Long Term Investments Are Not Risk Free: The Fallacy of Large Numbers and the Past Decade in Us Stock Markets

The S&P500 closed yesterday at 1,315.22 points. The first time the S&P500 stood at this level was April 1999. This past decade in the US stock markets has been a long-term investor’s nightmare. I’m referring mostly to retirement savings and households of course. The following chart is of the S&P500 index since 1999:

The rule of thumb in long-term saving is that stocks, over time, are the best investment option available as volatility gets averaged out and all that is left is to enjoy the average returns over the years.

Another rule is that the younger you are the riskier your investments should be since you have enough time to average out poor performance.

While financial advisors work according to these rules the academic world has had problems substantiating them on a solid academic basis.

Noble winning economist Paul Samuelson published an article on the subject in 1963 which is still referred to by almost any article ever since. The article was titled “Risk and Uncertainty: A Fallacy of Large Numbers”. In this article Samuelson describes a conversation between himself and his colleagues in which he offers a bet comprised of a better than 50%/50% chance of losing 100$ and winning 200$. A colleague soon replied he won’t accept a single bet but would accept a series of 100 bets. Samuelson argues his colleague is irrationally applying the law of averages to a sum and that accepting a string of bets when one identical bet is rejected is the “Fallacy of large numbers”. What does that have to do with the S&P500?

Essentially, in finance, we often consider stock investments as bets with some chance of losing x and winning (1+percent) of x. There is some chance a company will default and usually a better chance it will continue growing and with it our investments. As a life of a company much like a series of bets we can consider investment in such a way. Investing in an index is essentially diversifying our risk on many companies (usually within the same geography but no always). Thus we have access to such a series of promising bets.

The problem, however, can be understood intuitively. How is it that stock markets offer a premium on long-term investments (higher returns in the long run)? Where there are returns there must be risk. It seems Samuelson was on to something. Investing in stocks, even for the long-term, is accompanied by risk.

If you’re 20 and saving for 60 there is a good chance such a series of bets, or investments, will yield high returns. However, there is also a chance the last bets will result in heavy losses.

Financial advisors offer life-cycle investing to counter that effect. Invest up to 60% (just an example) in stocks when until 40, 30% until 50 and 10% until 60. By reducing your exposure you’re reducing risk. But isn’t the series of bets supposed to average at the end? Won’t I be losing return on investment? And most dangerous of all, what happens if by 40 I haven’t been able to generate high returns on investment simply because the economy in those years exactly was in a recession? It seems we can’t have it all.

The point I wanted to convey in this post is that there is always risk when investing in stocks. Investing for the long-term has proven so far but don’t assume you will generate 12% on average, each year, by investing in the S&P500 just because it did so from the 1950’s.