## Gap in giveaways and disposal

There is a gap in the market between second hand sales and garbage disposal, and I’m not sure what’s a good way to address it.

These are things that you own that might be useful for someone, but you don’t know who it might be useful for. If one such person is located, you are willing to give the stuff away for free, but you don’t want to make any effort or spend anything to dispose it.

The part of London I used to live in had evolved a simple way of achieving this – people would simply leave stuff out in their front yards very close to the footpath (the compounds didn’t have gates). People walking past were free to pick up whatever they wanted, and after things had been left out for a sufficient period of time, the council would be called and they would pick it up as “garbage”.

Unfortunately when I moved out of London earlier this year, the house we were living in was on the main road (right next to Ealing Broadway station), and this method of disposal of unwanted things wasn’t available to us. And we had to incur significant cost to dispose of some of our stuff.

The wife put up some of them on the UK equivalent of OLX, and managed to sell off a lot of our stuff for not very high amounts (though I think we got more for our mixie than what we’d paid for it 10 years ago). We made money, yes, but it possibly wasn’t significant enough to cover the cost of my wife’s time.

And then there were the books – there were no second hand bookshops available that would pay anything reasonable for the books. So I had to actually cart all the books to the local Oxfam centre to be given away to charity (apart from stuff friends picked up).

Clothes, similarly, had to be dropped off at a charity centre (there was a Cancer Research UK shop right across the road from our house, so that helped). Again, I don’t know if everything we left there was used, but that was the lowest cost way for us to dispose of them.

Coming back, this gap in the market exists in India as well. The market is a bit better here because you have house cleaners and cooks and drivers you interact with on a regular basis, who are happy to take your unwanted stuff off you and dispose it. The problem is that they are picky on what they take and dispose – they have transaction costs, just like us, and don’t want to take on stuff that they will find it hard to move on.

And what makes matters worse is that even putting it in the trash is not a proper solution here – the municipal trash collectors ask for a bribe to take these things off you!

In some sense, this is a classic market design problem – where the transaction cost of the sale overwhelms the value of items being bought and sold. The things we want to dispose of have value to someone, for which they might be willing to pay, but the costs of finding these people are so high that you end up paying to dispose them.

Basically what we need is a service where someone comes and picks up all your “semi-trash”, sorts through it to find stuff that might be useful for someone else and then transfer it to markets where it can reach people who want it. And things that aren’t useful to anyone will go into garbage.

The problem with this service is that there is a natural upper bound on what people will be willing to pay for this service – zero. And when you factor in the market for lemons here (people might use this to dispose of absolute garbage rather than semi-trash that might be useful for someone), you know why “solution doesn’t exist”.

## Monetising the side bets

If you were to read Matt Levine’s excellent newsletter regularly, you might hypothesize that the market for Credit Default Swaps (CDS) is dying. Every other day, we see news of either engineered defaults (companies being asked to default by CDS holders in exchange for cheap loans in the next round), transfer of liability from one legal entity to another (parent to subsidiary or vice versa), “orphaning” of CDSs (where on group company pays off debt belonging to another) and so on.

So what was once a mostly straightforward instrument (I pay you a regular stream of money, and you pay me a lumpsum if the specified company defaults) has now become an overly legal product. From what seemed like a clever way to hedge out the default risk of a loan (or a basket of loans), CDSs have become an over-lawyered product of careful clauses and letters and spirits, where traders try to manipulate the market they are betting on (if stuff like orphaning or engineered default were to happen in sports, punters would get arrested for match-fixing).

One way to think of it is that it was a product that got too clever, and now people are figuring out a way to set that right and the market will soon disappear. If you were to follow this view, you would thin that ordinary credit traders (well, most credit traders work for large banks or hedge funds, so not sure this category exists) will stop trading CDSs and the market will die.

Another way to think about it is that these over-legalistic implications of CDSs are a way by the issuer of the debt to make money off all the side bets that happen on that debt. You can think about this in terms of horse racing.

Horse breeding is largely funded by revenues from bets. Every time there is a race, there is heavy betting (this is legal in most countries), and a part of the “rent” that the house collects from these bets is shared with the owners of the horses (in the form of prizes and participation fees). And this revenue stream (from side bets on which horse is better, essentially) completely funds horse rearing.

CDSs were a product invented to help holders of debt to transfer credit risk to other players who could hedge the risk better (by diversifying the risk, owning opposite exposures, etc.). However, over time they got so popular that on several debt instruments, the amount of CDSs outstanding is a large multiple of the total value of the debt itself.

This is a problem as we saw during the 2008 financial crisis, as this rapidly amplified the impacts of mortgage defaults. Moreover, the market in CDSs has no impact whatsoever on the companies that issued the debt  – they can see what the market thinks of their creditworthiness but have no way to profit from these side bets.

And that is where engineered defaults come in – they present a way for debt issuers to actually profit from all the side bets. By striking a deal with CDS owners, they are able to transfer some of the benefits of their own defaults to cheaper rates in the next round of funding. Even orphaning of debt and transferring between group companies are done in consultation with CDS holders – people the company ordinarily should have nothing to do with.

The market for CDS is very different from ordinary sports betting markets – there are no “unsophisticated players”, so it is unclear if anyone can be punished for match fixing. The best way to look at all the turmoil in the CDS market can thus be looked at in the same way as horse rearing – an activity being funded by “side bets”.

## Government and markets

It’s been a while since I wrote a post like this one – I remember a decade ago, I used to flood my blog with such stuff.

In any case, last week, in response to the “10yearchallenge” meme, Nitin Pai of Takshashila wrote an Op-Ed in the Print on how India has changed in 10 years. While he admits that the country has grown and the lives of people has improved in some ways, the article leads with the headline that India should be be ashamed of what has happened in the last 10 years. This paragraph is possibly representative of the article:

While individual Indians seem to have done well over the past decade, India is more or less where it was. Worse, politics and policy priorities seem to have regressed to 1989.

Reading through the article (I encourage you to read it, it’s good – never mind the headline), I found a clear and distinct pattern in the kind of things where things have gotten better in India and where things have gotten worse.

Everything where markets function, or where the government doesn’t have much of a role, things have changed significantly for the better. Everything where the government has an outsized role, either because it is the government’s job or the sector is overregulated, things have gotten worse. So our cities have gotten more crowded. Infrastructure has gotten worse. Law and order has regressed. And this has had little to do with the party in power – whatever the government touched has regressed.

Looking at it in another way, Indians seem to be highly capable of making their lives better by coordinating using the invisible hand of the market. However, we seem incapable of making our lives better by coordinating using the government process.

From this perspective, there is one easy way to progress – basically reduce the government. Get rid of the overregulations. Get the government out of things where it shouldn’t be. Give a freer hand to the market.

Unfortunately, ahead of general elections this year, we see most parties taking a highly statist line. This is a real tragedy.

## How markets work

A long time back, there was this picture that was making the rounds on Twitter and (more prominently) LinkedIn. It featured three boys of varying heights trying to look over a fence to see a ball game.

Here is what it looked like:

These pictures were used to illustrate that equality of outcomes is not the equality of opportunity, or some such things, and to make a case for “justice”.

As it must be very clear, the allocation of blocks on the right is more efficient than the allocation of the blocks on the left – the tallest guy simply doesn’t need any blocks, while the shortest guy needs two.

And if you think about it, you don’t need any top-down “justice” to allocate the blocks in the right manner. All it takes is a bit of logical thinking and markets – and not even efficiently.

Think about how this scenario might play out at the ball park. The three boys go to see the ball game, and see three blocks at the fence. Each of them climbs a block, and we get the situation on the left.

Shortest boy realises he can’t see and starts crying. There are many ways in which this story can play out from here onward:

1. Tallest boy realises that he doesn’t really need that extra block, and steps down and gives it to the shortest guy, giving the picture on the right.
2. Tallest boy continues to stand on his block. Shortest boy realises that the tallest boy doesn’t need it, and requests him for the block. Assuming tallest boy likes him, he will give him the block.
3. Tallest boy continues on the block. Shortest boy requests for it, but tallest boy refuses saying “this is my block why should I give it to you?”. Shortest boy negotiates. Tells tallest boy he’ll give him a chocolate or some such in return for the block. And gets the block.
4. Tallest boy doesn’t want chocolate or anything else the shortest boy offers. In fact he might want to settle a score with the shortest boy and refuses to give the block. In this case, the shortest boy realises there is no point being there and not watching the ball game, and makes an exit. In some cases, the middle boy might negotiate with the tallest boy on his behalf, leading to the transfer of the block. In other situations, the shortest boy simply goes away.

Notice that in none of these situations (all of them reasonably “spontaneous”) does the picture on the left happen. In other words, it’s simply unrealistic. And you don’t need any top down notion of “justice” to enable the blocks to be distributed in a “fair” manner.

## Understanding Stock Market Returns

Earlier today I had a short conversation on Twitter with financial markets guru Deepak Mohoni, one of whose claims to fame is that he coined the word “Sensex”. I was asking him of the rationale behind the markets going up 2% today and he said there was none.

While I’ve always “got it” that small movements in the stock market are basically noise, and even included in my lectures that it is futile to fine a “reason” behind every market behaviour (the worst being of the sort of “markets up 0.1% on global cues”), I had always considered a 2% intra-day move as a fairly significant move, and one that was unlikely to be “noise”.

In this context, Mohoni’s comment was fairly interesting. And then I realised that maybe I shouldn’t be looking at it as a 2% move (which is already one level superior to “Nifty up 162 points”), but put it in context of historical market returns. In other words, to understand whether this is indeed a spectacular move in the market, I should set it against earlier market moves of the same order of magnitude.

This is where it stops being a science and starts becoming an art. The first thing I did was to check the likelihood of a 2% upward move in the market this calendar year (a convenient look-back period). There has only been one such move this year – when the markets went up 2.6% on the 15th of January.

Then I looked back a longer period, all the way back to 2007. Suddenly, it seems like the likelihood of a 2% upward move in this time period is almost 8%! And from that perspective this move is no longer spectacular.

So maybe we should describe stock market moves as some kind of a probability, using a percentile? Something like “today’s stock market move was a top 1%ile  event” or “today’s market move was between 55th and 60th percentile, going by this year’s data”?

The problem there, however, is that market behaviour is different at different points in time. For example, check out how the volatility of the Nifty (as defined by a 100-day trailing standard deviation) has varied in the last few years:

As you can see, markets nowadays are very different from markets in 2009, or even in 2013-14. A 2% move today might be spectacular, but the same move in 2013-14 may not have been! So comparing absolute returns is also not a right metric – it needs to be set in context of how markets are behaving. A good way to do that is to normalise returns by 100-day trailing volatility (defined by standard deviation) (I know we are assuming normality here).

The 100-day trailing SD as of today is 0.96%, so today’s 2% move, which initially appears spectacular is actually a “2 sigma event”. In January 2009, on the other hand, where volatility was about 3.3% , today’s move would have been a 0.6 sigma event!

Based on this, I’m coming up with a hierarchy for sophistication in dealing with market movements.

1. Absolute movement : “Sensex up 300 points today”.
2. Returns: “Sensex up 2% today”
3. Percentile score of absolute return: “Sensex up 3%. It’s a 99 %ile movement”
4. Percentile score of relative return: “Sensex up 2-sigma. Never moved 2-sigma in last 100 days”

What do you think?

## China, Reporting and Bias

The amount of attention that the rising Chinese stock market received over the last one year is nothing close to the attention that the falling market has received over the past month or so.

While the markets have fallen by at least a fourth, which is more than what the Dow Jones Industrial Average (DJIA) fell on Black Monday, the fact is that this followed nearly a year of insane rise in the markets, the fact is that markets are still up 80% over a year ago.

I hereby present two charts. Both are time series and hence drawn as lines, and both start from 1st of January 2014. The first shows the SSE Composite Index  (refer to Yahoo finance for a more interactive plot. I couldn’t embed the chart here).

The second shows the Google Trends for “China Stock Markets” over the same time period.

I don’t think I need to explain much further. On the way up, there was little commentary on China’s markets, apart from that there might be a bubble. On the way down, though, there is so much more!

The asymmetry in markets is rather intriguing!

## The NRN premium is over

With the resignation of Infosys President BG Srinivas and the subsequent drop in the share price in the markets today, the NR Narayana Murthy premium on the Infosys stock is over. Ironically, this happens almost exactly a year since NRN made a comeback to the company in an executive capacity.

The figure below charts how the Infosys stock and the market index (Nifty ) have moved in the last one year. In order to compare the two, we have indexed their prices as of 30th May 2013, just before NRN’s return was announced (the announcement was made as of 2nd June, but the sharp spike in Infy on 31st May 2013, when the broad market fell, can be attributed to insider trading by people in the know), to 100. Notice how the Infosys stock soared in the six months after NRN’s return. In January and February, the stock traded at a 60% premium to its pre-NRN value, while the nifty was practically flat till then.

And then things started dropping. Even when the broad markets rose in March-April this year, Infosys continued to fall. The rally in early-mid May took it along, but now the stock has fallen again. This morning (latest data as of noon), the stock has fallen by about 6% thanks to Srinivas’s departure, and we can see that the gap between Infy and the market has really narrowed.

Next, we look at the ratio of the Infy price to the market index. Again we index it to 100 as of 30th May 2013. This graph shows the premium in the Infy share price over the last year. Notice that for the first time, the premium has fallen below 10% (it’s currently 7%).

Finally, we will compare the Infy stock to the CNX IT index, which tracks the sector (that way, any sectoral premium in Infy can be extracted out). Again, we will plot the relative values of Infy to the CNX IT index, indexed to 100 as of 30th May 2013.

This graph looks like no other. What this tells us is that whatever premium Infosys enjoys over the broad market is a function of the sector, and that ever since the sharp drop in early March (on account of weak results), the NRN premium on the Infy stock relative to the sector has disappeared. As of now, compared to the sector, Infy is at an all time low.

Finally, a regression. If we regress infy stock returns against the returns in the IT index and Nifty, what we find is that Nifty returns hardly affect Infosys returns (R^2 of 7%), while the IT Index returns explain about 76% of Nifty returns. When regressed against both, Nifty returns come out as insignificant and the R^2 remains at 76%.

Putting all these statistics aside, however, the message is simple – the NRN premium on the Infy stock is over.

## Why standard deviation is not a good measure of volatility

Most finance textbooks, at least the ones that are popular in Business Schools, use standard deviation as a measure of volatility of a stock price. In this post, we will examine why it is not a great idea. To put it in one line, the use of standard deviation loses information on the ordering of the price movement.

As earlier, let us look at two data sets and try to measure their volatility. Let us consider two time series (let’s simply call them “series1” and “series2”) and try and compare their volatilities. The table here shows the two series:

What can you say of the two series now? You think they are similar? You might notice that both contain the same set of numbers, but jumbled up.  Let us look at the volatility as expressed by standard deviation. Unsurprisingly, since both series contain the same set of numbers, the volatility of both series is identical – at 8.655.

However, does this mean that the two series are equally volatile? Not particularly, as you can see from this graph of the two series:

It is clear from the graph (if it was not clear from the table already) that Series 2 is much more volatile than series 1. So how can we measure it? Most textbooks on quantitative finance (as opposed to textbooks on finance) use “Quadratic Variation” as a measure of volatility. How do we measure quadratic variation?

If we have a series of numbers from $a_1$ to $a_n$, then the quadratic variation of this series is measured as

$sum_{i=2 to n} (a_i - a_{i-1})^2$

Notice that the primary difference feature of the quadratic variation is that it takes into account the sequence. So when you have something like series 2, with alternating positive and negative jumps, it gets captured in the quadratic variation. So what would be the quadratic variation values for the two time series we have here?

The QV of series 1 is 29 while that of series 2 is a whopping 6119, which is probably a fair indicator of their relative volatilities.

So why standard deviation?

Now you might ask why textbooks use standard deviation at all then, if it misses out so much of the variation. The answer, not surprisingly, lies in quantitative finance. When the price of a stock (X) is governed by a Wiener process, or

$dX = sigma dW$

then the quadratic variation of the stock price (between time 0 and time t) can be shown to be $sigma^2 t$, which for t = 1 is $sigma^2$ which is the variance of the process.

Because for a particular kind of process, which is commonly used to model stock price movement, the quadratic variation is equal to variance, variance is commonly used as a substitute for quadratic variation as a measure of volatility.

However, considering that in practice stock prices are seldom Brownian (either arithmetic or geometric), this equivalence doesn’t necessarily hold.

This is also a point that Benoit Mandelbrot makes in his excellent book The (mis)Behaviour of Markets. He calls this the Joseph effect (he uses the biblical story of Joseph, who dreamt of seven fat cows being eaten by seven lean foxes, and predicted that seven years of Nile floods would be followed by seven years of drought). Financial analysts, by using a simple variance (or standard deviation) to characterize volatility, miss out on such serial effects.

## Stock market volatility spikes

The Indian stock markets have become especially volatile. Figure 1 shows the volatility of the Nifty in the last three years. As usual, we use a trailing 30-day quadratic variation as a measure of volatility. Don’t bother about the units of the y-axis, just look at the relative movement.

Notice that the volatility levels we have seen in the last month or so are unprecedented in the last three years. Let us take a closer look:

This gives us a better picture. Volatility was well under control till mid-August, when it started rising (since we use a 30-day trailing QV, this means that markets started getting choppy in mid-July). The volatility is now at an all-time high.

However, the official volatility index (India VIX) disagrees. According to this, volatility has actually dropped from its all-time high. The VIX also looks significantly choppy.

Perhaps this indicates some trading opportunity in options?