The location equation

Brian Miller took a statistical approach in order to find out what makes some areas more desirable places to live in than others

"Of course, the town’s in a great location," the agent said to me, in a way that indicated that this should be enough to recommend it to my client. And, of course, conventional wisdom is on his side. The mantra location, location, location’ is trotted out at the slightest hint of a property transaction, but his casual insistence on its importance had intrigued me. What does location’ actually mean?

As a former accountant I suppose it was natural that I decided to approach the subject from a mathematical angle. After all, I reasoned, if certain places were more desirable than others, there must be a price premium attached to the characteristics of those locations. But – and here was my dilemma – what are these characteristics and can they be defined in a way that could be measured against property values?

I began by brainstorming a list of those factors that I thought would make a French house more valuable, based on experiences with clients and my own preferences. Back copies of French Property News also gave me a couple of ideas about what potential buyers are looking for, as well as reference to that vast oeuvre of property market wisdom known as reality TV’.

Measurable factors

Climate, accessibility, proximity to attractive countryside and the sea were all obvious contenders, as were the size of a town, its history and the strength of the local economy. The challenge was to find some way of making these mainly intangible factors measurable. But that was also part of the value in the exercise; trying to get to grips with what buyers really mean when they use these terms.

Take climate, for example. What are we actually looking for in the French climate when we buy a property here? Less rain, more sun, clearer skies, reliable snow or just fewer seasons? Of course, the answer depends on what you’re planning to do in your new home, but it’s also a question of taste. Some buyers tell us that they want to live in La Rochelle because it is warmer than the UK, but when we ask them why they aren’t thinking about the south of France, where the temperatures are even higher, they say that it would be too hot.

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So any measurement of climate has to account for the fact that there isn’t always a direct relationship between the factor – heat in this case – and desirability of location. A similar problem arises in the case of accessibility where frequency of flights to a preferred destination may be of greater importance than how close to a property the nearest airport is.

Even some of the more obviously measurable characteristics of location gave me a problem. I decided that one of the easiest ways of determining how historic’ a particular location was would be to identify the age of the town or city. After testing a sample of four towns I quickly realised how na�ve this approach was. One of the wonderful things about the internet is the ease with which you can gather information from different sources.

However, one of the problems is that these sources can equally quickly give you quite a range of different answers. Internet research, for example, would tell me that a particular town was first documented in medieval times while the website for the commune itself would proudly inform me that it had a heritage going back to the Celtic era, some 15 centuries earlier. This exercise clearly wouldn’t be as straightforward as I’d hoped.

With a bit of trial and error – occasionally supplemented by wild guesses and a glass or two of our local wine – I narrowed the list of characteristics down to a dozen quantifiable factors and proceeded to test them against the current price of houses in 70 French towns and cities, as reported by the most recent Notaires de France survey. I excluded Paris and the �le-de-France area because I felt that the known high prices in the capital would skew the results unfairly.

What I ultimately wanted to achieve was a formula that could be used to calculate the likely price of a property in France, taking into account as few variables as possible; a location-valuation equation.

Using multiple regression analysis and correlation I tried to distil the essence of what buyers are really looking for when they talk about the ideal location’. What I came up with was a list of four factors that account for about three-quarters of the variation between house prices across the country. And the surprising part wasn’t so much which factors made a difference as which ones didn’t.

Early on in the analysis two factors came out as having a very strong correlation with property prices; annual sunshine hours and the size of population of the town or city itself. Neither of these was particularly surprising. It seems logical that where you have a large population the market for property is likely to be more active and prices will tend to be driven up. Similarly, larger towns will tend to draw more companies to them and the local economy will be stronger as a result.

Centres of population will, therefore, draw in more buyers and prices will rise. By definition, I suppose, a desirable location will become more populous over time. Sunshine hours turned out to be the best proxy variable for climate with neither average temperature nor absence of rain having such a strong link to house prices.

In fact, sunshine hours turned out to be the single most influential factor explaining 44% of the difference between house prices in different towns, just shading out city size which, on its own, managed 42%. These two factors combined explained just under two-thirds of house-price variability showing just how much overlap – or co-correlation to use the statistical term – there is between the two. In other words, large sunny cities are far and away the most desirable locations, but the residents of Nice, Montpellier and Marseilles could have told you that themselves.

Historical location

A couple of factors quickly – and surprisingly – ruled themselves out. The age of a city, whichever source I used, had a very weak correlation with prices. I had thought that there would be a value to living in a more historic location and the data suggested that this was the case – but only just. Even more surprising, at first glance, was the result in terms of accessibility. In the end I opted to use the distance between the town and the nearest port or airport as a measure for this, because it seemed to give the flexibility of choice that the buyers that I deal with are looking for. The results showed that this factor did have a small effect on house prices – but in the opposite direction! In other words, the nearer a town was to a port or airport the lower its prices were.

When I reflected on the numbers, the result did make some sense in as much as those towns with easy access out of the country might be disproportionately affected by migration, both inward and outward, which might act to keep prices down in a period of economic instability.

Another reason for this result could simply be my naivety. As someone who deals mainly with overseas buyers I suppose I am more likely to meet people for whom access is an issue. For French houseowners, accessibility may be more readily understood in terms of how easy it is to get to family and to work, or even to the national capital. I tested this theory out by calculating the correlation between property prices and distance from Paris. Although the link was better than for the accessibility variable, it still wasn’t particularly strong and didn’t make it into the final four characteristics.

The third factor that did have a positive impact on house prices was population density. Before you complain that this is simply a variant of the town size effect it may be worth explaining that I was actually trying to explore something completely different. Again, based on my experience of overseas buyers looking for second homes, I had thought that higher prices would be found where properties were less crammed together – after all France is renowned for its wide-open spaces.

I had, therefore, imagined that a city with broad boulevards, peaceful parks and expansive maisons de ville would win out against apartment blocks and high-rise developments. However, the evidence simply didn’t bear this out and the higher the density of population the higher, on average, house prices tend to be. This factor explained an additional 8% of price variability above and beyond that accounted for by the population of the town itself and hours of sunshine. In other words location isn’t just about big cities, it’s about big crowded cities, suggesting that property prices are driven up by features like swarming shopping malls, vibrant nightlife and bustling city centres.

Having failed to prove that space was a positive location factor I had a couple more attempts at trying to link house prices to something less functional than city life’. I did think that perhaps mountainous areas would prove popular but there was only a very weak statistical link between altitude and property values – and it was negative, so there was no case for the high life’. Then I thought about beaches, at the other end of the scale, and calculated the correlation between distance from the sea and property prices but again, to my surprise, found no explanatory connection.

It was while I was working through the distances to the sea that I began to notice an unusual pattern of results and so I tested something that, at the time, seemed illogical to me but ended up being the final factor in my location equation. What I had spotted was that although property prices in towns near the sea were, as I had expected, quite high so too were those on the eastern borders around Germany, Austria and Switzerland as well as those close to Italy and Spain. As a result I calculated the correlation between the Immoprix valuation and the distance from the edge’ of France, either the coast or the international border, whichever was closer.

Bingo! The statistical measure came up with a factor of -0.47 which, although not very large, was bigger than the other characteristics I had tested and gave me enough new data to formulate my final equation with a total explanatory value of nearly three-quarters of the price variability of French property. The minus sign means that the closer to the edge’ a town is the higher its property values, providing statistical evidence of the well-known phenomenon that houses in the centre of France are relatively inexpensive.

Holiday homes

Part of the explanation for this is the effect of the coast and the undoubted pulling power of beaches, corniches and harbours. But, there is another factor at work. Border towns are obvious locations for holiday homes and are places where international business is often done, as exemplified by Strasbourg, Colmar and Pau.

So, I had achieved my objective. I had identified the four factors which, at least statistically, comprise the key elements of location and, although some of the omissions were unexpected, I could at least understand the reasons why each of these factors was attractive. Sunshine hours, population, population density and proximity to the edge’ of the country are the features that tend to push house prices up. The French property market, it seems, is driven by a desire to live somewhere large, bustling, cosmopolitan and, most importantly, sunny. Not rocket science, perhaps, but the process of calculating my equation had, at least, made me think more carefully about what we mean by des res’.

Now that I’ve identified four elements of location that statistically account for over 73% of the value of French property, am I satisfied? Of course not. The accountant in me insists that I can’t close the books until I’ve found that other 27%!

Brian and Jacqueline Miller run property-finding company Ma Maison Parfaite in the Vend�eTel: 0033 (0)2 28 14 01 12www.mamaisonparfaite.com