The home loan lender HDFC in its latest investor presentation says that homes have seen an “improved affordability”. This goes against everything that one sees in the real estate sector these days, where prices have gone so high that most people wanting to buy a home to live in, can't.

The home loan lender HDFC in its latest investor presentation says that homes have seen an “improved affordability”. This goes against everything that one sees in the real estate sector these days, where prices have gone so high that most people wanting to buy a home to live in, can't.

So how did HDFC manage to come to such a conclusion? Allow me to explain.

In the graph above, HDFC points out that homes are more affordable than they have been at any point of time in the last ten years. It defines affordability as property prices divided by annual income. This number for 2015 comes in at 4.4. In 2014 it was at 4.6. In 2013 it was at 4.7. The last time the affordability number was lower than 4.4 was in 2004, when the number was at 4.3. Hence, homes are now more affordable than they were in the last ten years.

So far so good. What does affordability of 4.4 really mean? It means that the property values in 2015 were 4.4 times the annual income. The average annual income considered by the company is around Rs 12 lakh. And the average property value considered by the company is around Rs 52 lakh. Hence, while the property prices have been going up, so have incomes – hence housing has become more affordable. QED.

Of course, something is not 'quite' right about this calculation. But before we get into that, let me recount a war story here. During the course of the Second World War, the British Royal Air Force (RAF) wanted to protect its planes from the German anti-aircraft guns and fighter planes. In order to do that it wanted to attach heavy plating to its airplanes.

The trouble was that the plates that were to be attached were heavy and hence, they had to be strategically attached at points where bullets from the Germans were most likely to hit. Historical data on where exactly the German bullets hit the RAF planes was available. As Jordan Ellenberg writes in How Not to Be Wrong: The Hidden Maths of Everyday Life: “The damage[of the bullets] wasn't uniformly distributed across the aircraft. There were more bullet holes in the fuselage, not so many in the engines.”

If the data were to be interpreted in a straightforward manner, it would mean plating the area around the fuselage because that was what got hit the most. Nevertheless, the German bullets should also have been also hitting the engine because the engine “is a point of total vulnerability”.

A statistician named Abraham Wald realised this anomaly. As Ellenberg writes: 'The armour, said Wald, doesn't go where bullet holes are. It goes where bullet holes aren't: on the engines. Wald's insight was simply to ask: where are the missing holes? The ones that would have been all over the engine casing, if the damage had been spread equally all over the plane. The missing bullet holes were on the missing planes. The reason planes were coming back with fewer hits to the engine is that planes that got hit in the engine weren't coming back.” They simply crashed.

Another example that can be considered here is of people in a recovery room in a hospital. There will be more people with bullet holes in legs in comparison to people with bullet holes in chests. This in no way means that people don't get hit in chests. They sure do. It's just that people who get hit in the chest don't recover.

As Gary Smith writes in Standard Deviations: Flawed Assumptions Tortured Data and Other Ways to Lie With Statistics: 'Wald...had the insight to recognize that these data suffered from survivor bias...Instead of reinforcing the locations with the most holes, they should reinforce the locations with no holes.' Wald's recommendations were implemented and ended up saving many planes which would have otherwise gone down.

But why are we discussing wars and hospitals, when we started of with HDFC. The data used by HDFC to arrive at the conclusion of “improved affordability” also suffers from survivor bias. Allow me to explain.

When HDFC considers an average home price of around Rs 52 lakh and an average income of around Rs 12 lakh, it is possibly referring to a set of people who have approached HDFC for a home loan and bought one. In short, it is referring to a sample that it has ready access to. But the people approaching HDFC are possibly those who can still afford to buy a home. And they can do that primarily because their incomes have kept pace with the rise in home prices.

Nevertheless, what about all those people out there who want to a buy a home to live in, but can simply not afford it. Their incomes are simply not high enough and haven't kept pace with rising home prices. These people possibly do not form a part of HDFC's sample. And hence, the data suffers from a survivor bias. Given this, the conclusion of “improved affordability” is essentially wrong.

There are other points that can be made against the “improved affordability” argument. If the affordability has improved why are there so many unsold homes all over India? Reports put out by real estate consultants regularly point out to the huge number of unsold homes all over India. (You can read about it here and here).

Further, if the affordability has improved why is there such a huge shortage of homes in urban areas. As the latest Economic Survey points out: “The widening gap between demand and supply of housing units and affordable housing finance solutions is a major policy concern for India. At present urban housing shortage is 18.8 million units of which 95.6 per cent is in economically weaker sections (EWS) / low income group (LIG) segments and requires huge financial investment to overcome.” Obviously, HDFC does not cater to this group.

To conclude, it is worth remembering here what American writer Upton Sinclair once said: “It is difficult to get a man to understand something, when his salary depends on his not understanding it.” HDFC is in the business of giving out home loans and it would like to think that “all is well,” with the real estate sector and homes are affordable, but that is really not the case.

HDFC as a company has been doing well. In fact, in the last one year its loan book grew by 20%. Having said that, it is in the business of giving out home loans and it would like to think that “all is well,” with the real estate sector and homes are affordable, but that is really not the case.

(Vivek Kaul is the author of the Easy Money trilogy. He tweets @kaul_vivek)