On HDB resale flat prices

One of the things that I like about HDB website is you can check past 1-year resale transacted prices in Singapore. Granted, I wish they could give us more than 1 year data, but I guess 1 year data is good enough to help you to predict the current price in the estate that you want to buy.

Of course, ultimately each house is unique and you can’t really compare them directly like that. Nevertheless, we can still do a lot of things and narrow down our specifications as specific as we want. So, in the HDB webpage for resale flat price query, you can fill in your flat type that you want to buy — for example, a 3-room flat. Next, the estate, for example Queenstown. Finally, the resale approval date — you can collect data from 1-month range to 12-month range. I have collected the data from September 2011-2012 and here is what you will get:

We can easily note that there are 3 transactions which are way above the rest. They are 3-room Terrace flats which are located in Blk 50-58 Stirling Rd (you will see these units on your right/south side if you take the East-West Line from Commonwealth to Queenstown). From this alone you can already guess that we should look more deeper into the data and try to discriminate them even further. Moreover, the range of the prices is still too high even if you have excluded those Terrace flats. A 3-room flat in Queenstown can cost you from $300,000 to $500,000. This kind of range will not be helpful at all in planning your purchase. So, let’s parse the data even further. First, you need to note that every HDB town consists of several districts. Queenstown, for example, is divided into 7 districts:

(Taken from myqueenstown.blogspot.sg)

And Queenstown is a relatively old HDB town. Most of the HDBs in this estate were built during the 1970s, with the oldest ones located in Commonwealth district, where the earliest blocks were built in 1967. Nevertheless, there are some newer blocks in the estate. In Tanglin Halt, for example, there are several blocks (just beside the Commonwealth MRT station) which were built in 2008. And we won’t group them with the rest of Tanglin Halt. Other new blocks are located in Strathmore Ave, which were built in 2011. So far there is only 1 transaction in that area (basically because of the Minimum Occupying Period rule — and that who wants to sell a new house anyway?). In the past year (Sept ’11 – Sept ’12), the statistics (all values given, except for number of transcations, are the average value) for the distinct districts are as follow:

And, as what you will expect, the average psf (price per square foot) correlates (almost perfectly) with the year the blocks were built. (It still correlates greatly even if you remove the newer two points.) Correlation doesn’t necessarily mean causation, but in this case it does mean causation.

In the table above, it is clear that an HDB town is pretty diverse and hence you need to know the specific area of the particular unit that you want to buy so that you could make a fair comparison and hence a fair bid (vice versa, if you know the range of price around the unit, the seller won’t be able to fool you). For example, the median price of a 3-room flat in Queenstown in Q2 2012, as listed in HDB website, is $365,000. However, the median price of a 3-room flat in Commonwealth district in the same period is only $329,500. So, even if the asking price is $340,000 and the owner/agent claims that it is much cheaper than the median price in Queenstown, you should never fall to this. You should compare it with the median price in the same district. Of course, inevitable there will be variation in the flat price, but it will be caused by other factors such as flat maintenance, furnishing quality, etc. Similarly, don’t expect that you could buy a unit in Holland-Ghim Moh at $365,000, as the price in the district is significantly more expensive than that.

Now, the district-level data can be good enough in some cases, but you can go even further. I have given an example above, where I divided Tanglin Halt district into two (although that one is pretty obvious: 1970s flats shouldn’t be grouped with 2000s flats). Let’s take a look now at the Stirling-Mei Ling district (I like the juxtaposition of a Western name, Stirling, and a Chinese one, Mei Ling).

From the graph above, you might think that the price trend is decreasing in this district. Nevertheless, if you go to the area by yourself, you will notice that there are two types of flats in this area. First is the old linear slab blocks (Blks 152-154, 157-158, 162-171) and the other one is the point blocks (Blks 160, 161). And the units in point blocks are significantly more expensive than those in linear slab blocks.

Or, if you look at the graph above, these units are separated by the $440,000 line. So, again even within the same district you could see two different patterns. And note that it’s not like these two types are like the ones in Tanglin Halt, one built in 1970 and another in 2008. Both of these two types in Stirling-Mei Ling were built in 1970-71, and hence you wouldn’t be able to differentiate them by looking at the built-year alone. Moreover, you wouldn’t be able to differentiate them as well if you put “Mei Ling St” in the street name for the search in HDB website, since both of them are located in the same street. What you can do is to see the blocks by yourself or by looking at the data and try to see the pattern. If you can’t differentiate by built-year, try another variable. For this case the determining variable is floor area. All the units in the point blocks are 72 sqm, while those in linear slab blocks are 60 sqm (non-corner unit, not upgraded yet), 66/67 sqm (non-corner unit, upgraded), and 70 sqm (corner unit). How about the linear slab blocks, then, can we parse them even further?

The answer is yes, we can always go even further until the smallest unit (pun intended), but the thing is there might be some point where the return is diminishing as the difference might be too small to be significant in monetary terms. The bottom line is, more often than not, your budget and the range of price that you could afford to fork out. We have gone two steps from Queenstown as a whole to Stirling-Mei Ling linear slab blocks, and by doing so we have reduced the standard deviation from $67k to $26k.

If $52k (=2*$26k) range is good enough for you (which translates to ~$10-15k range for the down payment and might be reasonable enough for some), then you can start looking for the units there. Otherwise, you can dig into the data even further. There are still two differentiating factors: (1) purchase date (1-year data might be too long and the price from September 2011 might not be relevant any more, so we can reduce it to 3-month or 6-month data), and (2) flat area (as described above, 60/66/70).

First, the purchase date. Let’s group the data into 3-month periods:

Now, note that the standard deviation in the last 3-month does reduce the standard deviation, but only by a little bit. So, it is not really useful for this case.

Alternatively, let’s group the flats according to their flat areas:

Now, note that the largest standard deviation is for the 60 sqm units at $21k, which translates to $8-10k range for the down payment. The best estimate is for the 66/67 sqm units, which translates to $4-5k range for the down payment.

Finally, you can also group the flats according to their areas AND their purchase date. For example, for the 66/67 sqm units:

The standard deviation for the 66/67 sqm units’ prices has dropped from $11,463 (if you used all the data) to $8,144 if you used only the last 3-month data. These standard deviations are good enough in the sense that ultimately these are perhaps the variabilities in the quality of each unit which might range from beautifully renovated and maintained to look-like-crap unit, or for the direction that the unit is facing (N-S is more expensive than E-W), or for the nuances of the location of the unit (for example, in the Stirling-Mei Ling district, the units that are nearer to the Mei Ling Market and Food Centre are relatively more expensive). Can we model these variabilities mathematically? Yes, for some, but not really for others.

For example, you can attach a premium for the level where the unit is. HDB gives the level range as “01 to 05”, “06 to 10”, “11 to 15”, and so forth. Let’s assume that for every additional level range, there is a $5,000 premium to the unit. Hence a unit in level 01 to 05 will be $5,000 costlier if it moves to level 06 to 10. Using this assumption, I can reduce the standard deviation for the 66/67 sqm units’ prices even further from $8,144 to $4,041. And this $8k price range will translate to $2k range for the down payment.

But, how do you model for “distance to Mei Ling Market and Food Centre”? It’s not that you can’t, but that the return will already be so diminished — a $2k range for the down payment is already very, very good. You must just put it (and other factors) as “noise” for your model to make your life easier.

Now, using all the above assumptions (mainly the level premium), perhaps I can use them to make a model for my unit’s price. Assuming that a long-term behaviour of housing price is a steady increase, how if I fit a linear regression model to the data?

Of course, it is foolish to use this model to predict the price in 5 or 10 years time. Nobody knows the future. What I can use from this model is to estimate the price now using the recent trends and assuming that the current supply-demand fundamentals still hold (using this model, the estimated annual price increase rate for this neighbourhood is 2.93%, which is half of the current Y-to-Y rate for the whole Singapore at 5.72%). The owner can use this data to show the “reasonableness” of his asking price, or, likewise, the buyer can also use this data when he feels that the owner is asking too much. For example, using the recent trends, the base price for a non-corner, upgraded unit in Stirling-Mei Ling district now is $385,000. From there, the price will go up or down according to the “non-modelled” factors such as unit’s maintenance/renovation quality etc. Additionally, the owner will want to keep the upward trend and try to sell his unit as expensive as he/she can (and hence his “owner” basic becomes $395,000), but the buyer will want to buck the trend and push the curve downward (and hence his “buyer” basic becomes $375,000). But still, both parties can’t stray too far from the basic price.

And, finally, I would need to always update the model when the new data come in. Perhaps the very simple linear regression model is good enough for the current data (note that this model only applies to this very specific neighbourhood within a very specific time frame), but perhaps it isn’t any more when there is more new data. I just can’t keep telling myself that the current trend will stay forever. That would be delusional — and, in some cases, suicidal.

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