Why are markets bipolar?

I think most people would agree that the stock market is bipolar – i.e. that sometimes it prices stocks way too high, and sometimes it prices stocks way too low. But yet it’s very hard to make more money than the average in the stock market? How can these two seemingly contradictory statements be true?

It turns out that you have to just make a few simple assumptions and you can build a model with these characteristics: i.e. prices that are impossible to beat systematically, but that seem in retrospect to have been very very wrong.

The following is all adopted from Benoit Mandelbrot’s work. See here for more.

Let’s assume we have a company that has a discounted stream of earnings worth $1. Every day, the earnings can go up by $1, stay flat, or decrease by $1.

Let’s assume that there is some “momentum” to these earnings movements. For every streak of X days the earnings go up, let’s say that the expected value of the number of future days the earnings will go up is also X.

So, let’s say this company starts with $1 worth of future earnings, and the next day they have built that up to $2. Earnings may continue to grow, or fall, but the expected value of future earnings is now $3. This expected value is the price of the claim on the earnings, or in other words, the price of the stock.

There are lots of reasons an increase in earnings would portend a further increase in earnings: the company has more to invest in sales, marketing, or equipment, or could buy back stock (increasing the earnings per share).

If this is true, we’d then expect prices for future earnings to rise (and fall!) much faster than the actual earnings streams themselves. What this looks like, in graphical form, is this:
Screenshot 2014-03-31 15.11.30

Screenshot 2014-03-31 15.11.09
You can see the spreadsheet I used to put this together here [there is not much in the way of detailing the math, but if you’re interested, comment below and I’ll walk you through it].

Now, this is not a complete model by any stretch. It’s just an illustration of how prices can always be “right” in that they represent the current best guess about the value of a stream of earnings, and then appear wildly wrong a short moment later.

The four types of incertitude

This post was inspired by a recent tweet:

Which reminded me of one of my favorite lessons in grad school at LSE. The lesson is simple: we think about how many different ways there are to have incomplete information about the future.

A very simple way to think about it is to think about foresight is it having two dimensions: knowledge about what the potential outcomes are; and knowledge about how likely each outcome is.

Pulling a random card from a normal 52-card deck is a great example of perfect knowledge about both what the range of outcomes are and how likely each outcome is. Even though the outcome is uncertain, we have great mathematical tools for figuring out how we should behave in advance of knowing what the outcome ends up being. This is called “risk”.

But many situations are not so favorable. Asking a lady out, for example, has a few canonical outcomes (she says no, she says yes, she demurs, etc.), but the asker will in many cases not have a clue what the likelihoods are. This is called “uncertainty” – where you know what the outcomes are, but not the odds of each.

So now that we have the two axes – outcomes and likelihoods – we can define two more “perfect” endpoints on this two dimensional spectrum of incertitude.

“Ambiguity” is where you know what the likelihoods are, but not what the outcomes would be. As a contrived example, consider that you were dealt a hand that you weren’t allowed to look at. You would be dealt one more card that you’d be allowed to see. You’d have perfect knowledge about the likelihood of each card coming up, but, crucially, not how it would affect your hand. This type of incertitude is common in very complex situations where you can’t parse out the impact of any given outcome.

Finally, “ignorance” is where you have knowledge neither of what the outcomes are, or what their likelihoods are. These are the “unknown unknowns” that Donald Rumsfeld made famous.

Visually, the layout of different situations looks like this:

597_andy_s_fig_2

Different methods for handling the different forms of incertitude are listed in italics.

The most important thing, though, is to know where you are in this space. If you think you’re in “risk” space, but in reality you’re in “uncertainty”, you’re setting yourself up for a bad day, as the tools you’re using may rely on a probability distribution of outcomes to guide decision-making.

In my view, the bottom half of this matrix (as presented in the graphic) is significantly more common than the top. It’s very rare that we ever have a real distribution to work with; at least not one that we haven’t simply contrived or guessed at so that we could use friendlier, more comforting mathematical models.

In any case, “risk” is actually a very special case in this space, but most of the models you see for decision-making (i.e., the ubiquitous excel spreadsheet) are built around the “risk” case.

 

Another update to “Conflict”: Bangladesh

Bangladesh worries me. As I wrote here,

Bangladesh is the most densely populated country in the world, with 150 million people crammed into an area the size of New York State. It also lies in lowlands, and a 1 meter rise in sea levels would flood about 10% of the land. Clearly, with so many people in such a small area, this would create problems. In addition, many people don’t know that Bangladesh used to be “East Pakistan”, or the eastern of two predominantly Muslim regions of the former British colony, and it shares with modern India (Bangladesh’s neighbor) and Pakistan in their violent history. It’s not hard to imagine a scenario where sea level rises (among other negative climatic changes) cause massive displacements of people in a context that cannot support that other than violently.

There is a great story today in the New York Times about how climate change is affecting Bangladesh. Read it and let me know what you think.

 

What I’ve been up to

February was a crazy travel month. I packed trips to Casablanca, DC, Tahoe, London, and Venice (and not to mention the airports of Chicago, New York, Paris, Brussels, and Frankfurt) into the span of 31 Jan to 2 March.

Lately, I’ve been thinking about insurance and risk. It’s funny when things you’ve worked on a while ago and since discarded pop back into your life. Three and a half years ago I wrote my master’s thesis on the relationship between insurance, climate change, and capital investment. Somewhat randomly I was asked to put together a short paper on this topic for New Climate Economy, where I am a Senior Programme Officer, where I’ll get the chance to show off some of the ideas that I developed.

The gist is that since insurance markets clear annually (a little bit longer for some reinsurance contracts), exposure to long-term risks (like climate change), can’t be traded with existing insurance instruments. Weather is a draw from a distribution, whereas climate is the distribution itself.

So in many regions there is an acute risk that premia will rise substantially in the future. This already happened on the East Coast of the US after Sandy. But this risk can’t be transferred, since no forward / futures markets exist for insurance.

In the end there are two reasons this is of concern: First, the lack of a market for this risk means that those holding it can’t dispose of it directly, and may be unequipped to handle it. The premia for, say, windstorm insurance for a residence could rise so substantially that it becomes unaffordable, or that this rise in prices causes a substantial hit to the home equity value.

The second concern is that a lack of pricing for this risk causes a distorted investment picture, and not only will there be no risk cover for those ultimately affected, but the absence of a signal on future risks causes even more people and property to be exposed to them.

So that’s what I’ve been doing and thinking about. À bientôt!