This essay is an exploratory look into the housing market, using London as the starting point. Housing is interesting because there is no obvious fundamental to tie the price to. This is in contrast to say stocks where the price of a company should, at least in practice, be tied to the current and discounted future expected profits. Of course like any market I would still expect housing to be internally consistent, where no house sells for much more or less than other similar houses in the same area. This internal consistency however, does not protect you from bubbles and the mass delusion that my house is not mispriced because look at what next door sold for! Clearly having some fundamental to tie house pricing to would be very useful as a way to spot bubbles. Ideally though we would like to be able to go further and use predictions about the fundamental to in turn predict future house pricing.
Most housing investors tend to have one of two strategies. The first is to buy an old house and renovate it and the second is to predict which areas are ‘on the up,’ which areas are about to be gentrified. This is more of an art than a science but classic clues are improved transport links, better shops and bars and good (but perhaps in need of work) housing stock. I even heard one investor who bought based on wherever a new Starbucks was about to be built. Looking at the data for house prices between 1995 and 2014 we find that there is no obvious relationship between the initial mean house price in 1995 and the amount the index has increased by 2014. Some cheaper areas were gentrified a lot other areas where not.
All of these strategies though are fundamentally unsatisfying because it still feels a lot like guesswork. My mum manages and invests in property for a living and it is interesting talking to her because she would much rather invest a million pounds on a flat in Chelsea (a comparatively expensive area) than say three houses in Lewisham (a comparatively cheap area). Her argument is that people will always want to live in Chelsea. Initially I thought this argument seemed a little naïve but actually it bears a striking resemblance to Warren Buffett’s approach to investing in stocks. Buffett argues that, just in the same way it is difficult to predict which area will be gentrified next, it is very difficult to predict which companies will succeed. In fact even if you are sure that say, the car or the plane (as they most certainly did) are going to change the world that does not make it any easier to pick the winners from the losers. So Buffett’s approach is to ask what will technology not change? Who is on top now and is likely to remain there? This strategy has led to safe and unsexy investments in companies like Coca Cola and Wrigley’s chewing gum rather than the roulette table of trying to predict the next Facebook or Google.
Nonetheless it seemed to me that imbedded in my Mum’s preference for Chelsea was the hidden assumption that rich people are going to get richer faster than poor people will. And this gave me the idea that the fundamental that could be used to tie down housing prices should be income and in particular how well different strata of the income distribution are doing and are expected to do in the future. Put simply if you expect there to be more inequality with the rich accelerating away from the poor then you would expect expensive areas like Chelsea to be a better investment. If you expect income inequality to go down with lower income people getting richer faster than higher income people a cheaper area like Lewisham may be a better investment.
Income and property prices
The first step was to investigate whether there was a relationship between property prices in an area and the incomes of people in that area. Intuitively it seems like there should be but there are also good reasons to think there may not be. Firstly property markets are not particularly liquid because people buy and sell houses relatively infrequently. Furthermore, housing’s relatively low running costs mean that once you own a property even if your income is relatively low you can continue to live there. Perhaps you bought your house with your low income decades before and then just been fortunate to have the value of the house rise a lot since. Similarly even if your income is much higher than your house suggests you may have already put down roots in an area, with all your friends and family nearby so even though you could afford a more expensive house you do not move. And finally you would expect there to be quite a lot of variation in how much of their income people would want to spend on housing versus other goods. What we find though is actually there is quite a strong relationship between mean house price and mean income across the boroughs of London.
Above is a regression of mean house prices in the 32 boroughs of London on the mean income of people in those boroughs. The house price data is from the Land Registry’s House Price Index and the income data from HMRC’s Survey of Personal Incomes. The House Price data is released on a monthly basis and so it was averaged out for the tax year to match the HMRC’s data. In this case the data is from 2011. What we find is a very high R² of 0.936 suggesting the model has a lot of explanatory power. The t-statistics are statistically significant with very small p-values. And in fact, this is not surprising because if you eye-ball the graph the data certainly looks fairly linear.
However it is important to do some robustness checks to make sure the assumptions of linear regression are being met, particularly to check whether the errors look random or not. Which as you can see from the rvf plot the residuals clearly do not.
I thought the lack of normality and randomness of the errors might be caused by non-normal mean income and mean house price variables. So I tried using ladder, gladder and qladder functions on Stata to suggest possible transformations.
First I found that mean income can be considerably improved by transforming it to 1/meanincome² where from ladder we can see that we get a χ² of just 0.69 which is pretty good.
This is also reflected in the gladder plot which shows visually the different transformations and how normal they look. As with ladder 1/square looks the best.
The 1/square transformation looks especially good in the qladder plot which is sensitive to deviations at the extremes.
However unfortunately we find that for mean house price no similarly good transformation exists.
1/square is again the best, but this time only the best of a bad bunch. The qladder plot in particular is not that good.
And in fact I found that if we regress the new variables 1/meanhouseprice² on 1/meanincome² in addition to losing explanatory power the rvfplot does not improve that much because the errors still do not look very random.
Use income as predictive variable of property prices?
Given that there is clearly some sort of relationship between property prices and income I thought it might be interesting to try and use income as a predictive variable for future property prices. In the above example I used income and property data from the same tax year but it would not be that surprising if perhaps there was a lag effect where income increases and then it takes a few years before that is converted into an increase in property prices.
To investigate this I regressed mean house prices for each year across all the different mean income years that I have in my dataset. Thus we take the mean income data for the tax year 2000 as the explanatory variable for 12 regressions for mean house price from the year 2000 to 2012.
What we find is roughly what you would expect which is that the mean income data for the year 2000 has more explanatory power for year 2000 mean house prices than the mean income data for the years following that. However, when we consider the other years we find that this pattern is not maintained.
Instead it seems like some years the mean income data has more explanatory power than other years, or perhaps more intuitively, some years the housing prices are more in sync with income distributions (2005 and 2005) and other years more out of sync with the income data (2000 and 2002).
Surprisingly housing data is more in sync with income for 2005 and 2006, the years just preceding the financial crisis. It seems a reasonable hypothesis that the housing market should be explained by incomes in that area and so years where there is a larger disconnect such as in 2000 and 2001 might suggest a good time to purchase for a potential investor. Having said, the variations in R² are pretty small and I have not done robustness checks as I would expect similar problems transforming the data as before.
One thing is clear, it seems unlikely that changes in London’s overall income distributions can be used to predict changes in future house prices. This is especially true as income data is only available two years afterwards (so for the tax year 2014 only 2012 data is currently available).
Borough by borough income and property price data
The next step I thought would be to try to see if there were any patterns in the borough by borough housing and income data.
What I noticed was that more expensive areas seemed to recover much quicker from the recession than cheaper areas. As an example Kensington & Chelsea and Islington seem to be already back to trend. This is in contrast to many cheaper areas where increases in income in recent years has not be converted into higher house prices. This led me to hypothesis that perhaps poorer people were being disproportionally credit constrained.
As you can see boroughs with mean house prices that were less than £350000 in 2007 by 2012 had suffered decreases in house price value. This is contrast to boroughs with mean house prices in 2007 above about £350000 where their prices increased. And in fact the seemingly linear relationship has a pretty good R² of 0.935. The question then is whether this constraint is a long term phenomena or a short-term one. If it is short-term it would make sense to invest in the cheaper areas whilst the house prices are temporarily lower because of short-term increases in lending standards.
However when I investigated the amount of leverage for the different housing boroughs I found that the least leveraged areas where the most expensive. Admittedly all the mean income data is pre-tax but given the tax rules vary from person to person I could not think of an intelligent way to estimate the average tax rate for each borough.
So in conclusion it seems like the best area to invest in is Kensington & Chelsea. There are several reasons for this.
Firstly in the last twenty years house prices have increased seven times in Kensington & Chelsea compared to just three, four or five times in other areas. Clearly to invest in an area simply because historically it has increased the most is unwise but on the other hand at least it gives a positive trend.
Secondly the leverage of residents in Kensington & Chelsea is the lowest of all the boroughs suggesting that the increase in prices is not a function of lax lending standards pre-recession. Having said that, I suspect many Kensington & Chelsea residents may own multiple properties so they might actually be more leveraged than I initially imagined. Also as previously mentioned, incomes are pre-tax so it is possible I’m underestimating the amount of leverage.
Thirdly increasing inequality particularly as the most wealthy’s incomes are increasing at a faster rate than everyone else’s is likely to lead to even greater increases in house prices in Kensington and Chelsea.
And finally there are very high numbers of foreign buyers, who tend to invest primarily in the prime areas of central London including Kensington and Chelsea. In fact, according to property experts Knight Frank as many as 28% of buyers of properties over £1 million do not live in the UK. Having said that it is possible that foreign demand will slow down with the introduction of a new capital gains tax for foreigners when they sell homes in the UK from April 2015.
The next step in the research will I think to try and investigate these factors further.