Green and Red Marbles

In November 2007 I was in the audience for a presentation from a fellow financial planner (not a trader) on why it was “statistically smart” (his words) to stay invested in the market all the time. The timing of this speech missed the top of the market by a matter of a few weeks, and its main topic centered on the use of green and red marbles to make the speaker’s point. I thought that we were due for a red marble, which I will get back to in a moment.

A few months later, February 2008, I was asked to give a presentation on general economic conditions to a local chamber of commerce and its members. I focused my speech on the dangers of being invested in a wildly overvalued stock market and how the collapse of the housing market and its effects on the stock market was going to affect “almost everyone you know” (my exact words), and I warned the audience that “if they weren’t prepared to panic (i.e. – sell stocks) at the top,” which was already behind us on the calendar as I spoke, “then they better not panic at the bottom.” I also said, “that given comparable historical examples, the bottom is likely to be approximately -50% south of where the market rests right now.”

From the time of the speech to the subsequent low in the S&P500 in March 2009, the market lost -51.01%. Here’s the chart:

I really don’t mean to brag, so let’s call how close I was a lucky guess. Given what I know now about trading and how I have applied the lessons I learned over the last several years, there’s no way I should be bragging about that prediction because I made nary a dime from my own insight. At the time I was an asset allocator like my colleague in the first paragraph, so my bragging about that call is similar to what some mutual fund managers can claim from that era, that they lost less than the market did over that time frame. “Give me another wildly overvalued market like that one,” a refrain I have repeated many times since 2010, “and I will make my F.O. money* and walk away from this business and become a wooden boat builder or engage in some other pastime that does not have me staring at market prices, spreadsheets and economic data most waking hours of each working week.”

Well, here we are, overvalued again and ripe for a fall, similar to 2000 and 2007. My F.O. money is sitting in the market waiting for me to extract it after the inevitable decline. But what about those red and green marbles? Thanks for reminding me, as I have a point to make.

The financial planner’s argument for staying invested at all times was predicated on a simple statistic; since 1951 up to and including 2007, the S&P500 experienced 42 positive years and 15 negative years, or stated as it was in the speech, “70% of the time the market has a positive year.” Then he stated, “Now imagine an opaque jar filled with 100 marbles, 70 of which are green and 30 of which are red. You reach your hand in the jar to pull out a marble. Which color do you think you are more likely to grab?”

It makes absolutely perfect intuitive sense that you should answer, “GREEN!,” with as loud as your voice can fill the room. To go on record publicly with my cohort and since I liked to occasionally exercise my contrarian sarcastic side, I shouted out, “RED!” The speaker looked my way and smiled but did not pry to let me explain myself; he was, after all, a colleague and understood why I said that. His guests just thought I was being a smart ass, which was fine by me.

So why did I answer “red” when the correct answer to the marble question is clearly green? Because the market is not like an opaque jar of colored marbles, though in that scenario it is similar in that the jar would have a memory, so to speak. I will explain. In the case of actual market returns since 1951, the more green marbles that are withdrawn from the jar, the more likely it becomes that you will pull a red marble. Let’s look at actual returns since 1951, the first year of my sample. I’m going back in time now.

We’ll assume that the 70% rule still applies (actually it was 74% – 42 positive years divided by 42 positive years plus the 15 negative years = 74%) even if we don’t pull the marbles in their correct historical order. Each marble is labeled with a given year and its associated return. I randomly withdraw 1998, a green year. That leaves us with 41 positive years and 15 negative years, or a 73% possibility that the next draw will be positive. You know what’s going to happen from here, the more positive numbers you pull from the jar, the more likely that eventually you will pull a red marble.

The speaker’s argument, however, and to be fair, was more complex than that. He said we start each new year with the same number of marbles and the same probability, starting from 100 with 70% of them being green. My counter argument was and still is, that you have to take valuations into account when determining your odds of pulling a positive year out of the jar, or as I have alluded to, the market has a memory unlike a fresh jar of marbles waiting to be pulled one by one.

Current valuations on the S&P500 are very similar to 2000 and 2007. The likelihood of pulling a red marble is increasing. If I assign a weight to the next marble pulled from the jar, it may in fact be green labeled with some positive return, but the risk of pulling a red marble with a large negative number far outweighs the likelihood of another green marble no matter what the return.

I have not lost my marbles.

* – If you need an explanation for the letters F.O., look no further than Jackie Gleason’s character in Smokey and the Bandit. You can probably find it in YouTube.