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At Yahoo: Strange Numbers


My latest at Yahoo: Strange Numbers:

I moved my house recently, and in the process discovered that I needed a hose pipe. In the hardware store, the conversation went like this, translated from Hindi, minus the paan stains:

“I need a 3/4th inch water pipe”

“It’s Rs. 95 per kg.”

“Oh. But I have no idea how many kilograms I’ll need”, I said, wondering why anyone would sell hose pipe by the kilogram.

“Or you can pay Rs. 9 per foot, if that works for you.”

Happier, I said, “Yes, that’s so much better. 15 feet please”

The shopkeeper measured 15 feet of pipe and proceeded to weigh it. And he told me:

“Sir, your pipe weights just 900 grams. I just saved you money. Rs. 95 per kg sounds bigger than Rs. 9 per foot, but for you the Rs. 95 was better. Small numbers are attractive, not necessarily cheaper.”

Lesson learnt, I said, humbled some more because I was supposed to be the numbers guy.

The lure of small numbers, in this case, was purely inexperience – since I had no idea how many kilograms I would need, I chose the per-foot calculation. That the shopkeeper decided to give me an education was fortunate; I would have otherwise gone home happy to have paid Rs. 135 for what should have cost me Rs. 86.

I’ve seen this in stocks as well – to the uninitiated, a share at Rs. 10 sounds cheaper than one at Rs. 1,000 – but given companies have different number of shares issued, and a different profit per share, the Rs. 10 share might be the most expensive you’ve bought. In the US, they often fix this by doing a “share split” – converting one share into two, such that a $100 share becomes two shares of $50 each, thus looking cheaper.

That’s not easy in India, because of a law concerning the “face value” – typically Rs. 10 per share (which is what it would have cost when the company was small, private, and just starting up). When you split the share, the face value goes down as well – so a Rs. 10 share can become a Rs. 5 share, or even a Rs. 1 share – but current laws don’t allow face values to go less than Rs. 1 per share. A Hindustan Unilever share has a face value of Rs. 1, and trades at Rs. 300. Even if HUL’s shareholders want to make it cheaper, no further split is possible. What could happen is that HUL could “capitalize” reserves, taking accumulated profits and converting them to shares by offering 1 share as a “bonus”. This works exactly like a split in that the price falls correspondingly, except the face value doesn’t change.

There is no reason to think of the word “bonus” in any positive way, other than that you see a lower price point that seems attractive. The negative? Taxes. Let’s say you owned 100 shares worth Rs. 2,000, and you get a 1:1 bonus (1 extra share for each current share). You will get an additional 100 shares and the price will fall to Rs. 1,000. Let us say you bought the shares at Rs. 800 a long time back, and you want to sell the shares in a few months – the taxation rules indicate that the first 100 shares are “long-term”, on which you gain Rs. 200 per share, and pay no tax because long term equity capital gains are exempt. On the remaining 100 “bonus” shares, the cost is assumed to be zero, and since you sold them before a year after the bonus date, you will pay short term capital gains tax on the entire sale proceeds of Rs. 100,000. (In a split, the cost price is divided appropriately, so this tax issue doesn’t apply)

The numbers game gets us on the other side as well. In Bangalore, I spoke to a few vegetable vendors who sell in a local farmer’s market. They borrow in their villages from moneylenders – take Rs. 100 in the morning and return Rs. 110 the next day, the Rs. 10 being interest. Non-compounded, this is an interest rate of 3,650%. Consider then that a microfinance company offers them a loan at 38% instead – to them it’s a gargantuan saving; but to us city dwellers used to single digit deposit rates, it sounds usurious. Context is everything, but it’s sometimes sacrificed in the altar of column centimetres.

Eddie Izzard talks about how our neurons short-circuit in his hilarious gig, Dressed to Kill. (Video)

“Pol Pot killed 1.7 million people. We can’t even deal with that! You know, we think if somebody kills someone, that’s murder, you go to prison. You kill 10 people, you go to Texas, they hit you with a brick, that’s what they do. 20 people, you go to a hospital, they look through a small window at you forever. And over that, we can’t deal with it, you know? Someone’s killed 100,000 people. We’re almost going, “Well done! You killed 100,000 people? You must get up very early in the morning. I can’t even get down the gym! Your diary must look odd: “Get up in the morning, death, death, death, death, death, death, death – lunch- death, death, death -afternoon tea – death, death, death – quick shower.”

If you were told to flip a coin, and it came up heads ten times consecutively, would you bet that it will be tails on the next flip? The mathematician would say the odds are still 50% – that the past doesn’t impact the future. The Gambler’s fallacy makes us believe it has to be tails next, because on average the coin should have as many heads as tails, but we believe we’re closer to the turnaround point now – in reality, it could go an infinite number of heads before it flips tails. The street-smart will tell you that if the coin turns up heads ten times, the game is probably rigged.

The Gambler’s fallacy is often employed in market strategies that buy stocks that are battered just because they’ll be the next to turn around. But what is down today could go down much more – indeed, when the Bear Stearns stock fell 50% from $60 to $30, there were calls to buy because it’s down fifty percent! It eventually was sold to JP Morgan for $10.

In India, when stocks go crazily in either direction, I tend to side with the street-smart guy – the game isn’t entirely fair, so play at your own risk. And while you’re at it, only buy hose pipe by the kilogram.


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