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.

>"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."

That would be a mathematician who is not familiar with

Bayes's formula for calculating the probability in this

case. :-/

>Anon: Any mathematician would think the odds are 50% for any fair coin flip, regardless of the past, Bayes or not 🙂 Bayes's formula may be applied to check if a coin is fair or not, of course.

>I respectfully disagree. If the mathematician did not

have any knowledge of the ten consecutive heads he

would put the odds at 50% assuming a fair coin. However,

given this knowledge the odds will now be for 11

consecutive heads, which is very low indeed (1/2048).

>We must agree to disagree – regardless of history, the probability of the next flip is 50%. The coin doesn't know it's history!

What you have calculated is the probability of getting 10 heads in a row (actually, 1/1024). When you have already gotten 10 heads in a row, the chance of getting the 11th head = 50%. If you look all the way back from the beginning, the changes of getting 11 heads in a row was 1/2048, but the past is not where the probability is being calculated.

>So we are arguing whether probability is an intrinsic

property of the coin or *our* best guess of an outcome

given the extent of our knowledge – the former is

called the "frequentist" approach and the latter the

"bayesian" approach (more here http://scienceblogs.com/goodmath/2008/04/schools_of_thought_in_probabil.php).

>This is interesting post. In fact quite similar to situation of giving preference to CMP of stocks with the thought that cheaper is better instead of analyzing P/E and EPS.

>its logical

most people buy in bulk in kgs

foot measure is for small quantity

same goes with tonnes and kgs in agri commodities

the dealer was a good soul

>Deepak,

It was surprising to note that they measure pipes' in Kilograms!

I agree with you. The probability is 50%, for the next coin flip, as all the prior outcomes ( all heads have already occurred).

best,

m

>Thanks for this post. Only now I understand the difference between bonus and split.

>Small number always attracts if you are a buyer. Very nice article. keep going.