The chattering classes profess confusion over discrepancies in the various house price indexes. There are several indexes published regularly and closely watched, with plausible claims to statistical validity:

• Nationwide (August – £164654)
• Halifax (August not available yet)
• Land Registry (August [for July] £178364)
• Rightmove (August – £229816)

The Rightmove index represents asking prices, and is unsurprisingly much higher than any of the others – which represent actual sold prices. No problem there.

The Nationwide and Halifax are our long-term biggest mortgage lenders, and their indexes represent the sale price of houses purchased with a mortgage. Reassuringly, these indexes are closely correlated (graph: BBC News), so we can infer that any differences between the two lenders’ markets (who they lend to) are not important. That might not hold for smaller, specialist lenders, but we can surmise that these fairly represent the mainstream.

What seems to have the pundits baffled is why the Land Registry differs from the Nationwide and Halifax. There is a time lag, said to be around 3-4 months, built in to the Land Registry compared to the others. But that doesn’t explain the divergence we now see, as noted today by the FT.

It seems to me there is a perfectly simple explanation, and that we can extrapolate from it what will happen at a hypothetical turning point where confidence returns to the market. The issue is that the downturn is affecting different parts of the market in different ways.

Let’s consider a hypothesis with some plausible assumptions:

• Tighter mortgage conditions have a disproportionate effect at the lower end of the market, particularly first-time-buyers. Higher up the market, rich people are less reliant on mortgages.
• Therefore the reported 60%[1] drop in numbers of transactions is concentrated primarily at the lower end.

That’s enough. Let’s put some representative numbers to these assumptions[2]. The numbers themselves don’t matter: feel free to vary them, consistent with the assumptions. Your results will differ from mine, but they’ll still demonstrate why the observed discrepancy exists. Just to emphasize the point, we’ll take one figure way in excess of what any of the indexes tell us (of now): an actual drop of 20% across the entire market!

Applying that to some representative price points, we hypothesise:

• First time buyer, down from £150000 to £120000
• Mid-market, down from £250000 to £200000
• High-end, down from £500000 to £400000

In “normal” times – before the crash – there’s little doubt that the majority of transactions were in the lower price ranges. Let’s say the above price points represent 60%, 35% and 5% respectively of the market. That gives us a pre-crash average of (0.6 * 150000 + 0.35 * 250000 + 0.05 * 500000) = £202500, which is roughly consistent with published figures (for sale prices, not asking prices).

Now we know that the crash has affected the bottom end disproportionately, and left the top end relatively intact. Let’s put some figures to that too, bearing in mind that the overall drop in activity is reported as being at least 60%[1]. Suppose activity levels are down by 70%, 50% and 10% at our three price points. That gives us an overall percentage drop of (70 * .6 + 50 * .35 + 10 * .05) = 60%.

Now, here’s the crux. Let’s calculate the average post-crash price with the above figures, bearing in mind that we have assumed each individual house is down by 20%. Our post-crash distribution of market segments have changed:

• First time buyers: 60% reduced by 70% = 18% of the pre-crash market
• Mid-market: 35% reduced by 50% = 17.5% of the pre-crash market
• Top-end: 5% reduced by 10% = 4.5% of the pre-crash market.

That’s a total of just 40% of the pre-crash market (the 60% reduction). So what we see is different shape of post-crash market:

• First-time buyers: 18% * 2.5 = 45%
• Mid-Market: 17.5% * 2.5 = 43.75%
• Top-End: 4.5% * 2.5 = 11.25%

So with the 20% drop in price of each individual house, we get an average of

(45 * 120000 + 43.75 * 200000 + 11.25 * 400000) / 100 = £186500

as compared to our pre-crash

(60 * 150000 + 35 * 250000 + 5 * 500000) / 100 = £202500

That’s a percentage fall of 100 * (202500 – 186500) / 202500 = 7.90%.

While individual houses have fallen by 20%, the market average – and hence the published statistics – has lost a mere 7.9% in our model. That’s actually smaller than the current falls reported by the Nationwide and Halifax!

Now my gut feeling is that the figures I’ve used may be conservative: the market skew may be much bigger than that (bearing in mind reports about first-time-buyers being near-eliminated, rather than 45% or the market as above). That would indeed be consistent with the mere 2% fall recorded in the Land Registry index.

Now it’s not hard to see how the discrepancy arises. The mortgage lenders see a different market profile to the land registry. We could perform a similar analysis with some more numbers: say 95% of first-time-buyers, 75% in the mid market, and 50% at the upper end have mortgage, we see their figures are biased towards the market sector that’s been most affected. I’ll leave it as an exercise to the reader to calculate hypothetical Nationwide/Halifax indexes based on those numbers (or choose your own).

Side-Effect: Rise of the Rental Market

A well-documented fallout from the crash is the rise of the rental market:

• People unwilling to sell at current prices are letting their houses instead.
• People waiting for further falls are choosing to rent for the time being, even those who could afford to buy.

So suddenly the rental market has changed. The quality has risen – with lots more houses than before that the owners thought good enough to live in themselves! And the status of tenants has risen too: it’s no longer so heavily dominated by those too poor to get a mortgage (and too honest to lie for one). And because the UK rental market is traditionally small (most people own their own home), the effect on it is disproportionately large. Even if the traditional rental market (the rich exploiting the poor) were little-changed, the overall market has risen with the coming of the new landlords and tenants.

Predicting the bottom of the market

Supposing this month, we were to hit the bottom of the market. Confidence suddenly returns. All the prospective buyers who are currently renting decide it’s time to buy.

• The profile of the market returns to “normal”. The statistics catch up with the individual houses, so a 7.9% drop suddenly becomes a 20% drop in the published indexes.
• Corollary: the sharpest adjustment to the Land Registry index. If it happens after more than a year of falls (so the indexes aren’t measuring from the top of the bubble) it will not merely catch up with, but overshoot, the Nationwide and Halifax indexes in terms of year-on-year percent falls.
• Even so, the market doesn’t return to bubble-level, because the mortgage lenders have got burnt giving out pyramid-scheme money willy-nilly.
• The top end falls off the rental market, leaving only the poor as tenants for all those buy-to-let landlords.

Clearly the key to that is the first point. Such a sudden fall in the indexes is going to kill of that returning confidence. Corollary: there will be no sudden return of confidence, now or anytime: it’ll be a gradual thing, with several years in the doldrums after the sharp falls have gone. That fits the pattern of past house price corrections, including the 1989-97 one[3].

The third is also interesting, as it could mean (far) more buy-to-let landlords in trouble with falling rents and far-more-fallen sale prices. That’ll be the point Bradford&Bingley (the specialised buy-to-let mortgage lender who just raised money on very unfavourable terms in a rights issue) will be in real trouble. With any luck, the Northern Rock fallout will be so visibly horrendous by then that the government of the day will have the guts not to pour in yet more taxpayers money to do the same for B&B.

So what will the house price statistics look like as the market bottoms? Well, the key is that activity has to return to the lower end of the market, and that’ll be gradual. But from the above analysis, we’ve got a visible sign. So long as the Land Registry index trails the Nationwide and Halifax (over and above the 3-4 month difference in reporting time), we can infer that real prices are falling ahead of any of the indexes. When the Land Registry starts catching up could be a good time to look for a bargain. Once it’s caught up, we’re back to a saner, and lower, market, and we can finally start to take the statistics at something closer to face value again.

[1] From memory, and very probably wrong. Not important – you can get a similar analysis with a different (large) percentage drop.

[2] This is the kind of analysis mathematicians do all the time: take a complex problem and get a handle on it by making simplifying assumptions. It’s useful in that it can provide a good insight into “what if” questions – how does it affect the overall picture if different inputs vary, or if our working assumptions are incorrect. My degree was in Maths, and my first professional job after graduating involved precisely this kind of operational analysis.

[3] Mathematicians will often prove a result by an approach of assume the contrary, and show that implies a logical contradiction. Mine isn’t a mathematical proof of anything, but it’s a similar kind of argument.