Sensex returns are not same as stock market returns

"You know I was listening to this stock market expert on TV," she said.

"And what was he talking about?" I asked.

"So, this guy kept repeating that over a period of time, returns delivered by the stock market are significantly higher than returns delivered by anything else."

"Hmmm."

"He basically cited Sensex returns in order to make his point. Between 1986 and now, the Sensex has given a return of 13.4% per year, which is pretty decent. At the beginning of January 1986, the Sensex was at 561 points. Now it's close to 36,000 points."

"Yup. On the face of it, it sounds very decent."

"But it isn't?"

"Well, the argument is a little more nuanced."

"Hmmm."

"Let me tell you a story from the Second World War."

"Oh V," she said. "History again!"

"The British Royal Air Force (RAF) wanted heavy plating attached on its airplanes, in order to protect them from German anti-aircraft guns and fighter planes."

"Why are we talking planes here?" she asked.

I ignored her question and continued.

"The plates were heavy and hence, had to be attached to areas of the plane that were the most vulnerable. Interestingly, data for where exactly the German bullets hit the British planes was also available."

"This is getting interesting."

"As Jordan Ellenberg writes in How Not to Be Wrong: "The damage wasn't uniformly distributed across the aircraft. There were more bullet holes in the fuselage, not so many in the engines."

"This basically meant that area around fuselage was getting hit the most. Right?"

"Well, it wasn't as simple as that. A statistician by the name of Abraham Wald realised that things weren't what they seemed."

"It wasn't a case of what you see is what you get?"

"Yeah. As Ellenberg writes: "The armour, said Wald, doesn't go where bullet holes are. It goes where bullet holes aren't: on the engines...The missing bullet holes were on the missing holes. 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.""

"That's very interesting."

"Let me give you another example here. If you ever go to a hospital, you will see more people recovering with bullet holes in their legs than in their chests. This does not mean that people don't get hit in chests. They do. It's just that they don't recover from being hit in the chest."

"Oh, V, where do you come up with such examples."

"Well. As Gary Smith writes in Standard Deviations: "Wald...had the insight to recognise that these data suffered from survivor bias...Instead of reinforcing the locations with the most holes, they should reinforce the locations with no holes." Interestingly, the recommendations made by Wald were implemented and ended up saving many planes which would have otherwise gone down."

"Now how all this linked to what we were talking about?"

"We talked about Sensex returns between 1986 and 2018. Right?" I asked.

"Yes."

"The stocks that made up for the Sensex in 1986, were very different from the stocks that made up for the Sensex in 2018. Right?"

"Yes."

"Basically, companies that did badly, kept getting dropped from the Sensex, and companies that did well, survived. At the same time, newer companies came into the index."

"True."

"So the Sensex that you see in 2018 is different from the original Sensex of 1986. It suffers from a huge survivorship bias. Hence, calculating Sensex returns and projecting them to be overall returns of the stock market, comes with its share of problems."

"Fair point," she said.

"Then there is the case of judging mutual fund performance. As Ellenberg writes: "Mutual funds don't live forever. Some flourish, some die. The ones that die are, by and large, the ones that don't make money. So judging a decade's worth of mutual funds by the ones that still exist at the end of ten years is like judging our pilot's evasive manoeuvres by counting the bullet holes in the planes that come back.""

"Ah okay."

"The point being that whenever people throw a number around, always try and look at the assumptions that it is based on."

(The example is hypothetical)

Vivek Kaul is the author of the Easy Money trilogy