Starting out on the Wrong Foot: An exploration of early bought-in lots and overall auction outcomes
Art auctions are intentionally structured to create excitement at the beginning of the auction. “Within a sale, artworks are not positioned in a sequence that honors art history or chronology, as they used to be, but rather to spark excitement.”¹ Pieces that are expected to exceed their estimates are placed at the beginning of the sale, with the intent of warming up the auction, building enthusiasm, and encouraging bidding. This logic suggests that the good performance of lots early on in the auction will have a positive effect on those later in the auction. It has been shown that anchoring effects are present in art auctions as well, meaning that the price at which a lot sells is anchored to the price at which it previously sold.² The strategic placement of lots suggests that not only is the price at which a lot sells tied to the price at which it previously sold, but it can be tied to the price of the lot sold immediately before it.
However, after a recent Post-War and Contemporary auction in December, where the first two lots were bought-in, and the rest of the auction performed below expectations, one begins to wonder if the opposite applies as well. If the first lot in an auction is bought-in, does that significantly affect the performance of the whole auction? If so, can bought-in lots early on in an auction be an indicator for how the rest of the auction will go? To further explore these questions, we would like to take this inquiry another step further and test whether this is applicable both for sell-through rates and performance rates. Meaning, we would like to explore if the outcome of the beginning of the auction has an effect, or acts as an indicator, for the outcome of the rest of the auction and then determine whether the sell-through rate or the performance rate is a better indicator of outcome.
Before we begin, we’d like to touch upon some previous research regarding ordering and anchoring effects in art auctions. There is something known in auction theory called the “afternoon effect” or the declining price anomaly. This effect, where overall performance of lots declines over the course of the auction, has been observed in art, wine, and other auctions whether or not they are intentionally ordered.³ Thus, in order to maximize efficiency, larger, more important lots receive priority placement and are often placed toward the beginning of the auction. While this tactic may help amplify a bidder’s emotions and in turn influence their buying behavior early on in the auction, as the sale progresses, a decrease in both performance and sell-through rate can be observed.
Furthermore, an extension of the declining price anomaly has been observed in the ordering of auctions as well. Kremer, Kubik, Mei & Moses explore an agreement between Sotheby’s and Christie’s to alternate the first sale during an auction week during the late 90’s.⁴ They observe that “in weeks when the house that goes first has relatively expensive paintings compared to the other house, the average sale premium is eight percentage points higher. This translates to about a 21% higher sale premium relative to the unconditional mean sale premium (which is 0.37).”⁵ From this, they conclude that the order in which items are sold has an effect on auction revenues.
So, assuming that the lots at the beginning are expected to do best, if things go poorly is it all downhill from there? Despite all the past research on anchoring-effects in repeat sales and estimate, lot and auction order, there is little that has been done to investigate whether the performance and probability of sale of a lot are affected by the lots that preceded it in auction. This is what we aim to accomplish in this work.
In our analysis, we are using data from Christie’s, Phillips, and Sotheby’s Post-War and Contemporary auctions from 2010 through 2020. First, we would like to explore the existence of the “afternoon effect” in both sell-through rate and lot performance in order to gain a better understanding of the final results. To drive into our main question, we will first aim to determine if the outcome of a lot has an effect on the one directly after that. To do so, we will look at the sell-through lag and performance lag individually and then the correlation between the sell-through and performance on each other. After determining whether and how the outcome of a lot affects the one directly after it, we will investigate the effects of early outcomes on the overall auction outcome. This will be done by calculating the average sell-through rate and performance of the first five lots and the rest of the lots separately for each auction and then calculating the correlation between the two.
We hypothesize that the outcome of a lot will have a small effect on the one directly following it, but no effect on the rest. However, we believe that it may be possible that there is a correlation between the combined outcome of the first five lots and the outcome of the rest of the auction.
The above figure illustrates this effect in Arthena’s data by showing the percentage of lots sold, and the performance of a lot (hammer price as a proportion of the low estimate) in relation to the placement of the lot in the auction. This effect has been further proven with more rigorous statistical analysis by Beggs and Graddy in “Declining Values and the afternoon effect: evidence from art auctions”. While we hypothesize that there is a correlation between outcome of the first few lots and the outcome of the rest of the auction, particularly when the beginning of the auction does poorly, it is very possible that this perceived effect is due to the fact that probability of sale and mean performance is already declining over the course of the auction which will be important to note going forward.
The following graph plots the relationship between the logarithm of a lot’s performance and the logarithm of the prior lot’s performance. What we see here is that there appears to be no strong relationship between the two.
To confirm these suspicions, we calculate the correlation value between the two and find it to be 0.262523. A correlation value of 1.0 indicates a perfect positive correlation, with 0 indicating no correlation whatsoever. Values above 0.7 are considered strong, between 0.5 and 0.7 are considered moderate, and anything under 0.4 is considered weak to no correlation. Calculating the correlation values between prior performance and lot status as well as prior lot status and lot status, show very low correlation values as well, 0.171958 and 0.094881 respectively.
Though it seems that a single lot does not have a significant effect on the following lot, that is not to say that the cumulative effect of the outcome of multiple lots cannot. The next portion of this analysis looks at the outcomes of the first five lots of each auction and their relationship with the outcome of the rest of the auction.
This plot shows the relationship between the mean performance of the first five lots of each auction and the mean performance of the rest of the auction. A correlation value of 0.429326 confirms that there is in fact a mild correlation between the two. Interestingly enough, the correlation value between the average sell-through rate of the first five lots and the average sell-through rate of the rest of the auction have a correlation value 0.486990. From this, we conclude that an auction’s outcome largely has little to do with the performance of the first five lots, unless those early lots yield outcomes that are particularly bad or particularly good.
In conclusion, we have determined that there does not seem to be a strong relationship between the performance or lot status of a lot and the outcome of the lot following it. Whether or not a lot sells and how well it does has likely to do with the lot itself, and other environmental factors unrelated to the outcome of the other lots in the auction. However, we do notice that there seems to be a mild correlation between the overall outcome of the beginning of the auction on the outcome of the rest of the auction. This mild correlation could signify that the outcome of the first five lots has some, albeit minor, impact on the tone for the rest of the auction. On the other hand, we know that correlation does not automatically imply causation. It is very possible that this correlation signifies that the outcome of the beginning of the auction could merely be an indicator of what was already going to be a good or bad day at auction.
