Damming the Nile and diapers

One of the greatest engineering problems in the last century was to determine the patterns in the flow of the Nile. It had been clear for at least a couple of millennia that the flow of the river was not regular, and the annual flow did not follow something like a normal distribution.

The matter gained importance in the late 1800s when the British colonial government decided to dam the Nile. Understanding accurately the pattern of flows of the river was important to determine the capacity of the reservoir being built, so that both floods and droughts could be contained.

The problem was solved by Harold Edwin Hurst, a British hydrologist who was posted in Egypt for over 60 years in the 20th Century. Hurst defined his model as one of “long-range dependence”, and managed to accurately predict the variation in the flow of the river. In recognition of his services, Egyptians gave him the moniker “Abu Nil” (father of the Nile). Later on, Benoit Mandelbrot named a quantity that determines the long-range dependence of a time series after Hurst.

I’ve written about Hurst once before, in the context of financial markets, but I invoke him here with respect to a problem closer to me – the pattern of my daughter’s poop.

It is rather well known that poop, even among babies, is not a continuous process. If someone were to poop 100ml of poop a day (easier to use volume rather than weight in the context of babies), it doesn’t mean they poop 4ml every hour. Poop happens in discrete bursts, and the number of such bursts per day depends upon age, decreasing over time into adulthood.

One might think that a reasonable way to model poop is to assume that the amount of poop in each burst follows a normal distribution, and each burst is independent of the ones around it. However, based on a little over two months’ experience of changing my daughter’s diapers, I declare this kind of a model to be wholly inaccurate.

For, what I’ve determined is that far from being normal, pooping patterns follow long-range dependence. There are long time periods (spanning a few diaper changes) when there is no, or very little, poop. Then there are times when it flows at such a high rate that we need to change diapers at a far higher frequency than normal. And such periods are usually followed by other high-poop periods. And so on.

In other words, the amount of poop has positive serial correlation. And to use the index that Mandelbrot lovingly constructed and named in honour of Hurst, the Hurst exponent of my daughter’s (and other babies’) poop is much higher than 0.5.

This makes me wonder if diaper manufacturers have taken this long-range dependence into account while determining diaper capacity. Or I wonder if, instead, they simply assume that parents will take care of this by adjusting the inter-diaper-change time period.

As Mandelbrot describes towards the end of his excellent Misbehaviour of markets , you can  use so-called “multifractal models” which combine normal price increments with irregular time increments to get an accurate (fractal) representation of the movement of stock prices.

PS: Apologies to those who got disgusted by the post. Until a massive burst a few minutes ago I’d never imagined I’d be comparing the flows of poop and the Nile!

When is a war a war?

War is an inherently political instrument used to achieve a political objective, so a credible political adversary is necessary for war to be war.

As the US Presidential election race hots up (or gets more one-sided, depending upon your interpretation), people continue to refer to former President George W Bush leading the US into two “wars” in Iraq and Afghanistan. Thinking about it, I’m not sure the two can actually be classified as wars.

To use a chess analogy, real wars seldom end in checkmate – they most often end in resignation, or an agreed draw. War is an instrument that is used to achieve a political objective, to get the other party to do what you want them to do.

And so war ends when one side has established such an utter dominance over the other that the counterparty decides that to resign, or “surrender” is superior to continuing fighting the war.

For this to happen, however, the counterparty needs to have a political leadership that is able and willing to take a decision, following which the war actually stops. In the absence of such a political leadership, the war will continue indefinitely until “checkmate”, and assuming that the losing side’s force “decays exponentially”, it can take a really long time for it to actually get over.

So based on this definition that war is a political instrument used to achieve a political objective, I’m not sure what happened in Iraq and Afghanistan can actually be classified as “war”.

The “government” of the day in Afghanistan (Taliban), for example, would have never come to the negotiating table with the US, so short of complete annihilation, there was no other “objective” that the US could achieve there.

Iraq, on the other hand, possessed credible political leadership (Saddam Hussein) when the US invaded, but by actually killing him, the US denied themselves the chance of a “real victory” in terms of a negotiated settlement. A game of chess might end when the king is mated (remember that the king never “dies”, only trapped), but in a situation such as Iraq, the battle will rage until each member of the opposing force is taken out.

And so fighting continues to this day, over a decade since it started, with no hope of it ending in the near future. Real wars never go on indefinitely.

Half life of pain

Last evening, the obstetrician came over to check on the wife, following the afternoon’s Caesarean section operation. Upon being asked how she was, the wife replied that she’s feeling good, except that she was still in a lot of pain. “In how many days can I expect this pain to subside?”, she asked.

The doctor replied that it was a really hard question to answer, since there was no definite time frame. “All I can tell you is that the pain will go down gradually, so it’s hard to say whether it lasts 5 days or 10 days. Think of this – if you hurt your foot and there’s a blood clot, isn’t the recovery gradual? It’s the same in this case”.

While she was saying this, I was reminded of exponential decay, and started wondering whether post-operative pain (irrespective of the kind of surgery) follows exponential decay, decreasing by a certain percentage each day; and when someone says pain “disappears” after a certain number of days, it means that pain goes below a particular  threshold in that time period – and this particular threshold can vary from person to person.

So in that sense, rather than simply telling my wife that the pain will “decrease gradually”, the obstetrician could have been more helpful by saying “the pain will decrease gradually, and will reduce to half in about N days”, and then based on the value of N, my wife could determine, based on her threshold, when her pain would “go”.

Nevertheless, the doctor’s logic (that pain never “disappears discretely”) had me impressed, and I’ve mentioned before on this blog about how I get really impressed with doctors who are logically aware.

Oh, and I must mention that the same obstetrician who operated on my wife yesterday impressed me with her logical reasoning a week ago. My then unborn daughter wasn’t moving too well that day, because of which we were in hospital. My wife was given steroidal injections, and the baby started moving an hour later.

So when we mentioned to the obstetrician that “after you gave the steroids the baby started moving”, she curtly replied “the baby moving has nothing to do with the steroidal injections. The baby moves because the baby moves. It is just a coincidence that it happened after I gave the steroids”.

Wedding videos and optimising reception queue lengths

In the past I’ve dissed wedding videos, claiming that they don’t add any value (as no one ever watches them) and only serve to slow down the queues during receptions. While I maintain that the way they are currently shot still hold up reception queues, I’ve revised my opinion about their general usefulness.

So my in-laws are preparing for the wedding of their second daughter (my sister-in-law), and in order to “revise” what needs to be done, my wife suggested we watch our wedding video. So since last night we’ve been watching our wedding videos, and I must say it’s been quite useful.

For not only are wedding videos inherently entertaining, they also capture nuances of the wedding that still photographs cannot capture. It was pertinent, for example, to observe the order in which my relatives were garlanded as we were being welcomed into the wedding ceremony.

We also got to observe how bad the crowd was immediately after the wedding when people rushed to wish us and hand over their gifts (bad but not that bad). And rather embarrassingly for me, the video showed my failed attempt at cutting the ceremonial ribbon to enter the wedding hall (I have astigmatism which my contact lenses don’t correct, which affects my perception of depth). The video also allowed me to note that the scissor to cut the ribbon was handed to me by a bureaucrat aunt, someone who I guess is well used to handing over scissors in that fashion!

Having watched the reception part of the video, though, I continue to maintain that video recordings hold up the reception procedure, and result in inordinately long queues. Moreover, the way videos are currently shot cause severe embarrassment and discomfort for the guests.

For those that are unfamiliar with south indian wedding receptions, this is what happens – you join a (typically long and wide) queue, and when you get to the head of the queue, walk on stage to greet the couple and hand over your gift. Then you all line up for the photo. So far so good.

Then you hear the click of the photographer’s shutter, and start moving, and the videographer instructs you to stay. For he is taking a “panning shot” across the width of the stage. Some 30 seconds later, the videographer instructs you to move, and the bride and groom ask you to have dinner and show you the way off stage.

The embarrassing bit for the guests, in my opinion, is that having struck a photogenic pose for the photo, they are forced to hold this pose for the duration that the videographer pans. Considering that photogenic poses are seldom comfortable, this is an unpleasant process. Moreover, guests aren’t aware when exactly the videographer is covering them, so there’s a chance they might be caught on camera making awkward body movements (possibly due to the discomfort).

Thus, I propose that rather than having the video camera straight on (next to the principal photographer) and getting a panning shot taken, the videographer should position himself on one side of the stage (the opposite side from which the guests are entering), and take a profile view of the guests wishing the bride.

This way, they capture on camera guests in more natural gestures, and the “best” front view would have anyway been captured by the still photographer. The guests can then be asked to move on as soon as the photographer’s shutter clicks (a more natural exit moment), and the time spent by each group of guests on stage could come down by more than 50% (thanks to panning time saved). And this can result in a drastic reduction in expected waiting time for a guest!

While I’d like to implement this procedure at my sister-in-law’s wedding (so what if I thoroughly failed to keep the queue length under control at my own wedding? At least I should use my learnings elsewhere!), the problem would be in finding videographers who are willing to reposition themselves.

In some sense, the videographer standing straight on, and guests waiting for a long time is a kind of a Nash equilibrium, and videographers won’t move to side on unless there’s sufficient demand from hosts to cut queue lengths at their weddings! And since moving videographers to side on is not an intuitive solution, the demand for this move from hosts will also be small.

So I guess unless we can find a videographer who is willing to experiment (not too easy), we will be stuck with front-on videos, uncomfortable guests in front of the camera, and impatient guests in the line!

Betting by other means

In India, officially, sports betting is illegal. Of course, there are lots of “underground” betting networks which we will not go into here. This post, instead, is about a different kind of “betting” on sports.

I’ve long maintained that Mahendra Singh Dhoni is grossly overrated as a cricket captain. While he did win that ICC World T20 in 2007 (back then his captaincy was pretty good), since then he’s shown himself to be too conservative as a captain. In that sense, I’m glad he retired from Tests (thus relinquishing captaincy as well) in 2014, paving the way for the more aggressive Virat Kohli to lead.

Even in limited overs games, I’ve maintained that while in the past he’s been instrumental in orchestrating chases, that ability is now on the wane, with last night’s choke being the latest example of him botching a chase. Earlier this year as well, he choked a chase in Zimbabwe. There are more such examples from the IPL as well.

Given last night’s fuck-up, I think it’s a great time to replace him as captain for limited overs games. I’m not hopeful of this happening, though, and this is in part due to the “betting at another level” that happens in elite sport.

Back in 2011 or 2012, a hashtag called #SachinRetire started making the rounds on Twitter. The context was that with the 2011 world cup having been won, it was a great opportunity for Sachin Tendulkar to retire on a high note. He continued playing on, though, in the hope of hitting “100 100s in international cricket”, the result of which was mostly mediocre cricket on his part.

Tendulkar’s 100th 100 finally came a year after his 99th, in an Asia Cup match against Bangladesh. He scored at a strike rate of 78, in a match India lost. A lot of the blame for the loss can be put on his slow rate of scoring, and consequently, on the 100th 100 hype.

It was another good opportunity to retire, but he continued playing, until a special Test series was organised in 2013 so that he could retire “at home”.

The dope in sports circles in those days was that while Tendulkar himself was keen to go, there were plenty of endorsements he was involved in, and those sponsors would have had to take a loss if he retired. Thus, the grapevine went, he had to take his sponsors into confidence and “prepare them” in order to choose an opportune time to retire.

Endorsements and sponsorships are the “other kind of betting” I mentioned earlier in the post. As soon as a sportsperson “makes it”, there is a clutch of brands who wants to cash in on his popularity by asking him to endorse them. The money involved makes it a good deal for the sportsperson as well.

By choosing to sponsor a sportsperson and getting him to endorse their brand, sponsors are effectively taking a bet on the player’s career – the better the player’s career goes, the greater the benefit for the brand from the sponsorship deal. In case the player’s career stalls, or he is caught in a scandal, the brand also suffers by association (think Tiger Woods or Maria Sharapova).

The concern with betting on sports in India is that bettors might try to influence the results of matches they’ve bet on, by possibly fixing them. This, along with “protecting the poor punter” are reasons why betting on sports is banned in India.

The problem, however, is that with this “other kind of betting” (sponsorships), the size and influence of the bettors (sponsors) means that there is a greater chance of the bettors seeking to influence the results of their investments.

A sponsor, for example, will not be happy if their “sponsee” is left out of his team, for whatever reason. Any negative impact on the sponsee’s career, from being dropped, to being demoted from captaincy to being sold to a “lesser club” negatively affects the brand value of the sponsor (by association).

And so, in cases where it’s possible (I can’t imagine a sponsor trying to influence Jose Mourinho’s decision, for example), the sponsor will try to influence selection decisions where it might benefit them. So Tendulkar’s sponsors will lobby with selectors to keep him in the team. Dhoni’s sponsors will lobby to keep him as captain. And so forth.

I’m not advocating that some kind of regulation be brought in to curb sponsors’ influence – any such regulation can only be counterproductive. All I’m saying is that betting already exists in Indian cricket, except that rather than betting on matches, bettors are betting on players! And so there is no real argument to ban “real” sports betting in India.

At least in that case, sponsors will be able to hedge their investments in the market rather than seeking to influence the powers behind the sport!

 

Brexit

My facebook feed nowadays is so full of Brexit that I’m tempted to add my own commentary to it. The way I look at it is in terms of option valuation.

While the UK economy hasn’t been doing badly over the last five years (steady strictly positive growth), this growth hasn’t been uniform and a significant proportion of the population has felt left out.

Now, Brexit can have a negative impact on two counts – first, it can have a direct adverse impact on the UK’s GDP (and also Europe’s GDP). Secondly, it can have an adverse impact by increasing uncertainty.

Uncertainty is in general bad for business, and for the economy as a whole. It implies that people can plan less, which they compensate for by means of building in more slacks and buffers. And these slacks and buffers  will take away resources that could’ve been otherwise used for growth, thus affecting growth more adversely.

While the expected value from volatility is likely to be negative, what volatility does is to shake things up. For someone who is currently “out of the money” (doing badly as things stand), though, volatility gives a chance to get “in the money”. There is an equal chance of going deeper out of the money, of course, but the small chance that volatility can bring them out of water (apologies for mixing metaphors) can make volatility appealing.

So the thing with the UK is that a large section of the population has considered itself to be “out of the money” in the last few years, and sees no respite from the existing slow and steady growth. From this background, volatility is a good thing, and anything that can shake things up deserves its chance!

And hence Brexit. It might lower overall GDP, and bring in volatility, but people hope that the mix of fortunes that stem from this volatility will affect them positively (and the negative effects go to someone else). From this perspective, the vote for Brexit is a vote of optimism, with voters in favour of Leave voting for the best possible outcome for themselves from the resulting mess.

In other words, each voter in the UK seems to have optimised for private best case, and hence voted for Brexit. Collectively, it might seem to be an irrational decision, but once you break it down it’s as rational as it gets!

Liquidity and the Trump Trade

The United States Treasury department has floated a new idea to improve liquidity in the market for treasury bonds, which has been a concern ever since the Volcker Rule came into place.

The basic problem with liquidity in the bond market is that there are a large number of similar instruments trading, which leads to a fragmented market. This is a consequence of the issuer (the US Treasury in this case) issuing a new bond every time they wish to borrow more money, and with durations being long, many bonds are in the market at the same time.

The proposed solution, which commentators have dubbed the “Trump Trade” (thanks to the Republican Presidential candidate’s penchant for restructuring debt of his companies), involves the treasury buying back bonds before they have run their full course. These bonds bought back will be paid for by newly issued 10-year bonds.

The idea here is that periodic retirement of old illiquid bonds and their replacement by a new “consolidated” bond can help aggregate the market and boost liquidity. This is not all. As the FT ($) reports,

The US Treasury would then buy older, less liquid and therefore cheaper debt across the market, which could in theory then be reissued at a lower yield. In recent months, yields on older issues have risen more than those for recently sold debt, suggesting a deterioration in liquidity.

This implies that because these “off the run” treasuries are less liquid, they are necessarily cheaper, and this “Trump Trade” is thus a win. This, however, is not necessarily the case. Illiquidity need not always imply lower price – it is more likely that it leads to wider spreads.

Trading an illiquid instrument implies that you need to pay a higher transaction cost. The “illiquidity discount” that many bonds see is because people are loathe to holding them (given the transaction cost), and thus less people are willing to buy them.

When the treasury wants to buy back such instruments, however, it is suddenly a seller’s market – since a large number of bonds need to be bought back to take it off the market, sellers can command a higher spread over the “mid price”.

Matt Levine of Bloomberg View has a nice take on the “IPO pop” which I’ve written about on this blog several times (here, here, here and here). He sees it as the “market impact cost” of trying to sell a large number of securities on the market at a particular instant.

Instead the typical trade of selling, say, $1 million of a bond with $1 billion outstanding, and paying around 0.3 percent ($3,000) for liquidity, you want to sell, say, $1 billion worth of a bond with zero bonds outstanding. That is: You want to issue a brand-new bond, and sell all of it in one day. What sort of bid-ask spread should you pay? First principles would tell you that if selling a few bonds from a large bond issue costs 0.3 percent, then selling 100 or 1,000 times as many bonds — especially brand-new bonds — should cost … I mean, not 100 or maybe even 10 times as much, but more, anyway. No?

Taking an off-the-run bond off the market is reverse of this trade – instead of selling, you are buying a large number of bonds at the same time. And that results in a market impact cost, and you need to pay a significant bid-ask spread. So rather than buying the illiquid bond for cheap, the US Treasury will actually have to pay a premium to retire such bonds.

In other words, the Trump Trade is unlikely to really work out too well – the transaction costs of the scheme are going to defeat it. Instead, I second John Cochrane’s idea of issuing perpetual bonds and then buying them back periodically.

These securities pay $1 coupon forever. Buy these back, not on a regular schedule, but when (!) the day of surpluses comes that the government wants to pay down the debt. Then there is one issue, with market depth in the trillions, and the whole on the run vs. off the run phenomenon disappears.

People don’t worry enough about liquidity when they are trying to solve other liquidity worries, it seems!