**Affordable Housing Formula for Singapore Property**

In managing a property market, the most important consideration, above all else, is supply.

Yes, demand fueled by low interest rates can cause headaches. It makes it cheaper for households to buy homes and overextend themselves, which, in turn, may lead to a housing bubble.

However, in the digital age, the demand side of the property can be managed using public policy, big data, and technology. As we detailed in 3 Reasons it’s Safe to Remove Additional Buyer’s Stamp Duty (ABSD), prudent underwriting, speculation controls, and pricing transparency can temper demand and protect against housing bubbles.

Indeed, the Cooling Measures have been quite effective at dampening demand. According to SRX Property, monthly transaction volume is down 60.3% in the HDB resale market and 77.3% for private apartments.

However, this progress has come at a cost. During the last four years, as we reported in Balancing Home Affordability with Appreciation, the property market has not kept up with inflation and has lagged Gross Domestic Product (GDP) and median income. These results are not good for those who have earmarked their homes for retirement or those who see their homes as an investment hedge against inflation.

Furthermore, there are many industries tied to property – from construction to banking to home furnishings. When the market is down, those industries suffer. At a time when China’s economy is faltering, Europe struggles on both the economic and political front, and the USA’s recovery is underwhelming, the last thing we should want is an underperforming property market.

The challenge, then, is to balance housing affordability with price appreciation in the property market. In Time to Set Targets for Singapore’s Private Markets, we introduced the Affordable Housing Stock Formula:

This new algorithm makes it more efficient to manage the supply side of the property market and, therefore, achieve a balance in home affordability and price.

The key to this formula is X-Value^{TM} technology and big data sets. X-Value is a computer’s estimate of the market value of any apartment or a landed home in Singapore.

Our ability to measure the value of Singapore homes means that we can measure the housing stock available to any household income bracket at any point in time. Here is how the Affordable Housing Stock Formula works.

There are three steps to calculating S_{Ii}, which is the additional supply of housing required to ensure that there is sufficient housing for the designated income bracket:

- Define affordable housing;
- Identify the stock of affordable housing currently available for each income bracket;
- Calculate the additional supply of housing required.

*Define Affordable Housing*

SINGSTAT has defined the different income brackets in Singapore, which we define I_{i} where I stands for income and i represents the different income bracket segments.

For example purposes, we will designate i as the $2,000-$2,900 income bracket.

│I_{i}│is the number of households in I_{i}. In this example, there 69,600 households in the $2,000-$2,900 income bracket.

Since we want everyone in the income bracket to be able to afford a home, we designate the minimum income in the bracket as min(I_{i}). In our example min(I_{i}) = $2,000.

"A" represents the number of years needed to pay off a property by annual income. This variable should be defined by the Government as part of its affordable housing policy. For our purposes, we assign the value 5 to A, which means we define affordable housing as a home that is worth five times the minimum annual salary for the income bracket ($2,000 x 5 x 12).

Where did we get 5? We found in our research that 5 years is common among worldwide property analysts. However, the number does not have to be 5. It is completely up to the authorities as they are the ones accountable for their housing policy.

Continuing on our example, an affordable home for the $2,000-$2,900 income bracket is $120,000.

*Identify Affordable Housing Stock*

Step two is to determine the existing number of homes that are currently affordable for each income bracket.

The X-Value computer system values, in real-time, all homes – HDB, landed, and private apartments. We designate the computed value as P_{j}, which is the X-Value of each home.

For example, suppose there are 1.3 million homes in Singapore (i.e., N = 1.3 million). P_{1} is the X-Value for the first home, P_{2} is the X-Value for the second home, and so on until we have calculated P_{1,300,000}.

Now that we have 1.3 million homes valued in real-time, we identify the number of homes that are affordable for each income bracket. P_{j} is affordable for a particular income bracket if it is less than or equal to Affordability as determined in step one. In other words, P_{j} is affordable to I_{i} if P_{j<}Affordability _{Ii }where Affordability_{Ii} = 12 x min (I_{i}) x A.

In the case of the income bracket [$2,000 - $2,999], if the home’s value is less than or equal to $120,000, the home is deemed affordable.

Since we are dealing with computers, we need to speak in machine language. This means assigning a one (1) or a zero (0) to each home. The X-Value system looks at every home value (P_{j}) and determines if it is affordable for each income bracket. If the home is affordable, it assigns a one (1). If it is not affordable for that income group it assigns a zero (0).

In our formula, we describe the count of an affordable home for a particular income bracket as Y_{j,AffordabilityIi}. In our example, if home j has an X-Value (i.e., P_{j}) less than or equal to $120,000 (i.e., Affordability_{Ii} where I_{i} is the [$2,000 - $2,999] income bracket), the computer assigns a one (1) to it. In other words, Y_{1, $120k }= 1 if the first home is < $120k.

Now that the X-Value system has tagged all the homes as either affordable (i.e., 1) or not affordable (i.e., 0), it counts up the number of affordable homes for each income bracket. In our formula, we define│ Y_{j,AffordabilityIi} │as the total number of affordable homes in each income bracket.

Therefore, as a logical consequence, the following formula represents the summation of all the affordable homes out of a total of N = 1.3 million homes for a selected income bracket:

In our case, say that the number of affordable homes for the income bracket [$2,000 - $2,999] is 50,000 units.

*Additional Supply of Affordable Housing*

Once we know the current number of affordable homes available for each income bracket, we can determine if we need to build more homes to achieve the Government’s affordable housing goals. However, before we do this, we must determine ß, which is the Affordable Housing Adjustment (AHA).

The AHA incorporates two policy decisions. T_{Ii} represents the Government’s homeownership target for each income bracket while F_{Ii} accounts for a forecasted increase or decrease in the number of households in each income group. As such ß_{Ii} = T_{Ii} x F_{Ii}.

Continuing our example, say the Government sets 95% homeownership for our income bracket [$2,000 - $2,999]. At the same time, policy analysts expect an increase of 3% in the number of households in this bracket over the next five years. (They recognize that they need 3-5 years to be able to construct additional housing.) This gives us a ß_{Ii} of 0.95 multiplied by 1.03, which equals 0.9785.

With this ß_{Ii} (i.e., AHA), we can calculate the additional supply of houses needed for each income group. We designate this result S_{Ii} and solve for it using the following equation:

In our example, S_{Ii} = 0.9785 multiplied by 69,600 existing households minus 50,000 affordable homes equals 18,104 homes needed to meet the homeownership goal of 95% for the income bracket [$2,000 - $2,999].

As a recap, in order to achieve 18,104 homes, we made three transparent policy decisions and the rest of the calculations were done by the X-Value system. First, we defined Affordability (A) as five times annual salary. Second, we set a homeownership target of 95%. Third, we forecast an increase of 3% over the next five years.

After calculating the shortfall in affordable homes currently on the market for each income bracket, the policy actions fall into place. We can think of four options to achieve home affordability:

- Apply one-size-fits-all Cooling Measures to the entire market. The downside to this approach is that the measures are blunt so they may or may not achieve the home affordability objectives for each income bracket but they will cause a reduction in market value for every homeowner and place downward pressure on GDP growth;
- Build additional homes to make up for the affordable housing shortfall in each income bracket;
- Ease the underwriting limits on specific housing types for selected households so the latter has manageable monthly mortgage payments. As a safeguard against default, this option would probably require the Monetary Authority of Singapore (MAS) and/or banks to set up reserves to fund defaults. (X-Value could serve as the valuation basis of these reserves.);
- Subsidize selected households with GIC investment returns or tax payer funds.

Our preference would be options 2, 3, or 4 as they are targeted, measured, and, in our opinion, more efficient and equitable (for homeowners, aspiring homeowners, and the economy) than option 1.

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