The potential effect of US baby-boom retirees on stock returns

The potential effect of US baby-boom retirees on stock returns

North American Journal of Economics and Finance 30 (2014) 106–121 Contents lists available at ScienceDirect North American Journal of Economics and ...

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North American Journal of Economics and Finance 30 (2014) 106–121

Contents lists available at ScienceDirect

North American Journal of Economics and Finance

The potential effect of US baby-boom retirees on stock returns夽 Haim Kedar-Levy ∗ Ben Gurion University of the Negev, Faculty of Business and Management and Ono Academic College, P.O.B. 653, Beer-Sheva 84105, Israel

a r t i c l e

i n f o

Article history: Received 13 May 2013 Received in revised form 22 August 2014 Accepted 25 August 2014 Available online 6 September 2014 Keywords: Predictability Demography Baby-boom Asset pricing Aging

a b s t r a c t Empirical studies demonstrated that US baby boomers consumption and savings patterns have affected economic aggregates over the past decades, among them equity returns. Boomers’ retirement is expected to mitigate the demand for equities until 2050, but its impact varies with the specific population age structure along decades. This paper employs a dynamic asset pricing model with optimum consumption and portfolio rules to estimate aging effects on S&P500 returns between 1950 and 2050. Calibration for demographic and economic data between 1950 and 2005 yields model estimates that significantly explain the moving average of S&P500 returns. Further, taking into account the present value of expected demographic effects until 2050 suggests that the S&P500 was fairly priced at the heart of the financial crisis, on April 2009, but overpriced thereafter. © 2014 Elsevier Inc. All rights reserved.

夽 I am indebted to Kenneth J. Arrow, Dan Galai, Carl Ulrichl, and Itzik Venezia for helpful discussions and insights. I am grateful for comments by participants at the Bank of Israel Research Seminar and the Ben-Gurion University of the Negev research seminar, as well as participants of the 2006 Far-Eastern meeting of the Econometric Society, Beijing, China, and 2006 FMA meeting, Salt Lake City, Utah. I assume full responsibility for any remaining errors. ∗ Tel.: +972 8 6472569; fax: +972 8 6477697.

E-mail address: [email protected] http://dx.doi.org/10.1016/j.najef.2014.08.004 1062-9408/© 2014 Elsevier Inc. All rights reserved.

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1. Introduction Population economists conjecture that disproportional changes in young, prime-age, and old cohorts change the aggregate demand for real assets, financial assets, and consumption, among other economic variables. Young cohorts borrow, primarily in order to acquire real estate, prime-age cohorts are the major savers in the economy, and the old generation consumes its savings. In 2005 post-war baby-boomers started retiring in the USA, Europe, Japan, and other developed countries, raising policy and planning questions such as pension planning, social security, demand for real and financial assets, economic growth, and more (Arnott & Casscells, 2004; Bloom, Canning, & Sevilla, 2002). One of the major issues is asset valuation: upon retirement, a large cohort of baby-boomers will face a smaller pool of buyers as they liquidate real and financial assets. Siegel (1998, p. 41) illustrates this notion by writing: “The words’Sell? Sell to whom?’ might haunt the baby boomers in the next century.” Theoretical models such as in Jagannathan and Kocherlakota (1996), Brooks (2000), Abel (2001), Storesletten, Telmer, and Yaron (2007), Constantinides, Donaldson, and Mehra (2002), Goyal (2004), Cocco, Gomes, and Maenhout (2005), and others predict a significant decline in the prices of real and financial assets. While a few authors hypothesize a “meltdown”, this outcome is questionable given empirical estimates, such as in Poterba (2001), which documents little predictability of demographic measures on stock returns. This paper quantifies rational expectations of aging effects on equilibrium equity returns between 2010 and 2050 in a dynamic asset pricing model, accounting for aggregate labor income, optimum consumption, and asset allocation. We substantiate our future model predictions by demonstrating that estimates of past aging effects between 1950 and 2005 significantly explain S&P500 returns. In light of Poterba (2001) and other empirical findings, whereby demographic effects were not priced ex-ante in financial, real estate, and consumer product markets, we further estimate the implications of myopic expectations. We conclude that if the 2002–2007 average Price/Earnings (P/E) ratio indeed did not reflect expected boomers’ retirement, it should have declined by 47% to about 14. The 14.14 P/E ratio of early 2009, triggered by the financial crisis, met that level. However, stock prices bounced in late 2009–2010, and because the P/E ratio between 2010 and 6/2014 was measured in the low 20s, we conclude that aging effects were priced only partially as of mid-2014. Empirical findings on aging effects deserve a closer look. Liu and Spiegel (2011) estimate empirically the S&P500 P/E ratio until 2030, and project a declining price path until 2021, followed by a recovery. While according to their estimates the cumulative S&P500 return between 2010 and 2021 be negative 13%, and by 2030 positive 20% vs. 2010, our predictions are somewhat different. According to our model predictions, the most severe boomer’s retirement impact occurs around 2010, with diminishing effects that almost vanish in 2050. In two papers, Poterba (2001, 2004) estimates the theoretical predictions for asset prices’ meltdown in real and financial asset markets upon baby-boomers’ retirement by analyzing the 1995 and 2001 surveys of consumer finances, respectively. Poterba finds weak support for the historical baby-boomers’ effect on equity prices. Projecting the estimates until 2050, Poterba concludes in both papers that baby-boomers’ retirement will not impose a significant decline in equity returns between 2020 and 2050, since the demand for equities would be maintained due to bequest motives. This conclusion is consistent with our estimates, though for different reasons. Referring to Poterba, Abel (2001) developed a rational expectations general equilibrium model that accounts for bequest motives and concludes that equity prices boost at prime-age and decline at retirement, even though the model predicts that bequest motives support the demand for equities. In spite of the availability of relatively reliable demographic predictions, many researchers find that prices adjust to varying demographic states on the run, but not ex-ante, as rational pricing would imply.1 Lee (2013) finds empirical support for the behavioral life-cycle hypothesis whereby variations in demographic clientele explain long-term dividend yield strategies. DellaVigna and Pollet (2007)

1 Mankiw and Weil (1989) find that the real estate market responded to contemporaneous changes in the mass of the 25–40 age cohorts. Therefore, baby-boomers’ demand for housing in the 1970s and 1980s faced limited supply, resulting in increasing prices. Using postwar US data, Bakshi and Chen (1994) were the first to report that average age increased equity returns through consumption growth rate. Brooks (1998) shows that both stock and bond prices increase with the proportion of prime-age cohorts in developed economies. Bergantino (1998) estimates that about 40% of the increase in housing prices between 1965 and 1980 could be attributed to boomers’ increased demand.

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claim that investors’ inattention to predictable changes in consumption and investment opportunities, demonstrating that predictable demographic trends 5–10 years ahead had a significant effect on agesensitive industries (toys, bicycles, beer, life insurance, and nursing homes), as well as on their average returns. Bergantino argues that as the young boomers came into prime-age 20 years later, their demand for savings accounted for about 30% of the increase in equity prices between 1985 and 1999. Ang and Maddaloni (2005) and Geanakoplos, Magill, and Quinzii (2004) provide additional evidence that equity prices respond to changes in demographic structure in a predictable way. Ang and Maddaloni test five developed countries (France, Germany, Japan, UK, and US) over the period 1900–2001 and additional 15 countries over the period 1920–2001, and conclude that an increase in the proportion of retirees significantly predicts a decrease in equity premium for one, two, and five years ahead. We estimate aging effects in a dynamic asset allocation model based on Merton (1971). We assume a single risky asset, the market portfolio of all real assets, and a riskless asset that yields a given interest rate. We solve for the optimal portfolio and consumption rules with Hyperbolic Absolute Risk Aversion (HARA) preferences. We calibrate the model for postwar US financial markets data and estimate aging impacts twice: first, we use age distributions between 1950 and 2005 and regress model estimates on the five-year moving average of annual S&P500 returns; this regression is significant at 5%. Second, we apply the 2004 US Census Bureau cohort size projections until 2050 to estimate potential babyboom retirees’ effect on equity returns. We estimate the proportional size and weighted average age of each cohort, and, using these proportions, estimate the population-wide weighted average life expectancy at current age based on Arias (2004). We find that the estimated annual return impact, i.e., the decline in (percentage points of) equity return at the benchmark economy is −2.40% in the neighborhood of 2010, –1.68% near 2020, and has smaller effects in subsequent decades. Finally, we conduct comparative static analyses for key parameters. Ceteris paribus, equilibrium returns on the risky asset are most sensitive to the riskless rate, equity risk, and investors’ life expectancy. The rest of the paper is organized as follows: Section 2 derives optimal consumption and portfolio rules with labor income; in Section 3 we calibrate the model for the USA and estimate aging effects. We conduct sensitivity analyses in Section 4 and summarize in Section 5. 2. Optimum portfolio and consumption rules Assume a Merton (1971) economy with a single real asset (the market portfolio) that yields a constant return to scale dividend yield. Financial claims on the real asset are traded in the stock market, together with a riskless bond. The stock price dynamics is given by the Itô process (1) dPt = dt + zt dt Pt

(1)

where  is the instantaneously constant expected rate of return on the stock, and  2 its instantaneous variance. The riskless bond earns instantaneous interest rate r, and is available at zero net supply. There exist price-taking investors/consumers who are identical in all aspects except in their horizon. In this section we solve optimum portfolio and consumption rules for a single investor/consumer and in the following section aggregate across age cohorts. The stock value held at t by the investor is St = Nt Pt , ∀ t, where Nt is the number of shares and Pt their price. The bond value is Dt = Qt Bt , ∀ t, where Qt is quantity of bonds and Bt their price. Let ˛t = St /Wt and 1 − ˛t = Dt /Wt , where Wt is total wealth at t. Consumption per period is denoted Ct dt, and we assume a constant wage income, dg = G dt. The total change in wealth over time is representable as changes in prices and in quantities dWt = Nt dPt + Qt dBt + dNt (Pt + dPt ) + dQt (Bt + dBt ), where the two right-most terms are additions to wealth from non-capital gain sources, i.e., available income. Therefore, by definition (G − Ct )dt ≡ dNt (Pt + dPt ) + dQt+dt (Bt + dBt+dt ).

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Given the price dynamics in (1), the expected next period wealth is Wt + dWt+dt = Nt Pt+dt + Qt Bt+dt + (G − Ct )dt = Wt (1 + (r + ˛t ( − r))dt) + (G − Ct )dt + ˛t Wt zt dt.

(2)

Assume the investor has a HARA utility function defined over consumption, C 1− 

U(C, t) = e−t

 C

1−



+

,

(3)

/ 1, and (C/(1 − ) + ) > 0. The where  > 0 is the investor’s subjective rate of time-preference,  = parameter  determines the displacement from the origin of the HARA utility function. Define con˜ sumption in excess of labor income as C(t) = C(t) − G, and let the investor/consumer maximize the expected utility of excess consumption,





T

˜ U{C(s)}ds ,

Max E0

(4)

0

conditional on W(0) = W0 and subject to the budget constraint (2). The first order optimality conditions must satisfy



˜ t) + JW dW + 0 = Max U(C, ˜ {˛,C}



1 JWW dW 2 , 2

where subscripts represent partial derivatives. The first order condition with respect to consumption yields the standard condition equating marginal utility of consumption with the marginal utility of wealth:



0=

−1

C˜ + 1−

− JW .

The first order condition with respect to the optimal asset allocation, ˛t , yields ˛t = −

JW  − r . JWW W  2

(5)

Replacing the partial derivatives of the value function in (5) yields the optimum demand for the risky asset at period t. The optimum asset allocation rule with finite horizon T is2 ˛∗t Wt =

−r ı 2



Wt +



G ( − r) (1 − er(t−T ) ), (1 − er(t−T ) ) + r r 2

(6)

where ı ≡ 1 −  is the Relative Risk Aversion (RRA) parameter. The optimal consumption schedule is linear in wealth C˜ t∗ = t Wt + ˇt , with

(7)



t ≡ ( − ) /ı 1 − e

− (t−T ) ı

 ,

in which  = r + ( − r)2 /(2ı 2 ), and



ˇt ≡

2

( − ) (G + ı)/r 1 − er(t−T )



ı 1−e

− (t−T ) ı



− ı.

See Merton (1971, p. 395), Eq. (71) for (6) and Eq. (70) for (7).

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Multiply and divide the right-most element in (6) by ı and reorganize to obtain ˛∗t Wt

−r = ı 2



(1 − er(t−T ) ) Wt + (G + ı) r

(8)

Eq. (8) indicates that investor’s optimum asset allocation rules incorporate labor income effects throughout the remaining lifetime. The annuity ı represents, upon capitalization by the discount factor (1 − er(t−T) )/r, the present value of the investor’s minimum lifetime consumption (see Kingston, 1989 for a related interpretation).3 For Constant Relative Risk Aversion (CRRA) preferences the parameter  is zero, and the present value of minimum lifetime consumption plays no role for optimum asset allocation.

3. Aging effects on equity returns In this section we derive formally and then estimate empirically aging effects in the USA between 1950 and 2050. Changes in the economy-wide weighted average remaining lifetime across cohorts capture the impact of aging on equity returns. We aggregate demand for equity and consumption across cohorts, and calibrate the model to postwar US data. This allows us to compare model predictions first with historical average return realizations, and then forecast equilibrium returns at different decades between 2010 and 2050. To test the model on historical data we start by solving for the equilibrium price on 2005, assuming all parameters are constant, and then by solving backwards for the 2000 equilibrium price, given the 2000 demographic state and expected parameters for 2005. By repeating this process recursively to 1950 we find the expected demographic term-structure of stock returns. The resulting return estimates are regressed against historical S&P500 returns. A similar recursive estimation of returns is conducted with respect to the decades starting in 2050 and ending in 2010. Finally, we conduct sensitivity analyses with respect to key parameters in the economy. An investor’s remaining time to horizon (life) enters the optimal portfolio and consumption decisions through the term T − t. If this term is calculated based on exogenous demographic data, it facilitates calculation of the aggregate demand for assets at different demographic states, indexed by s. For example, if in state s the economy-wide weighted average of investor’s age is ts (0 < ts < Ts ), then a long Ts − ts implies a relatively young society, whereas a shorter Ts − ts implies an older society. Therefore, changes in this measure through time represent the process of aging. Rewrite (8) in terms of quantities and prices Nt Pt∗ =

−r ı 2

Nt Pt + Qt Bt +

G + ı (1 − er(ts −Ts ) ) r

.

(9)

The total number of shares outstanding at t is Nt , and the asterisk represents the equilibrium stock price at t. Because consumption mitigates wealth accumulation, it must be subtracted from wealth when calculating the demand for the risky asset. Subtracting (7) from period t wealth, and dividing ∗ , we find the price changes as the aging state is changing. This yields the expected through by Pt−dt rate of return, E(m∗t ), between successive periods,

E

Pt∗

∗ Pt−dt

− 1 = E(m∗t ) =

−r Pt−dt Nt  2 ı







Wt 1 − t − ˇt +

G + ı (1 − er(ts −Ts ) ) r

− 1.

(10)

3 Kedar-Levy (2006) estimated the demographic implications of changes in this value in a simpler model, with no consumption or labor income but with heterogeneous agents, and reported that it may obtain a positive expected value, albeit small.

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Table 1 Assumed benchmark parameters for calibration.  r   ı

7.60% 1.39% 11.85% 1.00% 4

 G W S D

−25.30 10 100 52.38 47.62

This table presents the list of parameters necessary to calibrate the model for postwar US data in order to facilitate estimation of aging effects on equilibrium equity returns. The choices of wealth, risk preferences, and labor income are restricted by reasonable levels of RRA on one hand, and on aggregate market data such as the ratio between equity and bonds, on the other. Sensitivity analyses are given in Section 4.

The impact of aging can be approximated by using the partial derivative (11) below, which captures the change in E(m∗t ) with respect to changes in aggregate horizon Ts ,



(ts − Ts ) Wt e ı 2







⎥ ⎢  2 + G + ı ⎥ ⎢ ⎥ ⎢ (ts − Ts ) ⎥ ⎢ ı 1−eı ⎥ ⎢ ⎢ ⎛ ⎞⎥ ∂E(m∗t ) ⎥ ⎢

= ⎥ ⎢ ∂Ts Pt−dt Nt ı2 ⎢ ⎥ ⎜ ⎟ ⎥ ⎢ ⎜ ⎥ ⎢ ⎜ r(ts −Ts ) ı rer(ts −Ts ) (1 − e ı (ts − Ts ) ) − 2 e ı (ts − Ts ) (1 − er(ts −Ts ) ) ⎟ ⎟ ⎢ × ⎜e − ⎟⎥  2 ⎥ ⎢ ⎜ ⎟ ⎣ ⎝ (ts − Ts ) ⎠⎦ ır 1 − e ı

(11)

where = −r and ≡  − . Note that this partial derivative captures linear approximation of 2 changes in ts − Ts only, while (10) accounts for the accurate, non-linear changes both in expected returns and aging. We compare both estimation approaches below, starting with the latter. In Section 3.1 we present the calibration particulars of the model for post-war US data, serving as our benchmark economy. In Section 3.2 we calculate equilibrium returns for past demographic states between 1955 and 2005, and verify that the model conforms to the data. Section 3.3 presents modelimplied equilibrium returns based on demographic projections between 2000 and 2050, based on Eq. (10). 3.1. Calibration Our benchmark for the numerical analysis uses the parameters listed in Table 1, aiming to calibrate the model for postwar US data. The total real equity return was 7.60% (real value appreciation plus real dividend yield), measured as the historical average between 1/1948 and 12/2007, before the 2008 crash. The historical standard deviation of the real return was 11.85%, and the average real annual riskless rate was 1.39%.4 RRA is assumed to be 4.0 for the benchmark case (this value complies with Constantinides, 2002; Mehra & Prescott, 1985, and others). Investors’ wealth is assumed 100, used as a numéraire for the displacement parameter , as the latter is adjusted to yield a ratio of 1.1 between equity and bond values.5 Annual wage income is assumed 10% of wealth, and subjective time preference is assumed  = 1%. A solution of (11) with the parameters presented in Table 1 yields a positive derivative, which implies that the longer the horizon, the higher will be the demand for equities. This result complies with Bodie, Merton, and Samuelson (1992), Viceira (2001), Goyal (2004), Cocco et al. (2005) and others.

4

Robert Shiller data, http://www.econ.yale.edu/∼shiller/data.htm. Based on Federal Reserve Statistical Release, Flow of Funds Accounts of the US, 3, 2006, Table L.100, the average equity/debt ratio during the years before the 2008 crash was 1.107. 5

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Table 2 Model returns based on 1950–2005 demographic data and Actual S&P500 Returns. Year 1950 1955 1960 1965 1970 1975 1980 1985 1990 1995 2000 2005

Model return (%)

Five year average actual return (%)

10 years moving average (%)

8.8 8.9 8.6 7.9 7.8 7.8 8.1 8.3 8.3 8.0 7.9

12.6 9.5 10.4 9.4 5.1 −2.8 9.5 13.8 13.0 18.0 −0.2 11.6

11.1 9.9 9.9 7.2 1.1 3.3 11.6 13.4 15.5 8.9 5.7

The second column from the left shows model estimates of equilibrium returns given US historical demographic data. Actual S&P500 returns are presented over the following two columns: five-year averages made up of 2.5 years before and 2.5 years after June of the indicated year and 10-year moving average.

3.2. Compliance with historical data Our historical demographic dataset includes total US population distribution by age at five-year intervals, between 1950 and 2005, as detailed in Appendix A. We use 2005 rather than later data in order to avoid the impact of the 2008–2009 financial crisis on the data. Life expectancy conditional on current age has been calculated based on Arias (2004).6 The sum of conditional life expectancy and age for each cohort yields the estimated age at death. Therefore, by dividing the number of expected years of living by the expected age at death in each cohort we obtain the normalized value for the horizon, (Tc − tc )/Tc (c stands for cohort). Population-wide life expectancy, age, and the normalized remaining life for the entire population were calculated as weighted averages, 

with cohort proportions qc serving as weights, yielding (Ts − ts )/Ts =

qc (Tc − tc )/Tc .

c

The estimated aging impacts on returns for each of the five-year population estimates are compared with return realizations. Actual return is calculated based on S&P500 monthly returns, averaged over five years: 2.5 years before and 2.5 years after June 30 of the relevant year. For example, our return estimate for 1950 is based on average monthly returns between 1/1948 and 12/1952. Monthly returns are annualized geometrically. Model-implied returns and S&P500 five-year average returns are presented in the second and third columns of Table 2. The fourth column shows a moving average of actual returns over two five-year periods. A graphical representation of the data is given in Fig. 1. Clearly, the model-implied returns are highly correlated with the historical S&P500 average. From both Table 2 and Fig. 1, one can see that the five-year averages are extremely volatile as compared to the model estimates. The reason is that the model accounts solely for the demographic impact on returns, while actual returns exhibited severe fluctuations such as the energy crises of the mid-1970s and the technology stock prices bubble and burst of the late 1990s. In order to assess statistically the relationship between actual returns and model predictions, we have regressed the latter on the former using the following regression model Yt = ˛ + ˇXt + εt ,

(13)

where Xt is the model generated return for period t, Yt = (Rt−1 + Rt ) /2, and Rt is the S&P 500 average return for the period starting 2.5 years before and ending 2.5 years after June 30th of year t. These

6 The methodology presented in Arias (2004) is based on 2002 demographic data. While life expectancy changed between 1950 and 2002, we use her analysis due to unavailability of similar data from the 1950s. Nevertheless, we have conducted a sensitivity analysis and found that a 5% decrease in life expectancy increases the demographic impact on equilibrium return by about 0.04–0.07%, depending on the estimated period.

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Fig. 1. Historical demographic effects and actual S&P500 averages S&P500 moving average (left axis), and model return (right axis) are highly correlated. The actual data is far more volatile than the estimates implied by the model.

regression results are statistically significant, with an F significance value of 0.0489 and R2 =36.5% (t statistics listed under the coefficients). Yt = −0.438 + 6.408Xt . −1.88

2.27

(14)

We therefore conclude that historical stock returns are explained by the model if noise is averaged away. 3.3. Projected demographic effects In order to draw estimates of baby-boomers retirement effects on equity returns, we use the US Census Bureau data (3/2004) of population projections between 2010 and 2050 (available at 10-year intervals, Appendix C), as well as life expectancy tables based on Arias (2004) (Appendix B). We use population projection data to calculate cohort densities through decades, as presented in the lower part of Appendix C. Next, using the life expectancy table in Appendix B, we calculate (Ts − ts )/Ts for each decade. Using remaining horizon estimates, we solve for the relevant age impact on returns as the demographic states change across decades in two ways. First, we estimate the total aging effect by using Eq. (10). Our estimates start by assuming that the benchmark parameters apply to the 2050 age pyramid. We then enter the 2040 age data, and solve for the equilibrium price and implied expected return at 2040, effectively assuming that investors act rationally and fully account for the expected aging effects between 2040 and 2050. By backward solving the model to 2010 we obtain the term structure of expected stock returns, which accounts for the expected demographic changes. As a result, this calculation accounts for the joint effects of all model parameters in calculating expected returns. Second, we contrast this calculation with the approximate effect of aging alone, as calculated by using the partial derivative (11). A plot of both term structures of expected stock returns between 2010 and 2050 is given in Fig. 2. The term structure of expected stock returns is calculated twice, first by backward-solving the model using expected parameters, starting at 2050 and ending at 2010. Second, aging impact alone on equilibrium returns is approximated by using derivative (11). Both techniques yield similar results in 2010 and 2050, but the latter is higher by 16 basis points in 2020, 18 basis points in 2030, and 10 basis points in 2040. Fig. 2 shows that the annual return impact of boomers aging is highest around 2010, and mitigates toward 2050. To assess the sensitivity of these results to various assumptions, we use the calculation

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Fig. 2. Term structure (TS) of expected stock returns with changing demographic states: 2010–2050.

based on derivative (11), addressing first the impact of life expectancy. The results are summarized in Table 3. Panel A is based on the benchmark estimate of an average normalized life expectancy (0.561, i.e., average normalized age of 0.439.) The second column from the left shows how normalized age increases (and hence the horizon declines) from 0.439 in 2010 to 0.469 in 2050. The percentage increase in normalized age starts at 4.24% between the first and second decades, but it diminishes gradually, until leveling at 0.19% between 2040 and 2050. The most interesting finding reported in Table 3 is the impact of aging on equilibrium return, presented in the right-most column. The impact starts with a decline of −2.40% from the long-term 7.60% average in the benchmark at 2010, i.e., the model predicts an average annual return of 5.20% near 2010. The impact declines gradually to a negligible impact of −0.11% near 2050 as the impact of aging fades. The average annual decline in equilibrium return over the entire period 2010–2050 is 185 basis points. This finding is higher than the 60–100 basis points per annum decline as estimated by Geanakoplos et al. (2004).

Table 3 Expected aging impact on equity return based on demographic estimates. Year

Change in normalized age

Annual return impact (% points)

Panel A: Benchmark life expectancy 0.439 2010 0.452 2020 2030 0.463 0.468 2040 0.469 2050

Average normalized age

4.24% 2.92% 2.41% 1.18% 0.19%

−2.40% −1.68% −1.41% −0.69% −0.11%

Panel B: Benchmark life expectancy +5% 0.417 2010 0.429 2020 0.440 2030 2040 0.445 0.446 2050

4.24% 2.92% 2.41% 1.18% 0.19%

−2.36% −1.65% −1.37% −0.67% −0.11%

Panel A of the table links between average normalized age of the US population and equilibrium return impact by using derivative (11). The benchmark expected return is 7.60%; therefore, the model-implied return with aging effects in 2010 is 7.60 − 2.40 = 5.20%, as plotted in Fig. 2. Life expectancy is calculated based onAppendix B and mean age is based onAppendix C. Panel B represents the implications of a longer life expectancy of 5% above the benchmark. Return impact declines because a longer life expectancy implies a more gradual change in asset allocation toward bonds as retirement is nearing.

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Given the empirical findings whereby expected demographic effects are largely ignored in stock markets, a relevant question is: what is the difference between the average S&P level on 2010 and the model-implied index level? Or, in other words, what is the demographic price impact that was not reflected in the 2010 S&P500 index? To answer this question we first estimate the accumulated demographic effects between 2011 and 2050. Second, we assume that average earnings satisfy constant returns to scale (as did Geanakoplos et al. (2004) and Liu and Spiegel (2011)), therefore the average Price/Earnings ratio should change only in response to the change in relative price. Denoting the annual demographic impact between t and t + 1 as t it+1 , the aggregate impact is given by 10

10

10

Impact2010 = (1 + 2011 i2020 ) (1 + 2021 i2030 ) (1 + 2031 i2040 ) (1 + 2041 i2050 )

10

− 1.

(15)

Replacing the annual return impacts presented in Panel A of Table 3 for the relevant variables in (15), we find that the 2010 average P/E ratio should be 47% lower than the 2050 ratio. The question of what may serve as a relevant P/E ratio benchmark in 2050 is difficult to answer, primarily because the historical P/E ratio since 1/1945 fluctuated between 6.64 and 44.20 (in 12/1999, at the height of the internet bubble). Rather than assuming a benchmark, we take the 1/2002–12/2007 average P/E of 25.877 as a benchmark because it starts after the technology bubble burst and it ends before the 2008 crisis hit stock markets. If the demographic effects for 2010–2050 were not priced in the market on 12/2007, then possibly the 2008–2009 crisis triggered aged investors to rebalance their portfolios by selling stocks and buying bonds, as they should have done earlier but did not. Because by our estimations the aggregate demographic effects as of 2010 imply a 47% decline in the benchmark P/E ratio of 25.87, then it should be 13.71 around 2010. The 2008–2009 crisis reduced the average P/E ratio to 15.88, with the lowest recorded in 3/2009 at 13.32. Between 2/2009 and 4/2009 the P/E ratio was 14.14, but it increased to 21.42 between 10/2010 and 9/2011. To put these numbers in perspective one should notice that between 1/1945 and 12/1989, a period of 45 years, the average P/E ratio was 14.54 with a standard deviation of 4.44, while during the nearly 22 years between 1/1990 and 9/2011 average P/E ratio was 25.61 with a standard deviation of 7.24. To summarize, our calculations suggest that while for a few months “two wrongs made a right”, i.e., the crisis reduced the P/E ratio to appropriately reflect the ignored expected demographic effect, prices increased during 2009–2011 to levels closer to the pre-crisis period. To visualize past and expected S&P500 trends we combined past return estimates between 1950 and 2005 with future estimates until 2050 in Fig. 3. This figure is comprised of two panels: Panel A represents the calculation based on Eq. (10), which fully accounts for the demographic effects as calculated backwards from 2050 to 2010. Panel B, on the other hand, is based on (11) and assumes that investors act myopically, looking only one decade ahead. Assuming that as of our last empirical observation, 2005, the demographic effects were not priced in the market, the model projects that whether acting rationally or myopically, the present value of the demographic impact in the neighborhood of 2010 would result in the lowest annual returns over the 100 years of our study. If investors account for the entire horizon of expected boomer’s aging the present value of all future effects would reduce the 2002–2007 average S&P500 index by about 47%, as presented in Panel A of Fig. 3. However, if they act myopically the impact is less severe, as presented in Panel B. Our calibration depends on the choice of specific values for the various parameters, and hence the estimates would be more informative if sensitivity analyses were conducted for key parameters. 4. Sensitivity analyses Sensitivity analyses for three key parameters are presented with respect to their impact on the value of derivative (11). Each parameter is measured over a range of 20% above and below its benchmark value, while all other parameters remain constant. The two most important parameters appear to be the equity premium and the standard deviation of equities. The other most relevant parameter is the normalized age of the representative investor. Specifically, the proportion of wage income out

7

Robert Shiller data of Cyclically Adjusted PE ratio, CAPE, between 1/2002 and 12/2007.

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Fig. 3. Model-implied aging effects on equilibrium rates of return vs. Realized S&P500 returns. Model-implied returns vary smoothly due to demographic fluctuations (left axis), while 5-year and 10-year moving averages of S&P500 are substantially more volatile (right axis). Panel A plots model-implied returns as if investors rationally account for expected demographic effects to 2050, given the price level at the end of 2005. One can readily see the sharp decline between 2005 and 2010. However, Panel B shows that if investors behave myopically and ignore demographic effects beyond the nearest decade, the decline between 2005 and 2010 is smaller.

of wealth, and the impatience parameter , have minute effects on derivative (11) and hence on the impact of aging on returns. In what follows we discuss a number of issues concerning some of the parameters. As noted, the three most important parameters affecting the demand for risky assets are the expected rate of return on equities, their standard deviation, and the riskless rate of return, jointly forming the market price of risk in financial markets, or the Sharpe ratio. In addition to their role in closed economies, international asset pricing models postulate that domestic Sharpe ratios are key determinants of international flows of funds: in a frictionless global economy differences in the reward to risk will result in flows of funds that would ultimately equate market prices of risk across countries, yielding the world Sharpe ratio. Our model explicitly ignores the role of international flow of funds, but allows the analysis of changes in the local Sharpe ratio. In the following sensitivity analyses we explore the effects of marginal changes in the parameters constructing the Sharpe ratio the impact of aging on returns. We disregard the source of change, whether resulting from international flow of funds or local reasons, and hence also ignore plausible fiscal effects of flow of funds.

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Fig. 4. Sensitivity analyses: the effect of key parameters on the impact of aging. The effects of changing key model parameters ±20% vs. their benchmark value on the measure of aging impact on returns, by derivative (11).

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An increase in the equity premium, either by increasing the expected equity return or through a decline in the riskless rate, increases the (negative) aging impact, and vice-versa. An increase in the standard deviation of equity returns reduces this impact in a convex schedule. Both effects are presented in the first two panels of Fig. 4 with respect to the aging impact between 2010 and 2020. For example, a 5% increase in the benchmark equity premium (Panel A), from 6.41% to 6.52%, increases the aging impact from −2.40% to −2.52%. An additional important parameter is life expectancy. The estimates in Panel-A of Table 3 are based on the assumption that cohort-dependent life expectancy estimates remain constant until 2050 across all cohorts. As demonstrated over the past century, life expectancy increases with medical care, improved nutrition, and other factors. As Panel C in Fig. 4 shows, aging impact declines with life expectancy. The return impact of this result is shown in Table 3: a 5% increase in life expectancy reduces the aging impact by 4 basis points in 2010, from −2.40% to −2.36%. This impact hardly exists in the very long term, near 2040 and 2050. We note, without adding a table due to space considerations, that the marginal impact declines as life expectancy further increases. Lastly, it can be argued that capital flows from surplus countries would enter the U.S. if asset prices be comparatively lower. Feroli (2006) explored such effects on G-7 countries in an OLG model, and found partial explanation for capital flows, yet the impact of flows on equilibrium returns has not been validated. 5. Summary Theoretical models argue that since retirees liquidate savings for consumption and since equities are riskier than bonds, retirees will sell equities first to a smaller pool of young cohorts, thus driving their prices down. With the anticipated postwar US baby-boomers’ retirement, some hypothesize an asset market “meltdown” between 2020 and 2030. This paper is aimed to quantify the price impact of boomers’ investment decisions between 1950 and 2050. Our model accounts for aging effects due to labor income, optimal consumption, and optimal portfolio rules of the aggregate investor. Predictions of the model between 1950 and 2005 were regressed on moving averages of realized S&P500 returns, and were found significant (5%). Based on the finding that the model explains the data, we project demographic effects on equity returns between 2010 and 2050. The model was calibrated for postwar parameters of US financial markets, as well as the 2004 Census Bureau population aging forecast until 2050. Our major findings indicate that the expected annual rate of return on equities will fall short of the historical rate of 7.60% by 2.40 percentage points in the neighborhood of 2010, −1.68% near 2020, −1.41% near 2030, 0.69% near 2040, and −0.11% near 2050. Assuming that as of late 2007 asset prices did not reflect expected demographic effects, we calculate the present value of all future effects to 2050. We find that the 2008 and early 2009 market drop due to the financial crisis reduced the P/E ratio of S&P500 to 14.14, a level that is close to that estimated by the model. Therefore, the increase of the P/E ratio to the low 20s in 2009–2010 reflects underpricing of the US boomers’ effect. We conduct sensitivity analyses with respect to a number of key parameters, such as the expected equity premium, equity risk, and life expectancy, but find that their impact is smaller than the potential effects of aging by two orders of magnitude. Appendix A. Table A1.

1950 0–4 5–19 20–44 45–64 65–84 85+ Total 0–4 5–19 20–44 45–64 65–84 85+ Total

17,237 36,576 59,510 31,447 12,298 744 157,812 10.9% 23.2% 37.7% 19.9% 7.8% 0.5% 100%

1955 19,263 42,609 59,639 34,489 14,291 782 171,073 11.3% 24.9% 34.9% 20.2% 8.4% 0.5% 100%

1960 20,849 50,340 60,157 37,712 16,134 967 186,159 11.2% 27.0% 32.3% 20.3% 8.7% 0.5% 100%

1965 20,444 57,692 62,368 40,347 17,797 1148 199,796 10.2% 28.9% 31.2% 20.2% 8.9% 0.6% 100%

1970 17,814 61,249 67,016 43,367 19,237 1429 210,112 8.5% 29.2% 31.9% 20.6% 9.2% 0.7% 100%

1975 16,583 60,201 75,474 44,872 21,185 1850 220,165 7.5% 27.3% 34.3% 20.4% 9.6% 0.8% 100%

1980 16,777 56,271 86,705 45,294 23,505 2365 230,917 7.3% 24.4% 37.5% 19.6% 10.2% 1.0% 100%

1985 18,318 53,202 97,363 45,750 25,740 2682 243,055 7.5% 21.9% 40.1% 18.8% 10.6% 1.1% 100%

1990

1995

2000

2005

19,710 53,753 103,072 47,721 28,374 2908

20,465 57,220 104,827 53,689 30,085 3318

19,830 61,458 105,060 62,728 30,963 4115

20,408 63,096 104,934 73,065 31,699 5012

255,538 7.7% 21.0% 40.3% 18.7% 11.1% 1.1%

269,604 7.6% 21.2% 38.9% 19.9% 11.2% 1.2%

284,154 7.0% 21.6% 37.0% 22.1% 10.9% 1.4%

298,214 6.8% 21.2% 35.2% 24.5% 10.6% 1.7%

100%

100%

100%

100%

Population Division of the Department of Economic and Social Affairs of the United Nations Secretariat, World Population Prospects: The 2004 Revision and World Urbanization Prospects: The 2003 Revision, http://esa.un.org/unpp, 04 September 2006; 1:58:38 AM.

H. Kedar-Levy / North American Journal of Economics and Finance 30 (2014) 106–121

Table A1 United States of America Total Population by age group; five-year estimates (thousands).

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Appendix B. Table A2. Table A2 Abridged life table for the total population: United States, 2002. Age

0–1 1–5 5–10 10–15 15–20 20–25 25–30 30–35 35–40 40–45 45–50 50–55 55–60 60–65 65–70 70–75 75–80 80–85 85–90 90–95 95–100 100+

Probability of dying between ages x to x + n

Number surviving to age x

Number dying between ages x and x + n

Person-years lived between ages x and x + n

Total number of person- years lived above age x

Expectation of life at age x

n qx

lx

n dx

n Lx

Tx

ex

0.006971 0.001238 0.000759 0.000980 0.003386 0.004747 0.004722 0.005572 0.007996 0.012066 0.017765 0.025380 0.038135 0.058187 0.088029 0.133076 0.201067 0.304230 0.447667 0.599618 0.739020 1.000000

697 123 75 97 335 468 464 545 777 1163 1692 2375 3478 5104 7272 10,025 13,132 15,874 16,252 12,024 5,933 2,095

100,000 99,303 99,180 99,105 99,008 98,672 98,204 97,740 97,196 96,419 95,255 93,563 91,188 87,711 82,607 75,335 65,310 52,178 36,304 20,052 8,028 2,095

99,389 396,921 495,706 495,311 494,345 492,189 489,871 487,395 484,164 479,362 472,292 462,186 447,838 426,603 395,866 352,791 294,954 222,013 140,041 67,822 23,056 5,675

7,725,787 7,626,399 7,229,477 6,733,771 6,238,460 5,744,116 5,251,927 4,762,056 4,274,661 3,790,497 3,311,135 2,838,843 2,376,658 1,928,820 1,502,217 1,106,350 753,560 458,606 236,593 96,552 28,730 5,675

77.3 76.8 72.9 67.9 63.0 58.2 53.5 48.7 44.0 39.3 34.8 30.3 26.1 22.0 18.2 14.7 11.5 8.8 6.5 4.8 3.6 2.7

Source: Arias (2004), p. 39.

Appendix C. Table A3. Table A3 Projected population of the United States, by age: 2000–2050 (in thousands except as indicated. As of July 1. Resident population, leading dots indicate sub-parts).

Population Total 0–4 5-19 20-44 45-64 65-84 85+ Percent of total Total 0-4 5-19 20-44 45-64 65-84 85+

2000

2010

2020

2030

2040

2050

282,125 19,218 61,331 104,075 62,440 30,794 4,267

308,936 21,426 61,810 104,444 81,012 34,120 6,123

335,805 22,932 65,955 108,632 83,653 47,363 7,269

363,584 24,272 70,832 114,747 82,280 61,850 9,603

391,946 26,299 75,326 121,659 88,611 64,640 15,409

419,854 28,080 81,067 130,897 93,104 65,844 20,861

100.0 6.8 21.7 36.9 22.1 10.9 1.5

100.0 6.9 20.0 33.8 26.2 11.0 2.0

100.0 6.8 19.6 32.3 24.9 14.1 2.2

100.0 6.7 19.5 31.6 22.6 17.0 2.6

Source: U.S. Census Bureau, 2004, “U.S. Interim Projections by Age, Sex, Race, Internet Release Date: March 18, 2004.

100.0 6.7 19.2 31.0 22.6 16.5 3.9 and

100.0 6.7 19.3 31.2 22.2 15.7 5.0 Hispanic

Origin,”

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