American Economic Association Art as an Investment and Conspicuous Consumption Good Author(s): Benjamin R. Mandel Source: The American Economic Review, Vol. 99, No. 4 (Sep., 2009), pp. 1653-1663 Published by: American Economic Association Stable URL: http://www.jstor.org/stable/25592524 . Accessed: 26/02/2014 07:29 Your use of the JSTOR archive indicates your acceptance of the Terms & Conditions of Use, available at . http://www.jstor.org/page/info/about/policies/terms.jsp . JSTOR is a not-for-profit service that helps scholars, researchers, and students discover, use, and build upon a wide range of content in a trusted digital archive. We use information technology and tools to increase productivity and facilitate new forms of scholarship. For more information about JSTOR, please contact support@jstor.org. . American Economic Association is collaborating with JSTOR to digitize, preserve and extend access to The American Economic Review. http://www.jstor.org This content downloaded from 147.251.185.122 on Wed, 26 Feb 2014 07:29:41 AM All use subject to JSTOR Terms and Conditions American Economic Review 2009, 99:4, 1653-1663 http-J/www.aeaweb. org/articles.php ?doi=10.1257/aer. 99.4.1653 Art as an Investmentand Conspicuous Consumption Good By Benjamin R. Mandel* A spate of recentmedia announcements on record auction sales might lead one tobelieve that art as an asset class has come of age. However, it is clear that thedeterminants of an artwork's value are distinct from equities and other investmentsbecause, unlike "pure" financial instru ments, art is also a consumption good. Art owners take pleasure in its intrinsicvalue (e.g., for aesthetic pleasure or as a "storehouse" of an artist's deftness), and to theextent that itis a luxury good, theyderive additional enjoyment from the signal of wealth that owning a masterpiece transmits. It is themixture of pecuniary and nonpecuniary payoffs to ownership thatmakes artworks both compelling topurchase and difficult tovalue. I exploit this insight to explain why themeasured risk premium of a portfolio of artworks is low compared to other risky assets. In a consumption-based pricing model, an asset's risk premium is a function of thecovariance of itsreturnswith agents' marginal utility of consump tion; agents need tobe compensated if theasset pays off in a period of already high utility.As a luxurygood, relative art demand is an increasing function ofwealth. Therefore, positive shocks to income increase thedemand, price, and returns to art inperiods of high consumption utility, implying a high riskpremium. This intuition is at odds with empirical studies thatquantify the average financial returns of paintings relative tomore traditional investment vehicles. These studies find thatart1often underperforms relative to equities and bonds.While therehave been stunning individual success stories in art investment, long-termaverage returns are lower than for equity and, in several cases, the mean real return of "risk-free" government bonds exceeds thatof art, implying a negative risk premium. The savings motive for art purchases is not suf ficient to explain thisobservation. From a theoretical perspective then, artmust be treated differentlyfrom equities and other risky assets. Unlike an equity, art offers no claim on an underlying stream of payments. In fact, returnson art are largely independent of any production-side factors: thehigh-end market is dominated by themasterstrokes of dead artistswho are ratherunlikely to dilute theirexist ing stocks,2 and many living artists are relegated to thedomain of fad,3avocation, or financial * Department of Economics, University ofCalifornia, Davis, 1Shields Avenue, Davis, CA 95616 (e-mail: brmandel@ ucdavis.edu). I gratefully acknowledge constructive suggestions by Kevin Salyer, two anonymous referees, and par ticipants in the 2008 conference of theAssociation forCultural Economics International. Any remaining errors or omissions are mine. 1 Examples of art price indexes include: Robert C. Anderson (1974), John P. Stein (1977), William J.Baumol (1986), Bruno S. Frey and Werner W. Pommerehne (1989), Nathalie Buelens and Victor A. Ginsburgh (1993), William N. Goetzmann (1993), James E. Pesando (1993), Madeleine de laBarre, Sophie Docclo and Ginsburgh (1994), Pesando and Pauline M. Shum (1996, 2008), Corinna Czujack (1997), and JianpingMei andMichael Moses (2002).2 Stein (1977) uses this reasoning to argue that auction sales represent a sampling from a fixed stock of artworks, while Robert B. Ekelund Jr.,Rand W. Ressler, and JohnK. Watson (2000) point out that there is an observable rise in the value of artists' work around the time of their death. The latter observation alludes to the value of limiting future production of close substitutes for existing artworks. 3 In a model of customs and fads in consumer behavior, B. Douglas Bernheim (1994) describes how the desire for status causes agents to conform to social norms despite heterogeneous underlying preferences. Sushil Bikhchandani, David Hirshleifer and Ivo Welch (1992) attribute the dynamics of conformity behavior to incremental changes in information flows. Both status and imperfect information are important factors in the art market, so we expect fad behavior to be particularly pronounced, especially for living artists forwhom the status and legacy of theirworks are uncertain. 1653 This content downloaded from 147.251.185.122 on Wed, 26 Feb 2014 07:29:41 AM All use subject to JSTOR Terms and Conditions 1654 THEAMERICANECONOMIC REVIEW SEPTEMBER2009 ruin (i.e., the supply ofworks by living artists has little ifany bearing on theprices theyfetch). Moreover, reasonable people can disagree on exactly "what is art?,"which makes its supply essentially arbitrary.Thus itis thedynamic demand forart that is theonlymeaningful driver of investment returns. Demand factors forart assets include thedemand for savings (as in any investmentvehicle), and I propose a novel "utilitydividend" that is increasing in thevalue of art.The utilitydividend is a special featureof demand for luxurygoods. Peter J.Kalman (1968) firstoutlined thegeneral class of utility functions containing both quantities and prices. Utility fromgoods prices, in turn, has appeared in economic writings at thevery least since Thorstein Veblen's The Theory of the Leisure Class (1899). It formalizes the satisfaction derived from the conspicuous consumption of, or in this case investment in,high-priced luxuries.While art does not affect consumption decisions forother goods (by construction herein), ityields incremental utilitywhen itsprice is high; effectively,an increase in theprice of art is an upward shift inan agent's contemporaneous marginal utility of consumption. In this article, I specify and calibrate a consumption-based capital asset pricing model as in Robert E. Lucas, Jr.(1978) topredict thedynamic returnsand riskpremium of theartasset. Indeed, themodel predicts a low and possibly even negative riskpremium forart. Since art demand is a function of income, itsprice and returns risewhen the economy is robust.Concurrently, when theprice of art is high, themarginal utility of consumption is shifted upward due to theutility dividend. Since the covariance of the art asset's payoff and marginal utility is increased by the utility dividend, the typically positive consumption-based risk premium fora procyclical asset is offset or even reversed (i.e., art can act as a type of insurance thatpays off in times of high marginal utility of consumption). The model thus succinctly bridges the demand for luxury goods with thedemand for art as investments,and can be interpretedmore broadly as an application of conspicuous consumption4 in an environment where goods embody this dual nature. The paper proceeds as follows. The next section brieflydocuments the literaturedescribing themeasurement and underperformance of art returns. Section II thenoutlines the basic assumptions of themodel and simulations in Section III. Section IV concludes. I. Art PortfolioReturns The empirical literaturemeasuring average art prices is extensive, and the estimated long run real returnon art is quite low.According to a survey by Orley C. Ashenfelter and Kathryn Graddy (2003), real art returnestimates range from0.6 to 5.0 percent forpaintings in general, as shown inTable 1.The returns are quite heterogeneous across (and even within) periods and index constructionmethodologies;5 in largepart, this isdue to thedifficultyof constructing aver age price changes forhighly distinct and illiquid6 goods. This illiquidity creates selection issues 4 See, among others, Kaushik Basu (1987), Yew-Kwang Ng (1987), Ottmar L. Braun and Robert A. Wicklund (1989), Norman J. Ireland (1994), Wolfgang Pesendorfer (1995) and Betsy M. Wearing and Stephen Wearing (2000) forprevi ous applications in quality uncertainty, taxation, psychology, regulation, design innovation, and smoking behavior, respectively. 5 There are two predominant methods for calculating price change indexes forpaintings: (i) repeat sales regression, which uses painting fixed effects to control for idiosyncratic price variation (but requires at least two price observations per painting), and (ii) hedonic regression, which controls for a vector of painting characteristics (but is subject to bias from systematic changes in these characteristics). For detailed comparisons of index methods as applied to art, see Ginsburgh, Mei, and Moses (2006) and Olivier Chanel, Louis-Andre Gerard-Varet and Ginsburgh (1996). 6 Observations of art returns are extremely limited relative to other assets, though the quantity of available data has been increasing in recent empirical work. The most common sources forart pricing data are auction house sale records and collections of historical sales assembled by Enrique Mayer (various years) and Gerald Reitlinger (various years). This content downloaded from 147.251.185.122 on Wed, 26 Feb 2014 07:29:41 AM All use subject to JSTOR Terms and Conditions VOL.99NO. 4 MANDEL: ARTASAN INVESTMENTAND CONSPICUOUSCONSUMPTIONGOOD 1655 Table 1?Survey of Measured Financial Returns for Paintings and Prints Nominal Real return return Author(s)Sample Period Method percent percent Anderson (1974) Paintings in general 1780-1960 Hedonic 3.3 2.6 1780-1970 Repeat sales 3.7 3.0 Stein (1977) Paintings in general 1946-1968 Assumes ran- 10.5 dom sampling Baumol (1986) Paintingsingeneral 1652-1961 Repeatsales0.6 Frey and Pommerehne (1989) Paintings in general 1635-1949 Repeat sales 1.4 1950-1987 Repeat sales 1.7 Buelens and Ginsburgh (1993) Paintings in general 1700-1961 Hedonic 0.9 Pesando (1993) Modernprints 1977-1991 Repeatsales1.5 Goetzmann (1993) Paintings in general 1716-1986 Repeat sales 3.2 2.0 de laBarre et al. (1994) Great Impressionist 1962-1991 Hedonic 12.0 5.0 Other Impressionist 1962-1991 Hedonic 8.0 1.0 Chanel et al. (1996) Paintings in general 1855-1969 Hedonic 4.9 Paintings in general 1855-1969 Repeat sales 5.0 Goetzmann (1996) Paintings in general 1907-1977 Repeat sales 5.0 Pesando and Shum (1996) Picasso prints 1977-1993 Repeat sales 12.0 1.4 Czujack (1997) Picassopaintings 1966-1994 Hedonic8.3 Mei andMoses (2001) American, Impressionist, 1875-2000 Repeat sales 4.9 old masters Notes: Sources for art pricing data are auction house sale records and collections of historical sales assembled by Reitlinger (various years) and Mayer (various years). In the calculation of price indexes, repeat sales regression uses painting fixed effects to control for idiosyncratic price variation (requiring at least two price observations), and hedonic regression controls for a vector of painting characteristics. Returns are annual and themedian real return of paintings in general (including Mei andMoses 2002) is 2.6 percent. Source: Ashenfelter and Graddy (2003, Table 1).The final row refers to a working paper version ofMei and Moses (2002). indata collection and itcan be argued thatart price indexes reflectmore of an upper bound to investment returns: nonrepeat sales which henceforth became worthless are not included,7 nor are transaction costs of sale or those paintings thatdo not reach theirreservation prices at auction (i.e., inclusion in the index is conditional on sale and theremay be a relationship between value increases and theoccurrence of a transaction).8With this inmind, I focus on the long-runreturn measures of "paintings in general," includingMei andMoses (2002), togauge theupper bound of the expected unconditional return on art assets. Mei andMoses (2002) compile price observations for three classes of paintings sold at Sotheby's and Christie's inNew York between 1950 and 2000, and search forprior sales of those paintings at auction. Their database, across all classes and including multiple (i.e., at least two) sales of the same painting numbered approximately 5,000. Prior studies using a repeated sales methodology employed 3,329 (Goetzmann 1993), approximately 1,900 (Chanel, Ge'rard-Varet, and Ginsburgh 1996), 1,198 (Frey and Pommerehne 1993), and 640 (Baumol 1986; Buelens and Ginsburgh 1993) price pairs, respectively. Of note, however, more observations do not necessarily generate higher returns estimates. Pesando (1993) and Pesando and Shum (2008) use substantially larger samples of art print sales (i.e., identical renderings of the same image) of 27,961 and 80,214 price pairs, respectively, and estimate average annual returns of about 1.5 percent.7 Goetzmann (1996) documents high (20 percent) "obsolescence" rates for paintings (i.e., the frequency at which they disappear from the auction records over time).8 Mei and Moses (2002) point out that these biases are mitigated in part by the survivorship bias of artists (i.e., included data is for artists who are already established and does not capture the initial appreciation of theirworks), and Goetzmann (1993) notes thathigh-value donated works tomuseums are also censored from the index of returns. This content downloaded from 147.251.185.122 on Wed, 26 Feb 2014 07:29:41 AM All use subject to JSTOR Terms and Conditions 1656 THEAMERICANECONOMIC REVIEW SEPTEMBER2009 Table 2?Comparison of Real Returns for Art and Financial Assets ArtS&P 500 Dow Gov. bond Corp. bond T-Bill Periodpercent percent percent percent percent percent 1950-1999 Mean 8.2 8.9 9.1 1.9 2.21.3 SD21.3 16.1 16.2 9.59.22.3 1900-1999 Mean 5.2 6.7 7.4 1.4 2.01.1 SD35.5 19.8 22.2 8.68.4 4.9 1875-1999 Mean 4.9 6.6 7.4 2.0 2.91.8 SD42.8 8.7 20.8 8.08.0 4.8 Notes: Asset returns are the average annual return calculated over the sample period, with the standard deviation shown in italics below. Real returns are calculated by subtracting inflation (US CPI growth) from nominal returns. Art returns are based on repeat sales regression index methodology for the sample of paintings inMei and Moses (2002). Financial returns are based on data from theFederal Reserve Board and Global Financial Data (5th edition). Source: Mei andMoses (2002, Table 1). Table 2 compares the index of art returns constructed byMei and Moses (2002) to other investmentvehicles. In terms ofmean return, inmany cases art is outperformed by financial securities: in every instance, art is outperformed by equity though underperformed by bonds. Considering themedian real returnforpaintings ingeneral (fromTable 1)of 2.6 percent, artonly slightly outperforms long-runbond returns and underperforms corporate bonds. As an upper bound, this implies a small or even negative riskpremium. In termsof volatility, art unambiguously has thehighest variance of all assets, up to twice or three times thatof theDow Jones industrial index or corporate bonds. Thus, given low average real returns, art is often a dominated asset in a portfolio that seeks tomaximize returns and minimize variance. Estimating mean-variance-efficient portfolios using Harry M. Markowitz's (1959) framework of diversification, Pesando (1993) argues that,despite theirhigh variance, art prints should be included in a low risk portfolio with 180-day Treasury Bills since T-Bill and art returns are negatively correlated.9 In contrast, both Baumol (1986) and Goetzmann (1993) find an index of art tobe a strictlydominated asset. Several of the studies inTable 1 also find a significant,positive correlation between art and equity returns,e.g., Stein (1977) and Goetzmann (1993). On theother hand,Mei andMoses (2002) estimate lower correlations between painting returnsand equities (see Table 3) and relatively less systematic risk fora portfolio of paintings, which suggests thatthe timingof art payoffsmakes itattractive as an investment. As theempirical literatureon thedesirability of art as an asset disagrees largelydue todiffer ences indata and empirical methodology, I turnto the theoryof consumption-based asset pricing topredictwhich view should prevail. II. Modeling Luxuries as Assets I proceed by assuming thatdemand factors fully determine equilibrium art prices and bear special features unique to luxurygoods; specifically, thevalue of art factors intoutilitydirectly. Veblen (1899) coined the term"conspicuous consumption" to referto consumption that is unre lated to the intrinsicvalue of a good. A casual observer of prices for thewears on Madison Avenue inNew York or themobile phone market inChina would conclude thatcertain classes of goods are intended primarily to signal wealth. Models of consumer behavior employing this insighthave sought to formalize the idea thatutility is derived not only from the quantity of 9 However, Pesando (1993) also concludes that art prints should not be included in optimal mean-variance efficient portfolios with expected returns of greater than 3 percent. This content downloaded from 147.251.185.122 on Wed, 26 Feb 2014 07:29:41 AM All use subject to JSTOR Terms and Conditions VOL. 99NO. 4 MANDEL: ARTASAN INVESTMENTAND CONSPICUOUSCONSUMPTIONGOOD 1657 Table 3?Correlation of Real Art Returns with Financial Asset Returns Art index 1.00 S&P 500 index 0.041.00 Dow industrial 0.03 0.991.00 Government bonds -0.15 0.330.28 1.00 Corporatebonds -0.10 0.380.33 0.95 1.00 TreasuryBills -0.03 0.27 0.25 0.61 0.63 1.00 Notes: Shown are pair-wise correlation coefficients for real asset returns over the period 1950-1999. Art returns are based on repeat sales regression index methodology for the sample of paintings inMei and Moses (2002). Financial returns are based on data from theFederal Reserve Board and Global Financial Data (5th edition). Source: Mei and Moses (2002, Table 1). consumables, but by theirvalue. Kalman (1968) investigates theproperties of utility functions containing prices and theircorresponding demand functions; Laurie S. Bagwell and Bernheim (1996) model luxury goods purchases as a signal to society with subsequent externalities; Ng (1987) argues that luxurieswhose value enters intoutility are a good candidate for taxes since theydo not affect the consumption decisions vis-a-vis other consumption goods; andMichele Piccione andAriel Rubinstein (2008) model luxuries as goods thatsatisfyboth the"psychologi cal need of owning a precious commodity" and redistributewealth. The conventional wisdom of art investing is tobuy themost notedworks inorder toobtain the highest returns, though according tomore rigorous empirical testing,masterpieces often under perform the (already low) art index.The datasets of both theMei andMoses (2002) and Pesando (1993) suggest thatbuying highly prized and valuable paintings or prints is a poor investment strategy.10This observation is particularly poignant in lightof the fact that it is precisely these raremasterpieces thatought toyield thehighest conspicuous consumption boon toutility.11 The model below merges the literatureon consumer behavior for luxuries with thatof the consumption-based theoryof asset pricing. Imodel utilityas increasing and concave in thevalue of artcollectibles while allowing forart topersist (withoutdepreciation) into thenext period with the opportunity for resale. Art is thus a hybrid of consumption and investment since utility is derived both from thevalue of contemporaneous artpossession and theexpected capital appreci ation of artholdings in thefuture.Each period, every agent in theeconomy makes thecalculation of how much real income to invest in savings instruments (i.e.,bonds, equities, and art) and how much to consume. The Lucas asset pricing model then solves for the value of each instrument implied bymarket clearing in thefinancial and goods markets. Each agent faces the following trade-off:at themargin, theutilityof giving up consumption tobuy a piece of art exactly equals itsexpected conspicuous consumption benefitplus capital returnnext period.12 10 De la Barre, Docclo, and Ginsburgh (1994) find that great Impressionists return 4 percent higher than other Impressionists, though Ashenfelter and Graddy (2003) find no "masterpiece" effect for Impressionist art and a return of 50 percent less forcontemporary masterpieces.11 An alternative explanation for the underperformance ofmasterpieces isposited byMei andMoses (2005): auction houses tend to upwardly bias price estimates forhigh-priced works which correlates with subsequently poor investment returns. That credulous investors systematically overpay due to the influence of auction house price estimates seems consistent with a story inwhich (rational) investors receive nonpecuniary benefits from high-priced art purchases.12 For ease of exposition, I specify art as entering into utility in an additively separable manner. As a result, the marginal utility of consumption (i.e., non-art consumption) and the pricing of all other assets is unchanged from the standard framework. This is consistent with the result inNg (1987) that "diamond" good prices do not affect the con sumption quantities of regular consumption goods (hence, they are good candidates for taxation). This content downloaded from 147.251.185.122 on Wed, 26 Feb 2014 07:29:41 AM All use subject to JSTOR Terms and Conditions 1658 THEAMERICANECONOMIC REVIEW SEPTEMBER 2009 III. Model and Simulations Consider a representative agent settingwith a stochastically growing endowment of some homogeneous consumption good, v, growing at rate 7, where the latter follows a three-state Markov process: (i) yt+\ = it+\yr As an approximation, art production will be ignored: each agent is endowed with one unit of art.That is,whereas an equity represents a claim to the stochastic streamof a consumption good, artworks, at, are supplied inelastically and bear no association to theendowment process of the consumption good. The art investor seeks tomaximize thenet present value of her utility flows,which depends on: (i) expected capital gains, and (ii) expected utility "dividends" from art purchases. Both of thesemotivations gauge theprice of art,pf: theformer is simply thepercentage change in theart price and the latteris a function of thevalue of artwhich enters directly intoutility as follows: rl~a (a naY~a (2) u(c?atp?)= -?? + (af ,v J w iri J 1? a 1- a where ct is theagent's choice of theconsumption good, atpf is thevalue of her art collection, and a isher coefficient of relative risk aversion. The agent chooses consumption levels, ct, risk-free bonds, bt+l, equities, st+u and art, at+l, given current price realizations, p\ (i G {b,s,a}), to solve the following utilitymaximization problem: 00 (3)max E0 Y.^^t,atpf) s.t: (4) bt+ st(Pt + y,) + atPta> ct+ bt+lpbt+ sM pst+ aM pf. The first-orderconditions of thisproblem are: (5) Bond : p,Vfo) = PEt[u\cM)\, (6)Equity : pfu'(c) = (3Et[u'(ct+l)(yt+l + p'+l)}, (7) Art : p?u'(ct) = /3Et[aJ?p?+ ?'y(7,)=/??,[7,'+r(1+ ^(7,+,))], This content downloaded from 147.251.185.122 on Wed, 26 Feb 2014 07:29:41 AM All use subject to JSTOR Terms and Conditions VOL. 99NO. 4 MANDEL: ARTASAN INVESTMENTANDCONSPICUOUS CONSUMPTIONGOOD 1659 (9)^(7,) = /??,[7('+rw(7,+i) (1+ "(7,+iT?)] In equilibrium, prices adjust toclear thegoods and financial markets subject to thenecessary conditions (5), (8), and (9). A. Calibration The empirical startingpoint forpricing the art asset relative to other financial instruments is amodel of the equity riskpremium. Thomas A. Rietz (1988) posits a solution toRajnish Mehra and Edward C. Prescott's (1985) equity premium puzzle (and therelated risk-freeratepuzzle) by modeling a low probability "crash" state inanArrow-Debreu asset pricingmodel. For reasonable degrees of timepreference and risk aversion, themodel predicts a high equity riskpremium and low risk-freerate, as observed in postwar US data. In the simulation below, Rietz's three-state model is augmented to include theart asset.13 The economy has threediscrete states: (i) a high-growth state (7, = 1+ m + v), (ii) a low growth state (7, = 1 -hm ? v), and (iii) a crash state (7, = k (1+ m)). These states evolve accord ing to the following transitionprobabilitymatrix: 7T 1? 7T? S S 1? 7T? 5 IT5 Vi Vi0 where 5 is theprobability of entering the crash state.14Deriving expressions for themean, stan dard deviation, and covariance of endowment growth, equating these expressions to reasonable values forUS data (i.e.,?[7,] = 1.018; sd[7,] = 0.036; cov[yt9%_i] = ?0.16), and assuming crash state parameters (S and k), I solve forvalues ofm, v, and tt.Then, using these calibrated parameters, I solve for theunconditional expected financial returnsof bonds, equity, and art. B. Simulation Table 4 presents the resulting riskpremia given assumptions about theunderlying parameters of themodel. The firstrow assumes a timediscount of 0.99 and theprobability of a crash occur ring tobe 0.001 (withk= 0.5). As a firstapproximation, I simulate themodel with an art risk premium restricted tobe zero (row I): the corresponding coefficient of relative risk aversion is 6.56 with an equity returnof 7.85 percent and a risk-freerate of 2.02 percent. These returns for stocks and bonds are almost equal to the long-termactual returns shown inTable 2 and are hence consistentwith theobserved equity risk premium.Moreover, as inRietz (1988) the crash state allows fora coefficientof relative risk aversion thatisnot "too high" tomatch thisempirical fact. The simulated standard deviations forequity and art are low relative to thedata but are ordinally roughly correct: equity returns are more volatile than the risk-free return, and art is as volatile as equity. Finally, thecovariance of artwith the risk-freerate is negative, and thatof art and equity ispositive, which is consistentwithMei andMoses (Table 3) and other empirical studies. 13 The Rietz framework is an elegant way tomodel an empirically plausible equity risk premium and risk-free rate without encumbering themodel with toomuch complexity. As Iwill illustrate, the results of this paper are not depen dent on the crash state. 14 Note both the symmetry of the high and low states in the first two rows, as well as the ephemeral nature of the crash state in the third row. This content downloaded from 147.251.185.122 on Wed, 26 Feb 2014 07:29:41 AM All use subject to JSTOR Terms and Conditions 1660 THEAMERICANECONOMIC REVIEW SEPTEMBER2009 Table 4?Predicted Returns and Risk Premia for Art and Equity Risk Risk-free Equity Equity risk Art Art risk Probability aversion return return premium return premium Cov (art, Cov (art, of crash (5) (a) percent percent percent percent percent risk-free) equity) (I)O001 6\56 2m 785 5^83 102 O00 -0.0027 0.0059 3.83 7.74 7.66 (II)0.001 6.1 3.83 8.35 4.52 2.00 -1.83 -0.0025 0.0055 3.71 7.45 7.34 (III) 0.001 6.9 0.20 7.23 7.03 2.04 1.84 -0.0028 0.0062 3.87 7.92 7.86 (IV)0.0001 10 2.62 10.09 7.49 2.23 -0.39 -0.0046 0.0100 5.75 10.01 10.04 (V)0.001 6.56 3.36 9.25 5.89 2.23 -1.13 -0.0027 0.0060 3.87 7.80 7.70 (VI)0.001 6.56 1.38 7.46 6.08 2.07 0.69 -0.0032 0.0071 4.12 8.49 8.40 (VII) 0.001 6.56 2.23 8.25 6.02 2.24 0.01 -0.0055 0.0102 5.99 10.05 10.17 Notes: The standard deviation of asset returns is shown below average returns in italics, and is based on 1million peri ods of model simulation. The model is calibrated to postwar US data, and endowment growth follows a three-state Markov process with probability S of entering a transient crash state with growth rate 0.5 (see Section IIIA). Row I restricts the art risk premium to be zero. Rows II and III decrease and increase the coefficient of relative risk aversion, respectively. Row IV simultaneously decreases the probability of crash and increases agents' risk aversion and time discount. In rows V-VII, the calibration assumptions are changed: rowV assumes a higher average endowment growth rate of 2 percent; row VI assumes a higher endowment standard deviation of 0.4; row VII assumes a greater negative lag covariance of -0.25. The results are also suggestive that art is dominated by equity as a "pure" financial asset. Given lower returns,equal variance, and positive covariance, equity is strictlypreferred toart in a mean-variance-efficient portfolio.15 Moreover, since art and equity are nearly perfectly corre lated in themodel (i.e., arthas a beta of one),16expected returns should be equalized. The return on art ismarkedly lower.Agents are willing to accept this low financial return,however, since there is an augmenting utilitybenefit toholding artwhen prices are high. Figure 1 illustrates the simulated returnsof equity, art, and bonds inrelation to the three states of endowment growth (the thick solid line).The thin solid line depicts the risk-freeratewhich is stronglycountercyclical due to consumption-smoothing behavior. The equity and art returns,on theother hand, move procyclically and in tandemwith one another, and since theart return is a pure capital gain (i.e., an ex-dividend return) theirdifference bounds thenonpecuniary benefits toholding art. In period 13, there is an unlucky draw from the endowment growth distribution and consumption growth crashes. That theordering of returns is preserved, and thatequity and art returnsare similar in thecrash state, suggests that it is not the crash per se thatgenerates the low art riskpremium, but rathermore systematic behavior. The remaining rows inTable 4 present comparative statics for themodel. Row II shows the resultingasset returnsand covariances when riskaversion is lowered (i.e., theirintertemporalelas ticityof substitutionincreases). As expected, both equity and bond returns increase as agents are 15 Using var(jc + y) = var(x) + var(v) + co\(x,y), the combined variance of an art/equity portfolio is larger than for either alone. 16 Very high correlation between art and equity, while in line with Goetzmann (1993) and Stein (1977), is in sharp contrast to the low (positive) correlation measured byMei and Moses (2002). One potential way to reconcile thatfind ingwith themodel is if the relationship between equity income and art returns is not contemporaneous. It is likely that the lowmeasured correlation is not capturing market behavior that actually occurs over several periods. This content downloaded from 147.251.185.122 on Wed, 26 Feb 2014 07:29:41 AM All use subject to JSTOR Terms and Conditions VOL. 99NO. 4 MANDEL: ARTASAN INVESTMENTAND CONSPICUOUS CONSUMPTIONGOOD 1661 20-|-j y A A A '\ i\ /\___ 0 [?w?raa?Endowment .Bond ?- ?Equity mm Art] 1 f 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 Period Figure 1.Simulation of Endowment Process and Asset Returns Notes: The figure illustrates 25 of 1million simulated periods, chosen to bracket a crash state (period 13). The speci fication of themodel and average asset returns can be found inTable 4, row I. The model is calibrated to postwar US data, and endowment growth (the thick solid line) follows a three-state Markov process with probability 0.001 of enter ing a transient crash state with growth rate 0.5 (see Section IIIA). more willing to shiftconsumption over time. Since art returnscombine capital gains with utility dividends, the comparative static exposes which factor dominates; in this case, the conspicuous consumption utilitydividend increases for lowera, which drives down thefinancial returnby two basis points.Thus theart riskpremium is small and negative. For higher riskaversion (row III), the converse holds and theart riskpremium is small and positive. In both cases, and fora wide range of specifications of themodel, theart return is about 2 percent.This stabilityreflects the fact that theprice entersdirectly intoutility,which agents prefer tokeep on an even keel over time. Italso increases one's confidence thatthe low theoretical art return is a robustfinding. In row IV of Table 4, an alternative way of generating a 7 percent equity risk premium is to lower theprobability of thecrash while increasing the agent's risk aversion. As above, the result is an art returnof 2 percent and a slightlynegative art riskpremium. Interestingly,thisnew for mulation increases the covariance of the art asset with both equities and bonds.17 Finally, the calibration assumptions are revisited to examine their impact on themodel's pre dictions. Row V presents themodel simulation results under the assumption that the average endowment growth rate ishigher (i.e., 2.0 versus 1.8 in thebaseline case). For bonds and equity, asset returns are significantlyhigher, as the stochastic variation in the endowment is a smaller proportion of average total consumption. The same applies forart, though thiseffect ismitigated by the utility dividend; the return increases, but by a small amount, and the art risk premium becomes negative. Rows VI and VII increase the standard deviation and lag covariance of the endowment, respectively. In times of high endowment variation, asset returnsdecrease (again, with art returnsnot changing bymuch) and the art risk premium becomes positive. The model fails in replicating the high standard deviation of art returns and theirhigher variability than 17 However, since the variance of equity also increases, the near-perfect correlation of art and equity returns is unaffected. This content downloaded from 147.251.185.122 on Wed, 26 Feb 2014 07:29:41 AM All use subject to JSTOR Terms and Conditions 1662 THEAMERICANECONOMIC REVIEW SEPTEMBER 2009 equity returns.High art returnvariability could be obtained by significantly increasing the lag covariance of the endowment, though thiswould likely result in a risk-freerate far above that observed, as well as an unrealistically high variance of equity returns.The biases inherent in empirical measurement of art returnsmay also be skewing thevariance statisticupward. IV. Conclusions This paper reconciles theobservations of a burgeoning, volatile artmarket and (on average) low long-termreturnswith the consumption-based motive for savings. Financial returnsare low since they tell only part of the story: theprice of art reflectsnot only thedesire to smooth con sumption over time as forany investmentvehicle, but also theutility derived from itsconspicu ous consumption. The utilitydividend, in turn,endogenously moderates the level of art returns. While the cyclicality and variance of artwork returns are similar to those of equity?they are both driven by the stochastic endowment process?art investorsneed tobe compensated by less infinancial terms for the risks theyare incurring. One could relate thismodel to the empirical analysis of the causal linkages between equity markets and artmarkets as inAndrew C. Worthing ton and Helen Higgs (2003) and Chanel (1995). Here, equitymarkets are related toartmarkets, thoughnot forthe same reasons.Whereas those authors reason thatequity returnsprovide a boon to income which, in turn, increases art consumption, here the savingsmotive forholding art is sufficientto create a positive covariance between art and equity. Further, since themodel also presupposes a constant endowment of artwork, it is notwell equipped topredict thedemand and portfolio share of art in a settingwith fewer restrictionson production. The labormarket implications of thattypeofmodel are beyond the scope of thispricing exercise, but remain importantareas of potential advance. Though applied to the low or negative riskpremium observed for indexes of art, the logic of themodel is by nomeans limited topaintings. The same could be said of any good with a low rate of depreciation that is conspicuously consumed, any good with sentimental value, or,more broadly, any good or investmentwith nonpecuniary benefits.What is important is thepotential toblur thebright theoretical distinction between consumption and investmentbehavior. Finally, thispaper provides food forthoughtforthemyriad dilettante art aficionados. In a boast, a friendonce toldme thathis artwas a better investmentthanall other assets, includingfinancial securities and real estate.Accounting forhis utility in tellingme so, thatis indeed likely. REFERENCES Anderson, Robert C. 1974. "Paintings as an Investment." Economic Inquiry, 12(1): 13-26. 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