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

Matt Levine’s latest newsletter describes a sucker of a trade:

 

  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).

I mean, who even buys structured notes nowadays?

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.

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 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.

Bankers predicting football

So the Football World Cup season is upon us, and this means that investment banking analysts are again engaging in the pointless exercise of trying to predict who will win the World Cup. And the funny thing this time is that thanks to MiFiD 2 regulations, which prevent banking analysts from giving out reports for free, these reports aren’t in the public domain.

That means we’ve to rely on media reports of these reports, or on people tweeting insights from them. For example, the New York Times has summarised the banks’ predictions on the winner. And this scatter plot from Goldman Sachs will go straight into my next presentation on spurious correlations:

Different banks have taken different approaches to predict who will win the tournament. UBS has still gone for a classic Monte Carlo simulation  approach, but Goldman Sachs has gone one ahead and used “four different methods in artificial intelligence” to predict (for the third consecutive time) that Brazil will win the tournament.

In fact, Goldman also uses a Monte Carlo simulation, as Business Insider reports.

The firm used machine learning to run 200,000 models, mining data on team and individual player attributes, to help forecast specific match scores. Goldman then simulated 1 million possible variations of the tournament in order to calculate the probability of advancement for each squad.

But an insider in Goldman with access to the report tells me that they don’t use the phrase itself in the report. Maybe it’s a suggestion that “data scientists” have taken over the investment research division at the expense of quants.

I’m also surprised with the reporting on Goldman’s predictions. Everyone simply reports that “Goldman predicts that Brazil will win”, but surely (based on the model they’ve used), that prediction has been made with a certain probability? A better way of reporting would’ve been to say “Goldman predicts Brazil most likely to win, with X% probability” (and the bank’s bets desk in the UK could have placed some money on it).

ING went rather simple with their forecasts – simply took players’ transfer values, and summed them up by teams, and concluded that Spain is most likely to win because their squad is the “most valued”. Now, I have two major questions about this approach – firstly, it ignores the “correlation term” (remember the famous England conundrum of the noughties of fitting  Gerrard and Lampard into the same eleven?), and assumes a set of strong players is a strong team. Secondly, have they accounted for inflation? And if so, how have they accounted for inflation? Player valuation (about which I have a chapter in my book) has simply gone through the roof in the last year, with Mo Salah at £35 million being considered a “bargain buy”.

Nomura also seems to have taken a similar approach, though they have in some ways accounted for the correlation term by including “team momentum” as a factor!

Anyway, I look forward to the football! That it is live on BBC and ITV means I get to watch the tournament from the comfort of my home (a luxury in England!). Also being in England means all matches are at a sane time, so I can watch more of this World Cup than the last one.