It's a numbers game, maybe like Bingo. |

Nobody knows the future, but developing our skills in probability analysis will make us better at preparing for it.

We can use probability at any level - global, country, market, industry, company. We can use it for an event, for example the probability of the price of gold increasing or the trend of interest rates.

For this example, we'll use probability at the U.S. market level.

The question we'll attempt to answer using probability is "does the bull market have more to run, or are we at the top?"

### Step 1 - Identify the key factors

We'll begin by listing the factors that influence, not just any bull market, but this one. Remember, the factors I choose and the probabilities I assign are my decisions. You may come up with different factors and different probabilities.

In my opinion, this bull market was created in the aftermath of the global financial crisis. It was built on earnings, incredibly loose monetary policy and a new tool called quantitative easing. As those factors change the nature of the market will change.

In considering what I think are the key factors of this market, I'll look at other factors coming into play: fiscal stimulus, tariffs, a movement toward less globalization/more isolation and less friendly immigration policies.

Finally there is always a wild card, a black swan event - a surprise event that packs a wallop but seems obvious in hindsight.

Having selected the factors we want to use, we build an equation:

Market change =

*a*(earnings) +

*b*(monetary policy) +

*f*(black swan)

Where

*a, b, c,*are the probabilities associated with the factor they are attached to.

### Step 2 - Assign Relative Weights

The next step is to relatively weight each factor. For me, I think that monetary policy has been twice as important than earnings earnings and a black swan event could be twice as important as monetary policy. I therefore give weights of 1, 2, and 4 for earnings, monetary policy and black swan respectively.

### Step 3 - Evaluate and Assign Probabilities

The next step is to look at what could impact the factors. Once the factors are evaluated, we must decide on a probability between -1 and 1. A positive probability indicates that I believe the outlook for the factor is favorable to a continued bull run (in this example). A negative probability indicates that the outlook is not favorable.

#### Earnings

Tax cuts may increase earnings. Companies may be able to keep more of what they earn and their sales might increase if people have more disposable income. Earnings might decrease because of rising inputs from tariffs and wages. Out of country sales may drop in retaliation for tariffs and antagonistic international policies. Population growth will slow if immigration becomes more difficult which indicates less demand for goods and services.

In my opinion, the earnings effect has run it's course. There are more factors now to weigh on earnings than to support them. The sign is therefore negative and I also feel the probability is relatively high. Let's say -70%.

#### Monetary Policy

This past 10-year long cycle has been unique with it's use of quantitative easing. The policy poured an enormous amount of liquidity into the market and kept interest rates very low. It's in in the process of unwinding now; the bonds that were purchased during QE are maturing and not being replaced. This reduction in bond demand is pushing up yields. The federal reserve has also been raising it's benchmark rate and has signaled that further hikes are in the cards.

If stock market started to drop, could the Fed change course and re-instate QE? Yes they could (not that they

*would*) if inflation isn't a factor. If it is, they will have to make that their priority, in my opinion.

Currently it looks like the Fed is doing a good job of normalizing monetary policy. They've gotten rates up and inflation is under-control. However, it would be imprudent to ignore the inflationary factors currently in play: tax cuts, tariffs, full-employment. If inflation starts to kick in and I believe it will, they'll have to tighten things up.

I feel the probability of the monetary policy becoming more restrictive to be high and the effect to be negative. I'll estimate -80%

#### Black Swan

A black swan event is by definition difficult to predict. It could be anything, but is should have some relevance in what's going on now. Here's some ideas: the collapse of sovereign monetary systems and the development of an international, gold backed cyber-currency. Trade war that heats up to hot war. Trump's unconventional and unprecedented policies work out in a spectacular fashion.

You could give probabilities to all the black swans you identify or you can just work with the one you think is most important or likely.

I'll work with all three for this example.

Let's say they all warrant a relative "4" for strength of impact. What counts next is the probabilities. The first example, I'm going to give a probability of .5%. The second 15%, the third 7%. The signs are negative, negative, positive. Because they all have the same weighting I can just sum the probabilities of the individual black swan events to get a black swan probability. The probability of a black swan event in this example is -.5%-15%+7%=-8.5%.

Note, use a weighted average if you decided the strength of impact numbers should be different. For example if you think the numbers are 3, 4 and 5, the formula would be -.5*(3/12) - 15*(4/12) + 7*(5/12).

### Step 4 - Put It All Together

We then plug the numbers into the equation we already created:

Market Change = -.7 x 1 -.8 x 2 -.085 x 4 = -.7-1.6-.34 = -2.64

The model indicates that the bull market will change into a bear market. It doesn't say "when" however, but the magnitude of the number is relevant. This equation could range in theory from a value of -7 to +7, but you'll never have a probability of 100% on any of the factors so in reality the range is less than that, maybe -6.3 to 6.3

As you work with probability and get better at it, the final number's magnitude will begin to communicate something to you about the timing.

Thanks for reading.

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