Here is how far.

Two sisters, one fund, one year

Ana and Bea own the same fund for the same calendar year.

The fund falls 20% in the first half and rises 25% in the second. Multiply it out, 0.80 × 1.25, and the fund ends the year exactly where it started. Its return for the year is 0%.

Ana starts with $10,000. On July 1, at the bottom, she adds another $10,000. Her $8,000 plus the new $10,000 is $18,000, and the second half’s 25% takes it to $22,500.

Bea starts with $20,000. On July 1, at the same bottom, she needs cash and takes $10,000 out. Her $16,000 becomes $6,000, and the second half’s 25% takes it to $7,500.

Same fund. Same year. Same 0%.

Ana put in $20,000 and has $22,500. She is $2,500 ahead.

Bea put in $20,000, took out $10,000, and has $7,500. She is $2,500 behind.

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Why the balance doesn’t tell you

Ask Ana’s statement how she did and it shows a balance that went from $10,000 to $22,500: up 125%. Almost all of that is her own deposit. A balance counts saving as if it were return, which flatters anyone who adds money and punishes anyone who takes some out.

The fund’s own figure doesn’t tell her either. It says 0%, correctly, because the fund didn’t do anything. But Ana did: she added money at the bottom, and her dollars rode the recovery.

So there are three numbers for one person in one year: +125% (the balance), 0% (the fund) and the one she actually earned.

What’s the difference between time-weighted and money-weighted return?

Time-weighted return chains together the fund’s returns between each deposit and withdrawal, so the size and timing of the money don’t matter. It answers: how did the investment do? It’s the fair way to judge a fund manager, who doesn’t decide when you add money. That’s why fact sheets and benchmarks use it.

Money-weighted return gives each dollar weight for the time it was invested. It answers: what did my money earn? It’s an internal rate of return, the single rate at which everything you put in grows into everything you took out plus what’s left.

For Ana it’s about +16.9% a year. For Bea, about −16.9%. The fund: 0%.

Neither sister was wrong about the fund. They were wrong only if they read the fund’s number as their own.

How do you calculate your own?

The spreadsheet way is exact and free.

List every date money went in or out of the investments, with the amount. Money you put in is negative; money you took out is positive.

Add one last row: today’s date and today’s value, as a positive number.

Use =XIRR(amounts, dates) in Excel or Google Sheets.

Ana’s rows are −$10,000 on January 1, −$10,000 on July 1, and +$22,500 on December 31. XIRR returns about 17%.

A simpler approximation, the Modified Dietz method, needs no solver: divide the gain by the starting balance plus each flow weighted by the share of the period it was invested. Ana’s gain is $2,500. Her base is $10,000 plus half of $10,000, or $15,000. $2,500 ÷ $15,000 is 16.7%, close to the exact answer.

Both methods depend on the same discipline: recording every dollar that crossed the line into or out of the investments, on the date it crossed. The deposit that gets missed becomes “return”. The withdrawal that gets missed becomes a “loss”.

The Eudos Academy lesson on this: Your Return vs. the Investment’s.

Which number should a family watch?

Both, for different things.

The time-weighted figure judges the investments. If a fund trails its benchmark on a time-weighted basis for years, that’s a fact about the fund.

The money-weighted figure judges the family’s own experience: the timing of its saving, its withdrawals, the cash it needed in a bad year. That’s the one that says what the family’s money did. It’s also the one most families never see, because the account that holds the money is built to report on itself, not on the family’s choices.

Bea’s year is the one to remember. Nothing about the fund was bad. A withdrawal at the bottom, taken because cash was needed, turned a 0% year into a $2,500 loss. That’s a cash-planning fact as much as an investment fact. It’s the reason a measure of returns belongs next to a measure of runway.

What the number is not

It is not a grade on anyone’s decisions. Bea may have had a good reason to need the cash in July. Money-weighted return records what happened; it doesn’t say what should have.

It is not a forecast. A strong money-weighted year says the timing worked, not that it will again.

And it is not a reason to time deposits. Ana didn’t know July was the bottom. The point is only to measure the year honestly, after the fact.

Nothing here is advice. It’s the arithmetic, explained plainly.

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If you want the instrument behind the writing: Eudos is a family office in software. It keeps a ledger of the money that moves into and out of a family’s investments, measures returns on the capital actually invested, and shows IRR for each holding and each portfolio, so a deposit is never counted as a gain. It’s in private beta; the waitlist is at eudos.com.

To see growth and return side by side on a family’s numbers, open the demo, a fictional family’s wealth with no sign-up. On its dashboard, the breakdown table shows each member’s Growth · 12m, which counts money added, next to IRR · all-time and IRR · YTD, which don’t.

It is really two payments wearing one name. Part of it is interest: the price of using the bank’s money for another month. The rest is principal: your own money, moved from your checking account into your house, where it stays yours. One is spent. The other is saved. A budget that adds them together is counting savings as spending, and on a long mortgage that error grows every single month.

This is the Eudos Academy lesson on down payments, principal and equity, taught the long way.

Two payments in one

Take the example above: a $500,000 home, $100,000 down, a $400,000 loan at 7% for 30 years. Taxes, insurance and upkeep are left out, because they are spending and nobody disputes it.

In the first year, the household pays $31,934. Of that, $27,871 is interest and $4,063 is principal. Eighty-seven cents of every dollar rents the money. Thirteen cents buys the house.

That is the honest way to describe interest: it behaves like rent. It pays for the use of something you do not own yet, and once paid it is gone. Principal behaves like a deposit into an account you cannot easily withdraw from. The account is called equity.

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The split moves

The payment never changes. What it buys does, a little every month, because interest is charged on the balance and the balance keeps falling.

• Year 1: $27,871 interest, $4,063 principal

• Year 5: $26,563 interest, $5,372 principal

• Year 10: $24,319 interest, $7,615 principal

• Year 15: $21,139 interest, $10,796 principal

• Year 20: $16,630 interest, $15,304 principal

• Year 25: $10,239 interest, $21,695 principal

• Year 30: $1,179 interest, $30,756 principal

The crossing comes in month 242, a little past year twenty: the first month in which more of the payment goes to the house than to the bank. Over the full 30 years the household pays $558,036 of interest to borrow $400,000.

None of that is a judgment about mortgages. It is what amortization means: interest first, ownership later.

What counts as return

Ten years in, the loan balance is $343,250. If the house rose 3% a year, it is worth about $671,958, and the household’s equity is $328,708.

That equity came from three places:

• $100,000: the down payment, your money;

• $56,750: ten years of principal payments, also your money;

• $171,958: appreciation, the only part the house earned.

This is the distinction the lesson exists to teach. Equity growth is not investment return. Most of the $328,708 is the household’s own savings, arriving a month at a time. Counting principal payments as the house “performing” flatters every leveraged property, because it credits the asset with money the owner put in. The clean way to score a property is to put the down payment and each principal payment in as contributions and to count only the change in value as the return.

Interest belongs on the other side of that page. Over the same ten years it came to $262,595, the cost of living in the house on borrowed money, the way rent is the cost of living in someone else’s.

How it shows up in the wealth picture

Here is why this is a measurement problem rather than a housing one.

Count the whole payment as spending and two numbers go wrong together. The savings rate looks lower than it is: in year ten of the example, $7,615 of real saving is filed as a bill. On a $250,000 income that is three points of savings rate gone missing, and by year twenty it is six. And the spending trend looks flatter than it is, because a growing share of the “housing” line was never spent at all.

Count none of it, on the other hand, and the month looks richer than it is. The cash still left the account. Whether the household can cover its bills for six months depends on the whole payment, principal included, because the bank wants all $2,661 either way.

Family offices hold both truths on one page: interest as a cost, principal as a transfer into an asset, and the full payment in the cash plan. It is not complicated. It is simply rarely done.

What the number is not

It is not a case for paying a mortgage off early, or against it. That choice depends on the rate, the alternatives, taxes and how much cash the household wants on hand, and it changes as rates move.

It is not a rent-versus-own verdict. Interest works like rent, but owning carries costs this essay leaves out (taxes, insurance, repairs) and benefits it leaves out too (a fixed payment that inflation shrinks, and the appreciation itself).

And it is not tax guidance. Mortgage interest may be deductible for some households and not others, which changes what the interest really costs. That is a conversation with an accountant, with the numbers in hand.

The older word

The word itself carries the lesson. Mortgage comes from Old French: mort gage, a dead pledge. The pledge died either way: when the debt was paid and the land was freed, or when it was not and the land was lost.

What it never did was change what the money was. Every payment was partly the price of the pledge and partly the slow buying back of the land. The first part was spent. The second part was kept. It still is.

Nothing here is advice. It’s the arithmetic, explained plainly.

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If you want the instrument behind the writing: Eudos is a family office in software. Link a mortgage payment to its loan and Eudos counts only the interest as spending, records the principal as debt repaid, and still counts the whole payment in your cash runway. It measures a property’s return on your equity, with appreciation, not your own principal, as the return. It’s in private beta; the waitlist is at eudos.com.

To see it first, open the demo, a fictional family’s wealth with no sign-up. On its Cash Flow page, link the 418 Linden mortgage payment to its loan. Of the $3,960, $1,581 is interest at 3.1%. The other $2,379 is principal.

The thread that followed ran to dozens of replies, and almost none of them were about the 6%. They were about foreclosure timelines, state taxes, deeds in lieu, liquidity and inflation. Taken together they answered the question better than any one reply could. Seller financing is uncommon because the extra interest it pays is small, and the list of things that interest has to pay for is long.

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Two ways to lend $400,000

Illustrative round numbers, simple first-year yields, income tax only. They show a method; they do not describe anyone, and none of it is advice.

A seller has $400,000 to lend. One way is to lend it to the buyer of the house at 6%, secured by the house. The other is to lend it to the United States by buying 10-year Treasuries yielding 5.3%.

The buyer: $24,000 a year in interest.
The Treasury: $21,200 a year.

The difference, $2,800 a year, is the spread: 0.7 percentage points. Every reason to prefer one loan over the other has to fit inside it.

What the $2,800 has to buy

One borrower instead of a government. A Treasury’s interest arrives whether or not any particular person keeps a job. The buyer’s arrives only if this one household does. Suppose a default costs $28,000 by the time it is resolved: about a year of missed payments ($24,000) plus legal fees. That one event erases ten years of the extra $2,800. Put the other way, the spread breaks even only if a default like that comes no more often than once a decade, a one-in-ten chance every year, on a single loan.

A bank lending to thousands of buyers can price that chance from its history and absorb it across the pool. Spread the same $400,000 across 100 notes of $4,000 and one default touches 1% of the money. (That assumes equal notes and defaults that don’t all arrive together; 2008 showed what happens when they do.) The seller has one note. There is no average, only what this buyer does.

Time, if it goes wrong. Foreclosure is slow, and how slow depends on the state. Every month of waiting is about $2,000 of interest not received ($24,000 ÷ 12), before counting the principal, the taxes and insurance the seller may have to keep paying, or the condition of the house when it comes back. A deed in lieu of foreclosure, where the buyer signs the house back, is faster and cheaper, when the buyer agrees to sign.

Liquidity. A Treasury sells in one click on any trading day. A private note can be sold too, but it means finding someone who wants one household’s IOU, and that someone will want a discount. The seller who finances is committing the money for as long as the buyer takes to pay or refinance.

Rate moves, in both directions. Liquidity can pay. If 10-year yields fell from 5.3% to 4.3%, that $400,000 of Treasuries would be worth about $432,000, 8% more, and could be sold to lock it in. If yields rose to 6.3%, it would be worth about $371,000, 7% less. The note never shows either move on a statement. That doesn’t make it immune. A 6% note in a 7% world is worth less to anyone who might buy it, and a 6% note in a 4% world tends to be refinanced away: the buyer pays it off early, and the seller reinvests at 4%. The note’s value moves like the bond’s. It just isn’t priced every day.

State tax, which can erase the spread entirely. Interest on Treasuries is exempt from state income tax. Interest on a private note is not. In California, in the 24% federal bracket with a 9.3% state rate, the note keeps 4.00% after tax, about $16,010 a year, and the Treasury keeps 4.03%, about $16,110. The 6% loan to one household pays less after tax than the 5.3% loan to the government. The crossover is a state rate of about 8.9%: above it, the Treasury wins outright. In a state with no income tax the note keeps its lead, but the lead shrinks from $2,800 to about $2,130.

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What the spread doesn’t pay for

Inflation is often raised as a reason to prefer real estate to bonds. Fair enough, but the seller who finances no longer owns the real estate. The buyer does. The seller owns a fixed stream of dollars, exactly like a bondholder.

At 4% inflation, $400,000 repaid after ten years buys about $270,000 of today’s goods, note and Treasury alike. After inflation, the note earns about 1.9% a year and the Treasury about 1.25%. Inflation hits both loans the same way, so the spread is still the only difference between them. The protection that comes from owning the house belongs to the person living in it.

What the seller gets that isn’t in the rate

None of this makes seller financing a bad trade. It means the 6% is the wrong place to look for the reasons to do it.

The installment method. A seller with a large taxable gain on the property can generally report the gain as the principal arrives, rather than all in the year of sale. Spreading a gain over several years can keep more of it in lower brackets. (On a primary home, the $250,000 or $500,000 exclusion often covers the gain anyway.)

A sale that might not happen otherwise. A buyer the bank won’t serve, or a property the bank won’t lend on, can still sell. Sellers who finance sometimes get a higher price for that reason, and the higher price is part of their return, even though it never shows up in the rate.

Principal back sooner. A Treasury repays all $400,000 at the end. A 30-year note at 6% pays $2,398 a month, $28,778 a year, and returns some principal with every payment. Not much at first: in year one, $23,866 is interest and $4,912 is principal. But each payment lowers what is at risk.

A wider spread where the risk is wider. One reply in the thread was lending on raw land at 8%: $32,000 a year on $400,000, $10,800 more than the Treasury. That spread is nearly four times as wide, and land doesn’t fall apart if it has to be taken back. The size of the spread should follow the size of the risk. When it doesn’t, the lender is working for less than the job pays.

How it shows up in the wealth picture

Here is why this is a measurement problem rather than a real estate one.

A note receivable is one of the least visible assets a family can own. No brokerage holds it, so no statement shows it. It lives in a folder of paper and a row in a spreadsheet, usually carried at its remaining balance, which tells the family how much it is owed and nothing about how the loan is doing.

The questions that matter are all measurable. Did the payments arrive when the schedule said they would? What did the note actually return, counting the months that were late or missed? What did it keep after state tax, and what would the same money have earned in Treasuries over the same months? Family offices keep private loans on that kind of page, with what was scheduled beside what was received, the balance left, and the after-tax yield beside the benchmark. A loan that looks fine on paper can be earning less than a Treasury, and only the side-by-side shows it.

What the number is not

It is not a verdict on seller financing. The arithmetic depends on the state, the bracket, the buyer, the property and the terms, and it changes as rates move.

It is not legal guidance. The rules for financing a buyer, and for taking a property back, vary by state and by how often you do it. That is a conversation with a lawyer and an accountant, with the numbers in hand.

And it is not a reason to fear lending. Every bond is a loan. The point is only that the extra yield is a price, and a price should be compared with what it buys.

The older maxim

“Neither a borrower nor a lender be; for loan oft loses both itself and friend.” Shakespeare gave the line to Polonius in Hamlet, around 1600, in a speech of advice to his son that is mostly remembered for being pompous.

As a rule for money, it is wrong: every saver with a bond fund is a lender, and most are better off for it. As a description of lending to one person, it is close to exact. A private loan can lose the money and the relationship together, and the lender carries both. The spread is what the lender is paid for that. Whether it is enough is arithmetic, and the arithmetic is worth doing before the papers are signed.

Nothing here is advice. It’s the arithmetic, explained plainly.

If you want the instrument behind the writing: Eudos is a family office in software. It keeps a private note beside the Treasuries, brokerage accounts and properties in one encrypted place, records each payment as it arrives, and measures what each asset actually returned, side by side. It’s in private beta; the waitlist is at eudos.com. To see it first with a demo family's numbers, no sign-up: eudos.com/demo

It is called the step-up in basis, and most people who benefit from it never knew it was there. That is fine when it works. The trouble is that it fails just as quietly, through ordinary decisions made years earlier by people who meant well, and the cost is only discovered when the heirs sell.

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What basis is, and why it matters

Basis is what you paid. When you sell, the tax falls on the difference between the price and the basis, not on the price. A share bought for $10 and sold for $100 is taxed on $90.

For most of a life that arithmetic is fixed. Hold the share for thirty years and the basis is still $10; the gain, and the tax waiting on it, only grows. At death the rule changes. For most assets that pass through an estate, the heir’s basis becomes the fair market value on the date of passing, so the gain the owner never realized simply stops existing for income-tax purposes. (Whether the estate owes estate tax is a separate question, and for most families the answer is no.)

The arithmetic

Illustrative round numbers, federal tax only. They show a method; they do not describe anyone, and none of it is advice.

A parent holds stock bought for $100,000 and now worth $1,000,000. The gain embedded in it is $900,000. There are three ordinary ways it leaves the parent’s hands.

Sold during life. The $900,000 gain is taxed. At the top federal rate on long-term gains plus the net investment income tax, 23.8% in all, the bill is $214,200. The family keeps $785,800.

Given away during life. A gift carries the giver’s basis with it. The child now owns a $1,000,000 position with a $100,000 basis, and the whole $900,000 gain travelled with the shares. Sell next year and the tax is due on all of it, at the child’s rates. That can be less than the parent’s rate, which is exactly why gifting appreciated stock is sometimes the right move. But the gain was not erased. It was handed down.

Held until death. The heir’s basis becomes $1,000,000. Sell the next month at $1,000,000 and there is no gain to tax. The family keeps the full $1,000,000.

Same stock, same family, same value. A $214,200 difference decided by nothing but timing and the form the transfer took.

Where the step-up is lost

None of these is exotic. Each is an ordinary decision that looked sensible when it was made.

Simplifying before the end. An aging parent sells the concentrated position to “clean things up” and leave cash instead. It feels responsible. It triggers the full tax on a gain that, held a little longer, would never have been taxed at all.

Gifting the wrong asset. A parent gives away the stock that has grown the most, because it is the most generous gift, and keeps the cash. The heirs later inherit the cash (no gain to erase) and already own the stock (gain intact). Reverse the two and the family’s tax changes by six figures.

The passing gift that comes back. A child gives appreciated stock to a passing parent, expecting to inherit it back at a stepped-up basis. The code anticipated this: if the parent dies within a year of the gift and the property passes back to the giver or the giver’s spouse, it keeps the old basis.

Assets in the wrong kind of trust. A revocable living trust is included in the estate, and its assets step up. An irrevocable trust designed to keep assets out of the estate generally does not; in 2023 the IRS confirmed that assets in an irrevocable grantor trust that are outside the estate get no step-up. Some of those trusts let the grantor swap assets in and out, which is how practitioners move low-basis assets back into the estate before death. The power has to be written into the trust, and someone has to use it.

How the house is titled. When a married couple in a community-property state owns an asset as community property, both halves step up at the first passing. In most other states, jointly held property steps up only the half that belonged to the spouse who passed.

Retirement accounts. A traditional IRA or 401(k) has no basis to step up at all. The heirs pay ordinary income tax as they withdraw. Families that plan to leave “the portfolio” to the children often discover that the portfolio was two very different things.

No records. A step-up is only as good as the date-of-passing valuation behind it, and a carryover basis is only as good as the purchase records behind it. Stock bought in 1994 through a broker that no longer exists, or a building whose improvements were never totaled, becomes a basis nobody can prove.

The twin nobody mentions

The rule cuts both ways. An asset worth less than its basis at passing steps down. The unrealized loss disappears with the owner, and the heirs cannot use it. A loss that could have offset gains, or three thousand dollars a year of income, is simply gone.

So the same arithmetic that says “hold the winners” says something less comfortable about the losers: they are worth selling while the owner is alive to use the loss.

How it shows up in the wealth picture

Here is why this is a measurement problem rather than a legal one.

A statement shows two positions, each worth $1,000,000. One was bought for $950,000; the other for $100,000. They look identical, and they are not. Sold today at 23.8%, one leaves $988,100 in hand, the other $785,800. Held to passing, they leave the same. Given away, the difference goes with them.

Which one to sell when the family needs cash, which one to give, which one to hold: every one of those decisions turns on a number the statement does not print. Family offices keep it on one page as a matter of routine, as a column beside the market value, usually headed “unrealized gain” or “embedded gain,” with the date each lot was acquired. Not because they are planning anyone’s passing, but because the decision of what to sell is made every year, and it is made badly without that column.

What the number is not

It is not a reason to hold something you would otherwise sell. A position that no longer belongs in the portfolio can cost more in concentration than it saves in tax.

It is not estate planning. The rules above are general, the exceptions are many, state law matters, and the right structure for a family is a conversation with its lawyer and accountant, with the numbers in hand.

And it is not morbid. It is the same arithmetic as every other decision about selling, with one date in it that the family would rather not think about.

The older maxim

“In this world nothing can be said to be certain, except death and taxes.” Benjamin Franklin wrote it in 1789, in a letter about the new Constitution, and the line has outlived the letter by two centuries.

The step-up is the one place in the code where the first certainty cancels part of the second. It is also the one place where the cancellation depends entirely on decisions made while nobody was thinking about either. Franklin’s pairing is a joke about the inevitable. The step-up is a reminder that what is left behind is not.

Nothing here is advice. It’s the arithmetic, explained plainly.

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If you want the instrument behind the writing: Eudos is a family office in software. It records the cost basis and acquisition date of every position, shows the gain embedded in each one, lists the positions below cost, and keeps them beside every account, property, entity and trust in one encrypted place. It’s in private beta; the waitlist is at eudos.com To see it first with a demo family's numbers, no sign-up: eudos.com/demo

It is a genuinely useful instrument. It is also the easiest way in personal finance to feel richer while becoming poorer, because every part of it is designed to leave the portfolio looking untouched.

Ask someone with such a line what it is costing them and they will quote the rate. Ask what it has cost them, in dollars, against what the borrowed money earned, over the years it has been open, and the answer is a pause. Nothing they use was built to tell them.

Why the cost is invisible

Sell a share and something visible happens. The position shrinks, the cash appears, a tax form arrives in February. The transaction leaves a mark on every statement it touches.

Borrow against the share and nothing visible happens at all. The position sits where it was, at full value, in an account whose name might now say “pledged” in small type. The loan lives on a different statement from a different department. The interest is debited monthly from cash, often the cash in the collateral account itself, so that it never crosses the household’s checking account and is never seen as spending. The brokerage app, opened on a good day, shows the same green number it always did.

This is not deception. It is the ordinary result of each provider reporting the one thing it can see. The lending desk sees a loan. The brokerage sees a portfolio. Neither sees the household, which is the only place the two numbers meet.

Family offices meet them on one page as a matter of routine. The line’s balance sits under the portfolio it is secured by, its interest is a line item beside the portfolio’s return, and the two are compared every quarter under a heading like “cost of carry.” Not because borrowing is wrong. Because a borrowing whose cost nobody adds up is a decision nobody is making.

The arithmetic

Four steps, using illustrative round numbers. They show a method; they do not describe anyone, and none of it is advice.

Step one: the carry. A household borrows $1,000,000 against a $3,000,000 portfolio at 7%. The interest is $70,000 a year. That is the plain cost, and it is paid whether markets rise or fall. Whatever the borrowed million was used for, the portfolio it is secured by now has to earn $70,000 a year, on top of everything else it was going to do, merely for the household to stand still.

Step two: what selling would have cost instead. Suppose the household wanted $1,000,000 in hand and the stock is worth two and a half times what it cost, so that 60 cents of every dollar sold is gain. Capital-gains tax falls on the gain, not on the proceeds. To net a million the household sells about $1,167,000 of stock, of which $700,000 is gain; at a combined 23.8% federal rate the tax on that gain is about $167,000, and $1,000,000 is left in hand. (Had every dollar sold been gain, the tax would have been $238,000 on the same sale; the basis is what keeps it lower.) Borrowing avoids that payment now. This is the whole case for the line, and it is a real one: $167,000 kept invested is $167,000 that goes on compounding.

The arithmetic behind it:

Stock sold: $1,166,600

Gain in it, at 60 cents per dollar: $700,000

Tax at 23.8% of the gain: $166,600

Left in hand: $1,000,000

But notice what was actually bought. The tax was not cancelled. It was deferred, and the household paid $70,000 in year one for the deferral. In year two it pays another $70,000. By the middle of year three the interest paid exceeds the tax that was avoided, and the tax is still owed the day the stock is finally sold. The line does not remove the bill. It rents time.

Step three: whether the rent was worth it. Renting time is worth it when the thing you kept earns more than the rent. Compare two households. One sold $1,167,000 of stock and has $1,000,000 in hand, tax paid, no loan. The other borrowed, has the same $1,000,000 in hand, still owns the $1,167,000 of stock, and owes $1,000,000 at 7%.

The second household is ahead by exactly what the retained $1,167,000 earns, and behind by $70,000 a year. Break-even is a return of about 6% on the retained stock. Above that, borrowing was the better move; below it, selling was. In a year the portfolio returns 12%, the line earned its keep handsomely. In a year it returns 2%, the household paid $70,000 to keep an asset that made $23,000. In a year it falls 20%, the household lost $233,000 on stock it could have sold, and paid $70,000 for the privilege.

Written as a sentence: the line is a bet that the portfolio will beat its own borrowing rate, renewed every year, with the household’s other assets as the stake. Most people who hold one have never seen the sentence. They have seen the rate.

Step four: the mark. A pledged line has a rule inside it that a mortgage does not. The lender will advance only so much against the collateral, commonly half or less of its value, and the ratio is tested every day. With $3,000,000 securing $1,000,000, the household is borrowing a third of the collateral. If the portfolio falls 30%, the collateral is $2,100,000 and the loan is 48% of it, a whisker under the limit. If the portfolio falls 40%, the collateral is $1,800,000, the loan is 56% of it, and the lender asks for $100,000 by tomorrow, or sells stock to get it.

That is the part the arithmetic in step three leaves out. The line does not merely cost interest. It converts a market fall into a liquidity event, at the exact moment the household is least able to meet one, and the forced sale realizes the very gain the line was opened to defer, now at a lower price. The stock a household can hold through a crash is stock nobody can make it sell. Pledged stock is not that.

How it shows up in the wealth picture

Here is where the invisibility does its real damage, because it reaches the one number that is supposed to be honest.

Net worth is assets less debts. Borrow $1,000,000 and spend it, and net worth falls by whatever was spent, as it should. Borrow $1,000,000 and reinvest it, and net worth does not move at all: the new asset and the new debt cancel. The portfolio, though, is now $4,000,000 supported by $3,000,000 of the household’s own money, and every percentage point the market moves is worth a third more to the household than it was, up and down alike.

A dashboard that shows the portfolio’s growth without the line’s growth beside it is now reporting on a bigger portfolio than the household owns. In a rising year it flatters; the assets grew, the line stood still, the household looks like a better investor than it was. In a falling year it slanders, in the same proportion. The honest reading is three numbers together: how much the assets grew, how much the borrowing grew, and what the difference did to the household’s own equity. On the household from step one, whose own equity is $2,000,000, a year in which the $3,000,000 portfolio rose 8% while the line grew by $150,000 of interest and further draws is a year in which the assets made $240,000 and the household’s equity rose $90,000, about 4½%. Both numbers are true. Only one of them is the household’s.

The interest itself deserves a line of its own. Debited from the collateral account, it reads on a feed as a withdrawal, money the household took out. It is nothing of the kind: the household took nothing; the lender did. Counted as a withdrawal it disappears into the same bucket as a transfer to checking, and the cost of the line is once again invisible, this time inside the very tool that was supposed to add it up. It is a cost of carrying the position, and it belongs beside the position’s return, not among the household’s transfers.

What the number is not

It is not an argument against borrowing. The line is a tool, and for a household with a concentrated position, a large one-off need and a long horizon, it can be the right one. The failure mode is not borrowing. It is borrowing without the four numbers: the carry, the tax deferred, the break-even return, and the fall that triggers the call.

It is not a forecast. Whether the portfolio beats the rate next year is unknowable, and a tool that said otherwise would be selling advice. What can be known is what happened last year, and the year before, and whether the bet has been paying.

And it is not a monthly number. A carry is a slow cost against a slow return. Once a quarter, the line’s interest for the period beside the portfolio’s return for the period, is enough to see whether the arrangement is earning its keep.

The older maxim

Three sayings were carved at the entrance to the temple at Delphi. Two of them everyone knows: know thyself, and nothing in excess. The third is less quoted, and it is about exactly this. Engýa, pára d’áta: give a pledge, and ruin is near. The Greeks meant standing surety for another person’s debt, and every farmer who lost his land to a neighbor’s default understood why it belonged beside the other two.

A pledged line is standing surety for your own future self. The household of today borrows against the household of the year the market falls, and signs on its behalf. That can be a fair bargain. The Delphic point is only that it should be a knowing one, and the first maxim on the wall says how: know what you are pledging, what it costs to carry, and what happens to it on the bad day.

Measurement does not answer whether to borrow. It puts the pledge on the same page as the portfolio, which is where the decision was always being made, whether or not anyone was watching.

Nothing here is advice. It’s the arithmetic, explained plainly.

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If you want the instrument behind the writing: Eudos is a family office in software. It shows a portfolio’s growth beside the growth of the borrowing secured on it, books the line’s interest as a cost of carry rather than money withdrawn, and keeps the household’s own equity as the number that matters, alongside every account, property, entity and collection in one encrypted place. It’s in private beta; the waitlist is at eudos.com. To see it first with a demo family's numbers, no sign-up: eudos.com/demo

Yet that one number explains more about a household’s long-run wealth than the return on any account it holds.

Here is the pattern, and almost everyone recognizes it once it is named. Income rises. A raise, a better year in the business, a partner going back to work. Nothing dramatic is bought. There is no boat. And yet, two years later, the monthly surplus is about what it was before the new income. The money arrived, and it was absorbed, and no single decision can be pointed to. The economists’ term is lifestyle inflation. The more honest term is drift.

WHY NOBODY MEASURES IT

Every statement you receive reports a level. This month’s spending, by category, with a pie chart. The card issuer will happily tell you that dining was 14% of the total. What no statement reports is the slope: how much faster spending is rising than income, over a span long enough to mean something.

That is not an oversight. A level is a fact about one account in one month, which is all any single provider can see. A slope requires every account, income as well as outflow, over two comparable periods, adjusted for the fact that prices themselves moved. It requires the consolidated picture. And as the first essay argued, the consolidated picture is nobody’s product, so nobody computes it.

Family offices do. It is one of the first things they put on the quarterly page, under a dull heading like “household run rate.” Not to scold anyone. Because a family that does not know its own trajectory cannot plan anything else.

THE ARITHMETIC

Three steps, using illustrative round numbers. They illustrate a method; they do not describe anyone.

Step one: spending growth against income growth, monthly, like for like. Take the last twelve months and the twelve before them. A household earned $10,000 a month in the earlier year and $10,800 in the latest: income up 8%. It spent $7,000 a month and now spends $7,490: spending up 7%. Both figures are monthly rates over the months each window actually covers, so a year that started mid-stream is not compared unfairly with a full one.

Seven against eight sounds fine. Spending grew slower than income. Read on.

Step two: how much of each new dollar was spent. Income rose by $800 a month. Spending rose by $490. So 61 cents of every additional dollar earned went out again as higher spending. The other 39 cents was kept. That ratio, the share of the raise that was absorbed, is the number that statements never show and that determines whether a raise changes anything.

At 61 cents the raise changed something, a little. At 100 cents, which is common, the raise changed the household’s standard of living and nothing else. Above 100 cents, which is not rare, the raise financed spending growth it could not cover, and the difference came from somewhere, usually a card.

Step three: take out the prices. Some of that 7% is not the household at all; it is the grocery store. If consumer prices rose 3% across the span, real spending growth is (1.07 divided by 1.03) minus 1, about 3.9%. That is the part that reflects the household rather than the cost of living. It is smaller than the headline, and it is the honest figure. A household whose spending grew exactly with prices did not drift. Its life got more expensive, which is a different problem with a different remedy.

Two cautions on that real figure. "The household" is a broad term: it includes a new child, a medical year and a move as readily as a nicer car, and the arithmetic cannot tell them apart. And the price index is a national basket; a household whose own costs ran ahead of it, say because most of its spending is rent in an expensive city, will see some genuine price inflation land in the real figure. So the careful reading is "spending grew about 4% beyond general inflation," not "the household chose to spend 4% more."

Put the three together and a sentence emerges that no platform shows this household: spending is growing about 4% a year in real terms, and roughly three fifths of every raise is being absorbed. That is a description, not a verdict. But it is a description that was previously unavailable, and it changes what the household knows about itself.

WHY THE SLOPE MATTERS MORE THAN THE LEVEL

Return for a moment to the savings rate, the fraction of income kept. In the example it moved from 30% to 30.6%. Barely. Which is the point: a household whose spending rises almost as fast as its income can earn more every year for a decade and never raise its savings rate. The raises are real. The wealth they could have built is not, because it was quietly converted into a slightly larger life, one indistinguishable month at a time.

Compare two households with the same income path over ten years. One absorbs 100 cents of every raise. The other absorbs 50. Neither feels deprived; the second simply lets half of each increase land in the balance sheet instead of the budget. By year ten the second household’s annual saving is several times the first’s, and the compounding on top of that has only begun. No investment decision separates them. Only the slope.

That is what makes this the most important number nobody measures. Investment returns are uncertain and mostly outside anyone’s control. The absorption ratio is neither. It is the one variable in a household’s wealth equation that is entirely its own, and it is invisible until someone does the subtraction.

WHAT THE NUMBER IS NOT

It is not a judgement about spending. Spending is what wealth is for; a household that measured its drift and decided, with open eyes, to spend the whole raise on a year the children will remember has done nothing wrong and everything right. The failure mode is not spending. It is not knowing.

Nor is it a target handed down by someone else. A tool that says “spend less” is giving advice, and advice is exactly what a measurement should not be. The arithmetic here says only what happened: how fast, against what, after prices. What the household does with that is the household’s business.

It is also not a monthly panic. Drift is a slow phenomenon and it deserves a slow instrument. Two twelve-month windows, compared once a quarter, is enough. Anything faster measures noise.

THE OLDER QUESTION

The Greeks did not have a word for lifestyle inflation, but they had the question underneath it. Eudaimonia is usually translated as flourishing, and Aristotle’s point about wealth was that it is instrumental: useful precisely insofar as it serves a life worth living, and empty when it becomes the life. A household that drifts is not living badly. It has simply stopped choosing. The raise arrives and the life expands to fit it, and the choosing that could have happened, the deliberate decision about what this money is for, never takes place because nobody saw there was a decision to make.

Measurement returns the decision. That is all it does, and it is a great deal.

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Nothing here is advice. It’s the arithmetic, explained plainly.

The arithmetic in this essay, as a reference page: eudos.com/academy/lifestyle-inflation

If you want the instrument behind the writing: Eudos is a family office in software. It measures spending growth against income growth, after prices, over two comparable periods, and shows the share of each raise in income that was absorbed, alongside every account, property, entity and collection in one encrypted place. It’s in private beta; the waitlist is at eudos.com. To see it first with a demo family's numbers, no sign-up: eudos.com/demo

Almost nobody can tell you what their wealth did.

Not the account — the whole of it. The house and the mortgage on it. The rental property and the equity actually at work in it. The business. The LLC that holds the business. The 401(k), the crypto wallet, the watch collection, the credit card balance quietly compounding against everything else. Ask what that entire picture earned last year — one number, honestly computed — and the conversation goes quiet.

This isn’t a personal failing. It’s a structural one, and it’s worth being precise about why it exists, because the reason tells you what an honest answer would have to look like.

Accounts get measured because accounts are products

Every number you receive about your money is produced by someone who sells the container it sits in.

The brokerage measures the brokerage account, beautifully, because the account is the product. The bank measures the bank account. The retirement platform measures the retirement plan. Each of them reports on their slice with great polish and zero interest in the rest, because the rest is someone else’s product.

Your wealth — the consolidated thing, the actual balance sheet of your life — is nobody’s product. So nobody measures it. The most important financial number you have goes uncomputed not because it’s impossible, but because no one is paid to compute it.

Wealthy families noticed this a long time ago. It’s the first thing a family office actually does — before the estate planning, before anything exotic. A family office is, at its core, a group of people paid to know: what is owned, what is owed, what it all earned, measured the same way every quarter. The measurement is the service. Everything else is built on top of it.

Everyone else is left assembling the picture from a dozen flattering fragments — or not assembling it at all.

What honest measurement looks like

Three examples of the arithmetic, using illustrative round numbers. (That’s what they are — illustrations of a method, not projections of anything.)

A rental property’s return is earned on your equity, not the bank’s money. Say a $500,000 property appreciates 4% in a year — $20,000. Headlines would call that a 4% return. But if you put $100,000 down and the bank put in the rest, that $20,000 landed on your $100,000. Before rent, costs, and interest, your equity moved 20%, not 4. Add the rent collected, subtract the mortgage interest and the costs of ownership, and you get the real figure — often very different from 4%, in either direction. Because leverage runs both ways: in a year the property falls 4%, your equity doesn’t fall 4%. It falls hard. The 4% number isn’t wrong; it’s just measuring the house. You own the equity, not the house’s press release.

A debt and a portfolio measured apart both look fine. Measured together, one of them is winning. A credit card charging 24% on a $20,000 balance costs $4,800 a year, with perfect certainty. A portfolio earning 9% is doing well, with no certainty at all. Reported separately — one statement from the card, one from the brokerage — each number sits in its own world and neither asks about the other. Put them on the same screen and something becomes visible that neither statement shows: the same balance sheet is paying a certain 24 and earning an uncertain 9 at the same time. Nothing more needs to be said about it. That’s the point of measurement — done properly, the arithmetic speaks and nobody has to give you advice.

New money is not growth. A portfolio starts the year at $200,000 and ends at $260,000. Up 30%? If $50,000 of that was deposits, no. The investments earned roughly $10,000 — call it 5%, once you account for when the money arrived. Plenty of tools will happily show you the 30, because the 30 feels wonderful and feeling wonderful retains subscribers. An honest calculation credits your saving to your saving and your returns to your returns, and never lets one wear the other’s clothes. They are different virtues. Confusing them flatters you today and misinforms every decision after.

None of this is advanced. It’s arithmetic — the same arithmetic a family office runs as a matter of routine. What’s rare isn’t the math. It’s having all the inputs in one place, and a reason to compute the answer honestly rather than flatteringly.

Why the flattery is the default

Here is the uncomfortable part: most tools that measure your money are paid in ways that reward keeping you pleased rather than informed.

An app monetized by ads wants your attention, and green numbers hold attention. A platform paid a percentage of the assets it manages has opinions about where your assets sit. A “free” aggregator that sells your data is measuring you for someone else’s benefit. In each case the measurement is shaped — sometimes subtly, sometimes not — by what the measurer is paid to want.

A measurement worth trusting has to come from somewhere with nothing to gain from the answer. That is a design constraint, not a feature. It means no advertising, no selling of data, no percentage of assets, no commissions on what the numbers might convince you to do. Just the arithmetic, done the same way whether it makes your year look good or not.

What this publication is

Roughly every few weeks, one piece of that arithmetic, explained plainly: what a return really is once the bank’s money is subtracted. What debt genuinely costs next to what a portfolio genuinely earns. How families structure what they own and pass it on with intention. And underneath all of it, the older question the Greeks called eudaimonia — what is the wealth actually for?

No stock picks, no hustle, no scoreboard.

Subscribe now

Nothing here is advice. It’s the arithmetic, explained plainly.

The arithmetic in this essay, as a reference page: eudos.com/academy/growth-vs-irr

If you want the instrument behind the writing: Eudos is a family office in software — every account, property, entity, and collection in one encrypted place, measured the way a team of professionals would measure it. It’s in private beta; the waitlist is at eudos.com. To see it first with a demo family's numbers, no sign-up: eudos.com/demo