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Fiddling with value: violins as an investment?

I. INTRODUCTION

In this article, we analyze the prices of violins using two
different datasets: one
dataset

 includes 337 observations on repeat
sales of the same violins at auction and at dealer sales starting in the
mid-nineteenth century, and the other dataset includes over 2,500
observations on sales of individual violins at auction since 1980. The
purpose of this article is to give some indication as to whether violins
are a viable alternative investment that might be part of a
diversified

 portfolio and to determine if some types of violins have had higher
returns than other types of violins.

Despite the growing discussion of alternative investments in the
economics and finance literature, the growing number of wealthy
individuals, funds and syndicates that invest in violins, and the
interest in violins as a collateralizable asset, the only previous study
of
violin
 family of stringed musical instruments having wooden bodies whose backs and fronts are slightly convex, the fronts pierced by two f-hole-shaped resonance holes.
 prices published in an academic journal was a study by Ross
and Zondervan (1989) of repeat sales of 17 Stradivaris. This dearth of
academic analysis is most likely due to the difficulty in gathering
information on the sale prices of violins. Compared to real estate and
even art, the market for
high-end

adj. Informal
1. Appealing to sophisticated and discerning customers:

2.
 violins is “thin” and many
violins are sold through dealers rather than auctions, resulting in
difficulty gathering the data.

To preview our results, overall real returns for the dataset on
repeat sales for the period 1850-2009 have been approximately 3.5%. Real
returns to the overall portfolio of individual sales at auction since
1980 have also been about 3.3%, not including transaction commissions.
The price path has been stable with a slightly
negative correlation

 to
stocks and bonds. The overall returns mask differences in returns
between different types of violins. It is believed that
“better” violins are sold through dealers rather than through
auction houses. Indeed, the real return on dealer sales for 1850-2008
was 4.32% and the real return to violins sold at auction for the same
period was 2.86%. Since 1980, Modern Italian instruments sold at auction
have increased steadily in price relative to Old Italian instruments
sold at auction.

This article proceeds as follows. The violin market is discussed in
Section II, and in Section III we discuss the data and our
estimation

 methodology. In Section IV we present our
regression
 in psychology: see defense mechanism.


regression

In statistics, a process for determining a line or curve that best represents the general trend of a data set.
 results, and in
Section V we interpret our regressions. We conclude in Section VI.

II. THE MARKET FOR VIOLINS

A. How the Market Works

Fiddles–the term used by dealers and collectors to refer to even
the finest violins–are sold through both auction houses and dealers and
also directly from one
musician

 or collector to another. The main
sellers and buyers of these instruments, other than dealers, are
musicians, collectors (often foundations), and investors. Individual
musicians have used various schemes to purchase a good instrument,
including borrowing from banks that
specialize

v.
1. To limit one’s profession to a particular specialty or subject area for study, research, or treatment.

2. To adapt to a particular function or environment.
 in loaning funds against
musical instruments and assembling syndicates to raise money. Most
collectors, both private and institutional, loan out their instruments
to talented musicians. The musician typically pays all insurance and
maintenance costs (but not a rental fee); insurance costs range from
about 0.5% to about 2% of the value of an instrument. There are also
buyers who are interested in purchasing violins primarily as an
investment, as part of a diversified portfolio. These instruments are
then also loaned out to musicians, who pay insurance and maintenance.

Violins are sold through both auction houses and dealers. The
relative size of the various markets is very difficult to gauge. Through
conversations with dealers and analyzing our auction data, we speculate
that auction sales make up between 10% and 20% of the market. One
advantage of transacting through a dealer is that it is easier to borrow
and try out the instrument (though auction houses also accommodate a
small number of potential buyers in this manner). Furthermore, dealers
will often accept “trade-ins” as long as the fiddle is traded
for one of a similar or higher value. The main advantages of buying (and
selling) through auction is transparent pricing.

The importance of dealers in the violin market makes a calculation
of returns more difficult than in markets where assets are primarily
publicly traded. As auction prices are verifiable, auction prices are
preferable data on which returns can be
analyzed
  
tr.v. an·a·lyzed, an·a·lyz·ing, an·a·lyz·es
1. To examine methodically by separating into parts and studying their interrelations.

2. Chemistry To make a chemical analysis of.

3.
, as one cannot be
certain about the reliability of price announcements of dealer sales.
Furthermore, it is likely that only prices from
favorable
  
adj.
1. Advantageous; helpful:

2. Encouraging; propitious:

3.
 dealer sales
are
publicized
  
tr.v. pub·li·cized, pub·li·ciz·ing, pub·li·ciz·es
To give publicity to.

Adj. 1. publicized – made known; especially made widely known
publicised
. However, as the very top instruments are usually not
sold through auction, but through dealers, a sample selection problem
clearly exists. We approach this problem as follows. We first analyze
our repeat sales data using all prices that we have collected, both from
auctions and dealers. We then split the sample into two subsets. In the
first
subset

, all second sales were at auction, and in the second
subset, all second sales were through dealers. We then discuss sample
selection bias resulting from just using auction sales and possible
problems with sample selection bias using dealer sales. We can then
discuss our
hedonic
  
adj.
1. Of, relating to, or marked by pleasure.

2. Of or relating to hedonism or hedonists.


[Greek h
 estimates, which use only auction sales data, within
this context.

B. Previous Work on Violin Prices

The one academic study that we know of is by Ross and Zondervan
(1989). In this study, they examine a repeat sales dataset of 17
Stradivaris that were bought and sold a total of 29 times between 1803
and 1982. They find an average real return over this period of
approximately 2%, equal to the long-run real rate of interest. There
have been several other attempts to measure returns to violins, but
these studies neither have used auction data nor have been published in
refereed journals.

III. DATA AND METHODOLOGY

A. Data on Repeat Sales

The data on repeat sales were gathered from both the original
auction catalogs and price sheets from the main auction houses, from
business records, and from secondary sources. These sources are listed
in Appendix B. The auction sales data are all reliable and verifiable.
It is the belief of the authors that the dealer sales data are reliable,
but of course the prices are the result of self-reporting by dealers and
buyers. In the later years, the dealer prices may suffer from further
sample selection bias as many of the later dealer prices were collected
from newspaper articles and the business press. Only sales that do well
may be reported.

For our repeat sales database, we have 259 fiddles comprising 337
observations–some of the violins in our dataset were sold more than
twice. When we
assembled
  
v. as·sem·bled, as·sem·bling, as·sem·bles

v.tr.
1. To bring or call together into a group or whole:

2.
 the data, we excluded sales where the holding
period was less than 5 yr. (1) We did this for two reasons: first, we
wanted to focus on longer-run returns, and second, several of the
instruments appeared to have been sold twice in the same year by the
same auction house. On average, in the overall dataset, violins were
held for 32 yr, with a minimum holding period of 5 yr and a maximum
holding period of 147 yr. This does not necessarily mean that violins
are held on average for 30-yr periods; it is likely (especially for some
of the longer holding periods) that some violins in our sample changed
hands between recorded sales either privately or through dealers. In our
dataset, we have 119 observations of repeat sales at auction, 124
observations of repeat dealer sales, 29 observations where the purchase
was at auction and the sale was a dealer sale, and 65 observations where
the purchase was through a dealer and the sale was at auction. These are
typical high-quality instruments by top Old Italian makers, including
168 instruments by Stradivari and 33 by del Gesu. (2)

We also split our regressions into two subsets. In the first
subset, the purchase was either at an auction or through a dealer and
the sale was at auction. In the second subset, the purchase was either
at an auction or through a dealer, and the sale was through a dealer. We
split the sample in this way to address the concern that better violins
are often sold privately, and the returns to these violins may be
different. The average holding periods are similar in each of the
subsets, at 31 yr when the sale is at auction and 32 yr when the sale is
through a dealer, though again, actual holding periods are probably
because of unobserved transactions. It is to be noted that auction sales
are
overrepresented
  
adj.
Represented in excessive or disproportionately large numbers:  
 in our database, as they likely comprise only
between 10% and 20% of the market.

For the regressions, we use prices including buyers’
commissions. Other studies such as the
Mei

 and Moses’s (2002) study
on art prices include commissions, and we would like this study to be
comparable. Auction houses usually report prices including buyers’
commissions; also, dealers usually report the price the buyers pay, and
then keep a percentage for themselves, if they are acting as an

intermediary

See financial intermediary.
. Sellers’ commissions at auction are
negotiable

 and
unknown to us. We consider buyers’ and dealers’ commissions
when interpreting our regression results below. We estimate the index in

GBP

 as most purchases and sales were recorded in GBP.

B. Data on Individual Sales

A complete description of the data collection for individual sales
is in Appendix B. The characteristic that we focus on and include in our
regressions and that is recognized to have a huge influence on price is
maker. Altogether, the database consists of violins by more than 100
different makers spanning four centuries and representing virtually all
of the important schools of violin making. As we control for maker in
the hedonic regressions, we only included violin makers that had at
least two observations in our dataset.

The schools represented in our data are the Old Italian school,
comprising 1,059 observations on violins made in
Italy
 , Ital. Italia, officially Italian Republic, republic (2005 est. pop. 58,103,000), 116,303 sq mi (301,225 sq km), S Europe.
 between 1580 and
1850, the Modern Italian School, comprising 1,004 observations on
violins made in Italy between 1820 and 1982, and the French school,
comprising 394 observations on violins made between 1775 and 1948. The
remaining observations were made by various other schools, with the
largest other school being Old non-Italian. Table 1 below provides
summary statistics on these instruments.

Note that Old Italian instruments are on average over triple the
price of Modern Italian and French instruments. Again, we report prices
and estimate the indices in GBP.

C. Methodology

Each violin is a unique instrument, and the problems incurred in
measuring returns to violins are similar to the problems incurred when
measuring the returns to art. The result is that there will be some

ambiguity

Delphic oracle

ultimate authority in ancient Greece; often speaks in ambiguous terms. [Gk. Hist.: Leach, 305]

Iseult’s vow

pledge to husband has double meaning. [Arth.
 in the construction of a single index of the movement of
prices over time. One concern about simply using average prices is that
price rises may be exacerbated during booms as better instruments may
come up for sale–which has generally happened with art. In general,
average prices indicate variability over time in violin prices that
might be better described as movements in the
heterogeneity

n.
The quality or state of being heterogeneous.


heterogeneity

the state of being heterogeneous.
 of the
quality of the objects offered, rather than movements in prices for the
same objects.

The two primary types of indices used for
heterogeneous

 objects are
based on regressions known as “hedonic models” and
“repeat sales models.” In hedonic models, differences in items
are controlled for by including a small number of hedonic
characteristics. Repeat sales models, in effect, include a
dummy
variable

 for each item [see Ashenfelter and Graddy (2003, 2006) for a
full discussion of the two types of indices and their use in estimating
returns to art]. A repeat sales model is better able to control for
differences in items across time, but these models usually rely on only
a small proportion of those items that have come to market. It is often
argued that items that are sold twice are “different” from
other items that come to market and thus sample selection issues are
present. With hedonic indices, all items that are sold can be used, but
the controls for differences in quality are incomplete. The usual
analysis is complicated as we have both auction sales and dealer sales
in our repeat sales dataset, but only auction sales in our hedonic
dataset. Because of the concern that better violins may be sold by
dealers, we cannot just ignore the dealer sales data as is done with
other unique assets such as art.

Our strategy in this article is to estimate both types of models
with different datasets and with different subsets. We then compare
estimates from both models and in this manner gain some confidence that
our indices reflect true market movements.

The Repeat Sales Model. Our repeat sales model is based on the
regression,

(1) In ([P.sub.is] / [P.sub.ib]) = [T.
summation
 n. the final argument of an attorney at the close of a trial in which he/she attempts to convince the judge and/or jury of the virtues of the client’s case. (See: closing argument)
 over
(t=1)][[beta].sub.t][[delta].sub.t] + [[epsilon].sub.i,t],

where [[beta].sub.t] is the average return in period t of violins
in the portfolio, [[delta].sub.t] are
dummy

 variables for each of the
periods in the dataset, and [[epsilon].sub.i,t] is an error term. The
observed data consist of purchases and sales of auction price pairs,
[P.sub.ib] and [P.sub.is], of the individual violins (i indexes the
instruments, b denotes purchase, and s denotes sale) that comprise the
index, as well as the dates of purchase and sale. We estimate this model
using the entire sample, a
subsample
  
n.
A sample drawn from a larger sample.

tr.v. sub·sam·pled, sub·sam·pling, sub·sam·ples
To take a subsample from (a larger sample).
 including observations where the
(second) sale was at auction and the purchase could have been through a
dealer or at auction, and a subsample where the (second) sale was
through a dealer and the purchase could have been through a dealer or at
auction.

Because of the relatively small number of observations, as in
Goetzmann (1993), we estimate returns for 10-yr periods. Please see
Appendix A for a thorough discussion of the repeat sales model.

The Hedonic Model. Our regressions are based on the model

(2) In [P.sub.it] = [alpha][X.sub.i] + [T.summation over (t=1)]
[[gamma].sub.t][[tau].sub.t] [[eta].sub.it],

where [P.sub.it] is the price of violin i at time t, Xi are hedonic
characteristics which consist of 128 dummy variables representing maker
and [[tau].sub.t] are 29 dummy variables representing years from 1981 to
2006. The [[eta].sub.it] is an error term. We estimate this model for
the entire sample and separately for Old Italian instruments, for Modern
Italian instruments, and for French instruments.

IV. RESULTS

We first analyze and present the results for the repeat sales model
for the full dataset and with subsets of the repeat sales dataset. We
then estimate the hedonic model using the full dataset on individual
sales. We then split the dataset on individual sales into the various
schools and look at the relative returns of the various schools.
Finally, we compare our results.

A. Repeat Sales Regression Results

The estimation results for the repeat sales model are presented in
Table 2. We present ordinary least squares (
OLS

) estimates and estimates
using the standard Case and Shiller correction. The annual returns for
the OLS regressions are then calculated as [e.sup.[beta]/10]-1. The
annual returns for the Case Shiller regressions are calculated as
[math], where [[sigma].sup.2]] is defined as the cross-sectional

variance

 of assets held in any 10-yr period. We adjust the estimate by
[[sigma].sup.2]/2 because of the well-known problem that the regressions
estimate the
geometric mean

 across assets, but we are interested in the

arithmetic mean

 across assets. The cross-sectional variance is estimated
as the
coefficient
 /co·ef·fi·cient/ ()
1. an expression of the change or effect produced by variation in certain factors, or of the ratio between two different quantities.

2.
 on the number of periods held (estimated as .035 with
a t-statistics of 2.29) in the second stage of the Case and Shiller
regression. (3,4)

The mean return is then calculated as the Tth root of the ratio of
the index in period T divided by the index in period 1. Thus, our
indices indicate that the mean
nominal return

The rate of return on an investment without adjustment for inflation. While nominal return is useful in comparing the returns from different investments, it can be a very misleading indication of true investor earnings on an investment.
 for the period 1850-2009
is 6.15%.

The above regressions include both auction sales and dealer sales.
Observations in which the second sale is at auction make up 54% of
sales. As discussed above, auction sales probably make up between 10%
and 20% of the market. In order to understand whether the auction repeat
sales are different from the dealer repeat sales or not, we separate the
dataset into subsamples. We report the Case and Shiller estimates in
Table 3 for the two different subsamples. The results are
instructive
  
adj.
Conveying knowledge or information; enlightening.


in·structive·ly adv.
.
The repeat sales where the second sale was at auction averaged a mean
nominal return of 5.49% per year since 1850, and the repeat sales where
the second sale was to a dealer averaged a mean nominal return of 6.98%
per year since 1850. If we split the sample into auction only sales and
dealer only sales, the results are similar. The mean return to the
auction only sales is 5.46% for the entire period, and the mean return
for the dealer only sales is 6.93% for the entire period. The results
indicate that dealer sales have resulted in higher returns than auction
sales; there are two likely reasons for the difference. First, it could
be that the returns to better violins are higher and that a higher
percentage of these instruments are sold through dealers. Alternatively,
it is possible that the dealer sales data that have been collected is a
selected sample since successful sales as measured by high prices are
more likely to be publicized.

[FIGURE 1 OMITTED]

The graph in Figure 1 shows the three indices: the all auction
index, the index where a violin is sold at auction in the second sale,
and the index where a violin is sold privately at the second sale. The
three indices follow a similar path, though the auction sales have
consistently underperformed the reported dealer sales.

B. Hedonic Model Regression Results

The full sample results for the hedonic model are presented in
Table 4. Intuitively, y in Table 4 for a particular period is the
average of the
natural logarithm

 of price, conditioning on the maker of
the instrument. The index in year t is then calculated as [MATHEMATICAL
EXPRESSION NOT
REPRODUCIBLE
  
v. re·pro·duced, re·pro·duc·ing, re·pro·duc·es

v.tr.
1. To produce a counterpart, image, or copy of.

2. Biology To generate (offspring) by sexual or asexual means.
 IN
ASCII
 or  a set of codes used to represent letters, numbers, a few symbols, and control characters. Originally designed for teletype operations, it has found wide application in computers.
]. The mean nominal return for the
portfolio of violins included in the dataset for the entire time period
is approximately 7.49% and the standard deviation in estimated returns
over the period is approximately 9.24%. When the regression is run only
with time dummies, the [R.sup.2] is about .15, indicating that the maker
dummy variables explain about 60% of the variation in log price. Hence,
the time dummies and the maker characteristics explain the series well.

Figure 2 plots the nominal hedonic index for 1980-2008, both in GBP
and in U.S. dollars. The figure also plots nominal indices of total
returns of the S&P, U.S. 10-yr bonds, and the Mei Moses art index.
(5) The Mei Moses art index is a U.S. dollar index. As Figure 2
demonstrates, the rise in violin prices has been steady. From 1980 to
2008 it has underperformed stocks and bonds. It does not seem surprising
that the overall returns to violins are lower than stocks and bonds;
these instruments are primarily tools of trade and usually only
secondarily considered to be an investment. They provide non-monetary
dividends in the form of enjoyment, both to musicians and to most
collectors and investors; musicians may enjoy monetary rewards in the
form of more successful careers. Although in the figure it looks as if
art has recently outperformed violins as an alternative investment, in
the first quarter of 2009 the Mei and Moses art index was down 35%,
making the returns to violins since 1980 similar to those of art.

We have several different schools of violin making in our dataset.
It is interesting to break the dataset up into subsamples and compare
returns between these samples.

C. Results for the Various Schools

Table 5 breaks up the individual dataset into a sample of
instruments from the Old Italian school of violin making, a sample
containing violins made by the Modern Italian school, and a sample made
by the French school. The price indices are plotted in Figure 3.6 Very
interestingly, Modern Italian instruments have steadily outperformed Old
Italian and French instruments.

It is interesting to look at the relative prices of the various
makers in our dataset. In Appendix Tables [C.SUB.1]-C3 we present the
regression coefficients on each of the makers in the Old Italian school,
the Modern Italian school, and the French school. One point to note from
these tables is that the range in prices for different makers is much
greater for the Old Italian school than it is for the French school or
the Modern Italian school. Furthermore, in this dataset of prices,
unsurprisingly, Stradivari and del Gesu (
Guarneri
  or  , family of violinmakers of Cremona, Italy. The first craftsman of the family was

Andrea Guarneri, c.
) appear to be the most
valued Old Italian makers, and Pressenda and Rocca are the most valued
Modern Italian makers.

[FIGURE 2 OMITTED]

[FIGURE 3 OMITTED]

The results from the hedonic dataset are so consistently greater
year by year for the Modern Italian school that it is interesting to
speculate why the differences in returns may be occurring. There is a
large absolute price difference between Modern Italian and Old Italian
instruments, and due to the run-up in the past couple of decades in
violin prices relative to inflation, Old Italian instruments have become

unaffordable
  
adj.
Too expensive:


un
 to many musicians. Furthermore, they are in short supply.
Many participants in the trade believe that there is a growing
realization that Modern Italian violins are very good instruments and
they are now purchasing these instruments. Because of the expense of Old
Italian instruments, Modern Italian instruments have been promoted into
the set of “professional” violins.

Given the difference in returns to instruments belonging to the Old
Italian school and instruments belonging to the Modern Italian School,
it is interesting to look for differences in returns between nineteenth-
and twentieth-century Modern Italian instruments. These regression
results are available on request, but the primary conclusion is that
there is virtually no difference in returns to Modern Italian violins
constructed in the different decades. Furthermore, one can look if there
are differences in returns between Old Italian instruments constructed
prior to 1750 and those constructed after 1750. Again, there are no
differences in returns.

D. Comparing the Hedonic and Repeat Sales Results

If we compare all returns for fine violins at auction in the repeat
sales dataset for the period 1980-2009, we get returns of 6.28% versus
returns of 7.49% for the equivalent period in the individual sales
dataset. These numbers are not significantly different from one
another–the estimated mean for the repeat sales data relies on just
three data points which are estimated returns for the various decades.
The closest comparison that we can make between the two datasets is that
of auction only repeat sales of Old Italian instruments with individual
sales (auction only) of Old Italian instruments. When we do a repeat
sales Case and Shiller regression on this subset (auction only and Old
Italian only) which contains 85 observations (vs. 119 if observations on
all schools are used), we get returns of 5.4% from 1850 to 2009 and we
get returns of 5.83% for the period 1980-2009. This compares with a
return of 6.67% for Old Italian instruments in the individual sales
dataset.

The difference in point estimates probably exists for a number of
reasons. Firstly, the period returns are only estimates of the actual
returns–it is
reassuring
  
tr.v. re·as·sured, re·as·sur·ing, re·as·sures
1. To restore confidence to.

2. To assure again.

3. To reinsure.
 that the averages of these estimates are still
relatively close. Secondly, it could be that the correction for taking
the average of the logarithms in the repeat sales model could be
underestimated, skewing the repeat sales mean slightly downward. (7)
Thirdly, in the repeat sales model, we have imposed constant returns
within decades. Finally, this may be resulting from unobservable
time-invariant effects that drop out in the repeat sales regressions,
but are biasing the results in the hedonic regressions (see
Hausman

 and

Taylor
 city (1990 pop. 70,811), Wayne co., SE Mich., a suburb of Detroit adjacent to Dearborn; founded 1847 as a township, inc. as a city 1968. A small rural village until World War II, it developed significantly in the second half of the 20th cent.
 1981).

The end result that our hedonic indices using auction results are
similar for the period to the repeat sales indices using auction results
gives us confidence about our results, as neither dataset nor method is
ideal.

V. INTERPRETATION

Before we begin to interpret our results, it is interesting to

summarize
  
intr. & tr.v. sum·ma·rized, sum·ma·riz·ing, sum·ma·riz·es
To make a summary or make a summary of.


sum
 our results and compare real returns overall and for the
various subsamples of our data, with real returns on
other assets

Assets of relatively small value. For financial reporting purposes, firms frequently combine small assets into a single category rather than listing each item separately.
. We
present these returns in Table 6. In order to compare full year results
for all assets, we report returns in this table through 2008. (8) The
first point to note is that in the long run, violins appear to have
outperformed both art and treasury bonds. From 1980 to 2008, it appears
that stocks, bonds, and art have all out-performed violins, but as noted
earlier, in the first quarter of 2009, the art market was down 35%; this

downturn

A decline in security prices or economic activity following a period of rising or stable prices or activity.
 is not reflected in these numbers. The violin market appears to
have held up so far for this time period. The 1980-2008 data also
indicate that violins have been less volatile than other assets.

It can be seen from the table that real returns in the two violin
datasets, despite the differences in composition and the differences in
periods, are nearly identical. Looking at the differences in the
underlying returns to different types of violins, this is probably
mostly coincidence. From the individual data subsets, we can see that
Modern Italian instruments have outperformed Old Italian instruments,
and yet Modern Italian instruments comprise only about 9% in our repeat
sales sample but about 40% of our sample of the individual sales
dataset. Furthermore, we have no dealer sales included in our individual
sales dataset, but dealer sales at the second sale (which may indicate
better instruments) comprise 46% of our repeat sales sample.

It may be tempting to adjust our repeat sales returns for an
estimated composition of 20% auction sales and 80% dealer sales. This
would give us an overall real return of 4.02%. Yet, this does not
address the relative composition of Modern instruments versus Old
Italian instruments, and the returns are still subject to sample
selection issues in that it is likely that only favorable dealer sales
are reported in the press. Hence, we choose to report that overall
returns in this dataset, noting the composition of the dataset, are
3.5%.

It has to be noted that the returns to violins are slightly
negatively
correlated
  
v. cor·re·lat·ed, cor·re·lat·ing, cor·re·lates

v.tr.
1. To put or bring into causal, complementary, parallel, or reciprocal relation.

2.
 with stocks. If we
regress

 the real returns to
violins on the real returns to the S&P from 1980 to 2008, we get an
alpha coefficient of .0307 (t = 1.87) and a beta of -.0593 (t = -.7),
indicating uncorrelated returns of about 3%. As Mei and Moses (2002)
noted for the art market, we are finding returns greater than the risk
free rate that have low correlation with stocks. While at first glance
this may appear surprising, the market for fiddles is
illiquid

, has high
transactions cost, and is, at the end of the day, a very small asset
class. Many of the standard assumptions of the
capital asset pricing
model

 do not hold.

Furthermore, in keeping with the Mei and Moses approach, we have so
far not taken into account the role of commissions. The effect of
commissions on returns could be significant, depending on the
assumptions regarding holding period of assets and total commissions;
sellers’ commissions are not published and are negotiable, and
buyers’ commissions depend upon the price paid and have changed
over time. If we assume an average commission rate of 15% and that
violins change hands on average approximately every 30 yr, then the
return should decrease by about .5% per year. However, if we were to
assume a 30% commission rate (based on an average 20% buyer’s
commission plus a 10% seller’s commission), and if we assumed more
realistically that violins change hands every 20 yr, than our returns
should decrease by about 1.5%, which is very significant. When comparing
the returns to holding stocks and bonds, commissions could play a very
important role.

The final point to note in Table 6 is the low correlation of
returns from Modern Italian instruments with returns from Old Italian
instruments. This low correlation indicates that a portfolio of
stringed
  
adj. Music
1. Having strings. Often used in combination:

2. Produced by stringed instruments:
 instruments should be well-diversified among the various schools of
violin making.

VI. CONCLUSION

In conclusion, the real returns to a portfolio of all violins since
1980 have averaged about 3.3% and long-run returns since 1850 have
averaged about 3.5%. Furthermore, they have a slightly negative
correlation to stocks and bonds, making them a candidate for inclusion
in a diversified portfolio based on past performance, and they have had
a relatively low variance in returns. Probably, it is most important to
note that even using only auction sales data (which may underestimate
returns), returns to violins compare very
favorably
  
adj.
1. Advantageous; helpful:

2. Encouraging; propitious:

3.
 to assets other than
stocks, and have a slightly negative correlation to stocks and bonds.

ABBREVIATIONS

GLS

:
Generalized

adj.
1. Involving an entire organ, as when an epileptic seizure involves all parts of the brain.

2. Not specifically adapted to a particular environment or function; not specialized.

3.
 Least Squares

OLS: Ordinary Least Squares

APPENDIX A: REPEAT SALES ESTIMATION METHOD

Our
regression equation

 begins with a standard repeat sales model
used to estimate real estate and art indices where it is assumed the
return for asset i in period t can be broken up into the return for a
price index of the portfolio of assets and an individual error term,

(A1) [r.sub.i, t] = [[beta].sub.t] + [[epsilon].sub.i,t],

where [r.sub.i,t] is the continuously compounded return for a
particular art asset i in period t, [[beta].sub.t] is the average return
in period t of paintings in the portfolio, and [[epsilon].sub.i,t] is an
error term. (9)

The observed data consist of purchase and sales of auction price
pairs, [P.sub.i,b] and [P.sub.i,s] of the individual violins that
comprise the index, as well as the dates of purchase and sale. Thus, the
logged price relative for violin i held between its purchase date and
its sale date may be expressed as

(A2) [MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII].

This summation suggests that the difference in logs of sale prices
should be regressed on a number of dummy variables that span the period
over which the asset is held. The coefficient on the dummy variable for
a particular period will represent the average of the natural logarithm
of the returns of all of the assets held in that specific period.
Because of the summation, the t in effect drops out of the regression:
each observation is the return for a particular asset. However, the
errors will be heteroskadastic because of the summation; they will
depend upon the number of time periods held.

Theory (by first differencing a hedonic model with fixed effects)
suggests that the dummy variables for each pair should equal 1 at the
time of sale, -1 at the time of purchase, and 0 in all other periods. In
this case, the coefficients on the dummy variables represent a price
index. Pesando (1993) uses this methodology. Goetzmann (1992) shows that
it is more efficient to allow the dummy variables to equal 1 during the
periods between purchase and sale, zero otherwise, and then do
generalized least squares (GLS) using weights suggested by Case and
Shiller (1987). In this case, the coefficients on the dummy variables
represent returns. Goetzmann (1993) and Mei and Moses (2002) let the
dummy variable equal 1 for an entire period if the painting was held
before the current period and for any part of the current period.
Otherwise it equals zero. We modify the construction of the dummy
variables first by letting the dummy variable equal 1 if the violin was
held for the entire period, letting it equal the proportion of the
period held if it was held for less than an entire period [note that our
periods are 10 yr in length as in Goetzmann (1993)], and letting it
equal zero otherwise. This allows us to use data on violins that were
held within a 10-yr period, and also more accurately describes the
holding periods.

In the first stage of Case and Shiller’s (1987) method, the
log of the ratio of the sale price to purchase price is regressed on
time dummy variables. In Case and Shiller’s method in the second
stage, a regression of the squared residuals from the first stage is run
on a constant term and the number of periods held between sales. The
linear specification for the second stage of Case and Shiller results
partially from the independent identically distributed (iid) assumption
on the errors in the return of the underlying asset i in period t (this
is where the term for number of periods

held appears) and partly because Case and Shiller put in a constant
term to describe the transaction-specific error. The slope coefficient
can be directly interpreted as an estimate of the cross-sectional
variance in a period and therefore is used to correct for the known bias
in the repeat sales estimates as described below.

In the third stage, a generalized least squares (weighted)
regression is run that repeats the stage one regression after dividing
each observation by the square root of the fitted value in the second
stage.

The regressions present estimates of the average of the log of the
one period return of the portfolio of assets (the geometric mean).
However, for the single period returns, we are interested in the
arithmetic means across assets (Geotzmann 1992). Thus, resulting from
Jenson’s
inequality
 in mathematics, statement that a mathematical expression is less than or greater than some other expression; an inequality is not as specific as an equation, but it does contain information about the expressions involved.
, the estimates are downward biased by one-half
of the cross-sectional variance. In the Case and Shiller results, we
correct for this downward bias by adding half of the coefficient on the
number of periods held terms in the second-stage regressions to the
estimated [[mu].sub.t] Thus, for a 10-yr period, our yearly returns are
calculated as [(
exp

abbr.
1. exponent

2. exponential
([[mu].sub.t] + [[sigma].sup.2]/2).sup.1/10].

APPENDIX B

Repeat Sales Data

The data on the dealer sales were gathered from “Violin

Iconography
  [Gr.,=image-drawing] or  [Gr.,=image-study], in art history, the study and interpretation of figural representations, either individual or symbolic, religious or secular;
 of
Antonio

 Stradivari” (Goodkind 1972) and
“Antonio Stradivari: His Life and Work” (Hill and Sons 1901).
Further sources for the dealer repeat sales include ”
Catalog
 descriptive list, on cards or in a book, of the contents of a library. Assurbanipal’s library at Nineveh was cataloged on shelves of slate. The first known subject catalog was compiled by Callimachus at the Alexandrian Library in the 3d cent. B.C.
 descriptif des instruments de
Stradivarius

 et Guarnerius del Gesu”
(Les Amis de
la Musique

, Spa 1994), the
Jacques
 (French for Jacob and James) can refer to:

People with the surname of Jacques:

  • Antoine A.


 Francais Business
Records at the
Smithsonian Institution
 research and education center, at Washington, D.C.; founded 1846 under terms of the will of James Smithson of London, who in 1829 bequeathed his fortune to the United States to create an establishment for the “increase and diffusion of
 (these also include the business
record of
Emil

EMIL Endoscopic Microcapsule Locomotion
EMIL Easter, Memorial Day, Independence Day, Labor Day
 Herrmann), and the papers of
Gerald

 Segelman from the
Segelman Trust (2009) (in Mr. Black’s Violins: The Obsession of
Gerald Segelman). Dealer sales data were also gathered from
miscellaneous news stories from a variety of publications and the web
page http:://stradivariinvest.com.

The data on repeat sales at auction were gathered from both the
original auction catalogs and price sheets from the main auction houses
that sell, or have sold, violins and from the secondary sources
(Goodkind 1972; Hill and Sons 1901). Catalogs from years prior to 1965
were accessed primarily at the
British Library
 national library of Great Britain, located in London. Long a part of the British Museum, the library collection originated in 1753 when the government purchased the Harleian Library, the library of Sir Robert Bruce Cotton, and groups of manuscripts.
 and in the archives of

Bonhams

.

Individual Sales Data

We began putting together the dataset on individual sales by
merging data on violin sales from “The Red Book: Auction Price
Guide of Authentic Stringed Instruments and Bows” (2006) and
“Database: Sales of
String Instruments

 1984-2006″ (2006) and
from sales listed on the web site www.cozio.com (accessed 2009). (10)
None of these datasets included all auction houses, so we went back to
the original catalogs to fill in the missing sales. We included
instruments sold by the major auction houses:
Sotheby’s

,
Christie’s, Bonhams, Phillips, Tarisio, Bongartz and
Skinner
 , B(urrhus) F(rederick) 1904-1990.

American psychologist. A leading behaviorist, Skinner influenced the fields of psychology and education with his theories of stimulus-response behavior.
, as
well as other auction venues: Ader Tajan in Paris, Babuino in
Rome
 Ital. Roma, city (1991 pop. 2,775,250), capital of Italy and see of the pope, whose residence, Vatican City, is a sovereign state within the city of Rome.
, Da

Salo
 
 on the
Internet

,
Dorotheum

 in
Vienna
 , Ger. Wien, city and province (1991 pop. 1,539,848), 160 sq mi (414 sq km), capital and largest city of Austria and administrative seat of Lower Austria, NE Austria, on
,
Etude
  
n. Music
1. A piece composed for the development of a specific point of technique.

2. A composition featuring a point of technique but performed because of its artistic merit.
 Tajan in Paris,
Gardiner-Houlgate in
London
 city (1991 pop. 303,165), SE Ont., Canada, on the Thames River. The site was chosen in 1792 by Governor Simcoe to be the capital of Upper Canada, but York was made capital instead. London was settled in 1826.
, and
Vichy
 , city (1990 pop. 28,048), Allier dept., central France, on the Allier River. Vichy’s hot mineral springs have made it one of the foremost spas in Europe.
 in Paris. In addition, we checked
the catalogs to ensure that we included only full-size instruments
listed as “by” a particular maker and represented in good
physical condition.

APPENDIX C

                                              TABLE C1
                                        Old Italian Makers

                                                         Multiples
                                               Standard  of Lorenzo
                                 Obs.  Coeff.   Error    Ventapane

Stradivari, Antonio                45    3.19    0.11       24.29
Guarneri, del Gesu                  6    3.14    0.21       23.12
Guarneri, Pietro (of Venice)        3    2.41    0.29       11.12
Bergonzi, Carlo                     4    2.27    0.25        9.66
Montagnana, Domenico               10    1.92    0.17        6.85
Guadagnini, Joannes Baptista       51    1.85    0.11        6.34
Guarneri, Joseph (fit. Andreae)    13    1.84    0.16        6.27
Guarneri, Pietro (of Mantua)       14    1.70    0.15        5.50
Amati, Nicolo                      25    1.44    0.13        4.23
Ruggieri, Francesco                19    1.28    0.14        3.61
Goffriller, Matteo                 10    1.26    0.17        3.53
Guarneri, Andrea                   22    1.25    0.13        3.49
Bergonzi, Nicola                    3    1.24    0.28        3.47
Balestrieri, Tommaso               27    1.08    0.13        2.95
Serafin, Santo                     14    1.03    0.15        2.81
Storioni, Lorenzo                  22    1.00    0.13        2.73
Gagliano, Alessandro               11    0.92    0.17        2.50
Camilli, Camillo                   20    0.90    0.14        2.45
Gobetti, Francesco                  7    0.88    0.20        2.41
Mantegazza, Pietro                  5    0.87    0.23        2.39
Amati, Antonio & Girolamo          21    0.86    0.13        2.37
Tononi, Carlo                      13    0.84    0.16        2.31
Amati, Girolamo (II.)               6    0.78    0.21        2.19
Emiliani, Francesco                 6    0.78    0.21        2.17
Gagliano, Gennaro                  20    0.77    0.14        2.16
Gagliano, Nicola                   68    0.76    0.10        2.13
Cappa, Gioffredo                   21    0.73    0.13        2.07
Rogeri, Giovanni Batista           17    0.71    0.14        2.03
Mezzadri, Alessandro                2    0.70    0.34        2.01
Gagliano, Ferdinando               31    0.69    0.12        1.99
Ceruti, Giovanni Battista          12    0.68    0.16        1.97
Grancino, Giovanni                 28    0.66    0.12        1.93
Grancino, Giovanni Battista         5    0.60    0.23        1.82
Landolfi, Pietro Antonio            9    0.59    0.18        1.81
Deconet, Michele                   16    0.59    0.15        1.80
Landolfi, Carlo Ferdinando         24    0.53    0.13        1.70
Maggini, Giovanni Paolo            13    0.52    0.16        1.69
Baldantoni, Giuseppe                2    0.52    0.34        1.69
Sorsana, Spirito                   10    0.45    0.17        1.56
Gagliano, Giuseppe                 36    0.41    0.12        1.51
Golfriller, Francesco               3    0.40    0.28        1.49
Costa, Pietro Antonio Dalla         6    0.34    0.21        1.41
Testore, Carlo Giuseppe            13    0.34    0.16        1.40
Testore, Carlo Antonio             46    0.34    0.11        1.40
Calcagni, Bernardo                 14    0.33    0.15        1.40
Tecchler, David                    11    0.32    0.17        1.38
Gagliano, Giuseppe & Antonio       17    0.26    0.14        1.29
Gagliano, Giovanni                  7    0.25    0.20        1.29
Gragnani, Antonio                  24    0.23    0.13        1.25
Tononi, Giovanni                   15    0.21    0.15        1.23
Gabrielli, Giovanni Battista       29    0.19    0.12        1.21
Celoniatus, Giovanni Francesco      7    0.10    0.20        1.11
Ventapane, Lorenzo                 28    0.00                1.00
Castello, Paolo                    23   -0.03    0.13        0.97
Carcassi, Lorenzo & Tommaso        53   -0.04    0.11        0.96
Pallota, Pietro                     3   -0.05    0.28        0.95
Eberle, Tomaso                     21   -0.07    0.13        0.93
Dall'Aglio, Giuseppe                8   -0.14    0.19        0.87
Testore, Paolo Antonio              7   -0.18    0.20        0.84
Odoardi, Gisueppe                   2   -0.18    0.34        0.83
Cordano, Jacopo                     3   -0.23    0.28        0.80
Amati, Dom Nicolo                  12   -0.23    0.16        0.80
Alberti, Ferdinando                 2   -0.38    0.34        0.69
Albani, Matthias                   14   -0.54    0.15        0.59

TABLE C2
Modern Italian Makers

                                            Standard   Multiples
                            Obs.   Coeff.    Error     of Ettore
                                                       Soffritti

Pressenda, Joannes F.         37     2.03     0.12       7.62
Rocca, Giuseppe               43     1.93     0.12       6.91
Ceruti, Giuseppe               2     1.14     0.29       3.14
D'Espine, Alexander            9     1.12     0.17       3.05
Ceruti, Enrico                14     0.95     0.15       2.57
Rocca, Enrico                 10     0.93     0.16       2.55
Fagnola, Hannibal             57     0.87     0.12       2.39
Poggi, Ansaldo                 9     0.49     0.17       1.64
Scarampella, Stefano          32     0.49     0.13       1.64
Fiorini, Giuseppe             22     0.43     0.14       1.54
Oddone, Carlo Giuseppe        31     0.42     0.13       1.52
Sacconi, Simone Fernando       5     0.40     0.20       1.50
Gagliano, Antonio (II)         2     0.30     0.30       1.35
Bisiach, Leandro              66     0.28     0.12       1.32
Guadagnini, Francesco          9     0.27     0.17       1.31
Ornati, Giuseppe              16     0.24     0.14       1.27
Bisiach, Carlo                13     0.21     0.15       1.23
Sgarabotto, Gaetano           19     0.20     0.14       1.22
Pedrazzini, Giuseppe          67     0.19     0.12       1.21
Praga, Eugenio                 2     0.19     0.30       1.21
Postiglione, Vincenzo         34     0.16     0.13       1.17
Genovese, Riccardo             6     0.15     0.19       1.16
Degani, Eugenio               79     0.05     0.12       1.05
Antoniazzi, Riccardo          21     0.04     0.14       1.04
Jorio, Vincenzo                2     0.03     0.29       1.03
Candi, Cesare                 18     0.02     0.14       1.02
Farotti, Celeste              14     0.01     0.15       1.01
Soffritti, Ettore             13     0.00                1.00
Pollastri, Gaetano            17     0.00     0.14       1.00
Garimberti, Ferdinando        14     0.00     0.15       1.00
Sannino, Vincenzo             28    -0.04     0.13       0.96
Capicchioni, Marino           28    -0.06     0.13       0.94
Antoniazzi, Romeo             38    -0.07     0.12       0.94
Degani, Giulio                61    -0.09     0.12       0.92
Bisiach, Giacomo &            23    -0.14     0.13       0.87
 Leandro
Sgarabotto, Pietro             9    -0.15     0.17       0.86
Pistucci, Giovanni            13    -0.17     0.15       0.84
Gadda, Gaetano                48    -0.32     0.12       0.73
Antoniazzi, Gaetano            7    -0.35     0.18       0.70
Gagliano, Raffael &            2    -0.39     0.29       0.68
 Antonio
Marchetti, Enrico             16    -0.45     0.14       0.64
Contino, Alfredo              35    -0.46     0.13       0.63
Sderci, Igenio                 3    -0.55     0.25       0.58
Bignami, Otello               11    -0.95     0.16       0.39

TABLE C3
French Makers

                                                      Multiples
                                                       of Jean
                                            Standard   Baptiste
                            Obs.   Coeff.   Error      Vuillaume

Lupot, Nicolas                25     0.21     0.09       1.23
Vuillaume, Jean Baptiste     164     0.00                1.00
Pique, Frangois               16    -0.42     0.11       0.65
Pacherele, Pierre              7    -0.56     0.16       0.57
Bernardel, Auguste            42    -0.96     0.07       0.38
 Sebastien
Chanot, Georges               37    -1.01     0.08       0.36
Aldric, Jean-Francois         11    -1.08     0.13       0.34
Silvestre, Pierre              2    -1.14     0.31       0.32
Gand, Gand & Bernardel        60    -1.18     0.06       0.31
Bernardel, Gustave            30    -1.26     0.08       0.28

REFERENCES

Ashenfelter, O., and K. Graddy. “Auctions and the Price of
Art.” Journal of Economic Literature, 41, 2003, 763-87.

–. “Art Auctions,” in Handbook on the Economics of Art
and Culture, edited by V. Ginsburgh and D. Throsby.
Amsterdam
 , city (1994 pop. 724,096), constitutional capital and largest city of the Kingdom of the Netherlands, North Holland prov.
, The
Netherlands: Elsevier, 2006, 909-45.

Bailey, M. J., Muth, R. F., and H. O. Nourse. “A Regression
Method for Real Estate Price Index Construction.”
Journal of the
American Statistical Association

, 58, 1963, 933-42.

Baumol, W. J. “Unnatural Value: Or Art Investment as Floating
Crap Game.” American Economic Review Papers and Proceedings, 76,
1986, 10-14.

Case, K. E., and R. J. Shiller. “Prices of Single-Family Homes
Since 1970: New Indexes for Four Cities.”
New England
 name applied to the region comprising six states of the NE United States—Maine, New Hampshire, Vermont, Massachusetts, Rhode Island, and Connecticut. The region is thought to have been so named by Capt.
 Economic
Review, September-October 1987, 45-56.

Database Sales of String Instuments 1984-2006, Stolberg, Germany:
Holfter GmbH, 2006.

Eichboltz, P. M. A., “A Long Run House Price Index: The
Herengracht Index, 1628 1973.” Real Estate Economics, 25, 1997,
175-92.

Goetzmann, W. N. “The Accuracy of Real Estate Indices: Repeat
Sale Estimators.” Journal of Real Estate Finance and Economics, 5,
1992, 5-53.

–“Accounting for Taste: Art and Financial Markets over Three
Centuries.” American Economic Review, 83, 1993, 1370-76.

Goodkind, H. K. Violin lconography of Antonio Stradivari 1644-1737.
Larchmont, NY: author, 1972.

Hausman, J. A. and W. E. Taylor “Panel Data and Unobservable
Individual Effects.” Econometrica, 49, 1981, 1377-98.

Hill, W. E. and Sons. Antonio Stradivari: His Life and Work.
London: author, 1901.

Hosios, A., and J. Pesando. “Measuring Prices in
Resale
 n. selling again, particularly at retail. In many states a “resale license” or “resale number” is required so that the state can monitor the collection of sales tax on retail sales.


RESALE.
 Housing Markets in Canada: Evidence and Implications,” Journal of
Housing Economics, 1, 1991, 303-17.

Les Amis de la Musique. Catalog descriptif des instrnments de
Stradivarius et Guarnerius del Gesu (a facsimile of the notebook of
Charles-Eugene Gand (1870-1889), Spain: Les Amis de la Musique, 1994.

Mei, J., and M. Moses. “Art as an Investment and the
Underperformance of
Masterpieces

.” American Economic Review, 92,
2002, 1656-68.

“Online Database of Stringed Instruments,” www.cozio.com,
Cozio Publishing. Accessed 2009.

Pesando, J. E. “Art as an Investment: The Market for Modern
Prints.” American Economic Review, 83, 1993, 1075-89.

The Red Book: Auction Price Guide of Authentic Stringed Instruments
and Bows. Alexandria, VA: Donald M.
Cohen

, 2006.

Ross, M. H., and S. Zondervan. “Capital Gains and the Rate of
Return on a Stradivarius.” Economic Inquiry, 27, 1989, 529-40.

Segelman Trust. Mr. Black’s Violins: The Obsession of Gerald
Segelman, Papers of Gerald Segelman. Boston: Cozio Publishing, 2009.

Smithsonian Institution. The Jacques Francais Business Records
(including the business records of Emil Herrmann), 1844-1998.

(1.) In one of the first studies of returns to art, Baumol (1986)
excludes paintings with holding periods of less than 20 yr. Goetzmann
(1993), by design, excludes paintings with holding periods of less than
10 yr.

(2.) The complete repeat sales dataset can be found at
http://people.brandeis.edu/~kgraddy/data.html.

(3.) The constant is interpreted as a transaction-specific error
and is estimated as .279 with a t-statistics of 4.24.

(4.) The negative
autocorrelation

 in period returns that is present
during the very early periods is a known problem with repeat sales
indices. Goetzmann (1992) proposed a Bayesian correction that puts
additional restrictions on the return path. As we are primarily
interested in the returns in later periods and in averages over the
entire time period, we note the problem, rather than put additional
assumptions and structure on the returns.

(5.) The source for total returns on the S&F and U.S. 10-yr
bonds is Global Financial Data. The source for the Mei and Moses art
index is Beautiful Asset Advisors.

(6.) In a previous version of the article, we estimated separate
returns for Stradivaris and del Gesus. These returns were very volatile,
and a number of periods could not be estimated due to lack of data. Even
with the new data, these returns remain very volatile, as every sale has
a large impact on the index. In this version, we have therefore decided
to group these sales with other Old Italian instruments.

(7.) In the Case and Shiller correction, the transaction-specific
error is not used in calculating the cross-sectional variance of asset
returns; furthermore, the individual asset returns in a particular
period are assumed to be independent and identically distributed (iid),
which may not be an appropriate assumption for an
infrequently
  
adj.
1. Not occurring regularly; occasional or rare:

2.
 traded
asset.

(8.) Data through April 2009 were used to calculate the violin
returns. In the case of the repeat sales indices, these returns would be
identical to returns calculated through April 2008 because of the
assumption of constant returns in any 10-yr period. In the hedonic
indices, the coefficient on the 2009 dummy variable was not used to
calculate the returns.

(9.) This methodology was developed by Bailey, Muth. and Nourse
(1963) and used by Case and Shiller (1987), Hosios and Pesando (1991),
and Eichholtz (1997), for the real estate market, and subsequently used
by Goetzmann (1993), Pesando (1993), and Mei and Moses (2002) for the
art market. In these articles, [[pi].sub.i.t] is assumed to be
uncorrelated over time and across paintings.

(10.) Previous editions of “The Red Book” were published
by Samuel W. Eden.

KATHRYN GRADDY and PHILIP E. MARGOLIS *

* The authors thank
Victor Ginsburgh

, Jonathan
Hamilton
 city (1990 est. pop. 3,100), capital of Bermuda, on Bermuda Island. It is a port at the head of Great Sound, a huge lagoon and deepwater harbor protected by coral reefs.
, Ben
Hebbert, Tim
Ingles

, Blake Lebaron, Michael Moses, and Bill Taylor for
their comments. The authors also wish to thank Michael Moses and
Beautiful Asset Advisors for sharing the updated Mei Moses Art Index.
They would also like to thank an anonymous
referee

 for very helpful
comments on an earlier version.

Graddy: Associate Professor of Economics,
Brandeis University
 at Waltham, Mass.; coeducational; chartered and opened 1948. Although Brandeis was founded by members of the American Jewish community, the university operates as an independent, nonsectarian institution.
, 415
South Street MS 021, Waltham, MA 02454. Phone 781-736-8616, Fax
781-736-2269, E-mail kgraddy@brandeis.edu

Margolis: President, Cozio Publishing, Hanflaenderstr. 41, 8640
Rapperswil, Switzerland. Phone 41 (0)55-210-09-72, Fax
41(0)55-210-09-73, E-mail pmargolis@cozio.com

doi: 10.1111/j.1465-7295.2010.00269.x

TABLE 1
Summary Statistics for Individual Sales Dataset

                                  Mean

All

Sale price              44,207 [pounds sterling]
Sale date                         1995
Year built                        1825
No. of makers                      129
No. of observations              2,669

Old Italian

Sale price              76,158 [pounds sterling]
Sale date                         1994
Year built                        1740
No. of makers                       64
No. of observations              1,059

Modern Italian

Sale price              23,054 [pounds sterling]
Sale date                         1996
Year built                        1910
No. of makers                       44
No. of observations              1,004

French

Sale price              24,999 [pounds sterling]
Sale date                         1995
Year built                        1853
No. of makers                       10
No. of observations                394

                                  Min.

All

Sale price               965 [pounds sterling]
Sale date                         1980
Year built                        1580
No. of makers
No. of observations

Old Italian

Sale price              5,733 [pounds sterling]
Sale date                         1980
Year built                        1580
No. of makers
No. of observations

Modern Italian

Sale price               965 [pounds sterling]
Sale date                         1980
Year built                        1820
No. of makers
No. of observations

French

Sale price              2,785 [pounds sterling]
Sale date                         1980
Year built                        1775
No. of makers
No. of observations

                                   Max.

All

Sale price             1,832,004 [pounds sterling]
Sale date                          2009
Year built                         1986
No. of makers
No. of observations

Old Italian

Sale price             1,832,004 [pounds sterling]
Sale date                          2009
Year built                         1850
No. of makers
No. of observations

Modern Italian

Sale price              192,252 [pounds sterling]
Sale date                          2009
Year built                         1982
No. of makers
No. of observations

French

Sale price              114,393 [pounds sterling]
Sale date                          2009
Year built                         1948
No. of makers
No. of observations

Notes: Prices are in 2005 GBP and include buyers'
commissions.

TABLE 2
Repeat Sales Regressions

                            OLS (first stage)

                                     Annual
Period           [beta]    t-stat.   return     Index

1850-1859          0.186      0.57     1.88%       1.20
1860-1869          0.237      0.94     2.40%       1.53
1870-1879          0.725      3.12     7.52%       3.15
1880-1889          0.347      1.65     3.53%       4.46
1890-1899          0.630      2.55     6.51%       8.37
1900-1909          0.236      1.03     2.39%      10.60
1910-1919          0.577      2.72     5.94%      18.87
1920-1929          1.103      5.19    11.66%      56.84
1930-1939         -0.347      -1.7    -3.41%      40.18
1940-1949          0.012      0.05     0.12%      40.67
1950-1959          0.708      2.84     7.34%      82.57
1960-1969          1.025      4.91    10.79%     230.09
1970-1979          1.783     11.63    19.52%    1368.61
1980-1989          1.335      9.75    14.28%    5200.86
1990-1999          0.353      2.56     3.59%    7399.75
2000-2009          0.108      0.69     1.09%    8246.83
Adj.-[R.sup.2]                         0.950
Obs.                                 337
Mean return                            5.84%

                          Case Shiller (linear)

                                     Annual
Period           [beta]    t-stat.   return     Index

1850-1859         0.3769      1.14     4.02%       1.48
1860-1869         0.204286    0.83     2.24%       1.85
1870-1879         0.749723    3.39     7.97%       3.99
1880-1889         0.324856    1.62     3.48%       5.62
1890-1899         0.598302    2.48     6.35%      10.40
1900-1909         0.265487    1.21     2.87%      13.80
1910-1919         0.600631    2.95     6.38%      25.60
1920-1929         1.065179    5.21    11.43%      75.59
1930-1939        -0.28098    -1.42    -2.60%      58.08
1940-1949         0.020422    0.08     0.38%      60.33
1950-1959         0.650701    2.65     6.91%     117.68
1960-1969         1.074911    5.27    11.54%     350.87
1970-1979         1.7768     12.29    19.65%    2110.58
1980-1989         1.288993   10.08    13.96%    7794.78
1990-1999         0.361003    2.81     3.86%   11381.15
2000-2009         0.125018    0.83     1.44%   13124.44
Adj.-[R.sup.2]                         0.938
Obs.                                 337
Mean return                            6.15%

Notes: The data include sales through April 2009.

TABLE 3
Repeat Sales Regressions: Subsamples

                         Auction-auction and dealer-
                                auction sales

                            Case Shiller (linear)

                                       Annual
Period            [beta]    t-stat.    return
                                                     1.00
1850-1859          -0.221     -0.42    -2.07%        0.81
1860-1869           0.531      0.75     5.57%        1.40
1870-1879           1.038      1.71    11.06%        3.99
1880-1889          -0.018     -0.04    -0.07%        3.96
1890-1899           0.324      0.59     3.41%        5.54
1900-1909           0.195      0.56     2.09%        6.81
1910-1919           0.832      2.36     8.80%       15.84
1920-1929           0.842      2.26     8.91%       37.19
1930-1939          -0.912     -2.19    -8.61%       15.11
1940-1949           0.715      1.47     7.54%       31.27
1950-1959           0.530      1.24     5.57%       53.77
1960-1969           0.975      3.42    10.37%      144.26
1970-1979           1.806     10.88    19.93%      887.97
1980-1989           1.212      8.44    13.02%     3020.43
1990-1999           0.262       1.9     2.78%     3973.50
2000-2009           0.197      1.29     2.11%     4896.49
Adj.-[R.sup.2]                          0.949
Obs.                                  184
Mean return                             5.49%

                        Dealer-dealer and auction-
                               dealer sales

                           Case Shiller (linear)

                                       Annual
Period            [beta]    t-stat.    return
                                                     1.00
1850-1859           0.959      1.95    10.17%        2.63
1860-1869           0.197      0.76     2.09%        3.24
1870-1879           0.614      2.57     6.44%        6.05
1880-1889           0.553      2.42     5.80%       10.62
1890-1899           0.487      1.84     5.09%       17.45
1900-1909           0.335      1.19     3.51%       24.65
1910-1919           0.455      1.84     4.76%       39.24
1920-1929           1.265      5.27    13.60%      140.42
1930-1939          -0.173     -0.78    -1.61%      119.35
1940-1949          -0.230     -0.78    -2.18%       95.74
1950-1959           0.718       2.4     7.55%      198.32
1960-1969           1.064      3.44    11.34%      580.82
1970-1979           1.767      6.04    19.45%     3433.72
1980-1989           1.687      6.44    18.50%    18749.06
1990-1999           0.845      2.75     8.93%    44109.32
2000-2009           0.030      0.06     0.41%    45933.30
Adj.-[R.sup.2]                          0.957
Obs.                                  153
Mean return                             6.98%

Notes: The data include sales through April 2009.

TABLE 4
Hedonic Regression Results: Full Sample

Year             [gamma]    t-stat.        Index   Return

1980                                       1.00
1981             0.156857    1.74          1.17     16.98%
1982             0.188583    2.16          1.21      3.22%
1983             0.491044    5.89          1.63     35.32%
1984             0.571341    7.5           1.77      8.36%
1985             0.743109    9.79          2.10     18.74%
1986             0.694333    9.16          2.00     -4.76%
1987             0.910804   12.47          2.49     24.17%
1988             1.10146    15.17          3.01     21.00%
1989             1.151037   15.63          3.16      5.08%
1990             1.275318   17.1           3.58     13.23%
1991             1.300403   17.16          3.67      2.54%
1992             1.41717    18.48          4.13     12.39%
1993             1.481164   19.65          4.40      6.61%
1994             1.540986   19.52          4.67      6.16%
1995             1.600802   20.69          4.96      6.16%
1996             1.618454   20.33          5.05      1.78%
1997             1.567104   20.18          4.79     -5.01%
1998             1.672806   22.24          5.33     11.15%
1999             1.641515   21.25          5.16     -3.08%
2000             1.668991   22.41          5.31      2.79%
2001             1.638644   22.07          5.15     -2.99%
2002             1.755917   23.3           5.79     12.44%
2003             1.769383   22.62          5.87      1.36%
2004             1.744384   23             5.72     -2.47%
2005             1.762941   23.98          5.83      1.87%
2006             1.897455   25.69          6.67     14.40%
2007             1.790318   23.66          5.99    -10.16%
2008             1.921782   25.52          6.83     14.05%
2009             2.094461   22.17          8.12     18.85%
Years            29         F-statistic:
                             111.25
Makers           128        F-statistic:
                             74.10
Constant           8.846     (0.068)
[R.sup.2]          0.821
Obs.             2669
Mean return                                          7.49%
Standard                                             9.24%
  deviation of
  return

TABLE 5
Hedonic Regression Results: Indices and Returns

              Old    Italian  Modern  Italian          French
Year          Index  Return   Index   Return   Index   Return

1980          1               l                1
1981          1.15    13.93%  1.00     -0.11%  1.33     28.66%
1982          1.09    -4.94%  1.19     17.76%  1.54     14.26%
1983          1.37    22.24%  2.05     54.11%  2.03     28.08%
1984          1.50     9.43%  2.33     12.78%  1.99     -2.34%
1985          2.18    37.15%  2.28     -2.03%  2.52     23.65%
1986          2.09    -4.07%  2.47      7.76%  1.56    -47.82%
1987          2.36    12.34%  3.03     20.67%  2.72     55.67%
1988          2.73    14.43%  3.62     17.60%  3.10     13.05%
1989          2.83     3.70%  3.96      9.15%  3.11      0.21%
1990          3.42    18.81%  4.32      8.64%  3.37      7.95%
1991          3.12    -9.08%  4.96     13.78%  4.12     20.26%
1992          3.51    11.62%  6.05     19.90%  3.87     -6.34%
1993          3.56     1.54%  6.54      7.82%  4.33     11.18%
1994          4.23    17.09%  6.62      1.11%  4.89     12.19%
1995          4.54     7.14%  6.29     -5.11%  5.51     11.94%
1996          4.73     4.06%  7.33     15.30%  5.59      1.44%
1997          3.81   -21.65%  6.86     -6.55%  4.39    -24.17%
1998          4.71    21.22%  7.54      9.49%  4.79      8.72%
1999          4.65    -1.31%  7.76      2.84%  4.06    -16.50%
2000          4.05   -13.73%  8.50      9.15%  4.86     18.09%
2001          4.14     2.24%  8.65      1.74%  3.97    -20.33%
2002          5.18    22.41%  8.97      3.63%  4.56     13.88%
2003          5.06    -2.48%  8.21     -8.96%  4.99      9.04%
2004          5.52     8.76%  7.95     -3.14%  5.18      3.70%
2005          4.83   -13.36%  9.14     13.92%  4.28    -18.97%
2006          5.92    20.40%  10.02     9.23%  5.06     16.65%
2007          5.13   -14.35%  9.13     -9.38%  4.46    -12.65%
2008          5.22     1.68%  11.90    26.58%  6.18     32.72%
2009          6.50    21.92%  12.01     0.89%  7.95     25.17%
Years         29              29               29
Makers        64              43               9
Constant        Yes             Yes              Yes
[R.sup.2]       0.8             0.82             0.75
Obs.         1059            1004              394
Mean return            6.67%            8.95%            7.41%
Standard              13.73%           12.75%           20.57%
 deviation

Notes: Includes sales through April 2009.

TABLE 6
Comparison of Real Returns

                              Standard   Correlations    U.S.
Asset                   Mean  deviation    S&P 500      bonds
                        (%)      (%)

Individual sales data (1980-2008)

S&P 500                 6.55      17.87         1.000
U.S. treasury bonds     6.83       9.45         0.143    1.000
Art (Mei Moses)         4.57      17.22         0.025   -0.136
Fine violins (auction)  3.33       7.78        -0.136   -0.150
Old Italian (auction)   2.34      11.17        -0.0538  -0.1574
Modern Italian          5.40      14.93        -0.218   -0.0289
  (auction)
French (auction)        2.96      18.39        -0.1569  -0.0827
Repeat sales data
S&P 500                 6.12
  (1875-2008)
U.S. treasury bonds     2.47
  (1850-2008)
Art (Mei Moses)         2.26
  (1875-2008)
Fine violins            3.50
  (1850-2008)
Fine violins (auction)  2.86
Fine violins (dealer    4.32
  sales)

                                     All        Old      Modern
                        Art (Mei   violins    Italian    Italian
Asset                    Moses)   (auction)  (auction)  (auction)

Individual sales data (1980-2008)

S&P 500
U.S. treasury bonds
Art (Mei Moses)            1.000
Fine violins (auction)     0.184          1
Old Italian (auction)      0.216     0.7124          1
Modern Italian            -0.0827    0.6038     0.1416          1
  (auction)
French (auction)          -0.0947    0.6995     0.4408     0.2971
Repeat sales data
S&P 500
  (1875-2008)
U.S. treasury bonds
  (1850-2008)
Art (Mei Moses)
  (1875-2008)
Fine violins
  (1850-2008)
Fine violins (auction)
Fine violins (dealer
  sales)

                         French
Asset                   (auction)

Individual sales data (1980-2008)

S&P 500
U.S. treasury bonds
Art (Mei Moses)
Fine violins (auction)
Old Italian (auction)
Modern Italian
  (auction)
French (auction)        1
Repeat sales data
S&P 500
  (1875-2008)
U.S. treasury bonds
  (1850-2008)
Art (Mei Moses)
  (1875-2008)
Fine violins
  (1850-2008)
Fine violins (auction)
Fine violins (dealer
  sales)

Notes: The total return series for stocks and bonds were taken
from Global Financial Data. Returns for art were provided by
Beautiful Asset Advisors. The inflation rates were taken from
global insight. Returns for violins were deflated using the U.K.
price index, and returns for other assets were deflated using the
U.S. price index.