Brain teaser: of stocks, flows, apples and oranges.

A couple of weeks ago, I received a text that was described to me as a “finance brain teaser” from [redacted].

The brain teaser

Sam has $50. He keeps a running tally of his spending activity and the balance remaining in his ledger.

Spent ($) Balance ($)

20 30

15 15

9 6

6 0

...….… ……….

50 51

......... ........

Where did the extra $1 come from? Explain!

My response

My snap back response: “What are you asking me? That’s like measuring apples and oranges — they’re both fruit and make delicious juice but when it comes to dessert, apple pie works well — orange pie not so much…” Suffice it to say that I received an equally snappy reply. I love you [redacted] aka Mom.

Explanation

While it is true that the amount of expenditure and the balance remaining after each transaction are related, these measures are qualitatively different and should be looked at through disparate lenses. One is a “flow” and the other is a “stock”. Wikipedia defines the difference between the two types of measures as follows: “A stock is measured at one specific time, and represents a quantity existing at that point in time… which may have accumulated in the past. A flow variable is measured over an interval of time. Therefore, a flow would be measured per unit of time (say a year).”

To better illustrate why comparing these two measures is like comparing “apples and oranges”, let us make a slight modification to the brain teaser. We can divide the first $20 expenditure into two transactions, each an expenditure of $10. All subsequent transactions remain unchanged and we use the same ledger methodology for recording of the transactions. As seen below, comparing the sums of the two ledger categories is of little use.

Spent ($) Balance ($)

10 40

10 30

15 15

9 6

6 0

...….… ……….

50 91

......... ........

Key takeaway

It can be dangerous to assume that “numbers are just numbers”. Context matters. It is critical that we understand what is being measured, why it is being measured, over what time period it is being measured, etc. In the world of business finance, it is advisable to pause before rushing to perform financial analysis, inputting data into spreadsheets, calculating ratios, putting together financial projections, etc. We should first develop an understanding of underlying assumptions, the effects of seasonality, changes in operation environment (eg, due to changes in legislation, technology, competitive landscape, customer preferences), and other factors such as unusual events.

Further notes

I would suggest that the challenge with assessing dissimilar attributes, as seen in the brain teaser, is only a start. In the real world, which is much more complex than Sam’s ledger, we are further challenged by the difficulty with using quantitative measures to assess non-linear, and even qualitative matters.

For those interested in exploring this subject area, I recommend the work of Nassim Nicholas Taleb as a useful introduction for developing perspective around risk assessment, risk management and improved decision-making.

• Kumi Bradshaw helps Bermuda companies measure, grow and harvest business value. For help with business advisory, brokerage or valuation, e-mail kumi@firmadvisory.com