## 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 Balance Sheet View of Life

The basic idea of this post is that interpersonal relationships (not necessarily romantic) need to be treated as balance sheets and not as P&L statements, i.e. one should always judge based on the overall all-time aggregate rather than the last incremental change in situation.

Just to give you a quick overview of accounting, the annual statement typically has two major components – the P&L statement which reflects what happened between the last release of the statement and the currrent point, and the balance sheet which reflects the position of the company at the point of time of release of the statement.

I think Bryan Caplan had made this point in one of his posts, but I’m not able to find it and hence not able to link it. The point is that you should look at relationships on a wholesome basis, and not just judge it based on the last action. The whole point is that there is volatility (what we refer to in my office as “the dW term”) and so there are obviously going to be time periods during which you record a loss. And if on each of these occasions you were to take your next course of action based on this loss alone, you are likely to be the loser.

I’m not saying that you should ignore the loss-making periods and just move on. You do need to introspect and figure out what you need to do in the next accounting period in order to prevent this kind of a loss from repeating. You will need to “work the loss”, not make a judgment to break the relationship based on it. I think a large part of the problems in this world (yeah, here goes another grand plan) stems from people using one-period losses in order to take judgments on relationships.

Another thing is not to generate the accounting statements on a shorter time period. This is similar to one funda I’d put long ago about how you shouldn’t review your investments at extremely short intervals since that will lead to a domination of the volatility term (dW) and thus cause unnecessary headache. You might notice that corporates rarely release their accounts statements more frequently than once a quarter – this has more to do with volatility than with the difficulty in generating these statements.It is similar in the case of interpersonal relationships. Don’t judge too often – the noise term will end up dominating.

One caveat though – very occasionally the last loss may be so bad that it more than wipes out the balance sheet and takes to zero (or even less) the value of the firm. In that kind of a situation, there is no option but to shut down the firm (or break the relationship) and move on. Once again, however, the clincher in the decision to break up has to be the balance sheet which has gone to zero (or negative) and not just simply the magnitude of the last loss.

Life based on a balance sheet view is a balanced life.