1. Summary of evidence on TDF rebalancing

This section summarizes the evidence that TDFs rebalance within a few months after differential asset class returns to restore the desired asset-class allocations. We describe the evidence from PSS that documents how the actual rebalancing trades of TDFs across asset classes match what one would expect given asset-class returns and the stated fund strategies.

First, how should we expect TDFs to rebalance? Consider a TDF with $1 of assets, a target weight of S* invested in equity funds and a target weight of 1 − S* invested in bond funds. Further assume that the TDF is at its target allocation at the beginning of the period and that the target shares do not change (no move along the glide path) during the period. As shown in the second panel of Table 1, following equity and bond asset returns of R ^E and R ^B, the TDF needs to sell the equity fund in the amount of −S*(1 − S*)(R ^E − R ^B), and buy the same amount of the bond fund (row 2). These same quadratic patterns hold when there are fund inflows or outflows, or when there are more than two asset classes.Footnote ³

Table 1. TDF rebalancing in response to asset class returns

Note: This table shows the formula for rebalancing that restores the target asset allocation of a TDF after realized asset class returns R ^E (equity) and R ^B (bond). The target equity share is S* and the target bond share is 1 − S*. The TDF is assumed to hold the target allocation at the beginning of the period and to reinvest all dividends paid out by the underlying mutual funds. Dividends declared by the TDF are assumed to be reinvested by investors. TDF asset value at the beginning of the period before the asset class returns is normalized to $1. The formula in this table assumes zero net flow to the TDF. V denotes the value of the portfolio before trades and flows, or 1 + R ^B + S*(R ^E − R ^B).

Source: Parker et al. (Reference Parker, Schoar and Sun2023).

The rebalancing formulae – the last row of Table 1 – show that the better an asset class performs, the more the TDF must sell of that asset class and buy of the other asset class to rebalance. That is, TDF strategies are contrarian at the level of asset classes.

Importantly for testing, these formulae predict how different TDFs should rebalance: the amount of equity or bonds that a given TDF must sell in response to a positive excess return on that asset class is a quadratic function of its desired equity share, with a maximum for a TDF with a 50 percent desired equity share. This result is intuitive: for the same amount of differential asset class moves (R ^E − R ^B), a TDF with 100 or 0 percent equity share has no need to rebalance, and a TDF with 50 percent equity share faces the largest distortion to its asset allocation.

Second, do TDFs actually rebalance as predicted? While TDFs have some discretion over rebalancing across asset classes, the answer is that TDF rebalancing is contrarian and quadratic as predicted. Further, one can measure the timing of the rebalancing. PSS shows that TDFs rebalance within a couple of months with passive funds rebalancing rapidly and more active funds rebalancing more slowly.Footnote ⁴

PSS develops a relatively standard method to measure rebalancing trades by TDFs, but we describe it precisely here because we use the same measures later in our paper. Given holdings data of the underlying mutual funds by TDF k in quarter q, define the dollar amount of the ‘total trade’ for each share class (c) as the change in the value of holdings in excess of the value predicted by the quarterly share class return, that is, TotalTrade _ckq = MV _ckq − MV _ck,q−1(1 + r _cq). The observations from each holding to the TDF-by-asset-class level are aggregated to obtain $TotalTrade_{kq}^y$ where y stands for either the equity (E) or the fixed income (B) asset class. Given these amounts, the ‘flow-driven trade’ by a TDF of an asset class is measured as the dollar flow to the TDF allocated pro rata to lagged portfolio weight of the asset class. Finally, the ‘rebalancing trade’ is the difference: $Rebalancing_{kq}^y = TotalTrade_{kq}^y -FlowDrivenTrade_{kq}^y$. To match the formulae in Table 1, where the total assets of the TDF are assumed to be $1, the dollar rebalancing trades are normalized by the lagged total assets of the TDF.Footnote ⁵ The return on equity, R ^E, is the average return on domestic equity and foreign equity weighted using lagged TDF portfolio weights, thus is TDF-specific.

Before quantifying the relationship between predicted and actual rebalancing at the TDF level, Figure 4, reproduced from PSS, shows in broad terms that the rebalancing trades are contrarian at the asset-class level and that they match the quadratic pattern of the simple formula quite well. For each range of stated equity share, the median rebalancing across periods and TDFs with that stated equity share in response to a 10 percent excess return on equity in a quarter fits the quadratic function well for equity and slightly less well for bonds (panels (a) and (b) of Figure 4). For example, when R ^E − R ^B = 10%, a TDF with 0.65 equity share is expected to sell 2.3 percent of its portfolio value in stocks, which is also what the median fund sells. Rebalancing with respect to bonds also has a quadratic shape, but the magnitude is lower than predicted. Panels (c)–(f) show the results for passive and active TDFs separately. The smaller magnitude in bond rebalancing is due to active TDFs.

Figure 4. Median rebalancing by equity share.

Note: The connected lines plot the median ratio of rebalancing by TDFs in each stated equity-share group: greater than 90%, greater than 80% up to 90%, … but the bin centered at 0.25 includes all TDFs whose equity share is at or below 30%. The outcome variable is the amount of rebalancing trade (in equity or bonds) scaled to show the amount of rebalancing for each 10% movement in R ^E − R ^B. The dotted line represents the theoretical predicted magnitude of the ratio at the midpoint of each interval. (a) and (b) use the full sample, (c) and (d) use the sample of passive TDFs whose holdings in index mutual funds are at least 50% of their portfolio values, and (e) and (f) use the sample of active TDFs whose holdings in index funds are less than 50% of their portfolio values.

Source: Parker, Schoar, and Sun (Reference Parker, Schoar and Sun2023).

It is worth noting that TDFs designed for young and old investors engage in different degrees of this counter-cyclical rebalancing. Most TDFs start with a large desired share of equity – on the order of 90 percent – until roughly 25 years before retirement. The desired equity share declines smoothly over time to reach roughly 40 percent 10 years after the target date. Therefore, an aging population (such as for the United States) can generate stronger counter-cyclical rebalancing demand, according to life cycle models, than a young population does.

To be more precise (and not limit analysis to the median TDF in each group), Table 2 presents a subset of the results on rebalancing contained in PSS and highlights three key findings in PSS about TDF rebalancing. First, during a quarter, TDFs rebalance roughly 80% of the amount predicted by the rebalancing formulae. Columns 1–2 show that TDFs rebalance 44, 70, and 83 percent of the predicted amount of equity in the same month as the return differential (row 1), by 1 month after the return (row 2), and by 2 months after (row 3) respectively. These coefficients trace out the monthly speed of rebalancing for the average TDF in equity funds. Control variables (added in column 2) make little difference to the estimated coefficients.

Table 2. TDF rebalancing as a fraction of predicted rebalancing, 2008–18

This table presents a subset of results in estimating the relationship between actual rebalancing by TDFs in quarter q and the predicted values of rebalancing given the TDFs' equity shares and realized differential asset-class returns during the third, second, and first months of quarter q and during q − 1 in the period 2008Q3–2018Q4. Observations are at the TDF quarterly level. Rebal(E)_q/TNA _q−1 (Rebal(FI)_q/TNA _q−1) in columns 1–4 (5–8) is TDF-level rebalancing trade in quarter q with respect with equity (bond), divided by $TDF{\mkern 1mu} {\kern 1pt} TNA$ in quarter q − 1 and winsorized at 1% and 99%. Pred.rebal _q,m=t stands for predicted rebalancing in response to the realized return of the tth month of quarter q < ddollar > Pred.rebal _q−1 stands for the value of predicted rebalancing in response to the realized return of quarter q − 1. R ^E is approximated by the weighted average between total US and foreign equity market return. Control variables include lagged quarter's log $TDF{\mkern 1mu} {\kern 1pt} TNA$, log $Series{\mkern 1mu} {\kern 1pt} size$, $Cash{\mkern 1mu} {\kern 1pt} share$, and current quarter's $TDF{\mkern 1mu} {\kern 1pt} flow{\mkern 1mu} {\kern 1pt} rate$, $TDF{\mkern 1mu} {\kern 1pt} quarterly{\mkern 1mu} {\kern 1pt} return$, and $Years{\mkern 1mu} {\kern 1pt} to{\mkern 1mu} {\kern 1pt} retirement$. Standard errors are clustered two ways by TDF and quarter.

*p < 0.1; **p < 0.05; ***p < 0.01.

Source: Table 3 of Parker et al. (Reference Parker, Schoar and Sun2023).

Second, passive TDFs rebalance more rapidly and more completely than active TDFs do. Splitting the sample of TDFs according to whether the majority of assets are invested in index funds or actively managed funds, column 3 shows that 50 percent of the predicted rebalancing is implemented within the same month for passive TDFs, and 85 percent by the end of the quarter. In contrast, column 4 shows that only about 40 percent is implemented by active TDFs within the same month, an amount which is not statistically significant. Similarly, passive TDFs completely return to desired shares within the same quarter, while active TDFs still have 27 percent of the way to go at the end of the quarter. As expected, portfolios of passive TDFs track their desired asset allocations more closely than active TDFs.

Third, smaller and less statistically significant coefficients in columns 5–8 suggest that TDF rebalancing in fixed income is weaker and slower. However, this finding may not reflect true economic exposure over time because TDFs' use cash and derivatives to rebalance fixed income exposures.Footnote ⁶

We now turn to describing that data that we use in our analysis of the role of TDFs in stabilizing the equity market during the pandemic.

2. Data on TDFs, funds, stocks, and returns

To maintain consistency, our use of data largely follows PSS.

TDFs: We obtain quarterly fund characteristics and holdings of TDFs from the CRSP Mutual Fund Database. TDFs are identified from fund names containing target retirement years at 5-year intervals ranging from 2000 to 2070, then manually cleaned using the TDF series names listed in the Morningstar annual TDF research reports. Most holdings of TDFs are other mutual funds which we link to the CRSP Mutual Fund Database using the CUSIP codes of the share classes. We use this matching to categorize each holding as domestic equity, foreign equity, or fixed income.

Equity mutual funds: Using CRSP, we construct a dataset on the underlying mutual funds that focuses on domestic equity mutual funds (CRSP objective codes starting in “ED”, i.e., Equity-Domestic). We use funds sold both to retail and institutional investors, and aggregate different share classes to the fund level. For each mutual fund, the percent ownership by TDFs is the total of TDF holdings (across all share classes) by the total assets of the fund.

Individual stocks: Our panel dataset of monthly stock return, price, volume, and market capitalization is built from CRSP and financial data from Compustat. We include all stocks traded on the New York Stock Exchange, NASDAQ, and American Stock Exchange. We use Thomson Reuters and MFLINKS to measure stockholding by TDFs through mutual funds. For concerns over lack of liquidity, we drop stocks with market capitalizations that place them in the bottom 5 percent of NYSE stocks or with beginning-of-month prices below $5 (penny stocks), following Jegadeesh and Titman (Reference Jegadeesh and Titman2001).

In Table 3, we present the summary statistics on TDFs, equity mutual funds, and stocks in our sample period 2019–22. Compared with the earlier period of 2008–18 studied in PSS, TDFs have higher but more volatile returns during the more recent period and have a reduced cash share. There are more passive TDFs in the new sample and the underlying mutual funds are more likely to be passive. We also observe that TDF ownership at the fund level and its indirect ownership at the stock level are both higher than in the earlier sample period. At the fund level, the average TDF ownership increased from 10 to 13 percent. At the stock level, TDF indirect ownership is doubled, from 0.64 to 1.28 percent.

Table 3. Summary statistics of TDFs, equity mutual funds, and stocks, 2019–22

Note: For TDFs, $Target{\mkern 1mu} {\kern 1pt} year$ is the target retirement year stated in the fund name. $Years{\mkern 1mu} {\kern 1pt} to{\mkern 1mu} {\kern 1pt} retirement$ is $Target{\mkern 1mu} {\kern 1pt} year$ minus current year. $Series{\mkern 1mu} {\kern 1pt} size$ is total size across TDFs in a series (a collection of TDFs with the same manager(s) but different target retirement years). $Passive{\mkern 1mu} {\kern 1pt} TDFs$ are those with more than 50% of their assets invested in index funds. For mutual funds, Fund flow rate is the quarterly growth rate in assets in excess of that implied by net fund return. Fraction held by TDFs is the total value of TDF holdings of a fund divided by Fund size. Fund family size is the total size of funds managed by a management company. Fund age is the years since inception of the oldest share class of a fund. Expense ratio is the weighted-average net expense ratio across share classes. Return volatility is the 1-year standard deviation in the monthly returns. For stocks, Monthly return is the monthly total return of a stock. 4-Factor market beta is the monthly return adjusted for market, SMB, HML, and momentum factor returns using betas estimated with the pre-window (1996–2005, requiring 24 monthly return observations). TDF ownership refers to the fraction of a stock owned indirectly by TDFs through mutual funds. Mutual fund ownership is the fraction of a stock owned by equity mutual funds that have no investment from TDFs. Market capitalization is total shares outstanding times the share price. Monthly volume/Shares out. is monthly trading volume normalized by the number of shares outstanding.

Source: CRSP.

Market excess returns: We study monthly returns during from January 2019 to December 2022 inclusive. We measure equity returns as the total return of the US equity from CRSP, and bond returns as the pre-fee return on the Vanguard Total Bond Market Index Fund. Figure 5 plots of the cumulative returns of the US equity market and the differential returns between equity and bonds during this pandemic period.

Figure 5. Cumulative return of the stock market in excess of the bond market, 2019–22.

Note: The cumulative excess return of the value-weighted monthly total US equity market (R ^E, solid line) less the Vanguard Total Bond Market Index Fund (R ^E − R ^B, dashed line) during 2019.1–2022.12. Both index levels are normalized to 1 at the start of 2019.

Source: CRSP.

Following a sharp drop of 20 percent in the equity market during February–March 2020, the market experienced a rapid recovery, followed by strong performance in 2021, and a correction period with high volatility in 2022. Equity and bond returns have a correlation of 0.34 during this period, thus both the run-up in 2021 and the correction in 2022 appear smaller for the differential asset class return R ^E − R ^B than for R ^E.

3. The stabilizing effects of TDF ownership on equity mutual funds during the pandemic

The extreme stock market volatility during the COVID-19 pandemic period of 2019–22 provides a useful window into the stabilizing effects of TDFs as well as a test of this effect during a crisis. The unprecedented volatility of the economy during the pandemic changed lots of economic relationships, and TDFs may have delayed rebalancing or even changed strategies. Similarly, retirement investors may have moved money out of TDFs in response to poor performance. Either of these changes would have made TDFs less market contrarian and reduced their stabilizing effects. This section builds on the evidence that we presented in Figure 2 and shows that, in fact, TDFs acted as stabilizer during the pandemic; they sold stock funds when the stock market did relatively well and bought them when it did poorly. For example, following the stock market crash of March 2020, we observe significant investment by TDFs into equity mutual funds during March and April of 2020, consistent with 70 percent of TDF rebalancing in equity being completed within the contemporaneous month and month following a differential asset class return (Table 2).

Quantifying and generalizing this example in steps, we first study fund flows to equity mutual funds with different levels of TDF ownership during the months in which the difference in return between equity and bonds exceeded 8 percent. The fund flow rate for mutual fund j in month m is measured as the growth rate (in percent) in assets in excess of the realized net fund return, or (TNA _j,m − TNA _j,m−1(1 + r _j,m))/TNA _j,m−1 where TNA _j,m is total net assets and r _j,m is net return. We sort equity funds into high-TDF and low-TDF groups using the average TDF investment in 2018.

Table 4 shows that during the months of the pandemic with extreme returns, domestic equity funds with higher TDF exposure experience higher flows when equity underperforms bonds, and vice versa.Footnote ⁷ Means tests between the two groups show that several differences are statistically significant based on data for that 1 month alone. For example, during March 2020 when equity underperformed bonds by 12.7 percent, equity funds that had low-TDF investments (measured in 2018) saw an outflow of 4.2 percent of assets, while those with high-TDF investment experienced 2.9 percent outflow. The difference is statistically significant with a p-value of 0.03. Similarly, most differences in the flows in the other months are aligned with the predicted signs and are often statistically significant. Thus, TDFs do appear to offer counter-cyclical flows to the underlying mutual funds during the pandemic period in months when the stock market crashed or boomed.

Table 4. Flows to equity funds with high- and low-TDF ownership during months with extreme market returns

Note: Fund flow rates in percentages to equity mutual funds with high- and low-TDF holdings in months during 2019.1–2022.12 where differential return between equity and bond is larger than ±8%. Subsamples based on average TDF investments in funds in 2018 above and below median and do not include funds not held by TDFs. Differences in means between sub-samples and two-sided p-values are reported.

Source: CRSP.

Second, to quantify the average effects of TDFs on fund flows, we estimate the sensitivity of fund flows to both the current month and the lagged month's differential asset class performance in proportion to the fraction of the mutual fund that is held by TDFs (at the end of the previous quarter) using data from the entire pandemic period. We run the following regression:

(1)$$\eqalign{FundFlow_{\,j, m} & = \beta _1( R^E-R^B) _m + \beta _2( R^E-R^B) _m \times Frac.TDF_{\,j, q-1} \cr & \quad + \beta _3( R^E-R^B) _{m-1} + \beta _4( R^E-R^B) _{m-1} \times Frac.TDF_{\,j, q-1} + \gamma Frac.TDF_{\,j, q-1} \cr & \quad + \beta _5( R^E-R^B) _m \times Index_j + \beta _6( R^E-R^B) _{m-1} \times Index_j + \theta X_{\,j, m} + \xi _j + {\epsilon }_{\,j, m}} $$

In the equity fund sample, because retail investors typically invest more into equity funds when the stock market does well, we expect β ₁ and β ₃ to be positive for equity funds (Warther, Reference Warther1995; Edelen and Warner, Reference Edelen and Warner2001; Ben-Rephael et al., Reference Ben-Rephael, Kandel and Wohl2011). But, because TDF equity funds and buy bond funds when the stock market does well, we expect the main coefficients of interest, β ₂ and β ₄, to be negative. These coefficients measure the contemporaneous (β ₂) and lagged (β ₄) effect of greater TDF investment on fund flows following a positive return on the asset class of the fund. Equation (1) further allows the differential asset class returns to interact with an indicator for index funds to allow for potential different return-chasing dynamics in index funds and actively managed funds.

In the sample of bond funds, we expect the reverse response to excess returns on the stock market because TDFs rebalance into bonds when equity outperforms. That is β ₂ and/or β ₄ should be positive for bond funds.Footnote ⁸

We estimate equation (1) using only mutual funds with some TDF ownership at some point during the sample to avoid a large number of zeros in the regressions (with similar results using the entire sample). Further, since percent flow rates are noisy, especially for smaller funds, we drop observations below 1 percent or above 99 percent within the distribution for each asset class. Control variables X _j,m include fund characteristics that have previously been found to affect fund flows, specifically fund size, fund family size, fund age, net expense ratio, and return volatility. To allow for the correlations in errors in cross sections and within the same fund over time, we cluster standard errors two-ways by time and fund.

Table 5 shows that TDF ownership stabilized inflows and outflows from mutual funds during the pandemic period. Table 5, columns 1 and 2 present the estimates from equation (1) without and with fund fixed effects for all domestic equity funds in our sample. First note that the inclusion of fund fixed effects has little impact on the estimated coefficients, suggesting that the flow sensitivity to cross-sectional differences in returns and TDF ownership is similar as that to time-series changes in returns and changes in TDF holdings. Second, the coefficients on (R ^E − R ^B)_m, (R ^E − R ^B)_m−1 and on their interactions with Index suggest that equity fund flows chase equity market performance and slightly more so in index funds.Footnote ⁹ For the typical non-index equity fund that has no holding by TDFs, a 10 percent decline in the stock market is associated with an outflow of 0.46 percent of assets under management $( \widehat{{\beta _1}})$ in the month of the return and an additional outflow of 0.22 percent of assets under management $( \widehat{{\beta _3}})$ the following month, based on estimates in column 1.

Table 5. Effect of TDF ownership on mutual fund flows, 2019–22

Note: The dependent variable $Fund{\mkern 1mu} {\kern 1pt} flow$ is the growth rate in fund assets in excess of the realized net fund return. R ^E − R ^B is the excess return of the US total stock market over the US total bond market. The sample in columns 1–4 (5–8) includes retail and institutional domestic equity funds (corporate bond funds) which are held by any TDF during the sample period. $Frac.by{\mkern 1mu} {\kern 1pt} TDFs$ is measured as the fraction of fund assets held by TDFs, measured at the end of the previous quarter. Control variables include the lagged month's log $Fund{\mkern 1mu} {\kern 1pt} size$, log Fund family size, current month's log Fund age, Expense ratio, and lagged Return volatility. Standard errors are clustered two ways by time and fund.

*p < 0.1; **p < 0.05; ***p < 0.01.

Source: CRSP.

Our key result however is that this trend-chasing behavior is significantly reduced for funds with higher TDF ownership. The coefficients on the interaction terms with TDF ownership, $\widehat{{\beta _2}}$ implies that, in response to a decline in the stock market, the associated outflow is reduced by 24 percent in the month of the return (1.09 × 0.1/0.46) for each 10 percent of the mutual fund that is owned by TDFs, and by a total of 38 percent ((1.09 + 1.52) × 0.1/(0.46 + 0.22) = 0.261/0.68 = 0.38) on average over the month of and following the stock market decline. The estimates imply that the average TDF rebalances by a similar amount in the month of the return and the month after ($\widehat{{\beta _2}}$ and $\widehat{{\beta _4}}$ respectively), consistent with the timing of rebalancing by TDFs in the period prior to the pandemic (Section 1).

This contrarian trading behavior is stronger for index funds that are held by TDFs than it is for actively managed funds (as seen in columns 3 and 4). Rebalancing in index funds is also faster. Column 3 shows that rebalancing in index funds is stronger in the contemporaneous month as the return shock, while column 4 shows that rebalancing in actively managed funds is stronger in the following month. The greater and more rapid rebalancing in index funds almost surely reflects differences in TDFs rather than differences in rebalancing across funds within TDFs. The Vanguard TDFs for example hold index funds (and derivatives) and rebalance to desired equity exposure on a daily level, while Fidelity TDFs that tend to invest more in active funds and also have more discretion and allow equity share to vary over time to seek higher total returns and to save on trading costs.

For corporate bond mutual funds, Table 5 also shows that rebalancing by TDFs into bond funds when equity outperforms is passed on to the underlying fund level, and mainly in the following month (in columns 5–8, $\widehat{{\beta _4}}$ is consistently positive and significant).

In sum, we find that TDF ownership in mutual funds had a significant contrarian effect on equity fund flows during the pandemic. Thus, even in this time of extreme economic disruption, neither a reduction in rebalancing by TDFs nor active rebalancing out of TDFs by retirement investor undid the automatic TDF rebalancing that is documented in the pre-pandemic period by PSS. The typical automatic rebalancing by TDFs and inertial behavior by TDF investors respectively meant that TDFs continued to produce contrarian flows to equity funds. Did these funds stabilize the stock and bond markets during the pandemic? We turn next to evidence on the effect of TDFs on return differentials across stocks.

4. TDF ownership and stock returns during the pandemic

This section shows that, because TDFs buy stock funds when the overall stock market does poorly and sell stock funds when the stock market does well, they affect both the co-movement between stocks and market and the individual volatility of stocks.

4.1. TDFs lower stock return sensitivity to recent market performance

Because TDFs have a contrarian effect on fund flows which then put counter-cyclical pressure on stock prices, we expect stocks with higher indirect holdings by TDFs – through the mutual funds that TDFs invest in – to have lower sensitivity to systemic shocks that move the stock or bond markets. PSS shows evidence in line with this hypothesis during the decade before the pandemic, and hypothesized an increasingly important role for TDFs and TDF-like strategies. Here we use the pandemic market movements to test this hypothesis.

We estimate the impact of TDF trading on monthly ‘alphas’, which are monthly returns in excess of the returns one would expect based on their historical correlation with standard systemic risk factors and the realizations of these risk factors (described in more details below). We run the following regression using monthly data from 2019 to 2022, a period with both sizable TDF assets and high market volatility:

(2)$$\eqalign{Alpha_{iml} & = \lambda _1( R^E-R^B) _m \times TDF_{iq-1} + \lambda _2( R^E-R^B) _{m-1} \times TDF_{iq-1} + \gamma TDF_{iq-1} \cr & \quad + \xi X_{im} + \delta _1X_{im}( R^E-R^B) _m + \delta _2X_{im}( R^E-R^B) _{m-1} \cr & \quad + Return_{im-1} + Return_{i, m-6{\ \rm to\ }m-2} + \theta _{ml} + {\epsilon }_{im}} $$

where i indexes the stocks, m represents a month, l refers to the three-digit Standard Industrial Classification (SIC) industry classification, and (R ^E − R ^B)_m and (R ^E − R ^B)_m−1 are the current and lagged months' excess return of equity over bonds. The coefficients λ ₁ and λ ₂ measure the effect of TDF ownership on stock returns by measuring differences in risk-adjusted returns among stocks that are held in different amounts (indirectly) by TDFs. These are the coefficients on the asset class returns interacted with lagged percentage of indirect TDF ownership at the stock level, calculated as TDF _i,q−1 = Σ_jka _ij,q−1b _jk,q−1 for stock i in the lagged quarter q − 1, where a _ij,q−1 is the fraction of stock i held by mutual fund j and b _jk,q−1 is the fraction of mutual fund j held by TDF k. Our analysis also controls for the typical co-movement of stock returns within industries by including industry(3-digit SIC)-by-time fixed effects (θ _ml). If TDFs stabilize stock returns, then λ ₁ and λ ₂ should be negative. The analysis clusters the standard errors two-ways by time (year–month) and stock.Footnote ¹⁰

In addition to controls directly included in equation (2), we control for typical differences in returns for different stock by using the risk-adjusted monthly return of the stocks as the dependent variable rather than the raw return. We follow a standard four-factor risk adjustment model, which includes Market-rf (the excess return of the total equity market over the risk-free rate), small-minus-big (SMB or the size factor), high-minus-low (HML or the value factor) (Fama and French, Reference Fama and French1993), and momentum (Carhart, Reference Carhart1997). An issue with this risk adjustment is that TDF trading can directly affect the sensitivity of a stock's return to the performance of the market, that is, TDFs lower the market beta of stocks, which is the main effect we want to measure. To alleviate this problem, we estimate the factor betas using the period 1996–2005 which is before the PPA of 2006, so that the betas are (largely) free of TDF impact. We require at least 24 observations for each beta estimate and winsorize the alphas at 1 percent and 99 percent to account for the fat tails due to extreme movements unrelated to TDF trading.

Table 6 shows that higher TDF ownership is associated with lower sensitivity to market momentum. That is, when the overall stock market does well, stocks that have a large indirect TDF ownership perform worse than they should have given their (pre-TDF-period) risk-factor exposure and the movement in these risk factors. This lower return is consistent with their underperformance because they are being disproportionately sold by TDFs when the overall stock market return is relatively high. In column 1, a specification without controls, the coefficient on (R ^E − R ^B)_m × TDF _iq−1 indicates that a 1 percent higher TDF ownership of a stock implies a 0.051 lower sensitivity of the four-factor alpha of that stock to the contemporaneous market return. We offer an interpretation of the magnitude below.

Table 6. TDF ownership and stock return sensitivity to market performance

Note: This table examines the relationship between indirect TDF ownership and monthly stock return sensitivity to differential asset class performance during 2019–22. The dependent variable 4-factor alpha is the risk-adjusted return winsorized at 1% and 99%, where the factors include Market-rf, SMB, HML (Fama and French, Reference Fama and French1993), and momentum (Carhart, Reference Carhart1997). The beta loadings are estimated using monthly stock returns during 1996–2005 in columns 1–5, 2006–15 in column 6, and 2009–18 in column 7. Each estimation requires 24 monthly return observations. TDF_{q_ 1} (%) is the share of a stock indirectly owned by TDFs measured at the end of the previous quarter expressed in percentage points. Control variables include log of lagged values of Market capitalization, Monthly volume/Shares out., Market-to-book ratio, and lagged values of Dividend yield 12m, ROE, Investment, Illiquidity, and Mutual fund ownership. Standard errors in this table are clustered two ways by time and stock.

*p < 0.1; **p < 0.05; ***p < 0.01.

Source: CRSP.

We also find that TDF ownership significantly stabilizes the returns on a stock the month after the market return: the coefficient on (R ^E − R ^B)_m−1 × TDF _iq−1, which was not precisely estimated in PSS, is significant and just over half the size of the contemporaneous effect during the pandemic period. The fact that there is a large and measurable lagged effect – consistent with the delayed rebalancing documented in the previous section – may be due to the larger size of TDFs or the larger size of the market movements in this more recent period than in the period studied by PSS.

When adding stock characteristics in column 2 as controls, the estimated effect of TDF ownership becomes slightly stronger. In column 3, we further control for the stock return lagged by 1 month and the cumulative return from month m − 6 to m − 2 to account for both short-term reversal and medium-term momentum in the stock returns. We observe a strong negative coefficient on the 1-month lagged return, consistent with the well-known reversal effect. However, controlling for lagged returns does not change our estimates of the TDF effect in the contemporaneous month.

Controlling for interactions of market returns with stock-level characteristics does not alter the estimated TDF effect, implying that the TDF effect is distinct from the potential effects of other stock characteristics on return dynamics. Columns 4 and 5 show the main coefficients when we include the full set of stock characteristics interacted with both (R ^E − R ^B)_m and (R ^E − R ^B)_m−1. The set of characteristics include log of lagged market capitalization, trading volume, the market-to-book ratio, lagged trailing-twelve-month dividend yield, ROE, investment, illiquidity, and the holdings by mutual funds that are not held by TDFs. If our results were entirely driven by the different characteristics of TDF-held stocks, we would expect the main coefficients on the interaction terms between differential asset class returns and indirect TDF investment to disappear in this specification. In fact, the effects of TDFs remain significant.

One possible concern is the use of the period 1996–2005 to estimate the stock betas and so to infer risk-adjusted returns, our alphas in equation (2). For example, if betas varied dramatically over time, our measure would then be poor and possibly introduce bias. In addition, the mechanical requirement for a stock to be traded during the pre-window excludes a large fraction of observations which may be important for testing our hypothesis. Below we offer several pieces of evidence to alleviate these concerns.

First, the stock betas do not move much in a way that is correlated with (indirect) TDF ownership. Though stock betas have on average risen over time, the change is not dramatic relative to the standard deviation within each estimation window.Footnote ¹¹ The table also shows that the lowest-TDF quintile is the most affected by the mechanical data restriction problem, thus the procedure mostly excludes ‘control’ stocks which are less affected by TDFs. Further, the newer firms that were not traded during the earlier window are tilted toward technology companies, so these companies which had abnormal performance during our period are actually under-represented in our sample and so are not driving our results.Footnote ¹²

Our results are also somewhat robust to some plausible alternative ways of calculating the betas used in risk adjusting stock returns. In columns 6 and 7 of Table 6, we report results using the alternative windows 2006–15 and 2009–18. As expected, the estimated same-month TDF effect $( \hat{\lambda }_1)$ becomes much smaller and statistically insignificant, because estimated betas in these more recent windows absorb some of the TDF effect.Footnote ¹³ However, the effect of the lagged R ^E − R ^B ($\hat{\lambda }_2$, not taken out by the estimated beta) is almost the same as in the other columns. This result reassures that the main effect of using the early pre-2006 window for beta is to prevent the TDF effect from being taken out by the risk adjustment, thus allowing the estimation of $\hat{\lambda }_1$.

4.3. TDFs lower return volatility

We next examine whether TDF ownership of a stock is associated with lower volatility of the returns on that stock during the pandemic period. For this analysis, we collapse the stock panel to one cross section by calculating the standard deviation of monthly returns during the period and the likelihood of extreme returns (monthly returns higher than 10% or lower than −10%). We then examine whether these volatility measures are negatively related to TDF investments in the stocks. To avoid the regressors being affected by the dependent variables, we take the TDF indirect ownership from 2018 by averaging the four quarters. Table 7, panel A shows the summary statistics of the stock-level volatility measures. The average monthly return standard deviation during this 4-year period is about 13 percent, and in 37 percent of the monthly observations, a stock has an ‘extreme return’ where the absolute magnitude of the monthly return is larger than 10 percent, confirming the overall high volatility during this period.

Table 7. TDF ownership and stock return volatility

Note: Panel A presents summary statistics of the cross section of stocks with volatility measures based on 2019–22. Panel B examines the relationship between TDF ownership and stock return volatility. SD monthly return (%) measures the standard deviation of monthly returns during the 4-year window expressed in percentages. Likelihood of extreme returns (%) is the fraction of months where the absolute value of the stock return is larger than 10%, expressed in percentages. Frac. by TDFs (%) is the percentage of a stock indirectly owned by TDFs measured as an average during 2018. Frac. by MFs (%) is the percentage of a stock owned by mutual funds with zero-TDF investment measured as an average during 2018. Control variables include logs of Market capitalization, Monthly volume/Shares out., Market-to-book ratio, and Dividend yield 12m, ROE, Investment, and Illiquidity, all measured as an average during 2019. Robust standard errors are reported.

*p < 0.1; **p < 0.05; ***p < 0.01.

Source: CRSP.

Figure 3 shows that stocks in higher quintiles of TDF indirect ownership in 2018 had lower stock return volatility during the pandemic period. Column 1 in panel B of Table 7 shows a continuous regression version of this result: stocks with greater ex ante TDF ownership have lower raw return volatility during the turbulent markets of 2019–22. Column 4 also shows that they have a lower likelihood of extreme returns. But this pattern could be due to the different characteristics of stocks that TDFs choose to own. To address this possibility, we run a cross-sectional regression with a full set of controls for stock characteristics that have been found to be associated with differential returns.

Focusing first on the role of TDFs that are unrelated to general mutual fund ownership (columns 2 and 5), we still find that stocks with greater ex ante TDF ownership have both lower raw return volatility and lower likelihood of extreme returns, but both relationships are slightly smaller. Second, in columns 3 and 6, we control for log of market capitalization, trading volume, the market-to-book ratio, and trailing-twelve-month dividend yield, ROE, investment, and illiquidity, all measured with 2018 values. The coefficient on TDF ownership drops in half again, but, even with this full set of controls, remains highly statistically significant.

To conclude, even based on the smallest estimates in columns 3 and 6, those with all controls, a 1 percent higher TDF ownership share is associated with 0.4 percent lower standard deviation of return volatility and 1.6 percent lower likelihood of realizing extreme returns.

5. Returns from trading before or with TDFs

One question one might ask is whether the stabilizing effect of TDFs might in the future be eliminated by other strategies that trade against these funds. Put differently, have TDFs made retirement investors ‘smarter’ investors with the additional benefit of stabilizing stock prices, or have TDFs made retail investors more exploitable by other traders with more sophisticated strategies?

While a full answer to these questions requires a complete model and correct understanding of these investors' goals, a partial answer comes from studying whether the TDF trading strategy was profitable during the pandemic, or whether trading against the automatic rebalancing in these retirement funds would have been profitable. PSS investigates this before the pandemic, when retail investors were moving money into equity funds in response to positive excess returns on the stock market. In this case, one might expect sophisticated arbitrage capital to trades against these general retail/institutional flows and alongside TDFs, suggesting that TDF strategies might produce better risk-adjusted returns. However, during the pandemic retail investors traded in the opposite direction to that in normal times, buying the pandemic dip, for example. In this case, TDFs and retail investors would have traded together in a macro-contrarian manner, and one might reasonably ask whether sophisticated capital was trading against or alongside TDFs and whether doing so would have produced better risk-adjusted returns over this period.

Following PSS, we consider one long-short strategy that (infeasible) trades and holds for the month of an asset-class return (and the contemporaneous TDFs rebalancing), and one long-short strategy that (feasible) trades and holds for the month following the returns (and so trades alongside slower TDF rebalancing). To trade alongside TDFs, both of these strategies short high-TDF stocks and buy low-TDF stocks (at the start of the month in question) when the stock market return is high and take the opposite position when the market return is low (and hold for a month). The profit of these strategies approximates the profit from the aggregate rebalancing trading by TDFs while using stocks with low-TDF exposure as a hedge. As before, we sort stocks into quintiles based on TDF ownership in each quarter and then form portfolios every month based on the sign of the excess equity market return.

Consider the first strategy that takes its position prior to the asset class return during a month: if (R ^E − R ^B)_m < 0, it goes long the highest TDF quintile of stocks and shorts the lowest TDF quintile at the beginning of month m and holds until the end of the month. If (R ^E − R ^B)_m > 0, the strategy takes the opposite long-short position. This strategy is impossible in practice because it requires knowledge of aggregate returns during a month at the start of the month. It also involves risk. Figure 6, panel A shows that the cumulative risk-adjusted return of this strategy is 40 percent over 4 years 2019–22, or about 83 bps per month on average. We interpret this excess return as (infeasible) upper bound to the profit of a cross-sectional trading strategy that trades in the same direction, but ahead of, TDFs.

Figure 6. Returns from TDF-based long-short trading strategy.

Note: This figure shows the cumulative four-factor alphas from investing in a portfolio of stocks with the highest TDF ownership and shorting a portfolio with the lowest TDF ownership when the excess stock market return in the current month (panel (a)) or previous month (panel (b)) is negative, and the reverse when the excess stock market return is positive. The sample includes NYSE-, NASDAQ-, and AMEX-traded stocks with market capitalizations that are above the fifth percentile on the NYSE and with beginning-of-month prices above five dollars. Stocks are sorted into quintiles according to their average indirect TDF ownership in 2018.

Consider the second strategy that trades along with TDFs in the month following a return, month m: if (R ^E − R ^B)_m−1 > 0, go long the highest TDF quintile of stocks and short the lowest quintile during month m, and the reverse when (R ^E − R ^B)_m−1 < 0. Because this strategy trades the month after a return, it is feasible. This strategy trades alongside the slower rebalancing TDFs, which we show are primarily the active TDFs. Panel B of Figure 6 shows that this strategy of trading along with active TDFs still generates positive profits. In fact, somewhat surprisingly it is only slightly less profitable than the infeasible strategy that trades ahead of TDFs. That said, the key point for us is that sophisticated capital would not have been able to exploit predictable rebalancing by TDFs during this period: feasibly trading against TDFs would have generated a loss of 30 percent return over 4 years.

In sum, the TDF rebalancing the month after a return seems to be profitable in a cross-sectional sense during the pandemic period. It does not seem to be profitable to trade against TDFs based on the previous month return. Thus arbitrage capital should not be allocating funds to trading strategies that would reduce the cross-section price impact of TDF trading going forward.

6. Concluding remarks

TDFs have become an important financial instrument for retail investors, largely following the 2006 Pension Protection Act which qualified TDFs to serve as default options in 401(k) retirement plans. At present, 90 percent of employers offer TDFs as the default options in their retirement plans, and TDFs manage one-quarter of all 401(k) plan assets.

But while TDFs were designed to be optimal for households taking returns as given, they have had an unintended and significant stabilizing impact on mutual fund flows and on stock returns during the period of market volatility around the pandemic. Because TDFs rebalance portfolios by selling stocks when the stock market rises and buying stocks when the market falls, they have acted as a market-stabilizing force. These findings complement and extend the evidence of Parker et al. (Reference Parker, Schoar and Sun2023) based on the period before the pandemic when TDFs were growing and economic outcomes were more typical. We show that even during the unprecedented volatility of the last few years, TDFs have stabilized the funding of the mutual funds that they disproportionately invest in, and they have stabilized the prices of stocks that they (indirectly) disproportionately hold.

If the amount of funds invested through TDFs continues to grow, or as the population ages and remains in TDFs so that more TDF assets are near a 50 percent equity share implying maximum rebalancing, the contrarian trading of these types of funds may start to have greater effects on aggregate market returns. By putting downward pressure on stock prices after market increases and upward pressure after market drops, contrarian strategies are likely dampening overall stock market fluctuations. That said, at the moment these market-wide effects cannot be measured well given market volatility, a reasonable estimate of the elasticity of the level of the overall stock market to TDF trading, and the size of the TDF sector at the moment. TDF macro-contrarian trading is also likely affecting the serial correlation of returns, and increasing the correlation between stock and bond returns, but again in ways too small to evaluate or quantify to date.

Finally, we should emphasize that any stabilizing effect of TDFs on the stock market may or may not be beneficial for the stock market, the economy, or even the TDF investor. If a given stock market movement is an inefficient, transitory fluctuation in market prices, then trading by TDFs may increase market efficiency by reducing the deviation of prices from their efficient fundamental values. Alternatively, if a fluctuation is instead an efficient response to fundamentals (e.g., a permanent change in aggregate dividends), then trading by TDFs may decrease market efficiency (and/or TDFs would lose some returns to arbitrage capital that trades to restore fundamental prices).

An alternative design choice for TDFs that would not require a stand on whether fluctuations are or are not efficient would be to take a macro-optimal perspective and structure the TDFs to hold a portfolio comprised of an age-dependent combination of a risk-free asset and the market portfolio of all risky assets (consisting of whatever share of stocks and bonds there are in the market portfolio). As people aged, the TDF would have them hold more of the risk-free asset and less of the market portfolio, but as the stock market fluctuated, the TDF would only adjust the balance between all risky assets – stocks and bonds – and risk-free short term debt.