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The impact of retirement wealth upon portfolio composition of individuals
NOKI’H-HOILAND
The Impact of Retirement Wealth upon Portfolio Composition of Individuals James A. Ligon
This study uses time series data to consider the effect of retirement wealth upon individuals’ portfolio composition. When home equity is regarded as retirement wealth or a consumption good, retirement wealth is negatively correlated with the percentage of intermediate-term bonds, long-term bonds, and equities in individual portfolios. The relationship remains significant for long-term bonds and equities when individuals’ holdings are regressed on retirement wealth and other macroeconomic variables. A similar but less significant relationship exists when home equity is regarded as a financial asset. Elasticity estimates for these assets suggest changes in retirement wealth can have significant impact on individual portfolio holdings.
I. Introduction Given that Social Security is not a perfect substitute for other assets, participation is generally mandatory, and benefits are not marketable, it is likely that changes in expected Social Security benefits would affect optimum portfolio choices among other assets. Private pension wealth may also impact portfolio choice because of similar, although not identical, characteristics. This microeconomic impact has macroeconomic implications through financial outcomes (e.g., interest rate and term structure determination) and real outcomes (e.g., corporate investment). Understanding these implications is clearly important for policy purposes. While the literature regarding the effect of Social Security and private pensions upon the overall level of saving by individuals in the United States is extensive, there have been very few studies of the effects of Social Security and private pension wealth upon the composition of individual household portfolios.’ Two econometric studies, Dicks-Mireaux and King (1982) and Hubbard (19851, have considered the impact of retirement wealth upon portfolio composition using cross sectional data. Both studies found Social Security to impact individual portfolio
Department of Economics, Finance and Legal Studies, The University of Alabama, Tuscaloosa, Alabama 35487. Address reprint requests to Dr. James A. Ligon, Department of Economics, Finance and Legal Studies, The University of Alabama, P.O. Box 870224, Tuscaloosa, Alabama 35487-0224. ‘See Feldstein (1974) for an exposition of the basic theoretical issues regarding the impact of Social Security on overall savings levels, Esposito (1978) for a review of and citations and Hubbard (1987) for an excellent bibliography of more recent work. Journal of Economics and Business @ 1995 Temple University
1995; 47:303-316
to pre-1978
literature,
0148-6195/95,‘$09.50 SSDI 0148-6195(95)00014-I
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J . A . Ligon
choice, but differed with respect to type of and manner in which particular assets were affected.2 The present study contributes to our knowledge of portfolio composition effects of Social Security and pension wealth [hereafter, retirement wealth (RW)] by using time series data. The study considers the correlation over time between retirement wealth and other financial assets held by households. Examination of the partial correlations between retirement wealth and the shares of certain financial assets held in the individual's discretionary portfolio reveals strong correlations between retirement wealth and certain assets. The relationship between retirement wealth and these assets is then examined more closely by considering the relative explanatory power of retirement wealth versus a set of other predictors. The next section discusses how nondiversifiable mandatory Social Security may impact individual portfolio composition. Section 1II describes the data, defines the variables analyzed, and considers the partial correlations between retirement wealth and certain financial assets. Section IV examines more closely the relationship between retirement wealth and those financial assets with which it is most closely correlated. Section V summarizes and concludes the study.
II. Potential Impact of Retirement Wealth The study seeks to examine actual portfolio effects that retirement wealth may produce. Since the analysis is positive, rather than normative, in nature, we do not assume perfect capital markets. The capital market imperfections with the most potential impact on the analysis are that assets are not infinitely divisible, transaction costs are significantly greater than zero, and borrowing is constrained. These imperfections significantly influence behavior because most individuals are relatively small investors with little or no market power. These factors may influence individual portfolio construction by forcing individuals to balance risk minimization (for a given expected return) with transaction cost minimization. Since borrowing is constrained, individuals must also insure that the timing of portfolio cash flows meets portfolio objectives. The objective of individual portfolio management is assumed to be the satisfaction of future consumption needs. This may include the desire to make bequests as a final form of consumption. Some of these consumption needs may have well defined horizons, e.g., a new car, a college education for a child, or retirement income. Immunization is a well recognized duration-ba~d strategy for reducing the risk that future cash-flow obligations (e.g., savings objectives) will not be met.3 If Using Canadian data, Dicks-Mircaux and King (1982) found that Social Security wealth decreased the likelihood of ownership of deposits, bonds, and home equity and increased the likelihood of car ownership, while private pension wealth increased thc likelihood of ownership of deposits, bonds, cash, stocks, car, and home cquity. They found little impact on the amount held given that the asset was owned. Using U.S. data, Hubbard (1985) found that Social Security reduced the likelihood of annuity ownership and increased the likclihotnl of car ownership and home equity, while private pension wealth had positive impact on the likelihood of stock, savings bond, and car ownership. In contrast to Dicks-Mircaux and King, Hubbard also lk)und Social Security increased the demand for deposits, bonds, cars, and savings bonds, given ownership, and decreased the demand tk)r stocks, annuities, and home cquity, given ownership, while private pensions had little effect on demand givcn ownership. 3Scc Fabozzi (1993), for cxamplc. Fong and Vasicck (1984) show that focused immunization strategies provide greater risk reduction than barbell-type strategies. Although frequently applied in fixcd income contexts, Bostock, Wcn)lley, and Duffy (1989) show duration-based strategies can bc uscfut for determining the appropriate bond-equity mix in pension fund portfolios.
Retirement Wealth and Portfolio Composition
305
constraints on borrowing exist and transactions costs are high, individual investors may pursue such duration matching strategies because they do not view securities of differing durations as perfect substitutes. Thus, some degree of market segmentation or preferred habitats, where habitats are dictated by individuals' savings objectives, is likely to prevail among individual investors. Individual investors would tend to prefer short-term (long-term) assets for short-term (long-term) savings objectives. A possible implication of such behavior on portfolio composition is that increases in retirement wealth may decrease the need for private retirement saving, decreasing the need for longer duration assets in individual portfolios.
III. Partial Correlation Analyses A. The Data and Variable Definitions Data regarding expected Social Security wealth were taken from Leimer and Lesnoy (1982). Leimer and Lesnoy reexamined the results of Feldstein (1974) concentrating on Feldstein's measure of Social Security wealth. Feldstein had originally developed five measures of gross Social Security wealth and six measures of Social Security wealth net of taxes. The measures differed in the way individuals were assumed to take future benefits into account. Correcting for a computer programming error in Feldstein's original estimates, Leimer and Lesnoy reproduced the I1 measures of Social Security wealth using Feldstein's algorithm. In addition, Leimer and Lesnoy also developed their own algorithm for the l l different measures of Social Security wealth, which they contend provides better estimates of those people likely to receive benefits. Thus, there are 22 distinct measures of Social Security wealth. 4 Data for pension fund reserves, the total financial assets of households, deposits held (including checking deposits, savings deposits, time deposits, money market fund shares, and currency), U.S. Savings Bonds held, other treasury securities held, corporate equities held (including mutual fund shares and direct holdings), life insurance reserves, and home equity were taken from the Board of Governors of the Federal Reserve System, Balance Sheets for the U.S. Economy 1947-1986 (1987). ~ Assets such as investment in unincorporated businesses and miscellaneous financial assets were omitted to insure that the financial asset matrix is of full rank and because it is less likely that a causal link exists between such investments and retirement wealth. Because of limitations in the data, some of the variables involve
4Thc particular way in which the measures werc constructed does not appear relevant to the results obtained here and, accordingly, in the interest of brevity, the details of construction arc not discussed here. The 22 separate measures werc retained in the analysis primarily to test the sensitivity of the results to thc definition of Social Security wealth. For the interested reader, a detailed discussion of the various measures and their rationales is provided in Lcimer and Lesnoy (1982), pp. 611-614. Since the measures of Social Security wealth presented by Lcimcr and Lcsm)y were expressed in terms of 1972 dollars, the Social Security wealth variable was first adjusted to the nominal dollars for the year in question using the consumer price index befc~re calculating the ratio variable actually used in this analysis. SPension fund reserves were used to estimate the value of private pension wealth. The amount of treasury securities of each maturity held by households was estimated by multiplying the total treasury securities held by households times the percentage of such securities of each maturity class held by "other private investors." ttomc equity was computed by adding the values of owner-occupied structures and owncr-oceupicd land and subtracting the value of home mortgages.
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measurement error, but the expected impact of this error is to bias the correlation and regression coefficients toward zero. The proper treatment of home equity depends upon how individuals view this asset. In one sense, home equity represents a durable consumer good that provides a flow of value. Viewed in this light, home equity could properly be omitted from a study of the effects of retirement wealth on portfolio composition. However, the real value of home equity does not generally depreciate significantly, and, for most households, its nominal value would be expected to have appreciated over the data period studied. Thus, home equity differs from other consumer durables in that it serves as a significant source of individual wealth. Given this, it might be appropriate to view home equity as simply another portfolio asset. The difficulty with this view is that most individuals probably do not view home equity as simply another portfolio asset, in that it is considerably less liquid than other forms of financial wealth. Rather, individuals may view their home equity as a store of value that may be liquidated at or during retirement to provide additional consumption. Under this view, home equity is best viewed as another form of illiquid retirement wealth, not unlike Social Security and private pension wealth. In fact, home equity probably serves all three roles for individuals. Accordingly, the analysis is conducted under three alternative assumptions regarding home equity: (1) that it is a form of illiquid retirement wealth and we should analyze the response of financial asset allocations to all three forms of illiquid retirement wealth (Social Security, private pensions, and home equity), (2) that it is not a form of illiquid retirement wealth, but rather, is just like any other asset in the financial portfolio and should be treated accordingly, and (3) that it is durable consumer good and best excluded from the analysis. Data were available for all relevant variables for the period 1947-1977. The unavailability of Social Security wealth measures for more recent dates and changes in the Federal Reserve Board's reporting procedures precluded further extension of the time series with this data set. Rather than introduce additional measurement error by attempting to extend the time series with different overlapping data sources, it was decided to use this 31 year period for the analysis. One positive externality of excluding more recent data is that the period studied allows one to observe the impact of Social Security and private pension wealth over the most significant period of growth in this form of wealth. The variables used in the analysis are listed and defined in Table 1. Because the variables in which we are interested are, in fact, ratios, many of the econometric problems associated with the use of ratios are not present. See Kuh and Meyer (1955). An additional advantage associated with using ratios is that questions of real versus nominal wealth are avoided. The use of a different denominator for retirement wealth than for the other financial wealth variables insures that no spurious correlation is introduced between retirement wealth and the other financial variables. On the other hand, correlations between the other financial variables are affected because of the common denominator used to define them. Accordingly, the analytic approach taken was a partial correlation analysis between retirement wealth and the other financial assets. The correlation of retirement wealth with each financial asset is determined, holding the effects of the other financial assets constant. [See Morrison (1983), pp. 95-104, for a discussion.] Since there are 22 different measures of Social Security wealth, there are 22 different
R e t i r e m e n t W e a l t h a n d Portfolio C o m p o s i t i o n
307
T a b l e 1. V a r i a b l e Definitions Retirement wealth
Deposits
Savings bonds Equities Life insurance Very short term bonds (M _< 1 yr.) Short term bonds (1 < M < 5) Intermediate term bonds (5 < M < 10) Long term bonds ( M > 10) Home equity
The percentage of total household financial wealth (including Social Security, private pensions, and, where applicable, home equity) held in Social Security, private pension, and, where applicable, home equity wealth The percentage of household non-retirement wealth (non-RW) financial wealth held in checking, savings, and time deposits, money market funds, and currency (non-RW financial wealth is financial wealth excluding Social Security, private pension wealth, and, where applicable, home equity) The percentage of household non-RW financial wealth held in U.S. Savings Bonds The percentage of household non-RW financial wealth held in corporate equities (including those held in mutual fund shares) The percentage of household non-RW financial wealth represented by the cash value of life insurance held The percentage of household non-RW financial wealth held in (non-savings bond) U.S. Treasury securities with maturities of l year or less The percentage of household non-RW financial wealth held in (non-savings bond) U.S. Treasury securities maturing in 1-5 years The percentage of household non-RW financial wealth held in (non-savings bond) U.S, Treasury securities maturing in 5-10 years The percentage of household non-RW financial wealth held in (non-savings bond) U.S. treasury securities maturing in more than 10 years The percentage of household non-RW financial wealth represented by the value of owner-occupied structures plus the value of owner-occupied land less the value of home mortgages. Under assumption 1, home equity is included in retirement wealth. Under assumption 2, home equity is included in non-RW financial wealth. Under assumption 3, home equity is excluded from both retirement wealth and non-RW financial wealth
measures of retirement wealth. The correlations are examined for each of these 22 different measures.
B. Results The results of the partial correlation analyses are summarized in Table 2. Summaries are presented for each of the three assumptions regarding the proper treatment of home equity: (1) as illiquid retirement wealth, (2) as a portfolio asset, and (3) as a consumption good. 6 When home equity is treated as iUiquid retirement wealth or as a consumption good, the most significant partial correlations are displayed by bonds with maturities between 5 and 10 years (intermediate-term bonds), bonds with maturities over 10 years (long-term bonds), and equities. These assets are significantly negatively correlated with retirement wealth for 22 of the retirement wealth measures (for intermediate-term bonds), 22 measures (for long-term bonds), and 18 measures (for equities) under assumption 1 and significantly negatively correlated with retirement 6The complete partial correlation analyses and the complete regression analyses discussed in the following section are available on request from the author.
T a b l e 2. P a r t i a l C o r r e l a t i o n C o e f f i c i e n t s o f A s s e t s w i t h R e t i r e m e n t W e a l t h Treasury bonds Deposits Sav. bonds
Equities
Life ins.
M<
lyr
1
5
10
M>
10
H o m e equity
Home equi~ treated asilliquidretirement wealth N u m b e r of measures where sign was No. of m e a s u r e s significant at the 5% level Avg. square of partial cor. coeff.
+
17 5
18 4
22 0
7 15
19 3
0 22
22 0
22 0
+
1 0
0 0
18 0
0 0
10 0
0 12
22 0
22 0
0.04294
0.04407
0.37469
0.04495
0.12476
0.18734
0.41121
0.38594
Home equi~ treated asponfoKo asset No. of m e a s u r e s where sign was No. of m e a s u r e s significant at the 5% level Avg. square of partial cor. coef.
-
+
1
21
-
0
+
5 0.10007
20 2 13 0 0.19837
11 11 0 4 0.07039
4 18 0 12 0.14403
12 10 4 0 0.08170
7 15 0 0 0.02192
15 7 5 0 0.10033
21 1 0 0 0.05463
5 17 0 12 0.19012
Home equi~ trea~d as a consumptiongood N u m b e r of m e a s u r e s where sign was No. of m e a s u r e s significant at 5% level Avg. square of partial cor. coef.
-
+
12 10
-
0
+
1 0.05310
18 4 5 0 0.09598
22 0 18 0 0.24092
7 15 0 3 0.06261
15 7 11 0 0.12582
2 20 0 12 0.14567
22 0 20 0 0.32017
22 0 22 0 0.29381
o
Retirement Wealth and Portfolio Composition
309
wealth for 20, 22, and 18 measures (respectively) under assumption 3. The squared partial correlation coefficients for intermediate-term bonds, long-term bonds, and equities, respectively, are 0.41121, 0.38594, and 0.37469 under assumption 1, and 0.32017, 0.29381, and 0.24092 under assumption 3. Under assumption 2 the most significant partial correlations are between retirement wealth and savings bonds (significantly negative for 13 measures), life insurance (significantly positive for 12 measures), and home equity itself (significantly positive for 12 measures). However, perhaps the most significant impact of including home equity as a portfolio asset is to decrease the significance of the correlations between all financial assets and retirement wealth. Under assumption 2 none of the average squared partial correlation coefficients exceeds 0.2. This effect is probably attributable to the fact that including home equity in the portfolio of financial assets substantially reduces the weights of all other assets in the portfolio. The significant weight of home equity combined with the mildly positive correlation between home equity and retirement wealth tends to mask other effects. The similar patterns under assumptions 1 and 3 are perhaps unsurprising. The observed pattern is consistent with a duration-based investment strategy on the part of individual investors who substitute away from longer duration financial assets as their illiquid retirement wealth increases. As noted above, the partial correlation between home equity and (other) retirement wealth is generally positive and often significant. Thus, including home equity as retirement wealth simply increases the level of retirement wealth and reinforces the significance of the negative correlation between intermediate-term bonds, long-term bonds, and equities and retirement wealth. In order to determine whether the relationship between retirement wealth and intermediate-term bonds, long-term bonds, and equities can be explained by other economic factors, regression analyses were conducted. The results are discussed in the following section.
IV. Regression Analyses Individual holdings of certain portfolio assets appear to have significant correlation with retirement wealth. To analyze the explanatory power of retirement wealth relative to other factors affecting portfolio structure, additional explanatory variables are included with retirement wealth in a series of time series regressions. The additional variables included are the ex post real interest rate, real personal disposable income, and the percentage of the population over age 65. The real interest rate is a component of required returns on both fixed income and equity securities and, hence, could be expected to influence relative asset holdings. 7 7In a prior specification the ex ante real interest rate and expected inflation were included in the regression analyses. Expected inflation was assumed to follow a martingale process. The ex ante real rate was then the annual return on U.S. Treasury bills minus the prior period's percentage change in the c o n s u m e r price index. However, neither of these measures was significant in any of the regressions. It seems reasonable to a s s u m e that this insignificance could be attributable to the fact that the data used are annual observations and that individuals adjust their inflation expectations m u c h more quickly than annually. Lacking the data to compute monthly inflation expectations to correct this problem, another approach is simply to use the ex post real interest rate. If people adjust their inflation expectations very quickly, this measure will provide a better measure of the true "ex ante" rate than the ex ante m e a s u r e constructed from the prior year's data. That is the approach adopted here. The real rate so constructed produces results that are intuitively appealing.
310
J.A. Ligon Specifically, individuals would be expected to change the duration of their portfolio holdings with changes in the real interest rate. Individuals might be expected to lengthen duration during periods when real rates are falling and to shorten duration during periods when real rates are rising. Real disposable income measures wealth effects on portfolio choice, including changes in investor risk aversion related to wealth. The percentage of the population over 65 provides another measure of the extent to which individual investors practice duration-based portfolio management. Older people would be expected to have shorter horizons and, thus, shorter duration portfolios. The inclusion of further explanatory variables was rejected because of the small sample size. The ex post real interest rate was computed by taking the annual return on U.S. Treasury bills minus the percentage change in the consumer price index. Data regarding the return on Treasury bills and the consumer price index were taken from Ibbotson Associated, Inc.'s SBBI 1989 Yearbook. Real personal disposable income was calculated by converting personal disposable income to 1977 dollars using the consumer price index. Data regarding personal disposable income were taken from the Board of Governors of the Federal Reserve's Flow of Funds Accounts (1979). Data regarding the percentage of the population over 65 were taken from the Historical Statistics of the United States: Colonial Times to 1970 with updates from the StatisticaI Abstract of the United States 1971-1978. The percentages of non-RW financial wealth held in intermediate-term bonds, long-term bonds, and equities were then regressed on retirement wealth, the ex post real interest rate, real personal disposable income (in trillions of dollars), and the percentage of the U.S. population over age 65. Ordinary least squares estimates exhibited significant autocorrelation. The equations were reestimated to correct for this autocorrelation. Harvey (1991) refers to the correction method used as the two-step full transform method. Although this technique effectively transforms the data from a regression in levels, arguably the analysis one desires, into a regression of a function of first order first differences (for a first order autoregressive process), it was deemed preferable to other estimation techniques. 8 A first order autocorrelative process effectively removed the autocorrelation from the estimates in virtually all cases. As before, separate estimates were obtained for each of the 22 measures of retirement wealth. Tables 3 and 4 present summaries of the regression results under assumption 1 (home equity as retirement wealth) and assumption 2 (home equity as a portfolio asset), respectively. The regression results under assumption 3 (home equity as a consumption good) are omitted because they are qualitatively similar to those under assumption 1.9 Each table presents statistics for the regression of intermedi-
8In the presence of autoregression the ordinary least squares estimators are unbiased and consistent, but are neither efficient or asymptotically efficient. Also, for positive autocorrelation, such as we have here, the estimates of the variances of the ordinary least squares coefficients are downwardly biased, implying conventional confidence intervals on the coefficients are meaningless [Granger and Newbold (1974)]. Estimation of the variables as a cointegrated series, as suggested by Engle and Granger (1987) was deemed undesirable because of the poor small sample properties of these estimators. See Stock (1987) and Banerjee, et al. (1986). 9The regressions under assumption 3, where home equity is treated as a consumption good, are more similar to those presented in Table 3 than to those presented in Table 4, although significance levels are somewhat lower than those observed in Table 3. These results are available on request from the author.
0 22 0 0
22 0 0 22
0 22
22 0
R e t i r e m e n t wealth Ex post real interest rate Disp. pers. inc. Percent of pop. over age 65
22 0
0 22 0.7848
22 0
0 22
Retirement wealth Ex post real interest rate Disp. pers. inc. Percent of pop. over age 65
0 22
22 0 0.8949
22 22
0 0
R e t i r e m e n t wealth Ex post real interest rate Disp. pers. inc. Percent of pop. over age 65
Average R-square
0.3277
Average R-square
Average R-square
-
0.006202 -0.039735
22 0
0 22
-0.329805 18.97586
- 0.69546 0.166923
Average Durbin W a t s o n statistic
19 0
0 0
Equity hoMings
0 22
22 0
-0.02261 -0.01947
Average Durbin Watson statistic
18 22
0 0
Long-termbond holdings
0.0010776 -0.05039
-0.00556 0.011293
Avg. coef. value
Average D u r b i n - W a t s o n statistic
0 0
0 0
lntermediate-termbond holdings
+
+
Indep. variable
No. of m e a s u r e s where coef. was No. of meas. where coef. sig. @ 5%
T a b l e 3. S u m m a r y o f R e g r e s s i o n S t a t i s t i c s f o r D e t e r m i n a n t s o f H o l d i n g s ( H o m e e q u i t y t r e a t e d as illiquid r e t i r e m e n t w e a l t h )
1.716
0.859 0.894
1.049 2.655
1.462
-6.131 7.465
- 2.756 0.687
1.382
3.351 4.664
-2.726 - 2.603
-
-
Avg. t-stat.
O
¢:k
r-, ~r
t~
g
7~
Average R-square
Retirement wealth Ex post real interest rate Disp. pers. inc. Percent of pop. over age 65
Average R-square
Retirement wealth Ex post real interest rate Disp. pers. inc. Percent of pop. over age 65 0 22
22 0
22 0
0 22 0.7137
22 0
0 22
0.8744
22 22
0 0
0.3516
0 17
22 5
Average R-square
22 0
0 22
Retirement wealth Ex post real interest rate Disp. pers. inc. Percent of pop. over age 65
-
+
Indep. variable
0 22
0 0
Equi~holdings
19 0
0 0
Long-~rmbondholdings
0 0
0 22
In~rmed~-terrnbonds
+
0 0
4 0 0.000615 -0.01606
-0.00697 0.009757
Avg. coef. value
0.003932 -0.28173
-0.01979 -0.01680
-0.328376 17.76049
0.55886 0.131167
Average D u r b i n - W a t s o n statistic
22 0
10 0
Average D u r b i n - W a t s o n statistic
0 18
11 22
Average D u r b i n - W a t s o n statistic
-
No. of m e a s u r e s where coef. was No. of meas. where coef. sig. @ 5%
T a b l e 4. S u m m a r y o f R e g r e s s i o n S t a t i s t i c s f o r D e t e r m i n a n t s o f H o l d i n g s ( H o m e e q u i t y t r e a t e d as a p o r t f o l i o a s s e t )
1.844 0.550
1.322
2.317 2.852
- 2.204 - 2.444
1.747
1.510
- 6.090 5.520
-
1.310 2.680
0.607 - 0.285
-
Avg. t-stat.
O
Retirement Wealth and Portfolio Composition
313
ate-term bond, long-term bond, and equity holdings on retirement wealth, the real interest rate, disposable personal income, and the percentage of the population over age 65. The statistics presented include the number of retirement wealth measures where the coefficient was positive or negative, and the number of measures where this coefficient was significant at the 5% level, the average of the coefficient values and t-statistics for the 22 regressions, and the average of the R-squares and Durbin-Watson statistics for the 22 regressions. In Table 3, where home equity is regarded as retirement wealth, the only variable significantly related (all 22 measures, average t-statistic 2.655) to intermediate-term bond holdings is the ex post real interest rate. Since the two-step full transform method used essentially produces a regression on first differences, the positive relationship suggests that when real interest rates are rising, individuals increase their holdings of intermediate-term bonds. A significantly negative relationship is observed between long-term bond holdings and retirement wealth (18 measures, average t-statistic -2.726), the real interest rate (22 measures, average t-statistic -2.603), and percent of the poPulation over 65 (22 measures, average t-statistic -4.664), while disposable personal income (22 measures, average t-statistic 3.351) is significantly positively related to long-term bond holdings. The results are intuitively appealing. Rising real interest rates result in a shift from longer-term to shorter-term bonds. Long-term bonds holdings increase with income and decrease with an aging population. Increasing retirement wealth decreases long-term bond holdings. These findings are consistent with duration-based portfolio management. A significant negative relationship is observed between equity holdings and retirement wealth (19 measures, average t-statistic -2.756) and disposable personal income (22 measures, average t-statistic -6.131), while the percentage of the population over age 65 is positively related (22 measures, average t-statistic 7.465) to equity holdings. The increased holdings of equities by an increasingly aged population may be related to tax incentives. Since the cost basis of equities is stepped up to current market value at death, older individuals may be inclined to liquidate equities as a last resort. 1° Decreased holdings of equities when personal income rises may be a business cycle effect. Increases in the rate at which personal disposable income rises could occur at or after the peak of business cycle, when corporate earnings may have peaked. Thus, individuals may reduce holdings of equities at these times and increase them during troughs in the business cycle, when personal disposable income is rising slowly (or falling) and equities may appear relatively cheap. As in the case of long-term bonds, increasing retirement wealth would be expected to decrease individuals' holdings of relatively longer duration equities, which is what we observe here. In Table 4, where home equity is treated as a portfolio asset, we find a very similar relationship between holdings of each of the three financial assets and retirement wealth, the real interest rate, disposable personal income, and the percentage of the population over age 65. The explanatory variables generally retain the same signs as they did in the regressions of Table 3 and coefficient values are generally similar. The primary impact of including home equity as a
10I am
grateful to an anonymousreviewerfor this suggestion.
314
J.A. Ligon portfolio asset is to reduce the significance of the relationships between the explanatory variables and the asset holdings. For example, in the regressions on long-term bond holdings, the average t-statistics for all explanatory variables fall and the coefficient on retirement wealth is significant for only 11 measures (versus 18 under assumption 1). Also, in the regressions on equity holdings, the average t-statistics for all explanatory variables fall and the coefficient on retirement wealth is significant for only 10 measures (versus 19 under assumption 1). Thus, inclusion of home equity in the financial asset portfolio dampens, but does not eliminate, the negative relationship between long duration assets and retirement wealth. The partial correlation analyses of Table 2 and the regressions summarized in Tables 3 and 4 demonstrate that (1) a generally negative relationship exists between retirement wealth and the holdings of intermediate-term bonds, long-term bonds and equities; (2) this negative relationship remains even when one controls for the real interest rate, disposable personal income, and the relative age of the population; (3) the relationship is frequently statistically significant across different retirement wealth measures with respect to long-term bonds and equities. The question remains whether this relationship is large enough to be of practical significance. To determine this, the elasticities at the means of intermediate-term bond holdings, long-term bond holdings, and equity holdings with respect to changes in retirement wealth were computed. These elasticities were computed for each assumption regarding home equity and appear in Table 5. The elasticities indicate that a 1% increase in retirement wealth results in a roughly 1.5% decrease in intermediate-term bond holdings, a decrease of somewhere between 2.2 and 2.8% in long-term bond holdings, and a decrease of somewhere between 0.8 and 1.1% in equity holdings. These elasticities are large enough to suggest a relatively significant impact on portfolio holdings over time. Equity holdings, which represent a larger component of individual portfolios than treasury bond holdings, are relatively less affected by changes in retirement wealth. Long-term bond holdings are the most affected by changes in retirement wealth.
V. C o n c l u s i o n s The percentages of equities and long-term treasuries held by individual investors declined over the 31 year period 1947-1977. The evidence presented here indicates that it is possible that this decrease is related, in part, to increases in retirement wealth. The coefficients of retirement wealth in the long-term treasuries and equities regressions were consistently negative and significant for certain measures of retirement wealth, both when home equity was treated as a consumer good (and,
T a b l e 5. E l a s t i c i t i e s o f A s s e t H o l d i n g s w i t h R e s p e c t to R e t i r e m e n t W e a l t h
(Evaluated at the means) Assets Assumptions
Intermediate-term bonds
Long-term bonds
Equities
H o m e equity as retirement wealth H o m e equity as a portfolio asset H o m e equity as a consumption good
- 1.53330 -1.68049 - 1.41879
-2.83719 -2.20740 -2.20304
- 1.18182 -0.83459 -0.82742
Retirement Wealth and Portfolio Composition
315
hence, excluded from the analysis) and when it was treated as a component of illiquid retirement wealth. When home equity is treated as an element of the financial portfolio, it represents a significant portion of that portfolio. The principal effect of this is to dampen the significance of the observed relationships between other portfolio holdings and other economic variables, including retirement wealth. The partial correlation results are consistent with the interpretation that either more people have acquired home equity as a result of increased retirement wealth or people have acquired a greater amount of home equity than they otherwise would have in the absence of increased retirement wealth. This effect appears to overshadow most other impacts on the individual's portfolio under this assumption. The limitations of this data set, both with respect to the length of the time period and measurement error, prevent a more precise estimation. However, the evidence presented here suggests that the impact of retirement wealth upon the composition of individual portfolios may be greater than is generally supposed. The failure to recognize the true depth and breadth of the effects results from a focus upon the relation of retirement wealth to the overall level of savings. This study suggests that a fuller understanding of the impact of retirement wealth upon savings can be gained by consideration of its impact upon individual portfolio composition.
The author wishes to thank Patricia Danzon, David Cheng, participants at the 1993 Southwestern Finance Association Annual Meeting, an anonymous reviewer, and the editor, Kenneth J. Kopecky,for helpful comments on prior drafts. I also wish to thank the Huebner Foundation for its financial assistance.
References Banerjee, A., Dolado, J., Hendry, D. F., and Smith, G. 1986. Exploring equilibrium relationships in econometrics through static models: Some Monte Carlo evidence. Oxford Bulletin of Economics and Statistics 48:253-277. Board of Governors of the Federal Reserve System. 1979. Flow of Funds Accounts 1949-1978. Washington, DC: Board of Governors of the Federal Reserve System. Board of Governors of the Federal Reserve System. 1987. Balance Sheets of the U.S. Economy, 1947-1986. Washington, DC: Board of Governors of the Federal Reserve System. Bostock, P., Woolley, P., and Duffy, M. Jan.-Feb. 1989. Duration-based asset allocation. Financial Analysts Journal 45:53-60, 80. Dicks-Mireaux, L., and King, M. A. 1982. Portfolio composition and pension wealth: An econometric study. NBER Working Paper 903. Engle, R. F., and Granger, C. W. J. 1987. Co-integration and error correction: Representation, estimation, and testing. Econometrica 55:251-276. Esposito, L. May 1978. Effect of Social Security on saving: Review of studies using U.S. time-series data. Social Security Bulletin 41:9-17. Fabozzi, F. J. 1993. Bond Markets, Analysis and Strategies, 2nd ed. Englewood Cliffs, NJ: Prentice-HalL
316
J.A. Ligon Feldstein, M. S. 1974. Social Security, induced retirement, and aggregate capital formation. Journal of Political Economy 82(5):905-926. Fong, H. G., and Vasicek, O. A. December 1984. A risk minimizing strategy for portfolio immunization. Journal of Finance 39:1541-1546. Granger, C. W. J., and Newbold, P. 1974. Spurious regression in econometrics. Journal of Econometrics 2:111-120. Harvey, A. 1991. The Econometric Analysis of Time Series, 2nd ed. Cambridge, MA: The MIT Press. Historical Statistics of the United States: Colonial Times to 1970. Washington, DC: U.S. Government Printing Office. Hubbard, R. G. 1985. Personal taxation, pension wealth, and portfolio composition. Review of Economics and Statistics 42:53-60. Hubbard, R. G. 1987. Uncertain lifetimes, pensions, and individual savings. In Issues in Pension Economics (Z. Bode, J. B. Shoven, and D. A. Wise, eds.). Chicago: The University of Chicago Press, pp. 175-206. Kuh, E., and Meyer, J. R. 1955. Correlation and regression estimates when the data are ratios. Econometrica 23:400-416. Leimer, D. R., and Lesnoy, S. D. 1982. Social Security and private saving: New time-series evidence. Journal of Political Economy 90(3):606-629. Morrison, D. F. 1983. Applied Linear Statistical Methods. Englewood Cliffs, N J: Prentice-Hall. Statistical Abstract of the United States, Series 1971-1978. Washington, DC: U.S. Government Printing Office. Stock, J. H. 1987. Asymptotic properties of least squares estimators of cointegrating vectors. Econometrica 55:1035-1056. Stocks, Bonds, Bills, and Inflation 1989 Yearbook, 1989. Chicago: Ibbotson Associated, Inc.
The Impact of Retirement Wealth upon Portfolio Composition of Individuals James A. Ligon
This study uses time series data to consider the effect of retirement wealth upon individuals’ portfolio composition. When home equity is regarded as retirement wealth or a consumption good, retirement wealth is negatively correlated with the percentage of intermediate-term bonds, long-term bonds, and equities in individual portfolios. The relationship remains significant for long-term bonds and equities when individuals’ holdings are regressed on retirement wealth and other macroeconomic variables. A similar but less significant relationship exists when home equity is regarded as a financial asset. Elasticity estimates for these assets suggest changes in retirement wealth can have significant impact on individual portfolio holdings.
I. Introduction Given that Social Security is not a perfect substitute for other assets, participation is generally mandatory, and benefits are not marketable, it is likely that changes in expected Social Security benefits would affect optimum portfolio choices among other assets. Private pension wealth may also impact portfolio choice because of similar, although not identical, characteristics. This microeconomic impact has macroeconomic implications through financial outcomes (e.g., interest rate and term structure determination) and real outcomes (e.g., corporate investment). Understanding these implications is clearly important for policy purposes. While the literature regarding the effect of Social Security and private pensions upon the overall level of saving by individuals in the United States is extensive, there have been very few studies of the effects of Social Security and private pension wealth upon the composition of individual household portfolios.’ Two econometric studies, Dicks-Mireaux and King (1982) and Hubbard (19851, have considered the impact of retirement wealth upon portfolio composition using cross sectional data. Both studies found Social Security to impact individual portfolio
Department of Economics, Finance and Legal Studies, The University of Alabama, Tuscaloosa, Alabama 35487. Address reprint requests to Dr. James A. Ligon, Department of Economics, Finance and Legal Studies, The University of Alabama, P.O. Box 870224, Tuscaloosa, Alabama 35487-0224. ‘See Feldstein (1974) for an exposition of the basic theoretical issues regarding the impact of Social Security on overall savings levels, Esposito (1978) for a review of and citations and Hubbard (1987) for an excellent bibliography of more recent work. Journal of Economics and Business @ 1995 Temple University
1995; 47:303-316
to pre-1978
literature,
0148-6195/95,‘$09.50 SSDI 0148-6195(95)00014-I
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choice, but differed with respect to type of and manner in which particular assets were affected.2 The present study contributes to our knowledge of portfolio composition effects of Social Security and pension wealth [hereafter, retirement wealth (RW)] by using time series data. The study considers the correlation over time between retirement wealth and other financial assets held by households. Examination of the partial correlations between retirement wealth and the shares of certain financial assets held in the individual's discretionary portfolio reveals strong correlations between retirement wealth and certain assets. The relationship between retirement wealth and these assets is then examined more closely by considering the relative explanatory power of retirement wealth versus a set of other predictors. The next section discusses how nondiversifiable mandatory Social Security may impact individual portfolio composition. Section 1II describes the data, defines the variables analyzed, and considers the partial correlations between retirement wealth and certain financial assets. Section IV examines more closely the relationship between retirement wealth and those financial assets with which it is most closely correlated. Section V summarizes and concludes the study.
II. Potential Impact of Retirement Wealth The study seeks to examine actual portfolio effects that retirement wealth may produce. Since the analysis is positive, rather than normative, in nature, we do not assume perfect capital markets. The capital market imperfections with the most potential impact on the analysis are that assets are not infinitely divisible, transaction costs are significantly greater than zero, and borrowing is constrained. These imperfections significantly influence behavior because most individuals are relatively small investors with little or no market power. These factors may influence individual portfolio construction by forcing individuals to balance risk minimization (for a given expected return) with transaction cost minimization. Since borrowing is constrained, individuals must also insure that the timing of portfolio cash flows meets portfolio objectives. The objective of individual portfolio management is assumed to be the satisfaction of future consumption needs. This may include the desire to make bequests as a final form of consumption. Some of these consumption needs may have well defined horizons, e.g., a new car, a college education for a child, or retirement income. Immunization is a well recognized duration-ba~d strategy for reducing the risk that future cash-flow obligations (e.g., savings objectives) will not be met.3 If Using Canadian data, Dicks-Mircaux and King (1982) found that Social Security wealth decreased the likelihood of ownership of deposits, bonds, and home equity and increased the likelihood of car ownership, while private pension wealth increased thc likelihood of ownership of deposits, bonds, cash, stocks, car, and home cquity. They found little impact on the amount held given that the asset was owned. Using U.S. data, Hubbard (1985) found that Social Security reduced the likelihood of annuity ownership and increased the likclihotnl of car ownership and home equity, while private pension wealth had positive impact on the likelihood of stock, savings bond, and car ownership. In contrast to Dicks-Mircaux and King, Hubbard also lk)und Social Security increased the demand for deposits, bonds, cars, and savings bonds, given ownership, and decreased the demand tk)r stocks, annuities, and home cquity, given ownership, while private pensions had little effect on demand givcn ownership. 3Scc Fabozzi (1993), for cxamplc. Fong and Vasicck (1984) show that focused immunization strategies provide greater risk reduction than barbell-type strategies. Although frequently applied in fixcd income contexts, Bostock, Wcn)lley, and Duffy (1989) show duration-based strategies can bc uscfut for determining the appropriate bond-equity mix in pension fund portfolios.
Retirement Wealth and Portfolio Composition
305
constraints on borrowing exist and transactions costs are high, individual investors may pursue such duration matching strategies because they do not view securities of differing durations as perfect substitutes. Thus, some degree of market segmentation or preferred habitats, where habitats are dictated by individuals' savings objectives, is likely to prevail among individual investors. Individual investors would tend to prefer short-term (long-term) assets for short-term (long-term) savings objectives. A possible implication of such behavior on portfolio composition is that increases in retirement wealth may decrease the need for private retirement saving, decreasing the need for longer duration assets in individual portfolios.
III. Partial Correlation Analyses A. The Data and Variable Definitions Data regarding expected Social Security wealth were taken from Leimer and Lesnoy (1982). Leimer and Lesnoy reexamined the results of Feldstein (1974) concentrating on Feldstein's measure of Social Security wealth. Feldstein had originally developed five measures of gross Social Security wealth and six measures of Social Security wealth net of taxes. The measures differed in the way individuals were assumed to take future benefits into account. Correcting for a computer programming error in Feldstein's original estimates, Leimer and Lesnoy reproduced the I1 measures of Social Security wealth using Feldstein's algorithm. In addition, Leimer and Lesnoy also developed their own algorithm for the l l different measures of Social Security wealth, which they contend provides better estimates of those people likely to receive benefits. Thus, there are 22 distinct measures of Social Security wealth. 4 Data for pension fund reserves, the total financial assets of households, deposits held (including checking deposits, savings deposits, time deposits, money market fund shares, and currency), U.S. Savings Bonds held, other treasury securities held, corporate equities held (including mutual fund shares and direct holdings), life insurance reserves, and home equity were taken from the Board of Governors of the Federal Reserve System, Balance Sheets for the U.S. Economy 1947-1986 (1987). ~ Assets such as investment in unincorporated businesses and miscellaneous financial assets were omitted to insure that the financial asset matrix is of full rank and because it is less likely that a causal link exists between such investments and retirement wealth. Because of limitations in the data, some of the variables involve
4Thc particular way in which the measures werc constructed does not appear relevant to the results obtained here and, accordingly, in the interest of brevity, the details of construction arc not discussed here. The 22 separate measures werc retained in the analysis primarily to test the sensitivity of the results to thc definition of Social Security wealth. For the interested reader, a detailed discussion of the various measures and their rationales is provided in Lcimer and Lesnoy (1982), pp. 611-614. Since the measures of Social Security wealth presented by Lcimcr and Lcsm)y were expressed in terms of 1972 dollars, the Social Security wealth variable was first adjusted to the nominal dollars for the year in question using the consumer price index befc~re calculating the ratio variable actually used in this analysis. SPension fund reserves were used to estimate the value of private pension wealth. The amount of treasury securities of each maturity held by households was estimated by multiplying the total treasury securities held by households times the percentage of such securities of each maturity class held by "other private investors." ttomc equity was computed by adding the values of owner-occupied structures and owncr-oceupicd land and subtracting the value of home mortgages.
306
J.A. Ligon
measurement error, but the expected impact of this error is to bias the correlation and regression coefficients toward zero. The proper treatment of home equity depends upon how individuals view this asset. In one sense, home equity represents a durable consumer good that provides a flow of value. Viewed in this light, home equity could properly be omitted from a study of the effects of retirement wealth on portfolio composition. However, the real value of home equity does not generally depreciate significantly, and, for most households, its nominal value would be expected to have appreciated over the data period studied. Thus, home equity differs from other consumer durables in that it serves as a significant source of individual wealth. Given this, it might be appropriate to view home equity as simply another portfolio asset. The difficulty with this view is that most individuals probably do not view home equity as simply another portfolio asset, in that it is considerably less liquid than other forms of financial wealth. Rather, individuals may view their home equity as a store of value that may be liquidated at or during retirement to provide additional consumption. Under this view, home equity is best viewed as another form of illiquid retirement wealth, not unlike Social Security and private pension wealth. In fact, home equity probably serves all three roles for individuals. Accordingly, the analysis is conducted under three alternative assumptions regarding home equity: (1) that it is a form of illiquid retirement wealth and we should analyze the response of financial asset allocations to all three forms of illiquid retirement wealth (Social Security, private pensions, and home equity), (2) that it is not a form of illiquid retirement wealth, but rather, is just like any other asset in the financial portfolio and should be treated accordingly, and (3) that it is durable consumer good and best excluded from the analysis. Data were available for all relevant variables for the period 1947-1977. The unavailability of Social Security wealth measures for more recent dates and changes in the Federal Reserve Board's reporting procedures precluded further extension of the time series with this data set. Rather than introduce additional measurement error by attempting to extend the time series with different overlapping data sources, it was decided to use this 31 year period for the analysis. One positive externality of excluding more recent data is that the period studied allows one to observe the impact of Social Security and private pension wealth over the most significant period of growth in this form of wealth. The variables used in the analysis are listed and defined in Table 1. Because the variables in which we are interested are, in fact, ratios, many of the econometric problems associated with the use of ratios are not present. See Kuh and Meyer (1955). An additional advantage associated with using ratios is that questions of real versus nominal wealth are avoided. The use of a different denominator for retirement wealth than for the other financial wealth variables insures that no spurious correlation is introduced between retirement wealth and the other financial variables. On the other hand, correlations between the other financial variables are affected because of the common denominator used to define them. Accordingly, the analytic approach taken was a partial correlation analysis between retirement wealth and the other financial assets. The correlation of retirement wealth with each financial asset is determined, holding the effects of the other financial assets constant. [See Morrison (1983), pp. 95-104, for a discussion.] Since there are 22 different measures of Social Security wealth, there are 22 different
R e t i r e m e n t W e a l t h a n d Portfolio C o m p o s i t i o n
307
T a b l e 1. V a r i a b l e Definitions Retirement wealth
Deposits
Savings bonds Equities Life insurance Very short term bonds (M _< 1 yr.) Short term bonds (1 < M < 5) Intermediate term bonds (5 < M < 10) Long term bonds ( M > 10) Home equity
The percentage of total household financial wealth (including Social Security, private pensions, and, where applicable, home equity) held in Social Security, private pension, and, where applicable, home equity wealth The percentage of household non-retirement wealth (non-RW) financial wealth held in checking, savings, and time deposits, money market funds, and currency (non-RW financial wealth is financial wealth excluding Social Security, private pension wealth, and, where applicable, home equity) The percentage of household non-RW financial wealth held in U.S. Savings Bonds The percentage of household non-RW financial wealth held in corporate equities (including those held in mutual fund shares) The percentage of household non-RW financial wealth represented by the cash value of life insurance held The percentage of household non-RW financial wealth held in (non-savings bond) U.S. Treasury securities with maturities of l year or less The percentage of household non-RW financial wealth held in (non-savings bond) U.S. Treasury securities maturing in 1-5 years The percentage of household non-RW financial wealth held in (non-savings bond) U.S, Treasury securities maturing in 5-10 years The percentage of household non-RW financial wealth held in (non-savings bond) U.S. treasury securities maturing in more than 10 years The percentage of household non-RW financial wealth represented by the value of owner-occupied structures plus the value of owner-occupied land less the value of home mortgages. Under assumption 1, home equity is included in retirement wealth. Under assumption 2, home equity is included in non-RW financial wealth. Under assumption 3, home equity is excluded from both retirement wealth and non-RW financial wealth
measures of retirement wealth. The correlations are examined for each of these 22 different measures.
B. Results The results of the partial correlation analyses are summarized in Table 2. Summaries are presented for each of the three assumptions regarding the proper treatment of home equity: (1) as illiquid retirement wealth, (2) as a portfolio asset, and (3) as a consumption good. 6 When home equity is treated as iUiquid retirement wealth or as a consumption good, the most significant partial correlations are displayed by bonds with maturities between 5 and 10 years (intermediate-term bonds), bonds with maturities over 10 years (long-term bonds), and equities. These assets are significantly negatively correlated with retirement wealth for 22 of the retirement wealth measures (for intermediate-term bonds), 22 measures (for long-term bonds), and 18 measures (for equities) under assumption 1 and significantly negatively correlated with retirement 6The complete partial correlation analyses and the complete regression analyses discussed in the following section are available on request from the author.
T a b l e 2. P a r t i a l C o r r e l a t i o n C o e f f i c i e n t s o f A s s e t s w i t h R e t i r e m e n t W e a l t h Treasury bonds Deposits Sav. bonds
Equities
Life ins.
M<
lyr
1
5
10
M>
10
H o m e equity
Home equi~ treated asilliquidretirement wealth N u m b e r of measures where sign was No. of m e a s u r e s significant at the 5% level Avg. square of partial cor. coeff.
+
17 5
18 4
22 0
7 15
19 3
0 22
22 0
22 0
+
1 0
0 0
18 0
0 0
10 0
0 12
22 0
22 0
0.04294
0.04407
0.37469
0.04495
0.12476
0.18734
0.41121
0.38594
Home equi~ treated asponfoKo asset No. of m e a s u r e s where sign was No. of m e a s u r e s significant at the 5% level Avg. square of partial cor. coef.
-
+
1
21
-
0
+
5 0.10007
20 2 13 0 0.19837
11 11 0 4 0.07039
4 18 0 12 0.14403
12 10 4 0 0.08170
7 15 0 0 0.02192
15 7 5 0 0.10033
21 1 0 0 0.05463
5 17 0 12 0.19012
Home equi~ trea~d as a consumptiongood N u m b e r of m e a s u r e s where sign was No. of m e a s u r e s significant at 5% level Avg. square of partial cor. coef.
-
+
12 10
-
0
+
1 0.05310
18 4 5 0 0.09598
22 0 18 0 0.24092
7 15 0 3 0.06261
15 7 11 0 0.12582
2 20 0 12 0.14567
22 0 20 0 0.32017
22 0 22 0 0.29381
o
Retirement Wealth and Portfolio Composition
309
wealth for 20, 22, and 18 measures (respectively) under assumption 3. The squared partial correlation coefficients for intermediate-term bonds, long-term bonds, and equities, respectively, are 0.41121, 0.38594, and 0.37469 under assumption 1, and 0.32017, 0.29381, and 0.24092 under assumption 3. Under assumption 2 the most significant partial correlations are between retirement wealth and savings bonds (significantly negative for 13 measures), life insurance (significantly positive for 12 measures), and home equity itself (significantly positive for 12 measures). However, perhaps the most significant impact of including home equity as a portfolio asset is to decrease the significance of the correlations between all financial assets and retirement wealth. Under assumption 2 none of the average squared partial correlation coefficients exceeds 0.2. This effect is probably attributable to the fact that including home equity in the portfolio of financial assets substantially reduces the weights of all other assets in the portfolio. The significant weight of home equity combined with the mildly positive correlation between home equity and retirement wealth tends to mask other effects. The similar patterns under assumptions 1 and 3 are perhaps unsurprising. The observed pattern is consistent with a duration-based investment strategy on the part of individual investors who substitute away from longer duration financial assets as their illiquid retirement wealth increases. As noted above, the partial correlation between home equity and (other) retirement wealth is generally positive and often significant. Thus, including home equity as retirement wealth simply increases the level of retirement wealth and reinforces the significance of the negative correlation between intermediate-term bonds, long-term bonds, and equities and retirement wealth. In order to determine whether the relationship between retirement wealth and intermediate-term bonds, long-term bonds, and equities can be explained by other economic factors, regression analyses were conducted. The results are discussed in the following section.
IV. Regression Analyses Individual holdings of certain portfolio assets appear to have significant correlation with retirement wealth. To analyze the explanatory power of retirement wealth relative to other factors affecting portfolio structure, additional explanatory variables are included with retirement wealth in a series of time series regressions. The additional variables included are the ex post real interest rate, real personal disposable income, and the percentage of the population over age 65. The real interest rate is a component of required returns on both fixed income and equity securities and, hence, could be expected to influence relative asset holdings. 7 7In a prior specification the ex ante real interest rate and expected inflation were included in the regression analyses. Expected inflation was assumed to follow a martingale process. The ex ante real rate was then the annual return on U.S. Treasury bills minus the prior period's percentage change in the c o n s u m e r price index. However, neither of these measures was significant in any of the regressions. It seems reasonable to a s s u m e that this insignificance could be attributable to the fact that the data used are annual observations and that individuals adjust their inflation expectations m u c h more quickly than annually. Lacking the data to compute monthly inflation expectations to correct this problem, another approach is simply to use the ex post real interest rate. If people adjust their inflation expectations very quickly, this measure will provide a better measure of the true "ex ante" rate than the ex ante m e a s u r e constructed from the prior year's data. That is the approach adopted here. The real rate so constructed produces results that are intuitively appealing.
310
J.A. Ligon Specifically, individuals would be expected to change the duration of their portfolio holdings with changes in the real interest rate. Individuals might be expected to lengthen duration during periods when real rates are falling and to shorten duration during periods when real rates are rising. Real disposable income measures wealth effects on portfolio choice, including changes in investor risk aversion related to wealth. The percentage of the population over 65 provides another measure of the extent to which individual investors practice duration-based portfolio management. Older people would be expected to have shorter horizons and, thus, shorter duration portfolios. The inclusion of further explanatory variables was rejected because of the small sample size. The ex post real interest rate was computed by taking the annual return on U.S. Treasury bills minus the percentage change in the consumer price index. Data regarding the return on Treasury bills and the consumer price index were taken from Ibbotson Associated, Inc.'s SBBI 1989 Yearbook. Real personal disposable income was calculated by converting personal disposable income to 1977 dollars using the consumer price index. Data regarding personal disposable income were taken from the Board of Governors of the Federal Reserve's Flow of Funds Accounts (1979). Data regarding the percentage of the population over 65 were taken from the Historical Statistics of the United States: Colonial Times to 1970 with updates from the StatisticaI Abstract of the United States 1971-1978. The percentages of non-RW financial wealth held in intermediate-term bonds, long-term bonds, and equities were then regressed on retirement wealth, the ex post real interest rate, real personal disposable income (in trillions of dollars), and the percentage of the U.S. population over age 65. Ordinary least squares estimates exhibited significant autocorrelation. The equations were reestimated to correct for this autocorrelation. Harvey (1991) refers to the correction method used as the two-step full transform method. Although this technique effectively transforms the data from a regression in levels, arguably the analysis one desires, into a regression of a function of first order first differences (for a first order autoregressive process), it was deemed preferable to other estimation techniques. 8 A first order autocorrelative process effectively removed the autocorrelation from the estimates in virtually all cases. As before, separate estimates were obtained for each of the 22 measures of retirement wealth. Tables 3 and 4 present summaries of the regression results under assumption 1 (home equity as retirement wealth) and assumption 2 (home equity as a portfolio asset), respectively. The regression results under assumption 3 (home equity as a consumption good) are omitted because they are qualitatively similar to those under assumption 1.9 Each table presents statistics for the regression of intermedi-
8In the presence of autoregression the ordinary least squares estimators are unbiased and consistent, but are neither efficient or asymptotically efficient. Also, for positive autocorrelation, such as we have here, the estimates of the variances of the ordinary least squares coefficients are downwardly biased, implying conventional confidence intervals on the coefficients are meaningless [Granger and Newbold (1974)]. Estimation of the variables as a cointegrated series, as suggested by Engle and Granger (1987) was deemed undesirable because of the poor small sample properties of these estimators. See Stock (1987) and Banerjee, et al. (1986). 9The regressions under assumption 3, where home equity is treated as a consumption good, are more similar to those presented in Table 3 than to those presented in Table 4, although significance levels are somewhat lower than those observed in Table 3. These results are available on request from the author.
0 22 0 0
22 0 0 22
0 22
22 0
R e t i r e m e n t wealth Ex post real interest rate Disp. pers. inc. Percent of pop. over age 65
22 0
0 22 0.7848
22 0
0 22
Retirement wealth Ex post real interest rate Disp. pers. inc. Percent of pop. over age 65
0 22
22 0 0.8949
22 22
0 0
R e t i r e m e n t wealth Ex post real interest rate Disp. pers. inc. Percent of pop. over age 65
Average R-square
0.3277
Average R-square
Average R-square
-
0.006202 -0.039735
22 0
0 22
-0.329805 18.97586
- 0.69546 0.166923
Average Durbin W a t s o n statistic
19 0
0 0
Equity hoMings
0 22
22 0
-0.02261 -0.01947
Average Durbin Watson statistic
18 22
0 0
Long-termbond holdings
0.0010776 -0.05039
-0.00556 0.011293
Avg. coef. value
Average D u r b i n - W a t s o n statistic
0 0
0 0
lntermediate-termbond holdings
+
+
Indep. variable
No. of m e a s u r e s where coef. was No. of meas. where coef. sig. @ 5%
T a b l e 3. S u m m a r y o f R e g r e s s i o n S t a t i s t i c s f o r D e t e r m i n a n t s o f H o l d i n g s ( H o m e e q u i t y t r e a t e d as illiquid r e t i r e m e n t w e a l t h )
1.716
0.859 0.894
1.049 2.655
1.462
-6.131 7.465
- 2.756 0.687
1.382
3.351 4.664
-2.726 - 2.603
-
-
Avg. t-stat.
O
¢:k
r-, ~r
t~
g
7~
Average R-square
Retirement wealth Ex post real interest rate Disp. pers. inc. Percent of pop. over age 65
Average R-square
Retirement wealth Ex post real interest rate Disp. pers. inc. Percent of pop. over age 65 0 22
22 0
22 0
0 22 0.7137
22 0
0 22
0.8744
22 22
0 0
0.3516
0 17
22 5
Average R-square
22 0
0 22
Retirement wealth Ex post real interest rate Disp. pers. inc. Percent of pop. over age 65
-
+
Indep. variable
0 22
0 0
Equi~holdings
19 0
0 0
Long-~rmbondholdings
0 0
0 22
In~rmed~-terrnbonds
+
0 0
4 0 0.000615 -0.01606
-0.00697 0.009757
Avg. coef. value
0.003932 -0.28173
-0.01979 -0.01680
-0.328376 17.76049
0.55886 0.131167
Average D u r b i n - W a t s o n statistic
22 0
10 0
Average D u r b i n - W a t s o n statistic
0 18
11 22
Average D u r b i n - W a t s o n statistic
-
No. of m e a s u r e s where coef. was No. of meas. where coef. sig. @ 5%
T a b l e 4. S u m m a r y o f R e g r e s s i o n S t a t i s t i c s f o r D e t e r m i n a n t s o f H o l d i n g s ( H o m e e q u i t y t r e a t e d as a p o r t f o l i o a s s e t )
1.844 0.550
1.322
2.317 2.852
- 2.204 - 2.444
1.747
1.510
- 6.090 5.520
-
1.310 2.680
0.607 - 0.285
-
Avg. t-stat.
O
Retirement Wealth and Portfolio Composition
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ate-term bond, long-term bond, and equity holdings on retirement wealth, the real interest rate, disposable personal income, and the percentage of the population over age 65. The statistics presented include the number of retirement wealth measures where the coefficient was positive or negative, and the number of measures where this coefficient was significant at the 5% level, the average of the coefficient values and t-statistics for the 22 regressions, and the average of the R-squares and Durbin-Watson statistics for the 22 regressions. In Table 3, where home equity is regarded as retirement wealth, the only variable significantly related (all 22 measures, average t-statistic 2.655) to intermediate-term bond holdings is the ex post real interest rate. Since the two-step full transform method used essentially produces a regression on first differences, the positive relationship suggests that when real interest rates are rising, individuals increase their holdings of intermediate-term bonds. A significantly negative relationship is observed between long-term bond holdings and retirement wealth (18 measures, average t-statistic -2.726), the real interest rate (22 measures, average t-statistic -2.603), and percent of the poPulation over 65 (22 measures, average t-statistic -4.664), while disposable personal income (22 measures, average t-statistic 3.351) is significantly positively related to long-term bond holdings. The results are intuitively appealing. Rising real interest rates result in a shift from longer-term to shorter-term bonds. Long-term bonds holdings increase with income and decrease with an aging population. Increasing retirement wealth decreases long-term bond holdings. These findings are consistent with duration-based portfolio management. A significant negative relationship is observed between equity holdings and retirement wealth (19 measures, average t-statistic -2.756) and disposable personal income (22 measures, average t-statistic -6.131), while the percentage of the population over age 65 is positively related (22 measures, average t-statistic 7.465) to equity holdings. The increased holdings of equities by an increasingly aged population may be related to tax incentives. Since the cost basis of equities is stepped up to current market value at death, older individuals may be inclined to liquidate equities as a last resort. 1° Decreased holdings of equities when personal income rises may be a business cycle effect. Increases in the rate at which personal disposable income rises could occur at or after the peak of business cycle, when corporate earnings may have peaked. Thus, individuals may reduce holdings of equities at these times and increase them during troughs in the business cycle, when personal disposable income is rising slowly (or falling) and equities may appear relatively cheap. As in the case of long-term bonds, increasing retirement wealth would be expected to decrease individuals' holdings of relatively longer duration equities, which is what we observe here. In Table 4, where home equity is treated as a portfolio asset, we find a very similar relationship between holdings of each of the three financial assets and retirement wealth, the real interest rate, disposable personal income, and the percentage of the population over age 65. The explanatory variables generally retain the same signs as they did in the regressions of Table 3 and coefficient values are generally similar. The primary impact of including home equity as a
10I am
grateful to an anonymousreviewerfor this suggestion.
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J.A. Ligon portfolio asset is to reduce the significance of the relationships between the explanatory variables and the asset holdings. For example, in the regressions on long-term bond holdings, the average t-statistics for all explanatory variables fall and the coefficient on retirement wealth is significant for only 11 measures (versus 18 under assumption 1). Also, in the regressions on equity holdings, the average t-statistics for all explanatory variables fall and the coefficient on retirement wealth is significant for only 10 measures (versus 19 under assumption 1). Thus, inclusion of home equity in the financial asset portfolio dampens, but does not eliminate, the negative relationship between long duration assets and retirement wealth. The partial correlation analyses of Table 2 and the regressions summarized in Tables 3 and 4 demonstrate that (1) a generally negative relationship exists between retirement wealth and the holdings of intermediate-term bonds, long-term bonds and equities; (2) this negative relationship remains even when one controls for the real interest rate, disposable personal income, and the relative age of the population; (3) the relationship is frequently statistically significant across different retirement wealth measures with respect to long-term bonds and equities. The question remains whether this relationship is large enough to be of practical significance. To determine this, the elasticities at the means of intermediate-term bond holdings, long-term bond holdings, and equity holdings with respect to changes in retirement wealth were computed. These elasticities were computed for each assumption regarding home equity and appear in Table 5. The elasticities indicate that a 1% increase in retirement wealth results in a roughly 1.5% decrease in intermediate-term bond holdings, a decrease of somewhere between 2.2 and 2.8% in long-term bond holdings, and a decrease of somewhere between 0.8 and 1.1% in equity holdings. These elasticities are large enough to suggest a relatively significant impact on portfolio holdings over time. Equity holdings, which represent a larger component of individual portfolios than treasury bond holdings, are relatively less affected by changes in retirement wealth. Long-term bond holdings are the most affected by changes in retirement wealth.
V. C o n c l u s i o n s The percentages of equities and long-term treasuries held by individual investors declined over the 31 year period 1947-1977. The evidence presented here indicates that it is possible that this decrease is related, in part, to increases in retirement wealth. The coefficients of retirement wealth in the long-term treasuries and equities regressions were consistently negative and significant for certain measures of retirement wealth, both when home equity was treated as a consumer good (and,
T a b l e 5. E l a s t i c i t i e s o f A s s e t H o l d i n g s w i t h R e s p e c t to R e t i r e m e n t W e a l t h
(Evaluated at the means) Assets Assumptions
Intermediate-term bonds
Long-term bonds
Equities
H o m e equity as retirement wealth H o m e equity as a portfolio asset H o m e equity as a consumption good
- 1.53330 -1.68049 - 1.41879
-2.83719 -2.20740 -2.20304
- 1.18182 -0.83459 -0.82742
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hence, excluded from the analysis) and when it was treated as a component of illiquid retirement wealth. When home equity is treated as an element of the financial portfolio, it represents a significant portion of that portfolio. The principal effect of this is to dampen the significance of the observed relationships between other portfolio holdings and other economic variables, including retirement wealth. The partial correlation results are consistent with the interpretation that either more people have acquired home equity as a result of increased retirement wealth or people have acquired a greater amount of home equity than they otherwise would have in the absence of increased retirement wealth. This effect appears to overshadow most other impacts on the individual's portfolio under this assumption. The limitations of this data set, both with respect to the length of the time period and measurement error, prevent a more precise estimation. However, the evidence presented here suggests that the impact of retirement wealth upon the composition of individual portfolios may be greater than is generally supposed. The failure to recognize the true depth and breadth of the effects results from a focus upon the relation of retirement wealth to the overall level of savings. This study suggests that a fuller understanding of the impact of retirement wealth upon savings can be gained by consideration of its impact upon individual portfolio composition.
The author wishes to thank Patricia Danzon, David Cheng, participants at the 1993 Southwestern Finance Association Annual Meeting, an anonymous reviewer, and the editor, Kenneth J. Kopecky,for helpful comments on prior drafts. I also wish to thank the Huebner Foundation for its financial assistance.
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