## How unexpected are 1-in-100 yr events?

I was chatting to someone about once-in-a-century events, and I was reminded of a book I read a while back which pointed out that understanding probability is a pretty recent thing. In fact, there haven’t been that many centuries in which people could talk knowledgeably about 1-in-100 years events.

(I should probably put a disclaimer right here that, just as it seems any public post  about poor grammar is bound to be riddled with grammatical errors, my post about probability is going to be full of  mistakes. So, I promise to fix them, if they are pointed out to me.)

A funny thing about 1-in-100 year events, like 1-in-100 year floods, or storms, or market busts, is that they can appear to come along more frequently than once every hundred years. But it looks like we’re stuck with the name.

A 1-in-100 year event is simply one that has a 1% chance of happening in any particular year, which means that, mathematically, you would “expect” there to be one, on average, every hundred years. But of course, some centuries will have more or less of them.

In fact, (making assumptions about the distribution of events,) you would expect 37% of centuries to never have a particular 1-in-100 year event. You also get exactly one 1-in-100 year event in around 37% of centuries. The rest (26%) have more than one.

While more than a quarter of centuries can see multiple occurrences of a 1-in-100 year event, it’s worth asking: how many times can such an event crop up in a century before you start to wonder if it’s really still a 1-in-100 year event. How many occurrences of 1-in-100 year events should you actually expect?

The answer depends on the threshold for unlikeliness. A reasonable standard might be that anything less than 5% probable is pretty improbable. Back in high-school, playing D&D role-playing games, throwing a 20 sided die and getting a 20 (i.e. a 5% chance) was enough to get you special results. It came up a few times every game, but it was something pretty unlikely indeed. So, let’s use that standard for now. (It’s also common elsewhere.)

So, how many occurrences of a 1-in-100 year event in a single century are needed before we get to a level that’s less than 5% likely (or, you would expect to occur in less than one century out of twenty)?

The answer is 4. It’s only when you get four of a 1-in-100 year event happening in the same century that you might want to start questioning whether something else is going on, because it’s all starting to get a bit improbable. Four or more of such an event should crop up in less than 2% of centuries.

So, in summary, you shouldn’t be shocked to see three of a 1-in-100 year event occur in the last hundred years – it’s perfectly expectable.

## Superannuation’s Legislative Risk

I recently got back from a short holiday in Canberra, our nation’s capital. Amongst other touristy things, we visited Old Parliament House, where there is an Australian Democracy Museum. One of the displays is on the past Prime Ministers, and when you see them all together, you realise that we’ve had a lot of them, in the century and a bit that we’ve run our own parliament.

In fact, from 1901 to 2010, we’ve had 31 changes of government. For those not doing the math as we go along, that’s one every three and a half years.

And for someone who is, say, 35 years old, and facing 25 years before they can get access to the money in their superannuation, there’s an expected 7 or so new governments that will have a chance to meddle with it in the mean time.

The risk of current and future governments impacting the performance of an investment through passing laws is called Legislative Risk. Unfortunately, laws that affect superannuation have been prime candidates in the past for government fiddling. In the future, given the rumours about the Henry Tax Review, it will almost certainly get further tweaking still.

If you’re an employee, participation in superannuation is compulsory, where 9% of the total salary package (or thereabouts) is locked away in the system. Unless employees are willing to go to the expense and effort of setting up a Self Managed Super Fund, their money is generally invested in Australian stocks and bonds. So, if you want to invest in say fine art, residential property, a family company or venture-capital backed start ups, you aren’t going to get any joy with super.

Despite the limited investment options and the long period that you can’t directly benefit from it, an investment in your superannuation gets beneficial tax treatment. This is its key advantage, and the very thing that is vulnerable to legislative risk – a risk that is real, based on past actions and rumoured future actions of our governments.

I think that most Australians would benefit from having some level of investment outside of superannuation (even if it’s just their home), in order to reduce their exposure to this risk.

## Sub-prime = Euphemism

I’m studying a subject called Risk Managment for Finance Sector Enterprises at the moment, so of course it mentions the sub-prime crisis and the global financial meltdown. In a couple of places. However, one of the links provided out to supplementary reading material is a great article about people such as Steve Eisman who knew about the disaster well in advance, called The End of Wall Street’s Boom by Michael Lewis. Here’s a particularly scary quote from it:

he draws a picture of several towers of debt. The first tower is made of the original subprime loans that had been piled together. At the top of this tower is the AAA tranche, just below it the AA tranche, and so on down to the riskiest, the BBB trancheâthe bonds Eisman had shorted. But Wall Street had used these BBB tranchesâthe worst of the worstâto build yet another tower of bonds: a âparticularly egregiousâ C.D.O. The reason they did this was that the rating agencies, presented with the pile of bonds backed by dubious loans, would pronounce most of them AAA.

Yes, this is how I can justify blogging as studying for the exam this week.