Anatomy of a Market Beater: Part V

In this series, I’ll be exploring whether there are any useful characteristics that separate stocks that beat a given benchmark index (“winners”) from those that lose (“losers”).

Suppose the benchmark index you are using is the NASDAQ.

Also, suppose that we are comparing stocks against the NASDAQ over a period of 365 days (the “test period”).

I ran 1,000 randomized trials on existing NYSE and NASDAQ stocks whereby for each trial: (1) a random date was chosen, (2) every existing stock was compared against the NASDAQ index over the period beginning with that random date and ending 365 days later. The stocks for each trial were grouped into either “winners” or “losers” depending on whether a stock’s overall growth over the 365-day period was greater (“winner”) or lesser (“loser”) than the NASDAQ.

The winners and losers were compared by days a stock would be beating or losing against the NASDAQ, the amount of that gain or loss (margin), and the absolute gain or loss that stock was experiencing.

Here’s what I found.

V. Cumulative Gains of Winners versus Losers

If we map out the cumulative median gains of the winner stocks versus the loser stocks at each point in time along the investment period from day 1 to day 365, we would get something that looks like this:

Figure 1. As an example, by day 50, a stock that ends up beating the market over a 365-day period would expect it to have a median cumulative gain of 4.75%, whereas a stock that ends up losing against the market over that same period would have an expected cumulative median loss of -0.88%.

No surprise here as stocks that beat the market overall tend to do better than those that don’t on a day by day basis. One interesting feature however is that the loser median per day rate is not as dramatic as the winner per day rate. So, the losers on a median average basis do not lose nearly as much as the winners gain.

Remember, this is an aggregation of 1,000 trials, so each line above is the median of 1,000 trials of median gains for each group of winners and losers. In other words, on each day, in each trial, each winner’s cumulative gain is calculated. The median value out of all the winners of that day of that trial is calculated. Since there are 1,000 trials, there are 1,000 median value samples. So, the lines above represent the median, median cumulative gain of a winner or loser stock respectively.

Because Figure 1 above is an aggregate of 1,000 trials we’d probably want to know how variable the figures of that aggregate are. In essence, how reliable is Figure 1?

Let’s first look at maximum and minimum figures:

Figure 2

Here we have the same graph as Figure 1, but this time they are bounded. The winner median, median cumulative gains (yellow) are bounded below by their minimum, median cumulative gains (redline), and the loser median gains (green) are bounded by their maximum median gains (blue).

As you can see, the spread of both winner and loser cumulative gains is quite vast.

To confirm how unreliable Figure 1 is, let us look at their deviation figures:

Figure 3

The blue and red lines represent the spread of cumulative gains within the winners and losers groups respectively. (Note because this is an aggregation of 1,000 trials, “spread” really means the median spread over those 1,000 spread samples). Losers tend to have a lower spread in cumulative gain figures amongst their ranks while winners tend to have higher variability. As the days progress, that variability increases for both groups but at a higher rate for winners than losers.

The green and yellow lines represent the spread of median cumulative gains of the winners and losers respectively over 1,000 trials. In short, they represent the spread of the lines in Figure 1 above.

What this says is (1) that identifying whether a stock is a winner or loser based on its cumulative gain on a given day is not very wise because their spreads are so high (see Figure 3, blue and red lines) — I mean look at the range of possible cumulative gains any given winner or loser stock might experience:

Figure 5. The left y-axis is for blue. The right y-axis is for red. The x-axis is the test day in the 365-day test period. As an illustration, on the last day, the absolute maximum a loser stock ever gained over a 365-day period while still losing against the NASDAQ was 104.8%! That must have been a 365-day period when the NASDAQ performed especially well.

Figure 6. As an illustration, on the last day, the absolute lowest gain a stock experienced over a 365-day period while still beating the NASDAQ was -60.6%!

Winners and losers can experience nearly the same types of cumulative gains as the other save for the last day, as that is the day that defines winner from loser: if you have a higher cumulative gain than the NASDAQ by period’s end, you are a winner, if not, you’re a loser.

…and (2) that identifying whether a group of stocks are winners or losers based on their collective cumulative gain is not as bad of a gamble because the spread is rather narrow (see Figure 3, yellow and green lines) while their regions are divergent (see Figure 1).

Here’s Figure 1 again but this time each line is bounded by lines representing plus and minus 1.5 times the median absolute deviation (MAD) of their median cumulative gains:

Figure 7

If a group of stocks you have is experiencing a median cumulative gain of X over NASDAQ on day Y, and X exists outside of the winner region bounded in Figure 7 by the teal and orange lines, then you should consider the possibility that at least one stock in your group is likely not going to be a winner by year’s end.

However, the winner region overlaps with the loser region bounded by the green and yellow lines. So, the amount of uncertainty that a loser exists in your group is quite high. As you can see, the upper bound of the loser region never dips below the lower bound of the winner region.

This is not the case when we look at marginal gains in the next article, and that is in part why marginal gains are more reliable than cumulative gains as a means for determining whether a group of stocks contain winners or losers prior to the close of an investment period of 365 days.

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