Wednesday, September 02, 2009

Housing Market Sensitivity to Interest Rate Changes

In an efficient housing market, we should expect a house to behave somewhat as a bond or dividend paying stock would with the par value / selling price of the home changing to reflect the market rates that apply to the asset and the expectations about future rates. Since homes are largely purchased with borrowed money and capital should move to the optimal risk/return relationship, we should expect this relationship to exist, in some form.

Now we might argue that the housing market is not efficient and while this may be true over short and medium time horizons, no market can behave inefficiently (gross over/under valuation) over longer time horizons and certainly not forever.

Let's use a simple example:

Bob's house could sell for $1,000,000 today.
It could rent for $36,000 per year.
The gross yield is 3.6% - similar to what could be earned on a 10 year government bond. We can use high quality bonds as a proxy for the rate of return we should expect on a house - government and agency bonds are very liquid and very safe.

Let's assume that for whatever reason (inflation expectations, competing returns, currency devaluation, etc) the yield rises to 5% and the rent stays the same. What will Bob's house be worth in the new environment? House Value * 5% = $36,000 or House Value = $36,000 / 5%
The house would be worth $720,000 in the new return expectation environment.

This may bring up a valid question: What if rents rise with inflation? Good question, keeping in mind all that is required to move the bond market is EXPECTATIONS about inflation and not inflation itself, so the idea of rising rents correlating with expectations about inflation may be questionable. Rising rents require rising wages and there can be a significant lags between inflation expectations and wage increases.

Assuming rents rise over 10% to $40,000, let's use the example above where return expectations are now 5%. House Value = $40,000 / 5% The house would be worth $800,000 in the new return expectation environment.

These examples are grossly oversimplified with many unaccounted factors. We can crunch the numbers all day long but what I have intended to show is that in a rising rate environment we can expect house prices to fall to meet expectations about the return required on an investment. What we have experienced since 1982 is a falling rate environment where 10 year Government of Canada bond yields have fallen from over 16% to under 4%.

Assuming $40,000 annual gross yield:
House Value at 4% = $1,000,000
House Value at 16% = $250,000

Can interest rates fall from the current level? Are they more likely to rise? Will they stay the same? What about inflation expectations? What will the market's reaction be to inflation expectations?

If you want the current level of house prices to be maintained then you should be hoping for inflation expectations to remain low, that rates stay low, and that rents keep pace with incomes for a very long time. This probably would not bode well for economic prospects and consequently incomes and rents but alas you cannot have your cake and eat it too!

This chart shows home prices correlated to mortgage rates. You can see that when mortgage rates were much higher, home prices were much lower and that when mortgage rates have been lower, home prices have been higher. There is a lower bound to mortgage rates but no upper bound so you could say that the risks are lopsided.

Disclaimer: I am not pretending that we should value all homes like a bond or stock since clearly there are other factors at play such as densification, gentrification, decay, depreciation of structures, among other potential rewards and risks (real estate is not fungible). Additionally, rents can rise and fall unlike bond coupons which remain constant until maturity. The dividend discount model may be a good way to value a home based on cash flows but it can get pretty complicated and we must assume growth factors which is tricky at best.


Robert Reynolds - GBA said...

Good post Mo.

I have watched the residential revenue property market in Victoria for about two years and there is NOTHING on the market right now. With current owners refinancing to lower their carrying costs while keeping rents constant there is no doubt they are making a great return, especially when compared to treasuries etc.

The few properties on the market are either junk or are priced in such a way that their price to income cap rate is north of 6%

mattiasa said...

Very interesting analysis. Thanks!

One question, though: does your chart plot real or nominal home prices?

mohican said...

I used nominal house prices for the chart. I intended to use real prices but I was in a rush and couldn't find the data set. There wouldn't be a lot of difference aside from the slope being less steep.

I can tell you that if I had a $1,000,000 cash to invest in a portfolio made up of 10 year government bonds, Canadian Utility Company Stocks, or BC real estate that the allocation to real estate would be less than 20%. The competing returns availabe from other sources make real estate very unattractive from an investment point of view today. For landlords who purchased at a much lower price and are happy with a low yield, I am sure they are happy to hang on since landlords tend to not look at opportunity cost and because transaction costs are so high with real estate.

vibe said...

So according to this analysis, if mortgage rates were 5% in 1950 nominal house prices should have been about $700,000?

I think you have to use real prices, or am I missing something?

mohican said...

The key to the valuation is the yield from rent. 1950 rents were much lower than they are today so the 5% yield would be calculated based on the rents of that time. The examples I have used are using rents from today. If we look at rents, rates, and values in 1950, I expect it would paint a similar picture.

The post isn't intending to portray a perfect model for valuing real estate but to give an indication of the impact that interest rates have on real estate prices if all other things are equal.

jesse said...

When financing rates are coupled tightly with housing prices, that's a sign of a bubble. An asset like real estate is capitalized over decades so a long-term view on financing is required. I get the nagging feeling such logic is notably absent among many of today's buyers.

Mortgage rates are not necessarily an indication of inflation expectations. It is often as simple as other investments vying for a limited pool of capital. Remember in the late '90s interest rates were high but CPI inflation was well contained. Real estate at that time had competitive cap rates by today's standard but ask people of the day why they didn't invest in real estate and often the answer was that other investments were returning far better.

Dave said...

I agree with the above post that this analysis would need to be in real prices.

Why don't you add the data from 1970 through 1982?

There might be a correlation, but you haven't shown causality. As an example, we could plot home prices against all sorts of things that declined in the last two decades (e.g. number of smokers per capita), but it doesn't mean these things are related.

mohican said...

I will look for my backup real price data set at some point - my original and updated set was corrupted. Two kids and a busy work life keep me on my toes. I agree that it would be best to show real prices but after all this blog is a hobby.

There is no publicly available price data prior to 1976.

I don't need a lesson in causation vs correlation and I realize that scientifically causation is difficult to prove. I'll state again that this blog is a hobby so the time and effort required to do thorough study is not available or prudent for me.

My advice is that if you feel you have a really important point to prove then you should take up the cause and do it yourself.

mattiasa said...

Here are some data sources which span 1975-2009:
* Mortgage rates
* Real housing prices
* Real rent index

I'm making some charts, but I unfortunately don't have time to finish them, tonight. I can say, however, that what I've seen so far seems to confirm mohican's claim: while the effect of inflation on prices may confound the numbers and chart, somewhat, the result with real prices is a negative correlation between house prices and mortgage rates.

Now, to be honest, I haven't spent enough time understanding "real" mortgage rates well enough to use them, but they are available in the above data sources. If someone would like to make an argument why they'd be better to use than the nominal mortgage rates, I'd be happy to consider it. I have the feeling that nominal rates are reasonable to use, though.

Also, because I don't know how the rent index relates to prices, I don't know how to use it to calculate a yield. I could just smash them together (i.e. divide), but I'd really rather understand it. :) Anyone have any insight? I'd love to compare the yield to the mortgage rates and maybe even some other asset classes.

patriotz said...
This comment has been removed by the author.
patriotz said...

The problem with comparing housing to bonds is the leverage factor. Nobody borrows money to buy a long bond (well almost nobody except short term speculators). A house buyer is using short or medium term debt to buy an income-bearing (rental value) asset with infinite maturity (because the house has no par redemption value).

House price sensitivity to interest rates is for real of course but I think it's mostly a matter of people just paying whatever price they can afford rather than considerations like present value (or any other investment concepts for that matter) which few buyers understand. The higher the rates, the lower the affordable price and vice versa.

jesse said...

"As an example, we could plot home prices against all sorts of things that declined in the last two decades"

It is common wisdom that smoking causes lung cancer. There is science to support the correlation between smokers and cancer onset, notably the ingredients that compose cigarettes are known to cause cancer during controlled in vitro experiments on lab animals.

The vast majority of homeowners carry mortgages and it should be obvious that higher interest rates mean they can afford less mortgage. There is therefore a direct causal link between mortgage rates and a leveraged asset class. The question is its sensitivity and whether other factors are more prevalent at determining prices, notably the widely-held belief that real estate is always a good investment in the long run.

The best counterexample is how Japan's prices have fallen for close to 20 years despite low interest rates. Other factors were obviously at play.

JimTan said...

Meanwhile, in the real world. What if unemployment levels off here?

VANCOUVER — British Columbia saw slight employment growth in August, but the provincial unemployment rate remained unchanged at 7.8 per cent as the number of workers jumping back into the job hunt offset job gains, Statistics Canada reported Friday.

Statistics Canada said the number of unemployed people in B.C. crept up in August, but once new jobs created were added in, some 6,200 people found work during the month with most being women over 25.

Some 7,700 women found work in August compared with 3,100 men who found positions at the same time.

However, the loss of some 4,600 positions in the youth sector weighed on those gains.

Nationally, Canada saw 27,100 new positions added to the workforce in August compared with 44,500 job losses in July.

The unemployment rate edged up to 8.7 per cent in August from 8.6 per cent the previous month.

The gains were led by part-time and private-sector employment, the federal agency said. There were 30,600 part-time jobs added in August, while 3,500 full-time positions were lost. Hardest hit was the manufacturing sector, which shed another 17,300 in August. The biggest gains were in the retail and wholesale trade, up 21,200, and finance and real estate, up 17,500.

Six provinces saw employment rise, with the biggest increases in Ontario, B.C. and Quebec. Alberta lost the most jobs in August.

vibe said...

I made some charts with the data mattiasa linked to.

First I redid the regression with real prices:

Prices vs Rates

Then I plotted the effect that rates had on prices over time based on the first regression:

Effect On Price

And finally I tried to plot actual prices with what they might have looked like had mortgage rates remained constant at 10% (the average for the period)

Actual and Adjusted Prices

A few notes:

-The data only goes to 2009 Q1 so we're missing the latest bump.

-The 80's bubble could have been even bigger than the current one if not for interest rates.

-Looks like we would have had a pretty big bubble even with higher rates. So I don't think low rates are gonna prevent the crash.


Oh and sorry for boring you Jim

mohican said...

great charts vibe:

I think those charts illustrate the point that while mortgage rates aren't the only determinant in prices, they play a significant role.

Thank you.

jesse said...

Vibe and mantissa, I would argue that the correlation between prices and financing,when affordability is maxed out, is not linear. This can be seen by the form of the dcf model which goes as 1/r

Affordability accounts for incomes(rents) so perhaps plotting affordability vs interest payments would be interesting.

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