Optimal Bidding Strategy for Maker Auctions
OOptimal Bidding Strategy for Maker Auctions
Michael Darlin ∗ , Nikolaos Papadis † , Leandros Tassiulas †∗ School of Management, and Yale Institute for Network Science, Yale University † Department of Electrical Engineering, and Yale Institute for Network Science, Yale University
Abstract —The Maker Protocol (“Maker”) is a decentral-ized finance application that enables collateralized lending.The application uses open-bid, second-price auctions to com-plete its loan liquidation process. In this paper, we developa bidding function for these auctions, focusing on the costsincurred to participate in the auctions. We then optimizethese costs using parameters from historical auction data,and compare our optimal bidding prices to the historicalauction prices. We find that the majority of auctions end athigher prices than our recommended optimal prices, and wepropose several theories for these results.
I. IntroductionAuctions have been used in numerous ways, in bothonline and offline contexts. A little-studied area hasbeen the use of auctions on public blockchains, andparticularly auctions used in the context of decentralizedfinance (“DeFi”) applications on Ethereum. Because alltransactions on the Ethereum blockchain are public,auctions conducted by DeFi applications can be studiedin a great level of detail.This paper examines the auctions of one particularDeFi application, the Maker Protocol (“Maker”). Thispaper contains the following insights.1)
Auction overview : We describe the process bywhich Maker auctions are executed, as well as thecharacteristics of the auctions within the frameworkof formal auction theory.2)
Optimal bidding strategy : We outline a conceptualmodel to understand bidder valuations. We thenapply the conceptual model to arrive at a proposedbidding strategy, which focuses on optimizing par-ticipation costs.3)
Historical comparison : We solve for the optimiza-tion of participation costs, based on parametersfrom historical auctions, and use these participationcosts to recommend optimal bidding prices. We thencompare our recommended bidding prices to actualauction prices, and propose reasons for differencesbetween the proposed strategy and historical results.The paper is organized in the following manner: Sec-tions II and III provide context on DeFi and the MakerProtocol, respectively. Section IV proposes a conceptualmodel to understand Maker auctions, and then proposesan optimal bidding strategy. Section V then definesthe costs to participate in Maker auctions. Section VI
The authors thank Florian Ederer for his helpful comments. Allerrors are our own. describes the process for optimizing participation costs,and then compares the optimized participation costs tohistorical auctions on the blockchain. Section VII pro-vides concluding remarks. Appendix A defines Makerauctions within the framework of formal auction theory.II. Decentralized financeEthereum, first launched in 2015, is a blockchain net-work powered by a Proof-of-Work algorithm, with Ether(“ETH”) as its currency. The network’s defining featureis its ability to execute smart contracts on the EthereumVirtual Machine [1]. The network has attracted a range ofpotential use-cases, with varying degrees of feasibility.One of Ethereum’s most visible use-cases has beenthe enablement of DeFi applications. These applica-tions use Ethereum smart contracts to enable financialtransactions, ranging from the relatively simple (lendingand borrowing) to the more complex (synthetic assettrading and liquidity pooling) [2]. The transactions arecommonly performed with stablecoins, which are cryp-tocurrencies with values intended to be pegged to theUS dollar at a 1:1 ratio. Stablecoins are often hostedby the same DeFi applications that enable lending andborrowing [3].A common metric for DeFi usage is Total Value Locked(“TVL”), which measures the amount of currency held insmart contracts used to conduct DeFi transactions. As ofDecember 31, 2018, TVL was measured at $275M; by July31, 2020, TVL was measured at $4.0B [4]. While TVL hasseveral limitations in capturing the true value of DeFiapplications [5], [6], its increase implies a general rise inDeFi usage since the beginning of 2019.Formal research on DeFi applications is relativelyscarce, as DeFi is a nascent technology in the onlyrecently-established field of cryptocurrency technology.Relevant research includes i) overviews of DeFi froman economic and legal perspective [7], [8]; ii) analysesof actual or potential exploits for DeFi applications [9],[10]; and iii) definitions of mathematical characteristicsfor DeFi applications [11], [12].III. Maker Protocol
A. Overview
The Maker Protocol, which was created in 2014 [13],is a DeFi application whose primary purpose is to facil-itate the creation of the DAI stablecoin. Users can send1 a r X i v : . [ q -f i n . T R ] S e p ryptocurrency (for example, ETH1) to a Maker smartcontract, which is referred to as the user’s “vault.” Thecryptocurrency deposited in the vault can be used tocreate DAI, which is recorded as a debt to the user. Whilethe debt remains outstanding, the original currency inthe vault is “locked” and serves as collateral for theoutstanding debt. Maker requires users to maintain aminimum “collateral ratio”, which is the ratio betweenthe value of locked collateral and the debt. If the collat-eral ratio falls below a certain threshold,2 the user’s vaultis liquidated [15].Similar to research on the overall DeFi industry, formalresearch on Maker is relatively meager. Three relevantpapers, all published in the past year, have focused ondisparate topics concerning the project: potential exploitsof Maker’s governance voting process [9], historical fail-ures in Maker’s pricing oracles [16], and a proposedmodel to evaluate default risk in Maker’s loan portfolio[17]. B. Auction process
In Maker’s liquidation process, the user’s collateral(“lot”) is put up for auction.3 The target proceeds (“tab”)include the value of the vault’s debt, plus a liquidationpenalty.4 All bids are submitted in DAI [18], and thebidders participating in the process are referred to as“keepers” [19].The auction is completed in two parts. First, in the“tend” phase, the payment amount increases until thetarget proceeds are met. Second, in the “dent” phase,the reward received (the lot) decreases, until the auctionreaches the maximum auction duration,5 or until nobidder is willing to bid lower than the current bid [18].Regardless of the auction phase, the progress of theauction can be measured through the auction price ofthe collateral, relative to the current market value of thecollateral.The auction reward must be unlocked by submittinga “deal” transaction. If the auction reward is less thanthe collateral originally offered in the auction (as a resultof decreasing bids in the dent phase), the difference isreturned to the user owning the liquidated vault [18].The results of a recent auction, completed in June 2020,are shown in Figure 1.
The first liquidations to use this auction process werecompleted in November 2019.6 Through July 31, 2020,approximately $20.7M in collateral has been liquidatedin this auction process [22].The most notable event in Maker’s auction processoccurred on March 12, 2020, when the price of ETHdropped in excess of 40%. The rapid drop led to manyvaults being liquidated after falling below the 150%collateral ratio [23]. In total, almost 4,000 liquidationsauctions were triggered on March 12, with a total valueof approximately $10.2M [22].Because of the high gas fees on the Ethereum net-work, many keepers were unable to submit bids onthe auctions. Without a robust network of bidders, thehandful of remaining bidders were able to submit zero-value bids. As a result, multiple vaults were liquidatedat prices of zero, and the vaults’ users did not receiveany excess collateral [23].Further explanation of the auction process, in thecontext of formal auction theory, is given in AppendixA. IV. Bidding strategy
A. Conceptual example
In order to define the bidding strategy for Makerauctions, we start with a conceptual example: biddingfor a jar filled with q quarters. The quarters have, intotal, a single market value, which can be expressed indollars as 0 . q . The seller does not hide the amount of q ; all bidders know the exact number of q , and thereforethe total value of the jar of coins. If no other factors werepresent, it may be predicted that all bidders would bidexactly 0 . q , because each bidder has exactly the samevaluation.However, we must consider two other components tothe bidder valuations.
1) Alternative-usage value:
While quarters are valuedat $0.25 cents by all bidders, the coins could be worthmore to certain individuals who could make additionalprofit with the coins. For example, the coins could bemelted down and the raw materials used to produce . q . Thealternative-usage value of the coins, in excess of 0 . q ,is defined as a for an individual bidder. In all futurereferences, a refers to the excess of the alternative-usagevalue over the market value, and not the alternative-usage value itself.
2) Participation costs: • Transaction costs : In this scenario, bidders mustpay a small fee to submit their bid, and anothersmall fee to collect the jar if their bid wins. Thetotal of these fees is defined as b . • Conversion costs : Bidders pay for the jar of coinsin cash, but they can carry only a limited amountof cash in their wallet. If several auctions tookplace at the same time, a bidder who won anauction would likely not have enough cash toparticipate in a second auction. In order to haveenough cash on hand, a bidder would need toperiodically visit a bank and exchange their coinsfor additional cash. The expense of visiting thebank (the cost of transportation, the value of losttime, etc.) are defined as c . • Cost of capital : If bidders increased the amountof cash held in their wallets, they would be able toavoid visiting the bank as frequently as when theyheld smaller amounts of cash. However, holdingcash in a wallet prevents bidders from earninginterest on cash deposited at the bank. The interestforegone when withdrawing cash from the bankis the cost of capital, defined as d .Taking those private value considerations into effect,the expected bid price for an individual bidder can bedefined as 0 . q + a − ( b + c + d ) (1)In theory, the bidder with the highest value of a − ( b + c + d ) would be able to bid the highest price for the jarof coins. B. Application to Maker auctions
In Maker auctions, the “jar of coins” is the collateralbeing auctioned. The collateral has a clearly-definedmarket value, and the value is known by all biddersbefore the auction commences.The additional components of the bidder valuationsare as follows:
1) Alternative-usage value:
Bidders can sell their collat-eral on the market, but they can also use the collateralto gain additional profits elsewhere on the blockchain.In theory, bidders could gain more profit by using thecollateral than they could holding DAI or US dollars.
2) Participation costs: • Transaction fees : In order to submit a bid (tendor dent), collect winnings (deal), or execute anyother transaction, bidders must pay a fee, knownas “gas fees” on the Ethereum blockchain. • Conversion costs : Bidders must convert the collat-eral they have won back into DAI, in order to con-tinue participating in auctions. Because biddersbid in DAI and receive back collateral of a differentcurrency, winning bidders will quickly run outof DAI. When converting collateral back to DAI,bidders must account for a loss in value whenexecuting a trade on a decentralized exchange.This loss is referred to as “slippage.” • Cost of capital : Bidders must invest some amountof capital in holding DAI; the expected return ontheir investment is their cost of capital.Applying Equation (1), the expected auction winnerwould be the bidder with the highest a − ( b + c + d ) ,where a is the alternative-usage value of the collateral,and b + c + d are the participation costs.Using this model, we would expect the followingconditions to be true. If participation costs are higherthan alternative-usage value, then the winning auctionprice would be below the market price. If the alternative-usage value and the participation costs are equal, thewinning auction price would be at the market price. Ifthe alternative-usage value is higher than participationcosts, the winning auction price would not (as mightbe expected) rise above the market price. Instead, thewinning auction price should be bounded by the marketvalue, because the highest bidder would be able to obtainthe collateral at market prices elsewhere, and would haveno incentive to bid above the market price. C. Two-person bidding example
We can apply our theory in a scenario with only twobidders, α and β , participating in a Maker auction. Weassume there is no alternative-usage value of the collat-eral to the bidders. Therefore, the only factors relevant tothe bidders are their participation costs. We also assumethat α ’s and β ’s participation costs are 2% and 3.5% ofthe collateral value, respectively.We assume that α and β will continue bidding theprice higher7 until the auction discount8 is equal oneof the bidder’s participation costs. β can only bid theprice up to 96.5% of the collateral value (a discount of-3.5%), while α can bid up to 98% of the collateral value(a discount of -2%). Therefore, α should always win inan auction setting, because α can bid at a higher pricethan β , without suffering a loss. ig. 2. Example auction with two bidders. Over the course of the 6-hour auction, the discount is reduced until it reaches the participationcost threshold of one of the bidders. At that point, the bidder with thelower threshold (the lower participation cost) will win the auction. D. Proposed bidding strategy
We first note that the value of alternative usage is akey component in determining the appropriate bid price.However, it is quite difficult to estimate the alternative-usage value for collateral. For purposes of this analysis,we focus primarily on participation costs, and only re-turn to alternative-usage values at the end of this paper.With that caveat established, we can then proposean optimal bidding strategy. From the examples givenabove, we arrive at the following proposals:1) Participation costs determine bidding strategy.2) The bidder with the lowest participation costs willalways win.3) Participation costs can be optimized to the lowestpossible amount for each bid value.
Fig. 3. Theoretical minimum auction discount
By optimizing participation costs to their lowest pos-sible total, a bidder could calculate the minimum partic-ipation costs required at every bid value. Dividing these costs into the market price yields a minimum auctiondiscount, expressed as a percentage (see Figure 3). Theminimum auction discount serves as a bidding thresh-old, because a bid with a discount smaller than theminimum auction discount (e.g. a higher price) wouldbe unprofitable. Therefore, a bidder should never bid ata smaller discount than the minimum auction discount,or (in equivalent terms) should never bid at a pricehigher than the market price subtracted from participa-tion costs. V. Participation costsHaving established the importance of participationcosts in determining bid valuations, we now define thespecific costs incurred to participate in Maker auctions.In order to determine the costs incurred, we createda bot to run as a keeper on the Kovan test network.The Kovan network is a test version of the Ethereumnetwork, and transactions executed on this network donot carry any monetary value. However, the functionalityof the Kovan network closely mirrors the main Ethereumnetwork. In addition, the Maker Protocol has set upidentical smart contracts on both Kovan and the mainEthereum network, which allows for testing under near-real conditions on the Kovan network.The keeper bot ran in May and June of 2020, andparticipated in a total of 42 auctions on the Kovannetwork. In addition to testing automated bidding, wealso manually executed certain transactions, such asexchanging collateral rewards (WETH) for DAI, and vice-versa (see full transaction history at [24]).After analyzing the transactions required to run thebot, we identified three types of participation costs:1)
Transaction fees : Gas fees to execute transactions onthe Ethereum blockchain.2)
Conversion costs : Slippage and trading fees forconverting currencies on decentralized exchanges.3)
Cost of capital : Implicit cost of holding capital incryptocurrencies.The costs listed above could be calculated from on-chain data, either directly (transaction fees and conver-sion costs) or indirectly (cost of capital). Although cost ofcapital is not directly incurred on the blockchain, its costis derived from the value of the currency held onchain,and we therefore included the costs in our analysis. Wedid not include costs that were not directly related to on-chain transactions, such as the cost of hardware, electric-ity, maintenance, and other equipment costs. While thesecost are incurred by keepers, we concluded that suchcosts were out-of-scope of our analysis, which focuseson the optimization of onchain costs.In the following sections, we define the specific com-ponents of participation costs.4 . Transaction fees
In Ethereum, charges for computing power are mea-sured in “gas” G . Each transaction on Ethereum takes upa certain amount of gas. For example, a transfer betweentwo non-smart contract addresses always takes up 21,000 G [25]. A transaction involving smart contracts wouldtake up a greater amount of gas, with the exact valuedetermined by the complexity of transaction.Miners then charge a fee for the use of Ethereum’scomputational power. This fee is called the “gas price” µ . The gas price is generally quoted in “gwei”, which isworth 10 − of a full unit of ETH (“ether”). The conversionfactor between ether and gwei is represented throughoutas g (cid:3) − .The total transaction fee is calculated as the gas usedmultiplied by the gas price, or G µ . The resulting answeris in gwei; to convert to ethers, the largest unit ofEthereum, the answer can be calculated as G µ g .
1) Bid fees:
For purposes of this exercise, we assumedthat bidders would not initiate (kick) an auction, andthat bids would only be submitted in the dent phase(gas used G dent ).If the auction is won, the rewards must be collected(gas used G deal ). G deal will only be incurred if the auctionis won. Therefore, we also incorporate the probability x of winning the auction. The total fee, expressed in termsof ETH, is F bid (cid:3) ( G dent + G deal x ) µ g (2)
2) Rebalance fees:
In the Maker system, DAI must besent to a smart contract, called the Vat, before the DAIcan be submitted for a bid. If a bid is won, the rewardis received in WETH. Assuming auctions are won at asteady rate, the available balance of DAI in the Vat will bedepleted over time, while the available balance of WETHin the Vat will increase over time.In order to ensure a sufficient amount of collateral isavailable for bidding, the currency balance in the Vatmust be periodically rebalanced, by converting WETHback to DAI. This operation cannot be performed insidethe Vat. Therefore, the following three transactions arerequired, all of which require gas:1) Removing WETH from the Vat ( exit )2) Converting WETH to DAI, using an exchange ( trade )3) Adding DAI back to the Vat ( join )The gas fees associated with these transactions aredefined as G exit , G trade , and G join , respectively. The threetransactions described above do not need to be executedafter every bid. Rather, their frequency depends on howquickly the Vat balance is depleted of the DAI neededto submit future bids, as well as the frequency of bidsbeing successful.It is assumed that a keeper will set a maximumamount of bidding capital in the Vat ( V max ), and a min-imum amount of capital ( V min ). The difference betweenthese two amounts is the “rebalance margin” R , or the amount of capital that is to be depleted before the Vat isrebalanced.Assuming the first transaction by a keeper sets the Vatcapital at V max , all subsequent bids will take up a certainpercentage of R , before the capital needs to be rebalancedat V min . Because the gas fees described above are onlyincurred when capital reaches V min (that is, when R isfully depleted), each bid can be ascribed a proportionalamount of gas fees, y , using the percentage the bid value B is of R .As an example, if V max is set at 10,000 DAI and V min is set at 7,500 DAI, then R is 2,500. A B of 1,000 DAI willrepresent 40% of R . If gas fees, calculated and convertedto DAI, are 0.2 DAI, then the gas fees ascribed to B are0.08 DAI (40% x 0.2).The proportional allocation does not, however, riseabove 100%. A B of 5,000 DAI would be 200% of an R of 2,500. However, the rebalancing of the portfoliofrom WETH back to DAI would be performed in a singletrade, not in multiple trades. Therefore, the proportionalallocation y would be calculated as 1 if B ≥ R , and BR otherwise.The allocated costs are further adjusted by the proba-bility x of winning the auction. Total rebalance fees aredefined as F rebal (cid:3) ( G exit + G trade + G join ) µ gx y (3) y (cid:3) (cid:40) B ≥ R BR else (4)
3) Total gas fees:
The final step to calculating gas feesis to convert the amount in ethers to an amount in DAI.This conversion can be accomplished by multiplying bythe WETH/DAI exchange rate. The exchange rate can bederived from the Uniswap reserves by calculating T T (seeSection V-B for a detailed explanation of these values). F total (cid:3) ( F bid + F rebal ) T T (cid:3) ( G dent + G deal x ) µ g T T + ( G exit + G trade + G join ) µ gx y T T (5) B. Conversion costs
As mentioned above, the account portfolio needs to beperiodically rebalanced between WETH and DAI. Thisrebalance occurs by trading WETH for DAI on an ex-change. To simplify our analysis, we assumed all tradeswere executed on Uniswap, the largest DeFi exchange bytrading volume.9Uniswap uses a “constant-product market-maker”model, with “liquidity pools” set up as reserves for T for token 0, and reserve T for token 1, the constant product k will always equal T T , in the absence of trading fees.Assuming that no trading fees are taken, the change ∆ T , caused by trading in an amount of T to theliquidity pool, can be used to calculate the total changein the liquidity pool. Given the constant product natureof the liquidity pool, the new value of k will be k (cid:3) ( T − ∆ T )( T + ∆ T ) (6)Rearranging the terms of Equation (6), the outputamount of T in a trade will be ∆ T (cid:3) T − kT + ∆ T (7)When trading fees are introduced to the liquiditypool, k now increases in proportion with trading fees γ , while still holding constant if fees are omitted fromthe equation. k (cid:3) ( T − ∆ T )( T + ( − γ ) ∆ T ) (8)Rearranging the terms of Equation (8), the outputamount of T in a trade will be ∆ T (cid:3) T − kT + ( − γ ) ∆ T (9)The implicit price in the liquidity pool before a trade, P , is given as P (cid:3) T T . The implicit price for the tradeitself, P , would be ∆ T ∆ T . Slippage S is defined as the lossin value executed after the trade, and can be calculatedas P − P P . In expanded form, S is calculated as S (cid:3) T T − T − T T T + ( − γ ) ∆ T ∆ T T T (10)After factoring the terms, S may be expressed as S (cid:3) γ T + ( − γ ) ∆ T T + ( − γ ) ∆ T (11)In the context of Maker auctions, ∆ T would normallybe the amount of WETH exchanged for DAI. However, ∆ T is dependent on the values of B and R , both ofwhich are expressed in terms of DAI. Therefore, weexpress ∆ T as an amount of DAI, with reserve T beingthe reserve for DAI. This conversion means that we aresolving for slippage on the conversion of DAI to WETH,and not WETH to DAI, as would be the case in reality.However, the nature of constant-product markets is suchthat the slippage calculation results in the same answer,regardless of which currency is used as the input token.If B ≥ R , then an amount of WETH, equal in valueto B , would need to be exchanged for DAI. Slippagewould be calculated with ∆ T equal to B (in DAI), andthe full slippage amount would be included in the costcalculation. If B < R , however, WETH would not need to be rebalanced until R was fully depleted over multipleauctions. Therefore, when B < R , slippage would becalculated with ∆ T equal to the R (in DAI), and theresulting amount allocated to the cost calculation bymultiplying by BR .The conditional aspects of this calculation are repre-sented by variables y (allocation of costs up to 100%) and z (the value to use in the calculation, expressed in termsof DAI). y is defined in Equation (4), and z is defined as z (cid:3) (cid:40) B if B ≥ RR else (12)The amount of slippage is also adjusted by the prob-ability x of winning the auction (if the auction is notwon, then no WETH will need to be exchanged). Finally,the slippage amount, which is in percentage form, ismultiplied by B , so that slippage costs are expressed interms of DAI. In expanded form, S can be calculated as S (cid:3) γ T + ( − γ ) zT + ( − γ ) z x yB (13) C. Cost of capital
The amount of DAI capital held in the Vat is allowedto fluctuate between V max and V min . However, the totalportfolio value does not change, as any DAI used to payfor a bid is replaced by WETH of roughly the same value.Therefore, we assume that V max represents the averagebalance held throughout the year. V max is then subjectto a capital charge r (also known as the “required rateof return”). The annual cost of capital is defined as K annual (cid:3) rV max (14) K annual can then be allocated to an individual bid,assuming a certain number of bids in a year, B year .Allocating equally to individual bids inherently assumesa constant rate of depletion throughout the year, includ-ing auctions won or lost. Because of this assumption,we do not need to explicitly include an adjustment forprobability x of winning an auction.In expanded form, the cost of capital ascribed to anindividual bid would be K bid (cid:3) rV max B year (15) D. Total participation costs
Total participation costs are defined as C (cid:3) F total + S + K bid (16)We measure C relative to B , as CB . Over smaller valuesof B , C deceases as a percentage of B , because of the fixedand semi-fixed nature of K bid and F total , respectively. Athigher values of B, however, C increases as a percentageof B , because of the increasing costs of S .6I. Optimization A. Optimization and constraints
In Equation (16), the two terms controllable by abidder are V max (maximum portfolio value) and R (re-balance margin). We undertook to solve for the lowestpossible participation costs, using auction-specific data,by adjusting the values for V max and R .We selected an appropriate time period to analyze (seefurther details in Section VI-B), during which 155 auc-tions were completed in the Maker system. We selectedthe final winning bid for each auction and then ran ouroptimization 155 times, with parameters derived fromthe winning bid for each auction. We then compared thetheoretical minimum auction discount, as recommendedby our optimization, to the actual discounts in ourhistorical data (see Section VI-C).The optimization was bounded by several constraints,in order to mirror real conditions: • The minimum value of the portfolio ( V max − R ) mustbe enough to cover the assumed bid value B . Thisconstraint also ensures that V max is greater than R ,which is necessary because R is subtracted from V max , and the resulting value cannot be negative. • The maximum portfolio value and rebalance margincannot be negative (infeasible), and the maximumportfolio value cannot be zero (this would signifynon-participation).The optimization is shown below in its full form.min V max , R ( G dent + G deal x ) µ g T T + ( G exit + G trade + G join ) µ gx y T T + γ T + ( − γ ) zT + ( − γ ) z x yB + rV max B year y (cid:3) (cid:40) B ≥ R BR else z (cid:3) (cid:40) B if B ≥ RR elses.t. V max − R ≥ BV max > R ≥ B and R . Considered independently,the functions resulting from the two branches are bothconvex. As we desired to know the values of R and V max that minimize the cost for a given value of B , we foundthe optimal of the two branches separately and thenchose the R and V max corresponding to the minimum cost of the two as the answer. The implementation wascompleted in MATLAB. B. Parameters and data collection
The full list of parameters used in our optimization isincluded below. Further explanation of these parametersis given in the following sections.
TABLE IOptimization parameters
Auction-specific
Param Value Definition Source B Variable Value of winning auction bid (1) µ Variable Gas price at time of bid (1) T Variable DAI reserve for ETH-DAI Uniswap pair (2) T Variable ETH reserve for ETH-DAI Uniswap pair (2)
Transaction fees
Param Value Definition Source G dent G deal G exit G trade G join g − Conversion from gwei to ethers (3) γ Cost of capital
Param Value Definition Source B year
365 Number of bids per year (1) r
40% Cost of capital for cryptocurrency (4)
Other
Param Value Definition Source x
15% Win probability for individual bid (1) (1) Maker auction data(2) Uniswap trading data(3) Ethereum specifications(4) Previous valuations TABLE IIOptimization variables
Objectives
Param Value Definition V max Variable Maximum value of portfolio R Variable Amount of depletion in V max before rebalancing
1) Auction-specific data:
We began by downloading allMaker auction events (kick, tend, dent, and deal) fromthe relevant Maker smart contract on the Ethereumblockchain [29]. All data was downloaded through anInfura node, which we queried using NodeJS runningon an Ubuntu 18.04 virtual machine.We downloaded the auction events from the beginningof the Maker liquidation process (November 13, 2019)through the date that the Maker auction process wasupgraded to use new smart contracts (July 28, 2020). Ouranalysis focused specifically on the period of March 23,2020 through July 28, 2020. The beginning date of March23 was chosen in order to exclude outliers, such as thezero-value bids of March 12, 2020, and a handful of bidsthat were submitted at prices many times higher thanthe prevailing market price (likely in error). The end date7f July 28, 2020 was chosen so that the auction processwould be consistent across all auctions analyzed.We also downloaded information on the Uniswapreserves for the ETH-DAI trading pair from Uniswap’sGraphQL node [30] (for version 1 of the Uniswap proto-col), and from the Uniswap smart contract for the ETH-DAI trading pair on the Ethereum blockchain [31] (forversion 2 of the protocol).From this data set, we were able to derive the auction-specific parameters, which changed from auction to auc-tion based on the auction settings or the conditions ofthe Ethereum network.We note that Uniswap upgraded their protocol fromversion 1 to version 2 on May 19, 2020. Since the upgrade,both version 1 and version 2 have had active ETH-DAItrading pairs, albeit with the majority of the volumeshifting to version 2 over time. In our optimization, weset T and T equal to the reserves of whichever pair hadthe larger reserves. In practice, this condition meant thatthe trading pair for version 1 was used through June25, 2020, and the trading pair for version 2 was usedthereafter.
2) Transaction fees:
Because of the complex calcula-tions required to estimate the gas usage for transactionsinvolving smart contracts, we used historical data toestimate the typical gas used for each Maker transactiontype (dent, deal, exit, and join), as well as for Uniswaptransactions (trade). For each event type, we selectedthe most recent 50 transactions (except for exit and join,which were downloaded as one set of 50 transactions),either from our database of auction events or from thetransaction history publicly available on Etherscan. Thisdata was downloaded between June 20 and June 22, 2020.We found that gas usage was higher for multi-steptransactions, in which multiple events were executed ina single transaction. We assumed that bidders would ex-ecute transactions step-by-step; therefore, we consideredonly transactions with a single event being executed.Within the group of single-event transactions, we chosethe gas usage with the most frequent occurrence in thedata. If multiple values had the highest occurrence, wechose the highest amount of gas usage.We note that the average cost for trading tokens varieddepending on the number of tokens involved; sometrades could involve trading from Currency A to B (twotokens), or Currency A to Currency B to Currency C(three tokens), and so on. In our analysis, we collecteddata from trades using up to four tokens, and then useda regression model to estimate the gas fees used for trad-ing. When t tokens were involved in a trade, the gas usedfor trading ( G trade ) was estimated at ( , t ) + , G trade .
3) Cost of capital:
The allocation of the cost of capitaldepends on the number of bids made in the year ( B year ).In the selected data set, 155 auctions were completed over the period of 128 days (March 23 through July 28),a rate of approximately 1.2 auctions per day. We roundedthis number to 1 bid per day, resulting in a value of 365for B year .The allocated cost also depends on the cost of capitalpercentage r , also known as the discount rate. Because ofthe uncertain nature of their future utility, cryptocurren-cies are generally valued using very high discount rates.While no single number can be defined as the appropri-ate discount rate, we observed that most valuations useddiscount rates between 30% at the low end [32] and 50%at the high end [33]. From this range, we chose the mid-point value of 40%, a rate which has itself been used inseveral prior valuations [34], [35]. A discount rate of 40%also falls within the range of returns expected for startupcompanies that are growing but still unprofitable [36], adescription applicable to many cryptocurrency projects.We note that the valuations referenced above assumecryptocurrencies have highly volatile prices when com-pared to the US dollar. To our knowledge, formal re-search has not examined the valuation of stablecoins,such as the DAI currency that we assume is being heldin a bidder’s portfolio. Stablecoins are designed to bepegged to the US dollar, and in theory could use a dis-count rate that approaches the risk-free rate. In practice,however, stablecoins have many riskful characteristicsthat would increase their risk premium above the risk-free rate. Defining a stablecoin-specific discount rate isoutside the scope of this paper, and for purposes of thisanalysis, we align our discount rate with those used byprior cryptocurrency valuations.
4) Other:
We calculated win probability x by aggre-gating all bids associated to the auctions included in ouranalysis (two auctions were initiated on March 22, butconcluded on March 23, which resulted in our historyextending back to March 22). We then calculated thetotal number of bids (1,011). Dividing the total numberof winning bids by the total number of bids resulted ina value of approximately 15% for x . C. Optimization results
After optimizing the participation costs in 155 auc-tions, we compared our optimal bidding price to theactual auction-winning bid prices.
TABLE IIIAuction sample characteristics
Bid value Count % $1 - $1,000 114 74$1,001 - $10,000 18 12> $10,000 23 15All 155 100
We first observed that the actual bidding price washigher than the optimal bidding price in 75% of the8
ABLE IVOptimization results
Bid value Actual > Optimal Actual < Optimal
Count % Count %$1 - $1,000 95 83 19 17$1,001 - $10,000 10 56 8 44> $10,000 12 52 11 48All 117 75 38 25 auctions. While this condition was true for over 80% ofauctions with a winning bid value equal to or less than$1,000, it was true for only slightly more than half ofauctions with a bid value greater than $1,000.
Fig. 4. Comparison of optimal markup or discount vs. actual markupor discount, for all bids up to $1,000Fig. 5. Comparison of optimal markup or discount vs. actual markupor discount, for all bids over $1,000
It may be theorized that individual bidders did notinclude cost of capital in their calculations, because thecost is implicit only. If participation costs only includedexplicit costs (transaction fees and conversion costs), thenthe resulting minimum auction discount may be closer to the actual auction discount. Therefore, we modified thecalculation of total participation costs to exclude cost ofcapital, with results shown in Table V.
TABLE VOptimization results, with cost of capital excluded
Bid value Actual > Optimal Actual < Optimal
Count % Count %$1 - $1,000 93 82 21 18$1,001 - $10,000 10 56 8 44> $10,000 12 52 11 48All 115 74 40 26
This modification changed the results of only two auc-tions, leaving the majority of bids still at a price higherthan optimal, with most above-optimal bids occurring inauctions with bid values of $1 to $1,000.
D. Discussion
From the results of the analysis above, it is evident thatthe majority of auction-winning bids were at prices thatwould not allow bidders to recoup their participationcosts. Our discussion of this seemingly unprofitablebehavior begins by considering two potential reasons,which are ultimately rejected as feasible explanations.We then describe three reasons that may serve asprobable explanations for this behavior.
Reasons not accepted
1) Infeasibility of optimal portfolio to individual bidders:
We acknowledge that it would be infeasible for biddersto adjust their portfolio size to be optimal at every valueof B . The bid value of each new auction cannot be knownin advance; in addition, multiple auctions with differentvalues can be triggered at the same time. In hindsight, wewere able to calculate what would have been the optimalportfolio size; in practice, however, it is impossible toadjust the value of V max and R to arrive at the optimalcost for every new auction. Therefore, bidders wouldneed to adjust their portfolio values to be optimal forjust one value of B .However, even if an individual bidder is unable toarrive at the optimal price for every auction, the totalityof bidders participating in an auction should reach anear-optimal price for each auction. For example, BidderA may be optimized for a B of $10,000, Bidder B for a B of $5,000, Bidder C for a B of $1,000, and so on. Withmultiple bidders optimized for a range of B values, eachauction should have a winning price that approachesthe optimal price for that auction. Therefore, we do notbelieve that the infeasibility of an optimal portfolio foran individual bidder explains the gap in optimal versusactual prices.9 ) Use of auctions as a trading mechanism: It maybe conjectured that bidders are not interested inmaking profits, but rather in exchanging DAI for WETHcheaply, which can be accomplished through the auctionprocess. However, the Maker auction process requiresmultiple transactions and a wait of up to several hoursbefore auction collateral can be collected. In contrast,decentralized exchanges allow DAI and WETH to betraded nearly instantaneously in a single transaction. Asa result, we believe it is unlikely that individuals woulduse the Maker auction process, in its current form, as atrading mechanism.
Proposed reasons
1) Indifference to cost of capital:
The cost of capital isan implicit cost that does not appear on a transactionrecord or a wallet balance. Therefore, some bidders maydisregard this cost when drawing up their bidding strat-egy. This condition may be particularly true for bidderswho hold cryptocurrency based on personal preference(such as to avoid using money in the traditional financialsystem), rather than as a financial investment. For thesebidders, the theoretical required return for cryptocur-rencies may be of little consequence in their day-to-daydecision-making.
2) Inexperienced actors:
Although some bidders may beindifferent to cost of capital, no bidder should be indiffer-ent to explicit onchain costs, such as transaction fees andconversion costs. However, as shown in Table V, three-fourths of bids submitted did not cover transactions feesand conversion costs. These results indicate certain bid-ders may not be aware of the full costs that are requiredto participate in Maker auctions. Although running anautomated keeper bot requires a high degree of technicalsophistication, we cannot dismiss the possibility thatsome bidders may devise their bidding strategy withouta comprehensive accounting of the requisite costs.
3) Altruistic actors:
Indifference to cost of capital orlack of experience may explain why certain bids donot cover all participation costs; these theories do notexplain why bids which are submitted at above-marketprices. Any bidders that submit bids at prices higherthan the market price are guaranteed to experience aloss on their portfolio value, even before subtractingparticipation costs.Although these bids may not be rational from a fi-nancial standpoint, they indicate the presence of othernon-financial motivations. Certain bidders may be mo-tivated to strengthen the Maker ecosystem as a wholeand prevent disruptive events, such as the zero-valuebids of March 12, 2020. These bidders can thereforelose money on a single bid, but still profit through thesmooth running of the system overall. Returning to ourconceptual “jar of coins” model, certain bidders mayhave an alternative value a for the collateral, which isthe guarantee that a smooth auction process secures the stability of the system overall. These bidders can bidabove the market price, because their total profit of a (alternative-usage) −( b + c + d ) (participation costs) ispositive. The value of a is a private-value componentfor each bidder, in what is otherwise a common-valueauction (as discussed in Appendix A).The identities of these altruistic bidders are unknownin the anonymous setting of the Ethereum blockchain.However, these bidders could include any individualor organization with an incentive to ensure the Makersystem runs smoothly.VII. ConclusionIn this paper, we have proposed an optimal biddingstrategy for Maker auctions, based on minimizing thecosts of participation. When comparing the proposedoptimal bidding price to historical data, we find that themajority of auctions were won at prices higher than theoptimal bidding price.We can suggest three avenues through which thisresearch can be further extended. First, the optimalbidding price may be modified by including additionalfactors that influence bidding behavior. Potential factorsto consider include the time at which the bid is placed inthe auction lifecycle, the number of bidders participating,and external conditions on the Ethereum blockchain.Second, our paper focused on prices above the optimalprice, and did not explore in detail why a quarter ofauctions finished at prices below the optimal price. Fur-ther research may uncover why certain auctions finish atprices that allow for bidder profits, while many othersdo not.Finally, the theoretical model will require modifica-tions under the newly proposed Maker auction system.This system has not been formally specified, but a pre-liminary proposal outlines the use of a Dutch auctionsystem, in which bid prices start high and graduallydecrease over time [37]. This change would allow bidsto be won in a single transaction, which opens thepossibility of using “flash loans” to bid on auctions with-out pre-existing capital. The new auction system willundoubtedly change the optimal strategy for bidders,and will provide a fresh area of research once the newprocess has been fully implemented.References [1] V. Buterin, “Ethereum Whitepaper,” https://ethereum.org/en/whitepaper/, accessed on Aug 12, 2020.[2] P. Vigna, “Bitcoin Is Riding High Again as InvestorsEmbrace Risk,” Wall Street Journal
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Appendix
A. Formal characteristics of Maker auctions
The following section defines the characteristics ofMaker auctions, within the framework of formal auctiontheory.
Ascending : Maker auctions are categorized as as-cending, or English, auctions, in that the price of thereward (the collateral) starts low and continues to risethroughout the auction process [38, p. 11]. The auctionsdo not, however, follow the process of Japanese auctions(a variant of English auctions), in which the auctioneerraises the price until all bidders drop out [39, p. 187].In the case of Maker auctions, individuals must submittheir own bids to raise the price, and they are allowedto make “jump bids”, which are bids that significantlyincrease the price above the minimum bid increments[38, p. 11].
Second-price : Maker auctions are equivalent tosecond-price auctions; if all bidders bid up to theirreservation price (the highest price they are willing topay), the winning bidder pays an amount equal to thereservation price of the second-highest bidder, adjustedfor the minimum bid increment [39, p. 10]. Maker auc-tions are not Vickrey auctions, however, as bids are notsealed. Therefore, bidders can learn about other bidders’behaviors, ex post , by reviewing transaction data on theEthereum blockchain (a method we use ourselves inSection VI).11he information to be gleaned about other bidders hastwo limitations. First, the only public information abouteach bidder is their address on the Ethereum blockchain.A bidder could easily use multiple addresses, whichmeans that any analysis of bidding history by addresswould be unable to capture, with certainty, the fullbehavior of individual bidders. Second, the auctions donot have a formal drop-out mechanism, whereby bidderscan formally signal they have ceased bidding. Biddersare able to submit a bid at any point in the auction, andthey do not need to signal their entrance or withdrawalfrom an auction. Therefore, without knowing when otherbidders have dropped out of a specific auction, a bidderis unable to collect information on the relative valuationsof other bidders while an auction is ongoing.
Single-unit : Maker auctions are single-unit, as eachauction sells a specified collateral amount, and eachbidder must bid for the entirety of the collateral, withoutany adjustments to quantity [40]. There can be multiplesingle-unit auctions that run simultaneously, dependingon the depth of liquidation volume.
Interdependent-value : Maker auctions have acommon-value component to them, albeit with adeparture from the conventional definition of common-value auctions. In the traditional model of common-value auctions, the item being auctioned has a singletrue value, but bidders do not know the true value exanteexante