# Capital gains and the rate of return on a Stradivarius.

CAPITAL GAINS AND THE RATE OF RETURN ON A STRADIVARIUS

I. INTRODUCTION

No name in the annals of violin-making has evoked more interest and sense of mystery than that of Antonio Stradivari. During his long lifetime (1644-1737) Stradivari probably made about 1,100 instruments, with about 700 violins being accounted for currently. Stradivariuses have been sold in 1986 at auction for over $300,000. Fakes are everywhere.

In spite of the wealth of price data on Stradivariuses, no systematic economic analysis of this data has been made. The central question for this paper is: "What is the rate of return on a Stradivarius?" "Rate of return" means the annual percentage increase in the price of a Stradivarius, as in the case of collectables. After converting all prices into dollars with 1967 purchasing power, the following equation is applied: P.sub.t.=P.sub.0.e.sup.rt., where P.sub.t is the most recent price and P.sub.0 is the preceding transaction price. r is the rate of return and t is the number of years elapsing between transaction dates of P.sub.t and P.sub.0.

In section II the rate of return on individual violins for four different periods is determined. Stradivari developed his skills over time, so that each violin is not an identical product. Regression analysis is used to show how these differences in quality are reflected in differences in price, but not in differences in rates of return (section III). In section IV the rate of return on a Stradivarius from 1803 to 1986 is determined. Finally, in section V other factors are considered that may influence the rate of return on a Stradivarius.

II. THE RATE OF RETURN ON INDIVIDUAL VIOLINS

Here data on sale prices of individual violins are examined, where there is more than one transaction over time. In addition, each of the sales is assigned to one of four periods--periods generally accepted by musicologists such as Henley [1961, 15-16] as encapsulating stages in Stradivari's development. Data are shown in Tables I to IV.

The Amati Period, 1665-90

Stradivari was apprenticed at the age of fourteen in the workshop of the famous Nicolo Amati where he received "on-the-job training." All creations during this period are worked on the pattern of Amati.

Table I shows three violins having at least two sales. To understand the table, consider the first row labeled "Soames." The violin was made by Stradivari in 1684. Transactions took place in 1907 and 1973 for $8,571 and $15,778, respectively. All prices are in 1967 dollars. The equation discussed above yields $15,778 = 8,571e.sup.r(66).

Based on this r (the rate of return) is 0.92 percent. In other words, the price of the Soames violin increased annually at a rate of 0.92 percent.

Typically there is a brokerage fee of 10 percent for individuals (6 percent for dealers) to sell a violin at Sotheby's or Christie's auction house. This, of course, reduces the rate of return on a violin. For example, to determine the rate of return on the Soames after brokerage costs, 10 percent was deducted from the 1973 price, changing it from $15,778 to $14,201. After eliminating brokerage costs, the price increases by 0.77 percent annually. The Nachez and Mercury violins were similarly analyzed. The Mercury had three different sales, so that there are two rates of return.

The Long Period, 1691-1700

During this period Stradivari made numerous changes in his art. The scroll is worked in more detail and the varnish is golden yellow. Stradivari modified the pattern by making the violin a little longer and slightly more narrow.

Table II shows data on four violins. Except for the 1933-36 period, the Falmouth had similar rates of return even though the interval between sales varied significantly: Seventy-four, six and forty-six years for the first, second, and fourth transactions, respectively.

The Golden Period, 1701-25

Stradivari was at the peak of his power at this stage of his development. The violins now had a wider outline forming a beautiful shape, with scrolls exquisitely carved. Seven violins with at least two transactions are shown with their rates of return in table III. Rates of return were all positive, with the exception of the second Viotti sale. For violins with three sales, two rates of return are shown.

The Late Period, 1726-37

During this period the decline in Stradivari's work is evident. The violins lacked the perfection of those built in former times. The varnish is usually brown and less transparent than previously. Some of the instruments were made by others under the direction of Stradivari. Note in Table IV that the Tarisio shows five rates of return before brokerage costs, with all rates of return being positive except one.

Table V and Figures 1 and 2 summarize the results for all periods. The rates of return after brokerage costs range from 4.19 percent for the Late Period to -1.16 percent for the Long Period. Overall the mean rate of return was 2.17 percent. Since the long-term real interest rate is about 2.5 percent (according to Baumol [1986, 12]), it appears that it is not possible to make a profit (on average) on a Stradivarius if one considers only the annual capital gain. This appears to be true for most collectible markets. Baumol found a median rate of return (defined as the annual capital gain) of 0.85 percent for paintings. The rate of return on rare coins (again defined as the annual capital gain) for the past five years has been 2.2 percent.

III. PRICES AND RATES OF RETURN ON VIOLINS MADE DURING DIFFERENT PERIODS

A Stradivarius is apparently not always a Stradivarius. Violins made by Stradivari in different periods vary significantly in quality. Theoretically, these qualitative variations should be reflected in different prices, though not in rates of return. Price differences are discussed next, and then differences in rates of return.

Price Differences

A hedonic index was developed to determine the impact of qualitative differences on prices. P.sub.t is the price of a violin in 1967 dollars. The time of a transaction is time, with 1803 = 1, 1804 = 2, etc. Amati, Long, and Late are dummy variables for each period. The Golden Period is omitted, and is implicit in the following equation. Dummy variables take on a value of one if the violin was made in the period, or zero if the violin was not made during the period. Data ran from 1803 to 1986 with specific observations for seventy-three years. Actual sales were observed in 131 instances; when there was more than one sale during a year, the average price was used. This reduced the number of observations to seventy-three, which yielded P = -13,117 + 364 time - 14,911 Amati - 13,152 Long - 1,400 Late. (-2.5624) (10.004) (-2.400) (-2.581) (-0.276) R equalled 0.511.

Note that the t-values shown in parentheses are all significant at the 5 percent level, except for the Late period. These results show that price increased, on average, by $ 364 each year. In addition, it shows that a violin made during the Amati Period has a price $14,911 lower than one made during the Golden Period. The Long and Late Period prices are also lower than the Golden Period prices.

Differences in Rates of Return for Different Periods

To find the rate of return within each period, we follow Baumol [1986, 12] by

regressing the log of real prices for each of the four periods against time, i.e., P.sub.t = ae.sup.rt.

In log-linear form this becomes P.sup.'.sub.t = a.sup.' + rt where p.sup.'.sub.t and a.sup.' are the log values of p.sub.t and a, respectively. t equals time, with t equal to one in 1803, equal to two in 1804, etc. r equals the annual percentage increase in the real price which is equal to the rate of return.

Table VI shows the results. The rate of return varies between 1.90 percent for the Long Period and 2.47 percent for the Late Period. All the coefficients were significant at the 5 percent level. From the results it appears that the rates of return are approximately equal, as would be theoretically expected in an efficient market.

Another approach is to pool the time series data with cross-sectional data for different periods when the violins were made, in order to test whether the intercept as well as the slope varies for different periods. Significant variations in the slope would indicate differences in rates of return for different periods. P.sup.'.sub.t is log of price; time starts with 1803 = 1; Amati, Long and Late are dummy variables. The results are t-values are shown in parentheses. R.sup.2 was .835. Except for the constant and time, none of the variables are significant at the 5 percent level. The rate of return on all periods is 2.18 percent. The intercept dummies, Amati, Long, and Late, are not statistically significant at the 5 percent level; nor are the slope dummies, (Amati)(time), (Long)(time), and (Late)(time), statistically significant at the 5 percent level. Thus it is a safe conclusion that rates of return are about the same for all periods. This is consistent with the results when individual equations were run for each period.

IV. THE RATE OF RETURN IGNORING WHEN THE VIOLIN WAS MADE

One could reason that sales for the four periods when the violins were made are distributed more or less randomly over the 1803-86 period. If so, this would signify that regressing price against time for all violins, even ignoring the date when the violin was made, should yield about the same return as in section III.

Table VII shows the results using prices in 1967 dollars. All the coefficients are significant statistically at the 1 percent level. For the entire period the rate of return is 2.18 percent, very close to the results found in Table VI. For the subperiods shown in Table VII the results are roughly the same as for the 1803-1986 period, except the 1956-86 period. The 1956-86 period probably is an aberration. The real price in 1956 was a puzzling $4,472, far below the 1938 price of $14,514 and the 1957 price of $11,196.

V. THE RATE OF RETURN ADJUSTED FOR INSURANCE,

TAXATION AND USER BENEFITS

The rate of return to this point has been defined as equal to the annual capital gain from the sale of a Stradivarius. However, other factors may have some impact on the rate of return. The results of adjustments for these such factors are shown in Table VIII.

Insurance

Insurance costs will reduce the rate of return. The most common premium on insurance is 0.45 percent of value, though it may be as low as 0.375 percent of value. For a violin that increases in price from $100,000 to $200,000 over a thirty-five year period, the rate of return before insurance is 2 percent. Allowing for insurance of $675 a year (.0045 times an average value of $150,000), the rate of return falls to 1.5 percent. Thus insurance costs reduce the rate of return by about 0.5 percent, assuming a premium of 0.45 percent of value. If a premium of 0.375 percent is assumed, the rate of return in reduced by about 0.4 percent.

Taxes

Capital gains taxes may also reduce the rate of return., In France, West Germany, Britain, Italy and Japan, capital gains are effectively free of taxation, so the return on a Stradivarius would be unchanged. However, in Canada the top capital gains tax rate is 17 percent, and in the United States (until 1986) the top capital gains tax rate was 20 percent. If the rate of return before taxes is 2 percent, the rate of return after taxes would be 1.6 percent, a reduction of 0.4 percent.

User Benefits After Maintenance

It is extremely difficult to determine user benefits after maintenance, because there is no rental market for Stradivariuses. Dealers have suggested that the maximum benefit after maintenance (or rental value) would be 3 percent of the value of a Strad. It should be noted that depreciation is zero if a Stradivarius is maintained in good condition. User benefits would be zero for those who buy and sell Stradivariuses strictly for the capital gain and do not use the Stradivarius. The rate of return was regressed against real gross national product and interest rates, but failed to produce significant coefficients. Attempts to regress the rate of return on the number of concerts annually or on the income flows to classical musicians were not successful because of the lack of good data over a sufficiently long period of time.

Allowing for insurance, taxes and user benefits after maintenance, the rate of return ranges from 4.77 percent to 1.27 percent, as shown in Table VIII. Thus it appears that investing in a Stradivarius may give a return in excess of the long-term real rate of interest of 2.5 percent if taxes are absent and the user benefits are significant; or an investmnet in a Stradivarius may give a rate of return below the long-term rate of interest if taxes are significant and user benefits are absent.

VI. CONCLUDING COMMENT

The results above indicate that the real rate of return on a Stradivarius is approximately 2 percent and equal to the long-run real rate of interest. This is true for sales of individual violins (Tables I to IV), or when violins are separated into periods when they were made (Tables V and VI) or when they were sold (Table VIII). When prices (rather than rates of return) are examined for different violins, prices turn out to be highest during the Golden Period and lowest for the Amati Period, as expected. These results are consistent with the opinion of Goodkind [1973, 6].

When adjustments are made for insurance, taxation and user benefits after maintenance, the rate of return ranges from 4.77 to 1.27 percent, depending on the assumptions made. "Optimistic" assumptions concerning insurance, taxation and user benefits lead to the conclusion that an investment in a Stradivarius is a good investment. This is contrary to the opinion of W. E. Hill and Sons (London violin dealers) who, in a letter to one of the authors, says, "We are very much against musical instruments such as violins being considered as investments." With "pessimistic" assumptions about insurance, taxation and user benefits, the view of W. E. Hill and Sons is warranted.

I. INTRODUCTION

No name in the annals of violin-making has evoked more interest and sense of mystery than that of Antonio Stradivari. During his long lifetime (1644-1737) Stradivari probably made about 1,100 instruments, with about 700 violins being accounted for currently. Stradivariuses have been sold in 1986 at auction for over $300,000. Fakes are everywhere.

In spite of the wealth of price data on Stradivariuses, no systematic economic analysis of this data has been made. The central question for this paper is: "What is the rate of return on a Stradivarius?" "Rate of return" means the annual percentage increase in the price of a Stradivarius, as in the case of collectables. After converting all prices into dollars with 1967 purchasing power, the following equation is applied: P.sub.t.=P.sub.0.e.sup.rt., where P.sub.t is the most recent price and P.sub.0 is the preceding transaction price. r is the rate of return and t is the number of years elapsing between transaction dates of P.sub.t and P.sub.0.

In section II the rate of return on individual violins for four different periods is determined. Stradivari developed his skills over time, so that each violin is not an identical product. Regression analysis is used to show how these differences in quality are reflected in differences in price, but not in differences in rates of return (section III). In section IV the rate of return on a Stradivarius from 1803 to 1986 is determined. Finally, in section V other factors are considered that may influence the rate of return on a Stradivarius.

II. THE RATE OF RETURN ON INDIVIDUAL VIOLINS

Here data on sale prices of individual violins are examined, where there is more than one transaction over time. In addition, each of the sales is assigned to one of four periods--periods generally accepted by musicologists such as Henley [1961, 15-16] as encapsulating stages in Stradivari's development. Data are shown in Tables I to IV.

The Amati Period, 1665-90

Stradivari was apprenticed at the age of fourteen in the workshop of the famous Nicolo Amati where he received "on-the-job training." All creations during this period are worked on the pattern of Amati.

Table I shows three violins having at least two sales. To understand the table, consider the first row labeled "Soames." The violin was made by Stradivari in 1684. Transactions took place in 1907 and 1973 for $8,571 and $15,778, respectively. All prices are in 1967 dollars. The equation discussed above yields $15,778 = 8,571e.sup.r(66).

Based on this r (the rate of return) is 0.92 percent. In other words, the price of the Soames violin increased annually at a rate of 0.92 percent.

Typically there is a brokerage fee of 10 percent for individuals (6 percent for dealers) to sell a violin at Sotheby's or Christie's auction house. This, of course, reduces the rate of return on a violin. For example, to determine the rate of return on the Soames after brokerage costs, 10 percent was deducted from the 1973 price, changing it from $15,778 to $14,201. After eliminating brokerage costs, the price increases by 0.77 percent annually. The Nachez and Mercury violins were similarly analyzed. The Mercury had three different sales, so that there are two rates of return.

The Long Period, 1691-1700

During this period Stradivari made numerous changes in his art. The scroll is worked in more detail and the varnish is golden yellow. Stradivari modified the pattern by making the violin a little longer and slightly more narrow.

Table II shows data on four violins. Except for the 1933-36 period, the Falmouth had similar rates of return even though the interval between sales varied significantly: Seventy-four, six and forty-six years for the first, second, and fourth transactions, respectively.

The Golden Period, 1701-25

Stradivari was at the peak of his power at this stage of his development. The violins now had a wider outline forming a beautiful shape, with scrolls exquisitely carved. Seven violins with at least two transactions are shown with their rates of return in table III. Rates of return were all positive, with the exception of the second Viotti sale. For violins with three sales, two rates of return are shown.

The Late Period, 1726-37

During this period the decline in Stradivari's work is evident. The violins lacked the perfection of those built in former times. The varnish is usually brown and less transparent than previously. Some of the instruments were made by others under the direction of Stradivari. Note in Table IV that the Tarisio shows five rates of return before brokerage costs, with all rates of return being positive except one.

Table V and Figures 1 and 2 summarize the results for all periods. The rates of return after brokerage costs range from 4.19 percent for the Late Period to -1.16 percent for the Long Period. Overall the mean rate of return was 2.17 percent. Since the long-term real interest rate is about 2.5 percent (according to Baumol [1986, 12]), it appears that it is not possible to make a profit (on average) on a Stradivarius if one considers only the annual capital gain. This appears to be true for most collectible markets. Baumol found a median rate of return (defined as the annual capital gain) of 0.85 percent for paintings. The rate of return on rare coins (again defined as the annual capital gain) for the past five years has been 2.2 percent.

III. PRICES AND RATES OF RETURN ON VIOLINS MADE DURING DIFFERENT PERIODS

A Stradivarius is apparently not always a Stradivarius. Violins made by Stradivari in different periods vary significantly in quality. Theoretically, these qualitative variations should be reflected in different prices, though not in rates of return. Price differences are discussed next, and then differences in rates of return.

Price Differences

A hedonic index was developed to determine the impact of qualitative differences on prices. P.sub.t is the price of a violin in 1967 dollars. The time of a transaction is time, with 1803 = 1, 1804 = 2, etc. Amati, Long, and Late are dummy variables for each period. The Golden Period is omitted, and is implicit in the following equation. Dummy variables take on a value of one if the violin was made in the period, or zero if the violin was not made during the period. Data ran from 1803 to 1986 with specific observations for seventy-three years. Actual sales were observed in 131 instances; when there was more than one sale during a year, the average price was used. This reduced the number of observations to seventy-three, which yielded P = -13,117 + 364 time - 14,911 Amati - 13,152 Long - 1,400 Late. (-2.5624) (10.004) (-2.400) (-2.581) (-0.276) R equalled 0.511.

Note that the t-values shown in parentheses are all significant at the 5 percent level, except for the Late period. These results show that price increased, on average, by $ 364 each year. In addition, it shows that a violin made during the Amati Period has a price $14,911 lower than one made during the Golden Period. The Long and Late Period prices are also lower than the Golden Period prices.

Differences in Rates of Return for Different Periods

To find the rate of return within each period, we follow Baumol [1986, 12] by

regressing the log of real prices for each of the four periods against time, i.e., P.sub.t = ae.sup.rt.

In log-linear form this becomes P.sup.'.sub.t = a.sup.' + rt where p.sup.'.sub.t and a.sup.' are the log values of p.sub.t and a, respectively. t equals time, with t equal to one in 1803, equal to two in 1804, etc. r equals the annual percentage increase in the real price which is equal to the rate of return.

Table VI shows the results. The rate of return varies between 1.90 percent for the Long Period and 2.47 percent for the Late Period. All the coefficients were significant at the 5 percent level. From the results it appears that the rates of return are approximately equal, as would be theoretically expected in an efficient market.

Another approach is to pool the time series data with cross-sectional data for different periods when the violins were made, in order to test whether the intercept as well as the slope varies for different periods. Significant variations in the slope would indicate differences in rates of return for different periods. P.sup.'.sub.t is log of price; time starts with 1803 = 1; Amati, Long and Late are dummy variables. The results are t-values are shown in parentheses. R.sup.2 was .835. Except for the constant and time, none of the variables are significant at the 5 percent level. The rate of return on all periods is 2.18 percent. The intercept dummies, Amati, Long, and Late, are not statistically significant at the 5 percent level; nor are the slope dummies, (Amati)(time), (Long)(time), and (Late)(time), statistically significant at the 5 percent level. Thus it is a safe conclusion that rates of return are about the same for all periods. This is consistent with the results when individual equations were run for each period.

IV. THE RATE OF RETURN IGNORING WHEN THE VIOLIN WAS MADE

One could reason that sales for the four periods when the violins were made are distributed more or less randomly over the 1803-86 period. If so, this would signify that regressing price against time for all violins, even ignoring the date when the violin was made, should yield about the same return as in section III.

Table VII shows the results using prices in 1967 dollars. All the coefficients are significant statistically at the 1 percent level. For the entire period the rate of return is 2.18 percent, very close to the results found in Table VI. For the subperiods shown in Table VII the results are roughly the same as for the 1803-1986 period, except the 1956-86 period. The 1956-86 period probably is an aberration. The real price in 1956 was a puzzling $4,472, far below the 1938 price of $14,514 and the 1957 price of $11,196.

V. THE RATE OF RETURN ADJUSTED FOR INSURANCE,

TAXATION AND USER BENEFITS

The rate of return to this point has been defined as equal to the annual capital gain from the sale of a Stradivarius. However, other factors may have some impact on the rate of return. The results of adjustments for these such factors are shown in Table VIII.

Insurance

Insurance costs will reduce the rate of return. The most common premium on insurance is 0.45 percent of value, though it may be as low as 0.375 percent of value. For a violin that increases in price from $100,000 to $200,000 over a thirty-five year period, the rate of return before insurance is 2 percent. Allowing for insurance of $675 a year (.0045 times an average value of $150,000), the rate of return falls to 1.5 percent. Thus insurance costs reduce the rate of return by about 0.5 percent, assuming a premium of 0.45 percent of value. If a premium of 0.375 percent is assumed, the rate of return in reduced by about 0.4 percent.

Taxes

Capital gains taxes may also reduce the rate of return., In France, West Germany, Britain, Italy and Japan, capital gains are effectively free of taxation, so the return on a Stradivarius would be unchanged. However, in Canada the top capital gains tax rate is 17 percent, and in the United States (until 1986) the top capital gains tax rate was 20 percent. If the rate of return before taxes is 2 percent, the rate of return after taxes would be 1.6 percent, a reduction of 0.4 percent.

User Benefits After Maintenance

It is extremely difficult to determine user benefits after maintenance, because there is no rental market for Stradivariuses. Dealers have suggested that the maximum benefit after maintenance (or rental value) would be 3 percent of the value of a Strad. It should be noted that depreciation is zero if a Stradivarius is maintained in good condition. User benefits would be zero for those who buy and sell Stradivariuses strictly for the capital gain and do not use the Stradivarius. The rate of return was regressed against real gross national product and interest rates, but failed to produce significant coefficients. Attempts to regress the rate of return on the number of concerts annually or on the income flows to classical musicians were not successful because of the lack of good data over a sufficiently long period of time.

Allowing for insurance, taxes and user benefits after maintenance, the rate of return ranges from 4.77 percent to 1.27 percent, as shown in Table VIII. Thus it appears that investing in a Stradivarius may give a return in excess of the long-term real rate of interest of 2.5 percent if taxes are absent and the user benefits are significant; or an investmnet in a Stradivarius may give a rate of return below the long-term rate of interest if taxes are significant and user benefits are absent.

VI. CONCLUDING COMMENT

The results above indicate that the real rate of return on a Stradivarius is approximately 2 percent and equal to the long-run real rate of interest. This is true for sales of individual violins (Tables I to IV), or when violins are separated into periods when they were made (Tables V and VI) or when they were sold (Table VIII). When prices (rather than rates of return) are examined for different violins, prices turn out to be highest during the Golden Period and lowest for the Amati Period, as expected. These results are consistent with the opinion of Goodkind [1973, 6].

When adjustments are made for insurance, taxation and user benefits after maintenance, the rate of return ranges from 4.77 to 1.27 percent, depending on the assumptions made. "Optimistic" assumptions concerning insurance, taxation and user benefits lead to the conclusion that an investment in a Stradivarius is a good investment. This is contrary to the opinion of W. E. Hill and Sons (London violin dealers) who, in a letter to one of the authors, says, "We are very much against musical instruments such as violins being considered as investments." With "pessimistic" assumptions about insurance, taxation and user benefits, the view of W. E. Hill and Sons is warranted.

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Title Annotation: | Stradivarius violins |
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Author: | Ross, Myron H.; Zondervan, Scott |

Publication: | Economic Inquiry |

Date: | Jul 1, 1989 |

Words: | 2460 |

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