Some quick maths on the effect of interest rates on house prices, supporting a forecast 10-15% drop in prices

[jesuslover07]

(Note: I made a post similar to this yesterday, which I deleted due to a gratuitous
error. Thanks to /@birch for pointing out the mistake!)

I did some rough calculations, and as a result I'm becoming more convinced that the
forecasts of 10-15% drops in housing prices are pretty reasonable.

I already leaned towards taking folk like Chris Joye at their word that a 15-25% drop
was reasonable, based on the bloke talking plenty of sense about how he arrived at that
number, and his being a verified non-permabear - previously arguing correctly that
prices would rise during the pandemic. This gives him a lot of credibility in my eyes.
And most banks are making similar projections. My own numbers here are for a somewhat
smaller drop - especially since Joye's forecast is assuming only a 100bp rate increase
and we've already exceeded that. But it's not crazy different. Maybe I'm a tad more
optimistic with the assumptions.

Anyway. The core fact is that prices are limited by loan serviceability.

Yearly principal+interest mortgage repayments on an

N

-year loan of size

L

with interest rate

r

, ignoring
intra-year compounding are:

annual_repayments = r L / (1 - (1 + r)^-N)

Assuming annual repayments for which someone meets serviceability requirements are
proportional to income

I

, and assuming loan size is proportional to the price

P

,
substituting

I

and

P

into the above equation and solving for

P

gives us a dumb
model of how prices might vary with income and interest rates:

P ∝ I / r × (1 - (1 + r)^-N)

The rate

r

in this equation is the rate used for serviceability tests - which would be
3% above the mortgage rate as per APRA requirements.

Assuming a 30-year loan, that mortgage rates are 2.4% above the cash rate and that peak
prices occurred when the cash rate was 0.1%, we can estimate price drops from peak in
various scenarios.

Assuming the cash rate increases to 2.85% (the median
forecast
of surveyed economists), and that nothing else changes (no income growth), this
oversimplified model says prices would fall by 24% from peak.

Sounds like a big drop!

However, some other things likely will change. For one, if that takes two years to play out,
then nominal income growth might be something like 7% (the resulting growth in house
prices won't be real, but we're talking nominal here). Also, it seems likely that APRA
will decrease the serviceability buffer from 3.0% to 2.5% once rates get a bit higher.
They might even decrease it more.

Take those assumptions into account and you get that prices will fall 15%.

And, 2.85% is the peak cash rate forecast by economists. By end of 2023 the median
forecast is 2.6%, which if fed to the above, gives a price fall of only 13%.

You can get more optimistic if you like: Rates won't necessarily stay where they are by
end of 2023. The CBA thinks rates will decline to 2.1%. If that happens, then when all
is said and done the drop in house prices would be only 9%.

So there's a range of scenarios there that I think reinforce the expectation of a drop
of 10-15%. You can be a bit more pessimistic and get it to a 24% drop if you like, but
you have to assume zero nominal wage growth and APRA holding their buffer constant. And
you can get a bit more optimistic and assume the CBA's forecast is on the money and get
it to a 9% drop. All in all 10-15% ends up looking like like a pretty reasonable
central expectation.

One thing ignored here is that deposits are not a fixed percentage of sale price: when
prices are lower, deposits are more likely to be a larger fraction of the sale price.
This helps serviceability and so will result in somewhat smaller price drops than the above model
says.

And of course it's a dumb and simple model that ignores everything else that would
affect demand for and supply of housing. It's just talking about the ability to get
credit and even then is super oversimplified.

Here's a sample of model outputs including the ones mentioned above, and some others:

Cash rate to 12.0%, all else equal: -60.8%
Cash rate to 3.50%, all else equal: -28.7%
Cash rate to 2.85%, all else equal: -24.3%
Cash rate to 2.60%, all else equal: -22.5%
Cash rate to 2.10%, all else equal: -18.7%

Cash rate to 12.0%, income +7%: -58.0%
Cash rate to 3.50%, income +7%: -23.7%
Cash rate to 2.85%, income +7%: -19.0%
Cash rate to 2.60%, income +7%: -17.1%
Cash rate to 2.10%, income +7%: -13.0%

Cash rate to 12.0%, income +7%, APRA buffer to 2.5%: -56.8%
Cash rate to 3.50%, income +7%, APRA buffer to 2.5%: -20.2%
Cash rate to 2.85%, income +7%, APRA buffer to 2.5%: -15.1%
Cash rate to 2.60%, income +7%, APRA buffer to 2.5%: -13.0%
Cash rate to 2.10%, income +7%, APRA buffer to 2.5%: -8.6%

 

[drradiaki18]

@jesuslover07 Lots of things you haven't considered here.
1. The psychological effect - prices rarely return to mean immediately. They tend to overshoot either way as FOMO or FOOP takes hold.

1. I've seen this mentioned previously, by why is APRA necessarily reducing the buffer? Particularly when the RBA has shown they will increase rates materially at a rapid pace.
2. Yes wages are increasing, but this is well below the level of inflation. 3% wage growth may not be enough to offset 7% inflation of expenses - serviceability could actually decrease
3. The TFF - the large funding facilities provided to the banks at 0.1% start rolling off from next year. As such, bank's cost of funds will start increasing materially as these are replaced (already seeing this on the business / corporate side). This will increase the need for out of cycle / larger increases to variable rates. CBA's forecast I imagine takes this into account somewhat - variable rates could likely stay unchanged even of the RBA rate declines.
4. If prices do decline 15-20%, banks will be a lot more selective with credit than they currently are. This could further reduce credit availability.

I'm sure there are many things I've missed, but ultimately there are a lot more downside risks to the 15-20% forecast than there are upside.

 

[billyboy]

@drradiaki18

Yes wages are increasing, but this is well below the level of inflation.

I don't see any indication that wages for the better-earning half of the population (ie the ones actually in the market to buy a house) are declining in real terms.

 

[drradiaki18]

@billyboy Inflation will be 7% by the end of the year. There is a zero percent chance real wages at any level don't go backwards.

 

[billyboy]

@drradiaki18 How would you know? Ask among your engineer, law, finance or banking friends whether their wage increases match inflation (currently in the 5%'s) or not. It's the real wages for the top earners that dictate house prices. Someone locked out of the market plays no role in house prices whatever his or her wage.

 

[jesuslover07]

@drradiaki18 For sure, there are other factors too which makes any quantitative forecasting exercise uncertain. It is just a dumb simple model about how income and rates affect prices.

But I do think income and borrowing power are the dominant factors. Chris Joye makes the point in this debate (@5:05) that historically house prices trend basically as you would expect with income and interest rates. It's not perfect, but it's clearly the main factor.

The psychological effect - prices rarely return to mean immediately. They tend to overshoot either way as FOMO or FOOP takes hold.

I honestly don't believe this plays much of a role on a timescale longer than a year or so. Most first home owners basically want to buy a home as soon as they can, they might wait up to a year but that gets old fast when you're comparing to renting. The same for investors trying to time the market.

I've seen this mentioned previously, by why is APRA necessarily reducing the buffer? Particularly when the RBA has shown they will increase rates materially at a rapid pace.

I am not sure why the discussion in the PropertyChat thread linked to elsewhere in this thread thinks APRA will reduce the buffer to 2.0%. But they increased it from 2.5% to 3.0% in the context of very low interest rates that we all knew were temporary. Once that's no longer the case, I would expect them to at least revert to 2.5%. I suppose if we end up at high interest rates that are expected to fall, maybe they'll go lower. But we don't have much history to go on - they haven't been using a buffer system for long, so I believe the 2.5% → 3.0% is the only change we've seen them make.

Most of the other points you make about poor wage growth and the TFF rolling off, also provide pressure to decrease the cash rate - so I don't think it's as simple as "prices go up, serviceability goes down" or "funding costs go up, interest rates go up". If people have less disposable income, the RBA doesn't need to suck as much out of them and so will reduce the cash rate (or not increase it as much). If banks' funding costs increase and that's not what the RBA wants, they'll lower the target cash rate to try to reduce other interest rates in the economy. Right now the existence of the TFF means the RBA have to be more contractionary than they otherwise would in order to control the availability of cash in the economy. Once it's rolling off, they will no longer need to be as contractionary.

 

[orthodoxforever]

@jesuslover07 Here's a link to CBA lending over the last decade or so.

https://imgur.com/a/7gZ0pKS

Looking at the right hand end you can see that existing PPOR and investors enjoy the cheap loans for 2020 and 2021. FHBers, on the other hand, drop off. FHBers, despite having access to cheaper rates than ever before were unable to keep up. To me that suggests that the availability of equity due to price rises allowed those already in the market to punch higher. The cheaper loans were absolutely part of the dynamic, but it needed cheaper loans AND the price increases to provide the security/deposit. This too will unwind and will cause an additional chunk of price drops, as the number of people in the market who can leverage equity plummets.

 

[royalrangerwv]

@orthodoxforever Go with the market cycles. Withdraw equity when the prices are high, use it when asset prices have dropped. There are lots of ways to use equity (not just equity loans) to achieve this. Liquidity and cash flow obvious quite key

 

[orthodoxforever]

@royalrangerwv The chart is for new mortgages, not refinancing.

 

[suzanne123]

@jesuslover07 Good work mate, not sure if you saw it but Redom on Propertychat did some calculations which seem to be similar to what you got to https://www.propertychat.com.au/com...owing-capacity-drive-what-happens-next.67610/.

Something you didn't mention which he does is the Stage 3 tax changes making a big difference to borrowing capacity for higher income earners. A single income earner on 200k will get a tax cut of $9,075, if you have a double high income household you double that. If you also had a reduction in APRA buffer, income increasing and rates moderating it could fuel a pretty quick recovery.

This part of the conclusion I think sums up the potential recovery pretty well and also mentions government benefits potentially blunting some of the drops in lower income areas.

Changes in values will not be distributed evenly. Borrowing power reductions are more severe the larger the mortgage size. Government grants and benefits assist lower priced homes too. This means that lowest quartile/half homes by value may fall less during the downturn (apartments, etc). However, the 2024 tax cuts are distributed to borrowers who purchase a greater share of upper quartile homes.

 

[jesuslover07]

@suzanne123 Thanks for the link, that's great. No, I hadn't seen it. So they reckon APRA will reduce the buffer to 2.0%, which would buoy borrowing power substantially. Here's what I get for that:

Cash rate to 12.0%, income +7%, APRA buffer to 2.0%: -55.6%
Cash rate to 3.50%, income +7%, APRA buffer to 2.0%: -16.3%
Cash rate to 2.85%, income +7%, APRA buffer to 2.0%: -10.9%
Cash rate to 2.60%, income +7%, APRA buffer to 2.0%: -8.6%
Cash rate to 2.10%, income +7%, APRA buffer to 2.0%: -3.9%

And let's say +3% income for the tax cuts and see what we get:

Cash rate to 12.0%, income +10%, APRA buffer to 2.0%: -54.3%
Cash rate to 3.50%, income +10%, APRA buffer to 2.0%: -14.0%
Cash rate to 2.85%, income +10%, APRA buffer to 2.0%: -8.4%
Cash rate to 2.60%, income +10%, APRA buffer to 2.0%: -6.1%
Cash rate to 2.10%, income +10%, APRA buffer to 2.0%: -1.2%

The most optimistic scenario there is barely any drop at all, though we've already dropped by more than that. Even if it's correct, we'll see further drops before income growth, tax cuts, and APRA buffer changes might bring prices back up - this would be the "V-shaped recovery" they're talking about in the propertychat thread.

 

[suzanne123]

@jesuslover07 Yeh in that scenario it is a small drop.

I think it's very optimistic expecting a V shaped recovery over a couple of years, but it is a possibility the same as a deeper extended downturn than these calculations suggest is also a possibility.

 

[cantgetright]

@jesuslover07 We are still .3% away from a -1.2% drop.

Australia doesn't just exist in Melbourne and Sydney.

 

[jesuslover07]

@cantgetright The CoreLogic 5 capital city aggregate index is down 1.5% from the peak, and that index is not just Melbourne and Sydney. It's true that the drop is dominated by Melbourne and Sydney, but it's big enough that the national average is down that much.

 

[cantgetright]

@jesuslover07 My bad. Was reading everything the wrong way. Sorry.

Out of curiosity? Do you know why everyone relies so heavily on a non-seasonally adjusted metric?

 

[jesuslover07]

@cantgetright No idea! Do we even know if they're seasonally adjusted? Some here have said (I haven't tried to verify) that the index is based on like, all sales in the last year or something like that, which if it were true would mean seasonal corrections wouldn't be needed.

It being based on such a long period of sales was brought up as an explanation for the index being so unresponsive to change. Bit weird to have a daily index though if it can only move much on a yearly timescale.

 

[stthomasmore]

@jesuslover07 Great work mate

So basically at worst return to 2019 prices

Far from the doomsayer projections

I think Ausfinance's resident permabear (we all know who I'm referring to lol) has been predicting 50% falls each of the past multiple years

So I think he actually needs more than 50% falls to match his rhetoric over the years