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Mean time between failures (MTBF) is the predicted elapsed time between inherent failures of a system during operation.
This would seem to be a handy metric to know in regards to our current economic expansion. Since the financial experts like to draw upon several hundred years of economic history to predict the future, let's attempt to do the same.
There have been 33 expansions since 1854 (not counting the one we are in). The following chart shows their distribution.
Click to enlarge.
Our current economic expansion began in June 2009. That means it is currently 33 months old. I have turned that bin red in the chart so that you can see where we are. As you can see, we're already on the back side of the peak. I know it feels like we just got out of a recession, but historically speaking that's not the case.
Let's use that data to generate new data. The following chart shows the historical cumulative probability of economic expansion failure (i.e., recession).
Click to enlarge.
64% of previous expansions lasted less than 36 months. Our current expansion is 33 months old. 76% of expansions lasted less than 45 months.
So on that note, there were "probably" better times in all of recorded history to bet the farm on the stock market.
This is not investment advice. I have no crystal ball telling me when the next recession will hit. It is simply the opinion of a saver not willing to risk his nest egg on supposedly "sure things".
And lastly...
The MTBF is typically part of a model that assumes the failed system is immediately repaired (MTTR), as a part of a renewal process. This is in contrast to the mean time to failure (MTTF), which measures average time to failures with the modeling assumption that the failed system is not repaired (infinite repair rate).
I must admit that MTBF may not be the perfect analogy for the handbasket we find ourselves in. The repairs do not seem all that immediate.
That said, there are always MTBBF and MTTB (mean time between bank failures and mean time to bailouts). So, hey, at least we can count on those. You won't find them in any financially innovative textbooks though. At least not yet, sigh.
Source Data:
NBER: US Business Cycle Expansions and Contractions
11 comments:
One problem:
"Another common misconception about the MTBF is that it specifies the time (on average) when the probability of failure equals the probability of not having a failure (i.e. an availability of 50%). This is only true for certain symmetric distributions. In many cases, such as the (non-symmetric) exponential distribution, this is not the case. In particular, for an exponential failure distribution, the probability that an item will fail at or before the MTBF is approximately 0.63 (i.e. the availability at the MTBF is 37%). For typical distributions with some variance, MTBF only represents a top-level aggregate statistic, and thus is not suitable for predicting specific time to failure, the uncertainty arising from the variability in the time-to-failure distribution."
However, this can mean that the MTBF is too optimistic.
CP,
This is only true for certain symmetric distributions.
It is funny your bring this up. There's nothing symmetrical about the first chart. That's why I chose not to use "bell curve" math.
exponential failure distribution
There's only so much more of that this country can take, lol. Sigh.
http://research.stlouisfed.org/fred2/series/FYFSD
is AFAICT the oldest data on FRED and it allows one to get a glimpse of how cyclic the pre-New Deal eras were.
This nation didn't have an excuse for being so mismanaged in the 19th century, other than that we're still kinda making things up as we go along.
In 1850 we had 8 people per sq mile -- 80 acres per person, more land than what Canada and Oz enjoy now. Better land, too.
We had so much land Congress started giving it away, and they were pretty corrupt about it.
The whole Populist thing was a reaction to the deflation of the 19th century (the price level fell 30% between 1870 and 2900), and man did the nation need the Progressive reforms it got, prior to WW I.
We need a new TR today, but alas I see his namesakes TR IV and V are Wall Street-tainted, LOL.
Troy,
The whole Populist thing was a reaction to the deflation of the 19th century (the price level fell 30% between 1870 and 2900)...
I'm not sure the market has the 30% price level fall to 2900 factored in yet? Hahaha!
Sorry, I could not help myself. I know it is just a typo. It isn't like I am even remotely immune to them myself. :)
In all seriousness, your typo made me think of Japan's situation since their housing bubble popped 20 years ago.
You could try another graph, though it has its limitations: given that the expansion has lasted so long, what is the odds of the expansion ending in the next xx months?
That said, it's not as if booms and busts occur randomly. We understand imperfectly the past, which gives us some modest guide to the present and future. The current expansion is sustained by abnormal monetary and fiscal policy, which makes me then it will end sooner, rather than later.
David Merkel,
Two thoughts.
1. I like your idea of another graph. I'll create in the next few days and post it.
2. I think you may be right about the abnormal policies making it end sooner rather than later. However, I offer an alternative. It could end later and simply end in a more spectacular way. The previous two expansions were both relatively long and look how they ended (stock market bubble and housing market bubble).
On the other hand, expansions didn't last so long in the 1970s, and abnormal policies are apparently trying to repeat that lack of success. Sigh.
The new chart is up.
MTBF is a binary analysis, 0 or 1, black or white, either it has not failed or it has failed. With MTBF, we just care that the system is performing better than the failure criteria, but we don’t usually care how much better. In this analysis, as long as the economy is expanding, that’s good enough.
There isn’t any consideration to the magnitude of expansion in relation to duration. I think that’s a key missing link here. Under the current structure, the longer the expansion, the better, regardless of magnitude. A shorter, stronger expansion would be trumped by a longer, weaker expansion. Also, it probably matters how deep the plunge was and how long it took the expansion to reach the previous high water mark, as well as how far above the previous high water mark an expansion took us.
Then, there are variations with time. In this case, you’re talking about a single system that’s constantly evolving. The system today isn’t the same system we had years ago. That said, “This time is different,” isn’t true since the same patterns and dynamics still apply. In a way, it’s similar to the difficulty of comparing a stock index today to the same index previously if changes have occurred (members, weighting, etc.). When we typically do MTBF work, say in my native aerospace industry, we’re talking about multiples that are generally of similar design and operating environment. Of course, complications pop up like retrofits, repairs, time in service, variations across the fleet, infant mortality, wear out, etc., but the data set (eventually…usually) harmonizes enough for us to find a steady-state MTBF.
All that said, being able to link probability and timeframe is hugely valuable to risk assessment. It has limitations, but it does yield useful insight.
Tim Russell,
There isn’t any consideration to the magnitude of expansion in relation to duration. I think that’s a key missing link here.
It is a most simplistic analysis. I'll give you that. There are so many variables to consider.
Under the current structure, the longer the expansion, the better, regardless of magnitude.
I might disagree with that. The expansion that ended in 2001 was the longest expansion on record (since 1854 anyway). It lasted exactly 10 years. How have we done since?
Of course, one data point does not make a proof. I simply offer it as food for thought.
Also, it probably matters how deep the plunge was and how long it took the expansion to reach the previous high water mark, as well as how far above the previous high water mark an expansion took us.
I think that is certainly a fair point. You could very well be right.
For what it is worth, I'm extremely bearish on where our country is headed. There are quite a few things that tell me this time is indeed different.
Check out my charts of employment and debt.
As an aerospace industry professional, you might find the second chart the most interesting. It involves taking our total credit market debt owed, converting it to pennies, and then seeing how far into space the stack would go.
Would you believe past Pluto? How's that for scary? Or is it scarier that we stopped stacking them and have seemingly peaked? Hard to say. Sigh.
Oh, and thanks for leaving a comment. :)
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