# Heads or Tails

I am reading the excellent work called How Not to Be Wrong: The Power of Mathematical Thinking. The author hits a topic I covered in my book The Power Curve: Smart Investing Using Dividends, Options and the Magic of Compounding that would be valuable to revisit during these volatile times. The concept revolves around the law of large numbers. It goes something like this:

If you have 100 people each flip a coin 10 times you will get a wide distribution of results, some of the people getting 3 heads and 7 tails (30% heads, 70% tails), a couple getting 8 heads and 2 tails (80% heads, 20% tails), a group getting 4 heads and 6 tails (40% heads, 60% tails), etc.

Now do the same experiment with each person flipping the coin 1,000 times rather than just 10. The distribution of results will be very different with not a single person getting 80% heads and 20% tails, rather almost everyone getting somewhere very close to 50% heads and 50% tails. In other words, the more flips of the coins, the more likely you are to end up with the expected result which is half heads, half tails. Of course if you do a single flip by definition you will get either 100% heads or 100% tails, if you do 2 flips you could easily get 100% heads, 0% tails, etc. – but you would never get that outcome if you flipped the coin 1,000 times. We know this intuitively; the statistical facts bear this out.

Now let’s apply this important objective, mathematical, idea to the stock market. On any given day the outcome of the stock market is binary – it is either up or down (I realize it could close exactly flat but for all intents and purposes stocks either close up or down on any given day). But we know from history – from approximately 40,000 ‘flips’ (about 200 years of daily stock market data) that over time ‘heads’ (let’s call heads being the market went up, tails the market declined) wins about 58% of the time. Translation: if 50%/50% represents the stock market never going up – that the number of up days matches exactly over long periods of time the number of down days in frequency and magnitude – like the flip of a coin – then stocks would be flat over long periods. But they have been anything but flat. $1 invested in stocks in 1802 would be worth over $700K today. Read that again – a single dollar invested in 1802 would have increased to more than seven hundred thousand dollars by the 2010’s.

Now would be a good time for a relevant aside. Since I made my first stock trade as a teenager in the mid-1980s, I have heard endless cries on how the stock market is ‘rigged’ against the little guy – or broken all together. The Flash Crash of 2010? Caused by high frequency traders the pundits screamed. The market is rigged; the little guy has no chance; why even bother. I have heard this theme espoused over and over and over – it continues to this day by politicians looking to earn a vote.

Well let me let you in a little secret: it is true, the market IS rigged! It just happens to be rigged in your favor. Investing in the stock market is like owning a magic coin that comes up heads 58% of the time. On any given flip it could end up as heads or tails but flip it enough times and heads will be the winner. By a lot. Vegas casinos – which truly are rigged – stack the odds in their own favor by a percentage point or two which is enough for them to make billions off of poor souls who think somehow the laws of statistics don’t apply to them. Well it turns out they do. Back to our magic coin… imagine being able to travel the country and bet unsuspecting participants. If a prey is unwilling to flip the coin at least a 100 times for example (if they are only willing to bet on 10 flips), you simply move on to the next sucker. But for those willing to wager on 100 (or some reasonably large number) of flips, you take that bet all day long. The law of large numbers will have your back every time.

So if the stock market is so rigged in the investor’s favor – to the tune of around 8% over time – then why does the average investor earn less than 1/3 of that – and why do many lose their shirts?

The answer is simple: they don’t flip the coin enough. They go into the game with the intention of flipping the coin 2,000 times for example, a 10 year time horizon which would be appropriate for someone in his mid-60s. For someone not even approaching retirement age, their investment horizon – the number of flips – would be far more than that despite that people often underestimate their true investment time horizon. So what happens? Where do they fail? Here:

After a couple hundred flips the Flash Crash occurs, they get scared after reading all the headlines about how markets are rigged, and they take their magic coin and go home – even though the market regained most of that day’s losses within minutes. Or worse yet, the investor had arbitrary stop loss orders that triggered during the moments of market declines which took stocks like mega-cap PG down 30%+ only to end up where it started by the end of the trading day.

A few hundred flips into a long-term investment program there is a barrage of stories about Greece’s eminent default on debt, this theme is repeated daily in the headlines for weeks, investors believe this is the beginning of the end and they bail on stocks.

A friend forwards a newsletter stating the US is doomed, that our currency is going to crash, and that you should put your entire portfolio in some combination of cash or gold, and you take action accordingly. Great content for selling newsletter subscriptions, not so great advice for wealth creation over time.

Any of the hundreds of dire predictions saying that ‘this time is different’ (and thus equity return prospects are dismal) I have heard over the last 30 years while the DOW has gone from 1,864 on June 23, 1986 to 17,809 as of this writing scares you out of the market. Translation: you take investment actions based on short-term emotions rather than long-term cold hard facts.

Bottom line: none of these events, not a single one of these 15 minutes of fame dire headlines, will cause your magic coin to stop working. Only you will keep you from reaping the benefits of participating in a ‘rigged’ stock market by letting any of the ‘the world as we know it is coming to an end’ headlines to cause you to put away your magic coin. Remember, the sources providing you these headlines (Jim Cramer, CNBC, whatever) are in the business of creating content to attract viewers so they can sell ads. They don’t know you, they don’t manage your money, and they have zero interest in whether you retire with enough money or not. Imagine if any of the financial talking heads came on the air and said, “….hold onto your stocks for the next 10 years and you will do just fine.” People would turn the channel (and thus ad revenue would dry up) looking for the commentator screaming “…run for the hills, a Trump presidency will cause stocks to crash 50%!...” That makes for great mass market entertainment, but it is potentially dangerous to your personal bank account.