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In a dynamic asset-pricing model with Hyperbolic Absolute Risk Aversion preferences, investors who have Decreasing Relative Risk Aversion have an age dependent component in their optimal asset allocation rule. Unlike conventional models, this component affects equilibrium equity returns due to demographic trends in the same direction suggested by (Poterba, J. M. (2001). Demographic Structure and Asset Returns.The Review of Economics and Statistics, 83 (4) 565–584; Poterba, J. M. (2004). The Impact of Population Aging on Financial Markets, NBER Working Paper No. 10851). Calibration to US data between 1950 and 2050 reveals that between 1950 and 1970 this effect potentially added 0.15% to the 7.79% post-war long-term return (actual was 8.39%). As boomers joined the labor market (1970–2004) this positive effect turned negative (0.17–0.34%). Ignoring consumption and wealth effects, the model implies that this effect will draw 0.06% annually between 2005 and 2015 but add 0.22% between 2016 and 2050.

It is well documented that disproportional changes in young, prime-age and old demographic cohorts change the aggregate demand for financial assets, real estate, and consumption. The typical assumption in population economics is that young need to borrow in order to invest, primarily in real estate, prime-age cohorts are the major savers in the economy and the old generation dis-save in order to consume. Overlapping generations (OLG) models, e.g., Constantinides, Donaldson, & Mehra (2002), and Constantinides and Duffie (1996), account for aggregate consumption and investment decisions and show that since investors in their old age use their savings for consumption, and since equities are riskier than bonds, retirees will sell equities first, thus drive their prices down and their expected returns up. When Storesletten, Telmer, & Yaron (2001) add idiosyncratic labor risk to the OLG model and allow trade across cohorts, they come to a similar conclusion, though in their calibrated solution equity positions at old age may still be up to 30%. Yet, the literature is still inconclusive about the effect of aggregate demand for savings on expected equilibrium returns. While Siegel (1998) and Campbell (2001) generally agree with the OLG model predictions on different theoretical grounds, Poterba, 2001 and Poterba, 2004 took an empirical approach and analyzed the US Surveys of Consumer Finances of 1995 and 2001, respectively. Unlike the theoretical models, he concludes that if demographic variables are at all relevant for equity pricing, the effect should be positive. This finding calls for a reexamination of the theoretical reasoning of demographic effects since aggregate demand for savings has far-reaching effects on financial markets, pension funding, social security schemes, etc. The goal of this paper is to demonstrate a positive aging effect on equilibrium equity prices that was not discussed in prior theoretical studies; it stems from an aggregate aging effect of investors with Hyperbolic Absolute Risk Aversion (HARA) utilities and Decreasing Relative Risk Aversion (DRRA) preferences. We show that disproportional changes in the age pyramid and especially changes in the proportion of old-age cohorts might affect equilibrium equity prices through the present value of investors’ lifetime subsistence level. This factor serves as a reference level for the investor when determining the optimal exposure to the risky asset, i.e., this is not an actual, observable, consumption parameter. We demonstrate the above-mentioned effect in a dynamic asset-pricing model where two investor groups with different preferences employ two optimal dynamic asset allocation strategies that enable us to clear the stock market by solving for equilibrium prices endogenously, through trade. This structure allow us to solve for the return generating process endogenously, thus capture demographic effects when equity supply is fixed1 and the expected return mean-reverts to a stationary long term value (as in Marton 1971, excluding the stochastic element). We refer to the two strategies as “contrarian” and “trend,” for notational simplicity. We demonstrate that the contrarian strategy is optimal for high risk-averse investors with Constant Relative Risk Aversion (CRRA) preferences and the trend strategy is optimal for investors with DRRA preferences under a HARA utility function.2 The contrarian is derived by solving for the Relative Risk Aversion (RRA) parameter that implies an optimal sell of units of shares upon a positive price change, and an optimal buy of units of shares when the price declines. Conversely, the trend strategy is optimal for a low risk-averse investor, and it is defined such that the investor buys units of shares upon a price increase, and vice-versa. Hence, we clear the demand and supply for shares period after period and reveal a lognormal price process that depends on the age-dependent demand for equities by the low risk-averse investors. In order to focus our analysis on the age-dependent factor of the trend (DRRA) investors, we assume that aggregate investors’ consumption is independent of demographic changes. The age-dependent factor, henceforth the “floor” in the trend strategy, is present in the optimal investment rule for an investor with DRRA preferences since the HARA utility function has a displacement factor. When the optimal asset allocation strategy is solved, this element stands for the present value of the investor's minimum lifetime consumption, or “subsistence consumption level” (Kingston, 1989). In the passage of time, this floor declines monotonically until is reaches zero when the investor dies, because the shortening horizon necessitates a smaller financial reservoir to finance remaining minimum consumption. The optimal asset allocation strategy determines that this floor should be subtracted from the investor's wealth and the remaining difference should be multiplied by a multiplier, greater than unity, in order to determine the amount of wealth that should be invested in the risky asset. Therefore, the amount that the DRRA investor allocates to the risky asset increases with age, resulting in an increased aggregate price level. We calibrate the model to post-war US data and solve for the model-implied mean price process under the assumption that the ratio of Labor Market Participation (LMP) to Total Population (TP) is perfectly negatively correlated with the floor. Since the LMP/TP ratio oscillates due to demographic trends, the resulting price process and the realized equity returns oscillate as well. Our calibration covers the period 1950–2050 and we assume that the 7.79% mean log return on the S&P composite (from Shiller's website) between 1950–12/2004 is the long-term return until 2050. We find that between 1950 and 1970 the floor effect could have added 0.15 to the 7.79% post-war long-term return, i.e., turning it 7.94%, while the actual was 8.39%. As boomers joined the labor market, between 1970 and 2004, the floor's positive effect turned negative, drawing 0.17–0.34% from the long-term mean, 7.45% between 1971–1995 and 7.62% between 1996–2004. The actual returns in these periods were 6.56 and 9.88%, respectively. We then project the calibrated model until 2050 and find that while ignoring consumption and wealth effects, the model implies an annual negative floor effect of 0.06% between 2005 and 2015 and a positive floor effect of 0.22% between 2016 and 2050. This latter result appears to comply with the empirical findings of Poterba, 2001 and Poterba, 2004 who estimates moderate positive demographic effects on equity prices as the US baby-boomers retire. Theoretically, demographic effects on equilibrium equity prices can be justified when aggregate preferences are age dependent. In a standard asset-pricing model, investors should discount any future deviations from the mean returns, definitely predictable demographics oscillations. Empirically though, investors seem to ignore, or fail to account for predictable demographic variables for other reasons. Mankiw and Weil (1989) argue that the market did not predict the increase in the post-war baby-boomers demand for housing in the 1970s–1980s, although demographic trends could have been used effectively to make such prediction. DellaVigna and Pollet (2005) argue that investors do not pay attention to predictable changes in the investment opportunity set and show that predictable demographic trends had a significant effect on age-sensitive industries/sectors (toys, bicycles, beer, life insurance, and nursing homes). However, they find that predictable demographic changes did not predict stock returns. Bergantino (1998) finds that about 40% of the increase in housing prices between 1965 and 1980 can be attributed to the baby-boomers’ increased demand. Bergantino further argues that since the young cohort came into the prime-age cohort 20 years later, their demand for savings accounted for about 30% of the increase in equity prices starting 1985. Abel (2001) extends this line of logic and argues that once the prime-age cohort starts retiring, between 2005 and 2010, their dis-saving effect will cause a decline in equity prices. Recent empirical evidence by Geanakoplos, Magill and Quinzii (2004), Bakshi and Chen (1994) and Ang and Maddaloni (2005) shows that equity prices respond to changes in demographic structure in a fairly predictable way. Ang and Madalloni 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 the change in the proportion of retired adults is a significant predictor of excess returns. This particular finding is one of the predictions of our model. In Section 2 we present the mapping of optimal portfolio rules and the aggregate trend and contrarian strategies. In Section 3 we show how the market clears and equilibrium prices are derived, and we show how demographic trends affects equilibrium prices. Section 4 summarizes.