staff | id | Peng huang | 440592680 | ye tian | 440360573 | ruojia li | 440607892 | yaxuan xu | 440606390 | luoyi shao | 440579164 | fuyuan liu | 440592897 |

Auction
Analysis Report invincible 6 analysis | BURWOOD
2015.4

Abstract
This report is mainly focus on the quantitative analysis of a fine art auction held by the Charleston’s auction house. In analyzing the result from the auction, this report applies stochastic dominance and mean-variance methodology on comparing estimated price with realized price of auction items. Then this report investigates the ‘hot’ auction items and auction items failed to sell in this auction by statistical data, the result shows that there are around 15 items can be considered as a ‘hot’ item in auction and no item failed to sell in our observation. And then the report has a descriptive analysis about bidders on this auction, and by calculating the ratio of numbers of bidders and the auction items, it gives out that this auction is also a ‘hot’ auction. After that, an estimated profit for this auction is calculated based on realized price of auction items, and a T-estimation method is applied on estimating the 99% confidence interval of average annual profit of the Charleston’s auction house. In addition, there is a comparison between ebay’s average annual profit and the auction house’s average, with a result that ebay has an obviously larger profit than the profit house.

1. Introduction
Auction, a trading mechanism, is a public selling process of items at their highest bid (The Free Dictionary). Formed in 1997, Charleston’s is the first and the most successful auction house that travels and sells auction goods in big cities in Australia (CHARLESTON’S FINE ART AUCTIONS 2015). It is well known for its professionalism by providing quality auction items and employing peak-bodies industries members (CHARLESTON’S FINE ART AUCTIONS 2015). Sydney Art Auction that we attended was held at 11am on 6th of Apr in 2015. The main auction goods of this auction, held by Lane Cove Council at 48 Longueville Road Lane Cove, are paintings, Persian and Oriental carpets, bronze sculptures, and home content.

2. Types of auctions
Types of auction have been categorized by William Vickrey in 1961 (Econport). Based on William’s theory, five auction types—English auction, Dutch auction, Sealed first-price auction, Sealed second-price auction and Multiunit auction—will be explored here.
• According to Krishna (2002), English auction can be simply expressed as open ascending price auction, that is, the subsequent bid posted by participants must be higher than the previous bid and consequently the items are sold at the highest bid (McAfee, P. and McMillan, J. 1987). In general, the items cannot be sold if the price does not exceed the minimum reserve price that the seller set before (McAfee, P., McMillan, J. 1987). English auction is used most commonly nowadays. Often, it is used to sell goods, artworks, antiques and real estate.
•Dutch auction, the opposite side of English auction, is an open descending price auction. Starting from a high asking price, Dutch auction is driven by participants who offer low subsequent bid, pushing the price lower and lower. The auction stops when one participant accepts the price or the reserve price of seller’s offer is met (McAfee, P., McMillan, J. 1987). This type of auction is not widely used, being aimed at selling perishable goods such as flowers, tobacco and fish.
• Sealed first-price auction is also called blind auction (Game Theory) because bidders don’t know others’ bids, as all participants give their bids at the same time. Each bidder can submit only one bid, contrary to the bidders in English auction who can submit several bids.
The only difference between sealed first-price auction and sealed second-price auction is that the final price is the second highest bid rather than the highest bid (Krishna 2002).
• Contrary to the above four auctions, which identical items must be sold in different auctions, Multiunit auction may have same items sold simultaneously.

3. Record all estimated price and realized price
The auction house has provided the estimated price for each auction item as the starting low price for bidders. Also, each item has a realized price bidden by bidders. 80 data have been recorded by us during the auction, and we found that the range of estimated price (9950 with minimum price of $50 and maximum price of $10000) is larger than that of realized prices (8350 with minimum price of $150 and maximum price of $8500). Fortunately, no items failed to sell in the auction.

4. Compare estimated prices to realized prices
4.1 Stochastic dominance
•As for stochastic dominance, there are two ways to valuate—first-order stochastic dominance and second-order stochastic dominance. According to Gan (2015), stochastic dominance, a tool to distinguish relative good or bad among random outcomes, can help us find out everyone’s preference order based on expected utility. Both first-order stochastic dominance and second-order stochastic dominance are established on the cumulative distribution function. Consequently, as to use stochastic dominance, we need to plot cumulative distribution function of estimated price and realized price firstly.
The base requirement of first-order stochastic dominance is that marginal utility is positive.
If for all W
Then: X dominates Y in terms of first-order stochastic dominance.
•As can be seen from the graph above, for the price lower than 8000, CDF (RP) is smaller than CDF (EP). But for the price higher than 8000, CDF (RP) is larger than CDF (EP). So there is no first-order stochastic dominance since the sigh of CDF (RP) minus CDF (EP) is not consistent. This implies that there is no superior price, between estimated price and realized price, that gives investors and auction house higher expected utility among the whole price range. However, if we limit the price at the range from 0 to 8000, we can make a conclusion that realized price dominates estimated price, meaning that realized price is preferred by auction house.
Apart from positive marginal utility, second-order stochastic dominance has more assumptions. It assumes that individuals are risk averse, that is, utility function is concave and increases at a decreasing speed (Gan 2015). Second-order stochastic dominance does not simply consider the value of each cumulative distribution function; it considers the total area under the function curve.

Graph 4.1 The CDF of estimated price (EP) and realized price (RP)

If for all W and for some
Then: X dominates Y in terms of second-order stochastic dominance.
•As we can see from the graph above, the total area under CDF (RP) is smaller than that under CDF (EP). Thus, a conclusion can be made that realized price dominates estimated price considering from the aspect of second-order stochastic dominance. Realized price provides higher expected utility and, as a consequence, is preferred by investors.

Why setting relative low estimated price?
•The reason why auction house set a relative low estimated price is obvious. This is an English auction and the subsequent bid must be higher than the previous bid. As long as estimated price can cover the cost of the auction item, the auction house can make profit under English auction. From my part of view, one reason of setting a relative low estimated price is that low starting price may promote more participants to bid and help the price of auction items increase continuously and rapidly. 4.2 Mean-variance Criteria
Based on our collected data, the mean and standard deviation of estimated price and realized price are calculated as follows:
Table 4.1 Mean and standard deviation of estimated prices and realized prices | EP | RP | Mean | 1466.375 | 2157.438 | Standard Deviation | 2056.751 | 2161.191 | Mean/Standard Deviation | 0.713 | 0.998 |

•If indifference curves are provided, then we can plot the two mean-variance points and indifference curved in a same graph, and figure out which point gives us higher utility. However, since we don’t have information about the indifference curves at all, we cannot make a precise comparison between these two prices. But at least, we can have a result of which one has a relative lower risk and a relative higher mean. As shown in Table 1, although there is no big difference between the standard deviation of estimated price and realized price, realized price has a much higher expected value than estimated price, which can provide a higher mean per unit of risk (0.998 compared with 0.713). It seems that realized price is better than estimated price because realized price has a relative high expected value at the same level of risk.
However, Mean-variance Criteria can be only used if the data follow normal distribution (Gan 2015). For a standard normal distribution, the skewness is 0 and the kurtosis is 3 (ENGINEERING STATISTICS HANDBOOK). Then we draw the histogram and calculate the skewness and kurtosis of estimated prices and realized prices. The results are shown in graph 2, graph 3 and table 2.
Graph 4.2 The histogram of estimated prices

Graph 4.3 The histogram of realized prices

Table 4.2 Skewness and Kurtosis of estimated prices and realized prices | EP | RP | Skewness | 2.179 | 1.352 | Kurtosis | 4.793 | 1.199 |
From the two graphs above, we can notice that both prices are positive skewed, which is verified by the absolute value of skewness (2.179 for EP and 1.352 for RP). In addition, kurtosis of EP and RP is 4.793 and 1.199 respectively, which is not close to 3. As a result, the distribution of estimated prices and realized prices are far away from normal. Since they are not Gaussian distributed, the conclusion we made based on Mean-variance Criteria cannot hold any longer.
For real life data which is not normally distributed, stochastic dominance criteria is a more convincing method to judge. To summary our previous analysis, there is no first-order stochastic dominance but realized price dominates estimated price from the aspect of second-order stochastic dominance. Although the result derived from Mean-variance Criteria is not reliable, it points out again that realized price is preferred than estimated price by both investors and auction house. This result implies that the auction is successful since the auction items are sold at a higher price than auctioneer’s estimation.

5. Observation of this art auction
Table 5.1 Hot items that bided in the auction items | Estimated price(A$) | Realized price(A$) | Kids on the Fence | 50 | 325 | L’ age de Soleil | 500 | 1150 | Sydney Matrix Red | 1000 | 2200 | Hand Made Hamadan | 300 | 600 |

During the auction, there were many bidders bid the identical items. According to the data that we collected during that period, over the 80 auction items, the situation that has the most bidders occurred once per 5 goods. Totally, there are 15 items display as ‘hot’ auction items, which means it has lots of bidders want the same item at the same times. Based on the catalogue of this arts auction, most of the hotter items are paintings, sculptures, and textures like carpets and tapestries. Especially, paintings are the most popular goods in the arts auction. For instance, the decorative print created by David Bromley which signed in plate was bided at 325 dollars. The initial estimated price is just 50 dollars. It was more than six times compared with the estimated price. Furthermore, some paintings were so popular that no one willing to give up them. They were almost bided at the maximum price of the auction. The reason why these arts items are bided vehemently is the collecting value. Approximately all of the items are created by the artists, who have been known about some time. Bidders regard as the future value or the expected value of these artworks. In addition, some artworks are unique. People cannot find another one in the world.

6. Reservation price
Reservation price is the least favorable price that sellers willing to sell the products or the highest price which buyers can accept (Richard Luecke 2003). The price of reservation exists in the most of items, because some bidders failed to achieve their desirable artworks on account of the exceed part of the highest price which they are willing to pay. For instance, some bidders could not purchase some arts in the auction since other bidders offered a higher price than they provided.
However, it is hard to estimate the reasonability of reservation price of the bidders. Diverse purchasers have various standards for each artwork. On the other hand, sellers’ reservation price is considered as reasonable. In generally, the costs of every item include the price provided by creators add kinds of fees, such as transaction costs, agency costs and so on. On the basis of the Charleston auction website, the premium of buyers includes GST and Charleston’s buyer’s premium of 19.8%. This is a levy of an industry standard auction.

7. Failure of Sale
A consider amount of bidders were attracted to the auction and according to our results, no failure sale was found during the entire process. However, there exist several reasons that may lead to the failure of the auction. One of the most significant factors is the pricing issues. The observation price is often considered the ruler of valuing certain commodity. If it is unfairly priced, usually refers to that the price is overestimated, bidders will refuse to call for overvalued item. Secondly, it is the commodity itself, whether the item is well described (that every bidder receive equal and sufficient information) or it is optimistic in collective value (that the influence of the artist and the quality itself) also determine if it is worth calling for. Thirdly, the atmosphere. When facing asymmetry information situation, bidders may not seem to call for items that no one else was interest. Certain concerns may arouse such as whether it is worth its price or does it have a good future value when commodities are “cold”.

8. Irrational Bidders
The word “irrationality”, as Ricardo Goncalves (2007) illustrated in his journal of Economic Behavior and Organization, is defined as the actions that one bidder tries to achieve a relatively more accurate true value of a commodity through outsmarting his opponent’s signal. In this case, winning the action is considered as the first priority rather than rational ones who drawback when reaching highest acceptable signal. Irrationals, usually positively correlated with aggressiveness, focus exclusively on adding bidding price without any strategies until all opponents could not or not willing to afford, is probably the main reason that cause the realized prices exceed the true value of the commodities.

Together with the previous paragraphs, bidders for items like “Kids on the fence”, “L’age de Soleil” and “Sydney Matrix Red” showed extraordinary high interest and competition during the action. At first when “Kids on the fence” was ready for call, no one forecasted that it could arouse such an intense competition, but soon left with two or three persistent bidders who kept increase calls without hesitation, even when price has exceeded four times of the estimated one. Similar situations occurred when paintings like “L’age de Soleil” and other commodities like Persian carpets were set for call where few competitors were left bidding for the same item. Considered with what is defined as irrational, we can definitely categorize these behaviors into irrationality.

9. Online or on-phone bidders
Generally, auction can also be held by bidding on internet or by phone and it occupies in a great proportion of e-commerce (1). According to the observation and investigation of this auction, there is no online or on-phone auction available and there are about 100 bidders in this auction.
For this auction we can approximately conclude it as a ‘hot’ auction because of reasons stated below: firstly, the ratio of 80 samples of items we observed and the numbers of bidders is 0.8, which means each bidder in this auction should buy 0.8 item. Secondly, there is no item that failed to sell in this auction as we observed. Thirdly, during the auction there are more than 2 bids for one item in average.

10. Ethical issue and profit of the auction house
The Charleston auction house is supervised by AVAA (Auctioneers & Valuers Association of Australia). The members in this association are required to be a practicing auctioneer and have statutory levels of experience and responsibility to provide a highest level of professionalism in the dealing with client, which is bounded with codes of ethics by the association.
According to the discipline of the AVAA, one of the codes of ethic is that members must not engage in conducting a misleading or deceptive activity and members must always act in the best interests of their clients within law. For the Charleston’s auction house, they are committed to provide the best fine art in Australia to the bidders and they provide a guaranteed catalogue of description of goods to make sure that bidders are assured of the peace of mind. In addition, the auction house is also comprised of professional personnel who have years of experience and can provide advice on the auction process and the goods on offer. Moreover, Members must keep themselves informed of their legal obligation and honor both the letter and the spirit of these obligations. According to this code, The Charleston’s auction house present the obligation on the auction lots catalogue to make sure the bidders can refer to the obligation. Overall the Charleston’s auction house can be regarded to be ethical to clients.
The Charleston’s auction house will charge a buyers’ premium 19.8% (inclusive GST 10%) if the lots are sold, so the auction house will generate a profit of 9.8% of the lots sold. the total realized price of 80 sample is $172595, so the profit of the sample is $16914.3. due to the limitation of information gathered from the auction house, it can only estimate the average annual profit by sample data. According to the central limit theorem, the 80 lots sample can be estimated by a normal distribution with a mean of 2157.44 and the standard deviation of 2161.19. To estimate a mean value of profit from the auction house with a 99% confidence, the confidence interval is with a range from $1459.13 to $2855.75. So the average income of the Charleston’s auction house is from $1459.13 to $2855.75 and the average profit of the auction house is from $142.99 to $279.86. Ebay’s average profit rate (quarterly) is 16.03%, so the annual average profit rate is 64.12%. Ebay’s equity value is 19.54Billion. The average ebay’s profit equals equity multiply by the average profit rate, $12529048.
Obviously, the ebay’s average annual profit is much larger than the profit of Charleston’s auction house. Since ebay is an international e-commerce organization, which has a larger corporate size than the Charleston’s auction house, the average annual profit is reasonable to be larger than the auction house.

11. Conclusion
According to the Sydney Art Auction’s research, several conclusions can be made:
•In our sample (80 data), the estimated price’s range is larger than realized price; it is worth mentioning that within in our sample’s observation, there is no hailed to sell in the auction. The main reason is our sample is not big enough that can observe every condition.
•Based on the data’s analysis, we find that a stochastic dominance criterion is a more convincing method to judge within that real life data which is not normally distributed. By our group member empirical analysis approach, we reach the conclusion that there is second order but no first stochastic dominance between estimated price and realized price, which indicates that risk adverse investor, would prefer selling at estimated price evaluated by auction house than actual realized price. This result implies that the auction is successful since the auction items are sold at a higher price than auctioneer’s estimation.
•Even though mean variance criteria provides the outcome that the auction house would choose estimated prices over realized prices, the result is not reliable as data is not normally distributed.
•People prefer to buy a product which has much more valuable in luxury price than the estimated price cause all of the items are created by the artists, who have been known about some time. Bidders regard as the future value or the expected value of these artworks. In addition, some artworks are unique. People cannot find another one in the world.
•Before enter an auction, sellers will always have an agreed reservation price with the price, so that items won’t be sold under this particular amount.
•Sometimes it is hard to estimate the reasonability of reservation price of the bidders, there will be some irrational bidders are expected in auctions. They may drive the realized price higher that the estimated range.

Additional Observations:
In this assignment, we have learnt knowledge covered auction, and the skill which use excel and graph to determine the data.
•In mention that the auction house charges fix percentage from buyer and seller for the transacted item. If auction house want to generate more profit, they need to change their model to attract more sellers and buyers. There are some quantitative methods such as use hypothesis testing and regression model to determine the main serviced customer. Statistical hypothesis testing plays an important role in the whole of statistics and in statistical inference; the auction house can use the statistical hypothesis to support that customers have different preferences on different auction goods. And then, we can use the regression model to determine which type of auction items can attract people’s attention. After figuring the most popular type, promotion strategy can take much more profit to the auction house.
•Auction house also can use sensitive and scenario analysis to determine that there is difference in willingness of purchase between high value customers and low customers. We can use the progressive charging model to attract the low value buyer’s purchasing willing. According to Gupta’ research (2006) that “progressive charging model can obtain optimal expected revenue and on optimal prices.”

Reference List
CHARLESTON’S FINE ART AUCTIONS 2015, Charlestons, viewed 06 April 2015,
< http://www.charlestons.com.au/who/>

ENGINEERING STATISTICS HANDBOOK, Measures of Skewness and Kurtosis, HANDBOOK, viewed 19 April 2015, < http://www.itl.nist.gov/div898/handbook/eda/section3/eda35b.htm >
Econport, Types of Auctions, Econport, viewed 08 April 2015,
< http://www.econport.org/content/handbook/auctions/commntypes.html >
Game Theory, Blind Auction, Game Theory.net, viewed 10 April 2015,
< http://www.gametheory.net/dictionary/auctions/BlindAuction.html >
Gan Q. 2015, Quantitative Finance: Stochastic Dominance (FINC6000), The University of Sydney, Sydney, 24 March, viewed 24 March 2015, <https://blackboard.econ.usyd.edu.au/bbcswebdav/pid-735940-dt-content-rid-925239_2/courses/FINC6000_SEM1_2015/L4%20Stochastic%20Dominance%286%29.pdf >
Gupta, D., Hill, A.V and Chameeva, T.B. 2006, A pricing model for clearing end-of-season retail inventory, European Journal of Operational Research, Volume 170, Issue 2,pp518-540.
Krishna, V. 2002, Auction Theory, USA: Academic Press, San Diego.
McAfee, P. and McMillan, J. 1987, ‘Auctions and Bidding’, Journal of Economic Literature (American Economic Association), vol. 25, no. 2, pp. 699-738.
Ricardo. G, 2007, Irrationality in English Auctions, Journal of Economic Behavior & Organization.
Richard Luecke (2003), Harvard Business Essentials: Negotiation, Harvard Business Press.
The Free Dictionary, The Free Dictionary by FARLEX, viewed 06 April 2015, <http://www.thefreedictionary.com/auction>
Vakrat, Y.; Seidmann, A. (2000). "Implications of the bidders' arrival process on the design of online auctions". Proceedings of the 33rd Annual Hawaii International Conference on System Sciences. p. 7. Doi:10.1109/HICSS.2000.926822. ISBN: 0-7695-0493-0.