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.

Black Money: Stocks and flows

Any physical quantity can be measured in two ways – as a “stock” and as a “flow”. Stock refers to the total amount of the quantity at a particular location at a particular time. Think, for example, of water in a reservoir. “The stock of water at XXX reservoir is 1000 cubic metres” is a “stock measurement” –  it tells us how much water was there at a particular point in time.

The other way of measurement is as a “flow”. This refers to the quantity of the quantity that “changes” or “passes through” between two fixed points in time. For example, we can say that “the flow of the water in my bathroom tap is 20 litres per minute” or “in the last one hour 100 litres of water flowed down my drainage pipe”. Dimensionally speaking, flow has a “quantity per time” dimension while stock has a “quantity” dimension. Flow, unless expressed as a rate of change, also has two points in time mentioned while stock is measured at a single point in time.

Moving from physical quantities (such as water) to financial matters, a company’s balance sheet is the measurement of stock, since it measures the assets and liabilities at a particular point in time (“as of 31st March 2014”). The profit and loss statement, on the other hand, is a measurement of flow, since it tells us about the revenues, costs and profits of the firm in a particular time period (“between 1st April 2013 and 31st March 2014”, for example).

Taking matters more global, any measurement of wealth is a stock, since it is measured at a particular point in time. Measurement of economic activity, such as GDP, on the other hand, is a flow, since it measures the quantity of activity over a period of time. A common fallacy is to compare stocks to flows (this piece in ET is a stellar example of this fallacy), though it must be mentioned that it’s a common practice in financial accounting, analysis and valuation (but there the dimensionality is maintained and recognised. It is common, for example, to divide inventory (a stock) by sales (a flow) to determine “how many days of inventory” a company has on hand). More worryingly, there is sometimes a worrying lack of understanding between stocks and flows when it comes to policy recommendations.

One of the features of the BJP’s campaign over the years, and especially in its run up to this year’s General Elections, is to “bring back black money stored abroad”.

Pop Quiz: Is black money stored abroad a stock or a flow?

During the duration of this “bring back black money” campaign, there have been many fanciful estimates of the amount of black money stashed away abroad and what that can do to India’s deficits if it can be “brought back”. Some of the WhastApp and email forwards estimate, extremely fancifully, what the bringing back of the black money can do to the USD/INR exchange rate even!

The problem with this whole idea of “bringing back black money abroad” is that it fundamentally attacks a particular stock of black money and not the flow (there you have the answer to the pop quiz). Black money stashed away abroad is “harmless” in that it just sits there without being used for any transaction. In that sense the value of that money is lower since it is not being constantly exchanged for something that is more valuable.

What should be of more of a concern to us is the “flow” of black money rather than the stock. Every time a transaction is financed by black money (i.e. without a paper trail or a receipt, and money changing hands in hard cash), the government loses out on the taxes that would have otherwise have to be paid on the transaction. The more the number and value of transactions that can be conduced “in black”, the more the incentive for people to do other transactions “in black” and keep their money in cash, and not accounted for. This has a multiplier effect in terms of number and value of transactions that are unaccounted, and thus help evade taxes.

Rather than one-time efforts to “bring back black money” which attack only the stock of black money, our policy should be geared towards cutting down the flow of black money. A regime of high stamp duties and low property taxes, for example, lead to the perverse incentive for under-invoicing the price of real estate and paying the difference in cash – the “saving” is such that even otherwise law-abiding citizens have an incentive to play along in the black money game and trade in cash. Enabling easier peer-to-peer mobile payments, for example, can have the effect of dramatically increasing the number of transactions that can be conducted without cash, and will be an important step in chipping away at flows of black money. Value Added Tax, with its “input credits” was designed as a system to check under-invoicing within a supply chain, but what if the entire supply chain of a particular commodity runs on cash without written contracts (social capital within business communities allows this, for example)?

Periodic attacks on the stocks of black money (stored either abroad or domestically) can bring in large amounts of money into government coffers and this might make such attacks glamorous. But they are tedious to implement and government resources are much better off employed in cutting off the flows of black money.

Reforming Bangalore’s Public Transport Network

This is based on a twitter rant on the same subject a few weeks back.

Bangalore’s public transport network has traditionally followed a hub-and-spoke model, with three hubs – Kempegowda Bus Station (aka “Majestic”), KR Market and Shivajinagar. It can be modeled, however, as a two-hub system, for Majestic and Market are quite close to each other and thus quite well-connected. It was probably not originally meant to be that way – for bus number 1 (not sure it still exists) ran from Jayanagar 4th Block to Yeshwantpur – basically from the south to the north-west corner of the city. Of course, it passed through Market.

Over time, however, the bus system has moved to an increasingly hub-and-spoke model. The BMTC (Bangalore Metropolitan Transport Corporation) did one exercise a few years back, trying to rationalize routes (it was partly due to an effort led by Ashwin Mahesh of Mapunity). However, while adding useful additions such as the ring routes (the “big circle” and the “chikka (small) circle” routes) and one or two “trunk routes” (that run right across town), what this revised template does is to further increase the primacy of the hubs. For example, the much talked about Big 10 routes are essentially arterial routes running from a point in the middle of town to some place along one of the highways leading out of Bangalore (they are not strictly hub routes, though, since some of them stop a short distance from a major hub).

The increase in primacy of hubs combined with metro construction (the two metro lines will criss-cross each othe at – you guessed it – Majestic!) has completely overwhelmed the hubs. It is impossible (unless you sacrifice copious amounts of time) to change buses at Majestic now, for the amount of time it takes for a bus to get into majestic and for a bus to get out of majestic is too high a transaction cost.

Moreover, changing buses at a terminus is not efficient, given the waiting times involved and the extra transaction costs of getting out of the terminus. What works better is changing buses at an intermediate stop. To use an anecdote, for two years (1998-2000) I traveled to school in Indiranagar (east Bangalore) from my home in Jayanagar (south Bangalore). I would take a bus going to Shivajinagar (Jayanagar-Shivajinagar is well connected – being a hub route) and get off at Richmond circle, from where I would take a bus from Majestic to Indiranagar (again a hub route, so well served). I could change buses while standing at the same bus stop (made things easier), and the frequency of buses on the two hub routes meant I would get to school easily (again the traffic in the 1990s was nothing compared to what it is now). I had the option of changing buses at a hub, but eschewed it due to transaction costs.

Coming back, what we need in Bangalore is to reformat the bus network in a way that mimics the patterns in which people travel. Right now the assumption of the BMTC seems to be that they should connect every area to a major hub, and then let people take it from there. What they do not take into account is that 1. traffic has grown much worse and 2. People put a higher value on their time nowadays, because of which the transaction cost of the old hub-and-spoke model is way too high. What they need to do instead is to design the network based on people flows.

The first step of such reform is to understand the patterns in which Bangalore moves. One way to do this would be via smart ticketing. A few years back buses in Bangalore started introducing smart ticketing machines, and your ticket would be a printout. However, that didn’t take off. If that can be reintroduced (in all buses) and coupled with destination based ticketing rather than leg based ticketing (for example, if I’m going from Jayanagar to Indiranagar via Richmond Circle I get on to the bus in Jayanagar and buy a ticket to Indiranagar directly. The same ticket allows me to travel on any bus between Richmond Circle and Indiranagar. This introduces complexity but can be done). This will give the BMTC information in terms of the routes on which people actually travel. And once that happens, an effort can be made to reformat the bus network.