> For the complete documentation index, see [llms.txt](https://laurence-wilse-samson.gitbook.io/textbooks/llms.txt). Markdown versions of documentation pages are available by appending `.md` to page URLs; this page is available as [Markdown](https://laurence-wilse-samson.gitbook.io/textbooks/financial-economics-claims-prices-holders/part-iv-the-investor-ecology/chapter_14_households.md).

# Chapter 14: Households as Investors

*Part IV: The Investor Ecology — Financial Economics: Claims, Prices, and Holders*

***

## Opening Episode: The Company That Changed a Form

In the spring of 1998, a large American corporation changed the way its 401(k) enrollment form worked. Nothing else changed: the same investment menu, the same employer match, the same vesting schedule, the same tax code. What changed was the position of a box. Before, a newly hired employee who wanted to save had to elect a contribution rate and an allocation; do nothing, and nothing happened. After, an employee who did nothing was enrolled automatically at three percent of pay, invested in the plan's money market fund. To *not* save now required filling in a form.

Brigitte Madrian and Dennis Shea had the plan's administrative records, which let them compare two cohorts at the same firm, in the same jobs, facing the same menu, differing only in which side of the change they were hired on. That is about as clean a natural experiment as household finance ever gets.

Participation among new hires went from roughly half to nearly ninety percent.

The magnitude is worth sitting with, because no economic variable moved. The price of saving did not change. The return on saving did not change. The information available to employees did not change; if anything it got worse, since the automatically enrolled cohort included people who had never thought about the decision at all. A model in which households solve a life-cycle optimization problem and act on the solution cannot generate a forty-point change in behavior from a change in stationery.

The second finding is the one this chapter is built on. Having been enrolled, the automatic cohort mostly stayed exactly where the plan put them: roughly three-quarters were still contributing at precisely the three percent default, with all of their balance in precisely the default fund, months later. Under the old opt-in regime, almost nobody had chosen either. Three percent was not a popular savings rate the employer happened to pick; it became a popular savings rate *because* the employer picked it. The money market fund was not an allocation anyone would recommend to a twenty-eight-year-old with forty years to retirement; it was where the money went because it was where the money went.

So the default did two things at once, pointing in opposite directions. It brought in savers who would otherwise have saved nothing — an unambiguous gain, concentrated among exactly the employees least likely to have participated before: the young, the low-paid, and, in Madrian and Shea's data, Black and Hispanic workers, for whom the participation gaps at this firm narrowed sharply. And it parked those savers at a rate too low and in an asset too safe to fund a retirement, where inertia held them. Some employees who would have chosen six percent in equities under opt-in ended up at three percent in cash under opt-out, because the default is a suggestion and the suggestion was heard.

Two decades of American retirement policy are an attempt to keep the first effect and fix the second. The Pension Protection Act of 2006 gave employers a safe harbor for automatic enrollment and, through the Department of Labor's qualified default investment alternative rules, told them which default *funds* would carry that protection — a list from which money market funds were absent and on which target-date funds were prominent. Automatic escalation followed the same logic, and by the 2020s the design had been written into federal law for newly established plans. The lesson had been learned, and the lesson was that the default is the policy instrument.

This chapter takes that lesson and asks what it does to asset markets.

Start where every Part IV chapter starts: Chapter 2's Table 2.5, the master holdings table. Households and nonprofits are its largest column, directly holding something like $25 trillion of a roughly $60 trillion US equity market, roughly $21 trillion of fund and ETF shares, and the entirety of the roughly $33 trillion pension-entitlement row, which exists nowhere else. Every other column is, at some remove, holding on behalf of that one. Table 2.6 records the direction of travel: households' direct share of corporate equity has fallen from roughly sixty percent in the mid-1970s to something like forty percent, while the intermediated share rose and defined benefit gave way to defined contribution.

Put the episode and the table together and the question forms. The largest holder sector in the financial system reaches most of its holdings through vehicles it did not choose, at contribution rates it did not select, in allocations set by a glide path — and its participation in risky assets moves forty points when a checkbox moves. What does a demand curve look like when it is generated that way? That is a question about the demand side of every market in this book.

***

## 14.1 What Theory Says

The normative theory of household portfolio choice is a large and well-developed body of work. Campbell's *Financial Decisions and Markets* is the standard graduate treatment. What follows is the part needed to see how far actual behavior sits from the benchmark.

The problem is this. A household lives for many periods, earns labor income while it works, consumes throughout, and decides each period how much to save and how to split the savings between a riskless asset and a risky one. It maximizes expected lifetime utility from consumption, subject to a budget constraint that carries wealth forward and to whatever borrowing limits it faces. Everything interesting in household finance comes from the fact that this is a *life-cycle* problem with *labor income* in it, and that labor income is neither tradable nor riskless.

Strip out the labor income and the answer is simple. Merton showed that with constant relative risk aversion, returns that are independently and identically distributed over time, and no labor income, the optimal share of wealth in the risky asset is a constant:

$$
w^{\ast} = \frac{\mu - r\_f}{\gamma \sigma^2}
$$

where $$\mu$$ is the expected return on the risky asset, $$r\_f$$ the riskless rate, $$\sigma^2$$ the return variance, and $$\gamma$$ relative risk aversion. Its content is entirely in what it says a household should *not* do: the optimal share depends on neither wealth nor age nor horizon. A twenty-five-year-old and a seventy-five-year-old with the same risk aversion hold the same portfolio, and the conventional advice to hold less equity as you age has no basis in this model.

Now put labor income back. A household that will earn wages for thirty more years already owns an asset: the present value of that future income. Call it human capital, $$H\_t$$, and let $$W\_t$$ be marketable financial wealth. The household's real balance sheet has $$W\_t + H\_t$$ on the asset side, and the portfolio decision that matters is the composition of *that* total. If the household wants a share $$w^{\ast}$$ of total wealth in risky assets, and if human capital is approximately safe — a stable salary in a stable job is closer to a bond than to a stock — then all of the risk must be loaded onto the tradable part:

$$
\frac{\text{risky assets}}{W\_t} = w^{\ast}\left(1 + \frac{H\_t}{W\_t}\right)
$$

This is the whole of the glide-path logic. Early in working life, $$H\_t$$ is large and $$W\_t$$ is small, the ratio $$H\_t/W\_t$$ is enormous, and the implied equity share of the *financial* portfolio exceeds one hundred percent — the young household should, if it could, hold a levered equity position. As the household ages, human capital is consumed and converted into financial wealth, $$H\_t/W\_t$$ falls toward zero, and the financial portfolio's equity share falls toward $$w^{\ast}$$. The theoretical age-glidepath is not a claim about horizon or about time diversification. It is an implication of an untraded asset being run down.

Three qualifications carry most of the modern literature, and each matters empirically.

**Human capital is not a bond.** For an employee whose wage tracks the stock market, or whose industry is cyclical, human capital has equity-like risk, and the implied financial equity share is correspondingly lower. Uninsurable labor income risk also generates precautionary saving and, with borrowing constraints, makes young households behave far more conservatively than the formula suggests.

**Fixed participation costs change the extensive margin.** If entering the equity market costs something — a time cost of learning, an account minimum, a psychic cost of unfamiliarity — a household with small financial wealth optimally holds no equity at all, because the premium on a $2,000 position does not cover the cost. This is the bridge to Chapter 5: if participation is limited for reasons like this, the marginal holder of equity risk is not the average consumer, and the consumption-based models are pricing equity off the wrong consumption series.

**Housing is not just an asset.** A house is a consumption good, an investment, a leveraged position, and a hedge against future rent, simultaneously. Section 14.4 takes this seriously, because for most households the house is the portfolio.

Theory predicts, then, a household that participates in risky asset markets, holds a diversified portfolio, tilts toward equity when young and away when old, borrows when young to the extent its constraints allow, and rebalances as prices move. What follows is what households actually do.

> **Box 14.1 — The company that changed a form**
>
> The chapter opens with a plan that changed one default and watched participation move. The case is worth stating precisely, because it is the cleanest natural experiment in household finance and because what it identifies is narrower than it is usually taken to be.
>
> The design is always the same. A firm operating a defined-contribution plan switches new hires from *opt-in* enrolment, in which an employee joins by returning a form, to *automatic* enrolment, in which the employee is enrolled at a stated contribution rate into a stated default fund unless he returns a form to decline. Nothing else changes: the same plan, the same investment menu, the same match, the same employees drawn from the same labour market a few months apart. Participation among new hires rises immediately and sharply, typically from something like half to something approaching nine in ten, and the change persists.
>
> Three features make this more than an interesting fact. The response is *immediate*, so it is not about learning. It is *largest for the youngest and lowest-paid employees*, which is the opposite of what a fixed cost of information would predict, since those are the workers for whom the stakes are smallest. And the enrolled employees overwhelmingly stay at the default contribution rate and in the default fund, sometimes for years, so the default sets not only whether they save but how much and in what.
>
> That last point is the one §14.6 needs. If the default determines the quantity and the allocation, then the plan sponsor who picks the default is choosing the portfolio of a large fraction of the American workforce. The parameter that governs household equity demand is not a preference. It is an administrative decision made by a benefits committee, and Box 14.2 is the statute that made that decision safe to take.
>
> The standard caution applies and the chapter takes it seriously. The experiment identifies the effect of a default on *this* plan's participants. It does not identify the effect on saving, because a household may reduce saving elsewhere, and the evidence on that offset is mixed.

***

## 14.2 What Households Do

### The Participation Puzzle

The largest single fact in household finance is that a great many households hold no equity at all.

The Survey of Consumer Finances, the Federal Reserve's triennial household survey, is the standard source. Counted generously — direct holdings of stock plus indirect holdings through mutual funds, retirement accounts, and trusts — something under sixty percent of US families have any equity exposure whatever. Counted narrowly, direct ownership of individual stocks is a minority activity, in the neighborhood of one family in five. The remaining forty-odd percent of American families are entirely outside the equity market, over a period in which the equity premium has been on the order of five to six percentage points a year.

**Table 14.1: Equity Participation by Income Group, US Families, 2022**

| Income group     | Any equity (direct or indirect) | Direct stock holdings | Any retirement account |
| ---------------- | ------------------------------- | --------------------- | ---------------------- |
| Bottom quintile  | 17%                             | 7%                    | 13%                    |
| Second quintile  | 40%                             | 11%                   | 35%                    |
| Middle quintile  | 60%                             | 17%                   | 56%                    |
| Fourth quintile  | 79%                             | 22%                   | 75%                    |
| Next 10% (80-90) | 91%                             | 40%                   | 89%                    |
| Top 10%          | 96%                             | 56%                   | 93%                    |

*Source: Survey of Consumer Finances 2022, Summary Extract Public Data, Board of Governors of the Federal Reserve System (file dated 29 March 2024); author's calculations, population-weighted over all five implicates. Income groups are the Bulletin's percentile bands. "Any equity" counts stock held directly or through funds, retirement accounts, annuities, trusts, and managed accounts; "any retirement account" counts quasi-liquid retirement accounts and excludes defined-benefit entitlements, which the survey does not value as an asset. The whole-population rates implied by the table reproduce the published 2022 figures exactly: 58.0 percent with equity in any form, 21.0 percent holding stock directly, 54.3 percent with a retirement account.*

![Figure 14.1: Who participates](https://846781005-files.gitbook.io/~/files/v0/b/gitbook-x-prod.appspot.com/o/spaces%2F3EupdX99vVBoNySDtmxb%2Fuploads%2Fgit-blob-0d7e171b31c031714bc27c4e604be1b50a15a598%2Ffig_14_01_who_participates.png?alt=media)

**Figure 14.1: Who participates.** Table 14.1 drawn. Three facts read off the bars. Participation is steeply graded by income on every measure — 17 percent of families in the bottom quintile hold equity in any form against 96 percent in the top decile — so the sentence "households own the stock market" is a sentence about a minority of households. The blue and teal bars are almost the same height in every group, which is the chapter's point about *how* households hold equity: participation is retirement-account participation, and the two series diverge only at the top, where the direct holder appears. And the orange bar is a minority everywhere and a rarity below the median — 7 percent in the bottom quintile, 17 in the middle, 56 at the top. The household who chooses a stock is a different population from the household who owns stocks. *Source: Survey of Consumer Finances 2022, Summary Extract Public Data, as printed in Table 14.1.*

The table's shape is the finding. Participation is not randomly distributed; it is a steep function of income and, more steeply, of wealth. So the non-participants are not a random sample of consumers, and any model that treats aggregate consumption as the marginal equity holder's is aggregating over a population most of whom hold no equity.

Why do they not participate? Four families of explanation, all doing some work. **Fixed costs**, as in §14.1: for a household with $3,000 of financial assets, the dollar return to figuring out a brokerage account is small. **Background risk and constraints**: a household with volatile earnings, no buffer, and expensive debt is rationally holding liquidity, and paying down an eighteen percent credit card balance is a riskless investment at eighteen percent that dominates the equity premium. **Information, trust, and familiarity**: participation rises with education and financial literacy, and is higher among households whose parents held stock. **Social interaction**: participation is higher among households that mix more with their neighbors, and the effect is concentrated in places where local participation is already high — which is what word of mouth, rather than information, would predict. Non-participation looks less like a preference than like an absence — of wealth, of access, of a plan at work, of anyone who ever suggested it.

Which points at the institutional answer. The share of households with *any* equity exposure has risen substantially since the early 1980s, and almost all of the rise came through retirement accounts. Households did not become more willing to hold equities. Employers began offering plans whose defaults hold equities.

### Under-Diversification and Employer Stock

Conditional on participating, households hold portfolios a mean-variance optimizer would not recognize. The median direct stockholder holds a handful of individual stocks — on the order of two to four — leaving an enormous quantity of idiosyncratic risk uncompensated by any model in Part II, and brokerage data find those holdings concentrated in local firms, employer-linked firms, own-industry firms, and firms recently in the news.

Calvet, Campbell and Sodini's study of the Swedish population register — every household's complete portfolio, which no US source matches — puts a welfare number on this, and the headline is deliberately two-sided. Most Swedish households are reasonably well diversified, largely because equity exposure arrives through funds rather than stock-picking, and the median loss from imperfect diversification is modest. But the distribution has a long tail: a minority bear diversification losses that are large in return terms, and they are disproportionately poorer, less educated, and less financially sophisticated. The households making the costliest mistakes are the ones least able to absorb them, and — the paper's sharper point — the ones most likely to respond to a bad outcome by exiting the market altogether, converting a temporary loss into a permanent one.

The purest case of voluntary under-diversification is employer stock in retirement plans. Around the turn of the millennium company stock accounted for something like a fifth of all 401(k) assets, and in individual plans the concentration ran far higher; Enron's employees held a majority of their plan assets in Enron stock when the company collapsed. Here the labor-income risk and the financial risk are the *same* risk, perfectly correlated — the exact opposite of what §14.1 prescribes for a household whose human capital is already tied to the firm. Benartzi documented the mechanism: employees allocated to company stock in proportion to its recent past return, treating the employer's stock as safe because it was familiar. Litigation, regulation, plan redesign, and target-date defaults have since brought the aggregate share into the low single digits of plan assets — a rare case of a documented household error engineered away by changing the menu.

### Home Bias, Domestic and Local

Households overweight what is near them, on every definition of near.

The international version is the oldest documented anomaly here. French and Poterba's calculation for the late 1980s found US investors holding roughly ninety-four percent of their equity in domestic stocks when the US was under half of world market capitalization, with Japanese and British investors equally parochial in their own directions. The bias has fallen — US investors now hold something like three-quarters to four-fifths of their equity at home against a US share of world market capitalization closer to sixty percent — but the residual is far larger than any transaction-cost or hedging story comfortably explains. Chapter 4 states the diversification loss in mean-variance terms; the puzzle is why households leave it on the table.

The local version is the same phenomenon at shorter radius. Investors overweight firms headquartered near them, firms in their own industry, and firms they meet as customers or employees. Huberman's study of the regional telephone companies found shareholders concentrated in each company's own service area — people held the phone company whose bills they paid. Familiarity is doing the work, and familiarity is not information: the overweighted firms do not, on average, outperform.

### Inertia and the Default

The Madrian-Shea result is not an isolated finding about enrollment. It is one instance of a general property of household portfolios, which is that they are close to static.

The typical participant in a defined contribution plan makes no trades in a typical year. Studies of plan administrative records repeatedly find median annual reallocation activity of zero, with a small minority of active traders generating essentially all recorded transactions. Contribution rates, once set, persist for years. Allocations, once set, are not rebalanced as markets move — so a participant's equity share drifts up in bull markets and down after crashes, which is passive market-timing in the wrong direction. Even the number of funds held shows the fingerprint of the menu rather than of optimization: participants spread contributions across the options offered, so the average participant's equity share depends partly on how many equity funds the employer happened to include.

The behavioral mechanisms — status quo bias, procrastination, choice overload, the cognitive cost of a complex decision — belong to Chapter 15. What belongs here is the institutional consequence. If households do not act, whoever specifies the default is specifying the portfolio, and the plan sponsor, the recordkeeper, and the regulator who defines the safe harbor become jointly the asset allocator for a large share of American retirement wealth. That is a very different picture of the demand side than a population of optimizing agents, and §14.6 draws out what it does to prices.

### Holding the Losers

One trading pattern is regular enough to name. When households do trade, they are markedly more likely to sell a position that has risen than one that has fallen. Odean's work on a large discount brokerage's records established the asymmetry cleanly: the proportion of gains realized substantially exceeds the proportion of losses realized, and the effect survives controls for rebalancing, for tax motives, and for mean-reversion strategies. It is also expensive — the winners sold subsequently outperform the losers retained, and in a taxable account the behavior inverts the tax rule of §14.5, which says to realize losses and defer gains. The disposition effect and its prospect-theory explanation are Chapter 15's; noted here as one more respect in which the household portfolio is not the solution to §14.1's problem.

***

## 14.3 Retirement Systems and the Institutionalized Household

### What the DB-to-DC Shift Transferred

Chapter 2's Table 2.6 records the shift: defined benefit plans held something like seventy percent of private pension assets in the mid-1970s and hold on the order of twenty percent now, with defined contribution plans and IRAs holding the balance. Chapter 16 works through what this did to the *institutions* — the disappearance of a professionally managed balance sheet with a duration target, and the pricing consequences for the long end of the curve. Neither is retold here.

The household-side statement is a statement about risk transfer, and it is worth being precise about which risks moved.

A defined benefit promise is a claim on the employer for a stated income stream in retirement: the household holds a claim, the sponsor holds the assets and four risks. **Investment risk**, that the assets underperform; **sequence risk**, that bad returns arrive at the worst moment; **longevity risk**, that the beneficiary lives longer than assumed; and **decumulation risk**, that a lump sum must be converted into lifetime income at an unknown price. A defined contribution plan transfers all four to the household and adds a fifth that did not previously exist: **the contribution decision itself**, since a DB accrual happens automatically as a function of service while a DC balance happens only if someone elects to save.

What the household received in exchange is real: portability between employers, ownership of the balance, a bequeathable asset, and freedom from the risk that the sponsor fails with the plan underfunded. The exchange was not simply a loss. But it handed those five risks to a decision-maker whom §14.2 has just characterized as one who does not fill in forms.

### Defaults as Infrastructure

The policy response was to stop asking the household to decide.

**Automatic enrollment** makes participation the default, as in the opening episode, and moves plan participation rates to the high eighties or above where it is used. **Automatic escalation** — the design Benartzi and Thaler proposed as "Save More Tomorrow," which commits employees in advance to raise their contribution rate out of future pay increases — addresses the second half of the Madrian-Shea finding, that defaults anchor people at low rates. Its original implementation raised participants' saving rates several-fold over a few annual raises, and it works because it exploits inertia rather than fighting it: having consented once, the employee does nothing, and doing nothing now means saving more.

**Qualified default investment alternatives** complete the architecture. The Pension Protection Act of 2006 and the Department of Labor rules under it gave sponsors relief from fiduciary liability for the investment performance of a default, provided the default falls into one of a small number of permitted categories — a balanced fund, a professionally managed account, or a life-cycle fund whose asset mix varies with the participant's age. Stable-value and money market funds, which is to say the fund the 1998 cohort of the opening episode sat in, do not qualify as long-term defaults. The regulation therefore did something unusual: it did not require any household to hold equities, and it did not prohibit any household from holding cash. It changed which choice happened automatically, and the money followed.

It followed to target-date funds, which hold a diversified portfolio whose equity share declines along a published glide path as the dated year approaches — the mechanical implementation of §14.1's $$H\_t/W\_t$$ logic, sold as one line on a menu. Assets in these vehicles run into the trillions, and among recently hired participants the modal portfolio is a single target-date fund holding the entire balance. What their flows do to markets is Chapter 17's subject. The household-side point is narrower and more surprising: the target-date fund is the first retail vehicle that delivers a theoretically defensible life-cycle portfolio to a household that has decided nothing. It is designed for the behavior documented in §14.2, not for the agent modeled in §14.1.

### The Coverage Gap

All of this machinery operates inside employer plans, which is where its limit lies. At any moment a substantial minority of private-sector US workers — on the order of a third, concentrated in small firms, part-time work, and self-employment — have no employer plan available at all, and access is strongly graded by firm size and wage: the workers least likely to have a plan are the workers least likely to save without one. For this group the default is that there is no default, and the machinery that raised participation to ninety percent inside plans does nothing.

Federal policy has expanded availability at the margin through tax credits for small-employer plans, pooled arrangements, and coverage rules for long-tenure part-time workers. More consequentially, a number of states have created automatic-IRA programs requiring employers without plans to enroll workers into a state-facilitated Roth IRA by payroll deduction, with an opt-out. That is the opening episode's design applied at the level of a state rather than a firm, and the early evidence is what the design predicts: participation far above voluntary IRA take-up, and most participants at the default rate in the default fund.

***

## 14.4 The Household Balance Sheet: Housing and Debt

Everything so far has concerned the financial portfolio. For most households it is the smaller half of the story.

### The House as the Portfolio

American households own owner-occupied real estate on the order of $50 trillion, against home mortgages on the order of $13 trillion — figures from Chapter 2's source, the Financial Accounts' household balance sheet, table B.101. Roughly two-thirds of households own their home. And for households in the middle of the wealth distribution, the house is not one asset among several; it is the asset.

**Table 14.2: Composition of Household Assets by Wealth Group, 2022 (shares of total assets)**

| Asset                                | Bottom 50% | 50th-90th percentile | Top 10% |
| ------------------------------------ | ---------- | -------------------- | ------- |
| Principal residence                  | 61.8%      | 49.1%                | 14.8%   |
| Other real estate                    | 2.5%       | 6.8%                 | 8.8%    |
| Retirement accounts                  | 8.0%       | 18.5%                | 14.6%   |
| Directly held equity and fund shares | 0.8%       | 5.1%                 | 21.9%   |
| Private business equity              | 1.0%       | 3.9%                 | 27.2%   |
| Deposits, bonds, and other           | 9.4%       | 11.4%                | 11.6%   |
| Consumer durables (vehicles etc.)    | 16.4%      | 5.2%                 | 1.1%    |

*Source: Survey of Consumer Finances 2022, Summary Extract Public Data, Board of Governors of the Federal Reserve System (file dated 29 March 2024); author's calculations, population-weighted, groups formed on the survey's own net-worth percentiles. Columns sum to 100 percent of family assets as the SCF measures them, which excludes defined-benefit pension entitlements and all consumer durables other than vehicles. The Distributional Financial Accounts (2026:Q1) put the same shares on the Z.1's basis and differ substantially — most of all for directly held equity and fund shares, where the DFA distributes a household-sector aggregate that is a residual and therefore much larger than what families report — so the two are not interchangeable and are not averaged here.*

![Figure 14.4: Four different portfolios](https://846781005-files.gitbook.io/~/files/v0/b/gitbook-x-prod.appspot.com/o/spaces%2F3EupdX99vVBoNySDtmxb%2Fuploads%2Fgit-blob-21f893f9fa9626613a82ceb6aa9a84a5985cb419%2Ffig_14_04_four_different_portfolios.png?alt=media)

**Figure 14.4: Four different portfolios.** Table 14.2 drawn, each bar the composition of one wealth group's assets. The rotation across the distribution is the whole content of the exhibit. Below the median the principal residence is 62 percent of assets and equity of every kind — direct, fund, and private business — is 2; at the top the two swap places, 15 percent housing against 49 percent equity. In between sits the group §14.4 is about: half its assets in the house, a fifth in retirement accounts, and a mortgage against the first of those. The bars are the SCF's own asset measure, which excludes defined-benefit entitlements and every consumer durable other than vehicles, so the bottom group's 16 percent in durables is mostly cars. Compare this with Figure 14.2, which asks the same question the other way round — not what each group holds, but who holds each asset — and note that the two exhibits use different data with different constructions, which is why the numbers do not line up cell for cell. *Source: Survey of Consumer Finances 2022, Summary Extract Public Data, as printed in Table 14.2.*

Read across the rows. The middle of the distribution holds a leveraged, undiversified, illiquid position in a single asset in a single geography, plus a retirement account. The top decile holds a business and a securities portfolio. These are not the same portfolio problem at different scales; they are different problems. A household whose net worth is house equity minus mortgage has an equity-like exposure to local house prices at a leverage ratio that would embarrass a hedge fund, and holds essentially none of the claims Parts II and III price.

The house is also four things at once, pulling in different directions. It is a **consumption good** yielding housing services. It is an **investment** with a return. It is a **hedge**: an owner is long the asset whose price determines her future cost of housing, so ownership immunizes her against rent risk — a real reason to hold a concentrated position that a pure portfolio model would call irrational. And it is a **leveraged position**, because the mortgage is the only cheap long-term leverage most households will ever be offered. The tax code adds a fifth consideration by taxing the implicit rental income at zero and, historically, subsidizing the interest. The result is a portfolio weight no financial-asset model would generate.

Home equity is also where much retirement wealth actually sits, particularly for the middle three quintiles, and it sits there in a form that is hard to spend. Retirees are strikingly reluctant to draw it down: they do not on average trade down, and reverse mortgages remain a niche product with a long history of adverse selection and reputational damage. A retirement system that has loaded much of the middle class's wealth into an asset its owners will not liquidate has a decumulation problem it has not solved.

The instrument-design literature makes the sharper version of the complaint. What is missing is not only a product for releasing home equity but a market for insuring it: an owner cannot buy protection against a decline in the value of the single asset that dominates her balance sheet. Shiller and Weiss's home-equity insurance proposal — a contract settling on a local house price index rather than on the individual property, so that neither an appraisal nor the owner's own maintenance decisions enter the payoff — is the standing statement of what such a market would look like, and its continued absence is the substance of Discussion Question 4.

### The Mortgage and the Leverage of the Household Sector

The mortgage is the largest liability class households issue, at roughly seventy percent of total household debt, with student loans, auto loans, and credit card balances behind it.

**Table 14.3: Household Debt and Leverage, United States**

| Measure                                              | 2007:Q4        | 2026:Q1        |
| ---------------------------------------------------- | -------------- | -------------- |
| Total household debt                                 | $14.2 trillion | $21.1 trillion |
| Mortgage share of household debt                     | 74%            | 66%            |
| Household debt / disposable personal income          | 134%           | 90%            |
| Household debt service / disposable income           | 15.8%          | 11.2%          |
| Homeowners' equity as share of household real estate | 54%            | 72%            |

*Source: Financial Accounts of the United States (Z.1), table B.101, through the FRED mirror (CMDEBT, HHMSDODNS, HOEREPHRE), with disposable personal income from the Bureau of Economic Analysis (DPI) and the debt-service ratio from the Federal Reserve Board's household DSR series (TDSP); data through 2026:Q1, retrieved 25 August 2026. The 2007:Q4 column is the quarter in which both debt to disposable income and the debt-service ratio peak on the current vintage; the debt stock itself peaks in 2008:Q3 at $14.5 trillion. Cross-check, Federal Reserve Bank of New York, Household Debt and Credit Report, 2026:Q2: total balances $18.8 trillion, of which mortgages and home-equity revolving $13.6 trillion, a 72 percent mortgage share. The New York Fed's consumer-credit-panel measure excludes nonprofits and the Z.1's other loans and advances, so it is the narrower object and the two are not averaged.*

The table records a deleveraging that is genuine but incomplete, and the debt-service row is the sharpest version of it: payments fall from 15.8 percent of disposable income to 11.2, a drop of 4.6 points, and rather more of that came from refinancing into lower coupons than from repaying principal. It comes with a compositional warning: aggregate ratios are the wrong object when the distribution is what matters. Debt is concentrated among households with much less than average wealth while the assets are concentrated at the top, so a sector-level leverage ratio understates the leverage of the households actually carrying the debt. The macroeconomic consequences of that mismatch belong to the companion macro volume and are cross-referenced rather than developed here.

![Figure 14.5: Household leverage](https://846781005-files.gitbook.io/~/files/v0/b/gitbook-x-prod.appspot.com/o/spaces%2F3EupdX99vVBoNySDtmxb%2Fuploads%2Fgit-blob-b6c4b85c09c35ca7bc8c4e66e0f7c8aa5e5ab325%2Ffig_14_05_household_leverage.png?alt=media)

**Figure 14.5: Household leverage.** Household debt as a share of disposable personal income and as a share of household total assets, quarterly since 1947, with NBER recessions shaded and Table 14.3's 2007:Q4 peak marked. The two lines share a numerator and differ only in the denominator, and they tell different stories about the same fifty years. Against income the sector's debt more than doubles, peaks at 134 percent, and falls back to the level of the mid-1990s. Against assets it moves inside a band a tenth as wide and ends near where it began, because the denominator — houses and equities — grew alongside the mortgage that helped finance it. Which measure is the right one is not a matter of taste: the debt is repaid out of income, and a leverage ratio whose denominator is the asset whose price the borrowing helped raise will look most reassuring exactly when it should not. The same reading applies to the corporate sector in Chapter 23 §23.2, where the market-value denominator does most of the work in measured leverage. Table 14.3's debt-service row is verified against these data in the builder but not drawn: the Board publishes that series from 2005 only, and a line beginning three years before the peak says nothing about the fifty years in front of it. *Source: Financial Accounts of the United States (Z.1), table B.101, through the FRED mirror (CMDEBT, TABSHNO), with disposable personal income (DPI) and the household debt-service ratio (TDSP); NBER recession dates. Author's calculations.*

### Refinancing Inertia

The mortgage also supplies household finance's most expensive documented friction.

A fixed-rate American mortgage contains a free prepayment option: when rates fall, the borrower can refinance at no penalty. Exercising it is worth real money — for a typical balance, a rate decline of a point or two is worth thousands to tens of thousands of dollars in present value. Yet a substantial minority of eligible borrowers do not exercise. Keys, Pope and Pope, examining a large sample of US mortgages during a period of sharply falling rates, found roughly a fifth of households failing to refinance when it was clearly optimal, at a median cost in the neighborhood of $11,000 each in foregone savings. Work on the Danish market, where refinancing is institutionally cheap and the data are complete, finds the same inaction and traces it to both a fixed psychological cost of acting and a failure to notice that the opportunity exists — with the failure concentrated among older, poorer, and less educated borrowers. The second of those is the limited attention of Chapter 15 §15.3 applied to the household's own balance sheet rather than to a company's earnings announcement: the opportunity is not evaluated and rejected, it is never brought into view.

Two features make this the cleanest friction in the chapter. First, the gain is nearly riskless and easily computed; this is not a case where the household might know something the researcher does not. Second, the loss flows to a specific counterparty. A borrower who fails to refinance keeps paying an above-market coupon, which is precisely the prepayment behavior that makes agency MBS valuable to its holders. Chapter 13 §13.3 prices that: household inaction is an input to the prepayment model, and the sluggishness of the average borrower is a parameter MBS investors estimate and trade on. The friction is not merely a welfare loss to households; it is a source of return to somebody else.

After the 2020-21 refinancing wave, the great majority of outstanding US mortgages carry coupons far below the prevailing market rate, which inverts the same option: moving house now means giving up a below-market loan. The resulting "lock-in" suppresses turnover, and household inaction that was once a cost has become, for those households, an asset they are reluctant to abandon.

> **Box 14.2 — The Pension Protection Act of 2006**
>
> Automatic enrolment worked long before it was common, and the reason it was not common is a legal one. This box is the statute that removed the obstacle, because a fiduciary rule is what turned a clever plan design into the default architecture of American retirement saving.
>
> Before 2006 a sponsor that enrolled employees automatically faced two problems. State wage-payment laws could be read to prohibit deducting from a paycheque without written authorisation. And a sponsor that chose a default *investment* for a non-electing participant bore fiduciary responsibility for that choice under ERISA, with no safe harbour — so the prudent default was a money market fund, which is prudent against a lawsuit and imprudent for a thirty-year-old.
>
> The Pension Protection Act of 2006 addressed both. It pre-empted the conflicting state laws for qualified automatic contribution arrangements, and it directed the Department of Labor to designate **qualified default investment alternatives**: categories of investment into which a sponsor may place a non-electing participant with relief from fiduciary liability for the resulting investment outcomes. The regulation that followed named three, and the first of them was a fund whose asset mix changes with the participant's age — the target-date fund.
>
> Read that sequence again, because it is the causal chain behind §14.6. A statute directed a regulator to designate default investments; the regulator named age-based funds; sponsors adopted them because the safe harbour made adoption cheap; and the target-date fund became one of the largest holder-types in US equity, buying on payroll dates at whatever price prevails and rebalancing on a birthday.
>
> Chapter 20's demand system would put it this way. The household sector's demand curve for equities became steeper because a rule made a particular kind of holder cheap to be, and Chapter 17 §17.1 supplies the second half: the funds those defaults bought were, increasingly, index funds.

***

## 14.5 Taxes and Asset Location

American households hold securities in three tax environments, and the differences are large enough to change the right portfolio.

A **taxable** account is taxed as it goes: interest and non-qualified dividends at ordinary rates, qualified dividends and long-term gains at preferential rates, and gains only when realized — which makes deferral itself valuable and the step-up in basis at death an outright forgiveness. A **tax-deferred** account (traditional 401(k) or IRA) is funded pre-tax, accumulates untaxed, and is taxed in full at ordinary rates on withdrawal. A **Roth** account is funded after tax and never taxed again. Choosing between traditional and Roth is a bet on one's own future marginal rate; because contribution limits are stated in nominal rather than after-tax dollars, a Roth dollar buys more shelter, which tilts the answer toward Roth for savers contributing at the cap.

**Asset location** is the separate question of *which* asset to put in *which* account, holding the overall allocation fixed. The classical prescription is unambiguous. Put the heavily taxed, high-yield assets — taxable bonds, high-turnover strategies, REITs — in the tax-deferred account, where their annual income compounds untaxed. Put equities in the taxable account, where they benefit from the preferential rate on qualified dividends and long-term gains, from deferral until realization, from loss harvesting, and from the step-up at death. Estimates of the value of getting this right run to tens of basis points a year, compounding.

Many households do the opposite. The empirical work on this is consistent: a large share of households hold their bonds in taxable accounts and their equities in tax-deferred ones, exactly inverting the prescription. The explanations are the chapter's explanations. **The menu**: a 401(k) is where most households' assets are, and the plan menu is equity-heavy and now defaults to a target-date fund that holds both stocks and bonds inside a single wrapper — which makes location a decision the household cannot make even if it wanted to. **Mental accounting**: the retirement account is labeled long-term, so the long-term asset goes in it, and the taxable account is labeled savings, so the safe asset goes there. **Liquidity**: money that might be needed before retirement cannot be locked up, and that money is held in cash and bonds, in taxable, for entirely sensible reasons that have nothing to do with tax.

**Tax-loss harvesting** is the taxable account's one distinctive strategy: sell a position trading below its cost basis, book the capital loss to offset realized gains and, up to a small annual limit, ordinary income, and immediately buy a similar but not "substantially identical" security so the market exposure is unbroken. The wash-sale rule polices the substitution over a thirty-day window. Two qualifications are usually left out of the sales pitch. The benefit is *deferral*, not forgiveness — harvesting lowers the basis, so the tax reappears on eventual sale, and the strategy's value is the time value of the deferred tax plus the possibility that the gain is never realized at all because of the step-up at death. And the opportunity depletes: after a long bull market a portfolio has few losses to harvest, which is why the strategy's marketing is most enthusiastic precisely when it has least left to offer.

***

## 14.6 Heterogeneity as a Pricing Input

This section is the chapter's reason for sitting where it does, at the head of Part IV.

Chapter 2's Table 2.5 shows the household sector directly holding roughly $25 trillion of a roughly $60 trillion equity market. An aggregate of that kind invites the reader to imagine a representative household holding a representative slice. The Federal Reserve's Distributional Financial Accounts — which distribute the Z.1 household balance sheet across wealth groups, quarterly — say otherwise.

**Table 14.4: Share of Each Household Asset Class Held by Wealth Group, 2026:Q1**

| Asset class                                           | Top 1% | Next 9% | Next 40% | Bottom 50% |
| ----------------------------------------------------- | ------ | ------- | -------- | ---------- |
| Directly held corporate equity and mutual fund shares | 50.1%  | 37.2%   | 11.6%    | 1.1%       |
| Private business equity                               | 52.9%  | 31.7%   | 14.4%    | 1.0%       |
| Pension entitlements                                  | 8.9%   | 41.1%   | 46.4%    | 3.6%       |
| Real estate                                           | 13.3%  | 30.3%   | 46.5%    | 9.9%       |
| Total net worth                                       | 31.6%  | 36.3%   | 29.6%    | 2.5%       |

*Source: Distributional Financial Accounts, Board of Governors of the Federal Reserve System, release of 18 June 2026 (data through 2026:Q1); author's calculations. The DFA distributes Z.1 aggregates using SCF shares rather than measuring the distribution directly. Rows sum to 100 percent; the shares computed here differ from the Board's own published shares file by at most 0.05 percentage points.*

![Figure 14.2: Who owns the risk](https://846781005-files.gitbook.io/~/files/v0/b/gitbook-x-prod.appspot.com/o/spaces%2F3EupdX99vVBoNySDtmxb%2Fuploads%2Fgit-blob-389700002e549fae0df0b7f36fed0cc8eb481ca2%2Ffig_14_02_dfa_concentration.png?alt=media)

**Figure 14.2: Who owns the risk.** Share of each asset class held by the top 1%, next 9%, next 40% and bottom 50% (Table 14.4) — the concentration figure §14.6 is built around and the data exercise Part A rebuilds. The darker block inside the top 1% is the top 0.1%, which alone holds 24 percent of directly held corporate equity. Corporate equity here is the directly held stake; equity inside defined-contribution pension accounts sits in pension entitlements instead. The bottom 50%'s share is printed in the right margin in every row, because on four of the five rows the block is too thin to hold it. The DFA distributes Z.1 aggregates using SCF shares rather than measuring the distribution directly. *Source: Distributional Financial Accounts, Board of Governors of the Federal Reserve System, release of 18 June 2026 (data through 2026:Q1); author's calculations.*

Three readings follow, in ascending order of consequence; Figure 14.2 draws the same shares for the most recent quarter.

![Figure 14.3: Concentration through time](https://846781005-files.gitbook.io/~/files/v0/b/gitbook-x-prod.appspot.com/o/spaces%2F3EupdX99vVBoNySDtmxb%2Fuploads%2Fgit-blob-b2edb73656e275d1fdb829ac7b3e7e528eb312c1%2Ffig_14_03_concentration_through_time.png?alt=media)

**Figure 14.3: Concentration through time.** The same distribution as Figure 14.2, for one asset class, quarter by quarter since 1989. The top one percent's share of household corporate equity and mutual fund shares rises from 43 percent to 50; the next forty percent of the distribution falls from 17 to 12; the bottom half never gets above two and is the sliver at the top of the stack. The path matters as much as the levels. The top share falls through the late 1990s, when the retail participation of the dot-com period pulled the middle in, and rises steadily from 2003, which is the period over which the direct-holding household of Table 14.1 was replaced by the retirement account of §14.3. What the figure cannot show is the counterfactual: pension entitlements are a different row of the Financial Accounts and do not appear here, so the middle of the distribution owns more equity risk than this exhibit assigns it. As in Figure 14.2, the DFA distributes a Z.1 aggregate using SCF shares rather than measuring the distribution directly, so the level is the Financial Accounts' and the split is the survey's. *Source: Distributional Financial Accounts, Board of Governors of the Federal Reserve System. Author's calculations.*

**Different assets have different owners.** Real estate and pension entitlements are the broadly held assets; directly held equity and private business equity are not. The bottom half of the wealth distribution holds something on the order of one percent of directly held corporate equity and roughly a tenth of household real estate. A shock to equity prices and a shock to house prices are shocks to different populations, which is why the two most recent US wealth drawdowns had such different distributional and macroeconomic signatures.

**The marginal holder of risk is rich.** If the top decile holds something like eighty-five percent of directly held equity, then the household whose willingness to bear equity risk actually clears the market is a wealthy one. This is the point Chapter 5 needs, and it is the point Chapter 2's summary flagged. The consumption-based model prices the equity premium off the covariance between returns and the marginal utility of the marginal investor. Test it against aggregate per-capita consumption and you have aggregated over a population most of whom hold no equity, whose consumption is smoothed by transfers, and whose marginal utility is irrelevant to the pricing of a claim they do not hold. Construct instead the consumption of equity *holders* and the series is more volatile and more strongly correlated with equity returns — which lowers the risk aversion required to rationalize the premium, without eliminating the puzzle. Limited participation does not resolve the equity premium puzzle. It changes the identity of the consumer the model is about, and Chapter 5 takes it from there.

**The household sector supplies two different demand curves at once.** This is the observation that carries into Chapter 20, and it is what the first five sections were assembled to support.

On one side sits the default-driven household of §§14.2 and 14.3. Its contributions arrive on payroll dates and are invested at whatever price prevails. Its allocation is a glide path indexed to a birthday. Its rebalancing is a calendar rule. It does not sell after a drawdown, it does not buy after one, and it does not respond to valuation because it does not observe valuation. In the language Chapter 20 will make formal, this holder's demand curve for equities is close to vertical: quantity demanded is a function of payroll and age, not of price. It is also enormous, and it is growing, because it grows mechanically with the wage bill and with each cohort that ages into the system.

On the other side sits the wealthy direct holder of Table 14.4, who owns most of the directly held equity and essentially all of the private business equity, whose taxable status makes realization decisions price- and tax-sensitive, who can lever, short, and reallocate, and who is the household counterparty most likely to be on the other side of a professional trade. This holder's demand curve has slope.

The composition matters more than either piece. What Chapter 2's Table 2.6 records — the fifty-year rotation from direct to intermediated household ownership — is, read through this section, a rotation in the *elasticity* of household demand. The share of household equity exposure arriving through vehicles whose purchases are governed by payroll dates and glide paths has risen steadily; the share arriving through a person deciding that a stock is cheap has fallen. If aggregate demand for equities is a wealth-weighted mixture of these two curves, then the mixture has been shifting toward the inelastic component for four decades. That is the household-sector foundation of the inelastic-markets claim, and it is why Chapter 20's demand system treats the identity of the holder as data rather than as a modeling convenience.

Figure 14.8 draws the two curves and then the mixture.

![Figure 14.8: Two household demand curves](https://846781005-files.gitbook.io/~/files/v0/b/gitbook-x-prod.appspot.com/o/spaces%2F3EupdX99vVBoNySDtmxb%2Fuploads%2Fgit-blob-7c8e0408b965848b5893b7fc1dd67c96c81248b5%2Ffig_14_08_two_household_demand_curves.png?alt=media)

**Figure 14.8: Two household demand curves.** Panel (a) is the section's two holders as demand curves for the same claim. The default-driven household's is close to vertical — its quantity is a function of payroll and age, and the price appears nowhere in the rule that generates it. The wealthy direct holder's has slope, because she is taxable, can lever and short, and is deciding. Both curves are drawn relative to each holder's own position at a price of one, so the panel compares slopes and not sizes; a curve's steepness, not its position, is what determines how far a price has to move to accommodate a flow. Panel (b) is the mixture, at three dates. As the share of household equity exposure arriving through payroll dates and glide paths rises, the wealth-weighted household curve rotates toward the vertical — from an elasticity of about 0.73 when most household equity was held directly to about 0.23 when most of it is not. That rotation is the household-sector foundation of the inelastic-markets claim, and it is worth being precise about what it is not: no household in the figure has become less rational, and nobody's beliefs have changed. What changed is the share of the sector's money that arrives through a rule rather than through a decision. The mixture shares are illustrative; the direction is the one Chapter 2's Table 2.6 records.

Two hand-offs close the chapter. The behavior that generates the inelastic curve — the inertia, the disposition effect, the extrapolation, the mental accounting that puts the bonds in the wrong account — is described here and explained in Chapter 15, which is why behavioral finance sits next door rather than in Part II. And the institutions to which households have delegated almost everything else — the plan sponsor who picks the default, the recordkeeper, the fund complex, the insurer who sells the annuity, the pension fund that still carries the promise — have their own liabilities, their own constraints, and their own reasons for holding what they hold. That is Chapter 16.

***

## Elsewhere in the Series

* **The full theory of household portfolio choice** — this is the one deferral in Part IV that points outside the series. J. Y. Campbell, *Financial Decisions and Markets: A Course in Asset Pricing* (Princeton, 2018), together with his 2006 presidential address, is the canonical treatment: intertemporal portfolio choice with labor income, the analytics of the glide path, and the normative apparatus §14.1 states without deriving. This chapter keeps what a reader needs to proceed and points there for the rest.
* **The Financial Accounts as a measurement system** — *Institutionalist Macroeconomics*, Chapter 3. Table 14.3's source and the household balance sheet's construction are documented there; Chapter 2 of this book keeps the primer.
* **Wealth and income distribution, and the macroeconomics of household leverage** — *Institutionalist Macroeconomics*, Chapter 25. Section 14.6 uses the distribution as a pricing input and stops; the consumption response to house prices, the distributional incidence of asset booms, and the debt-overhang literature are developed there.
* **Mortgage market structure, origination, and securitization** — the 2008 crisis volume for the originate-to-distribute pipeline and the underwriting collapse; this book's Chapter 13 §§13.3 and 13.5 for MBS pricing, prepayment modeling, and the convexity hedging that makes §14.4's refinancing inertia a traded parameter.
* **Within this book:** limited participation as an equity-premium resolution — Chapter 5. Home bias in mean-variance terms — Chapter 4. The behavioral mechanisms behind §14.2 — Chapter 15. Delegation, plan sponsors, and the institutions households hire — Chapter 16. Target-date and index flows as a market force — Chapter 17. Household demand as an estimated demand curve — Chapter 20.

***

## Summary

1. **Defaults govern household portfolios.** Madrian and Shea's natural experiment moved 401(k) participation among new hires from roughly half to nearly ninety percent by changing an enrollment form, and left most participants at the default contribution rate in the default fund. No price, return, or information changed. Whoever sets the default is choosing the portfolio.
2. **Theory predicts something households do not do.** With no labor income, the optimal risky share is a constant independent of age and wealth. With labor income treated as an implicit asset, the equity share of the *financial* portfolio should start above one and decline as human capital is consumed — the glide path's real derivation. Participation costs, uninsurable labor risk, and housing are the qualifications that carry the modern literature.
3. **A large minority of households hold no equity at all.** Under sixty percent of US families have any equity exposure and roughly one in five holds stock directly, with participation steeply graded by income and wealth (Table 14.1). Almost all of the postwar rise in participation came through retirement accounts rather than through households choosing to hold equities.
4. **Conditional on participating, households are under-diversified.** Median direct stockholders hold a handful of names; the Swedish register data show modest median diversification losses with a long tail concentrated among poorer and less sophisticated households; employer stock once approached a fifth of 401(k) assets, perfectly correlating financial risk with labor income risk, and was engineered down by changing the menu.
5. **Home bias survives at every radius.** Households overweight domestic equity against world market capitalization, and overweight local, familiar, and employer-linked firms within the domestic market. Familiarity is not information: the overweighted firms do not outperform.
6. **The DB-to-DC shift transferred five risks to the household** — investment, sequence, longevity, decumulation, and the contribution decision itself — in exchange for portability and ownership. Automatic enrollment, automatic escalation, and the QDIA safe harbor are the policy response, and target-date funds are what the safe harbor selected: the first retail vehicle that delivers a defensible life-cycle portfolio to a household that decides nothing. A third of private-sector workers are outside the system entirely, which is where state auto-IRA programs aim.
7. **For the middle of the distribution, the house is the portfolio.** A leveraged, undiversified, illiquid position in one asset in one geography, held for consumption, investment, rent-hedging, and leverage simultaneously (Table 14.2), with household leverage lower than its 2007 peak but concentrated among the households least able to carry it (Table 14.3). Home equity is where much middle-class retirement wealth sits, in a form its owners will not spend.
8. **Refinancing inertia is the cleanest documented friction.** Roughly a fifth of eligible US borrowers failed to exercise a nearly riskless option worth a median of about $11,000, and the Danish evidence traces the inaction to attention and a fixed cost of acting. The loss is somebody else's gain: sluggish prepayment is a parameter agency MBS investors estimate and trade (Chapter 13 §13.3).
9. **Asset location is worth real money and is commonly inverted.** Bonds belong in tax-deferred accounts and equities in taxable ones; many households do the reverse, for reasons of menu, mental accounting, and liquidity. Tax-loss harvesting defers rather than forgives, and depletes.
10. **Household heterogeneity is a pricing input, not a distributional footnote.** The top decile holds roughly eighty-five percent of directly held equity while real estate and pension entitlements are broadly held (Table 14.4). Two consequences: the marginal holder of equity risk is wealthy, so aggregate consumption is the wrong series for Chapter 5's models; and the household sector supplies two demand curves at once — a vertical, payroll-and-glide-path curve that has been growing for forty years, and a sloped curve belonging to wealthy direct holders. The rotation in the mixture is the household foundation of Chapter 20's inelastic markets.

***

## Key Terms

* **Participation puzzle**: The finding that a large share of households hold no equity at all despite a substantial and persistent equity premium; explained by some combination of fixed participation costs, background risk and borrowing constraints, and information, trust, and familiarity
* **Human capital**: The present value of a household's expected future labor income ($$H\_t$$); an untraded implicit asset whose safety and size determine the optimal risky share of the *financial* portfolio, and whose run-down over a working life is the derivation of the age glide path
* **Home bias**: The tendency of investors to overweight domestic securities relative to world market capitalization, and, at shorter radius, to overweight local, familiar, and employer-linked firms
* **Default effect**: The tendency of a household to remain in whatever allocation, contribution rate, or plan status it is placed in absent an active choice; the empirical basis for treating plan design as an asset-allocation decision made by the sponsor
* **Qualified default investment alternative (QDIA)**: A category of investment, defined by Department of Labor rules under the Pension Protection Act of 2006, into which a plan may default a non-electing participant while retaining fiduciary safe-harbor protection; balanced, managed-account, and life-cycle funds qualify, money market funds do not as a long-term default
* **Target-date fund**: A diversified fund whose equity share declines along a published glide path toward a dated retirement year; the dominant QDIA and the modal entire portfolio of recently hired plan participants
* **Asset location**: The allocation of a given portfolio across taxable, tax-deferred, and Roth accounts so as to minimize the present value of taxes — heavily taxed income in tax-deferred accounts, equities in taxable — as distinct from asset *allocation*
* **Distributional Financial Accounts (DFA)**: The Federal Reserve's quarterly distribution of the Z.1 household balance sheet across wealth groups, constructed by applying Survey of Consumer Finances shares to the aggregate; the source for Table 14.4 and for the concentration claim of §14.6

***

## Readings

### Required

* Campbell, J. Y. (2006). "Household Finance." *Journal of Finance* 61(4): 1553-1604. *The presidential address that named the field. Sets out the normative benchmark, the catalogue of household deviations from it, and the distinction between mistakes that are cheap and mistakes that are expensive. Read it as the syllabus for this chapter.*
* Madrian, B. and D. Shea (2001). "The Power of Suggestion: Inertia in 401(k) Participation and Savings Behavior." *Quarterly Journal of Economics* 116(4): 1149-1187. *The opening episode. Read the tables on the fraction of automatically enrolled participants sitting at both the default contribution rate and the default fund; that joint statistic is the chapter's thesis in one number.*

### Recommended

* Campbell, J. Y. (2018). *Financial Decisions and Markets: A Course in Asset Pricing*. Princeton University Press. *The full theory §14.1 compresses, including intertemporal portfolio choice with labor income. The deferral target named in "Elsewhere in the Series."*
* Benartzi, S. and R. Thaler (2004). "Save More Tomorrow: Using Behavioral Economics to Increase Employee Saving." *Journal of Political Economy* 112(S1): S164-S187. *Automatic escalation as a design that exploits inertia rather than fighting it.*
* Shiller, R. J. (2005). "Behavioral Economics and Institutional Innovation." *Southern Economic Journal* 72(2): 269-283. *The design argument behind §14.3's "defaults as infrastructure." Behavioral findings can be turned into institutions rather than into warnings, which is what automatic enrollment and the QDIA rules did. Read next to Benartzi and Thaler.*
* Hong, H., J. Kubik and J. Stein (2004). "Social Interaction and Stock-Market Participation." *Journal of Finance* 59(1): 137-163. *The fourth channel in §14.2's list. Sociable households participate more, and the effect is stronger where local participation is already high — a peer mechanism rather than an information one.*
* Calvet, L., J. Y. Campbell and P. Sodini (2007). "Down or Out: Assessing the Welfare Costs of Household Investment Mistakes." *Journal of Political Economy* 115(5): 707-747. *Complete portfolios for an entire population. The result is deliberately two-sided: modest median diversification losses, a long and costly tail, and the mistakes concentrated where they can least be afforded.*
* Calvet, L., J. Y. Campbell and P. Sodini (2009). "Measuring the Financial Sophistication of Households." *American Economic Review* 99(2): 393-398. *The companion to "Down or Out," and the paper that makes §14.2's tail claim quantitative: an index of sophistication built from the Swedish register, and the demonstration that the costly mistakes sort on it.*
* Odean, T. (1998). "Are Investors Reluctant to Realize Their Losses?" *Journal of Finance* 53(5): 1775-1798. *The disposition effect, measured. Read alongside Chapter 15, which supplies the explanation.*
* Dorn, D. and G. Huberman (2005). "Talk and Action: What Individual Investors Say and What They Do." *Review of Finance* 9(4). *Survey responses matched to the same investors' actual trades. A useful discipline on §14.2, where much of the evidence is either what households say or what they do, rarely both for the same household.*
* Mankiw, N. G. and S. Zeldes (1991). "The Consumption of Stockholders and Nonstockholders." *Journal of Financial Economics* 29(1): 97-112. *The original demonstration that separating the two populations changes what the consumption-based model has to explain; the empirical hinge between §14.6 and Chapter 5.*
* Geanakoplos, J., M. Magill and M. Quinzii (2004). "Demography and the Long-Run Predictability of the Stock Market." *Brookings Papers on Economic Activity* 2004(1): 241-307. *The life-cycle machinery of §14.1 aggregated up: if households save and dissave by age, the age composition of the household sector is itself a pricing input. The strongest version of §14.6's claim that the identity of the holder is data.*
* Keys, B., D. Pope and J. Pope (2016). "Failure to Refinance." *Journal of Financial Economics*. *The refinancing inertia of §14.4, with the dollar cost of inaction.*
* Shiller, R. J. and A. N. Weiss (1999). "Home Equity Insurance." *Journal of Real Estate Finance and Economics* 19(1): 21-47. *The proposal named in §14.4: index-settled insurance against a fall in house prices, designed around the moral hazard and appraisal problems that keep the market from existing. The theory-side answer to Discussion Question 4.*
* Shiller, R. J. (2003). "The Invention of Inflation-Indexed Bonds in Early America." NBER Working Paper 10183. *An instrument-design counterpart to §14.3's risk-transfer list: how a security that protects real income gets invented, and how long it takes to be adopted. Short, and useful against the decumulation problem of §14.4.*
* Investment Company Institute, *Investment Company Fact Book*, and Employee Benefit Research Institute / ICI, *401(k) Plan Asset Allocation, Account Balances, and Loan Activity* (both annual, free online). *The standing free sources for target-date assets, plan-level allocations, and the employer-stock series of §14.2.*

***

## Discussion Questions

1. **The default as a policy lever.** Automatic enrollment raises participation dramatically and anchors participants at the default rate in the default fund. A legislator proposes raising the statutory default contribution rate for new plans from three percent to eight percent. Set out the welfare argument for and against, distinguishing carefully between households who would have saved nothing, households who would have saved more, and households for whom the higher default is genuinely wrong — the liquidity-constrained, the heavily indebted, the young worker with high expected income growth. What does the Madrian-Shea evidence tell you about the relative sizes of these groups, and what does it fail to tell you? Then ask the question the paper cannot answer: does higher plan saving raise *total* household saving, or is it offset by borrowing elsewhere, and what data would settle it?
2. **Does heterogeneity break the representative agent?** The top decile of the wealth distribution holds roughly eighty-five percent of directly held equity (Table 14.4). Construct the argument that this invalidates a representative-agent asset pricing model — being precise about *which* step of the derivation fails, not merely asserting that people differ. Then construct the strongest defense: aggregation theorems that survive heterogeneity, the possibility that non-participants are marginal in some other market that ties their marginal utility to the stockholders', and the observation that a representative agent can be *constructed* to rationalize any set of prices. Which side does the stockholder-consumption evidence support, and how much of the equity premium puzzle does limited participation actually retire?
3. **Two demand curves.** Section 14.6 argues that the household sector supplies a nearly vertical demand curve (default-driven retirement flows) and a sloped one (wealthy direct holders), and that the mixture has rotated toward the vertical component for forty years. Design an empirical test. What observable variation would separate the two curves — payroll timing, cohort ages, plan-eligibility rules, glide-path reconstitution dates? What would you expect to see in returns around dates when the inelastic component's flows are mechanically large, and what would confound you? Compare your design with the index-inclusion evidence of Chapter 12 §12.9.
4. **The house that cannot be sold.** For households between the median and the ninetieth percentile of wealth, home equity is a large share of retirement resources, and retirees overwhelmingly decline to draw it down. State the problem in life-cycle terms: what is the household maximizing such that not spending home equity is optimal? Consider bequest motives, the rent-hedging value of ownership, medical-expense risk as a precautionary motive, and the transaction and emotional costs of moving. Then evaluate the instruments — downsizing, reverse mortgages, home-equity release products, long-term care insurance — and say why the market for each is smaller than the theory predicts. Which of your explanations are preferences and which are market failures, and does the distinction change what policy should do?
5. **Location versus allocation.** A household holds $200,000 in a traditional 401(k) and $50,000 in a taxable brokerage account, and wants a 70/30 stock-bond split overall. Work out the tax-efficient location, then list every reason the household might rationally deviate from it — including reasons that have nothing to do with error. Now add the constraint that the 401(k) offers only a target-date fund and three index funds, and that the household's default is the target-date fund. Which of §14.5's prescriptions survive contact with the menu, and what does that imply about who is actually making this household's asset-location decision?

***

## Problems

**Problem 1 — The glide path, with numbers.** A household has constant relative risk aversion $$\gamma = 4$$. The risky asset has an expected return of 7 percent and a standard deviation of 18 percent; the riskless rate is 3 percent. All wealth figures are in dollars.

(a) Compute the Merton share $$w^{\ast}$$ of §14.1, and state in one sentence what the formula says about the household's age. (b) Apply the glide-path identity to three households: one aged 30 with human capital of 1,200,000 and financial wealth of 50,000; one aged 50 with 600,000 and 400,000; one aged 65 with 0 and 1,000,000. Report the implied equity share of each household's *financial* portfolio. (c) The young household cannot borrow. At what ratio $$H\_t/W\_t$$ does a hundred-percent ceiling on the financial equity share begin to bind, and which of the three households does it bind for? (d) Human capital is not a bond. Suppose 30 percent of human capital's value behaves like equity and the rest like a riskless bond, so the household already holds an implicit equity position of $$0.3H\_t$$. Rewrite the identity and recompute the financial equity share for the household aged 50. By how many percentage points does it fall? (e) A commercial target-date fund holds 60 percent equities for a participant aged 50. Using the form of (d), find the equity fraction of human capital that would reconcile the commercial glide path with the theory at that household's $$H\_t/W\_t$$. Then name one household characteristic §14.1 says should move that fraction and that a dated fund cannot observe.

**Problem 2 — The cost of not refinancing.** A household holds a fixed-rate mortgage with a balance of 200,000 and 300 monthly payments remaining, at an annual rate of 6.5 percent compounded monthly. It can refinance the same balance over the same remaining term at 4.5 percent, for a one-time cost of 2,000. All figures are in dollars.

(a) Compute the monthly payment on each loan and the monthly saving. (b) Compute the present value of the saving over the full remaining term, discounted at the new rate, and net out the refinancing cost. Is the option clearly in the money? (c) Keys, Pope and Pope put the median cost of inaction at about 11,000. Holding the two-point rate decline, the 300-month term and the 2,000 cost fixed, what loan balance produces exactly that median net gain? What does the answer suggest about which households the median describes? (d) Roughly a fifth of eligible borrowers fail to act. Take an eligible population of 10 million and the 11,000 median. Compute the aggregate forgone saving, and state in one sentence who receives it and through which security (§14.4, and Chapter 13 §13.3). (e) Ten years on, the household holds the 4.5 percent loan, with 145,316 outstanding and 180 payments of 1,111.66 remaining, and the market rate has risen to 7 percent. Compute the present value of the remaining payments at 7 percent and compare it with the balance. State what the difference is worth to the borrower, and why the inertia that cost the household money in (b) is now an asset it is reluctant to give up.

**Problem 3 — A participation threshold.** Equity has an expected excess return of 5.5 percent and a standard deviation of 18 percent. A household with constant relative risk aversion $$\gamma$$ that participates optimally gains a certainty equivalent of $$(\mu - r\_f)^2/(2\gamma\sigma^2)$$ per year, expressed as a fraction of the financial wealth it invests. All wealth figures are in dollars.

(a) At $$\gamma = 4$$, compute the optimal risky share and the annual certainty-equivalent gain as a fraction of wealth. (b) Participation costs 500 once and 75 a year thereafter in time and account charges. At a discount rate of 3 percent, convert the one-time cost into an equivalent annual flow, add it to the recurring cost, and find the financial wealth at which a household is indifferent about participating. (c) Recompute the threshold at $$\gamma = 8$$, and again at $$\gamma = 4$$ with an equity premium of 3 percent rather than 5.5. Report the range the three calibrations span. (d) Table 14.1 puts equity participation at 17 percent in the bottom income quintile and 40 percent in the second. Is the range in (c) large enough to account for those rates on its own? State two facts from §14.2 that a fixed-cost story cannot deliver. (e) Invert the calculation. A household with 200,000 of financial wealth holds no equity. At $$\gamma = 4$$ and the 5.5 percent premium, what annual cost of participating would rationalize that? Say whether a number of that size is plausibly a *cost*, and what §14.2 offers instead.

**Problem 4 — Reading Table 14.4.** Use Table 14.4 together with the chapter's own aggregates: directly held corporate equity and mutual fund shares of about 46 trillion (roughly 25 trillion of equity and 21 trillion of fund and ETF shares, from the opening and §14.6) and household real estate of about 50 trillion (§14.4). All figures are in dollars.

(a) Compute the top decile's share of each of Table 14.4's four asset classes and of total net worth. (b) Express each of the four asset shares as a ratio to the top decile's net worth share. Which two classes are held more concentratedly than wealth itself, and which two less? (c) Equity prices fall 30 percent and house prices fall 20 percent. Compute the aggregate loss in each case and distribute it across the four wealth groups. (d) The equity shock is the larger in aggregate. Which shock costs the bottom half of the distribution more, and by what factor? Relate the answer to §14.6's claim that a shock to equity prices and a shock to house prices are shocks to different populations. (e) Now the pricing reading. Which of the two shocks should move the consumption of the marginal holder of equity risk more, and what does that do to the risk aversion Chapter 5's model requires? Then state the one methodological caveat the DFA's construction attaches to every number you have just computed.

**Problem 5 ★ — Two measurements of one household sector.** Table 14.2 and Table 14.4 both describe the distribution of household assets, and they cannot be combined. This problem shows why.

(a) State precisely what each table's cells are shares *of*. Then note that the dollars one wealth group holds in one asset class can be reached two ways: as the group's share of its own assets held in that class, times the group's total assets, which is Table 14.2's basis; or as the group's share of that class, times the class's total value, which is Table 14.4's basis. Write the identity that follows, and name the one further quantity a reader would need in order to convert either table into the other. (b) Take the top decile and the class "directly held corporate equity and mutual fund shares". Table 14.2 puts the first of those two shares at 21.9 percent and Table 14.4 puts the second at 87.3 percent. Use the identity to compute the ratio of the top decile's share of total household assets to the class's share of total household assets. (c) Table 14.4's last row puts the top decile's share of total net worth at 67.9 percent, and household debt is concentrated below the top decile, so the top decile's share of household *assets* is lower than its share of net worth. Use that with your answer to (b) to place an upper bound on the class's share of total household assets. Convert the bound into a floor on total household assets, using the chapter's figure of about 46 trillion dollars for the class, and compare that floor with a balance sheet that also carries about 50 trillion of real estate and about 33 trillion of pension entitlements. (d) The two tables are not measuring the same aggregate. Using the source notes to Tables 14.2 and 14.4, name the two differences in construction that produce the gap, and say which of the two equity figures is a residual. (e) Say which source you would use for each of three questions, and why: how concentrated equity ownership is; what the balance sheet of a median household looks like; and whether stockholders' consumption is more volatile than aggregate consumption.

***

## Selected Solutions

*Solutions to Problems 1 and 2 follow. Solutions to the remainder are in the instructor materials.*

**Problem 1.**

(a) $$w^{\ast} = (\mu - r\_f)/(\gamma\sigma^2) = 0.04/(4 \times 0.0324) = \mathbf{30.9}$$ **percent**. The sentence is that the formula says nothing about age at all: neither $$t$$ nor a horizon appears in it, which is §14.1's point about what the Merton share rules out rather than what it rules in.

(b) With human capital treated as safe, all of the risk loads onto the tradable part, so the financial equity share is $$w^{\ast}(1 + H\_t/W\_t)$$.

| Age | $$H\_t$$  | $$W\_t$$  | $$H\_t/W\_t$$ | Financial equity share |
| --- | --------- | --------- | ------------- | ---------------------- |
| 30  | 1,200,000 | 50,000    | 24.0          | **771.6%**             |
| 50  | 600,000   | 400,000   | 1.5           | **77.2%**              |
| 65  | 0         | 1,000,000 | 0.0           | **30.9%**              |

The glide path is in the third column, not in anyone's preferences. Nothing about the household's risk aversion changed between the rows.

(c) The ceiling binds when $$w^{\ast}(1 + H\_t/W\_t) \ge 1$$, that is when $$H\_t/W\_t \ge 1/w^{\ast} - 1 = \mathbf{2.24}$$. It binds for the household aged 30 by a factor of more than ten, and for neither of the others. The theory's advice to that household is to hold a levered equity position of nearly eight times its financial wealth, and the borrowing constraint reduces it to one — which is most of the gap between the model and §14.2's evidence, before any behavioral consideration is added.

(d) With a fraction $$\phi$$ of human capital behaving like equity, the household already holds $$\phi H\_t$$ of implicit equity, so the identity becomes

$$
\frac{\text{risky assets}}{W\_t} = \frac{w^{\ast}(W\_t + H\_t) - \phi H\_t}{W\_t}
$$

At $$\phi = 0.3$$ and the household aged 50: $$w^{\ast} \times 1{,}000{,}000 = 308{,}642$$, less $$0.3 \times 600{,}000 = 180{,}000$$, leaves 128,642 on 400,000 of financial wealth, or **32.2 percent** — a fall of **45.0 percentage points** from the 77.2 percent of part (b). One assumption about the character of an untraded asset, and the recommendation more than halves.

(e) Set the share to 0.60 and solve for $$\phi$$:

$$
\phi = \frac{w^{\ast}(W\_t + H\_t) - 0.60 W\_t}{H\_t} = \frac{308{,}642 - 240{,}000}{600{,}000} = \mathbf{11.4 \text{ percent}}
$$

So a commercial dated fund holding 60 percent equities for this household is behaving as though roughly an eighth of its human capital were equity-like. The characteristic §14.1 says should move that number is the covariance of the household's own labor income with the market — a tenured teacher and a commission-paid broker of the same age have very different $$\phi$$ — and a fund dated only on a retirement year cannot observe occupation, industry, or job security. *This is the honest form of the criticism of dated funds. It is not that the glide path is arbitrary; it is that the one parameter it should be conditioned on is the one the vehicle is forbidden to see.*

**Problem 2.**

(a) At $$0.065/12$$ over 300 months the payment is $$\mathbf{1{,}350.41}$$; at $$0.045/12$$ over 300 months it is $$\mathbf{1{,}111.66}$$. The monthly saving is $$\mathbf{238.75}$$.

(b) Discounting 238.75 for 300 months at $$0.045/12$$ gives a present value of **42,953**, and netting the 2,000 cost leaves **40,953** — about twenty percent of the loan balance. The option is not marginally in the money; it is in the money by a factor of twenty against its exercise cost.

(c) The present value of the saving is proportional to the balance at 0.2148 per dollar, so a net gain of exactly 11,000 requires $$(11{,}000 + 2{,}000)/0.2148 = \mathbf{60{,}531}$$. The median in the Keys-Pope-Pope estimate therefore describes a household with a *small* mortgage — about a third of this problem's balance and well below the national average loan size. That is the shape of the finding: the failure to refinance is concentrated among smaller, lower-income, less-financially-sophisticated borrowers, so the median household's forgone gain is much less than the median *dollar's*.

(d) $$10{,}000{,}000 \times 0.20 \times 11{,}000 = \mathbf{22\ \text{billion dollars}}$$ of forgone saving in the cohort. It is received by whoever holds the mortgage — which, after §13.2's securitization, is the holder of the agency pass-through, in the form of a pool that keeps paying an above-market coupon. Household inertia is a component of the prepayment S-curve's ceiling (Figure 13.1), and it is worth money to the security's holder. **An error in household finance is an asset in fixed income.**

(e) Discounting 180 payments of 1,111.66 at $$0.07/12$$ gives **123,679**, against an outstanding balance of 145,316. The household owes 145,316 on a loan a lender would now pay only 123,679 for, so the below-market coupon is worth about **21,637** to the borrower — roughly fifteen percent of the balance, and a larger sum than the median failure-to-refinance loss in part (c).

*The pair is the point. The same inertia is a loss in (b) and an asset in (e), because the borrower's option is one-sided: falling rates make it valuable to act, rising rates make it valuable to sit still, and doing nothing is the right policy in exactly one of the two states. A household that never acts collects the second and forgoes the first. That asymmetry is what makes the prepayment function in Chapter 13 §13.3 flatten at both ends, and it is the reason lock-in has become a constraint on housing turnover: the option the household is refusing to give up is one an efficient market would have priced into the house.*

***

## Data Exercise: Who Owns the Risk?

Every part of this exercise runs on free public data. It extends Part D of Chapter 2's exercise and produces the tables §14.6 asserts.

**Part A — Concentration over time (free data).** Download the Federal Reserve's **Distributional Financial Accounts** as a CSV from the Board's website. The release distributes the Z.1 household balance sheet across four wealth groups (top 1 percent, next 9, next 40, bottom 50) quarterly from 1989.

1. Plot the share of *corporate equities and mutual fund shares* held by each of the four groups, quarterly, over the full sample. Rebuild the first row of Table 14.4 for the most recent quarter and report how far your figures sit from the approximations printed there.
2. Repeat for pension entitlements, for real estate, and for total net worth, and put the four panels on one page. Describe how the *ordering* of the groups differs across the four assets, and write one paragraph on what that implies for the distributional incidence of an equity drawdown versus a housing drawdown.
3. The equity concentration series has a trend. Identify it, then ask whether it is driven by the numerator (the wealthy buying more equity) or by valuation (the equity they already held rising in price). Sketch how you would decompose the change, and say what the DFA alone cannot tell you.
4. State the DFA's central methodological limitation — it distributes Z.1 aggregates using SCF shares rather than measuring the distribution directly — and say what that implies for the precision of everything above.

**Part B — The household balance sheet (free data).** From the current **Z.1** release, take table **B.101**, Balance Sheet of Households and Nonprofit Organizations.

1. Rebuild Table 14.3. Construct, annually since 1980: total household debt, the mortgage share of it, household debt as a share of disposable personal income (the denominator is available from FRED), and homeowners' equity as a share of household real estate.
2. Mark the 2007 peak and the current value on each series. The deleveraging is visible in the ratio; check whether it is visible in the *level* of nominal debt, and explain the difference between the two statements.
3. Overlay the household debt service ratio (FRED series TDSP). It falls further than the debt-to-income ratio does. Decompose why, and identify how much of the improvement is refinancing into lower coupons — the flip side of §14.4's inertia.

**Part C — Participation (free data).** The Survey of Consumer Finances publishes summary tables alongside each triennial *Federal Reserve Bulletin* article, "Changes in U.S. Family Finances."

1. Rebuild Table 14.1 from the most recent summary tables: the share of families with any equity holdings, with direct stock holdings, and with any retirement account, by income percentile group.
2. Construct the same three series for every SCF wave available and plot participation over time by income group. The aggregate participation rate rose substantially from the early 1980s. Which income groups account for the rise, and does the timing line up with the spread of 401(k) plans and, after 2006, of automatic enrollment?
3. The SCF also reports direct and indirect equity separately. Compute the ratio of indirect to direct equity holdings by income group, and use it to state precisely which households the phrase "households are the largest holder of US equity" is and is not about.

**Part D ★ — SCF microdata (free but harder).** The full SCF public-use microdata files, with their five implicate replicates and sampling weights, are downloadable from the Board.

1. Reproduce your Part C participation rates from the microdata, using the weights and combining the implicates correctly. Confirm that you match the published summary tables; if you do not, the error is almost always in the implicate handling.
2. Estimate a linear probability model or probit of equity participation on income, net worth, age, education, and self-reported risk tolerance. Which covariate does the most work once wealth is controlled for? What does the *residual* variation suggest about the fixed-cost and the familiarity explanations of §14.2?
3. Restrict to households with a retirement account and regress the equity share of the retirement portfolio on age. Compare the fitted slope with the glide path of a large commercial target-date series (published in any provider's prospectus). Does the observed household glide path look like the theoretical one of §14.1, like the commercial one, or like neither?