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During a year end gathering last week, two friends approached me to resolve a dispute. One of them, a recently converted die-hard fan of data science, claimed that mathematics can solve qualitative questions through data. His other friend insisted that there are many qualitative factors that require experience and gut instincts to interpret. I was trying to decide which was more important: the huge juicy roasted chicken leg I was stuffing my face with, or calm the situation down before it escalated to a brawl. I chose the bird.
From my experience as an empiricist and data-driven consultant, the real question wasn’t about whether we can quantify the qualitative, but whether we can do it appropriately and convincingly. Here’s an example: In economics, we often infer behavioural insights by observing the choices of individual consumers. This concept is known as revealed preference.
Suppose you choose to eat apples over oranges (when only apples and oranges are available), and oranges over grapes (when only oranges and grapes are available), then by the principle of intransitivity, I can infer that you like apples more than grapes.
Now, if your entire community behaves like you do, then the price of apples will be higher because of higher demand. The price of apples will keep rising until the point where the community feels that they are indifferent between satisfying their preference for apples and settling for the cheaper grapes. The difference between this equilibrium price for apples and its initial price is a proxy value for the qualitative factor of “how much the community likes apples”.
The revealed preference approach is appropriate and relevant for real estate, a market with a large number of transactions on assets whose characteristics do not change much over time. By observing the transaction prices against housing characteristics, we are able to compute the average premium that consumers are willing to pay for them.
In a Swedish study, the author found that the discount for noise pollution can be as high as 30%. He obtained this figure by comparing the values of homes that have a noisy environment to quiet ones, while taking into consideration other housing characteristics in a single equation. This is known as the hedonic pricing model, a type of multivariate regression model used in real estate valuation:
α (alpha) measures the average home prices after stripping out the effects of all other housing characteristics. The β (beta) in front of each characteristic measures the magnitude of its influence on average home prices. For example, given the following truncated model:
The price of a 1000 square feet home in Downtown Core on the 10th floor is predicted to sell for S$1859 per sqft. We obtain this figure from the hedonic model: 1121 (alpha) – 1000 x 0.1 (sqft) + 10 x 7 (floor) – 265 (resale) + 119 (downtown core) + 914 (year 2017). Even though homebuyers and sellers do not explicitly price the premium of housing characteristics, but given a large enough sample, the hedonic pricing model allows us to decompose the complex consensus buying/selling decisions of into explanatory variables (magnitudes included).
Hedonic pricing models are robust and can be very accurate if the modellers know what characteristics to include. The predictive powers of the vanilla hedonic model can be further enhanced through the use of ensemble methods in Machine Learning, such as gradient boosting and random forest.
Auto-valuation companies (such as Zillow in the United States) that employ similar techniques have achieved error rates lower than 3%, thereby adding accuracy to the list of benefits of model-based techniques which includes objectivity, transparency, recency, and computation speed.
In Singapore, a new auto-valuation start-up Urban Zoom provides accurate real estate valuation for free. Although the site is still in beta testing, the predictive models are operational and return impressively accurate valuations. There are two advantages to using auto-valuation models as a reference:
1. Agents typically make 1% – 4% commission on a successful deal. This means that pushing for another $10,000 pays only $100 for this added effort (and possibly break a deal). Agents therefore are incentivised to be risk averse and will choose to close deals as fast as possible. Auto-valuation models give you an objective property value to help you keep your agent’s incentives in check.
2. Housing features that are important to you may not cost as much as you are willing to pay for them. Good salespeople have an ability to sniff out what you like and make a big deal out of them. Auto-valuation models give you an objective property value to help you ensure that you aren’t paying more than market premium.
Dr. Jack Hong is the co-founder of Research Room Pte. Ltd., a management consulting and advanced analytics company that delivers complex prediction and decision-making capabilities for commercial, government, and not-for-profit organisations. Dr. Hong has extensive research and commercial experience in applying advanced empirical science to drive business, financial and policy value chains. He is concurrently an adjunct faculty with the Singapore Management University (SMU).