## More On Direct Listings

Regular long-time readers of this blog might know that I’m not a big fan of IPO pops (I’ve written about them at least four times so far: one, two, three and four). You can think of this as Number Five, though this is specifically about Direct Listings.

In case you don’t have patience to click through and read my posts, what is the big deal about direct listings? And what is the problem with traditional IPOs? To put it simply, companies looking to raise capital through IPOs are playing a one-time game (you only do an IPO once), while companies that are investing in them are playing a repeated game (they participate in pretty much every IPO that comes on the market – ok may be not WeWork).

This means that investment banks, which stand between the buyer and the seller in such cases, have an incentive to structure the deal to favour the (repeated) buyers, and they price the IPO conservatively. This means that when the company actually lists on the market, it usually does so at a price higher than the IPO price, resulting in a quick win for the IPO investors.

This is injurious for the original investors in the company (founders, VCs, employees) since they are “leaving money on the table”. A pop of 10-20% is considered fair game (a price for the uncertainty on how the market will react to the IPO), but when MakeMyTrip lists 60% higher, or Beyond Meat lists 160% up, it is a significant loss to the early shareholders.

Over the last few months (possibly after the Beyond Meat IPO), Silicon Valley has woken up to this problem of the IPO pop, and suggested that the middleman (equity capital markets divisions of investment banks) be disintermediated from the IPO process. And their vehicle of choice for disintermediation is the direct listing.

A direct listing is what it is. Rather than raising fresh capital from the market, the company picks an auspicious date and declares that on that date its stock will list on the exchanges. The opening auction in the exchange on that day sets what is effectively the IPO price, and the company is public just like that.

Spotify was among the first well-known companies in recent times to do a direct listing, when it went public in 2018. Earlier this year, Slack did a direct listing as well. Here is Benchmark Capital’s Bill Gurley (a venture capitalist) on the benefits of a direct listing.

Direct Listing is all well and good when a company doesn’t have to raise capital. The question is how do you go public while at the same time raising capital (which is what a traditional IPO does)? Slack and Spotify were able to do the direct listing because they didn’t want capital from the IPOs – they just wanted to offer liquidity to their investors.

The New York Stock Exchange thinks it can be done, and has proposed a product where companies can use the opening daily auction to price the new shares being offered. There are issues, of course, about things like supply of shares, lock-ups, price support and so on, but the NYSE thinks this can be done.

NYSE’s President Stacey Cunningham recently appeared on the a16z podcast (again run by a VC, notice!) and spoke eloquently about the benefits of direct listing.

The SEC (stock regulator in the US) isn’t very happy with the proposal, and rejected it. Traditional bankers are not happy with the NYSE’s proposal, either, and continue to find problems with it (my main source of this angst is Matt Levine, who is a former ECM Banker and who thus has solid reasons as to why ECM Bankers should exist). In any case, the NYSE has refiled its proposal.

So what is the deal with direct listings?

In a way, you can think about them as a way to simply disintermediate the market. The ECM Banker, after all, is a middleman who stands between the buyer (IPO investor) and seller (company raising capital), helping them come up with a smooth deal, for a fee. The process has been set for about 40 years now, and has become so stable that the sellers think it has become unfair to them. And so there is the backlash.

Until now, the sellers were all independent entities with their own set of investors, and so they were unable to coordinate and express their displeasure with the IPO process. The buyers, on the other hand, play the game repeatedly, and can thus coordinate among themselves and with the middlemen to give themselves a sweet deal.

The development in this decade is that the same set of VC investors invest in a large number of go-to-public companies, and so suddenly you have sellers who are present across deals, and that has changed the game in a sense. And so direct listings are on every tech or investing podcast.

Among the things I wrote in my book (which came out a bit over two years ago) is that one important role that middlemen play is to reduce uncertainty and volatility in the market.

One concern with direct listings is that there can be a wide variation in the valuations by different players in the market, and the opening auction is not an efficient enough process to resolves all these variations. The thing with the Spotify and Slack listings was that there was a broad consensus on the valuation of these companies (more in line with public company valuations), a set of investors who wanted to get in and a set of investors who wanted to get out. And so it all went smoothly.

But what do you do with something like WeWork? The problem with private market valuations is that with players like SoftBank, they can be well divorced from market realities. In WeWork’s case, the range of IPO valuations that came up differed by an order of magnitude. And that kind of difference is not usually reconcilable in one normal opening auction (imagine a bid of 8 billion and an ask of 69 billion, and other numbers somewhere in between) without massive volatility going forward. In that sense, the attempted traditional IPO did a good job of understanding demand and supply and just declaring “no deal”. “No deal” is usually not an option when you do a direct listing.

OK I’ve written a lot I know (this is already 2X the length of my usual blog posts), so what do I really think about IPOs? I think all this talk about direct listings will shift the market ever so slightly in favour of the sellers. Companies will follow a mixed strategy – well known companies (consumer brands, mostly) with stable valuations will go for direct listings. Less well known companies, or those with unstable valuations will go for IPOs.

And in the latter case, I predict that we will move closer to a Dutch auction (like what Google did) among the investors rather than the manual allocation process that ECM bankers indulge in nowadays. It will have the benefit of large blocks being traded at time zero, at a price considered fair by everyone, and hopefully low volatility.

## Housing

The Bank of England’s Bank Underground blog has two excellent posts on house prices (first this one, then this one). The basic idea is that houses are assets, not goods, since the “goods” consumed is “living”, which is basically a point in time thing.

As the first of these posts points out:

You can’t buy flowers when they are cheap and store them for months until Valentine’s day. Similarly, you can’t store housing services by, say, renting two flats this year and saving one’s rental services for next year. So the price of rents is determined “on the spot” by the current balance of demand and supply of places to live. Add a load of extra people and/or make them richer and the higher demand pushes up rents. Boost supply and rents fall.

Combined with this comes the news that a friend’s parents have moved to Mysore (from Bangalore) for their retirement.

Taking these blogposts, and this piece of news, together, I’m beginning to reconsider my views on housing.

About 7-8 years back, I got “personal finance advice” that one needs to start “saving for retirement” at age 30, and one of the best ways of doing that is to buy a house. I was about to turn 30 around then, and I took this advice seriously enough to invest in an apartment in 2014. Looking at it five years on, I’m not sure buying a house for retirement in your thirties is the best idea.

For starters, India is (still) a fast-growing and fast-changing nation, so I have no clue what are going to be good places to live 10 years down the line (forget 30 or 40, at which point I’ll retire).

Secondly, my needs from a house now are very different from what they will be 30 or 40 years down the line. For example, right now, my daughter’s school is a “fixed point” (assuming I don’t want to change that), and I need a house that isn’t too far from there. As she grows up and grows out of school, this will cease to be a factor.

Similarly, the work that I do demands a certain pattern of travel in the city, and that again guides my choice of place to live. This is likely to change as the years go by as well.

Then, what I need from my house and my surroundings are likely to change as well. For example, I might want peace and quiet right now, and might be willing to take my car everywhere. At some other point in time, I might place a higher premium on shops in a walkable distance. Similarly, my preferences on entertainment activities might change as well.

Taking all this into account, making a housing decision now on where I want to live 15-20 years down the line is futile. There are simply too many variables and any decision I take now will only lock me in to something that is possibly not optimal.

From that point of view I need to look at my needs over the next 10-15 years (when things will change, but maybe not by that much) to make my current investing decisions. This includes rent/buy/sell decisions, taking into account whatever I’m optimising for now, and will in the next few years. And if I’m setting aside money to “buy a house for retirement” now, I should simply just focus on saving and growing that money so that I can make an informed decision at a time when it matters, and matters are more clear.

## 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”.

## Advertising Agencies: From Brokers to Dealers

The Ken, where I bought a year long subscription today, has a brilliant piece on the ad agency business (paywalled) in India. More specifically, the piece is on pricing in the industry and how it is moving from a commissions only basis to a more mixed model.

Advertising agencies perform a dual role for their clients. Apart from advising them on advertising strategy and helping them create the campaigns, they are also in charge of execution and buying the advertising slots – either in print or television or hoardings (we’ll leave online out since the structure there is more complicated).

As far as the latter business (acquisition of slots to place the ad – commonly known as “buying”) is concerned, typically agencies have operated on a commission basis. The fees charged has been to the extent of about 2.5% of the value of the inventory bought.

In financial markets parlance, advertising agencies have traditionally operated as brokers, buying inventory on behalf of their clients and then charging a fee for it. The thrust of Ashish Mishra’s piece in ate Ken is that agencies are moving away from this model – and instead becoming what is known in financial markets as “dealers”.

Dealers, also known as market makers, make their money by taking the other side of the trade from the client. So if a client wants to buy IBM stock, the dealer is always available to sell it to her.

The dealer makes money by buying low and selling high – buying from people who want to sell and selling to people who want to buy. Their income is in the spread, and it is risky business, since they bear the risk of not being able to offload inventory they have had to buy. They hedge this risk by pricing – the harder they think it is to offload inventory, the wider they set the spreads.

Similarly, going by the Ken story, what ad agencies are nowadays doing is to buy inventory from media companies, and then selling it on to the clients, and making money on the spread. And clients aren’t taking too well to this new situation, subjecting the dealers ad agencies to audits.

From a market design perspective, there is nothing wrong in what the ad agencies are doing. The problem is due to their transition from brokers to dealers, and their clients not coming to terms with the fact that dealers don’t normally have a fiduciary responsibility towards their clients (unlike brokers who represent their clients). There are also local monopoly issues.

The main service that a dealer performs is to take the other side of the trade. The usual mechanism is that the dealer quotes the prices (both buy and sell) and then the client has the option to trade. If the client feels the dealer is ripping her off, she has a chance to not do the deal.

And in this kind of a situation, the price at which the dealer obtained the inventory is moot – all that matters to the deal is the price that the dealer is willing to sell to the client at, and the price that competing dealers might be charging.

So when clients of ad agencies demand that they get the inventory at the same price at which the agencies got it from the media, they are effectively asking for “retail goods at wholesale rates” and refusing to respect the risk that the dealers might have taken in acquiring the inventories (remember the ad agencies run the risk of inventories going unsold if they price them too high).

The reason for the little turmoil in the ad agency industry is that it is an industry in transition – where the agencies are moving from being brokers to being dealers, and clients are in the process of coming to terms with it.

And from one quote in the article (paywalled, again), it seems like the industry might as well move completely to a dealer model from the current broker model.

Clients who are aware are now questioning the point of paying a commission to an agency. “The client’s rationale is that is that it is my money that is being spent. And on that you are already making money as rebate, discount, incentive and reselling inventory to me at a margin, so why do I need to pay you any agency commissions? Some clients have lost trust in their agencies owing to lack of transparency,” says Sodhani.

Finally, there is the issue of monopoly. Dealers work best when there is competition – the clients need to have an option to walk away from the dealers’ exorbitant prices. And this is a bit problematic in the advertising world since agencies act as their clients’ brokers elsewhere in the chain – planning, creating ads, etc.

However the financial industry has dealt with this problem where most large banks function as both brokers and dealers. It’s only a matter of time before the advertising world goes down that path as well.

PS: you can read more about brokers and dealers and marketplaces and platforms in my book Between the Buyer and the Seller

## Investing in ETFs

So I put some money in an ETF today. This isn’t the first time I invested in one. A long time back, before my then employer had bought and essentially killed Benchmark, I had invested in a couple of their ETFs – the Nifty ETF to get invest in the broad Indian market, and GoldBees to hedge against increase in the price of gold as I was planning my wedding.

I had some Rupees lying around in my bank account for a long time, and given that the Indian markets have tanked, I thought this is a good time to get invested. In fact, this isn’t the first time in recent times I’m having such a thought – about a month back I had put in more money into the Indian markets, but had then chosen a low cost index tracking mutual fund (and I’m not tracking how my investment is doing).

Anyway, today I decided to invest in ETFs since the transaction costs (in terms of both trading, and annual expenses) are much lower. A quick chat with a friend currently trading the Indian markets revealed that the SBI Nifty ETF is the best option to go with, and I was left with the small matter of just making the investment.

I’m generally happy with ICICI Direct as my broker, since in general the interface and app are pretty nice. Last month, the purchase of the mutual fund through the same app had been pretty simple. And I imagined buying the ETF will be easy as well. It wasn’t. And if I, as a professional investor with considerable capital markets experience, find it hard to invest in ETFs, I can only imagine how hard it might be for mango people to invest in them.

So the points of pain, in order, that prevent people from investing in ETFs:

1. Knowing that indexing exists. Most people seem to think that the only ways to invest are by researching the stocks themselves, or by paying an asset manager fairly hefty fees.
2. Once you know you can index, the fact that you can do it through an ETF. ETFs are again not well known, and not really marketed broadly since their fees are low (with Benchmark’s demise, we don’t really have ETF-first fund houses in India, like we have Vanguard in the US).
1. Related, even some of the more popular robo advisory funds in India largely use mutual funds, rather than ETFs.
3. Once you know you can index, and do so through an ETF, the next task is to find out which ETF you should invest in. Literature exists, but is not easy to find. My friend sent me this page, and asked me to select the fund with highest market size. Knowing that I want to invest in the broad market, and in large caps, the choice of SBI Nifty ETF was easy for me.
1. But it’s not so intuitive for a less sophisticated investor. For example, correlating asset size with liquidity isn’t exactly intuitive.
2. Different ETFs track different indices, and knowing which one to invest in is again not a trivial task.
4. Having selected an ETF to invest in, you go to your broker’s site or app (I used the app). And you need to know that ETFs are clubbed with equities, and not with mutual funds (not an intuitive classification for most people)
5. So I go to ICICI Direct’s Equities page, allocate funds to it (from my bank account, also with ICICI), and hit “buy”. There’s a text box where I need to enter what I’m looking for, and then there’s a dropdown that pops up.

I type “SBI”, and the first thing it shows is the SBI Bank Nifty tracker. This is followed by lots of bonds. I don’t know if it’s clever nudging on ICICI’s part to get you to invest in the Bank Nifty, since that has a significant exposure to ICICI, or if it’s something as mundane as alphabetical sorting. The latter is more likely.

6. Scrolling down the list past all the bonds, it’s not easy to know which is the SBI Nifty ETF. Because there’s a “SBI Nifty Next 50 ETF” (smaller caps, so more volatile, not something I want), and a few others with confusing names.
7. Then you need to enter the number of units you need to purchase. This is unlike in mutual funds where you just enter the amount you want to invest. Here I had to pull up a calculator to know exactly how many units I had to buy.
8. I hit “market order”, and then on the next screen I got a warning that since this wasn’t a particularly liquid instrument I was only allowed to post limit orders. So I had to guess what was a reasonable spread I was willing to pay, and put that. Thankfully the ETF was fairly liquid, and I got execution close to mid.

Honestly, I felt rather daunted at the end of the exercise, and I’m what most people would classify as a sophisticated investor. So there is no wonder that more people aren’t investing in ETFs.

The advantage of ETFs is extremely low fees (the fund I purchased today charges 7 basis points a year), and one downside of it is that it doesn’t allow for more marketing budget.

I’m beginning to think that the way to “solve” this market is by having a bundled ETF and robo advisory offering. Perhaps more on that later.

## Suckers still exist

1. You give Citigroup Inc. $1,000, when Amazon.com’s stock is at$1,339.60.
2. At the end of each quarter for the next three years, Citi looks at Amazon’s stock price. If it’s at or below $1,339.60, Citi sends you$25 and the trade continues. If it’s above $1,339.60, Citi sends you back your$1,000 and the trade is over.
3. At the end of the three years, Citi looks at Amazon’s stock price. If it’s above $1,004.70 (75 percent of the initial stock price), then Citi sends you$1,025 and the trade is over. But if it’s below $1,004.70, you eat the full amount of the loss: For instance, if Amazon’s stock price is$803.80 (60 percent of the initial stock price), then you lose 40 percent of your money, and get back only $600. Citi keeps the rest. (You get to keep all the premiums, though.) Anyone with half a brain should know that this is not a great trade. For starters, it gives the client (usually a hedge fund or a pension fund or someone who represents rich guys) a small limited upside (of 10% per year for three years), while giving unlimited downside if Amazon lost over 25% in 3 years. Then, the trade has a “knock out” (gets unwound with Citigroup paying back the client the principal) clause, with the strike price of the knockout being exactly the Amazon share price on the day the contract came into force. And given that Amazon has been on a strong bull run for a while now, it seems like a strange price at which to put a knock out clause. In other words, there is a high probability that the trade gets “knocked out” soon after it comes into existence, with the client having paid up all the transaction costs (3.5% of the principal in fees). Despite this being such a shitty deal, Levine reports that Citigroup sold$16.3 million worth of these “notes”. While that is not a large amount, it is significant that nearly ten years after the financial crisis, there are still suckers out there, whom clever salespersons in investment banks can con into buying such shitty notes. It seems institutional memory is short (or these clients are located in states in the US where marijuana is legal).

PS: Speaking of suckers, I recently got to know of the existence of a school in Mumbai named “Our Lady of Perpetual Succour“. Splendid.

## Dimensional analysis in stochastic finance

Yesterday I was reading through Ole Peters’s lecture notes on ergodicity, a topic that I got interested in thanks to my extensive use of Utility Theory in my work nowadays. And I had a revelation – that in standard stochastic finance, mean returns and standard deviation of returns don’t have the same dimensions. Instead, it’s mean returns and the variance of returns that have the same dimensions.

While this might sound counterintuitive, it is not hard to see if you think about it analytically. We will start with what is possibly the most basic equation in stochastic finance, which is the lognormal random walk model of stock prices.

$dS = \mu S dt + \sigma S dW$

This can be rewritten as

$\frac{dS}{S} = \mu dt + \sigma dW$

Now, let us look at dimensions. The LHS divides change in stock price by stock price, and is hence dimensionless. So the RHS needs to be dimensionless as well if the equation is to make sense.

It is easy to see that the first term on the RHS is dimensionless – $\mu$, the average returns or the drift, is defined as “returns per unit time”. So a stock that returns, on average, 10% in a year returns 20% in two years. So returns has dimensions $t^{-1}$, and multiplying it with $dt$ which has the unit of time renders it dimensionless.

That leaves us with the last term. $dW$ is the Wiener Process, and is defined such that $dW^2 = dt$. This implies that $dW$ has the dimensions $\sqrt{t}$. This means that the equation is meaningful if and only if $\sigma$ has dimensions $t^{-\frac{1}{2}}$, which is the same as saying that $\sigma^2$ has dimensions $\frac{1}{t}$, which is the same as the dimensions of the mean returns.

It is not hard to convince yourself that it makes intuitive sense as well. The basic assumption of a random walk is that the variance grows linearly with time (another way of seeing this is that when you add two uncorrelated random variables, their variances add up to give the variance of the sum). From this again, variance has the units of inverse time – the same as the mean.

Finally, speaking of dimensional analysis and Ole Peters, check out his proof of the Pythagoras Theorem using dimensional analysis.

Isn’t it beautiful?

PS: Speaking of dimensional analysis, check out my recent post on stocks and flows and financial ratios.

## Stocks and flows

One common mistake even a lot of experienced analysts make is comparing stocks to flows. Recently, for example, Apple’s trillion dollar valuation was compared to countries’ GDP. A few years back, an article compared the quantum of bad loans in Indian banks to the country’s GDP. Following an IPL auction a few years back, a newspaper compared the salary of a player the market cap of some companies (paywalled).

The simplest way to reason why these comparisons don’t make sense is that they are comparing variables that have different dimensionality. Stock variables are usually measured in dollars (or pounds or euros or whatever), while flows are usually measured in terms of currency per unit time (dollars per year, for example).

So to take some simple examples, your salary might be $100,000 per year. The current value of your stock portfolio might be$10,246. India’s GDP is 2 trillion dollars per year.  Liverpool FC paid £67 million to buy out Alisson’s contract at AS Roma, and will pay him a salary of about £77,000 per week. Apple’s market capitalisation is 1.05 trillion dollars, and its sales as per the latest financials is 229 billion dollars per year.

Get the drift? The simplest way to avoid confusing stocks and flows is to be explicit about the dimensionality of the quantity being compared – flows have a “per unit time” suffixed to their dimensions.

Following the news of Apple’s market cap hitting a trillion dollars, I put out a tweet about the fallacy of comparing it to the GDP of the United States.

A lot of the questions that followed came from stock market analysts, who are used to looking at companies in terms of financial ratios, most of which involve both stocks and flows. They argued that because these ratios are well-established, it is legitimate to compare stocks to flows.

For example, we get the Price to Earnings ratio by dividing a company’s stock price (a stock) by the company’s annual earnings per share (a flow). The asset turnover ratio is derived by dividing the annual revenues (a flow) by the amount of assets (a stock). In fact, barring simple ratios such as gross margin, most ratios in financial analysis involve dividing a stock by a flow or the other way round.

To put it simply, financial ratios are not a case of comparing stocks to flows because ratios by themselves don’t mean a thing, and their meaning is derived from comparing them to similar ratios from other companies or geographies or other points in time.

A price to earnings ratio is simply the ratio of price per share to (annual) earnings per share, and has the dimension of “years”. When we compute the P/E ratio, we are not comparing price to earnings, since that would be nonsensical (they have different dimensions). We are dividing one by the other and comparing the ratio itself to historic or global benchmarks.

The reason a company with a P/E ratio of 25 (for example) is seen as being overvalued is because this value lies at the upper end of the distribution of historical P/E ratios. So we are comparing one ratio to the other (with both having the same dimension).

In conclusion, when you take the ratio of one quantity to another, you are just computing a new quantity – you are not comparing the numerator to the denominator. And when you compare quantities, always make sure that you are being dimensionally consistent.

## 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.

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 utility of utility functions

That is the title of a webinar I delivered this morning on behalf of Kristal.AI, a company that I’ve been working with for a while now. I spoke about utility functions, and how they can be used in portfolio optimisation.

This is related to the work that I’ve been doing for Kristal, and lies at the boundaries between quantitative finance and behavioural finance, and in fact I spoke about utility functions (combined with Monte Carlo methods) as being a great method to unify quantitative and behavioural finance.

Interactive Brokers (who organised the webinar) recorded the thing, and you can find the recording here.

I think the webinar went well, though I’m not very sure since there was no feedback. This was by design – the webinar was a speaker-only broadcast, and audience weren’t allowed to participate except in terms of questions that were directly sent to me.

In the first place, webinars are hard to do since it feels like talking to an empty room – there is no feedback, not even nods or smiles, and you don’t know if people are listening. In most “normal” webinars, the audience can interject by raising their hands, and you can try make it interactive. The format used here didn’t permit such interaction which made it seem like I was talking into thin air.

Also, the Mac app of the webinar tool used didn’t seem particularly well optimised. I couldn’t share a particular screen from my laptop (like I couldn’t say “share only my PDF, nothing else” which is normal in most online chat tools), and there are times where I’ve inadvertently exposed my desktop to the full audience (you can see it on the recording).

Anyways, I think I’ve spoken about something remotely interesting, so give it a listen. My “main speech” only takes around 20-25 minutes. And if you want to know more about utility functions and behavioural economics, i recommend this piece by John Cochrane to you.