Mathematics of investing and life
Nalanda Capital is one of the most successful investment firms that have come up in the last couple of decades and one that has been an inspiration and source of learning for many of us at Marcellus. Anand Sridharan, an investor at Nalanda writes an entertaining yet enlightening blog on LinkedIn. This one, as the title says, is about the role of math in investing. In our interviews with potential new hires, we find that the most common answer to ‘why investing as a career?’ is ‘I love maths or I am good at maths’ or some variant of that. Anand busts that myth right upfront – “there’s very little math in investing. At best middle-school level, that too state-board”. However, he goes on to highlight some useful math concepts (still middle school level, perhaps high school at best) that help avoid falling into false narratives based on numbers while investing. Anand discusses multiplicative probabilities, decision trees, representativeness, (normalising) denominator and asymmetric odds.
“Why is there extreme dispersion in outcomes, from similar starting points?… Multiplicative probabilities can have an especially severe effect at the opposite end. As an example, Indian companies have had a disastrous experience with overseas acquisitions. Going in, these adventures didn’t seem particularly egregious. However, a whole host of seemingly small differences between acquirer and acquiree – context, people, culture, distance, distribution setup, weaker competitive position, business profile – made a big difference to the final outcome. While each difference, in itself, might have reduced odds of success by a small amount, their multiplicative effect was disastrous. An appreciation of this concept results in paranoia about avoiding ‘zeroes’ anywhere in the chain. Big-bang M&A, high debt or dodgy promoters can nullify a lot of other positives in a business.
What can you infer about normal times from a highly abnormal time?…Absolutely nothing! Due to a lack of representativeness. It’s as if there’s no lockdown in my part of the world. Dozens of calls are organized every day to provide running commentary on the red, orange and green of 100s of companies. I don’t know what to make of these. What matters is where things end up well after we’ve settled into (new) normalcy. It’s unclear how a highly abnormal, transient period would be even remotely representative of steady state. More generally, representativeness is a key filter in separating signal from noise. It’s the reason I prefer secondary data over primary research. In many industries, with some effort, secondary data covers the universe and isn’t limited to a biased sample. Further, it’s the outcome of millions of actual customer decisions made with real money. It’s not contrived opinions expressed by a few buggy humans who rarely know their real motivations. In times when reporting is based on moving anecdotes cherry-picked to grab eyeballs, representativeness is the first filter for any incoming data point.
Why are shockingly large numbers mostly meaningless?…Without a denominator, there’s no frame of reference. I’ve never figured why buggy humans hate the denominator so much. It practically deserves its own victimhood narrative. It’s not just media saying “Investors lost 1 lakh crore” instead of “Market fell a bit”. Professionals misleadingly claim “This business makes money”, referring to EBITDA rather than return on capital. The most important thing in investing – risk – is cleverly hidden as an innocuous ‘cost of capital’ in, wait for it, the denominator. Those who spend endless hours clicking and dragging the numerator fill out this crucial item as an afterthought, albeit with a few decimal points thrown in. More generally, numbers make more sense on a denominator-adjusted basis. Market share matters more than revenue growth. Ratios convey more than raw financials. Profit figures are to be normalized over a business cycle. Valuations are best viewed in context of long run percentile data. ‘Denominator’ is really a frame of reference rather than a place under a line. Without it, numerators fall somewhere between meaningless and dangerous.”