A one in billion trillion event

It seems like capital markets quants have given up on the lognormal model for good, for nobody described Facebook’s stock price drop last Thursday as a “one in a billion trillion event”. For that is the approximate probability of it happening, if we were to assume a lognormal model of the market.

Created using Quantmod package. Data from Yahoo.

Without loss of generality, we will use 90 days trailing data to calculate the mean and volatility of stock returns. As of last Thursday (the day of the fall), the daily mean returns for FB was 0.204%, or an annualised return of 51.5% (as you can see, very impressive!). The daily volatility in the stock (using a 90-day lookback period again) was 1.98%, or an annualised volatility of 31.4% . While it is a tad on the higher side, it is okay considering the annual return of 51.5%.

Now, traditional quantitative finance models have all used a lognormal distribution to represent stock prices, which implies that the distribution of stock price returns is normal. Under such an assumption, the likelihood of a 18.9% drop in the value of Facebook (which is what we saw on Thursday) is very small indeed.

In fact, to be precise, when the stock is returning 0.204% per day with a vol of 1.98% per day, the an 18.9% drop is a 9.7 sigma event. In other words, if the distribution of returns were to be normal, Thursday’s drop is 9 sigmas away from normal. Remember that most quality control systems (admittedly in industrial settings, where faults are indeed governed by a nearly normal distribution) are set for a six sigma limit.

Another way to look at Thursday’s 9.7 sigma event is that again under the normal distribution, the likelihood of seeing this kind of a fall in a day is $math ~10^{-21}$. Or one in a billion trillion. In terms of the number of trading days required for such a fall to arrive at random, it is of the order of a billion billion years, which is an order of magnitude higher than the age of the universe!

In fact, when the 1987 stock market crash (black monday) happened, this was the defence the quants gave for losing their banks’ money – that it was an incredibly improbable event. Now, my reading of the papers nowadays is sketchy, and I mostly consume news via twitter, but I haven’t heard a single such defence from quants who lost money in the Facebook crash. In fact, I haven’t come across too many stories of people who lost money in the crash.

Maybe it’s the power of diversification, and maybe indexing, because of which Facebook is now only a small portion of people’s portfolios. A 20% drop in a stock that is even 10% of your portfolio erodes your wealth by 2%, which is tolerable. What possibly caused traders to jump out of windows on Black Monday was that it was a secular drop in the US market then.

Or maybe it’s that the lessons learnt from Black Monday have been internalised, and included in models 30 years hence (remember that concepts such as volatility smiles and skews, and stochastic volatility, were introduced in the wake of the 1987 crash).

That a 20% drop in one of the five biggest stocks in the United States didn’t make for “human stories” or stories about “one in a billion billion event” is itself a story! Or maybe my reading of the papers is heavily biased!

PostScript

Even after the spectacular drop, the Facebook stock at the time of this update is trading at 168.25, a level last seen exactly 3 months ago – on 26th April, following the last quarter results of Facebook. That barely 3 months’ worth of earnings have been wiped out by such a massive crash suggests that the only people to have lost from the crash are traders who wrote out of the money puts.

The Global Financial Crisis Revisited

When we talk about the global financial crisis, one question that pops up in lots of people’s heads is about where the money went. Since every trade involves two parties, it is argued that every loser has a corresponding winner, and that most commentary about the global financial crisis (of 2008) doesn’t talk about these winners. Everyone knows about the havoc that the crisis caused when prices went down (rather suddenly). The havoc that the crisis caused when prices initially went up (rather slowly) is less well documented.

The reason winners don’t get too much footage is that firstly, they are widely distributed, and secondly they spent away all their money. Think about a stock or a CDO or a bond being a like a parcel that you play by passing the parcel. The only thing is that every time you receive the parcel, you make a payment, and then pass on the parcel after receiving a higher payment. Finally, when the whistle blows, one person has the parcel in his hand, and it explodes in his face, ruining him. We know enough about people like this. A large number of banks lost a lot of money holding parcels when the whistle blew. Some went bust, while others had to be bailed out by governments. We know enough of this story so I don’t need to repeat here.

What is interesting is about the winners. Every person who held the parcel for a small amount of time was a winner, albeit a small winner. There were several such winners, each of whom “won” a small amount of money, and spent it (remember that the asset bubble in the early noughties was responsible for increasing consumption among common people). This spending increased demand for various goods and services produced in several countries. This increasing demand led to greater investment in the production facilities of these goods and services. Apart from that, they also increased expectations of growth in demand of these goods.

The damage the crisis did on the way up was to skew expectations of growth in different sectors, thus skewing investment (both in terms of financial and human capital). The spending caused by “small wins” for consumers put in place unreasonable expectations, and by the time it was known that this increased demand came as a result of an asset bubble, a lot of capital had been committed. And this would create imbalances in the “real economy”.

Yes, the asset bubble of the last decade did produce winners. The winners begat more winners (people whose goods and services were bought). However the skewed expectations that the wins created were to cause damage in the longer term. Unfortunately, I don’t see this story being told adequately, when the financial crisis is being talked about. After all, the losers are more spectacular.

MLTR

This has nothing to do with any pop group, or any Michael or anyone learning to rock. It’s about this awesome easy-to-miss long undiscovered eatery in Gandhi Bazaar. You should definitely eat at Mahalakshmi Tiffin Room.

Situated on DVG road between Gandhi Bazaar main road and North Road it’s an old-style sit down restaurants. Small marble-topped tables with benches. Communal seating where strangers can share your table. An ancient cupboard displaying “cool drinks”. Blue walls. Waiters in dhotis. A small section cordoned off with the sign “families only”.

And divine food. Really awesome masala dosa (real masala dosa, not the species served at Vidyarthi Bhavan). Soft and oil-free khali dosas (yeah the restaurant is so old; they call it khali dosa and not set dosa). And strong coffee. And all served quicker than you could look around and take stock of the place.

I had been walking past the place for several years but it was only when Priyanka noticed it when we walked past it last April that I actually ate there. We had shared a masala dosa and a coffee then. And were so impressed that we left a 33% tip.

And it so happened that the same waiter Raju was there when we went last weekend. Again quick and efficient service. Awesome dosas. I think they make to stock the khali dosas – for they arrived within half a minute of our ordering.

Oh, and they have a weekly off on Saturdays.

Successful IPOs

Check out this article in the Wall Street Journal. Read the headline. Does this sound right to you?

MakeMyTrip Opens Up 57% Post-IPO; May Be Year’s Best Deal

It doesn’t, to me. How in the world is the IPO successful if it has opened 57% higher in the first hour (it ended the first day 90% higher than the IPO price)? To rephrase, from whose point of view has the IPO been the “best deal”?

What this headline tells me is that makemytrip has been well and truly shafted. If the stock has nearly doubled on the first day, all it means is that MMYT raised just about half the cash from the IPO as it could have raised. If not anything else, the IPO has been a spectacular failure from the company’s point of view.

The US has a screwed up system for IPOs. Unlike in India where there is a 100% book-building process where there is effectively an auction to determine the IPO price (though within a band) in the US it is all the responsibility of the bank in charge of the IPO to distribute stock (as far as I understand). Which is why working in Equity Capital Markets groups in investment banks is so much more work there than it is here – you need to go around to potential investors hawking the stock and convincing them to invest, etc.

Now, the bank usually gets paid a percentage of the total money raised in the IPO so it is in their incentive to set the price as high as they can (and the fact that they are underwriting means they can’t get too greedy and set a price no one will buy at). Or so it is designed.

The problem arises because the firm that is IPOing is not the only client of the bank. Potential investors in the IPO are most likely to be clients of other divisions of the bank (say, sales and trading). By giving these investors a “good price” on the IPO (i.e. by setting the IPO price too low), the bank hopes to make up for the commission it loses by way of business that the investors give to other divisions of the bank. If most of the IPO buyers are clients of the bank’s sales and trading division (it’s almost always the case) then what all these clients together gain by a low IPO price far outweighs the bank’s lost commission.

It is probably because of this nexus that Google decided to not raise money in a conventional way but instead go through an auction (it made big news back then, but then that’s how things always happen in India so we have a reason to be proud). Unfortunately they were able to do it only because they are google and other companies have failed to successfully raise money by that process.

The nexus between investment banks and investors in IPOs remains and unless there are enough companies that want to do a Google, it won’t be a profitable option to IPO in the US. Which makes it even more intriguing that MMYT chose to raise funds in the US and not here in India.