Does money matter in predicting future events?

List of Content

1. Introduction and Theoretical Fundamentals
1.1 Introduction
1.2 Definition of Prediction Markets
1.3 Theoretical Framework

2. Literature Overview
2.1 Real-money vs. Play-money
2.2 Other Factors With Influence on Forecasting Accuracy
2.3 Closed Prediction Markets

3. Data
3.1 Data Provider
3.2 Definition of Variables

4. Results
4.1 Overall Data
4.2 Real-Money vs. Play-Money: Portfolio Comparison
4.3 Real-Money vs. Play-Money: Direct Contract Comparison
4.4 Real-Money /Play-Money: Influencing Factors
4.5 Conclusion

References

Appendix

1. Introduction and Theoretical Fundamentals

1.1 Introduction

Sir Francis Galton discovered the phenomenon of crowd wisdom by studying submitted guesses from a public wager in 1906. A monetary price was awarded to the individual who most accurately estimated the weight of an exposed ox. By computing the mean and median of all 800 submitted guesses, he found that the mean showed a spread of mere 1 pound to the ex-post determined slaughtering weight (Surowiecki, 2004). Although no guess equalled the determined weight, crowds collectively predicted at much higher accuracy than the individual.

This simple principle of providing monetary incentives for truthful revelation and aggregation of dispersed knowledge still constitutes the underlying concept of modern prediction markets (they are also referred to as virtual stock markets, information markets, idea futures or forecasting markets). In recent year, political, economic, and academic interest in such market platforms has risen tremendously:

The United States' Defense Advanced Research Projects Agency launched a prediction market (Policy Analysis Market) in 2003 on political and economic events in the middle-east (Polk et al., 2003) to gain knowledge on future events. The project became politically instrumentalized and therefore was abandoned after a short period of time. Since then, private companies have utilized the economic potential and generate billions in trading volume (betfair.com) despite legal bans in many jurisdictions. Table 1 provides an overview of today’s large-scale international prediction markets. Platforms on which virtual money instead of real-money is traded have likewise grown in number and scale in the form of corporate planning tools as well as skill-based online gaming applications.

Academic interest focuses on the market prices of such platforms, which can be interpreted as probability of occurrence for underlying events. Implicit predictions have proven to yield accurate results on all kinds of future events (particularly political elections) under both incentive schemes.

This thesis aims to analyse whether forecasting performance in online prediction markets differs between real- and play-money: Do contracts on real-money predict better on a systematic level (irrelevant of underlying events) and how do equal contracts compare? What other factors influence forecasting accuracy?

These questions will be stressed against a novel dataset which has not yet been studied. Real-money data is drawn from public trading information on ipredict.co.nz, play-money data was collected in a closed play-money market operated by ipredict open to finance students between March and May 2009 under equal circumstances as the real-money platform^[1].

The remainder of the paper is subdivided in four consecutive parts. This section introduces a theoretical framework on the underlying concepts of prediction markets.

Specifically, it will outline why market prices equal probabilities of occurrence and imply general implications on trading behaviour. Section 2 discusses findings of previous studies and consolidates these into a current state of research. The third part defines the underlying dataset and relevant variables. Empirical results are discussed in section four. Descriptive statistics, interval and regression results are discussed on a portfolio level and in direct contract comparison.

1.2 Definition of Prediction Markets

Prediction Markets can be defined as markets for future events. Such platforms make it possible to obtain, aggregate and process information of dispersed knowledge. Two different contract categories require differentiation: binary (reveal probabilities of occurrence) and indexed (reveal mean values of the underlying index). Both payoff types are present in the analysed dataset of this study.

Binary contracts are stocks tied to events that either occur or do not occur at a specific date or time interval. Contracts pay off $1 (or $10, $100, respectively) in case an event happens, zero otherwise.A hypothetical example for a contract is whether or not the United Nations will impose additional sanctions against Iran before 31.12.2010, paying off $1 if the event occurs according to predefined sources within this interval; zero if it does not. A market price of $0.67 suggests that the last trading occurrence between traders implies a 67% probability of occurrence. Market prices are sometimes misinterpreted, as market prices above 0.50 (e.g. Abbildung in dieser Leseprobe nicht enthalten0.67) are falsely construed to forecast that the event will definitely occur. The sound interpretation, however, is that for 100 repetitions of the event, the event occurs 67 times. Section 1.2 explains the mechanics behind the interpretation of market prices as probabilities.

Indexed contracts pay out the corresponding value of an underlying indicator (e.g. stock prices, interest rates, exchange rates, GDP, industry-specific data, etc.) at a specific date or the mean over a specific range, respectively. A contract paying off $1 for each rounded thousand-digit of the Dow Jones Industrial Index at 31.12.2010 is an example for an indexedcontract/event. Assuming a value of 12,230 at expiry date this contract would pay off $12. The ex-ante market value (e.g. $8.71) reveals the market’s mean value of what the market believes that value will be upon expiry.

1.3 Theoretical Framework

The basic principle why market dynamics obtain and aggregate information more efficiently than centralized forecasts dates back to Hayek (1945) who discovered that a market mechanism in general performs better in revealing dispersed (asymmetric) knowledge among traders than centralized coordination. The following model shows that, regardless of the incentive structure design, market prices reflect the equilibrium in traded beliefs and can thus be interpreted as a probability of occurrence (Manski, 2004 ; Wolfers & Zitzewitz, 2006a). The model is limited to binary events, however, indexed contracts show similar trading characteristics for mean beliefs.

Binary events which are expected to occur (expiry value: $1) are denoted by Abbildung in dieser Leseprobe nicht enthalten, the counter event (expiry value: $0) is stated as Abbildung in dieser Leseprobe nicht enthalten, where Abbildung in dieser Leseprobe nicht enthalten + Abbildung in dieser Leseprobe nicht enthalten=1. The total number of participating traders equals T, of which each individual t is subject to a different individual information signal. This heterogeneity in information signals leads to different subjective beliefs (probabilities) for each contract, stated by Abbildung in dieser Leseprobe nicht enthalten. The assumptions of equally distributed initial wealth endowments , or trading funds, denoted by (Yi) and independency of the subjective probability from Abbildung in dieser Leseprobe nicht enthalten yields distribution of beliefs and endowment of P Abbildung in dieser Leseprobe nicht enthalten, Y) for each trader. Setting 𝑞a distribution of beliefs and endowment of P Abbildung in dieser Leseprobe nicht enthalten, Y). In relation to the market price Abbildung in dieser Leseprobe nicht enthalten rational traders buy contracts from the market whenever Abbildung in dieser Leseprobe nicht enthalten>Abbildung in dieser Leseprobe nicht enthalten and short-sell stock whenever Abbildung in dieser Leseprobe nicht enthalten<Abbildung in dieser Leseprobe nicht enthalten. Implicitly, Y/ Abbildung in dieser Leseprobe nicht enthalten or Y/Abbildung in dieser Leseprobe nicht enthaltenyields the number of contracts traded. It follows that the aggregated demand for contract, denoted by x, equals:

[1] x = 1/Abbildung in dieser Leseprobe nicht enthalten * E[y(Abbildung in dieser Leseprobe nicht enthalten>Abbildung in dieser Leseprobe nicht enthalten)]

and supply equals

[2] x = 1/Abbildung in dieser Leseprobe nicht enthalten * E[y(Abbildung in dieser Leseprobe nicht enthalten<Abbildung in dieser Leseprobe nicht enthalten)]

As the number of contracts held by each trader is a function of wealth endowment Y, the supply for contract,equals E(Y). Implicitly, the equilibrium only holds if demand equals supply:

[3] E(y) = (1/Abbildung in dieser Leseprobe nicht enthalten) * E[y * (Abbildung in dieser Leseprobe nicht enthalten> Abbildung in dieser Leseprobe nicht enthalten = (1/Abbildung in dieser Leseprobe nicht enthalten) * E[y * 1(Abbildung in dieser Leseprobe nicht enthalten

Manski (2004) further assumes statistical independence between y and Abbildung in dieser Leseprobe nicht enthalten which simplifies the equation to

[4] 1 = (1/Abbildung in dieser Leseprobe nicht enthalten) * P(Abbildung in dieser Leseprobe nicht enthalten> Abbildung in dieser Leseprobe nicht enthalten = (1/Abbildung in dieser Leseprobe nicht enthalten) * P(Abbildung in dieser Leseprobe nicht enthalten< Abbildung in dieser Leseprobe nicht enthalten

Under the assumption of continuous PAbbildung in dieser Leseprobe nicht enthalten) equation [4] transforms into

[5] 1 = P(Abbildung in dieser Leseprobe nicht enthalten> Abbildung in dieser Leseprobe nicht enthalten + P(Abbildung in dieser Leseprobe nicht enthalten< Abbildung in dieser Leseprobe nicht enthalten

Equation [5] yields the non-arbitrage condition for the trading beliefs of other traders.

This model demonstrates theoretical expectations on how rational traders behave.

In situations where Abbildung in dieser Leseprobe nicht enthalten =Abbildung in dieser Leseprobe nicht enthalten (e.g. trader t believes there is a 67% chance that the UN will impose additional sanctions at a market price of $0.67), no trade occurs. A higher spread between Abbildung in dieser Leseprobe nicht enthalten and Abbildung in dieser Leseprobe nicht enthalten increases demand/supply as the market price is perceived to be mispriced based on the individual information set available to all t. Heterogeneity in beliefs therefore increases the trading volume in terms of quantity, or number of traded contracts.

Wolfers and Zitzewitz (2006) based their model on the first draft of Manski’s study and showed that market prices further reflect the equilibrium of maximized individual’s logarithmic utilities. The simple form of the model is tied to two additional simplifying assumptions:

Logarithmic utility functions: Demand and supply of traders are linear functions of each trader’s beliefs. This excludes alternative types of risk-tolerance and fixed betting amounts per trader limiting the number of contracts. Since this very limitation is a common feature on online play-money prediction markets the influences of relaxing this assumption are discussed in section 4.

Changes in Y are only caused by contract payoffs: If the only factor causing ∆Y is the event itself, hedging-motivated trading activity of contracts is excluded. Hedging refers to trading motives based on other investments (e.g. hedging a short oil-futures position by buying contracts that Iran will be sanctioned, in expectation that this offsets losses from a rising oil price through the futures) or direct consequences from the event itself (e.g. Iranian oil facing the danger of becoming subject to export embargos – hedging by buying contracts in a prediction market). This limitation also involves the possibility to change Y by depositing or withdrawing money from the trading account.

In consideration of these assumptions, for all traders the number of contracts bought/sold becomes subject to the following maximization equation:

[6] max Abbildung in dieser Leseprobe nicht enthalten= Abbildung in dieser Leseprobe nicht enthalten log [y + Abbildung in dieser Leseprobe nicht enthalten Abbildung in dieser Leseprobe nicht enthalten)]+ (1-Abbildung in dieser Leseprobe nicht enthalten) log [y- Abbildung in dieser Leseprobe nicht enthalten)]

[7] Abbildung in dieser Leseprobe nicht enthalten = y Abbildung in dieser Leseprobe nicht enthalten

The market price is in equilibrium when aggregated supply equals aggregated demand:

[8] Abbildung in dieser Leseprobe nicht enthalten =Abbildung in dieser Leseprobe nicht enthalten

Further, assuming no correlation between (q) and (Y) [8] simplifies to:

[9] Abbildung in dieser Leseprobe nicht enthalten

and to:

[10] π = Abbildung in dieser Leseprobe nicht enthalten

As shown in the previous model, heterogeneity in beliefs and high wealth endowments have most influence on market price movements, as trading activity of rational traders is determined by the factors q (subjective beliefs), π (market prices), Y (wealth endowment) and risk aversion.

This yields implications relevant for the further scope of this thesis on how trading activity depends on the following factors: incentives for revelation, changes in wealth, and risk-tolerance. For increasing spreads between q and π and a given wealth endowment (Y) the number of supplied/demanded contracts increases. In a scenario where all traders hold identical beliefs relative to the current market price, no trading activity occurs. Hence, trading volume is sensitive to diversity in information signals and the willingness to reveal this perceived mispricing truthfully. Monetary rewards or punishment, respectively, are the underlying factors that lead prediction markets to aggregate information at higher accuracy than forecasting methods that do not offer analogue incentives schemes (surveys, polls). It is valid to derive the assumption that real-money markets create more severe incentives for revelation as real-money incentives show greater influence on individual utilities.

Higher wealth endowments at a given spread between market price and individual beliefs also has a positive influence on the number of contracts an individual is willing to trade. Any change in Y is either related to individuals depositing/withdrawing funds, payoffs from expiring contracts or buying/selling activity in active contracts. For incentive purposes, most play-money markets equip users with initial wealth endowment that only changes through trading activity and exclude the possibility to deposit/withdraw funds. Real-money platforms, on the other hand, allow changes in Y that are not related to trading activity through depositing/withdrawing funds from/to an external bank account. Assuming risk-averse trading behaviour, market prices at greater uncertainty (π close to 0.50) yield higher risk and are thus expected to generate lower trading volumes than contracts showing low levels of risk. (π close to expiry value as uncertainty about the outcome of the event diminishes). Therefore, as contracts approach expiry values ($1 or $0, respectively) trading volumes are expected to escalate under both incentive types in terms of number of observed trades. Assumed risk-averseness further leads to the expectation of low $ volumes in such trades since trading activity is motivated by low-risk trading gains rather than excess information about the event.

2. Literature Overview

Tziralis and Tatsiopoulos (2007) provide an overview of academic material on prediction markets between 1991 and 2006. Overall, 152 articles have been published with a rapid growth in number observable over recent years (Figure 1). This rich body of academic literature has agreed on the accuracy of prediction markets relative to alternative forecasting methods in political and sport related contracts (Berg et al., 1996; 2008a; 2008b; Pennock et al., 2001; Spann & Skiera, 2009).

2.1 Real-Money vs. Play-Money

Servan-Schreiber et al. (2004) analysed the forecast accuracy of real-money contracts (Tradesports.com), play-money contracts (Newsfutures.com) and experts trading probabilities (propabilityfootball.com) in 208 NFL games between September and December 2003. By taking the pre-game market price (markets were closed as soon as the sports event started) of these games 416 observations were analysed (208 are independent variables since Abbildung in dieser Leseprobe nicht enthalten + Abbildung in dieser Leseprobe nicht enthalten=1). The average forecast errors equal 0.439 for real-money markets and 0.436 for play-money markets. At a 90% confidence level both types of prediction markets performed better than the probability trading platform. Notably, real-money markets did not demonstrate higher forecast accuracy than play-money markets: “[...] prediction markets based on play money can be just as accurate as those based on real money” (Servan-Schreiber et al., 2004, p.250). The underlying dataset consisted of identical contracts in sports events from different platforms. Whether or not the non-existing spread was solely determined the incentive structures remained an open question.

Rosenbloom & Notz (2006) applied a Sequential Probability Ratio Test to sports (NFL 2003 season – North American team sports) and economic events (Dow Jones forecasts in 2004). Like the previously described paper, both events were traded as binary contracts on Tradesports.com and Newsfutures.com.

Again, no statistically significant spread in forecast accuracy between real- and play-money was observable for sport related contracts. For economic events, on the contrary, real-money did exhibit statistically significant (on a 5% level) higher forecast accuracy than play-money trading. Rosenbloom and Notz (2006, p.69) concluded:

“a closer look at the data strongly suggests that the results are market related […] We can only speculate on why there might be differences between popular sports events and other events […] Indeed, both effects may have occurred and only additional research, probably experimental, can address this issue successfully.”

Since no subsequent work addressed this very question, two fundamental questions are left open for additional research:

First, does real-money generate better forecasting accuracy regardless of the market type and applied methodology? Since results were found to be market-related, additional research of real-money and play-money contracts traded under equal external market circumstances is required.

Second, is the spread in accuracy related to contract categories or single contract specifics? Whereas no effect was found in sports-related contracts, economic events showed significance. This spread can either be inherent in the category (is play-money a proper incentive for sports events but not for economic-related contracts) or to the specific nature of contracts (e.g. higher uncertainty for sports events, which cannot be compensated for by efficient incentive schemes).

2.2 Other Factors With Influence on Forecasting Accuracy

Luckner (2008) discusses relevant studies based on various online platforms. Berg et al. (2000) consolidate findings of empirical studies on the IOWA prediction market, a prediction platform on political elections which has been operating since 1988. The study is limited to political, indexed contracts which pay off $1 for each per cent of votes or allocated seats a specific political party achieves in US or foreign elections. The dataset included 5 markets for presidential elections, 14 markets for other elections and 30 markets for non-US elections. A total of 237 predictions in 49 markets generated average forecast errors of 0.0137 for US elections, 0.043 for other US elections and 0.012 for non-US elections. The significant spread in overall forecast accuracy compared to the findings of Servan-Schreiber et al. (2004) and Rosenbloom and Notz (2006) is inherently tied to market factors (market maker, fees, deposit limits, etc.), contract design (sports/politics, binary/indexed) and market dynamics (trading volumes, quality of predictions, behavioural aspects).

A further study on the IOWA prediction market by Berg, Forsythe and Rietz (1996) reveals significant aspects about influencing factors on the variance of forecast errors.

Firstly, quantity (volume of trades) showed a significant positive influence on forecast accuracy. Forsythe, Rietz and Ross (1999) on the other hand, found highly accurate forecasting for small-scale laboratory based experiments. Likewise, Smith (1982) states that a number of individuals exposed to private information signals are sufficient for market efficiency. This calls into question whether trading volumes in fact influence forecast accuracy or whether high quality predictions can compensate for lower quantities. Second, some contract categories (presidential elections) attracted higher trading volumes than others. Third, trading activity grew in number and volume as contracts approached expiry. This finding supports the risk-averse nature of trading activity discussed above.

Arrow et al. (2008) postulates forecast accuracy to be dependent on days until expiry for contracts on the IOWA prediction market. Whereas volatility did not decrease substantially, trading prices tended to fluctuate more closely around the ex-post value as more information was available to trading individuals. However, this interpretation is based on a graphical interpretation of a linear relationship and lacks quantification.

2.3 Closed Prediction Markets

Closed prediction markets are limited to individuals meeting certain criteria (e.g. employees of specific company, students of a certain university) or are limited to certain physical environments (e.g. laboratory, office space).

Since the dataset studied in this paper was partly obtained through trading in a closed market environment, discussion is required whether markets with a limited number of participants have the same potential in forecasting accuracy as open ones.

Closed prediction markets aggregate information held by a comparably small number of individuals in possession of private information signals. Companies have successfully implemented closed prediction markets for sales forecasts, project management and R&D processes in recent years (Ivanov, 2009). These markets are usually operated as play-money markets implemented by third-party vendors. Besides Google, Hewlett Packard, Nokia, Motorola, Microsoft, Intel, Best Buy, Chrysler and have implemented internal markets (Cowgill et al, 2008 ; Wolfers & Zitzewitz, 2006b). Chen and Plott (2009) found sales forecasts generated by the closed HP market to be more accurate than figures by a central corporate planning unit. However, it is unclear whether the predictions within this market would have been more accurate when being traded in an open market. Does a small number of participants predict as well as an unlimited body of individuals? Does the higher amount of expertise knowledge compensate the lower degree of heterogeneity and quantity? Existing research is lacking answers to such form of comparison.

Summarising the current state of knowledge, prediction markets are agreed to be the most effective way of aggregating dispersed knowledge into accurate forecasts across various platforms, categories, contracts and methodologies in open and closed applications. The influence of incentives has been analysed in cross-platform comparison and found to be sensitive to different categories. Other studies found days-to-expiry and volumes to be significant drivers of forecasting performance. The role of quantities vs. qualities has not yet been analysed extensively – leaving the question of whether a higher number of predictors results in higher forecasting performance or whether predictions by a small number of well-informed participants can predict as effectively.

3. Data

3.1 Data Provider

Data was derived through Matt Burgess, the CEO of iPredict (http://www.ipredict.co.nz). This dataset has not been studied in previous works and thus allows new insights into what factors accuracy depends upon.

iPredict began development in 2007 and launched to the public in September 2008, two months before the last New Zealand election. iPredict is owned by the University of Victoria and is acknowledged by the New Zealand Securities Commission. Today iPredict has over 3,300 registered users who have completed 426,000 trades of 11.7 million futures contracts worth $4.2 million.

Concerning technological development, ipredict is one of the world’s most advanced prediction markets, offering several features that competing real-money markets are still missing. Most importantly, ipredict was the first real-money market to implement a modified form^[2] of Hanson’s market maker based on a logarithmic scoring rule (Hanson, 2002; 2003) for all traded contracts.

With few exceptions, other prediction markets (particularly real-money ones) apply continuous double auctions in which trading activity occurs when user-generated offers to buy or sell a stock at a defined price (optionally limited to a certain time range over which the offer is active) match in the order book.

Traders can choose between picking orders that already exist in the order book or set new prices which are contingent until matched by counterparty.

The major drawbacks of this trading mechanism are a lack in liquidity corresponding to substantial bid/ask spreads. This leads to a high numbers of unmatched offers and averts individual beliefs from influencing the current market price.

iPredict, on the contrary, subsidises liquidity and improves order clearing by operating an automated market maker based on Hanson’s findings.

The market maker operates in real-money and play-money markets as a virtual trader.

The purpose of this is to increase the number of matched orders without introducing bias, thus improving accuracy. The market maker continually makes offers to buy and sell according to a price schedule and seeding rules that are specified prior to the stock launch. This provides more accurate forecasts since information aggregation does not suffer from unmatched buy/sell orders.

Further, it is not sensitive to the number of traders active in the market. On the other hand, running this form of market maker exposes the operators to the risk of exposing proprietary funds and requires careful value-at-risk management to avoid arbitrary exploitation of market maker settings and monetary losses. The issue in running an automated market maker is its lack of sensitivity to new information, which is available to all human traders who process new information into an adjustment of individual beliefs.

Hence, market maker specifications are to be chosen carefully so that forecast accuracy does not suffer from individuals exploiting the market maker’s inability to adjust prices with reference to new information. To cope with these issues, ipredict’s market maker operates according to three settings decided at the time a new stock is established. The settings are:

Start Price: The initial market price which defines the price at which buy orders end and sell orders begin (default: 0.5).

Batch Size: The number of stocks offered at each price point.

Market Maker Sensitivity: All offers are made on an S-curve; the Sensitivity variable decides the steepness of this curve. The MM maker sets prices for all buy and sell offers using an S-curve. The formula for this S-curve is shown in [11].

Budget: Maximum loss during the lifetime of a contract. After the budget is exhausted, the MM quits operations on the side (buy/sell) that would put further value at risk.

For newly created contracts, the market maker calculates a price schedule according to equation [11]. Beginning from i=0, i increases in steps of 1 and computes a price for each marginal increase. Until this price is within 0.0001 of 0 computed prices are stored in arrays. Subsequently, this procedure is repeated for i decreasing in steps of 1. All buy/sell offers of the market maker are set according to the derived price schedule. 75% of all trades involved market maker activity as a buying/selling entity, the remainder was settled between two human traders.

[11] Abbildung in dieser Leseprobe nicht enthalten

where

i is ]–n; n[

n is defined by the value that produces a price within 0.0001 of 0 or 1, the minimum and maximum prices (which depends on the Sensitivity setting). The system requires the sensitivity value to be in the range 0–99.

The market maker was operated in an identical manner for real- and play-money contracts.

Real-money trades (681,347 observations) occurred on iPredict’s publicly available online market between 12.06.2008 13:59 and 06.03.2010 09:39. The dataset includes any trading observation within this time range. The license issued by the New Zealand Securities Commission imposes a number of restrictions on real-money event categories and user deposit amounts.

Contract variety is limited to political and economic contracts. Economic contracts are based on future interest rates, petrol prices and Official Cash Rate announcements; political contracts relate to elections, legislation and political scandals.

User deposits are limited to $500 per 6 calendar months. Gains in wealth (Y) from trading activity can exceed this limit with the current top trader holding a net worth of $7,600. Considering that iPredict has been operating for 2 years, a maximum amount of $2000 could have been deposited. Table 2 indicates a list of users’ net worth.

Play money data (22,914 trades) was derived from a market named “prophet” exclusively open to second/third-year finance students at the University of Wellington between March and May 2009. Users were endowed with an initial stake of 1000 credits; the best-performing ones received $30 at the end of the experiment. Since there is no limitation in the scope of contracts, play-money contracts were more diverse than real-money ones and were not limited to political/economic contracts. Although some economic contracts were available, the majority of contracts were not similar to those traded on real-money markets and therefore excluded from analysis. Hence, out of the 624 real-money contracts and 21 play-money contracts that have been traded on iPredict since launch 18 relevant contracts (14 real-money, 4 play-money) were selected for analysis( N=44,169). Table 3 lists selected contracts with relevant attributes for analysis. Additional specifications of the event are shown in Table 4. 39,314 observations involved real-money contracts, 4,855 were based on play-money.

Each data point included the following attributes: date/hour/min/sec of trade, volume (denoted in NZ $), price, seller ID, buyer ID, contract type (binary/index).

Forecast error (FE), days-to-expiry (D) and aggregated volumes were also analysed.

3.2 Definition of Variables

Forecast Error (FE)

The forecast error (FE) constitutes the most significant variable for the further empirical analysis. For a wide range of empirical studies it has been applied as an estimator of the accuracy of predictions through measuring the spread between Abbildung in dieser Leseprobe nicht enthalten and expiry value (Wolfers & Zitzwitz, 2004). Per definition, FE equals 0 at expiry; as the true outcome is observed. By calculating the error term of the estimated probability it is valid to extract information on the quality of prediction at any given date for any given contract. In order for prediction markets to generate accurate forecasts at each point the FE is optimally low or zero.

[12] 𝐹𝐸𝐷,𝑖= (𝜋𝐷,𝑖 − 𝜋[12] Abbildung in dieser Leseprobe nicht enthalten

where

i= all, market, category, contract,

D= days-to-expiry

The average forecast error (AFE) equals the mean of all traded prices at point t. AFE allows for cross-contract comparison at different days-to-expiry without risking to pick a non-representative (high spread to AFE over the period) FE at a single trading point. It was computed for certain intervals prior to expiry (10-day intervals) as well as over the entire contract lifetime.

[13] Abbildung in dieser Leseprobe nicht enthalten

3] 𝐴𝐹𝐸𝐷,𝑖= 𝐷=𝑚𝑎𝑟𝑘𝑒𝑡 𝑙𝑎𝑢𝑛𝑐ℎ𝐷=𝑡(𝜋𝐷,𝑖 − 𝜋𝐷=0,𝑖)² Days-to-expiry (D)

Days-to-expiry (D) denotes the length of time between expiry date and the date at which trading activity occurred (t). For each trading activity D was computed. It was set as the first independent variable for regression on FEs to measure influence on information availability to market participants. The closer a contract gets to expiry the more information about the relevant event/index is available to the market participants. It is assumed that additional information pushes Abbildung in dieser Leseprobe nicht enthalten closer to the final value and thus reduces the average forecast error. Whether this assumption holds and if this also implies a reduction in volatility of traded prices will show in the further scope of analysis. Since the expiry date was set to the point where the market maker pays off to contract holders, D equals 0 for the last observed trading point in all contracts:

𝐷=𝐷𝐷.𝑀𝑀.𝑌𝑌𝑌𝑌 ℎℎ:𝑚𝑚𝑡− 𝐷𝐷.𝑀𝑀.𝑌𝑌𝑌𝑌 ℎℎ:𝑚𝑚[13] D Abbildung in dieser Leseprobe nicht enthalten

The Servan-Schreiber et al. (2004) study took trading prices that occurred prior to the relevant sports match. Since the payoff was determined after the sporting events, FE did not converge or equal zero for last trading activity; uncertainty remained high as the underlying sports event had not taken place at the point of last trading.

On iPredict, trading activity is possible until the MM pays off contracts held by traders (which occurs whenever the true outcome of an event is known). Hence the spread between the final trading price and expiry diminishes as D decreases. Specifically, the relationship between D and FE is expected to be non-linear as for some events uncertainty remains high despite low D. This observation can be explained by diverse degrees of heterogeneity in beliefs. For instance, a contract on a publicly traded industry index five minutes prior to market closing bears less uncertainty than a contract on whether interest rates will be lowered five minutes prior to the official press conference in which the decision will be announced. Clearly, the latter carries a higher degree of uncertainty. D was measured for each trading activity.

To exclude D as influencing factor for measuring the influence of other parameters on different contracts, intervals were constructed for 10-day intervals of D.

Aggregated volume (AV)

Aggregated volume (AV) is the accumulated amount of discrete order volumes that have been traded until point t.

[14] Abbildung in dieser Leseprobe nicht enthalten

An increase in AV can either be related to the quantity of trades or the quality of traded beliefs. Therefore, average order volumes (V) were computed to differentiate between quality and quantity. It is assumed that both types positively influence forecast accuracy and therefore yield negative influence on FE. AV was computed for any trading point, including the final trading point revealing the overall traded volume over contract lifetime, and set as second independent variable in the regression model

[...]

^[1] This includes market maker settings, contract specifications, terms of use, etc.

^[2] Ipredict.co.nz operates a non-continuous version of Hanson (2003;2003) logarithmic scoring rule