One time-honoured pastime for Singaporeans like my Uncle John (name changed for privacy reasons) is in queueing up to buy 4D.
As someone who has never bought 4D, I wanted to understand how to optimise 4D betting, and if there is any way to diversify 4D bets, just like we should do when we invest.
Gambling and investing are both driven by returns and odds
Despite Uncle John's attempts to spot 4D number patterns or draw inspiration from birthdays, the generation of 4D numbers are truly random — a draw machine is carefully calibrated to ensure that all numbers have an equal chance of appearing.
Therefore, over the long run, the expected returns should be based on the probability of getting a striking a prize number and the prize money earned. The winnings and expected outcome for each $1 bet can be calculated based on the table below:
It is easy to assume that placing more bets would increase our probability of winning. Instead of betting $1,000 in a single number, why not spread it across 25 bets, $40 each, or even 500 bets at $2 each? Perhaps we can even spread it across different 4D draw dates so that we can spot patterns and adjust our strategies accordingly?
Unfortunately, we all know that does not work, because by spreading the bets wider, while you have a greater chance of striking the lottery, your strikes will yield smaller monetary rewards, and hence merely increase your chances of getting the expected outcome, which is to get back $0.659 for every $1 you put in.
Taken to the extreme, if you were to place a dollar bet on every single number, all 10,000 of them, you would get $6,590 back. That's the best you can do.
How to understand if you are speculating or investing
1. Your trading/investing behaviour and frequency
When we are speculating (read: gambling) instead of investing, we are inclined to look at the markets more, and make sporadic trades rather than investing in a consistent manner.
This type of behaviour has been particularly apparent during this COVID-19 crisis, where a study by economists showed that retail investors increased their trading activity by approximately 13.9% for every doubling of COVID-19 cases.
At the end of the day, we have our own personal opinions on whether stocks or index funds are expensive or cheap, which may lead to trading behaviour anchored not on scientific reason, but on guesses. We may choose to trade in and out of the market more based on how many guesses we have, but the more we indulge ourselves with such thoughts and such behaviour, the more we are speculating, instead of investing.
Read more: Why passive investing beats trading
2. How much/little investable cash you hold
Uncle John dedicates $200 religiously every month on 4D, buying a fixed combination of license plate numbers and birthdays.
Investing should be carried out with the same mindset (though for a different cause). We should do our budgeting, know how much we want to invest for our mid- and long-term goals, and invest that money religiously. We should accept that it is innately difficult to outguess the market and be persistent and consistent (like Uncle John) with depleting our cash holdings so that we put more money at work (also known as dollar-cost averaging).
In contrast, a gambler (market speculator) would in some cases be leveraging up to try to outsmart the market on random bets.
Read more: Finding patterns where there are none — Investing based on patterns
3. If you have diversified your holdings
Using the above charts on spreading out 4D bets, it is obvious that while concentrating your money in fewer bets gives you a better chance of a windfall, you also have huge uncertainty in returns. On the other hand, if you were to take more bets, the variance of outcome narrows, and there is a greater certainty that we get the mathematically expected returns (or loss of 0.341 per $1 put in 4D).
In a similar way, spread your investments over countries, sectors, and companies so that you are as diversified as possible, to get a better chance to capture economic growth.
The difference is diversification in investing is that the method is backed by science.
Diversification works best when the assets are either uncorrelated or negatively correlated with one another, so that as some parts of the portfolio fall, others are likely to rise. This will offset the volatility of individual investments and spread out your risk.
The ideal scenario is when the price correlation across assets within a portfolio is at or near zero. That means the price movement of one asset will have no effect on the prices of the other assets.
Nobel prize-winning economist Harry Markowitz called diversification "the only free lunch in finance". His theory is that if you hold a portfolio of investments that are not perfectly correlated, an investor can lower risk without sacrificing expected returns.
Simply put, spreading your investments across asset classes and geographies gets you the same reward with less risk. That’s the free lunch.
A study done by Dimensional Fund Advisors shows that missing out on the top performers in the global stock market (weighted by market cap, across developed and emerging market) will lead to significantly poorer returns.
By spreading your underlying exposure more thinly, you will have a lower chance of missing out on investments in companies that give higher returns, and hence give you a higher chance of hitting the 7-9% historical returns we can get from the equity markets.
4. Whether you focus on investment returns or costs
Market speculators and gamblers alike tend to focus on potential winnings and outcomes. To them, with the right strategy, right timing, with an element of luck, they would be able to make a bigger earning based on their ingenuity.
However, for market speculators, such an "investment strategy" comes with both explicit (trading and transaction fees) and implicit costs (bid-ask spread, time spent on managing investments and transferring money). These costs may or may not lead to higher investment returns. If we realise that we are spending more transaction costs than we expect to, then we are likely to be speculating than investing.
Rain or shine, Uncle John puts a more or less fixed amount of money into buying 4D, and is unperturbed by the outcome. While we know now there is a difference between investing and speculating, there is a lesson that we can take from his gambling resolve. If he can do it so consistently despite being uncertain about the outcome, why can't we do the same as investors?
Next on the Endowus Fin.Lit Academy
Read the next article in the curriculum: A simple glossary of investing terms
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