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A long time ago, when I had an idle six months or so, I came up with a theoretical model for chaotic systems from a roleplaying point of view. I was looking for a way to simulate the behaviour of the stock market in the Champions Universe. The result was 31 pages of 6-point type (the largest font size that I could use and still have some of the key tables fit on a single page of text). To test the system, I applied it to the conditions then operational in the real world stock market and found that it had a 98% correlation with reality in the long term.

The system never saw play. It was obviously completely unwieldy; it took a lot of effort and a lot of prep time to use. But, purely for the sake of stimulating the minds of our readers, I thought I would go through some of the logic steps that I followed way back when. Will I, or anyone else, ever use the resulting system? Probably not – this is likely to be a purely intellectual exercise.

Cycles Apon Cycles

The starting point was to suggest that the movements of the stock market were largely cyclic, trending towards a mean value. This is simple to achieve with an RPG: If we call the mean 1000, then we can have a range of plus-or-minus 1000 to play with.. If yesterday’s value was lower than 1000, then the odds favour an increase, so I used a 3d20 table in which 2/3 of the results were an increase and 1/3 was a further decrease. I then scaled the results as a proportion of a “typical” movement.

  • Lowest result: 3
  • Highest result: 60
  • 1/3 of 60 is roughly 20, so apply this as a negative modifier if yesterday’s result was below 1000.
  • 3d20-20 gives a range of -17 to +40. If the average change on a typical day on which the stock market went up was 100 points out of 1000, that would give 100/40=x2.5 factor.
  • So the bear market daily trend is +2.5 x (3d20-20).
  • 2/3 of 60 is roughly 40, so apply this as a negative modifier if yesterday’s result was above 1000.
  • 3d20-40 gives a range of -37 to +20. If the average change on a typical day on which the stock market went down was 100 points out of 1000, that would give 100/37 =x2.7 factor. The higher factor means that drops are going to be steeper than gains.
  • So the bull market daily trend is +2.7 x (3d20-40).
  • In actual practice, I didn’t use the +1/3 -1/3 ratio, I used a table that showed the likelyhood of a gain or loss according to how far the current value was from the mean.

I played around with the numbers a lot more, but that illustrates the general principle.

But there is also a weekly cycle, and a monthly cycle, and a yearly cycle, and a 7-year cycle, and an 11-year cycle. So do the same set of calculations for all of these, but divide the effects of these cycles into a constant modifier that gets applied each day to the result.

  • So if the 7-day cycle yields +21, that becomes +3 daily – and is then rerolled according to where the stock market ends up at the start of the next week.
  • Similarly, the 365.25/12 (monthly) cycle divides whatever the scaled result over that period is by 30.4375, so a change of -15 would become a daily modifier of -0.493 (3 decimal places is plenty).
  • The yearly cycle divides whatever the scaled result over that period is by 365.25. With maximum scaled change of say +150 points, that would be a daily modifier of +0.41.
  • The 7-year cycle divides whatever the scaled result over that period is by 2556.25 – but I would use 2500 as being close enough. The maximum scaled result might be +250/2500=+0.1.
  • The 11-year cycle divides whatever the scaled result over that period is by 4017.75 – but I would use 4000 as being close enough. The maximum scaled result might be +400/4000=+0.1.

Something I learned when playing around with the sums of Sine Curves and shifting one horizontally with respect to the other was that there were times when they would cancel out and times when they would add together. These same principles are the foundations of playing around with biorhythm results, which was a fun early application of home computers – unless you took the whole thing too seriously. This method uses a similar technique.

There have also been suggestions made that there is a 23-year cycle. And no, it had not escaped my notice that all these are prime numbers.

Variable cycle length

In the model that I created, I went a step further, and set up periodic cyclic adjustments in the length of the cycles. Since I was doing the whole thing with a piece of custom computer software I had written in BASIC, this was easy to do. I seem to recall assuming that the maximum permitted cycle change was limited to 10% of the average cycle length.

Long-term growth

The next thing that I factored in was the long-term trend – and by long-term, I’m talking 25 years or more. This is a constant trend, always upward. Small on a daily scale – around the +0.25 mark, as I recall (though memory might be faulty), this perpetually moves the goal posts. I kept this as a separate value to the daily summation of cycles so that they were always measured against a fixed basis. As I recall, part of this was a fixed increase and part of it was an amplification effect, so that actual daily swings increased in amplitude as the stock market grew.

For Greater Realism

The amplification effect has greater impact on losses in the downward part of any cycle and greater impact on the upward part of any cycle. My refined computer model and set of rules actually looked at each cycle and amplified it accordingly. Downward effects in general tend to be harsher, more sudden, and less frequent, so I also factored that in.

Similarly, in a recession (or worse yet, a depression), movements tend to be flattened, while in a boom things tend to be a bit more excitable. So I built a “prevalent mood” factor in which reduced daily changes or amplified them accordingly.

Day Of The Week

Stock Markets don’t generally trade over the weekend, or late at night each day. That means that the most dramatic changes tend to be on a Monday, when people scramble to catch up with the purchases and sales that they would have made over the weekend if they had been able. If the Saturday trend was up and the Sunday was down, that doesn’t matter too much. If both were down, then even if the Monday trend is upward, the market will tend to continue to decline. Any reasonable model has to factor that in – mine did.

Significant Events

There’s a whole heap of significant events that happen in a year, or a decade. I modelled these into three categories: Amplifiers, Bear Events, and Bull Events. Some of these happen regularly every year, like quarterly profit projections and end-of-financial year reports, others happen with lower frequency and less predictability, like natural disasters, or new industries, or new government initiatives. (EVERY government decision makes money for someone!)

Amplifying Events

Amplifiers are things like financial reports from big companies. If these are generally more positive than expected, the result will be a stock surge. If they are less positive than expected, the stock market will deflate. These tend to amplify the correlating cyclic effects – so an unexpectedly large profit announcement will amplify any cyclic trends that were upwards, while a more pessimistic announcement will amplify negatives. Add too many of these together and you get large-scale movements like recessions and booms.

To model these, you need to consider the overall composition of the stock market, and how much the largest companies on that market contribute to the whole. If the 100 largest companies are 40% of the market (they probably aren’t that much), then each has an influance of about 4%. A ten percent change in value is therefore 10% of 4% or plus-or-minus 0.4% of the total market value. And a ten-percent change in profits is a big deal that doesn’t happen very often – usually 1% is closer to the mark. But we’re only interested here in the extraordinary results.

Using this chain of logic, I decided that all I cared about were the ten companies with the biggest change in profits for the year. It didn’t matter who they were – simply determining their overall ranking would be enough to model what was going on. In practice, it turned out that the four biggest such rankings were more than enough. If those four were all positive, the results overwhelmed negative effects amongst the other six, and vice-versa.

That was enough to set a trend in the overall amplification factor, year-on-year. Of course, special attention had to be paid to new companies and closures/amalgamations/hostile takeovers but these were simple – exclude them because someone else will take their place. A company that is subject to a hostile takeover will improve the profitability of the new parent company, as will a merger.

Bear Events

Some random events are catastrophic and tend to pull the market down. But something I learned from my time working in the Insurance industry is that to some extent, these are predictable – you might not know where and when, but the larger the area / customer base, the more certain it is that something will happen somewhere in any given time period. Using these principles, I developed a table that randomly selected how long it would be before the next catastrophic bear event and how severe it would be. Each Bear Event not only amplified any downward trend, it compressed any upward market trend, and it reduced the overall size of the market as well.

These effects were simulated by adjustments to the various multipliers and modifiers on the cycles and to the overall results as well. The size of those adjustments was dictated by the severity and was termed the “significance”.

Each bear event also carried a third factor – rate of rebound. This was set up to use compound interest principles (sum of a geometric series) to determine how slowly the market would rebound from the catastrophic event. Some were deep and slow, others were deep but quick to recover; some were shallow and quick (and had little overall effect as a result) while others were slow but persisted for a long time.

The most cataclysmic bear event until recently, in the popular consciousness at least, tends to be the trigger for the Great Depression, when the stock market lost about 1/3 of it’s value in a 24-hour period. It’s worth noting that at the end of the Depression, the stock market was actually higher than it had been prior to the Wall Street Crash. In terms of actual losses, there have been a couple of more significant cataclysms since, but until the GFC none of them had quite acquired the popular cachet as the events of the late 1920s.

Crippling strike actions, Droughts, Wild Weather, and Banking collapses are all bear events.

Bull Events

I used the same principles for Bull Events. These tend to be less frequent than Bear Events, and less severe. Nevertheless, some events tend to bring an immediate surge to the market. Strangely, Wars being declared and Peaces being declared are both Bull Events. Though the constituent stocks involved will be different, the overall market reaction to both is generally positive.

Interestingly, I found that the rebound “downwards” after such events tend to only be about half the size expected unless a Bear event intervenes. Instead, the market ceases to rise very much in response to cyclic upswings, in effect “borrowing” from future increases to fund a consistently higher market value. Typically, too, what “rebound” there is tends to follow reasonably quickly – usually less than a week after the event, and often the next day.

Patterns Of Successive Bull & Bear Events

Given the random nature of the interval between successive bull and bear events, regardless of magnitude, it’s obvious that there can be four different patterns:

  • Bull-Bull
  • Bull-Bear
  • Bear-Bull
  • Bear-Bear

When I looked at these historically, I found that in each category, there was a change – I chose a flat 10% per event but it is probably a variable – that the market would overreact to the second of these. When a market overreacts, it resets the clock UNLESS the event that follows is of the same nature as the event that suffers the overreaction. When there is no overreaction, the % chance of an overreaction to the NEXT event simply increases by the 10% rate.

I think this has more to do with human psychology than with any actual impact on profitability or stock values.

Overreactions have the effect of boosting the significance of the event, but also bringing forward the recovery from the event.

Superheroics as Market Events

All this was for a world in which there was a globe-trotting organization of superheroes who went wherever the trouble was. When one showed up, it usually spelt trouble for that particular neighborhood because they tended to be there for a reason.

Superheroic interventions come as a paired Bear-Bull event outside the normal continuity of such things. Insurance companies tend to face massive payouts in their wakes, and manufacturing can be severely impacted, as can mundane things like freight deliveries that can have a big impact. Throw in the psychological impact on the population, and the Bear part of the equation is easy to see.

When they succeed, they rarely stick around to help with the cleanup – that only invites a second wave of trouble to an already damaged or devastated infrastructure. At the same time, a victory by “the good guys” has a definite morale-boosting effect on the general population and is followed by a phase of reconstruction. There are opportunities to modernize equipment, write off debts, and do other things that help the bottom line. There also tends to be national money – a sort of “disaster relief” – that flows into the local economy. Where businesses have been devastated, this simply helps pick them back up to where they were – but to anything that survived, it acts as a boost. So surviving a superheroic intervention tends to be an economic stimulus, at least locally.

Overall, then, Superheroes are good for the economy. That effect, plus the general confidence that results from security, means that new members are a positive market event – a Bull event – unless they are replacing old, established, hands. The loss of members is a negative market event, a Bear event. Public assessment of the reputations of the heroes plays into this as well – a new or returning member of massive popularity is a good thing, while the loss of a mistrusted member can even be a positive market event.

The best way of simulating all this to-ing and fro-ing about new members is to go back to where we started, with another extra “daily cycle” – but with the GM evaluating events in the campaign instead of rolling the 3d20. Similarly, the events of superheroic intervention are best simulated by an initial negative impact – a straight drop in the markets – followed by an additional weekly cycle in the positive direction.

Nowheresville

No community has yet engineered a crisis to bring about a superheroic intervention to stimulate the local economy in my game world. In general, politicians are too scared of the potential political fallout if they get caught engineering such a crisis. Nor has anyone attempted to stage a superheroic intervention in a bid to manipulate the stock market – most responsible businessmen are too conservative for that. But when governments or individuals feel their backs are against the wall, extremes of behavior can result… There are certainly a couple of plotlines there, waiting to happen.

Superheroic Spinoffs

Superheroes tend to come with baggage. The corporate entity that was building killer robots gets shut down by the superheroes, and the assets then get foreclosed by the banks and insurance companies – including the technology that went into those killer robots. With a little tweaking by some (hopefully) clever engineers, robot manservants and cleaners go on sale a year or so later. Heat rays, new energy sources, personal jetpacks and antigrav platforms and, well, you name it – they all have industrial applications. The presence of superheroes is generally good for the productivity of the world, and that’s a series of long-term bear events. Part of the thinking that I try to do whenever a villain is encountered in one of my campaigns is to decide how long it will take before that villain’s tech begins to seep into the general economy, and what shape it will take.

And, when I want a particular technology to enter general circulation, the best place to start is by introducing a supervillain using that tech into the campaign!

Superheroic Funding

Which brings up an interesting related question: where do superheroes get their money? Some are inventors – and everything said above about recovered villain-tech applies equally to on-general-sale hero-tech. Some use their abilities to predict the future. Some are inherently wealthy – but that wealth always has limits. Some have government funding – which always seems to have strings attached. The parent team to Zenith-3 in my campaign runs a four-star zero-G hotel in their asteroid base – with tickets stamped “at your own risk” – and one member has published a massively-popular book of philosophy (the profits from which he turned over to the team) which then became the basis of a cult (that was the bad news) which continues to funnel collections to the superheroes (which they aren’t all that comfortable accepting).

Superman used to repair a lot of the damage himself (at least temporarily), and help out on large civil construction projects, saving Metropolis a bundle. He would also squeeze the occasional lump of coal into diamonds, and had an instinctive knack for creating collectables, most of which he gave away. Add to that the tourist trade he brought in, and the occasional insurance company subsidy by the city government doesn’t seem so arduous. I used to think the stories where the Man Of Steel built bridges and so on overnight were light-weight – only when I started thinking about the economic impact of a superhero did I see that these “light” stories were an essential part of the “Superman Operation”.

If Lex Luthor wasn’t already the richest man in the world (or close enough to it), his many licenses and patents from anti-superman activity would surely have carried him to that point in a few short years. I wonder when he’ll figure that out, and what his reaction will be? An amusing thought on which to conclude!

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