Appreciation Is Not Your Return

Deflating is division, not subtraction

If a house grows 5 percent in a year and prices in general grow 2.5 percent, almost everybody writes 5 − 2.5 = 2.5 percent real. The correct operation is (1 + 0.05) ÷ (1 + 0.025) − 1 = 2.4390 percent. The reason is that the two rates apply to the same money at the same time: the house is worth 1.05 of what it was in nominal units, and each nominal unit now buys 1 ÷ 1.025 of what it used to buy, so the purchasing power of the house is 1.05 ÷ 1.025 = 1.024390 times what it was. Subtraction ignores the interaction between the two, and the interaction is exactly (n − i) × i ÷ (1 + i).

The annual error is 0.061 of a percentage point, which sounds like nothing and is nothing over a year. It is not nothing over a lifetime, because it compounds. After ten years the subtraction answer is 0.6 percent too high, after twenty 1.2 percent, after thirty 1.8 percent. On a $300,000 house held thirty years, the correct real multiple is 2.0605 and the subtraction multiple is 2.0976: $618,136.32 in today's money against $629,270.27, an overstatement of $11,133.95. The gap widens sharply with inflation: at 12 percent growth against 8 percent inflation the error is 0.2963 of a point, nearly five times as large. That is why the shortcut is harmless in a low-inflation decade and misleading in a high-inflation one.

The same arithmetic explains why long-run house-price charts look so different depending on whether they are labelled nominal or real, and why the statistical offices publish both. A nominal series over thirty years is dominated by the price level; a deflated series is the only one that answers the question people think they are asking, which is whether housing got more expensive relative to everything else. When a chart has no label, assume nominal — it is the flattering one.

What a price index cannot see: the cost of owning the thing

A house-price index tracks what buildings change hands for. It does not track anything that happens to a building between transactions, and quite a lot happens. Maintenance at an assumed 1 percent of value a year, property tax at 1 percent and insurance at 0.35 percent make 2.35 percent — $7,050 a year on a $300,000 house, paid whether or not the price moves. These are not one-off items and they are not optional: skip the maintenance and you are no longer tracking the index, because the index is priced on buildings that were maintained.

Netting the drag against real growth is a multiplication, not another subtraction: (1 + 0.024390) × (1 − 0.0235) − 1 = 0.0317 percent a year. Over thirty years that compounds to a factor of 1.0096, so a $300,000 house is worth $302,866.82 in today's money — three decades of 5 percent headline growth and the asset, considered purely as an investment, went nowhere. The number is startling and it deserves the caveat that goes with it: the 2.35 percent is an assumption, and in markets where property taxes are a small fraction of that figure the result is much less extreme.

It also deserves an offset, and the offset is the whole reason people own houses. Those costs buy something: shelter you would otherwise rent, or rent you would otherwise not collect. If you live in the house, the honest comparison is the drag against the rent you are not paying; if you let it, the drag is already inside the profit-and-loss account of our rental article and must not be counted twice. What the calculation does establish is narrower and still important: price growth alone, treated as a return, is not enough to pay for owning. The asset's case rests on the use of it, not on the index.

Transaction costs and the break-even hold

Buying costs money and selling costs money, and both are percentages of the price, which is what makes a short hold so expensive. Write b for the buying cost rate and s for the selling cost rate. You pay P(1 + b) to get in and receive P(1 + g)ⁿ(1 − s) to get out. Setting them equal gives (1 + g)ⁿ = (1 + b) ÷ (1 − s), so the break-even hold is n = ln[(1 + b) ÷ (1 − s)] ÷ ln(1 + g). With 8 percent to buy and 6 percent to sell, the factor is 1.08 ÷ 0.94 = 1.1489, and at 5 percent nominal growth n = 2.85 years.

Two things make that estimate optimistic. First, if you deflate the growth — and you should, because the costs are paid in the same money as the price — the same trade needs 5.76 years at 2.4390 percent real. Second, the buying cost varies enormously by market and is not something a buyer negotiates. In France, transfer duty on an existing home is roughly 5.81 percent of the price, or about 6.32 percent in the many départements that took the increase permitted from 2025, before notarial fees and disbursements are added; a total buying cost near 11.5 percent is realistic there, which pushes the break-even to 3.28 years nominal and 6.65 years real. In markets where a buyer's total closing cost is closer to 3 percent, the same 6 percent selling cost gives 1.87 years nominal and 3.79 real.

The break-even hold is the single most actionable number in this article, because unlike the growth rate it is fully known before you sign. You cannot forecast the market, but you can read the transfer duty, the notarial scale, the agency fee and the mortgage arrangement fee off the paperwork, add them, and ask whether you are confident of staying that long. If the honest answer is that you might move for work in two years, the market can rise 5 percent a year and you will still lose money — not through bad luck, but through arithmetic that was visible on the day you bought.

Leverage: the multiplier, derived

Everything so far cuts the same way, and this section cuts the other. Price growth applies to the whole asset. The lender's claim on the asset is fixed in nominal terms: if you borrow $240,000, you owe $240,000 whether the house is worth $200,000 or $400,000. So the entire movement in value, up or down, accrues to the equity holder. If E is your equity and P is the price, a growth rate g produces gP of value on E of capital, and the return on your capital is gP ÷ E = g ÷ (E ÷ P) — that is, the price growth divided by your deposit fraction.

The multiplier is therefore the reciprocal of the deposit fraction, and nothing else. On our $300,000 house, 5 percent growth is $15,000 whatever your financing. A 40 percent deposit of $120,000 turns that into 12.5 percent — a multiplier of 2.5. A 25 percent deposit of $75,000 gives 20 percent — a multiplier of 4. A 20 percent deposit of $60,000 gives 25 percent — a multiplier of 5. A 10 percent deposit of $30,000 gives 50 percent, and a 5 percent deposit of $15,000 gives 100 percent: the whole of your capital, returned in a year, on a market that moved 5 percent. Buying for cash gives 5 percent, a multiplier of 1.

This is the whole of the case for property as a wealth-building asset, and it is a real case. It is also the reason that comparing house-price growth with stock-market growth is comparing the wrong two numbers: almost nobody buys equities with a nine-to-one loan, and almost everybody buys a house that way. The interest on the loan is a genuine cost that must be set against the multiplied gain, but the multiplier itself is not an illusion. It is simply not a property of housing — it is a property of borrowing, and it would apply to any asset a lender was willing to finance at those terms.

The multiplier runs backwards too

Take the same $300,000 house, a 20 percent deposit of $60,000, buying costs of 8 percent ($24,000), so $84,000 of capital in and a $240,000 loan. Now sell after a short hold at 6 percent selling cost, ignoring the small amount of principal repaid. If prices are flat, the sale nets $282,000, the loan takes $240,000, and $42,000 comes back: you have lost exactly half your capital on a market that did nothing. If prices fall 5 percent, $27,900 comes back, a loss of 66.8 percent. If prices fall 10 percent, $13,800 comes back, a loss of 83.6 percent.

Notice how much of that comes from the transaction costs rather than from the market. A 10 percent price fall on a fifth-financed house is a 50 percent equity loss by the pure leverage multiplier; the extra 33.6 points are the 8 percent paid on the way in and the 6 percent paid on the way out, both multiplied by the same five. Leverage magnifies costs exactly as faithfully as it magnifies gains, and costs are the part you know in advance. This is the arithmetic behind negative equity: it does not require a crash, only a modest fall on a small deposit, and it arrives faster than most buyers expect because the friction is already inside it.

Your house is not the index

One last deduction is qualitative and it undoes the arithmetic in a different way. A published house-price index is a statistical construction: repeat-sales methods track the same buildings over time, hedonic methods adjust for the characteristics of what actually sold, and both exist precisely because the raw average sale price of a quarter mostly measures which kinds of homes happened to trade that quarter. None of these methods tracks your house, its street, its orientation, its energy rating or the extension you did not build. Applying an index to a specific property is an estimate with a wide error band and no confidence interval attached.

So use the appreciation figure for what it is good for. It is a sensitivity input: run the purchase at zero growth, at your central assumption and at a fall, and see which of those three you could survive. It is a comparison tool between markets, provided you compare deflated series with deflated series. What it is not is a return, and the surest sign that someone has confused the two is a sentence that adds a price-growth percentage to a rental yield and reports the sum as though it were money.

Frequently asked questions

Does the division rule matter at low inflation?

Barely, over one year, and increasingly over many. The error term is (n − i) × i ÷ (1 + i): at 5 percent growth against 2.5 percent inflation it is 0.061 of a point, and at 12 percent growth against 8 percent inflation it is 0.2963 of a point — nearly five times as large. Since the term is proportional to the product of the inflation rate and the real spread, it is negligible when either is near zero and material when both are sizeable. The practical rule is to divide always, because it costs nothing and it is right in both regimes, and to be suspicious of any long-run real-return figure that was produced by subtracting.

If ownership costs cancel real growth, is buying a mistake?

No, and the calculation was never an argument that it is. It says that price growth alone does not pay for ownership, which leaves the actual reason people own: the use of the building. An owner-occupier receives shelter that would otherwise cost rent, and that imputed rent is the return the price index cannot show. A landlord receives actual rent, accounted for line by line in our rental article, where those same ownership costs already appear as expenses. The mistake the calculation is aimed at is the specific one of treating a headline growth rate as though it were income — of saying a house made 5 percent a year and stopping there.

Should I add my mortgage interest to the transaction-cost calculation?

Not to the break-even hold as computed here, because that calculation asks a narrow question: how long before price growth covers the cost of getting in and out. Interest is a cost of financing, not a cost of transacting, and it belongs in the comparison against what you would otherwise have paid — rent, if you are an owner-occupier, or the rental account, if you are a landlord. Adding interest to the break-even without also crediting the rent avoided is the mirror image of the error this article is about: it counts one side of a comparison and not the other. Where interest does belong in this article is the leverage section, as the price of the multiplier.

Why does selling at exactly the purchase price lose half my capital?

Because the transaction costs are charged on the whole asset and paid out of your slice of it. On a $300,000 purchase with a 20 percent deposit, the 8 percent buying cost is $24,000 and the 6 percent selling cost is $18,000, so $42,000 of friction sits against $60,000 of deposit before the market has moved at all. Sell at the purchase price and $282,000 comes in, $240,000 goes to the lender, and $42,000 comes back out of the $84,000 you committed. The general form is that costs, like gains, are multiplied by the reciprocal of the deposit fraction — which is why the same round trip on a cash purchase loses 12.96 percent of the $324,000 committed rather than 50.

Which growth number should I put in the calculator?

Three of them, one at a time. Run zero, so you see what the deal looks like on the deductions alone. Run whatever central figure you can defend from a published, deflated series for your own country — the national statistics office and the central-bank or BIS property series are the citable places to get one. Then run a fall of the size your market has actually experienced in the past, which the same sources will show you. If the purchase only works on the third of those, you are not buying a house, you are taking a leveraged position on a price index, and the arithmetic in this article says exactly what that costs when it goes the other way.