We study and formulate arbitrage in display advertising. Real-Time Bidding (RTB) mimics stock spot exchanges and utilises computers to algorithmically buy display ads per impression via a real-time auction. Despite the new automation, the ad markets are still informationally inefficient due to the heavily fragmented marketplaces. Two display impressions with similar or identical effectiveness (e.g., measured by conversion or click-through rates for a targeted audience) may sell for quite different prices at different market segments or pricing schemes. In this paper, we propose a novel data mining paradigm called Statistical Arbitrage Mining (SAM) focusing on mining and exploiting price discrepancies between two pricing schemes. In essence, our SAMer is a meta-bidder that hedges advertisers' risk between CPA (cost per action)-based campaigns and CPM (cost per mille impressions)-based ad inventories; it statistically assesses the potential profit and cost for an incoming CPM bid request against a portfolio of CPA campaigns based on the estimated conversion rate, bid landscape and other statistics learned from historical data. In SAM, (i) functional optimisation is utilised to seek for optimal bidding to maximise the expected arbitrage net profit, and (ii) a portfolio-based risk management solution is leveraged to reallocate bid volume and budget across the set of campaigns to make a risk and return trade-off. We propose to jointly optimise both components in an EM fashion with high efficiency to help the meta-bidder successfully catch the transient statistical arbitrage opportunities in RTB. Both the offline experiments on a real-world large-scale dataset and online A B tests on a commercial platform demonstrate the effectiveness of our proposed solution in exploiting arbitrage in various model settings and market environments.
Drawing an analogy with the statistical arbitrage of security pairs trading @cite_15 in finance, in our paper, the campaign's CPA contract and its performance in RTB spot markets can be regarded as a pair of correlated securities. Statistically speaking, if the campaign's performance in an RTB market ensures that the average cost to acquire a conversion (i.e., eCPA) is lower than the payoff from the CPA contract, then a statistical arbitrage opportunity exists. Such opportunity could also be considered to be caused by informational inefficiency of the advertising market where the advertisers fail to lower their CPA payoff when their campaigns in RTB spot market have a good performance.
@cite_15
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We test a Wall Street investment strategy known as "pairs trading" with daily data over the period 1962 through 1997. Stocks are matched into pairs according to minimum distance in historical normalized price space. We test the profitability of several trading rules with six-month trading periods over the 1962-1997 period, and find average annualized excess returns of up to 12 percent for a number of self-financing portfolios of top pairs. Part of these profits may be due to market microstructure effects. Nevertheless, our historical trading profits exceed a conservative estimate of transaction costs through most of the period. We bootstrap random pairs in order to distinguish pairs trading from pure mean-reversion strategies. The bootstrap results suggest that the ?pairs? effect differs from previously documented mean reversion profits.