Bigger is the enemy of better investing

ELON Musk has had a remarkable 12 months. His net worth sextupled, largely on account of his stake in Tesla, which increased 740 per cent in 2020. Mr Musk isn't the only one rejoicing. Those with concentrated holdings in various technology companies and cryptocurrencies have likewise enjoyed once-in-a-generation returns. They should be celebrated for their achievements, but their outsized positions and gains are potentially sending the wrong message to ordinary investors.

Twitter and Reddit are replete with examples of individual investors who have become multimillionaires through concentrated investments that have increased a hundred-fold in a relatively short period of time. And many of them are proud to say they're keeping the faith and not reducing their exposure in the expectation of further massive gains.

Investing involves two decisions: what and how much.

The first is to identify the most attractive investment opportunities, and the second is to size those chosen investments to an appropriate level of risk. Some who get the first decision right but the second wrong by taking too much risk inadvertently wind up on various lists of the world's richest people.

Sadly, many more find themselves on the opposite end of the wealth distribution curve. Despite the critical nature of the sizing decision, it gets little attention. In the current environment, investors can reach the incorrect conclusion that bigger is always better as long as they have identified an attractive investment opportunity.

In research aimed at understanding how investors approach the sizing decision, we conducted a study in 2017 where graduate students and young investment analysts were given US$25 and offered the opportunity to bet on a 60/40 biased coin and get paid their final balance in cash, subject to a US$250 cap. The coin flip introduced uncertainty but removed the forecasting element, as participants could focus on how much to bet on a risky but positive expected return opportunity.

To our surprise, 30 per cent of the participants lost their entire bankroll and only a handful placed their bets in a sensible and systematic manner. Following a simple rule of betting 10 per cent to 20 per cent of one's bankroll on heads on each flip generates a 95 per cent chance of reaching the US$250 cap. However only 20 per cent of participants achieved this payout.

How does one lose money betting on a coin known to have a probability of landing on heads 60 per cent of the time? Simple, just bet all of your money on each flip. What's perhaps more surprising is that if you bet, say, 50 per cent of your wealth on heads on each flip, then the most likely outcome after 100 flips would be that you'd have lost 97 per cent of your starting wealth. That's what you'd get if your wealth went up by 50 per cent 60 times and shrank by 50 per cent 40 times.

Wealth or bankruptcy

Over many flips, the difference between betting the optimal 10 per cent to 20 per cent of wealth and the overly aggressive 50 per cent bet is the difference between growing wealth and heading towards bankruptcy.

The crux of the sizing decision is this: the bigger you bet on a series of favourable gambles, the higher your expected gain on each event. But if you bet too big, your most likely outcome over the series is to lose money.

Although our study was simply an illustration and no doubt suffered design flaws, the importance of investment size should be clear: even with a well-defined favourable opportunity it is easy to realise sub-optimal outcomes by over-betting. This goes beyond an academic concern as financial markets offer plenty of examples where over-sized positions have led to extraordinary losses, despite ultimately being sound investments. One of us had just such an experience as a partner at the hedge fund Long-Term Capital Management.

Frameworks do in fact exist for helping investors think about appropriate investment sizing.

John Von Neumann, one of the great mathematicians of the 20th Century, together with the economist Oskar Morgenstern, proposed a scaling framework in their seminal 1944 book, Theory of games and economic behaviour, which also established the field of Game Theory. They provided the formal mathematical foundation to the hypothesis made by Daniel Bernoulli in 1737 that a rational investor's objective should be to maximise the expected welfare, or utility, that they derive from wealth, rather than maximising the expected monetary value of their wealth.

Others such as Massachusetts Institute of Technology Professor Robert C Merton and Bell Labs scientist John Kelly gave us simple formulas, the "Merton Share" and the "Kelly Criterion", for the optimal amount of risk to take for a given expected return.

Investors can skip all the elaborate math and still avoid the pitfalls of taking too much risk by following a few simple rules: avoid a concentrated portfolio and shun leverage. In short, diversify and don't borrow.

It's taken a long time for retail investors to help themselves to the free lunch of diversification extolled by Harry Markowitz in 1952. Numerous academic studies have documented the tendency of investors to hold significantly undiversified portfolios all through the pre-Vanguard era up to the early 1990s. In the 1950s, the median number of stocks held by an individual investor was just two!

Concentrated holdings are sub-optimal

We seem to be witnessing something of a return to those days among Robinhood investors.

Very concentrated holdings are not only suboptimal for the individual, but they also impose a broader social cost in increasing wealth inequality. We hope and expect that this most recent movement of retail investors taking concentrated equity bets will be just a hiccup on the continued path towards more efficient investing as evidenced by the large fraction of the US$6 trillion of assets in retirement plans that are invested in diversified mutual funds, many of them indexed.

For those close to the technology who have a guiding hand in steering the future, concentration might indeed make sense, aligning incentives, motivating performance and helping maintain control. But when it comes to the long-term financial health of the vast majority of investors, history and simple math show that it pays to think carefully about sizing and concentration.

• Victor Haghani is the founder and CEO of Elm Partners, an investment management firm. He was also a founding partner of Long-Term Capital Management. Richard Dewey is a portfolio manager at hedge fund Royal Bridge Capital.