stage 1: UP
- Tether and Bitcoin Ponzi Ecosystem Stage 2: DOWN
- Binance Still Onboarding Fiat and Offering 50X to 125X Leverage
- The Tether-Binance Axis and the Great Crypto Crash of 2022

David. said...

Ben Munster reports on the advanced investment strategies used by "number go up" believers in Dumb Money: How to Get Rich in Ethereum Without Understanding It:

"These neophytes—young, relatively internet-savvy though still green when it comes to crypto—will sometimes offer vague talk affirming the tech’s groundbreaking potential, repeating the talking-point mantras of crypto thought leaders and Twitter personalities. More often than not, however, this functions as a mere pretext for putting a lot of money in it.

For many investors, there is only one real, credible value proposition: “Crypto” goes up, very high and very fast."

David. said...

David Gerard provides a comprehensive overview of the latest "regulatory clarity":

1) The Financial Action Task Force issued Updated Guidance for a Risk-Based Approach for Virtual Assets and Virtual Asset Service Providers. Gerard writes:

"The October 2021 revision is to clarify definitions, give guidance on stablecoins, note the issues of peer-to-peer transactions, and clarify the travel rule, which requires VASPs to collect and pass on information about their customers.

VASPs include crypto exchanges, crypto transfer services, crypto custody and financial services around crypto asset issuance (e.g., ICOs). VASPs must do full Know-Your-Customer (KYC), just like any other financial institution."

2) The US Office of Foreign Assets Control's Sanctions Compliance Guidance for the Virtual Currency Industry explains that:

"Members of the virtual currency industry are responsible for ensuring that they do not engage, directly or indirectly, in transactions prohibited by OFAC sanctions, such as dealings with blocked persons or property, or engaging in prohibited trade- or investment-related transactions."

In particular, US miners are required to blacklist wallets suspected of being owned by sanctioned entities. Gerard writes:

"Sanctions are strict liability — you can be held liable even if you didn’t know you were dealing with a sanctioned entity. Penalties can be severe, but OFAC recommends voluntary self-disclosure in case of errors, and this can mitigate penalties. You will be expected to correct the root cause of the violations."

3) The US Financial Crimes Enforcement Network issued Advisory on Ransomware and the Use of the Financial System to Facilitate Ransom Payments. Gerard writes:

"Insurers and and “digital forensic and incident response” companies have been getting more directly involved in ransomware payments — even paying out the ransoms. FinCEN expects such companies to: (a) register as money transmitters; (b) stop doing this.

A lot of ransomware gangs are sanctioned groups or individuals. Payments to them are sanctions violations."

David. said...

Via Claire Jones at Alphaville we learn that the Federal Reserve, the FDIC and the OCC have joined the party with a Joint Statement on Crypto-Asset Policy Sprint Initiative and Next Steps:

"Throughout 2022, the [agencies that regulate the financial system] plan to provide greater clarity on whether certain activities related to crypto-assets conducted by banking organisations are legally permissible, and expectations for safety and soundness, consumer protection, and compliance with existing laws and regulations"

David. said...

Wash trades aren't just the predominant volume on the blockchain, they're 70% of the volume on the unregulated exchanges too. The abstract of Crypto Wash Trading by Lin William Cong reads:

"We introduce systematic tests exploiting robust statistical and behavioral patterns in trading to detect fake transactions on 29 cryptocurrency exchanges. Regulated exchanges feature patterns consistently observed in financial markets and nature; abnormal first-significant-digit distributions, size rounding, and transaction tail distributions on unregulated exchanges reveal rampant manipulations unlikely driven by strategy or exchange heterogeneity. We quantify the wash trading on each unregulated exchange, which averaged over 70% of the reported volume. We further document how these fabricated volumes (trillions of dollars annually) improve exchange ranking, temporarily distort prices, and relate to exchange characteristics (e.g., age and userbase), market conditions, and regulation."

David. said...

Steven Diehl is out with another excellent diatribe in The Token Disconnect:

"After looking at this phenomenon for the last decade, I’ll give what I believe is the first rough draft of history. Silicon Valley ran dry on large breakthroughs in software, so we decided to invent the “blockchain”, a simulacrum of innovation that organically fermented from the anti-institutional themes in the Western zeitgeist to spawn an absurdly large asset bubble with absolutely nothing at the center. There is no there there, and crypto morphed into a pure speculative mania which attracted a fanatic quasi-religious movement fueled by gambling addiction and the pseudo-intellectual narrative economics of the scheme. All conversation around crypto is now simply the sound and fury of post-hoc myth making to rationalize away the collective incoherence of the bubble in a near perfect exemplar of the motivated reasoning of economic determinism."

David. said...

Number go down! Last night showed how thin the BTC-USD market is. David Gerard sums it up:

"Bitcoin crashed to $42,000 last night! Someone sold 1,500 BTC, and that triggered a cascade of sales of burnt margin-traders’ collateral of another 4,000 BTC. The Tether peg broke too."

So sales of 5,500 BTC, or 0.03% of the stock of BTC, crashed the price 20%. The market had trouble coming up with $231M.

David. said...

Joanna Ossinger reports that Small Group of Insiders Is Reaping Most of the Gains on NFTs, Study Shows:

"a new study from Chainalysis shows that a small portion of participants reap most of the gains.

Investing frequently in a wide array of collections appears to lead to the highest profits, Chainalysis said in its report. It added that whitelisting -- the practice of allowing a certain set of followers or others to purchase new NFTs at a much lower price than other users during minting events where a digital file is turned into a digital asset on a blockchain-- helps those people significantly.

Users who make the whitelist and later sell their newly-minted NFT gain a profit 75.7% of the time, versus just 20.8% for users who do so without being whitelisted,
...
“A very small group of highly sophisticated investors rake in most of the profits from NFT collecting,” the study said. “This is especially true in minting, where the whitelisting process gives early supporters of collection access to lower prices that result in greater profits. We also see possible evidence of the use of bots by investors looking to purchase during minting events, which could shut out less sophisticated users, and even result in failed transactions that cost them in fees.”

The practice of whitelisting appears to be similar to the preferential treatment of some insiders and investors that has long been practiced in the cryptocurrency world, especially with so-called initial coin offerings before the sales were shut down by regulators."

David. said...

Jordan Pearson reveals what everyone suspected all along, that "Satoshi Nakamoto" wasn't Craig Wright, but the CIA, in The CIA Is Deep Into Cryptocurrency, Director Reveals:

"There's a long-running conspiracy theory among a small number of cryptocurrency enthusiasts that Bitcoin's anonymous inventor, Satoshi Nakamoto, was actually the CIA or another three-lettered agency. That fringe theory is having a fresh day in the sun after CIA Director William Burns said on Monday that the intelligence agency has "a number of different projects focused on cryptocurrency" on the go."

Actually, this is a cover story. Nakamoto, SAtoshi was from a different three-letter agency.

Ronny said...

Per your reference of Stephen Diehl's work...you may or may not know that he works for a private blockchain startup. A bit of a flag that he hides that fact imho.

http://adjoint.io/

https://twitter.com/dystopiabreaker/status/1470126927818067969

David. said...

Josh WOlfe thinks The ‘To the Moon’ Crash Is Coming:

"To The Moon is not fundamental analysis. It is an inducement. It is an encouragement of belief. And the only thing that is fueling that rocket ship To The Moon is the credulity of others. There’s always a case for optimism, optimism of human ambition and capability of great technological and scientific discoveries. But if your main argument for owning an asset is that other people will own it, not because it has intrinsic value, but because there’s a greater fool—i.e. let's just hype it up and pump it and promote it until more and more fools get in—eventually, the smarter people that induced the fools are leaving them as the bag holders."

David. said...

Re: the accusation of Stephen Diehl's hypocrisy. He critiques permissionless blockchains. This is a different technology from the permissioned blockchains his company develops. His critique is of aspects of permissionless blockchains that permissioned blockchains lack.

David. said...

Andrew Hayward reports that LooksRare Has Reportedly Generated $8B in Ethereum NFT Wash Trading:

"LooksRare seemingly came out of nowhere to become the biggest rival yet to leading NFT marketplace OpenSea earlier this month, but there’s a big asterisk on the astronomical trading figures coming out of the platform.
...
NFT analytics firm CryptoSlam reported today that it has identified more than $8.3 billion worth of wash trading from LooksRare, making up the vast majority of trading volume on the marketplace to date."

"vast majority" = 87%

David. said...

In Cryptocurrency "market caps" and notional value, Molly White does an even better job than Jemima Kelly explaining why I try to always put cryptocurrency "price" and "market cap" in quotes. She concludes:

"there needs to be regulation and enforcement around inauthentic, predatory behavior in crypto—be it wash trading, undisclosed promotions, or intentional price manipulation.

Crypto exchanges and trackers should be clear about how market caps are being calculated—namely, which are being extrapolated only from trades against other cryptos, and essentially double-counted. They also need to be clearer about the enormous margins of error in their calculations: the entire market cap of crypto is represented on CoinMarketCap down to a tenth of a cent, but that level of precision is nowhere near possible.

Finally, journalists and others in media need to understand the true meaning of “market cap” and dollar value when writing about cryptocurrency, and convey that meaning to their readers."

David. said...

Vildana Hajric is another writer who has figured out that Crypto’s Real Value Was Never $3 Trillion:

"One big lesson is that market cap alone isn’t really a great measure of crypto’s economic value—and may even artificially inflate its overall size. While the market value has plunged from $3 trillion to about $1 trillion, the “true,” or realized, value of crypto has held steady in a narrow band. That’s because market cap reflects all the things that can amplify froth, such as leverage, wash trades, manipulation, dormant coins, and coins that never made it into circulation. Strip all that out, and crypto’s value has been remarkably steady through all the gyrations. What would push it higher? In a word, liquidity: more people investing in crypto as a store of value, rather than just trying to pump up the price of their favorite token."

In other words, need more "greater fools" who think that something with "price" this volatile is a store of value.

David. said...

From the department of "Well, Duh!" comes Shawn Tully's There’s a wild theory that the price of Bitcoin is being propped up—and the academic who proved manipulation in 2017 suspects it may be happening again:

"In 2018, [Griffin and Shams] coauthored a groundbreaking study showing that a single, still unidentified, Bitcoin “whale” almost singlehandedly drove the token’s giant run-up in late 2017 and early 2018 by distorting the trading in the token.

Toward the end of 2022, another mystifying trend caught Griffin’s eye. Despite the crypto crash and myriad other negative forces, every time Bitcoin briefly breached the $16,000 floor, it bounced above that level and kept stubbornly trading between $16,000 and $17,000. Almost unbelievably, as the crypto market has continued to unravel into 2023, Bitcoin has gone in the opposite direction, trading up 35% since Jan. 7 to $23,000."

David. said...

Anyone who thinks cryptocurrency "prices" represent organic supply and demand needs to read A twisted tale of celebrity promotion, opaque transactions and allegations of racist tropes by Elle Reeve and Samantha Guff. It starts from the January 2022 The Tonight Show with Jimmy Fallon and Paris Hilton:

"a YouTube time capsule showing the temporary alliance between celebrity marketing and the crypto industry. Bored Ape Yacht Club was not the biggest crypto phenomenon, but it was one of the top beneficiaries of celebrity hype. That celebrity hype, in turn, helped draw new consumers to crypto — an industry rife with manipulation and fraud, and one that US regulators are now giving more scrutiny in the wake of the collapse of crypto exchange FTX. But for a time, when crypto's prices seemed to have no limit, the money appeared too good for some to ask questions — questions like: Why are some of those apes wearing prison clothes?"

it documents how Hollywood agent Guy Oseary organized the celebrities to hype BAYC in return for massive rewards.

David. said...

The final version of CRYPTO WASH TRADING by Lin William Cong, Xi Li, Ke Tang and Yang Yang was published last December.