HDFC, an Elephant and the Blind Men of Hindustan

Once upon a time, there were seven blind men of Hindustan. One day they ran into a big elephant for the first time. Depending on which part of the elephant they touched – the ear, the leg, the tail or the trunk – they came up with their own explanation of what they had encountered.

Their experience was limited by the fact that none of them could see the elephant. They had only touched its parts. Hence, what one described was different from the other.

(Illustration from a 1916 American book of children’s stories: Wikipedia)

The hedge fund manager George Soros describes this phenomenon in his book The New Paradigm for Financial Markets: “People’s understanding is inherently imperfect because they are part of reality and a part cannot fully comprehend the whole.”

Both Soros and the parable tell us that our thinking is limited by our experiences. And based on these experiences, we arrive at what we think is nothing but the truth, but what we have is our version of what we think is the truth. Now hold this thought.

Housing in India has become more affordable. Or has it?

Housing Development Finance Corp. (HDFC) has had a huge role to play in making housing loans popular in India. The company shares an investor presentation, along with its financial results, every three months. It did so this time around as well after declaring results for April to June. This presentation has a chart that shows the affordability of homes in India.

Source: HDFC

The chart shows that the affordability of homes has improved over the years and has never been better than now. In 1995, the price of a house was 22 times the annual income of an average buyer. In 2021, it stood at an all-time low of 3.2 times the income of an average buyer.

This chart goes against the prevailing wisdom of residential housing being expensive. It also goes against the fact that real estate companies in India’s biggest cities are holding on to a huge inventory of unsold homes. So, if housing affordability were at its very best, the number of unsold homes would have come down over the years. Then there is the case of investors having bought homes and being stuck with them.

Further, housing loans would be growing at a faster pace. From March 2014 to March 2017, they grew by 18.1% per year on average. And from March 2017 to March 2020, they grew by 12.6% per year on average. (Data for outstanding housing loans of housing finance companies as of 31 March 2021 isn’t currently available. Hence, we look at the housing loan growth up until 31 March 2020, only.)

So, what gives? Is the HDFC data wrong? Not at all. But the interpretation is.

The trouble is that HDFC, like the blind men of Hindustan, has just looked at its own data and not the overall data and concluded that housing affordability has improved over the years. As Howard Marks writes in Mastering the Market Cycle: “We are those blind men. Even if we have a good understanding of the events we witness, we don’t easily gain the overall view needed to put them together. Up to the time we see the whole in action, our knowledge is limited to the parts we’ve touched.”

The survivorship bias

Politicians decide to go to war, but soldiers fight it. Nonetheless, even statisticians have an important role to play in it. Here’s another little story. (Apologies to everyone who loves to read in a linear fashion. My problem is I am a Quentin Tarantino fan, where everything is all over the place until it comes together).

While fighting the Second World War, the British Royal Air Force (RAF) ended up with a very strange problem. It needed to attach heavy plating to its fighter jets to protect them from gunfire from the German fighter planes and their anti-aircraft guns. The trouble was that the plating was heavy, and hence, it had to be used sparingly at the right points of the aircraft, where the Germans were most likely to attack.

Jordan Ellenberg writes about this in How Not to Be Wrong: The Hidden Maths of Everyday Life: “The damage [of the German bullets] wasn’t uniformly distributed across the [British] aircraft. There were more bullet holes in the fuselage, not so many in the engines.”

What did this data suggest? It suggested that the chances of the plane’s fuselage being attacked were higher, and that was the part of the plane that seemed to be the most vulnerable. QED. Thankfully, the British didn’t go by what the basic reading of data suggested because they would have been totally wrong. Instead, they chose to hear out Abraham Wald, a statistician.

As Tim Harford writes in How to Make the World Add Up: “Wald’s written response was highly technical, but the key idea is this: we only observe damage in the planes that return. What about the planes that were shot down?”

This data wasn’t available to the British RAF. 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. Hence, the planes were plated around the engine and not the fuselage as the data had originally suggested.

The original data in the British case had a survivorship bias built into it. It captured the bullet patterns of only those planes that made it back to the air force base and not every British plane that got hit by a German bullet.

Ellenberg explains this in another way: “If you go the recovery room at the hospital, you’ll see a lot more people with bullet holes in their legs than people with bullet holes in their chests. But that’s not because people don’t get shot in the chest; it’s because the people who get shot in the chest don’t recover.”

There is a similar problem with the data that HDFC has used to conclude that the affordability of homes has improved over the years. The chart tells us that the average price of a home financed by HDFC in 2021 was around Rs 51 lakh (look at property value on the left-hand side). Given that the chart has been made from its customer data, it represents the affordability level of people who approached HDFC for a loan and got one.

Nevertheless, does this imply better affordability all across the housing market? Not at all. All this tells us is that the affordability level of HDFC’s customers has improved over the years, or in other words, HDFC is ending up giving loans to only those customers who can afford to buy a house.

HDFC has no access to data regarding households that want to buy a house but find it expensive given that they don’t have enough money to make a downpayment and pay stamp duty and everything else that is needed to make a house a home.

Further, they don’t earn enough money to pay an EMI month on month, for years on end, to repay the home loan. This data is like that of the planes that got hit by bullets and didn’t make it back to the base. The data that HDFC has is like planes that got hit by bullets and made it back to the base.

Where else does survivorship bias show up?

A great example of this is when people compare stocks versus gold and conclude that stocks have given higher returns over the decades or even across centuries. The trouble is when they do this, they only look at companies that have survived and do not account for companies that have gone bust in the interim.

As Nick Barisheff writes in $10,000 Gold: Why Gold’s Inevitable Rise Is the Investor’s Safe Haven: “Stocks cannot be compared to gold when it comes to risk. Virtually all of the stocks that existed in 1700 no longer exist today, so, at some point, investors and their descendants would have lost their entire investment.” The gold is pretty much still around. (This is not a recommendation to buy gold instead of stocks, but just an illustration to explain that there is more to the entire issue than meets the eye).

A similar bias can be seen when studies on the performance of mutual funds are carried out. They typically don’t consider mutual funds which have shut down during the period. And this accentuates returns of funds that have survived. As Harford writes in the context of American mutual funds: “If you ignore all the investment funds that quietly disappear, the apparent performance is twice as good as the actual performance.”

When fund managers talk about the great returns generated by stocks and mutual funds which invest in stocks, this is something that they choose to ignore. Of course, the prospective investors don’t understand this.

Management gurus and survivorship bias

Management gurus in the business of developing general business principles from the past performance of companies become a victim of this bias as well. Most such gurus only look at companies that have survived and not the ones that went bust. This leads to its own set of problems. A great example of this is the famous management book In Search of Excellence written by gurus Tom Peters and Robert Waterman, the go-to book for managers for many years. The book offered management lessons from 43 outstanding corporations of its time.

The trouble is that their performance turned out to be the luck of the draw more than anything else. As Harford writes: “If they really were paragons of brilliant management, then one might have expected their success to last. If, instead, they were the winners of an invisible lottery, the beneficiaries of largely random strokes of good fortune, then we would expect that the good luck would often fail to last. Sure enough, within two years, almost a third of them were in serious financial trouble.” This was survivorship bias at work.

If Peters and Waterman had waited a few more years and written the book, many of their original companies wouldn’t have made it to the list, and some others might have. To be fair, while I use the example of Peters and Waterman here, many other business gurus have become victims of survivorship bias over the years as well.

So what does this tell us?

As individuals, we have limited experience and understanding of most things. But that doesn’t stop us from pontificating based on our own limited experience. The rise of social media has made this very easy. The trouble is that while one may not be the pontificating type, one easily falls victim to what other pontificating types are saying, at any given point of time, based on their limited experience and the echo chamber they belong to.

So, how do we solve this problem and not become victims of survivorship bias? By trying to understand the different sides to any issue before commenting on it? But that’s not feasible at all. Given that there are only 24 hours in a day and so many things that need to be done, it is important to choose the most critical issues and try and understand them well enough. Being selective is the need of the hour. Also, one need not have a view on everything. You don’t need an audience for everything that is going on inside that great mind of yours. How does that help in any way?

And when it comes to investing, it is most important to be aware of the different kinds of survivorship bias that exist to avoid getting financially conned. But, of course, given the deluge of information out there, the chances of getting intellectually conned continue to remain high. Hence, one can only prepare oneself and hope for the best.