## 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.