A Specialty Hedge Fund Is Considering the Purchase of a Jackson

Essay

A specialty hedge fund is considering the purchase of a Jackson Pollock painting. It estimates the value of the painting to be $185 million. In an auction, both the number of competing bids and the amount of the competing bids is uncertain. The hedge fund has maintained a file summarizing 10 recent art auctions that it believes are similar to the upcoming auction. It is considering a bid of $163 million and would like to evaluate its chances of winning the upcoming auction with this bid. $\begin{array}{|c|c|c|c|c|c|c|c|}\text { Bid Amount (As Fraction of Estimated Share Value) }\\\hline \text { Company } & \mathbf{1} & \mathbf{2} & \mathbf{3} & \mathbf{4} & \mathbf{5} & \mathbf{6} & \mathbf{7} \\\hline 1 & 0.817 & 0.884 & 0.756 & & & & \\\hline 2 & 0.771 & 0.863 & 0.825 & 0.819 & 0.851 & 0.786 & \\\hline 3 & 0.804 & 0.851 & 0.786 & & & 0.851 & \\\hline 4 & 0.880 & 0.756 & 0.874 & 0.877 & 0.910 & & \\\hline 5 & 0.890 & 0.804 & 0.819 & 0.860 & 0.880 & 0.880 & \\\hline 6 & 0.851 & 0.786 & 0.896 & 0.784 & 0.792 & 0.792 & \\\hline 7 & 0.881 & 0.786 & 0.804 & 0.819 & & & \\\hline 8 & 0.804 & 0.819 & 0.860 & 0.880 & 0.773 & & 0.824 \\\hline 9 & 0.819 & 0.896 & 0.877 & 0.860 & 0.784 & 0.819 & 0.880 \\\hline 10 & 0.756 & 0.804 & 0.786 & 0.786 & 0.819 & 0.885 & \\\hline\end{array}$
a. Construct a spreadsheet simulation model to determine the likelihood of the hedge fund winning the auction. Use a discrete uniform distribution between the minimum and maximum number of bidders in the 10 observed auctions to model the number of bidders in the Jackson Pollock auction. Fit a realistic distribution to the bid data to generate values of competing bid amounts.
b. For a bid amount of $163 million, estimate the probability of the hedge fund winning the auction?