- Email: [email protected]
All their eggs in one basket: Portfolio diversification of US households
JOURNALOF Journal of Economic Behavior and Oraanization
ELSBVIER
Vol. 27 (1995) 87-96
Economicl3ehavior & Okganization
-
All their eggs in one basket: Portfolio diversification of US households Morgan Kelly Department of Economics, Uris Hall, Cornell University, Ithaca, NY 14853, USA
Received 16 June 1993; revised 21 October 1994
Abstract This paper uses data from the Survey of Consumer Finances to assess how mean-variance efficiency describes the portfolio diversification of US households. It not seem to work well. The median stockholder owns a single publicly traded stock, in the company where he works. Looking at a sample of high income households
well does often
who accounted for one third of all publicly traded stock, the median holding is only ten stocks. Indirect stock ownership through mutual funds, defined contribution pension plans, IRA’s and trust funds is shown to have little power in explaining this poor diversification. Keywords: Portfolio diversification JEL classification:
Gil;
G14
1. Introduction
If finance textbooks are to be believed, investors hold an equally weighted portfolio of twenty or more stocks. By doing so they eliminate the idiosyncratic risk of individual stocks and face only undiversifiable risk, equal to the average covariance of returns of the portfolio. Such mean-variance efficiency represents one of the most basic forms of economic rationality and is the basis of asset return models such as CAPM and APT. The purpose of this paper is simply to see how well diversified are US 0167-2681/95/$09.50 0 1995 Elsevier Science B.V. All rights reserved SSDI 0167-2681(95)00006-2
88
M. Kelly/J.
of Economic Behavior & Org. 27 (1995) 87-96
households in reality, by using data from the 1983 Survey of Consumer Finances. ’ This contains detailed information on the asset holdings of a representative sample of 3665 households. It also contains a sample of 438 households in the top two percentiles of the income distribution. Portfolio diversification to eliminate idiosyncratic risk does not seem to describe the behavior of US households very well. The median US stockholder holds a single publicly traded stock. In violation of the consumption capital asset pricing model, this stock is very often in the company where the individual works. Of the 632 stockholders in the regular sample, only 35 held ten or more stocks, and only 11 of these held twenty or more. Cost of diversification does not seem an adequate explanation: three quarters of the households in the top quintile of stock ownership had fewer than ten different stocks. If we omit stock in the companies where the household members work on the grounds that many individuals get stock as a gift from their employers, while some hold stock for purposes of corporate control; the median holding rises to two. Counting the number of stocks owned directly clearly neglects indirect stock holdings through mutual funds, IRA’s, defined contribution pension plans or trust funds. If we omit individuals with such indirect holdings, the median stock holding rises; but only to two. In a regression explaining diversification of all stockholders these indirect ownership variables are all insignificant. These findings are in keeping with the pioneering studies of Blume and Friend (1975, 1978) who used data from the 1960’s. It might be argued that this finding is of little importance for the functioning of actual markets. Stock ownership is intensely concentrated and the individuals surveyed are mostly small players: median stock holding is only $3,800, and the median number of trades in the previous year was zero. However, the 1983 survey contains a sample of individuals with income in excess of $100,000: the top two percentiles of the population. The median individual in this sample had financial assets of $0.75 million, public stock holdings of $0.2 million, and traded stock five times in the previous year. These two percentiles accounted for 50 per cent of publicly traded stock owned by private individuals (Avery et al., 1984). In this period, private individuals owned 65 per cent of all stock (Shiller, 1984) so these individuals owned one third of the market. Such a high income sample was unavailable in earlier studies. Among this high income group, the median number of stocks held was only ten. This figure is unchanged if holdings of stock in the individual’s own company are omitted, and if the sample is restricted to those who held no stock indirectly. Stock in companies where the household works accounted for 29 percent of stock holdings.
’ Smaller follow-up surveys were conducted in 1986 and 1989, but their accuracy that of the 1983 survey and for that reason they are not used here.
is less certain than
M. Kelly/J.
of Economic Behavior & Org. 27 (1995) 87-96
89
There are two problems with using the number of stocks held as a measure of diversification. First, if the individual holds an unbalanced portfolio, the reduction in standard deviation is lower than it would be for a balanced portfolio, so the number of stocks held overstates diversification. On the other hand, some stocks provide more diversification than others. The survey used here provides no information on individual stocks held. However, earlier surveys indicate that most individuals hold severely unbalanced portfolios dominated by one or two stocks (Blume and Friend, 1975). Further, the performance of portfolios with few stocks was markedly inferior to portfolios with more stocks, indicating that the stocks held by individuals with few stocks did not offer better diversification than average (Blume and Friend, 1978, p. 52). As a description of investor behavior then, mean-variance efficiency does not seem to work very well. It seems perhaps that most individuals engage in stock picking in the belief, or hope, that their judgement is superior to that of the market; but that conjecture is not tested here. This poor diversification has two interesting implications which I outline briefly. First, the average return and standard deviation experienced by the most investors are very much worse than the market aggregates used in the Mehra and Prescott, 1985 equity premium puzzle would suggest. Secondly, the fall in the share of market value owned by private shareholders since the early 1980’s from nearly two thirds to less than half may be explained in part by a process of natural selection, with- well diversified institutional investors performing better than private investors employing a patently dominated strategy. Recent studies using micro data to study other aspects of stockholder behavior include Mankiw and Zeldes (1992) and Haliassos and Bertaut (1992). Arrondel and Masson (1990) find wealth to be an important factor in explaining diversification in a survey of French households. Ring and Leape (1987) study the poor diversification of households among different classes of financial asset, but do not look at number of stocks held.
2. Diversification of ordinary investors The number of publicly traded stocks held by individuals in the ordinary sample of the 1983 Survey of Consumer Finances is shown in Table 1. Each row represents one quintile of the population. Holdings vary from $3 million to $23. Two things are immediately evident. First, there is very poor diversification at all levels of stock holding. Only 36 households have ten or more stocks, and only 11 have twenty or more. Secondly, although diversification increases with portfolio size, there are many households with poor diversification despite large stock holdings. More than three quarters of the households in the top quintile hold fewer than 10 stocks.
M. Kelly/J.
90
of Economic Behauior & Org. 27 (1995) 87-96
Table 1 Ordinary sample. AI1 stock Value of Stock $
25-763 770-2,363 2,500~5,900 6,000-20,000 20,000-3M
Table 2 Ordinary
Number of Stocks 1
2-4
5-9
10-19
20+
113 97 79 51 34
12 20 40 48 32
1 8 7 22 32
0 1 0 3 21
0 0 0 2 9
sample. Exclude stocks in firms where household
works
Value of Stock $
Number of Stocks 1
2-4
5-9
10-19
20+
25-900 924-2,500 2,500-6,000 6,000-20,000 20,000-3M
71 51 34 19 7
13 24 41 42 23
1 9 10 18 27
0 1 0 4 19
0 0 0 2 8
Contrary to the intuition of consumption smoothing models that individuals should hold stock whose return has a low covariance with their own consumption, stock in the company where members of the household work accounts for 23 per cent of stock holdings. If such stock is omitted on the grounds that much of the smaller holdings represent bonuses from employers, while the larger holdings may be for reasons of corporate control, one third of the households disappear. Diversification improves, but not by much: the median holding is only two. See Table 2. Looking again at the top quintile, less than one third of the households hold ten or more stocks. It might be argued that this finding of poor diversification is a result of looking only at direct ownership of stock, and ignoring indirect holdings. Table 3 makes it evident that this is not the case. All households with mutual funds, defined Table 3 Ordinary
sample. Exclude households
Value of Stock $
25-1,000 l,OOO-2,500 2,600-6,000 6,000-15,000 15,500-1.4M
with indirect stock holdings
Number of Stocks 1
2-4
5-9
IO-19
20+
48 39 28 15 7
9 12 24 33 13
0 6 6 8 22
0 1 0 1 12
0 0 0 1 4
M. Kelly/J.
of Economic Behavior & Org. 27 (1995) 87-96
91
contribution pensions, IRA’s held with a broker, or trust funds were omitted. ’ For the 289 remaining individuals, the median stock holding is only 2 companies, and the pattern of diversification across quintiles is very similar to the case where households with indirect stock holdings are included. Table 4 shows the results of a logit regression to explain diversification. The following independent variables were used. 1. Total value of stock owned, including stock held through investment clubs. 2. The number of times during the previous year that the individual traded stock. 3. The percentage of stock in the household’s financial assets: the larger this is, the more important stock is to the individual and the better diversified he should be. 4. Age of head of household. 5. Did the head of household attend college? 6. Is the head of household a manager by occupation? 7. Is the head of household self-employed? 8. Advice from broker. This is set to one if the individual received investment advice from a broker and zero otherwise. Dummies for other sources of advice: accountants, lawyers, bankers and tax advisers; were tried and were not significant. is willing to take 9. Attitude to risk. This is set to one if the individual substantial or higher than average risk in order to earn a high return. 10. Value of whole life insurance policies as a percentage of household financial assets. Such endowment policies might be expected to proxy for lack of financial sophistication. 11. Value of term life insurance policies as a percentage of household financial assets. This is intended to measure the household’s attitude to risk and concern for the future. 12. Value of mutual funds as a percentage of household financial assets. Unfortunately no breakdown is available: this is the value of all taxable mutual funds. Equity funds compose only about one quarter of mutual funds. 13. Value of defined contribution pensions of head of household and spouse as a percentage of household financial assets. Once again, no information about the percentage of equity held in the pension plan is available. 14. Value of IRA’s and Keoghs as a percentage of household financial assets when the largest IRA is held with a broker. 15. Value of trust funds as a percentage of household financial assets. No information about trust fund composition is available.
2
The common assumption that mutual funds or other managed investments provide substantial diversification is perhaps questionable. As Robert Avery has pointed out to me, a casual glance at the year to year returns of most mutual funds indicates a variance very much greater than that of the market. Zeckhauser et al. (1991) find that simple “home made” portfolios dominate most mutual funds in terms of average return and standard deviation.
92 Table 4 Probability
M. Kelly/J.
ofEconomic Behavior & Org. 27 (1995) 87-96
of holding ten or more stocks: Ordinary
Sample
Variable
Column 1
Column 2
Column 3
Column 4
Constant
-4.84 * (0.84) 0.09 * (0.04) 0.12 * * (0.04) 2.38 * * (0.76) 0.18 (0.42) 0.67 (0.52) 0.24 (0.46) - 0.54 (0.95) 0.71 (0.45) 0.11 (0.46) -0.13 (0.09) -0.12 (0.12) 2.90 (1.85) - 0.38 (0.66) - 19.63 (19.89) 0.02 (0.40) 632 -0.147 0.28
-4.00 * * (0.83) 0.19 * * (0.07) 0.14 * * (0.05) 2.04 * (0.83) - 0.20 (0.45) 0.36 (0.54) 0.58 (0.50) - 1.27 (1.04) 0.51 (0.47) 0.01 (0.24) - 0.08 (0.09) - 0.07 (0.10) 4.07 (2.30) - 0.34
-5.18 * * (1.13) 0.22 * * (0.07) 0.16 * * (0.06) 1.98 (1.15) 0.14 (0.55) 0.45 (0.71) 0.97 (0.68) 0.22 (1.12) 0.47 (0.69) -0.92 (0.78) - 0.06 (0.09) -0.33 (0.37)
-4.56 ’ = (1.10) 0.20 * (0.09) 0.20 ’ * (0.08) 2.74 * (1.26) -0.18 (0.60) -0.45 (0.77) 1.60 * (0.83) - 0.03 (1.98) 0.90 (0.71) - 1.69 (0.94) -0.01 (0.06) -0.41 (0.46)
441 -0.104 0.41
289 - 0.133 0.39
l
Portfolio Value Number of Trades Share of Portfolio Age College Education Management
Job
Self Employed Advice from Broker Attitude to Risk Term Life Insurance Whole Life Insurance Mutual Funds Defined Contribution IRA’S
Trust Fund Number of Observations Mean log-likelihood Cragg-Uhler Pseudo-R*
(0.64) -21.46 (21.36) 0.23 (0.73) 424 -0.185 0.27
* denotes signifigance at 5% * * denotes signifigance at 1%
The households financial assets are defined as the sum of all liquid assets, bonds, stocks, mutual funds and trust funds. The dependent variable in the regressions is whether the household has ten or more stocks. The results were much the same when twenty stocks was the criterion, and when an ordered logit using the two categories was employed. The regression results are for the case where each observation is given equal weight.
M. Kelly/J.
of Economic Behauior & Org. 27 (I 995) 87-96
93
The results were very similar when Survey of Consumer Finances weights were employed. Column 1 indicates the results for all stocks, column 2 omits stocks in the firms where the household works. Only the portfolio variables: value of stock, number of trades, and proportion of financial assets in stocks; are insignificant. Personal characteristics (age, education, occupation, attitude to risk, advice from broker, life insurance) are all insignificant. The insignificance of working as a manager or being self-employed is in contrast to the older findings of Blume and Friend (1975). None of the variables for indirect stock holdings (mutual funds, IRA’s, defined contribution pensions and trusts) is significant, and the variable for mutual funds has the wrong sign. As mentioned above this may reflect measurement problems. Only for IRA’s do we have any information on the amount in equity and in this case, although the variable is insignificant, its coefficient is very large and negative. The overall explanatory power of the regressions as measured by the pseudo-R’ is low. Columns 3 and 4 report results for individuals with no indirect stock holdings, the former includes all stock holding, the latter excludes stock in companies where the household works. The overall fit of the regressions improves somewhat. Among the portfolio variables, the significance of share of financial assets held as stock falls substantially. Personal characteristics are again insignificant, except for working as a manager.
3. Diversification of the rich Although these findings about the lack of diversification among a representative sample of US households are surprising, the concentration of ownership of financial assets, and stocks in particular, means that it does not necessarily have any implications for the aggregate behavior of financial markets. For most households, their home is their only form of tangible wealth: only the very wealthy have non-negligible financial assets. In 1983 the top two percentiles of the income distribution received only 15 per cent of the income, and owned 20 per cent of the
Table 5 High income sample. All stocks Value in 000’s $
0.05-30 30-115 120-350 350-1,254 1,300-52,500
Number of stocks 1
2-4
5-9
10-19
20+
24 8 6 2 4
31 14 13 3 4
14 28 17 13 4
4 20 18 24 18
1 5 21 33 47
94
M. Kelly/J. of EconomicBehavior& Org. 27 (1995) 87-96
Table 6 High income sample. Exclude stocks in firms where household Value in 000’s $
Number of stocks 1
0.05-2s 25-100 100-300 300-962 979-25,000
works
23 6 2 0 2
2-4
5-9
10-19
20+
30 15 11 2 2
12 30 19 10 5
5 15 25 28 19
1 5 15 31 44
property. They owned, however, 30 per cent of financial assets and 40 per cent of publicly traded stock. At this time institutions owned only one third of the market. The behavior of this group is important for the behavior of financial markets. This section asks if the very rich are different from you and me, beyond the fact that they have more money. As Table 5Table 6Table 7 show, this group of large investors again shows substantial departures from mean-variance efficiency. The median number of stocks held is 10, even when stocks in the household’s own company is excluded, and when individuals owning stock indirectly are excluded. Stock in the firms where the household works accounted for more than a quarter of stock holdings. Looking at households without indirect stock holdings summarized in Table 7, the majority of the fourth quintile has fewer than 20 stocks, as has one quarter of the top quintile. Table 8 reports the results of same logits carried out earlier for the ordinary sample of households. This time the dependent variable is owning twenty or more stocks. similar patterns of significance were obtained when ten or more stocks was the criterion used. The first thing to notice is that the explanatory power of the regressions is even lower than it was for the ordinary sample. Looking at the complete sample of households in columns 1 and 2, value of stocks held is no longer significant. For the households in this sample brokerage, costs represent no barrier to diversification.
Table 7 High income sample. Exclude households Value in 000’s $
0.2-25 28.5-100 108-400 45%1,050 1,199-20,000
with indirect stock holdings
Number of stocks 1
2-4
5-9
10-19
20+
5 4 3 0 0
12 6 6 2 1
5 9 2 3 2
1 3 8 8 3
1 2 5 11 19
hf. Kelly/J. Table 8 Probability
of Economic Behavior & Org. 27 (1995) 87-96
95
of holding ten or more stocks: High Income Sample
Variable
Column 1
Column 2
Column 3
Column 4
Constant
-1.64 (1.08) 0.00 (0.05) 0.54 ’ * (0.11) 1.43 * * (0.54) 1.17 (0.71) - 0.86 (0.55) -0.44 (0.33) - 0.06 (0.44) 0.02 (0.36) -0.54 (0.30) -0.79 * * (0.28) -0.08 (0.21) - 0.30 (1.80) - 0.49 (0.83) - 2.83 (3.87) 0.06 (0.14) 377 - 0.456 0.14
- 1.61 * * (0.14) 0.05 (0.05) 0.54 * * (0.09) 0.99 * * (0.15) 1.35 * * (0.14) -0.98 * (0.14) -0.58 ** (0.14) - 0.20 (0.15) 0.01 (0.15) -0.39 ** (0.14) -0.75 * * (0.14) - 0.02 (0.14) -0.11 (0.16) -1.97 ** (0.16) -3.78 * ’ (0.16) - 0.09 (0.12) 357 - 0.443 0.15
-2.45 ’ * (0.25) 0.08 (0.07) 1.33 * (0.18) 1.08 * * (0.26) 1.27 * * (0.24) 0.03 (0.25) -0.61 (0.24) -0.52 * (0.26) -0.59 * (0.24) -0.85 * (0.25) -1.39 * * (0.22) 0.17 (0.18)
- 0.5% (1.37) 1.50 * * (0.52) 1.21 * * (0.38) - 1.23 (1.25) - 0.65 (0.62) - 0.20 (0.94) - 0.57 (0.73) -0.71 (0.88) 0.87 (0.68) - 0.80
129 - 0.387 0.24
121 - 0.337 0.31
Portfolio Value Number of Trades Share of Portfolio Age College Education Management
Job
Self Employed Advice from Broker Attitude to Risk Term Life Insurance Whole Life Insurance Mutual Funds Defined Contribution IRA’s Trust Fund Number of Observations Mean log-likelihood Cragg-Uhler Pseudo-R*
l
l
l
(0.64) -1.09 (0.45) 0.17 (0.24)
*
* denotes significance at 5% * * denotes significance at 1%
Looking at personal characteristics, many of the variables are now significant, but often with a sign opposite to what we would expect. Age is positive and significant, in keeping with Ring and Leape’s (1987) contention that individuals diversify as they age and acquire more information about the world. Risk taking has the expected negative sign, education has the wrong sign and is significant in one case, while the occupational variables have the wrong sign and, in one case
96
M. Kelly/J.
of Economic Behavior & Org. 27 (1995) 87-96
are significant. Most puzzling, holdings of term life insurance are strongly negative, but not whole life insurance, the opposite of what was expected. In contrast to the regular sample, there is evidence that indirect holdings of stock are associated with poorer diversification. Mutual fund holdings, IRA’s and defined contribution pensions are all negative, and the last two are highly significant when stock in companies where the household works are omitted. This may reflect the tendency of rich households to hold a greater share of their mutual funds and defined contribution pensions in equity, although this cannot be verified with the available data. Turning to households with no indirect stock holdings in columns 3 and 4, explanatory power again rises somewhat. Portfolio value is more significant, but the share of stocks in the household portfolio becomes strongly negative when own company stock is omitted. The patterns of significance of household characteristics are broadly similar to the results in columns 1 and 2.
Acknowledgements I would like to thank Robert Avery, Michael Haliassos, referee for helpful comments. All errors are mine.
and an anonymous
References Arrondel, Luc and Andre Masson (1990): Hypothese du cycle de Vie, Diversification et Composition du Patrimoine: France, 1986. Annales d’ Economic et de Statistique, 17, l-45. Avery, Robert, Gregory Elliehausen, Glenn Canner and Thomas Gustafson (1984) Survey of Consumer Finances, 1983. Federal Reserve Bulletin, 679-692. Blume, Marshall and Irwin Friend (1975) The Asset Structure of Individual Portfolios and Some Implications for Utility Theory. Journal of Finance, 30, 58.5-603. Blume, Marshall and Irwin Friend (1978) The Changing Role of the Individual Investor, New York: Wiley. Haliassos, Michael and Carol Bertaut (1992) Why Do So Few Hold Stocks? Working paper, University of Maryland. Ring, Mervyn and Jonathan Leape (1987) Asset Accumulation, Information, and the Life Cycle. Journal of Financial Economics, 29, 97-112. Mehra, Rajnish and Edward Prescott (1985) The Equity Premium: A Puzzle. Journal of Monetary Economics, 15, 145-161. Shiller, Robert (1984) Stock Prices and Social Dynamics. Brookings Papers on Economic Activity 2, 457-498. Zeckhauser, Richard, Jayendu Pate1 and Darryl1 Hendricks (1991) Nonrational Actors and Financial Market Behavior. NBER Working Paper 3731.
ELSBVIER
Vol. 27 (1995) 87-96
Economicl3ehavior & Okganization
-
All their eggs in one basket: Portfolio diversification of US households Morgan Kelly Department of Economics, Uris Hall, Cornell University, Ithaca, NY 14853, USA
Received 16 June 1993; revised 21 October 1994
Abstract This paper uses data from the Survey of Consumer Finances to assess how mean-variance efficiency describes the portfolio diversification of US households. It not seem to work well. The median stockholder owns a single publicly traded stock, in the company where he works. Looking at a sample of high income households
well does often
who accounted for one third of all publicly traded stock, the median holding is only ten stocks. Indirect stock ownership through mutual funds, defined contribution pension plans, IRA’s and trust funds is shown to have little power in explaining this poor diversification. Keywords: Portfolio diversification JEL classification:
Gil;
G14
1. Introduction
If finance textbooks are to be believed, investors hold an equally weighted portfolio of twenty or more stocks. By doing so they eliminate the idiosyncratic risk of individual stocks and face only undiversifiable risk, equal to the average covariance of returns of the portfolio. Such mean-variance efficiency represents one of the most basic forms of economic rationality and is the basis of asset return models such as CAPM and APT. The purpose of this paper is simply to see how well diversified are US 0167-2681/95/$09.50 0 1995 Elsevier Science B.V. All rights reserved SSDI 0167-2681(95)00006-2
88
M. Kelly/J.
of Economic Behavior & Org. 27 (1995) 87-96
households in reality, by using data from the 1983 Survey of Consumer Finances. ’ This contains detailed information on the asset holdings of a representative sample of 3665 households. It also contains a sample of 438 households in the top two percentiles of the income distribution. Portfolio diversification to eliminate idiosyncratic risk does not seem to describe the behavior of US households very well. The median US stockholder holds a single publicly traded stock. In violation of the consumption capital asset pricing model, this stock is very often in the company where the individual works. Of the 632 stockholders in the regular sample, only 35 held ten or more stocks, and only 11 of these held twenty or more. Cost of diversification does not seem an adequate explanation: three quarters of the households in the top quintile of stock ownership had fewer than ten different stocks. If we omit stock in the companies where the household members work on the grounds that many individuals get stock as a gift from their employers, while some hold stock for purposes of corporate control; the median holding rises to two. Counting the number of stocks owned directly clearly neglects indirect stock holdings through mutual funds, IRA’s, defined contribution pension plans or trust funds. If we omit individuals with such indirect holdings, the median stock holding rises; but only to two. In a regression explaining diversification of all stockholders these indirect ownership variables are all insignificant. These findings are in keeping with the pioneering studies of Blume and Friend (1975, 1978) who used data from the 1960’s. It might be argued that this finding is of little importance for the functioning of actual markets. Stock ownership is intensely concentrated and the individuals surveyed are mostly small players: median stock holding is only $3,800, and the median number of trades in the previous year was zero. However, the 1983 survey contains a sample of individuals with income in excess of $100,000: the top two percentiles of the population. The median individual in this sample had financial assets of $0.75 million, public stock holdings of $0.2 million, and traded stock five times in the previous year. These two percentiles accounted for 50 per cent of publicly traded stock owned by private individuals (Avery et al., 1984). In this period, private individuals owned 65 per cent of all stock (Shiller, 1984) so these individuals owned one third of the market. Such a high income sample was unavailable in earlier studies. Among this high income group, the median number of stocks held was only ten. This figure is unchanged if holdings of stock in the individual’s own company are omitted, and if the sample is restricted to those who held no stock indirectly. Stock in companies where the household works accounted for 29 percent of stock holdings.
’ Smaller follow-up surveys were conducted in 1986 and 1989, but their accuracy that of the 1983 survey and for that reason they are not used here.
is less certain than
M. Kelly/J.
of Economic Behavior & Org. 27 (1995) 87-96
89
There are two problems with using the number of stocks held as a measure of diversification. First, if the individual holds an unbalanced portfolio, the reduction in standard deviation is lower than it would be for a balanced portfolio, so the number of stocks held overstates diversification. On the other hand, some stocks provide more diversification than others. The survey used here provides no information on individual stocks held. However, earlier surveys indicate that most individuals hold severely unbalanced portfolios dominated by one or two stocks (Blume and Friend, 1975). Further, the performance of portfolios with few stocks was markedly inferior to portfolios with more stocks, indicating that the stocks held by individuals with few stocks did not offer better diversification than average (Blume and Friend, 1978, p. 52). As a description of investor behavior then, mean-variance efficiency does not seem to work very well. It seems perhaps that most individuals engage in stock picking in the belief, or hope, that their judgement is superior to that of the market; but that conjecture is not tested here. This poor diversification has two interesting implications which I outline briefly. First, the average return and standard deviation experienced by the most investors are very much worse than the market aggregates used in the Mehra and Prescott, 1985 equity premium puzzle would suggest. Secondly, the fall in the share of market value owned by private shareholders since the early 1980’s from nearly two thirds to less than half may be explained in part by a process of natural selection, with- well diversified institutional investors performing better than private investors employing a patently dominated strategy. Recent studies using micro data to study other aspects of stockholder behavior include Mankiw and Zeldes (1992) and Haliassos and Bertaut (1992). Arrondel and Masson (1990) find wealth to be an important factor in explaining diversification in a survey of French households. Ring and Leape (1987) study the poor diversification of households among different classes of financial asset, but do not look at number of stocks held.
2. Diversification of ordinary investors The number of publicly traded stocks held by individuals in the ordinary sample of the 1983 Survey of Consumer Finances is shown in Table 1. Each row represents one quintile of the population. Holdings vary from $3 million to $23. Two things are immediately evident. First, there is very poor diversification at all levels of stock holding. Only 36 households have ten or more stocks, and only 11 have twenty or more. Secondly, although diversification increases with portfolio size, there are many households with poor diversification despite large stock holdings. More than three quarters of the households in the top quintile hold fewer than 10 stocks.
M. Kelly/J.
90
of Economic Behauior & Org. 27 (1995) 87-96
Table 1 Ordinary sample. AI1 stock Value of Stock $
25-763 770-2,363 2,500~5,900 6,000-20,000 20,000-3M
Table 2 Ordinary
Number of Stocks 1
2-4
5-9
10-19
20+
113 97 79 51 34
12 20 40 48 32
1 8 7 22 32
0 1 0 3 21
0 0 0 2 9
sample. Exclude stocks in firms where household
works
Value of Stock $
Number of Stocks 1
2-4
5-9
10-19
20+
25-900 924-2,500 2,500-6,000 6,000-20,000 20,000-3M
71 51 34 19 7
13 24 41 42 23
1 9 10 18 27
0 1 0 4 19
0 0 0 2 8
Contrary to the intuition of consumption smoothing models that individuals should hold stock whose return has a low covariance with their own consumption, stock in the company where members of the household work accounts for 23 per cent of stock holdings. If such stock is omitted on the grounds that much of the smaller holdings represent bonuses from employers, while the larger holdings may be for reasons of corporate control, one third of the households disappear. Diversification improves, but not by much: the median holding is only two. See Table 2. Looking again at the top quintile, less than one third of the households hold ten or more stocks. It might be argued that this finding of poor diversification is a result of looking only at direct ownership of stock, and ignoring indirect holdings. Table 3 makes it evident that this is not the case. All households with mutual funds, defined Table 3 Ordinary
sample. Exclude households
Value of Stock $
25-1,000 l,OOO-2,500 2,600-6,000 6,000-15,000 15,500-1.4M
with indirect stock holdings
Number of Stocks 1
2-4
5-9
IO-19
20+
48 39 28 15 7
9 12 24 33 13
0 6 6 8 22
0 1 0 1 12
0 0 0 1 4
M. Kelly/J.
of Economic Behavior & Org. 27 (1995) 87-96
91
contribution pensions, IRA’s held with a broker, or trust funds were omitted. ’ For the 289 remaining individuals, the median stock holding is only 2 companies, and the pattern of diversification across quintiles is very similar to the case where households with indirect stock holdings are included. Table 4 shows the results of a logit regression to explain diversification. The following independent variables were used. 1. Total value of stock owned, including stock held through investment clubs. 2. The number of times during the previous year that the individual traded stock. 3. The percentage of stock in the household’s financial assets: the larger this is, the more important stock is to the individual and the better diversified he should be. 4. Age of head of household. 5. Did the head of household attend college? 6. Is the head of household a manager by occupation? 7. Is the head of household self-employed? 8. Advice from broker. This is set to one if the individual received investment advice from a broker and zero otherwise. Dummies for other sources of advice: accountants, lawyers, bankers and tax advisers; were tried and were not significant. is willing to take 9. Attitude to risk. This is set to one if the individual substantial or higher than average risk in order to earn a high return. 10. Value of whole life insurance policies as a percentage of household financial assets. Such endowment policies might be expected to proxy for lack of financial sophistication. 11. Value of term life insurance policies as a percentage of household financial assets. This is intended to measure the household’s attitude to risk and concern for the future. 12. Value of mutual funds as a percentage of household financial assets. Unfortunately no breakdown is available: this is the value of all taxable mutual funds. Equity funds compose only about one quarter of mutual funds. 13. Value of defined contribution pensions of head of household and spouse as a percentage of household financial assets. Once again, no information about the percentage of equity held in the pension plan is available. 14. Value of IRA’s and Keoghs as a percentage of household financial assets when the largest IRA is held with a broker. 15. Value of trust funds as a percentage of household financial assets. No information about trust fund composition is available.
2
The common assumption that mutual funds or other managed investments provide substantial diversification is perhaps questionable. As Robert Avery has pointed out to me, a casual glance at the year to year returns of most mutual funds indicates a variance very much greater than that of the market. Zeckhauser et al. (1991) find that simple “home made” portfolios dominate most mutual funds in terms of average return and standard deviation.
92 Table 4 Probability
M. Kelly/J.
ofEconomic Behavior & Org. 27 (1995) 87-96
of holding ten or more stocks: Ordinary
Sample
Variable
Column 1
Column 2
Column 3
Column 4
Constant
-4.84 * (0.84) 0.09 * (0.04) 0.12 * * (0.04) 2.38 * * (0.76) 0.18 (0.42) 0.67 (0.52) 0.24 (0.46) - 0.54 (0.95) 0.71 (0.45) 0.11 (0.46) -0.13 (0.09) -0.12 (0.12) 2.90 (1.85) - 0.38 (0.66) - 19.63 (19.89) 0.02 (0.40) 632 -0.147 0.28
-4.00 * * (0.83) 0.19 * * (0.07) 0.14 * * (0.05) 2.04 * (0.83) - 0.20 (0.45) 0.36 (0.54) 0.58 (0.50) - 1.27 (1.04) 0.51 (0.47) 0.01 (0.24) - 0.08 (0.09) - 0.07 (0.10) 4.07 (2.30) - 0.34
-5.18 * * (1.13) 0.22 * * (0.07) 0.16 * * (0.06) 1.98 (1.15) 0.14 (0.55) 0.45 (0.71) 0.97 (0.68) 0.22 (1.12) 0.47 (0.69) -0.92 (0.78) - 0.06 (0.09) -0.33 (0.37)
-4.56 ’ = (1.10) 0.20 * (0.09) 0.20 ’ * (0.08) 2.74 * (1.26) -0.18 (0.60) -0.45 (0.77) 1.60 * (0.83) - 0.03 (1.98) 0.90 (0.71) - 1.69 (0.94) -0.01 (0.06) -0.41 (0.46)
441 -0.104 0.41
289 - 0.133 0.39
l
Portfolio Value Number of Trades Share of Portfolio Age College Education Management
Job
Self Employed Advice from Broker Attitude to Risk Term Life Insurance Whole Life Insurance Mutual Funds Defined Contribution IRA’S
Trust Fund Number of Observations Mean log-likelihood Cragg-Uhler Pseudo-R*
(0.64) -21.46 (21.36) 0.23 (0.73) 424 -0.185 0.27
* denotes signifigance at 5% * * denotes signifigance at 1%
The households financial assets are defined as the sum of all liquid assets, bonds, stocks, mutual funds and trust funds. The dependent variable in the regressions is whether the household has ten or more stocks. The results were much the same when twenty stocks was the criterion, and when an ordered logit using the two categories was employed. The regression results are for the case where each observation is given equal weight.
M. Kelly/J.
of Economic Behauior & Org. 27 (I 995) 87-96
93
The results were very similar when Survey of Consumer Finances weights were employed. Column 1 indicates the results for all stocks, column 2 omits stocks in the firms where the household works. Only the portfolio variables: value of stock, number of trades, and proportion of financial assets in stocks; are insignificant. Personal characteristics (age, education, occupation, attitude to risk, advice from broker, life insurance) are all insignificant. The insignificance of working as a manager or being self-employed is in contrast to the older findings of Blume and Friend (1975). None of the variables for indirect stock holdings (mutual funds, IRA’s, defined contribution pensions and trusts) is significant, and the variable for mutual funds has the wrong sign. As mentioned above this may reflect measurement problems. Only for IRA’s do we have any information on the amount in equity and in this case, although the variable is insignificant, its coefficient is very large and negative. The overall explanatory power of the regressions as measured by the pseudo-R’ is low. Columns 3 and 4 report results for individuals with no indirect stock holdings, the former includes all stock holding, the latter excludes stock in companies where the household works. The overall fit of the regressions improves somewhat. Among the portfolio variables, the significance of share of financial assets held as stock falls substantially. Personal characteristics are again insignificant, except for working as a manager.
3. Diversification of the rich Although these findings about the lack of diversification among a representative sample of US households are surprising, the concentration of ownership of financial assets, and stocks in particular, means that it does not necessarily have any implications for the aggregate behavior of financial markets. For most households, their home is their only form of tangible wealth: only the very wealthy have non-negligible financial assets. In 1983 the top two percentiles of the income distribution received only 15 per cent of the income, and owned 20 per cent of the
Table 5 High income sample. All stocks Value in 000’s $
0.05-30 30-115 120-350 350-1,254 1,300-52,500
Number of stocks 1
2-4
5-9
10-19
20+
24 8 6 2 4
31 14 13 3 4
14 28 17 13 4
4 20 18 24 18
1 5 21 33 47
94
M. Kelly/J. of EconomicBehavior& Org. 27 (1995) 87-96
Table 6 High income sample. Exclude stocks in firms where household Value in 000’s $
Number of stocks 1
0.05-2s 25-100 100-300 300-962 979-25,000
works
23 6 2 0 2
2-4
5-9
10-19
20+
30 15 11 2 2
12 30 19 10 5
5 15 25 28 19
1 5 15 31 44
property. They owned, however, 30 per cent of financial assets and 40 per cent of publicly traded stock. At this time institutions owned only one third of the market. The behavior of this group is important for the behavior of financial markets. This section asks if the very rich are different from you and me, beyond the fact that they have more money. As Table 5Table 6Table 7 show, this group of large investors again shows substantial departures from mean-variance efficiency. The median number of stocks held is 10, even when stocks in the household’s own company is excluded, and when individuals owning stock indirectly are excluded. Stock in the firms where the household works accounted for more than a quarter of stock holdings. Looking at households without indirect stock holdings summarized in Table 7, the majority of the fourth quintile has fewer than 20 stocks, as has one quarter of the top quintile. Table 8 reports the results of same logits carried out earlier for the ordinary sample of households. This time the dependent variable is owning twenty or more stocks. similar patterns of significance were obtained when ten or more stocks was the criterion used. The first thing to notice is that the explanatory power of the regressions is even lower than it was for the ordinary sample. Looking at the complete sample of households in columns 1 and 2, value of stocks held is no longer significant. For the households in this sample brokerage, costs represent no barrier to diversification.
Table 7 High income sample. Exclude households Value in 000’s $
0.2-25 28.5-100 108-400 45%1,050 1,199-20,000
with indirect stock holdings
Number of stocks 1
2-4
5-9
10-19
20+
5 4 3 0 0
12 6 6 2 1
5 9 2 3 2
1 3 8 8 3
1 2 5 11 19
hf. Kelly/J. Table 8 Probability
of Economic Behavior & Org. 27 (1995) 87-96
95
of holding ten or more stocks: High Income Sample
Variable
Column 1
Column 2
Column 3
Column 4
Constant
-1.64 (1.08) 0.00 (0.05) 0.54 ’ * (0.11) 1.43 * * (0.54) 1.17 (0.71) - 0.86 (0.55) -0.44 (0.33) - 0.06 (0.44) 0.02 (0.36) -0.54 (0.30) -0.79 * * (0.28) -0.08 (0.21) - 0.30 (1.80) - 0.49 (0.83) - 2.83 (3.87) 0.06 (0.14) 377 - 0.456 0.14
- 1.61 * * (0.14) 0.05 (0.05) 0.54 * * (0.09) 0.99 * * (0.15) 1.35 * * (0.14) -0.98 * (0.14) -0.58 ** (0.14) - 0.20 (0.15) 0.01 (0.15) -0.39 ** (0.14) -0.75 * * (0.14) - 0.02 (0.14) -0.11 (0.16) -1.97 ** (0.16) -3.78 * ’ (0.16) - 0.09 (0.12) 357 - 0.443 0.15
-2.45 ’ * (0.25) 0.08 (0.07) 1.33 * (0.18) 1.08 * * (0.26) 1.27 * * (0.24) 0.03 (0.25) -0.61 (0.24) -0.52 * (0.26) -0.59 * (0.24) -0.85 * (0.25) -1.39 * * (0.22) 0.17 (0.18)
- 0.5% (1.37) 1.50 * * (0.52) 1.21 * * (0.38) - 1.23 (1.25) - 0.65 (0.62) - 0.20 (0.94) - 0.57 (0.73) -0.71 (0.88) 0.87 (0.68) - 0.80
129 - 0.387 0.24
121 - 0.337 0.31
Portfolio Value Number of Trades Share of Portfolio Age College Education Management
Job
Self Employed Advice from Broker Attitude to Risk Term Life Insurance Whole Life Insurance Mutual Funds Defined Contribution IRA’s Trust Fund Number of Observations Mean log-likelihood Cragg-Uhler Pseudo-R*
l
l
l
(0.64) -1.09 (0.45) 0.17 (0.24)
*
* denotes significance at 5% * * denotes significance at 1%
Looking at personal characteristics, many of the variables are now significant, but often with a sign opposite to what we would expect. Age is positive and significant, in keeping with Ring and Leape’s (1987) contention that individuals diversify as they age and acquire more information about the world. Risk taking has the expected negative sign, education has the wrong sign and is significant in one case, while the occupational variables have the wrong sign and, in one case
96
M. Kelly/J.
of Economic Behavior & Org. 27 (1995) 87-96
are significant. Most puzzling, holdings of term life insurance are strongly negative, but not whole life insurance, the opposite of what was expected. In contrast to the regular sample, there is evidence that indirect holdings of stock are associated with poorer diversification. Mutual fund holdings, IRA’s and defined contribution pensions are all negative, and the last two are highly significant when stock in companies where the household works are omitted. This may reflect the tendency of rich households to hold a greater share of their mutual funds and defined contribution pensions in equity, although this cannot be verified with the available data. Turning to households with no indirect stock holdings in columns 3 and 4, explanatory power again rises somewhat. Portfolio value is more significant, but the share of stocks in the household portfolio becomes strongly negative when own company stock is omitted. The patterns of significance of household characteristics are broadly similar to the results in columns 1 and 2.
Acknowledgements I would like to thank Robert Avery, Michael Haliassos, referee for helpful comments. All errors are mine.
and an anonymous
References Arrondel, Luc and Andre Masson (1990): Hypothese du cycle de Vie, Diversification et Composition du Patrimoine: France, 1986. Annales d’ Economic et de Statistique, 17, l-45. Avery, Robert, Gregory Elliehausen, Glenn Canner and Thomas Gustafson (1984) Survey of Consumer Finances, 1983. Federal Reserve Bulletin, 679-692. Blume, Marshall and Irwin Friend (1975) The Asset Structure of Individual Portfolios and Some Implications for Utility Theory. Journal of Finance, 30, 58.5-603. Blume, Marshall and Irwin Friend (1978) The Changing Role of the Individual Investor, New York: Wiley. Haliassos, Michael and Carol Bertaut (1992) Why Do So Few Hold Stocks? Working paper, University of Maryland. Ring, Mervyn and Jonathan Leape (1987) Asset Accumulation, Information, and the Life Cycle. Journal of Financial Economics, 29, 97-112. Mehra, Rajnish and Edward Prescott (1985) The Equity Premium: A Puzzle. Journal of Monetary Economics, 15, 145-161. Shiller, Robert (1984) Stock Prices and Social Dynamics. Brookings Papers on Economic Activity 2, 457-498. Zeckhauser, Richard, Jayendu Pate1 and Darryl1 Hendricks (1991) Nonrational Actors and Financial Market Behavior. NBER Working Paper 3731.