CrowdWorx Market and Algorithm Reference Information

Transcription

1 CrowdWorx Berlin Munich Boston Poznan White Paper Series CrowdWorx Market and Algorithm Reference Information Abstract Electronic Prediction Markets (EPM) are markets designed for the aggregation of distributed knowledge from employees, experts, and even the general public. EPMs resemble real stock exchanges in a number of aspects but are faced with challenges like low liquidity. These are addressed by using so called automatic market makers algorithms which are capable of providing infinite liquidity. This white paper introduces elements of Prediction Markets design and the market maker algorithms used in the proprietary prediction market system CrowdWorx SDS.

2 2 1 Introduction This document describes some technical aspects of Electronic Prediction Markets (EPM) in Social Decision Support for business. Specifically, the topics of market designs and price mechanisms will be discussed. It is worth to note, that there are also other betting mechanisms, besides markets, which are suitable and used for forecasting, e.g. dynamic pari-mutuel markets, which are a form of betting markets. In most cases however, EPMs offer similar or better forecasting performance. Definition: Market Design A market design consists of a set of rules for how the exchange of money and stocks is done in a stock exchange. Price formation mechanisms are a special part of those rules. The type of stocks, or more generally the contracts, which are traded on a stock exchange are theoretically not part of the market design but in practice they are an important design driver. Definition: Contract and Stock In EPMs a contract is a description of payoff rules for the parties involved in a transaction. It may also contain many details about how exceptions are to be handled, but in EPMs this is usually not of interest, especially when there is only play money involved, which allows participants to focus on trading without the need to worry about real money and legal conditions. A stock is used as the counting unit to determine how many contracts are transferred in a transaction. Market designs used in EPMs can be quite similar to the ones of real stock exchanges, c.f. Euronext (2007). A classification of market designs for EPMs yields the following structure. 1. Exchange-type markets, e.g. most real stock exchanges like DAX, NYSE, NASDAQ: Exchange-type markets are usually set as double-auction mechanisms, i.e. traders issues buy and sell. This direct exchange between real market participants gives this type of markets their name. Exchange-type markets need an IPO mechanism, i.e. Initial Public Offering when the initial finite number of stocks is sold from the stock owner to the market. After the IPO the actual exchange-type trading can start for which three important elements are the order book, where all buy and sell orders are stored, the order matching mechanism, which sorts the order book according to certain rules in order to achieve the maximum turn-over in money terms on the market, and finally if a market maker is involved then there is a price setting mechanism, which determines the quoted price for buy and sell orders in a given market situation Call design: Traders can issue orders during the so called call period, but those orders are only executed subsequently during the so called session period.

3 Without a market maker: This is the most common design for a call market. When there is no market maker, the usual rule for the price is that the price of the last traded stock at the end of the session period 1 is the current price of that stock With a market maker: A market maker is a trader which provides liquidity by standing ready to accept buy or sell orders from any trader. The details of market makers in EPMs shall be discussed below Continuous design: Here orders are offered for execution immediately, if specified so by the trader. There is no call or session period and trading is going on the whole time until the market closes at the end of the day Without a market maker: This is rather seldom in continuous design markets With a market maker. Very common in order to ensure continuous order flow. 2. Non-exchange type markets. This design group is very common in EPMs because it does not require many traders as in real stock exchanges in order to function efficiently. The main difference with exchange type designs is that non-exchange type designs have no order book and no personal trader-to-trader transactions. All transactions have the market maker at one side of the deal. In theory, it is possible to trade any type of contract on any market design. But in practice for a given contract type there are preferred market designs. Often a market is specified by a name which combines the contract type and at least partially the market design. In EPMs, a market corresponds to one question. Hence it is not unusual to have only one or a few contracts per EPM market. Various types of contracts are possible in EPMs. The most common ones are: - Binary contracts: This is a special type of contract used for Yes-or-No forecasting questions. This contract has an end value of either 0 or 1 (binary) conditional on whether a specified event occurs after market end or not. During market time the current price of this contract is between 0 and 1 which is interpreted as the probability of the underlying event to occur. o Single binary: When a prediction market has only one binary contract traded on it, it is called a single binary contract or single binary market. 2 Single binary contracts are used for Yes-No forecasts, e.g. Will the exchange rate rise?. The price of the stock, e.g. 0,44 EUR, is the probability that the event will happen, e.g. 44% likely to rise. o Multi binary: This is essentially the same as the single binary contract but there is more than one binary contract in the market. At the end of the market the final value of one of the contracts will be 1 and all the others will have a value of 0. 3 During market time the current prices all add up to unity, hence the prices of each contract can be interpreted as probabilities again. Those contracts are usually used to make predictions on related items, e.g. Which region will have the lowest growth this year?. The price of each contract in that market is the probability for that region to be the one with lowest growth. Multi binary contracts (or multi binary markets) are flexible because they can be 1 The session period is usually followed by another special period called random period where the session continues for an unspecified amount of time between 0 and 5 minutes and ends at a random time point within this time interval. This is done in order to prevent end-of-market price biases and partially also to prevent market manipulation. 2 As mentioned above, the two aspects of market design and contract type cannot be separated because the price mechanism and payoff rules are interlinked and therefore the name of the contract (or the market) is single binary. 3 This presumes that the multi binary contracts cover each possible outcome, which is usually not the case. When an event occurs which is not covered by one of the multi binary contracts then usually some special exception handling rules are invoked, e.g. all contracts close immediately at current market prices.

4 4 used to forecast any distribution, which must add up to 100, e.g. What will be market shares of companies in this year?. There are more variants of multi binary contracts, which we shall not consider here. - Index contracts: Those contracts are used to forecast a specific number, e.g. the number of cars an automaker will sell in region C. Here the price of the contracts is multiplied with a proper factor, which is a multiple of 10 and then interpreted as an amount with a given unit, e.g. the unit cars. In this example, the final value of the contract is the actual amount of cars which were sold, e.g. 45,000 cars, which makes the final value 0,45 (for a multiplier of 10 4 ). Again, there is the possibility to have one (single index) or more (multi index) index contracts in one prediction market, i.e. one forecasting question. - Combinatorial contracts: Here a basket of contracts is traded. The trader can specify how many stocks of each contract he or she likes to sell or buy. This makes only sense for multi binary questions. For example, in a multi binary market with 4 binary contracts a trader can issue the following combinatorial order: Buy 4 stock of contract 1, 2 stocks of contract 2, 7 stocks of contract 3, and 0 stocks of contract 4. Combinatorial contracts are one of the most complex EPM contracts. - Other contract types: Those would include, for example, conditional contracts where the value of a contract is conditional on two events, one being the forecasting question, e.g. How many cars will be sold? and the other being a control parameter, e.g. Given that the oil price is within interval 1, intervall2 or interval 3. 4 To be precise, the above EPM contracts are actually what is known as Futures. This is so because EPM contracts are usually not traded for an indefinite amount of time, like normal company shares, but receive a definite final value at the end of the respective prediction market, just like Futures contracts in real exchanges. We will, however, continue to use the terms stocks instead of Futures. 4 Other contract types might be applicable to EPMs as well, e.g. derivatives like options, swaps, bonds, but so far EPM research has not been dealing with these.

5 5 2 Market Designs utilized by CrowdWorx SDS 2.1 Elements of a market design At CrowdWorx a complete EPM market design is defined by the following elements: 1. User interface, where orders are entered, markets are observed etc. 2. Trader accounts, e.g. depot, cash account etc. 3. Order & contract attributes: Attributes which define an order and a contract. Since orders and contracts are highly interconnected those two parts of a market are designed simultaneously. The type of forecasts which should be performed (see above) govern most of the decisions in this part of a market design. 4. Price setting, e.g. in exchange type markets the order matching mechanism is a crucial part of this while in non-exchange type markets the market maker is the core of price setting. 5. Constraints: Trade limits, order limits, and other rules set by the market designers. 6. Special topics, e.g. rules for credit, costs of transactions (commissions) if any etc. The exchange-type market designs can be difficult and time-consuming to setup and calibrate in an organization that wants to use them for EPM predictions. This is due to the complex interaction between the order flow in the order book, the order matching algorithms and the price setting mechanisms. But their most critical aspect with respect to their application in EPMs is that they require quite a large number of active traders in order to function efficiently. Even when there are a few thousand traders only some of them will be active in a given market. This can cause an exchange-type prediction market to get stuck with too few transactions per trader and poor forecasting performance. To overcome this problem, CrowdWorx currently uses only non-exchange type market designs, i.e. there is no order book and no order matching mechanism, and no IPO is needed. Trading can start immediately and an automated market maker provides instant liquidity by standing ready to take any order and adjust prices accordingly. The system supports binary as well as index contracts. The supported market types include: - Single binary market, e.g. Yes-No forecasts with one binary contract - Multi binary market, e.g. many binary contracts in one market - Multi binary market connected, i.e. many binary contracts in one market, which must sum to a certain number - Single index market, e.g. forecast one number - Multi index market, i.e. many single index contracts in one market - Multi index market connected, many single index contracts in one market, which must some to a given number, e.g. to 100% or any other specified number - Single and multiple date contracts, forecast one or more dates, e.g. launch dates - Mixed markets: Markets which combine any of the above contracts in one market Those market types cover an extremely wide range of applications and further market designs have been done for special projects.

6 6 For each of the above contracts and market types there are many degrees of freedom to adjust rules and parameters in an optimal way for a given forecasting situation and trader population. However, we shall only focus on the market process and the price setting algorithms in CrowdWorx market designs. 2.2 The general market process of non-exchange type markets Regardless of the market design and contracts, the general market process on a non-exchange type prediction market is similar to that of real stock exchanges and is depicted in the following figure. Participants observe the development of sotck prices on a secure EPM website Yes No Participants assess public and private information <a href= > Automated market maker determines prices for all contracts = e e V1 B P contract 1 V1 V 2 B B + e End of EPM is fixed Participants decide whether to buy or sell & how much to trade Order Quantity BUY SELL Figure 1: Market process in non-exchange type EPMs. The significant differences of the above market process as compared to exchange type markets are: - As there is no IPO process, the trading starts immediately and stocks are issued as demanded, i.e. each time a trader desires to buy a stock, the market maker generates and delivers one stock to that trader. Conversely, each time a trader desires to sell a stock the market maker exchanges that stock for money and then removes that stock from the market. This instantaneous IPO process creates and destroys stocks instantly, so there is no need for a lengthy IPO and trading can start as soon as some forecasting question arises. From the point of view of the trader this instantaneous IPO process is perceived as a natural trading process, because without an order book it is not known where the stocks are coming from or where they are going

7 7 when sold. The traders hold only the stocks which they have purchased. There are no other stocks in that market. o Update 2011: CrowdWorx has developed a proprietary IPO process which can be used in exchangetype markets. Therefore, an IPO is not a distinguishing feature of exchange-type markets anymore. - Price setting: Depending on the type of contract traded different algorithms are used for the automated market maker. But the general idea of the automated market maker is always the same: o A price function P which takes as an input the number of stocks a trader wishes to buy or sell and returns the price for the next stock. For instance, before a trader issues an order he enters some amount of stocks to buy or sell and the larger the amount the higher the price will rise for the next stock. This process will be explained in more detail in the next section. o A function C returns the total cost or payout of an order. - Order attributes: Because the automated market maker only takes stock volumes as arguments and computes prices and costs or payouts instantaneously, there is no need and no possibility to enter limit prices or a validity period of an order. Hence all orders are so called market orders, i.e. they are executed immediately and non-partially. The attributes of the order are type of order - a buy, a sell or even short-sale - and the volume of stocks the trader wishes to transact. Finally, with the above framework of how a non-exchange type market works, it is possible to look in more detail at the core of such a market design: the automated market maker s algorithms.

8 8 3 Automated market makers in non-exchange type markets In this section the market maker algorithms behind the various contract and market types of CrowdWorx will be discussed. 3.1 Foundations The automated market makers, which are used in prediction markets are rooted in Decision Theory and Statistics where the goal is to elicit optimal estimates or guesses from experts or other people. This is done by the so called Proper Scoring Rules (see Savage, 1971). Definition Proper Scoring Rule A Proper Scoring Rule is a payoff rule for an agent, e.g. a real person, that uniquely maximizes the utility of the agent when his report r equals his personal belief b, i.e. the person tells what he or she truly believes. Definition Market Scoring Rule A Market Scoring Rule is based on a Proper Scoring Rule but is extended to accommodate the above requirements, (sequential trade, marginal gain of one order at market end ~ marginal improvement that order gives to the current forecast). It functions as a market maker because it stands ready to take any order and computes new prices for each contract as well as costs and payouts for any given order. The best known Market Scoring Rule is the logarithmic market scoring rule (LMSR) by Hanson (2007). The LMSR version of a Proper Scoring Rules has been shown to be the only such rule to fulfil all theoretical requirements of a proper scoring rule (Abramowicz, 2007). 3.2 CrowdWorx Linear Market Scoring Rule (LiMSR) CrowdWorx has been using the Hanson LMSR for some years but since 2010 the LMSR has been replaced by a proprietary linear Market Scoring Rule (LiMSR), which is not optimal in theoretical terms, but is easier to use for human participants. The LiMSR has the most simple underlying price function. For a contract i the current price Price i is a function of the starting price and the balance of yes and no stocks on this contract., with,,. The LiMSR can be used for trading Yes and No stocks whose number is represented by N i,yes and N i,no, respectively, or for short selling with N i,no then representing the number of short sold stocks. The constant

9 9 is the stock price increment for an additional stock bought or sold. The function has of course a number of limits which prevent for example a negative price. Based on this simple price function, the cost function can be written as the indefinite integral of the price function over N i,. The LiMSR of CrowdWorx follows the same basic idea as other Market Scoring Rules but has been developed with the practical requirements of human users in mind. In applications with clients we have seen LiMSR deliver excellent results as shown in Figure 2. The figure shows how the CrowdWorx LiMSR performs compared to a standard forecasting process of a large consumer goods manufacturer. The CrowdWorx LiMSR has been used to generate 136 forecasts for various consumer products over a three month trial period. The same products were forecasted by a standard forecasting process by the forecasting team of the manufacturer. The forecasting accuracy is measured as 1 the absolute percentage error (APE). If the APE > 1 the result is cast to a forecasting accuracy of 0%. 100,0% Monthly forecasting accuracy of LiMSR vs. internal forecasting method, in % 80,0% 60,0% 40,0% 20,0% 0,0% November December January Proprietary LiMSR Internal method Figure 2: Forecasting accuracy of the CrowdWorx LiMSR.

10 Point betting (PBET) CrowdWorx is one of the very few systems that uses multiple prediction market algorithms. Another one of the CrowdWorx algorithms is based on betting rather than stock trading. This algorithm is even simpler than the LiMSR but its usability is even better than that of LiMSR. While the PBET algorithm does not have the ideal theoretical properties of the Hanson LMSR, it has also proven to offer a top forecasting accuracy. 4 Beyond mechanisms and algorithms While the market design is the groundwork for Prediction Markets the single most important success factor for Prediction Markets is trader participation. Participants should not be forced to participate but rather have an intrinsic motivation to do so. To achieve this, an set of certain measure has to be taken: Picking relevant forecasting topics, Choosing participants, Conducting internal marketing for EPMs, Offering incentives for traders to participate, usually not monetary, but rather recognition, personal satisfaction of trade success, possibly also prizes in exchange for the virtual EPM currency etc. These activities constitute the second leg of a successful EPM implementation in an organization and they are quite beyond the analytical tasks which are performed during market design. 5 References Abramowicz, Michal 2007: The hidden beauty of the quadratic market scoring rule, The Journal of Prediction Markets, Vol. 1, No. 2, Buckingham University Press, Buckingham Euronext (2007): Euronext Book I - Harmonized market rules, Euronext N.V., Amsterdam Hanson, Robin (2007): Logarithmic Market Scoring Rules for modular Combinatorial In formation Aggregation, The Journal of Prediction Markets, Vol. 1, No. 1, Buckingham University Press, Buckingham Savage, L. J. (1971): Elicitation of Personal Probabilities and Expectations, Journal of the American Statistical Association, Vol. 66, No. 336

11 11 Contact You can find all our white papers series in the CrowdWorx resources section on CrowdWorx Social Forecasting is a global business analytics product, headquartered in Poznan, West Poland. We serve clients in Europe and North America with the full range of Social Decision Support services based on Collective Intelligence and State-of-the-Art Enterprise 2.0 methods. For more information on CrowdWorx please write to team@crowdworx.com or call an office near you. Berlin, Germany Rotherstr Berlin Germany Tel: Fax: Munich, Germany Isartalstraße Munich (Unterhaching) Germany Tel: Fax: Boston, USA 17 Stonecleve Rd. Wellesley (Boston), MA Tel: Fax: Poznan, Poland ul. Fredry Poznan Poland Tel: Fax: