Munich Personal RePEc Archive A new financial metric for the art market Charlin, Ventura and Cifuentes, Arturo VC CONSULTANTS, Santiago, CHILE, Financial Regulation Center Faculty of Economics and Business University of Chile Santiago, CHILE 23 September 2013 Online at https://mpra.ub.uni-muenchen.de/50186/ MPRA Paper No. 50186, posted 25 Sep 2013 16:53 UTC 1 A NEW FINANCIAL METRIC FOR THE ART MARKET (Working Paper, September 2013 version) Ventura Charlin (1) VC Consultants Santiago, CHILE e-mail: ventcusa@gmail.com Arturo Cifuentes Financial Regulation Center Faculty of Economics and Business University of Chile Santiago, CHILE e-mail: arturo.cifuentes@fen.uchile.cl (1) author to whom all correspondence regarding this paper should be addressed. Comments are welcome mailto:arturo.cifuentes@fen.uchile.cl 2 Abstract This paper introduces a new financial metric for the art market. The metric, which we call Artistic Power Value (APV), is based on the price per unit of area (dollars per square centimeter) and is applicable to two-dimensional art objects such as paintings. In addition to its intuitive appeal and ease of computation, this metric has several advantages from the investor’s viewpoint. For example, it makes it easy to: (i) estimate price ranges for different artists; (ii) perform comparisons among them; (iii) follow the evolution of the artists’ creativity cycle overtime; and (iiii) compare, for a single artist, paintings with different subjects or different geometric properties. Additionally, the APV facilitates the process of estimating total returns. Finally, due to its transparency, the APV can be used to design derivatives-like instruments that can appeal to both, investors and speculators. Several examples validate this metric and demonstrate its usefulness. Keywords Art markets Hedonic pricing Paintings Auction prices JEL Classification A12 C23 G11 Z11 Note: The authors would like to thank Robert Yang whose technical expertise was instrumental in preparing the database. In addition, the useful suggestions of Professor James MacGee (University of Western Ontario) are greatly acknowledged. 3 Background In the last thirty years, the art market –and more precisely, the market for paintings--has received an increasing amount of attention from economists, financial analysts, and investors. They have brought to this field the quantitative techniques already employed in more conventional markets. Not surprisingly, one topic that has received a great deal of attention is returns, specifically, how to compute returns for the art market. This is a challenging task not only because this market is still rather illiquid, at least compared with equities and bonds, but also because of its heterogeneity: every painting is essentially a unique object. Several authors have employed hedonic pricing models (HPMs) to estimate returns (e.g., Chanel, Gerard-Vanet, and Ginsburgh, 1994; Chanel, Gerard-Vanet, and Ginsburgh, 1996; de la Barre, Docclo, and Ginsburgh, 1994; Edwards 2004; Renneboog and Spaenjers 2013). Such models are suitable to manage product variety and can use all the available data. Their drawback, however, is that their application is limited by the explicatory power of the variables selected and sometimes it is difficult to fit a good model to the data (the academic literature frequently reports models with values of R 2 around 60% or below). Moreover, if the data are sparse (a common situation, especially for individual artists) the application of HPMs might not be possible (Galbraith and Hodgson 2012). An additional disadvantage of HPMs is the lack of stability that often affects the computation of the hedonic regression coefficients, coupled with the reliability--not to mention the not-so-straightforward interpretation--of the time dummies (Collins, Scorcu, and Zanola, 2007). A second alternative to estimate returns is to rely on repeat sales regressions (e.g., Anderson 1974; Baumol 1986; and Goetzmann 1993). While this approach has the advantage of using price data referring to the same object it has two disadvantages: a potential selection bias and the fact that it only employs a small subset of the available information. Ginsburgh, Mei, and Moses (2006) provide an excellent discussion on the merits of each approach plus a fairly complete literature review. Mei and Moses (2002); Renneboog and Spaenjers (2011); Higgs and Worthington (2005); Agnello and Pierce (1996); and artnet Analytics (2012) have dealt with the construction of art indices based on the two above-mentioned techniques or hybrid combinations of them. The question of which approach is better to estimate returns still remains open. This issue is far more vexing than it appears. Superficially, it might be interpreted as a choice between two methods that lead to the same answer based on computational ease. However, 4 there is no assurance that this is indeed the case. In fact, they might lead to different answers and it is not always clear which answer is the right one. Ashenfelter and Graddy (2003) have stated this point more forcefully: “The hedonic index gives a real return of about 4 percent, while the repeat-sales index results in a real return of about 9 percent! Which is correct?” Previous researchers have also focused on other topics. Just to name a few: Galenson (1999); Galenson (2000); Galenson (2001); Galenson and Weinberg (2000); and Ginsburgh and Weyers (2006) have looked at the creativity cycle of several artists (that is, the age at which they produced their best work). Renneboog and Van Houte (2002); Worthington and Higgs (2004); Renneboog and Spaenjers (2011); and Pesando (1993) have compared the returns of certain segments of the art market vis-à-vis more conventional investments. Coate and Fry (2012) and Ekelund, Ressler, and Watson (2000) have investigated the “death-effect” in the price of paintings. Edwards (2004) and Campos and Barbosa (2009) have looked at the performance of Latin American painters. Scorcu and Zanola (2011) used a hedonic model approach to study Picasso’s paintings, while Higgs and Forster (2013) investigated whether paintings which conformed to the golden mean commanded a price premium. And, Sproule and Valsan (2006) questioned the accuracy of hedonic models compared with the appraisals of experts. Other issues that have been investigated, some of them still with inconclusive answers, are: whether the lack of signature affects the auction price of a painting; the importance of the auction house (in essence, Sotheby’s or Christie’s versus lesser known auction houses); whether masterpieces tend to underperform when compared to less “expensive” paintings; the correlation between the art market and the major equity and fixed income indices; whether an artist can be described, based on its creativity-cycle curve, as conceptual (early bloomer) or experimentalist (late bloomer); as well as the relationship between, withdrawing a painting from an auction, and its future sale price. All these analyses have relied on statistical and modeling techniques commonly used in financial and economic analysis. In summary, although a great deal has been learned about the financial aspects of the art market in recent years, much needs to be understood, especially, from the investor’s perspective. Therefore, the purpose of this paper is to contribute to this effort by introducing a new financial metric that can facilitate the understanding of some of the issues already mentioned. In addition, we want to shift the focus towards the investor’s viewpoint and move away from the purely econometric models which, even though are interesting from an academic angle, offer little guidance to somebody concerned with pricing issues. Thus, our 5 goal is twofold: (i) to provide a new tool to enrich the analysts’ toolbox; and (ii) to facilitate the investors’ decision-making process by making it easier to assess the merits of a painting using some simple quantitative analyses. We should note that the application of HPMs and repeat sales regression models has so far focused, mainly, on estimating market returns aimed at building indices. Although these indices can be useful for performing econometric analyses and describing market tendencies, in general, they are less useful for investors. The chief reason is that investors are concerned with actual or realized returns (that is, total returns) instead of market returns (returns based on an “ideal” painting whose characteristics do not change over time). To put the point more forcefully: an investor has little use for an index that controls for quality and paintings’ characteristics. In fact, the investor wants information that actually captures these features as well as supply-demand dynamics. The metric introduced herein (a point we discuss in more detail later) captures exactly that. In the next section, we introduce and define the new metric. The following section describes the data sets employed in this study. After that we showcase several applications of the new metric, we then present a number of analyses to validate it, and finally, we suggest some future applications, before presenting our conclusions. A New Financial Metric Paintings, notwithstanding their artistic qualities, are essentially two-dimensional objects that can command--sometimes--hefty prices. Based on this consideration, it makes sense to express the value of a painting not using its price but rather a price per unit of area (in this study, dollars per square centimeter). We call this figure of merit Artistic Power Value or APV. By “normalizing” the price, the APV metric intends to offer the investor a financial yardstick that goes beyond the price, while not attempting to control for the specifics of the painting beyond its area. The intuitive appeal of this metric (which, no doubt, some purists might find distasteful) is obvious: simplicity, ease of computation, transparency, and straightforwardness. In fact, there is already a well-established precedent for this approach. For example, prices of other two-dimensional assets, such as raw land, are frequently quoted this way (e.g. dollars per acre, or euros per hectare). The same approach is sometimes used to quote prices of antique rugs. 6 More recently, many artisans, print makers, digital printing firms, and poster designers have started to quote price estimates using this same concept. Moreover, considering that the cost of materials (an important component of the production cost) employed in creating these two-dimensional objects is often estimated on a per-unit-of-area basis, the idea of extending the same notion to express the value of the final product is not far-fetched. Finally, the rationale for using the APV metric is not to negate the individuality of each painting or to trivialize the artistic process. It is really an attempt to synthetize in one parameter the financial value of a painting (or artists or body of work) with the goal of making comparisons easier. Additionally, many APV-based computations (a point treated in more detail in the subsequent section) can offer useful guidance for pricing purposes. Alternatively, we can think of the APV as an attempt to find a common factor to compare and contrast the economic value of otherwise dissimilar art objects. If we accept the thesis that two paintings --even if they are done by the same artist and depict the same theme- - are not only different but also unique, it is not possible to make a straight price-wise comparison. However, the APV metric, by virtue of removing the size-dependency, helps to make this comparison possible: in a sense the APV plays the role of “unitary price.” The Data Three data sets are employed in this study: Data Set A consists of 1,818 observations of Pierre-Auguste Renoir’s paintings auction prices and their characteristics covering the period [March 1985; February 2013]. The database was built based on information provided by the artnet database (www.artnet.com). Data Set B consists of 441 observations of Henri Matisse’s paintings auction prices and their characteristics covering the period [May 1960; November 2012]. The database was built based on information provided by the artnet database (www.artnet.com) and was supplemented by additional auction data from the Blouin Artinfo website (www.artinfo.com). Finally, Data Set C consists of 2,115 observations of paintings covering the period [March 1985; February 2013]. This data set gathers information from six artists (Alfred Sisley, Camille Pissarro, Claude Monet, Odilon Redon, Paul Gauguin, and Paul Signac) and was based on auction information provided by the artnet database. All prices were adjusted to January-2010 U.S. dollars (using the U.S. CPI index) and are expressed in terms of premium prices (when hammer prices were reported, they were 7 modified and expressed in terms of equivalent premium prices). Observations where the selling price was below US$10,000 or the APV was less than 1US$/cm 2 were eliminated. Sotheby’s and Christie’s dominate the data sets, as together they account for 86% of the sales. The selection of artists was somewhat arbitrary. The chief consideration was to effectively examine the merits of the APV metric without regard to the qualities of the painters selected. Renoir was an ideal choice because of the high number of observations available, which were distributed over a long period of time, and without time gaps. This situation facilitates the comparison between the APV metric and the HPMs (which require many data points to be built). Matisse data had the advantage of being distributed over a longer time span, but included less observations, and had a few time-gaps. Data Set C, despite its strong impressionist flavor, was not aimed at capturing in full the characteristics of the impressionist movement; it represents a group of painters who happened to live roughly at the same time and for which there were enough observations to make certain computations feasible. Nevertheless, and simply for convenience, in what follows we refer to this group as the Impressionists group. Renoir, despite his strong impressionist credentials was purposely left out of Data Set C. Otherwise, he would have dominated the group, making it highly correlated with Data Set A: an undesirable situation given the need to test the APV metric under different scenarios. In summary, the selection of artists was not done with the idea of deriving any specific conclusion regarding these painters or the artistic tendencies they represented; the leading consideration was to showcase the attributes and benefits of the APV metric. Table 1 summarizes the key features of the three data sets. Table 2 describes in more detail the characteristics of the painters in the Impressionist group (Data Set C). Notice that the APV distribution is far from normal: the differences between the arithmetic mean (average) values and the medians are manifest, with the means always higher than the medians. Additionally, the values of the skewness and kurtosis reveal a strong positively skewed distribution with “fat tails.” The Jarque-Bera (JB) statistic and its corresponding p- value (close to 0.000 for each of the three data sets) indicate that the APV is not normally distributed. These facts should serve as a warning against APV-based projections based on normality assumptions. Finally, the relatively high values of the coefficient of variation for several artists (Renoir and Matisse exhibit the most variability) are somehow evidence of what experts already know: even masters are uneven producers and their paintings differ 8 greatly in quality. Whether ranking artists by their average or median APV values is consistent with the critics’ assessment of their merits, it is a topic we leave for others to decide. Table 1. Description of the Three Data Sets and Key Statistics Data Set: A Data Set: B Data Set: C Artist Pierre-Auguste Renoir Henri Matisse Impressionists group Born–Died 1841–1919 1869–1954 NA Number of Sales 1,818 441 2,115 Period of Sales Mar 1985–Feb 2013 May 1960–Nov 2012 Mar 1985–Feb 2013 Average APV (US$/cm 2 ) 646 803 537 Standard Deviation (US$/cm 2 ) 1,331 1,332 786 Coefficient of Variation 2.06 1.66 1.46 Median APV (US$/cm 2 ) 377 308 311 Skewness 15.56 3.87 4.86 Kurtosis 344.06 19.83 31.87 Jarque-Bera 9,040,581.38 8,328.44 97,801.30 JB p-value 0.000 0.000 0.000 Table 2. Detailed Characteristics and Key Statistics of the Artists Included in Data Set C Artist Number of Sales Born–Died Average APV (US$/cm 2 ) Standard Deviation (US$/cm 2 ) Coeff. of Variation Median APV (US$/cm 2 ) Alfred Sisley 341 1839–1899 389 282 0.73 313 Camille Pissarro 586 1839–1903 432 335 0.78 338 Claude Monet 581 1840–1926 760 999 1.31 411 Odilon Redon 193 1840–1916 167 156 0.93 118 Paul Gauguin 167 1848–1903 1,138 1,631 1.43 465 Paul Signac 247 1863–1935 353 454 1.28 202 9 Applications of the APV Metric This section is intended to demonstrate the usefulness of the APV metric with the help of some examples. Comparisons among All Artists. The fact that the APV follows a highly non-normal distribution calls for comparisons to be based on the median rather than the average value. To this end we employ the median comparison test using the Price-Bonett variance estimation for medians (Price and Bonett 2001; Bonett and Price 2002), described in Wilcox’s (2005) review of methods for comparing medians. Table 3 summarizes the results of such comparison. The median values for each artist are shown along the diagonal with the values decreasing from top-left to bottom-right: Matissse 1 has the highest value (513 US$/cm 2 ) while Redon the lowest (118 US$/cm 2 ). The remaining entries in the table can be interpreted, using matrix notation, as follows: the (i, j) entry represents the median APV value of artist j minus the median APV value of artist i. Hence, Pissarro’s median APV exceeds that of Signac by 136 US$/cm2 while there is no significant difference between Gauguin and Matisse’s median APVs. Table 3. Comparisons among the APV Medians for All Artists (1985-2012 sales only) Median APV US $/cm 2 Difference among Medians Henri Matisse a Paul Gauguin Claude Monet Pierre- Auguste Renoir Camille Pissarro Alfred Sisley Paul Signac Odilon Redon Henri Matisse a 513 Paul Gauguin NS 465 Claude Monet 102** NS 411 Pierre-Auguste Renoir 136*** 88* 34* 377 Camille Pissarro 175*** 127** 73*** 39*** 338 Alfred Sisley 200*** 152** 98*** 64*** 25* 313 Paul Signac 311*** 263*** 209*** 175*** 136*** 111*** 202 Odilon Redon 395*** 347*** 293*** 259*** 220*** 195*** 84*** 118 NOTE: a : Median calculated from sales between 1985-2012 only; NS= Not Significant; *p<.10; **p<0.05; ***p<0.01 These calculations, trivial by all accounts, offer a convenient way to rank artists. They also offer useful guidance for pricing purposes. 1 In order to have similar periods for all comparisons among artists, we only considered the sales between 1985 and 2012 for Henri Matisse. 10 Portrait versus Landscape for a Given Artist. Certain painters, Modigliani for instance (although he is not part of this study) decidedly preferred the portrait (or “vertical”) orientation. Sisley and Signac, on the contrary, favored the landscape orientation. Table 4 compares, for all the artists considered here, the median APV as a function of the orientation using the median-comparison algorithm already described. The results are interesting and far from obvious. In the case of Sisley and Pissarro, the painting orientation does not affect the APV in a significant way. In the case of Matisse and Renoir, the difference in median APV values is highly relevant. More interesting is the fact that even though both were much “better” at doing portrait-oriented paintings, they did not seem to favor this orientation. They both painted-- at least according to these sets of observations--roughly the same number of portrait-oriented paintings and landscape-oriented paintings (203 and 237 in the case of Matisse; 843 and 949 in the case of Renoir). Finally, Monet and Signac were better at doing landscape-oriented paintings, at least as seen by the market. Table 4. Comparisons of APV Medians: Portrait (Vertical) versus Landscape (Horizontal) Oriented Paintings for each Artist Artist Portrait Landscape Portrait versus Landscape Difference US$/cm 2 P-Value Number of Sales Median APV (US$/cm 2 ) Number of Sales Median APV (US$/cm 2 )) Alfred Sisley 21 298 321 317 -19 NS Camille Pissarro 132 327 450 346 -19 NS Claude Monet 124 352 440 426 -74 <0.10 Henri Matisse 203 498 237 199 299 0.000 Odilon Redon 133 131 53 84 47 <0.01 Paul Gauguin 81 580 86 328 252 <0.05 Paul Signac 23 129 224 212 -83 <0.05 Pierre-Auguste Renoir 843 505 949 289 216 0.000 NOTE: Paintings with height=width are excluded from the table. NS: Not significant. In conclusion, the orientation of a painting, in most cases, has a definite influence on its market value. Comparisons of Different Subjects for the Same Artist. Tables 5, 6 and 7 display the median APV value, for each artist, as a function of three dummy variables, namely: (i) Still 11 life; (ii) Paysage 2 and (iii) People (whether the painting shows one or several human figures regardless of the amount of detail); 0 refers to the absence of the condition. Table 5. Comparisons of APV Medians: Still Life versus No Still Life for each Artist Artist Subject: Still Life=Yes Subject: Still Life=No Difference US$/cm 2 P-Value Number of Sales Median APV (US$/cm 2 ) Number of Sales Median APV (US$/cm 2 )) Alfred Sisley NA NA NA NA NA NA Camille Pissarro NA NA NA NA NA NA Claude Monet 59 279 522 424 -145 <0.05 Henri Matisse 69 335 372 308 27 NS Odilon Redon 58 214 135 86 129 0.000 Paul Gauguin 24 821 143 411 409 <0.05 Paul Signac NA NA NA NA NA NA Pierre-Auguste Renoir 364 302 1454 396 -94 0.000 NA: Not enough sales for this artist in this subject (<10 sales). NS: Not significant. Table 6. Comparisons of APV Medians: Paysage versus No Paysage for each Artist Artist Subject: Paysage=Yes Subject: Paysage=No Difference US$/cm 2 P-Value Number of Sales Median APV (US$/cm 2 ) Number of Sales Median APV (US$/cm 2 )) Alfred Sisley 282 311 59 321 -10 NS Camille Pissarro 325 342 261 340 2 NS Claude Monet 410 424 171 355 69 <0.10 Henri Matisse 143 161 298 459 -298 0.000 Odilon Redon 42 61 151 135 -74 0.000 Paul Gauguin 58 288 109 649 -361 0.000 Paul Signac 103 218 144 200 18 NS Pierre-Auguste Renoir 478 267 1340 429 -162 0.000 NS: Not significant. Clearly, certain artists did much better on certain topics: Redon (again, APV-wise; see Table 5) was more skillful when executing still lives while the opposite happened to Renoir. Matisse, Gauguin and Renoir (see Table 6) did much better when they avoided paysages. 2 For the sake of clarity we have used the French word (“paysage”) to refer to what in English is commonly termed “landscape” to avoid any misinterpretation since this term (“landscape”) was used in the context of the geometric orientation of the painting. 12 And Gauguin, Renoir and Matisse (see Table 7) commanded higher prices when their paintings included people. These considerations, again, are useful when appraising paintings. Table 7. Comparisons of APV Medians: People (one or many Persons) versus No People for each Artist Artist Subject: People=Yes Subject: People=No Difference US$/cm 2 P-Value Number of Sales Median APV (US$/cm 2 ) Number of Sales Median APV (US$/cm 2 )) Alfred Sisley NA NA NA NA NA NA Camille Pissarro 71 267 515 348 -82 <0.05 Claude Monet 12 338 469 415 -77 <0.10 Henri Matisse 190 586 251 206 381 0.000 Odilon Redon 25 56 168 124 -67 <0.01 Paul Gauguin 31 1115 136 388 727 <0.01 Paul Signac NA NA NA NA NA NA Pierre-Auguste Renoir 817 528 1001 285 243 0.000 NA: Not enough sales for this artist in this subject (<10 sales). Life-Cycle Patterns. The idea behind this concept is to explore how the quality of an artist's paintings (using the APV metric as a proxy) evolves over time. That is, as a function of the age at which the painting was executed. Or more precisely, identify the period(s) at which the artist produced its most valuable work (financially speaking). Figures 1, 2, 3 and 4 display the median APV values, as a function of the age-at-execution for Renoir, Matisse, Monet and Pissarro. That is, the artists for whom we had more than 400 observations. Figure 1. Pierre-Auguste Renoir Life-Cycle Creativity Curve 13 The patterns shown are interesting as they reveal quite different tendencies. Renoir (Figure 1) seems to have reached a peak around the mid-thirties and then experienced a slow decline. Matisse (Figure 2) enjoyed a strong peak in his early forties, and a minor peak around his late fifties followed by a sequence of peaks and valleys in his late years. Monet's career (Figure 3) is marked by two salient peaks: an early one (when he was thirty) and a later one (in his mid-sixties) while Pissarro's life (Figure 4) is characterized by a more jagged curve that exhibited no significant decline in his old age and is more "regular" than those of either Monet and Matisse. This situation is somewhat consistent with the fact that his coefficient of variation (0.78 from Table 2) is lower than that of Monet (1.31) and Matisse (1.66). Figure 2. Henri Matisse Life-Cycle Creativity Curve Figure 3. Claude Monet Life-Cycle Creativity Curve 14 Figure 4. Camille Pissarro Life-Cycle Creativity Curve Estimating Returns for Different Artists or Group of Artists. Tables 8, 9 and 10 present the year-to-year total returns for Renoir, Matisse and the Impressionists (based on the information provided by Data Sets A, B and C respectively) along with other key values. Notice the salient peak APV values (at year 1989 and then around 2007-2008) with their corresponding steep declines afterwards. They are consistent across the three data sets and are in agreement with trends already detected in the broader art market. The total return computation is straightforward. First, we compute for each year, the average APV value (avg-APV). This is simply the sum of the APV values of all the paintings sold during the year divided by the total number of paintings sold. Then, the year-to-year total returns are computed based on the average APV values for two consecutive years. In short, the return between years i and i+1 is simply [avg-APVi+1/avg-APVi] – 1. We have purposely carried out this calculation using the average (mean) APV-value instead of the median. In general, it is customary to rely on the mean to estimate returns (regardless of the type of distribution) since the mean captures better the influence of extreme values. 15 Table 8. Data Set A: Pierre-Auguste Renoir, Key Statistics and Year-to-Year Total Returns Year of Sale Number of Obs. Average APV (US$/cm 2 ) APV Stand. Dev. (US$/cm 2 ) 95% Conf. Interval* Coeff. of Variation Year-to-Year Total Return (APV) 1985 32 360 347 241 - 479 0.96 1986 41 446 432 319 - 575 0.97 0.239 1987 83 588 541 477 - 702 0.92 0.317 1988 70 1,051 1,098 795 – 1,308 1.04 0.788 1989 103 1,845 3,730 1,135 – 2,551 2.02 0.756 1990 93 1,415 1,960 1,018 – 1,804 1.39 -0.233 1991 31 426 336 313 - 540 0.79 -0.699 1992 43 491 525 336 - 649 1.07 0.152 1993 55 534 593 372 - 691 1.11 0.088 1994 45 370 281 287 - 453 0.76 -0.308 1995 75 386 428 288 - 484 1.11 0.045 1996 69 328 298 256 - 401 0.91 -0.151 1997 75 606 1,033 379 - 831 1.70 0.847 1998 77 409 695 250 - 569 1.70 -0.325 1999 75 437 435 339 - 537 1.00 0.068 2000 75 499 544 378 - 621 1.09 0.143 2001 49 430 663 248 - 615 1.54 -0.140 2002 38 485 495 331 - 641 1.02 0.128 2003 44 445 536 298 - 591 1.20 -0.081 2004 63 431 467 318 - 544 1.08 -0.032 2005 79 422 241 366 - 477 0.57 -0.020 2006 73 539 378 454 - 624 0.70 0.276 2007 94 667 657 530 - 799 0.99 0.237 2008 62 956 3,320 129 – 1,780 3.48 0.433 2009 59 442 356 352 - 532 0.80 -0.537 2010 65 541 481 423 - 663 0.89 0.223 2011 66 510 471 393 - 625 0.92 -0.057 2012 84 533 582 412 - 656 1.09 0.045 *The 95% confidence interval was computed based on a bootstrapping technique where we took 1,000 samples with replacement with size equal to the total number of observation in each year and computed a sample mean. The average and the standard deviation (standard error of the mean) based on the 1,000 means for each year was then computed for each year. We required a sample size of at least 10 observations to compute the confidence interval. 16 Table 9. Data Set B: Henri Matisse, Key Statistics and Year-to-Year Total Returns Year of Sale Number of Obs. Average APV (US$/cm 2 ) APV Stand. Dev. (US$/cm 2 ) 95% Conf. Interval* Coeff. of Variation Year-to-Year Total Return (APV) 1960 2 70 34 NA 0.49 1961 1 76 NA NA NA 0.092 1962 4 101 53 NA 0.52 0.333 1963 2 73 35 NA 0.47 -0.277 1965 3 64 33 NA 0.52 -0.067 1966 4 128 44 NA 0.34 1.014 1968 4 127 38 NA 0.30 -0.007 1970 7 222 87 NA 0.39 0.325 1971 5 63 65 NA 1.03 -0.716 1972 10 275 155 182 - 369 0.56 3.362 1973 7 620 800 NA 1.29 1.256 1974 9 413 516 NA 1.25 -0.334 1975 5 184 118 NA 0.64 -0.554 1976 10 141 57 104 - 178 0.40 -0.237 1977 9 248 163 NA 0.66 0.767 1978 9 173 105 NA 0.61 -0.302 1979 16 290 232 185 - 397 0.80 0.674 1980 7 253 124 NA 0.49 -0.128 1981 11 180 138 99 - 260 0.77 -0.290 1982 10 162 113 92 - 232 0.69 -0.097 1983 8 294 127 NA 0.43 0.810 1984 8 240 126 NA 0.52 -0.185 1985 11 306 200 189 - 424 0.65 0.278 1986 10 363 296 182 - 543 0.81 0.185 1987 13 446 300 288 - 604 0.67 0.228 1988 12 669 793 226 – 1,104 1.19 0.501 1989 12 1,411 1,252 722 – 2,096 0.89 1.108 1990 13 1,391 1,422 645 – 2,134 1.02 -0.014 1991 5 652 476 NA 0.73 -0.531 1992 9 1,134 974 NA 0.86 0.740 1993 11 710 766 280 – 1,127 1.08 -0.374 1994 6 362 357 NA 0.98 -0.489 17 Table 9. Data Set B: Henri Matisse, Key Statistics and Year-to-Year Total Returns (continued) Year of Sale Number of Obs. Average APV (US$/cm 2 ) APV Stand. Dev. (US$/cm 2 ) 95% Conf. Interval* Coeff. of Variation Year-to-Year Total Return (APV) 1995 10 1,137 1,452 257 – 2,021 1.28 2.138 1996 6 227 113 NA 0.50 -0.800 1997 11 666 656 289 – 1,044 0.98 1.930 1998 12 406 441 164 - 651 1.09 -0.390 1999 12 701 616 355 – 1,045 0.88 0.725 2000 7 1,426 1,685 NA 1.18 1.035 2001 18 717 567 467 - 968 0.79 -0.497 2002 8 1,037 722 NA 0.70 0.446 2003 3 166 47 NA 0.29 -0.840 2004 9 2,034 2,440 NA 1.20 11.290 2005 7 1,127 1,632 NA 1.45 -0.446 2006 8 1,402 999 NA 0.71 0.243 2007 23 2,073 3,013 803 – 3,307 1.45 0.479 2008 20 1,371 1,314 789 – 1,951 0.96 -0.339 2009 8 1,865 3,031 NA 1.63 0.360 2010 11 3,090 2,208 1786 – 4,423 0.71 0.657 2011 7 844 1,181 NA 1.40 -0.727 2012 8 902 1,706 NA 1.89 0.069 *The 95% confidence interval was computed based on a bootstrapping technique where we took 1,000 samples with replacement with size equal to the total number of observation in each year and computed a sample mean. The average and the standard deviation (standard error of the mean) based on the 1,000 means for each year was then computed for each year. We required a sample size of at least 10 observations to compute the confidence interval. 18 Table 10. Data Set C: Impressionists Group, Key Statistics and Year-to-Year Total Returns Year of Sale Number of Obs. Average APV (US$/cm 2 ) APV Stand. Dev. (US$/cm 2 ) 95% Conf. Interval* Coeff. of Variation Year-to-Year Total Return (APV) 1985 60 227 190 177 - 275 0.84 1986 58 243 196 193 - 292 0.81 0.070 1987 84 397 483 299 - 498 1.21 0.637 1988 72 790 1,321 493 – 1,094 1.67 0.988 1989 146 1,045 1,024 877 – 1,218 0.98 0.323 1990 62 648 395 546 - 749 0.61 -0.380 1991 36 404 466 263 - 543 1.15 -0.377 1992 40 307 240 232 - 382 0.78 -0.239 1993 60 333 249 269 - 398 0.75 0.084 1994 61 306 294 232 - 378 0.96 -0.082 1995 81 405 684 262 - 551 1.69 0.325 1996 69 373 405 276 - 465 1.08 -0.079 1997 87 438 510 334 - 544 1.16 0.173 1998 90 394 656 260 - 526 1.67 -0.101 1999 109 439 638 324 - 555 1.45 0.116 2000 80 582 897 385 - 784 1.54 0.325 2001 71 546 876 346 - 749 1.60 -0.062 2002 67 406 565 273 - 540 1.39 -0.257 2003 50 444 538 297 - 590 1.21 0.094 2004 75 502 945 286 - 720 1.88 0.130 2005 86 447 623 312 - 585 1.39 -0.109 2006 89 604 888 414 - 795 1.47 0.351 2007 105 863 1,170 635 – 1,091 1.36 0.429 2008 89 771 1,198 520 – 1,022 1.55 -0.106 2009 62 482 591 336 - 629 1.23 -0.375 2010 73 528 820 342 - 708 1.55 0.094 2011 58 464 532 330 - 601 1.14 -0.120 2012 95 645 787 479 - 807 1.22 0.388 *The 95% confidence interval was computed based on a bootstrapping technique where we took 1,000 samples with replacement with size equal to the total number of observation in each year and computed a sample mean. The average and the standard deviation (standard error of the mean) based on the 1,000 means for each year was then computed for each year. We required a sample size of at least 10 observations to compute the confidence interval. 19 Leaving aside the ease of computation (undoubtedly an attractive feature) some valid questions need to be answered. First, what does this return mean? And second-- and perhaps more relevant-- does this APV-based return agree with estimates computed with more popular approaches? Regarding the first question: the APV captures both, art market trends and supply- demand dynamics for the artist or artists considered, as it is based on actual sales. It does not intend to control the actual prices observed for any factor other than the area of the painting. Hence, the APV-based returns are really total (actual or realized) returns for the artist or artists in question (inflation has been removed since prices are expressed in January-2010 dollars). Some academics might feel that these returns are “contaminated” since we do not—in purpose we might add—control for factors such as the type of painting (subject matter), geometric features beyond the area, and the host of other variables that hedonic models normally employ to “explain” the price (dependent variable). The following analogy is useful to make our point that controlling for this factors, at least from an investor perspective, is not relevant. Suppose you are looking at the possibility of buying IBM stock and you have computed the average return in recent years based on the observed stock price. This return would correspond to an actual (or total) return. Consider now that IBM’s revenue (broadly speaking) comes from three sources: hardware, software, and consulting. Would you then attempt to control for revenue composition to arrive at a return figure reflecting the “average” or “typical” return? That is, a return based on an “ideal” revenue composition? Probably not. In fact, in all likelihood, the opposite is true. You want a return metric that actually captures the revenue composition variation. Well, the same goes for paintings. Renoir, for instance (and strictly from a return estimation viewpoint) can be thought of as a company that sells multiple products (paintings), all with different features, and whose stock value is captured by the APV. Therefore, the idea of estimating returns based on APV figures (and not controlling for any other variable beyond the area) is not only reasonable but also very much in line with commonly accepted return estimate practices. Moreover, market returns typically estimated with the time-dummy coefficients of the HPMs (a topic we deal with in more detail in the next section) are analogous—continuing with the IBM stock example—to returns based on a market index such as the S&P 500. While this information is surely useful to detect broad market tendencies, it is less useful for somebody who wants to buy a particular 20 painting by a specific artist instead of taking a position on the market as a whole. In summary, the fact that APV-based returns do not control for any factors beyond the area rather than being a weakness of the metric is a source of strength. The second question--regarding the degree of agreement between APV-based returns and returns calculated with other approaches--requires more thought. This issue is treated in detail in the next section. Finally, Table 11 summarizes the return results: (i) average year-to-year total returns; and (ii) cumulative returns for the relevant time-periods. Table 11. APV Year-to-Year Total Returns: Averages, Standard Deviations, and Cumulative Total Return using the APV Data Set A: Renoir Data Set B : Matisse Data Set C: Impressionists Average Total Return APV 8.16% 45.72% 8.30% Standard Deviation Total Return APV 35.58% 175.40% 31.47% Cumulative Total Return APV* 148.02% 1295.65% 284.21% *Cumulative total returns computed for 27 years for Data Sets A and C [1985-2012] and 52 years for Data Set B [1960-2012]. Repeat Sales Vis-à-Vis the Entire Data Set. Many analysts have estimated returns, for individual artists and groups of them, using only data from repeat sales. As pointed out before, a concern with this approach is that there could be a risk of selection bias. Table 12 shows the median APV values for each of the artists considered using: (i) all the observations (Total); and (ii) the repeat sales sub-set. In two cases (Matisse and Renoir) the differences are significant at the 5% level. And in four of the remaining six cases the discrepancies are marginally significant (significant at the 10% level). All in all these results support the view that a selection bias cannot be ruled out when dealing with repeat sales data. Furthermore, return estimates based on repeat sales regressions (despite the claim that one has controlled for all the “relevant” factors) should be regarded with suspicion because of this bias. The same goes for any other estimate based on repeat sales information. 21 Table 12. Comparisons of APV Medians: Total Sales versus Repeat Sales for each Artist Artist Total Sales Repeat Sales Total versus Repeat Sales Difference US$/cm 2 P-Value Number of Sales Median APV (US$/cm 2 ) Number of Sales Median APV (US$/cm 2 )) Alfred Sisley 341 313 118 327 -14 NS Camille Pissarro 586 338 146 378 -40 <0.10 Claude Monet 581 411 176 476 -64 <0.10 Henri Matisse 441 308 160 249 59 <0.05 Odilon Redon 193 118 36 91 28 <0.10 Paul Gauguin 167 465 37 612 -147 NS Paul Signac 247 202 90 180 22 <0.10 Pierre-Auguste Renoir 1818 377 426 425 -48 <0.05 In conclusion, the examples discussed in this section show that the APV metric is a useful tool that can provide a potential investor with a great deal of insight regarding the merits of an artist, groups of artists, or a particular painting. Validation of the APV Metric A useful way to assess the validity of the APV metric is to compare the results of calculations based on this metric and those obtained with other (presumably more established) methods. HPMs, in spite of their shortcomings, constitute a sound basis on which we can build some tests to explore the reasonableness of the APV-based computations. Total (Actual or Realized) Returns. A first examination consists of comparing the returns estimated with the APV metric and the returns calculated using HPMs. In order to determine a fair yardstick for comparison purposes we carry out two steps. First, we estimate individual HPMs for each of the three cases (Renoir, Matisse, and the Impressionists) using the entire corresponding data set. And second, in each case, we evaluate the resulting HPM, for each year, using the average characteristics of the paintings sold during the year, to arrive at a “representative” price corresponding to each year, Pi (where i denotes a year index). The year-to-year HPM-based returns are computed based on these prices, using the expression (Pi+1/Pi) – 1. Thus, the idea is to use the HPM to estimate the total return. 22 The HPMs employ the natural logarithm of the painting selling price as the dependent variable. The independent variables (right-hand side of the regression equation) involve: (i) linear and higher-order polynomial expressions based on the age of the artist at the time the painting was executed; (ii) in the case of Data Set C a dummy (binary) variable to account for the identity of the painter; (iii) linear and higher-order polynomial expressions based on variables associated with the geometry of the painting (area, height, width, aspect ratio, and diagonal) plus binary dummy variables accounting for medium (canvas) and special topics (nudes, still lives, flowers, etc.); and (iiii) a sequence of dummy (binary) variables associated with the year the painting was sold. The corresponding adjusted R 2’s (Renoir, Matisse, and Impressionists) are as follows: 0.75 (F= 137.47, p<.0001), 0.72 (F=18.78, p<.0001), and 0.67 (F= 77.39, p <.0001) respectively. In addition, we used White’s (1980) test for heteroscedasticity and the null hypothesis of homoscedasticity in the least-squares residuals was not rejected in each of the three samples (results can be provided upon request). Table 13 shows the comparison between the average year-to-year total return estimated with (i) the APV metric; and (ii) the HPMs applied as described before. Both estimates, in all three cases, are in close agreement. This fact is also consistent with the high correlation values reported as well as the visual comparison presented in Figures 5, 6 and 7. Table 13. APV and HPM-based Year-to-Year Total Returns: Averages, Standard Deviations, and Correlations Data Set A: Renoir Data Set B : Matisse Data Set C: Impressionists Average Total Return APV 8.16% 45.72% 8.30% Standard Deviation Total Return APV 35.58% 175.40% 31.47% Average Total Return HPM 7.64% 48.74% 8.36% Standard Deviation Total Return HPM 38.12% 162.67% 33.35% Correlation Total Ret. APV - Total Ret. HPM 0.79 0.89 0.82 23 Figure 5. Year-to-Year Total (APV and HPM) Returns for Pierre-Auguste Renoir Sales Figure 6. Year-to-Year Total (APV and HPM) Returns for Henri Matisse Sales 24 Figure 7. Year-to-Year Total (APV and HPM) for Impressionists Group Sales It might not seem evident that this is a fair comparison. However, we should notice that by evaluating the HPMs for each year, with the typical features of the paintings sold that year, one is capturing the two effects that influence returns: the market trend (reflected in the HPM coefficients associated with the time-dummy variables) and the specific characteristics of the paintings sold on a given year. The APV metric comingles these two factors (market trends and paintings features) in one figure. Therefore, the hedonic model framework (applied in the modified manner just described) seems appropriate to double-check the validity of the returns based on the APV metric. Market Returns. Provided one has enough data, hedonic models can also be used to obtain an estimate of the market return (as opposed to total return) between two consecutive years using a model fitted just using the data corresponding to those two periods (unlike the previous section in which the returns were estimated using a HPM built based on the entire dataset). The market return, under this variation of the hedonic model framework (assuming a log-price dependent variable) is simply Exp(β) – 1, where β is the coefficient associated with the year-of-sale (dummy) variable (0 if the painting is sold during the first year, 1 if it is sold during the second year). This is, in principle, another test that can be used to verify the soundness of APV-based returns: does the APV metric render reasonable estimates of market returns? The only problem is that the APV metric, by its very definition, does not lend itself naturally to isolate the market effects and the supply-demand effects (specific features of the paintings actually sold) and therefore, one cannot estimate directly, using the APV metric, the 25 market returns between two consecutive years. Thus, some modifications are required to design a test to check if the market returns implied by the APV metric make sense. We tackle this in three steps. Let us assume that we have three consecutive years (i, i+1, i+2) each with several observations. First, we group in one set all the auction data for years i and i+1 and compute APV(a), the average APV value considering all these observations as if they were made in the same year. Second, we group the data corresponding to years i+1 and i+2 in another set and compute APV(b), the average APV value considering all these observations as if they were made in the same year. And third, we estimate the market return between year i+0.5 and i+1.5 as λ = [APV(b)/APV(a)] – 1. The rationale for these calculations and assumptions is not straightforward, but it can be explained appealing to intuition. By comingling in one set all the APV observations corresponding to two consecutive years (say, i and i+1) we are, in effect —if not nullifying— at least mitigating the influence of the variations in the individual paintings’ characteristics. Thus, we are letting the market effect dominate. Furthermore, since APV(a) and APV(b) are based on adjacent years that actually overlap (year i+1 is common), this also tends to minimize the effect of the differences in individual paintings’ characteristics and privileges the market effects. This computational trick, which is actually tantamount to applying a low-pass filter to the time- history of APV values, is by no means perfect. But “smoothing” the time-history of the average APV values achieves the goal of reducing the effect of the individual paintings’ characteristics. This estimated return corresponds to a (shifted) one-year period return simply because the “time-distance” between the center-points of two consecutive periods is (i+1.5) – (i+0.5) = 1. We now need to estimate the market return between years i+0.5 and i+1.5 using a different approach to be able to make a meaningful comparison. To this end, we introduce a technique based on the HPM-framework applied to observations made in two adjacent periods (de Haan and Diewert 2011; Brachinger 2003). Consistent with the approach described in the previous paragraph we proceed as follows. We group all the information related to the paintings sold in years i and i+1 in one set (keeping track of the “year-of-sale effect” by means of dummy binary variable) and fit a HPM to these data. The market return between year i and year i+1 is estimated by Ra= Exp(βa)-1 where βa is the coefficient of the time dummy variable. We turn now to years i+1 and i+2 and determine a HPM analogous to the one estimated in the i and i+1 case. Here, Rb= Exp(βb)-1, where βb denotes the 26 coefficient of the time dummy variable, captures the market return from year i+1 to i+2. Finally, ω = (Ra + Rb)/2 provides an estimate of the market return between years i+0.5 and i+1.5. The above-mentioned calculations can only be carried out for Renoir and the Impressionist group. The Matisse data set (described in Table 9) contains several time gaps and lacks sufficient observations in most years; thus, for most consecutive years, it is not possible to fit a HPM. Consequently, the comparison between λ and ω, or, alternatively, the year-to-year market return estimated by (i) the APV-metric and (ii) the adjacent HPMs was only done for the two cases with enough data (Renoir and the Impressionists). In the case of Renoir, the values of the adjusted R 2 for the adjacent-period HPMs range from 0.67 to 0.82. For the Impressionists the adjusted R 2 values vary between 0.48 and 0.82. Table 14 summarizes the key comparison values. Figures 8 and 9 compare graphically the time-history of year-to-year market returns for the two data sets considered. As in the case of the total returns the comparison validates the estimates provided by the APV metric as they show agreement with the estimates based on hedonic model techniques. This is also in agreement with the high correlation values reported (0.85 and 0.91). From Table 14, we appreciate that in both cases (Renoir and the Impressionists) the standard deviation of market returns estimated by the APV metric (27.93% and 26.21%, respectively) are higher than those given by the HPMs (18.99% and 23.70%). This is to be expected since the “smoothing” approach employed to derive market returns from APV data is only approximate (the HPM is better suited to separate these effects in a more clear-cut manner). In any event, the preceding comparison provides evidence that, again, in spite of its remarkable simplicity the APV metric can provide reasonable accuracy with an important economy of computation. Table 14. Average Year-to-Year Market Returns: Based on (i) APV and (ii) Adjacent HPMs, and their Correlations Data Set A: Renoir Data Set C: Impressionists Average Market Return APV 4.80% 6.61% Standard Deviation Market Return APV 27.93% 26.21% Average Market Return HPM 4.60% 6.26% Standard Deviation Market Return HPM 18.99% 23.70% Correlation Market Ret. APV – Market Ret. HPM 0.85 0.91 27 Figure 8. Year-to Year Market Returns for Pierre-Auguste Renoir Based on (i) APV Metric and (ii) Adjacent HPM Approach Figure 9. Year-to Year Market Returns for the Impressionists Group Based on (i) APV Metric and (ii) Adjacent HPM Approach It is interesting to notice that the standard deviation of the market returns (using either approach, APV or HPM) is markedly lower than the standard deviation of the corresponding total returns (35.58% and 31.47% from Table 11). Intuitively, this makes sense: total returns —by virtue of not controlling for the characteristics of the paintings— exhibit more variability. Life-Cycle Patterns. Hedonic models have also been used in the past to investigate the age at which an artist produced its most valuable work. Typically, a HPM is fitted to the entire 28 data available (which normally cover several years) and then the natural logarithm of the average price versus the artist’s age-at-the-time-the-painting-was-executed, based on such model, is plotted. That is, the hedonic pricing equation is evaluated, for each age, using the average characteristics corresponding to that age. Figures 10, 11, 12 and 13 compare the curves obtained: (i) using the above-mentioned approach; and (ii) plotting the logarithm of the average APV versus age-at-execution. (In this case we used the average APV rather than the median, since the HPM-based curves are normally done with the mean.) All four graphs show very consistent trends between the two curves. In essence, the HPM-curves do not seem to offer anything more than the simpler APV-based curves show. Figure 10. Life-Cycle Creativity Pattern Profile, Pierre-Auguste Renoir: Comparison between (i) Log of APV profile and (ii) Log of Price (from HPM) profile Figure 11. Life-Cycle Creativity Pattern Profile, Henri Matisse: Comparison between (i) Log of APV profile and (ii) Log of Price (from HPM) profile 29 Figure 12. Life-Cycle Creativity Pattern Profile, Claude Monet: Comparison between (i) Log of APV profile and (ii) Log of Price (from HPM) profile Figure 13. Life-Cycle Creativity Pattern Profile, Camille Pissarro: Comparison between (i) Log of APV profile and (ii) Log of Price (from HPM) profile A more interesting point becomes obvious when we compare these life-cycle curves with those displayed before in Figures 1, 2, 3 and 4, which were obtained using the median APV instead of the Log(average-APV) or Log(average-Price). Obviously, the first group of curves shows much more clearly the evolution of life cycle patterns. To some extent, this is to be expected, as the Log-function tends to mitigate the effect of peaks and valleys. On the other hand, this calls into question the benefits of building these curves using the Log- function (regardless of the underlying variable) instead of using the "real thing", that is, the actual variable--for example the APV (with no Log applied). To sum up, the APV-based calculations, in all cases considered, yielded very similar results to those obtained with the hedonic models. This provides good evidence that the APV metric, despite its simplicity, offers results consistent with conventionally accepted methods. 30 This high degree of consistency might seem surprising. However, the following two observations can explain, appealing partly to intuition, the success of the APV: (1) regressing the logarithm of the price on just the area of the painting, for the case of Renoir, Matisse and the Impressionists, we obtained adjusted R 2’s values equal to 0.37, 0.26 and 0.33 respectively. Remember that the R 2’s values of the corresponding hedonic models were 0.75, 0.72 and 0.67 respectively. Hence, the APV metric --for all its roughness and simplicity— was able to explain, just by itself, almost half of what all the factors of the HPMs did; and (2) if we compute the correlation between the area of the paintings and the logarithm of the price for all the artists considered (Sisley, Pissarro, Monet, Matisse, Redon, Gauguin, Signac and Renoir) we obtain the following (fairly high) values: 0.36; 0.65; 0.48; 0.51; 0.55; 0.59; 0.68 and 0.61 respectively. These observations provide some basis for making an argument that using the area of a painting as a "normalization" factor is not that eccentric or bizarre; it has some sound foundation. Suggestions for Future Applications APV-based Derivatives and Index Contracts. The market for paintings lacks a widely accepted index or indices that could be used to design derivatives contracts for hedging and/or speculative purposes. We reckon that the reason is that the most popular indices (Mei- Moses index, artnet.com family of indices, AMR indices, etc.) while effective for the purpose they were designed--namely, tracking broad market trends—are unsuitable for financial contracts. The reason is that they involve certain elements (proprietary databases, discretionary rules in terms of which sales should be included, ad hoc combinations of repeat sales techniques coupled with some undesirable features of HPMs) that make them opaque and –at least in theory—vulnerable to manipulation. In contrast, indices such as the S&P 500 or the Barclays Capital bond indices family--which are based on well-defined and transparent rules—are easy to reproduce and difficult to game. Not surprisingly, derivatives contracts based on these indices have enjoyed wide market acceptance. We think that the APV metric provides a natural tool to create well-defined indices that could be the foundation for a derivatives art market. If one wishes to design an index to represent a specific market segment-- for example, the Impressionists-- the main point is to agree on the painters that should be part of the index. Once this issue is settled –a rule that must stay unaltered over time– what remains to agree upon is simply a mechanistic recipe to calculate the value of the index. For instance, it could be the average APV value of all the 31 paintings sold in public auctions in the last twelve months as long as their values exceeded US$ 50,000. A contract built around an index of this type could be used to gain exposure to this market or short it, in amounts much smaller than the typical price paid for a masterpiece. In that sense, these types of contracts could help to expand the investor base, and contribute to improve market liquidity. The operational details are similar, for instance, to those encountered in the agricultural derivatives market or commodities markets. This topic is presently under investigation by the authors. Testing the CAPM Validity in the Art Market. Several authors have investigated the validity of the CAPM model within the context of the art market. Although the results have been mixed we also think they have been irrelevant. The reason is that most authors — erroneously in our view— have placed on the left-hand side of the equation estimates of the market returns (obtained, in general, via the time-dummy coefficients of a suitable hedonic model). We reckon that the correct approach is to place on the left-hand side of the CAPM equation estimates of total returns—not market returns. These returns, of course, can be easily obtained with the APV. This suggestion might sound strange until one realizes that, for instance, if we were to apply the CAPM model to, say, IBM’s stock (to go back to our initial analogy) we would place on the left-hand side of the equation the return computed based on the price of IBM stock over some time period: in short, the total return. We would never place on the left-hand side the IBM return computed after controlling for whatever market factors might influence it (composition of revenue, number of employees, technology changes, etc.) In summary, it is quite odd that the validity of the CAPM within the art market context has been carried out using returns that do not capture supply-demand changes from period-to- period. At present, we are investigating this topic. Conclusions We have introduced an easy-to-compute financial metric suitable for two-dimensional art objects that is both intuitive and transparent. It has several appealing features: it is difficult to game since not much discretion comes into its evaluation (unlike hedonic models that are data intensive and often exhibit lack of stability); it can be applied to artists for whom there are few observations, albeit with all the caveats appropriate for small data sets; it facilitates comparisons between artists, between different types of paintings by the same 32 artist, or, paintings done by the same artist at different life-periods; it is also appropriate to explore artists’ consistency, by looking at its standard deviation or coefficient of variation; and, finally, it can be employed to construct well-defined total-return indices to create financial derivatives. However, it must be emphasized that the main goal of this new metric is to offer an investor a useful yardstick that captures, after normalizing by the area, a representative price. It is not the aim of the APV to control prices for characteristics or to build a market index based on a time-independent ideal painting. For these reasons the APV metric is ideally suited to compute actual returns. In terms of estimating returns, the APV metric offers two attractive features; (i) unlike repeat-sales regression models, it can use all the available data; and, (ii) unlike HPMs, whose effectiveness can depend substantially on the variables chosen and the analyst’s skill to select them, it gives a unique value: the actual total return. The comparison between APV-based total returns (or for that matter, any other figure of merit based on the APV metric) and a similar figure of merit based on HPMs techniques deserves some attention. The rationale for these comparisons is simply that hedonic models are, more or less, accepted as valid tools within the art market. Accordingly, some reasonable degree of agreement with a calculation based on hedonic models provides comfort that the new tool (the APV in this case) is not outlandish. In this regard, the examples described in the paper give validity to the soundness of the APV metric. At the same time, it should be mentioned that the examples presented here should be taken as a “proof of concept” and not as a definite claim of superiority in favor of the APV. We hope that other researchers will conduct more tests using the APV metric (and devise new applications) which, in due time, will lead to a more complete picture in terms of its advantages and drawbacks. Thus, we see the APV as a complementary tool to the conventional models, not as a substitute. Although the topic of this paper has been to introduce a new tool to the analyst’s toolkit, rather than questioning the virtues of the HPMs in the context of the art market, one thing is obvious: hedonic models, considering how data-intensive they are plus the additional limitations already mentioned, do not seem to offer a lot more insight than the simple APV metric--at least for the examples discussed in this study. Moreover, the high correlation 33 observed between total returns computed using the APV and those based on HPMs reinforces this point. In summary, we hope investors, financial analysts, and future researchers will be able to explore—and exploit— the financial merits of the APV metric. Our goal has been simply to introduce the tool, showcase a few applications, and perform some validation tests. Finally, the main advantage of the APV is that it is a (financial) metric and not a modeling technique; therefore, it is what it is, and it can always be computed. 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