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?

Narendra Modi should short the Nifty

The common discourse is that businesses like Gujarat chief minister Narendra Modi, and that India’s economic growth would get back on track if he were to become PM following the elections this summer. For example, this view was articulated well by my Takshashila colleague V Anantha Nageswaran in an Op-Ed he wrote for Mint last Tuesday, where he spoke of a “binary outlook for India” – either economic growth under Modi or further populism and stagnation under a Third Front.

Based on this view being the consensus, one can expect that the Indian stock market would go up significantly in case of a Narendra Modi victory, and would tank in case the Modi (and/or his party BJP) ends up doing badly. So what should Modi do?

He should short the stock markets, and fast. He needs money to run his campaigns, and he might be taking funds from friends and well-wishers, who expect some kind of payback in kind if/when Modi becomes PM. The question, however, is how he will pay them back in case he fails to become PM!

He will not have the power to pay back in kind. There is only so much he will be able to do as the Chief Minister of Gujarat. And given that he has got a lot of fair weather friends over the last couple of years, some of them might be disappointed that he didn’t become PM, and will ask for immediate payment. So how does Modi service these debts?

A part of his campaign budget should go into shorting the Nifty – perhaps by means of buying puts (with a May expiry – not sure they’re traded yet). This way, in case of his victory, he will end up losing his premium, but he will be able to pay back his creditors in kind, since he will be PM. In case he loses? The markets will tank anyway, and he will end up making a packet on these puts, which can then be used to pay back his current well=wishers!

Easy, no?

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.

Source: Yahoo
Source: Yahoo

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:

Source: Yahoo
Source: Yahoo

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.

Source: NSE
Source: NSE


Perhaps this indicates some trading opportunity in options?


I made some money in the markets last week. I bought the Nifty (September futures) at around 5190 on the 28th of August and cashed out at 5660 on the 6th of September. A fair trade I think, considering that so far in my life I’ve been a fairly poor investor (despite having worked as a quant at an investment bank and a hedge fund). This trade, however, raised more questions than answers.

Firstly, the markets have gone up significantly after I sold out. I exited at 5660. The Nifty closed today at well over 5900. Last couple of days I’ve been wondering if I panicked and cashed out too early. I must admit that when I entered I had a target price of 6000. However, given the rather choppy nature of the Indian markets, I decided that the 10% appreciation in 10 days was enough and cashed out. To that extent, I didn’t stay honest to the strategy I entered the trade in.

However, the reason I decided to cash out when I did was that I thought the market was going to top out and a steep fall was imminent. From that perspective, it made sense to cash out when I did. Yes, I might have made more money had I hung on for another two trading days, but there was no guarantee that the markets would continue to rise. In that sense I was happy pulling out.

More importantly when I cashed out, I realized that I’m still an amateur at investing. When you are a professional investor, you look at investment vehicles in terms of opportunity cost. If you wanted to pull out of the Nifty, you would do so only if you could put your money in another investment which would give you superior returns to what the Nifty would in the subsequent time period (technically hard currency is also an investment!), after accounting for the transaction cost of switching. As far as I was concerned here, though, I still invest basically for kicks (don’t invest huge amounts). So it’s basically about spotting a potential boom, riding it and then moving out. Light touch investing.

There are times when I want to get back to the world of investment (as a professional). I have some unique ideas for fund management. Perhaps I should use my next break in billable work to flesh that out. For now, check out my only other post on investing – on why you should not track your portfolio too closely. 

Bloomberg Watching

Two weeks back we were all given dual screens at office. A couple of days after that, those of us that had joined recently got Bloomberg logins. It’s a very restricted version of Bloomberg, with most of the strong features having been disabled. One feature that is enabled, though, is to get the graph of the daily price movement of a security, or an index.

It is necessary to have hobbies at work. It is humanly impossible to concentrate solely on the work for all the eight or ten hours that you spend at office. You need distractions. However, in order to prevent yourself from being too distracted, it helps having one or two very strong distractions. Distractions which can crowd out all other distractions. They can be called “office hobbies”.

In the past, my office hobbies haven’t really been constructive. In my first job, I was part of a PJ Club, and we would exchange horrible jokes. By the time I got to my next job, I had been addicted to Orkut, and kept refreshing it to check if I’d gotten any new scraps. Of course, when there is a cricket match on, the Cricinfo screen makes for a good office hobby. In the last ten days, the World Chess Championship has served my evenings well. However, it is important to have a sustainable hobby which could also be constructive. One which might have a small chance of making impact on your work. And most importantly, it would be ideal if the boss doesn’t really disapprove of your office hobby.

For the last week and half at work, my right screen (remember that I have two screens) has been reserved for Bloomberg Watching. A Bloomberg window is open there in full size, and I would’ve usually put the daily movement graph of the Nifty there. And it updates real-time. It’s like a video game. I just sit and watch. And get fascinated by the kind of twists and turns that the markets take.

Twenty years back, I would spend my evenings in the courtyard of my grandfather’s house in Jayanagar watching ants move about. I would be fascinated by their random, yet orderly movements. I would spend hours together watching them.

Around the same time, I used to play another game. I used to splash water on the (red-oxide coated) walls of my loo, and watch the different streams of water flow down as i crapped. I would get fascinated by the patterns that the water droplets would form, the paths that they would take, the way they would suddenly change speed when they intersected, and so forth. I would end up squatting there long after I’d been done with my crap.

So what I’m doing now is not exactly new. I just watch a point move. Orderly from left to right. Wildly fluctuating in the up-down direction. I look at the patterns and try to guess which animal they look like, or which country they look like. I get fascinated by the sudden twists and turns that the curve takes, and wonder about the collective wisdom of all market participants who are faciliating such movement. I occasionally scream out to my colleagues saying stuff like “nifty below 2600!” and they respond with a “behenchod…” or some equivalent of it.

As the day wears on, I realized that some animals I had recognized earlier in the day are hardly visible now. They are but specks in the larger graph that is the day. And then I realize that unless there was something truly special, the movement of the day will also soon be lost. It will be available for download from the same Bloomberg terminal but that will be about it. And so forth.

Occasionally I catch some unsuspecting soul on my GTalk list and spout such philosophy. I tell them about how after a while everything becomes insignificant. About how we will always be just small players in the larger system. The smarter among them will add their own philosophy to mine, and sometimes we come up with a new theory. The not so smart among them – they will ask me about my views on the market. And what would be good picks (this has been a regular question I’ve been asked ever since I got back into the finance industry but more about that later). And then they say something like how terrorists are the reason the stock markets are plunging, and how the government should protect investors’ money and stuff.

Some day I hope all of this will be useful. Some day I hope my eye for recognizing animals and countries where none exist will enable me to come up with some earthshaking strategy, which can make millions for my fund. However, now that doesn’t matter. All that matters is the unbridled joy of watching the ticker move up and down. Rise and fall. Take baby steps, and the occasional giant leap. It’s surreal.