PARISIAN ESTATES

The present research relies on two main data sources: the 1912 Parisian probate records on the one hand, which detail the holdings of all the Parisians who died in 1912, and the Data for Financial History (DFIH) database on the other hand, which contains information about price and dividend series (Pastore 2024).

French probate records are highly reliable. ^{Footnote 1} In 1791, after the abolition of the Old Regime tax privileges, an inheritance tax was imposed (impôts sur la succession), which meant bequests left at the death of an individual were recorded for tax purposes. ^{Footnote 2} Estate tax rates were not only kept at low levels, but also strictly enforced by severe sanctions and difficult to evade because of the requirements for financial institutions and public utilities to inform the fiscal administration when the name of the account owner changed. ^{Footnote 3} Piketty (Reference Piketty2011) stressed that there was ample evidence that this legal requirement has been applied relatively strictly in France, making the risk-reward of cheating extremely low. ^{Footnote 4} Eventually, an unfair estimation of the bequests would be detrimental to at least one of the heirs, which further disincentivized manipulation. ^{Footnote 5} Furthermore, changes in the structure of the fiscal system enhanced the quality of the probate records. Paris at that time was partitioned into nine independent fiscal zones managed by a fiscal office (bureau). ^{Footnote 6} After 1902, bequests, which used to be recorded in the bureau on which they geographically depended, were centralized in the fiscal zone of the decedent’s main residence and had to be declared by the family up to six months after the owner’s death (25 February 1901 Act). ^{Footnote 7} Therefore, in 1912, neither attrition nor mismatching issues between individuals and assets could occur.

Due to the difficulty of gathering data for each individual for each year from the beginning of the nineteenth century to the 1920s, the data from the tax records have been collected for the years 1872, 1882, 1892, 1897, 1902, 1912, 1922, and 1927. Only Parisian records were parsed because most of the French economic elite lived there, and a disproportionate share of the national wealth was concentrated in the city. ^{Footnote 8}

COMMUNITY VERSUS SEPARATE ASSETS

In France, the default matrimonial property regime was the “community of acquisitions,” under which both spouses remained the sole owners of the assets they acquired before marriage (separate assets), while those acquired after (community assets) fell under the community, regardless of who actually purchased them. Therefore, using the same notations as in Piketty, Postel-Vinay, and Rosenthal (Reference Piketty, Postel-Vinay and Rosenthal2014), the wealth of a household composed of husband i and wife j at time t is defined as:

(1)

where w _ijt is the total wealth of the household, $$a_{ijt}^C$$ the value of the community assets, $$a_{it}^S$$ and $$a_{jt}^S$$ the value of the separate assets of husband i and wife j, respectively.

Under this matrimonial regime, both community and separate assets accrued to the community. However, separate assets sold after marriage, for example, to purchase community assets, as well as bequests and inter vivos gifts received by one of the spouses, for example, dowries, had to be registered and reimbursed by the community to the original owner at her death. When the first spouse died, the community dissolved. The surviving spouse took possession of her separate assets and half of the community asset’s value. The other half and the decedent’s separate assets (net of liabilities), which altogether comprised the total wealth of the decedent at time of death, were taxed and redistributed to the heirs. If the husband died first, his net estate would therefore be:

(2)

with $$a_{it}^R$$ and $$a_{jt}^R$$ the value of the separate assets of husband i and wife j sold after marriage, and $$V_{it}^S$$ the value of the gifts received by husband i after marriage. ^{Footnote 9} The same held true if the wife died first, with replacing i by j.

As this information was vital for tax accuracy, the probate records specify for each asset owned by the decedent in 1912 whether it was a separate or a community asset. We therefore have details about all the community assets and separate assets owned by the decedent at time of death. Obviously, we do not have any information about the separate assets owned by the surviving spouse, since they were not needed to measure the decedent’s net wealth. The great advantage of the distinction between separate and community assets is that it gives two snapshots, instead of one, of the wealth of Parisian investors: her wealth at time of marriage on the one hand and her wealth at time of death on the other hand. As, again, separate assets accrued to the community, the first snapshot of wealth gives the value of uncapitalized bequests owned by the first spouse to die. “Uncapitalized” here refers to the nominal amount, in francs, the individual inherited, as all the accrued value on this original amount contributed to growing the community wealth.

Unlike actual assets valued at the time of death, separate assets sold after marriage were valued at the time they were sold, with no inflation correction and no information about the time they were sold. Similarly, bequests and gifts were valued at the time they were received, with no information about that time and no inflation adjustment. I make simpler assumptions than Piketty, Postel-Vinay, and Rosenthal (Reference Piketty, Postel-Vinay and Rosenthal2014) to estimate these times and adjust for inflation. ^{Footnote 10} I assume that asset sales took place 5 years after marriage (or immediately after if individuals died less than 5 years after being married), and bequests were received at age 30 (or at time of death if the decedent was younger). ^{Footnote 11} We therefore obtain the inflation-adjusted value of uncapitalized bequests:

(3)

with Q _t the price index at time of death t, Q _jt0 the price index at estimated time of asset sales for individual j, and Q _jt1 the price index at estimated time j received her bequests. Thus, $$b_{jt}^0$$ represents a measure of ex ante wealth, with assets valued at time t. The main limitations of this measure of ex ante wealth are twofold: first, it excludes single and widowed decedents, as the former exhibited only one snapshot of wealth at time of death, while the latter had their original separate assets merged with half the community assets and their share in the inheritance of the first deceased, which we cannot disentangle. Second, it includes all the returns that accrued to the portfolio before marriage. On this last point, however, marriage took place relatively early in the life cycle, and age at marriage was not correlated to wealth levels, making $$b_{it}^0$$ very close to the exact value of the wealth inherited by investor i. ^{Footnote 12} The correlation between matrimonial status and wealth at death was also quite weak (6 percent), although this relation is contaminated by age effect. ^{Footnote 13} Another benefit of using an ex ante measure of wealth is that it does not suffer from this age-wealth relationship.

PRICE SERIES

The second source of data, “Data for Financial History” (DFIH), stores financial time series. ^{Footnote 14} It contains a large amount of information about the two Parisian stock exchanges, the Parquet and the Coulisse, as well as about French and foreign public and corporate issuers. A striking feature of the Paris Bourse of that time was indeed the separation between an official segment, the Parquet, and an unofficial yet tolerated segment, the Coulisse, which mostly traded over-the-counter (OTC). ^{Footnote 15} Insofar as only data from the Parquet were available, and since some of the riskier assets were traded on the Coulisse, it is possible that the risk profile of investors might be slightly downward biased, in particular for the wealthiest ones, although there were only 21 available securities traded on the Coulisse between 1908 and 1912, compared to the 659 securities retrieved from the Parquet.

DFIH include price series, dividend flows, and re-adjustment factors to account for price distortions caused by corporate events like stock splits. Price series were built by sampling price data from the Cotes officielles every 15 days, for each year between 1795 and 1953. This means that I have a maximum of 25 data points per year for any asset. Assets were not continuously quoted on the stock exchanges as they are today, but were only priced when there were buy-and-sell orders from clients. If an asset was not traded on a specific day, it has no price for that day.

A DICTIONARY TO BRIDGE HISTORICAL SOURCES

A significant part of the present research has been to match the Parisian estates data with the financial series from the DFIH database. Since there was no common key between the exact name of the asset as displayed in the DFIH database and the way the 1912 fiscal administration categorized each asset, I built a dictionary to translate the asset name of the estates to its DFIH equivalent and vice versa. The matching was performed semi-automatically using pre-processing methods common to standard natural language processing. Financial assets were split into two broad categories based on their name and asset class, as recorded in the probate records: bonds (both public and private) and shares. For each asset in the probate records, a maximum number of 20 candidates were sorted from the full DFIH database based on the number of common words and lexicographical proximity. I discarded the assets with no matching candidate after manual verification in the DFIH table. ^{Footnote 16} I then manually selected the most relevant DFIH equivalent for the assets with at least one candidate. Of the 5,017 unique financial assets in the 1912 probate records, 2,099 (42 percent) were matched, and 659 were extracted from the DFIH database. The large attrition is due to the sampling methodology, as non-traded assets had no price for a given day, and to the fact that some assets were not publicly quoted.

The final dataset was constructed by combining information from both the probate records and the DFIH time series. I kept on the table only individuals who held at least one asset that I was able to match with its DFIH equivalent. Portfolio weights were assumed to be static, meaning that I evaluated portfolios’ performance from 1908 to 1912 as if their composition remained the same as in 1912, when the owner died. ^{Footnote 17} This assumption is not that unrealistic: Brunnermeier and Nagel (Reference Brunnermeier and Nagel2008) analyze how portfolio allocation changes as a result of wealth fluctuations and find evidence of strong inertia. Besides, French investors were likely to stick to a simple “buy-and-hold” strategy, as it was common in the United Kingdom according to Rutterford and Sotiropoulos (Reference Rutterford and Sotiropoulos2019): individuals added assets to their portfolio over their lifetime and kept them until death, which makes sense in a dynastic altruism framework. ^{Footnote 18} Ultimately, 1,718 portfolios were partially reconstructed. I chose to discard portfolios whose reconstructed value was less than half the total value of the actual portfolio, thus ultimately obtaining 1,329 reconstructed portfolios with a reconstruction rate of at least 50 percent. As bequests could only be computed for married decedents, I restricted most of the analysis on portfolios to the 578 portfolios of married investors with a reconstruction rate higher than 50 percent. Table 1 summarizes information about all individuals in the original dataset (Column (1)), those with some financial assets (Column (2)), and the portfolios of married investors reconstructed at least at 50 percent (Column (3)).

Table 1 DESCRIPTIVE STATISTICS FOR ALL INDIVIDUALS

Notes: Descriptive statistics for the main three tables (N being the number of individuals in each table). All financial and portfolio features are expressed in thousands of francs. The negative values for estates and wealth are due to debts, which were registered in the probate records.

Source: Author’s calculations.

Attrition, thresholds in the reconstruction rate, and subsetting to married investors naturally exclude many decedents and distort the wealth distribution. The wealthiest individual in the table, owning over 33 million francs in 1912, is not in the final set of reconstructed portfolios, despite being married. However, the wealthiest individual in the reconstructed portfolios, owning almost 10 million francs, belonged to the top wealth decile in the original table. Some of the largest portfolios are thus at least partially reconstructed. Some of the wealthiest investors owned large shares in private companies, which partially explains attrition. ^{Footnote 19} Even though the average net wealth is lower in the reconstructed portfolios of married investors than in the table with securities holders (525,741 francs versus 547,776 francs), the order of magnitude remains the same.

The attrition also changes the average composition of the portfolios. The share of equity on both French and foreign companies is much smaller in the reconstructed portfolios of married investors than in the whole table of securities holders, while the French rente, which was quite liquid and traded on the Parquet, was easily reconstructed. Table 2 shows the average fraction of wealth invested in each asset class for the security holders and the reconstructed portfolios. ^{Footnote 20} I formally test if the attrition modifies the composition of the reconstructed portfolios compared to the original ones. Since the asset class weights are not normally distributed in the two tables, I use a Mann-Whitney U-test with H ₀ : µ _S = µ _r , where µ _S is the mean of the asset class weights in the security holders table and µ _r is the mean of the asset class weights in the reconstructed portfolios table. The last column of the table shows the p-value of such a test, and apart from the French corporate bonds, H ₀ is rejected at near 0 levels. The analysis of the reconstructed portfolios of married investors, therefore, will be based on a sample where equity is underrepresented and bonds, notably public ones, are overrepresented.

Table 2 MANN-WHITNEY TEST RESULTS ON THE PORTFOLIO COMPOSITION OF SECURITY HOLDERS VERSUS RECONSTRUCTED PORTFOLIOS

Notes: This table shows the average fraction of wealth invested in each asset class for the security holders and the reconstructed portfolios of married investors. The last column shows the p-value of the Mann-Whitney U-test performed to test if the distributions of weights are the same in the two columns (Security Holders vs. Reconstructed Portfolios).

Source: Author’s compilation.

The size of the largest portfolios was absolutely huge. The average annual labor income of a coal mining worker in 1913 was about 1,800 francs, according to Trempe (Reference Trempe1971), so the average estate at death (526.2 thousand francs in the reconstructed portfolios) represented 292 years of labor income for a worker, and the maximum estate at death (9,935 thousand francs in the reconstructed portfolios) was about 5,500 years of labor income.

Chaulanges (Reference Chaulanges1970) estimates that in France in 1913, there were 384 savings accounts opened for every 1000 individuals. The other 616 individuals did not earn enough to save or were keeping a small cash buffer at home, and therefore would probably not appear in the probate records as they would leave no bequest at death. Hence, assuming the same distribution between Paris and regions, although Paris probably had a higher proportion of people owning a savings account, the probate records represent a picture of the top 40 percent of the wealth distribution in Paris in 1912. Indeed, the bottom wealth decile held, on average, 1,300 francs at death, in cash, savings accounts, or French rente. By contrast, in 2021, there were 55 million livrets A (savings accounts) in France owned by physical persons, that is, 81 percent of the total population.

WEALTH AND PORTFOLIO RECONSTRUCTION

I consider two measures of ex post wealth: the net estate at death, namely the net value of each individual’s assets minus liabilities registered in the probate records, and the total financial wealth, that is, the value of all the investor’s financial assets registered in the probate records. ^{Footnote 21} I proxy the ex ante wealth by the uncapitalized value of inherited bequests $$b_{jt}^0$$ . ^{Footnote 22}

The portfolio reconstruction rate is the ratio of the value of the reconstructed portfolio to financial wealth, that is, the percentage of the financial asset value that I have reconstructed from the DFIH series. Many portfolios were almost identical as they were only composed of French 3 percent rente and reached therefore a reconstruction rate equal to 1. ^{Footnote 23} The reconstruction rate negatively correlates with wealth, as shown in Figure 1: richer individuals faced looser capital constraints and could diversify across a much broader spectrum of assets, including less liquid ones, thus making their reconstruction less exhaustive. ^{Footnote 24}

Figure 1 PORTFOLIO RECONSTRUCTION RATE AND WEALTH

Notes: This figure shows the average portfolio reconstruction rate by decile of wealth (net estate) and the average portfolio reconstruction rate (dashed line) in the whole sample.

Source: See the text.

FINANCIAL AND NON-FINANCIAL ESTATES

Parisian portfolios were already remarkably diversified in 1912, even though the MPT had not yet been formalized. Late nineteenth-century financial innovations and higher expected returns progressively shifted wealthy individuals’ investments from traditional real estate holdings toward corporate shares and bonds, as noted by Piketty, Postel-Vinay, and Rosenthal (Reference Piketty, Postel-Vinay and Rosenthal2014). Figure 2 shows that the proportion of equity and corporate bonds in individual portfolios increased almost linearly with wealth but remained below the weight associated with real estate holdings, albeit not for the wealthiest. Real estate is by definition expensive, hence the steep increase at the bottom of the wealth distribution, but its weight remained roughly constant in the middle of the wealth distribution and dropped for the wealthiest, who invested more heavily in financial assets. ^{Footnote 25}

Figure 2 REAL ESTATE VERSUS EQUITY PER DECILE OF WEALTH

Notes: This figure shows the average percentage of wealth invested in real estate (black line) and corporate assets, namely corporate bonds and equity (gray line), by decile of net wealth at death. The “weight in portfolio” of real estate refers to the total value of the assets labeled in the probate records as real estate divided by the total value of the assets owned by an individual i. The same applies for corporate assets. The dashed lines represent the confidence interval, that is, the average +/– the standard error by decile, that is, $$\frac{{{\sigma _k}}}{{\sqrt {{n_k}} }}$$ with σ _k and n _k , respectively, the standard deviation and the number of individuals in bucket k.

Source: See the text.

The proportion of equity in the portfolio increased with wealth for French stocks, especially at the top of the wealth distribution, and in some convex way for foreign stocks, as shown in Figure 3, which is consistent with Piketty (Reference Piketty2014).

Figure 3 SHARE OF EQUITY IN AVERAGE PORTFOLIO BY DECILE

Notes: This figure shows the average fraction of net wealth at death invested in the shares of French (solid black line) and foreign (solid gray line) companies by decile of net wealth. The dashed lines represent the confidence interval.

Source: See the text.

A similar pattern existed for corporate bonds in Figure 4. Interestingly, holdings in foreign government bonds were also positively mapped to wealth, while the relationship between French bond weights and wealth was illustrated by a hump-shaped curve (see Figure 5). This difference in patterns suggests that French rente was treated as a safe haven and became therefore relatively less attractive for wealthier investors, while foreign bonds delivering higher yields were more speculative.

Figure 4 SHARE OF CORPORATE BONDS IN AVERAGE PORTFOLIO BY DECILE

Notes: This figure shows the average fraction of net wealth at death invested in the corporate bonds issued by French (solid black line) and foreign (solid gray line) companies by decile of net wealth. The dashed lines represent the confidence interval.

Source: See the text.

Figure 5 SHARE OF PUBLIC BONDS IN AVERAGE PORTFOLIO BY DECILE

Notes: This figure shows the average fraction of net wealth at death invested in the government bonds issued by France (solid black line) and foreign (solid gray line) countries by decile of net wealth. The dashed lines represent the confidence interval.

Source: See the text.

Comparing with Hautcœur (Reference Hautcœur1994), the actual composition of Parisian portfolios seems much more balanced between bonds and equity than the capitalization of companies on the Parisian stock exchanges: in 1913, corporate shares accounted for 86 percent of the total capitalization in Paris, while bonds only represented 14 percent. It could be that Parisian investors had a greater appetite for corporate bonds, while French shares were more demanded by foreign investors, as institutional ownership in France at the time, although not negligible, was limited to very liquid instruments, in particular French debt.

GEOGRAPHICAL DISPERSION OF INVESTMENTS

At the beginning of the twentieth century, British investor Henry Lowenfeld was already emphasizing the importance of geographical diversification to reduce portfolio volatility by seeking less-correlated assets, as idiosyncratic shocks in a country were unlikely to spread beyond its frontiers. Goetzmann and Ukhov (2006) claim that geographical diversification was well understood by early twentieth-century investors, both in Britain and in Europe. ^{Footnote 26} Similarly, in France, a substantial part of national wealth was invested abroad, and this proportion grew steadily in the early twentieth century. ^{Footnote 27}

Table 3 shows the weight of each region in the average portfolio per wealth decile. In 1912, 1,151 investors held at least one financial foreign asset, that is, 56.6 percent of the 2,033 security holders. Richer investors were less subject to home bias, as they allocated a larger weight of their portfolio to foreign assets, but not uniformly over all regions. A significant share of the portfolio value was allocated to Russia only, which is nonetheless lower than previous estimates, but remained relatively high across the whole wealth distribution. ^{Footnote 28} Apart from Russia, Southern America and Africa were the second and third most attractive regions for Parisian investors, respectively. ^{Footnote 29} A significantly lower share of the portfolios was devoted to Northern America, a result that is consistent with both Edlinger, Merli, and Parent (Reference Edlinger, Merli and Parent2011) and Esteves (Reference Esteves2011), who point out the remarkably low stake of French investments in this region. Consistently with Ageron et al. (Reference Ageron, Coquery-Vidrovitch, Meynier and Thobie2016), French investors shunned the Empire, which represented only 9 percent of the total net claims abroad in 1914.

Table 3 SHARE (IN PERCENT) OF EACH REGION IN FINANCIAL PORTFOLIOS BY DECILE OF WEALTH

Notes: This table shows the average fraction of financial wealth invested in foreign assets (equity, corporate bonds, government bonds) per region by decile of net wealth at death. For example, a 1912 Parisian decedent in the 2nd decile invested an average of 4.8 percent of his or her wealth in Russian assets. The last row shows the average for the whole sample. The “Total Foreign” column is the sum over the other columns.

Source: See the text.

SECTORAL ANALYSIS

The emergence of new industries (cars, electricity distribution, pharmaceuticals) and new technologies (creation of Air Liquide in 1902, artificial silk following Hilaire Chardonnet’s method), as well as the extension of transportation networks (the first metropolitan line opened for the 1900 Paris Exposition), considerably enlarged the spectrum of possible investments and thus provided investors with greater opportunities to diversify their risk. Table 4 shows the evolution of the fraction of financial wealth invested in various sectors per decile of wealth. Transport was the favorite industry of investors, and its weight rose quickly across the wealth distribution. ^{Footnote 30} Mining, which I isolate from industrials, rose quickly as well with wealth level. Many decedents held what the French probate records registered as “fonds de commerce” (commercial property), which I categorize as “retail” and which encapsulates small local shops as well as large stores, hotels, restaurants, and casinos. The negative relationship between retail holdings and wealth level suggests that a few “investors” were in fact small entrepreneurs or shop owners who lied at the bottom of the wealth distribution and left their commercial property as their main bequest when they died.

Table 4 SHARE (IN PERCENT) OF EACH SECTOR IN FINANCIAL PORTFOLIOS BY DECILE OF WEALTH

Notes: This table shows the average fraction of financial wealth invested per sector by decile of net wealth at death. For example, a 1912 Parisian decedent in the 4th decile invested an average of 1.4 percent of his or her wealth in the mining industry. The last row shows the average for the whole sample. Government bonds and unmatched assets make up the remaining fraction of financial wealth.

Source: See the text.

DIVERSIFICATION METRICS

I measure diversification through three variables: the number of assets in the portfolio, the sum of squared portfolio weights (SSPW), and portfolio entropy. The sum of squared portfolio weights (SSPW) in a portfolio i with K assets is computed as:

(4)

The weights associated with each asset equal the fraction of the total value of the decedent’s financial investments invested in this asset. SSPW takes values between $$\frac{1}{K}$$ (uniform distribution of weights across the whole range of assets) and 1 (a single asset in the portfolio). The third metric is the Shannon entropy, which is computed as follows:

(5)

Entropy represents the disorder within a system. Its application to portfolio theory has been scarce, yet insightful to improve measures of risk. ^{Footnote 31} The greater the portfolio diversification, the higher the associated entropy, which takes values between 0 (single asset) and log (K) (uniform distribution across all assets). ^{Footnote 32}

CONCENTRATION BY WEALTH LEVEL

Table 5 shows that, for the 2,033 security holders, the average portfolio was composed of 14.15 unique assets. The right-skewed distribution of each variable indicates that few individuals held very diversified portfolios. ^{Footnote 33} The maximum entropy and the minimum SSPW were achieved by the same individual, Isabelle de Gars de Tourcelles, whose net estate at death was estimated at 10,272,704 francs, the eighth richest individual in the sample. ^{Footnote 34}

Table 5 DISTRIBUTION OF DIVERSIFICATION VARIABLES

Notes: This table shows the distribution of the three diversification variables. N is the number of individuals in the sample with at least one financial asset with a strictly positive value.

Source: See the text.

Figure 6 shows the average number of holdings, SSPW, and portfolio entropy by percentile of total wealth and exhibits a positive and convex relationship between diversification and wealth, with the top percentile holding on average more than 70 unique assets. ^{Footnote 35} Compared to the results of Rutterford and Sotiropoulos (Reference Rutterford and Sotiropoulos2018), diversification increased faster with wealth for French investors than for British ones. ^{Footnote 36}

Figure 6 DIVERSIFICATION METRICS, AVERAGE BY WEALTH PERCENTILE

Notes: This figure shows the average value of each diversification variable by percentile of wealth (net estate). The number of assets (black line) is plotted against the left axis, while the SSPW (dark gray) and the entropy (light gray) are both plotted against the right axis.

Source: See the text.

Despite important theoretical developments in our understanding of the benefits of diversification, today’s portfolios do not seem more diversified than they used to be during the Belle-Epoque. Analyzing 40,000 U.S. households from 1991 to 1996, Goetzmann and Kumar (Reference Goetzmann and Kumar2008) show that individual portfolios were quite under-diversified across the whole period, with more than 25 percent of the portfolios being composed of a single stock. Nevertheless, a salient difference between 1912 and today’s investors is the ability of the latter to seek alternative ways of diversifying their risk through mutual funds. Bach, Calvet, and Sodini (Reference Bach, Calvet and Sodini2020) indeed show that Swedish middle-class investors achieved greater international diversification by investing in mutual funds, which also increased the average return on the bottom four deciles of the wealth distribution. Conversely, the burden of tight capital constraints was heavier on 1912 investors’ shoulders, as mutual funds were not only less developed than today, but also only proposed undiversified and very liquid investment vehicles that relied primarily on French debt, as stated by Hautcœur (2004). Therefore, the investment strategies offered by 1912 mutual funds were relatively similar to what modest households could achieve on their own.

LINEAR ESTIMATION AND RESULTS

To understand the impact of wealth on portfolio diversification, I rely on three diversification metrics and estimate the following equation:

(6)

where d _i is the diversification level of portfolio i proxied by the numbers of assets, the SSPW and the portfolio entropy, w _i the net wealth at death, π _i the portfolio value, and (x _k ) _k a set of control variables, namely age, gender, matrimonial status, and a dummy for France residence. The ratio $$\frac{\pi }{w}$$ , that is, the percentage of total wealth held in financial assets, is meant to test whether a priori diversified investors, that is, those holding for, example, real estate or artworks, sought the same level of diversification as those investing only in financial assets.

Table 6 shows the results obtained for each of the three specifications, using robust standard errors. Overall, the coefficients associated with the logarithm of wealth are statistically significant at the 1 percent level and have the expected sign: wealth is positively correlated with the number of holdings and entropy, but negatively correlated with SSPW. Keeping other variables constant, a 1 percent increase in wealth is associated with 0.051 additional unique assets in the average portfolio. Wealthier investors also tend to have more balanced portfolios, with a lower fraction of their capital invested per asset. The coefficient associated with the logarithm of wealth in the number of holdings specification is, however, much larger than in Rutterford and Sotiropoulos (Reference Rutterford and Sotiropoulos2018), which suggests that wealth effect was much more important in Paris at the beginning of the twentieth century than in late nineteenth-century Britain. Most of the magnitude of the R ² is conveyed by wealth itself, whose impact accounts for about 33 percent of the total variance of entropy.

Table 6 OLS ESTIMATES OF WEALTH EFFECT ON DIVERSIFICATION

Notes: This table reports the OLS estimates of regressing each diversification variable (the number of assets, the SSPW, and portfolio entropy) on the logarithm of wealth and a set of variables that are described in the Diversification Metrics section. The table reports robust (heteroscedasticity-consistent) standard errors in parentheses.

Source: See the text.

Women’s portfolios counted fewer assets on average, but without sacrificing portfolio balance, as entropy and SSPW were not impacted by gender. Investors who lived in France held more diversified portfolios, potentially because of the geographical proximity between investors and the Paris Bourse, which facilitated order transmission and information sourcing. Age and matrimonial status had virtually no impact on diversification. However, the larger the fraction of wealth invested in financial assets, the greater the diversification, which makes sense as Parisians already investing in non-financial assets, such as real estate and artworks, not only had less money left to invest in financial markets, but were also sufficiently diversified across other asset classes and therefore sought less diversification in their financial portfolio.

COMPARISON OF THE SMALL AND LARGE PORTFOLIO COMPOSITION

Table 7 and Table 8 show the most popular assets in the bottom two and top two deciles of net wealth at death, respectively. The portfolios at the two extremes of the wealth distribution exhibit some similarities as some of the most popular assets are the same, notably the French rente (3 percent) and the emprunt russe (Russian debt), which are present in both tables. The French rente of 3 percent accounts for more than 25 percent of the total wealth of the bottom 20 percent of investors. ^{Footnote 37} This percentage drops for the wealthiest but still remains above 10 percent, as Parisian investors still kept a significant share of their total wealth in this safe haven. The Russian debt seemed to have been very popular across the whole wealth distribution, consistent with Table 3.

Table 7 MOST POPULAR ASSETS (BY AGGREGATED VALUE) IN THE 20 PERCENT SMALLEST PORTFOLIOS

Notes: This table lists the most popular assets (by aggregated value) in the first two deciles of the wealth distribution (20 percent smallest portfolios). Assets are sorted in decreasing order; hence, the French rente 3 percent was the asset with the largest aggregated value in the bottom 20 percent of the wealth distribution. Value represents the total amount (in francs) of each asset owned by the bottom 20 percent of the wealth distribution. Percent Total Value is the percentage of the total wealth of the first two deciles each asset accounts for. Hence, the Ville de Paris 4 percent (bonds issued by the city of Paris with a coupon of 4 percent) represents 9 percent of the total wealth of the bottom 20 percent of investors. Prices and returns (if available) are computed from the DFIH time series.

Source: See the text.

Table 8 MOST POPULAR ASSETS (BY AGGREGATED VALUE) IN THE 20 PERCENT LARGEST PORTFOLIOS

Notes: This table lists the most popular assets (by aggregated value) in the top two deciles of the wealth distribution (20 percent largest portfolios). Assets are sorted in decreasing order; hence, the Chemins de Fer PLM (shares on Paris-Lyon-Marseille railway company) was the asset with the largest aggregated value in the top 20 percent of the wealth distribution. Value represents the total amount (in francs) of each asset owned by the top 20 percent of the wealth distribution. of the total wealth of the last two deciles each asset accounts for. Hence, the Emprunt russe 4.5 percent (bonds issued by the Russian Empire with a coupon of 4.5 percent) represents 3.9 percent of the total wealth of the top 20 percent of investors. Prices and returns (if available) are computed from the DFIH time series.

Source: Author’s calculations.

Some of the assets popular among the wealthiest but not among the smallest portfolios, such as the shares on the Suez Canal, were expensive and probably not affordable for the smallest investors. Yet, bonds on the Paris-Orléans railway company traded at 1,255 francs and were still popular among the bottom 20 percent of Parisian investors despite their relatively high price. The high returns on the Suez Canal shares (6.5 percent annualized returns from 1908 to 1912) suggest that the lighter capital constraints on the wealthiest investors pushed their Markowitz efficient frontier higher and offered them wider investment opportunities, which were not available to smaller investors, neither through their single stock picking activity nor through mutual funds, which tended to invest in safe assets with low risk and low returns.

Another striking difference between small and large portfolios is the higher degree of diversification of the latter compared to the former. Indeed, the top 10 assets of the bottom 20 percent of investors represented 65 percent of their total wealth, while the top 10 assets of the top 20 percent of investors accounted for only 34 percent of their total wealth. The tables also illustrate the relative preference of smaller portfolios for safe French rente while the wealthiest owned more equity and more international assets, notably the Emprunt Vice-Roi (Egyptian debt issued in 1870), which delivered high annualized returns through the observed period.

DISTRIBUTION OF RETURNS BY WEALTH LEVEL

A positive correlation between wealth and returns is intuitive but not trivial: Campbell, Ramadorai, and Ranish (Reference Campbell, Ramadorai and Ranish2019) find that small, undiversified portfolios of retail traders randomly outperform on average the portfolios of the wealthiest, but underperform in the long run due to the strength of compounded returns. ^{Footnote 38}

Due to the extreme sparsity of the price series, computing daily or even weekly returns was impossible; hence, I chose to only compute annual returns by subtracting the last and first available prices in the year. Volatility is computed straightforwardly as the weighted annualized standard deviation of returns, that is,, with w _i the vector weighting each asset in portfolio i, Σ the unbiased estimate of the variance-covariance matrix, and A an annualization factor, set to 25. ^{Footnote 39} The Sharpe ratio is computed as:

(7)

with r _i the average return on portfolio i over the period 1908–1912 and r _f the risk-free asset, set to 3 percent. ^{Footnote 40} Finally, alpha and beta were computed by ordinary least squares, from the regression:

(8)

with $$r_{i,t}^e$$ (resp. $$r_{M,t}^e$$ ) the excess return on portfolio i (resp. on the market) at each period t. Two variables were selected to proxy market returns: on the one hand, an experimental replication of the “CAC 40” of that time from the DFIH database, that is, an index tracking the performance of the 40 biggest French companies by capitalization over the period 1908–1912. On the other hand, a weighted sum of the returns on each asset—weighted by the fraction of the total value of the asset represented in the 1912 probate records.

Figure 7 shows the average Sharpe ratio by decile of inherited bequests for married investors. Although there is no apparent linear relationship between inherited wealth and risk-adjusted excess returns, the top two deciles were the only ones to generate a Sharpe significantly positive and higher than the average Sharpe across the distribution. T-tests confirm this result. ^{Footnote 41}

Figure 7 SHARPE RATIO BY DECILE OF EX ANTE WEALTH

Notes: This figure shows the average Sharpe ratio (solid black line) per decile of wealth (inherited bequests), with the standard error (dashed black line) and the average Sharpe ratio in the whole sample (dashed gray line).

Source: See the text.

RELATIVE PERFORMANCE PER ASSET CLASS

The previous section showed that the wealthiest tended to invest more in equity and international assets, notably public bonds issued by foreign governments. Can these differences in portfolio profiles explain why the wealthiest were able to generate greater Sharpe ratios?

Table 9 shows the weighted average annual performance over the period 1908–1912 for the three main asset classes, namely equity (corporate shares), corporate bonds, and public bonds. ^{Footnote 42} Capital gains are measured as $${C_t} = \frac{{{p_t} - {p_{t - 1}}}}{{{p_{t - 1}}}}$$ , with p _t the price at time t, and yield is measured as $${y_t} = \frac{{{d_t}}}{{{p_{t - 1}}}}$$ , with d _t the dividend or coupon paid in t. The maximum drawdown is computed as the largest downside move between any two data points over the period 1908–1912.

Table 9 ANNUALIZED PERFORMANCE (IN PERCENT) BY ASSET CLASS (1908–1912)

Notes: This table shows the average annual performance for each asset class (equity, corporate bonds, and government bonds) between 1908 and 1912. Performance is measured by the annualized returns (in percent), which is decomposed between capital gains (the change in percent in the price of the asset) and yield (which is either the dividend on shares or the coupon on bonds and not the yield to maturity). Volatility is the annualized standard deviation of returns. The maximum drawdown is the maximum loss (in percent) between two data points in the time series. The performance of each asset is assessed as a whole (“All”) and then split between those issued in France (“France”) and those issued in foreign countries (“Foreign”).

Source: See the text.

Foreign public bonds were the assets generating the greatest risk-adjusted returns. Equity was a riskier asset class in average than bonds, given its higher level of volatility and its larger drawdown, but delivered higher returns, mostly because of the bull market of that period, and possibly also reflecting a risk premium, although equity did not outperform bonds insofar as their risk-adjusted performance was similar. Consistently with LeBris (Reference LeBris2013) and Jorda et al. (Reference Jorda, Katharina Knoll, Schularick and Taylor2019), yields outperformed capital gains for bonds, but dividends underperformed capital gains for equity. Foreign assets seemed to outperform French ones, not only because public bonds outperformed French rente but also in equity, although French corporate bonds outperformed foreign ones.

Since wealthier investors held less French rente and more equity and foreign assets, this comparison between asset classes suggests that rich Parisians were looking for high-yield, risky assets. This finding is not trivial: as the age-wealth profile of investors became steeper, old and wealthy investors could have looked for relatively safe assets, consistently with the life-cycle theory. ^{Footnote 43} On the other hand, the portfolios of the richest were tilted toward the most profitable asset classes—foreign government bonds, and the riskiest ones—equities. The greater returns on equity due to the bull market of that period suggest that the portfolio performance of the wealthiest might be underestimated. Indeed, in Table 2, we showed that the reconstructed portfolios underestimated the fraction of wealth invested in equities. Since the wealthiest held relatively more equity in their portfolios, their performance is likely to be downward biased by the missing assets.

RELATIVE PERFORMANCE BY WEALTH LEVEL WITHIN ASSET CLASSES

Given the relatively low risk-adjusted returns on equity over bonds, the superior portfolio performance of wealthy investors cannot be explained by differences in portfolio profiles and inter-asset class relative performance. Table 10 confirms that the risk-adjusted returns for each asset class increased with wealth, apart from French rente, which offered a constant 3 percent return. This suggests that, within each asset class, wealthier investors were making better investment decisions, due to better stock-picking skills, information advantage, or portfolio advisers. Indeed, some stocks delivered excess returns over the long run, as shown by Le Bris, Goetzmann, and Pouget (2019) in the example of the Bazacle company, and could be adequately identified by well-informed and financially literate investors. ^{Footnote 44}

Table 10 RISK-ADJUSTED RETURNS (IN PERCENT) BY DECILE PER ASSET CLASS (1908–1912)

Notes: This table shows the average annual risk-adjusted return (in percentage) per asset class and country of issuance by decile of wealth (initial bequests) between 1908 and 1912.

Source: See the text.

ALPHA AND BETA DISTRIBUTION BY WEALTH LEVEL

Did the 1912 wealthy Parisian investors exhibit better investment skills, or was their performance mostly driven by the bull market of the late Belle-Epoque? Better investment skills would translate into greater alpha, while a higher correlation to the market would be captured by a greater beta. ^{Footnote 45}

The answer is twofold. First, top deciles largely benefited from the bull environment on the eve of WWI. Figure 8 shows the top four deciles had a positive beta to market returns, in contrast with the bottom deciles, which probably suffered from capital losses on French rentes during the period, while equities kept rallying. Second, top deciles were able to generate a positive alpha on average, which significantly differed from the alpha of the average portfolio, as shown in Figure 9. This could be explained by lighter capital constraints allowing wealthier investors to reach more optimal portfolios on a higher efficient frontier, but also by better investment skills or information advantage at a time when trading on insider information was not only possible, but also unsanctioned. Compared to the 2000s Swedish households analyzed by Bach, Calvet, and Sodini (Reference Bach, Calvet and Sodini2020), the 1912 Parisian investors also benefited from higher systematic risk, but unlike the former, generated a positive alpha on top of the market performance.

Figure 8 BETA BY WEALTH DECILE

Notes: This figure shows the average annual beta generated by wealth decile (initial bequests) between 1908 and 1912 (solid black line) with the standard error (dashed black line) and the average annual beta across the whole sample (horizontal dashed line).

Source: See the text.

Figure 9 ALPHA BY WEALTH DECILE

Notes: This figure shows the average annual alpha of the reconstructed portfolios by wealth decile (initial bequests) between 1908 and 1912 (solid black line) with the standard error (dashed black line) and the average annual alpha across the whole sample (horizontal dashed line).

Source: See the text.

RATE OF RETURN AND WEALTH TRAJECTORY

Parisians who inherited greater bequests did enjoy superior returns during the Belle-Eoque, partly favored by a bull market to which their portfolio was highly correlated, partly because of greater excess returns (alpha) on their investments. How did the superior performance of larger portfolios impact the distribution of wealth in the long run? Can we, at least partially, explain the rising wealth concentration during the Belle-Epoque with this heterogeneity in returns?

I consider a simple scenario where each decile earns its average return every year and that this return remains constant over time. I start in 1860, which is when most of the 1912 decedents became young adults, and compound their returns until 1910. Figure 10 plots the results of this simulation for the top 10 percent and the top 20 percent of investors (by initial bequests), and compares the simulation against the actual data presented by Piketty (Reference Piketty2014). Because I only consider married decedents with a reconstructed portfolio of at least 50 percent, the top decile in my table excludes some of the wealthiest individuals and therefore does not coincide with Piketty’s top decile. However, aggregating the top 20 percent gives a share of total wealth in 1860 equivalent to what Piketty estimates for the top decile of wealth. The greater returns top deciles earned on their wealth drives the concentration of wealth up throughout the period and roughly coincides with the actual rise in wealth concentration estimated by Piketty (Reference Piketty2014). It suggests that the positive correlation between wealth and returns on wealth was a significant driver of the growing wealth concentration during the Belle-Epoque.

Figure 10 EVOLUTION OF WEALTH CONCENTRATION (SIMULATION VERSUS ACTUAL) 1860–1910

Notes: This figure shows the share of the total wealth owned by the top deciles (top 10 percent and top 20 percent) of initial bequests (with the start date arbitrarily fixed to 1860) and the evolution of this share assuming the same return on wealth every year. The top decile (Piketty) data represent the actual share of the total wealth owned by the top decile as presented in Piketty (Reference Piketty2014).

Source: See the text.

I then repeat the same exercise, focusing on the top decile of inherited wealth, and consider two scenarii: one in which the top decile earns its superior returns, and one in which the top decile earns the average returns of the bottom decile during the whole period. Results are shown in Figure 11. The black line shows, as in Figure 10, that the fraction of the total wealth owned by the top decile kept growing at a rapid pace, assuming they owned every year their average returns (3.51 percent). On the other hand, assuming that the top decile earned the average returns of the bottom decile (2.96 percent), this fraction kept decreasing over time, as shown by the gray line. It suggests that heterogeneity in returns was a significant driver of the rise of wealth inequality during this period.

Figure 11 EVOLUTION OF WEALTH CONCENTRATION (SIMULATION WITH TOP AND BOTTOM DECILE AVERAGE RETURNS) 1860–1910

Notes: This figure shows the share of the total wealth owned by the top decile of initial bequests (with the start date arbitrarily fixed to 1860) and the evolution of this share, assuming the same return on wealth every year. The black line shows the evolution over time of this share, assuming the top decile earned its average return. The gray line shows the same evolution, assuming the top decile earned the average return of the bottom decile.

Source: See the text.

PORTFOLIO PERFORMANCE AND SOCIAL MOBILITY

One of the paradoxes of the Belle-Epoque was that despite following the constitution of the III Republic and Jules Ferry’s laws on free and secular education, the period was characterized by limited social mobility as the fruits of economic growth were not redistributed equally: bourgeois thrived while lower social classes stagnated or receded, as shown by Winock (Reference Winock2002). How did heterogeneity in portfolio performance explain the limited social mobility during the Belle-Epoque?

Table 11 shows the actual transition matrix from the distribution of inherited bequests to the distribution of net wealth at death in 1912. It is defined as:

(9)

Table 11 TRANSITION MATRIX BETWEEN DECILES OF INITIAL BEQUESTS AND DECILES OF NET WEALTH AT DEATH

Notes: This table shows the transition matrix for married investors, from the deciles of initial bequests (columns) to the deciles of net wealth at death (rows). For example, 19 percent of those who belonged to decile 4 of the initial bequest died in the 3rd decile of net wealth, while 9 percent of those who belonged to decile 3 of the initial bequest died in the 4th decile of net wealth.

Source: See the text.

with d _ij the number of married investors who were in the j ^th decile of initial bequests and the i ^th decile of net wealth at death, and d _j the number of married investors in the j ^th decile of initial bequests.

The transition matrix illustrates the low degree of social mobility in the table. The first 7 deciles had virtually no chance to reach the top decile, which is entirely filled with Parisians whose inheritance placed them already at the top of the wealth distribution. The first deciles seem to display some mobility, but this is due to the fact that small portfolios were very much alike, with a lot of investors starting with no bequest or tiny ones, hence the initial differences in endowments at the bottom of the wealth distribution were almost nonexistent. The low degree of social mobility can also be seen in the middle of the wealth distribution, with individuals from deciles 6, 7, and 8 rarely receding to lower deciles but also rarely making it to the top two deciles.

To estimate the impact of heterogeneous portfolio performance on social mobility, I perform a Monte Carlo simulation where, for each simulation, at each period from their marriage to their death (in 1912), investors randomly draw a return rate from the set of all possible rates of returns in the decile of initial bequests they belong to. ^{Footnote 46} Therefore, I obtain for each individual a sequence of returns, which I compound to obtain the distribution of capitalized wealth at death in 1912. For each simulation, I obtain a transition matrix that describes the transition from the deciles of initial bequests to the deciles of capitalized wealth at death, using the random sequence of returns each individual drew.

Table 12 shows the average transition matrix for 10,000 simulations. The bottom of the wealth distribution exhibits the same pattern of social mobility as in Table 11 because of the very small differences in initial endowments. However, given the huge endowments wealthy Parisians inherited, it was impossible for the bottom deciles to make their way to the top of the wealth distribution solely based on portfolio performance. Symmetrically, the probability for top deciles to recede to lower ones was near-zero because their initial endowments were so large that it would take a large underperformance versus smaller portfolios to recede to lower deciles, which was very unlikely given the superior returns the top decile enjoyed on their wealth. This simulation illustrates the analysis of Piketty (Reference Piketty2014) regarding the importance of inheritance, as the difference in initial bequests was so huge between the bottom and the top deciles that it could not be offset by portfolio performance. However, it also shows the role played by heterogeneity in portfolio performance in the growing concentration of wealth during the Belle-Epoque, as the relatively higher returns wealthy investors enjoyed on their large portfolios contributed to slowing social mobility. Indeed, the trace of the Monte Carlo simulated matrix (6.2) is larger than the trace of the actual transition matrix (3.2), which suggests that social mobility implied by portfolio performance was less important than actual social mobility. ^{Footnote 47} If we compare the 9th and 10th deciles in the bottom right corner between the two transition matrices, we can see that fewer investors receded to lower deciles in the Monte Carlo simulated matrix, which also suggests that portfolio performance alone was a significant driver of wealth concentration during the Belle-Epoque.

Table 12 MONTE CARLO SIMULATED TRANSITION MATRIX BETWEEN DECILES OF INITIAL AND FINAL BEQUESTS

Notes: This table shows the transition matrix for married investors, from the deciles of initial bequests to the deciles of final wealth simulated by a Monte Carlo with n=10,000.

Source: See the text.