Animal spirits to the dark side unleashed, as we entered the final month of summer. We had enjoyed a multi-year continuation of a tired economic growth regime, but there have been concerns lingering that this stimulus-fueled growth was starting to wane yet again; perhaps come to an end. This was one of the concerns we recently described in our new book, copula narratives, and which I elaborate on a little further below. How do we assess the meaning, for example, of continued reductions in monthly job growth, a variable that the central bank themselves conceded is “somehow” repeatedly overrepresenting the actual job market? And what do we make of the recent pick up in unemployment [up +0.6 percentage points off their cyclical low], which in our book I suggest is in the initial district of spelling outright economic doom?
Copulas
Copula
statistics are a measure of joint dependency of variables, when they’re at
their respective extreme values. We
study them for multiple reasons, and in concert with other quantitative topics
such as probability theory, macro governance issues, agency dynamics, and
machine learning. What we have seen is
the challenge of knowing how to calculate what should be plain probability statistics. Such as the probability that we are in a
recession now or in the near future. We
consider long-view data [an expression we’ll define later] that has persisted at
least about a century. And even there it
is tricky to understand why patterns have changed in more recent business
cycles.
As
an example, the length and frequency of economic contractions have changed a
lot since records were [ex post] tabulated in the mid-19th
century. Those tabularizations were also
open to subjectivity as shown in exceptions being rushed into conclusion,
during the already-historic, 2020 coronavirus outbreak. Still, in its extraordinary aftermath, we
might imagine continued challenges of predicting recessions based on these increasingly
questionable statistical characteristics.
Copula theory saw the comonotonic nature [i.e., when there
is joint dependency in two variables in at least one equal direction: such as a
stock and bond market crash at the same time] of labor and stock market data
makes sense, but also is connected to the breakage of these models with parametric
model risk. So, where there are simply a
complete shift in assumed new variable relationships.
New York Times
Lets’
take last weekend’s New York Times article [How to Cope When
the Markets Panic]
by Jeff Sommer, and one of over a dozen times we’ve been cited in this paper
[including a previous time this year on cracking lottery annuities: Those
Billion-Dollar Lottery ‘Jackpots’ Aren’t Even Half That Big]. The recent article looks at the idea of
assessing the blind chance of a recession, based on a frequentist theory of
measuring said part of time in the past, and -just as vital- inferring from it that
the same said statistic could be predicted to likewise continue in the future. However there we get very large differences
in results, based on a couple factors, such as which century of historic data
you use for the calculation. And also
the weight of evidence you give towards current data already leaning in a
certain direction, whether it is up, or down.
These are analytical prerequisites that should give a human operator
pause.
The
New York Times article leverages this more complicated discussion in one of
their own earlier 2022 articles [Bear Markets and
Recessions Happen More Often Than You Think], arguably
the most recent previous period which had its own somewhat-similar, mini growth
scare. That article explored a 2-year
horizon for a recession outburst, versus this same calculation being modified
to use a 1-year variable assumption instead.
Would the model be as exact over time, if you halved this forecasting
horizon from 2-years down to 1-year?
Additionally,
we’ll note we didn’t have a recession in the two years since. Everyone should also spend time on model
assumption analysis trying to understand if a 40% of so probability at that
time was therefore perhaps just a tad too high, or perhaps it is correct as is! This is something for you to better
understand since -either way- it is certainly within a close range of model uncertainty. Hence this model and advertised errors as
well, are the overall topic of this web log article.
[V]VIX
Let’s
discuss what happened in the markets of early August 2024. It’s tough to imagine the entire global markets
swinging around like an options-fueled, meme stock. Yet we also know market volatility -in a
generic sense- does exist at times and puts everything about us in awe, when it
does. But the multi-percentage daily
breakdown of the major indices a week ago, seemingly without a long-term market
wearing warning, was of particular note.
Here
we saw it occur in real-time, and everyone had to make sense of the
“unusualness” of what they were sensing.
Every time we must wrestle with these two major possibilities: was it merely
market volatility which rears every so many years, or did it have elements of a
complete breakdown and extensive contagion that was going to spill-over into
broader economic measures? Monday
morning of August 5, pre-market New York time to be exact, I saw the volatility
index [or VIX] print a high 60s. This
immediately stood out as the second highest spike level seen since the 2008 global
financial crisis [or GFC]. And as high
as it was, it almost completely disappeared below 40 by the end of that Monday,
and closed sub-30s by the end of the next day; all suggesting an odd couple day
trip.
VIX
looks at fear in the overall market index: the panicked rush to sell at a steep
bid-ask discount. While VVIX on the
other hand is a complimentary measure of strain in the market system. VVIX looks at the panic through the expected
annualized change in the VIX. Both are
useful to see and cross-verify, in concert, to get an overall read of the legitimacy
of market mood shifts.
This
measure indeed popped as well to nearly 200, one of the 4 highest spike times
since the GFC. Almost exactly 6 years
ago in August 2008 -a month prior to the fall of Lehman Brothers- it had leaped
close to 150. But without the same historical
context as the measure was first introduced only a couple years prior and
evidently not as clean to backward-interpolate!
What was the VVIX telling us recently, and why did it not align with the
ever changing but correlated VIX? Yes a
pop to a high level is a signal, though of course these pop-ups are different
it appears than the level from the GFC era.
In
the charts above we show these distribution rankings, copula style, and notice
a clear comonotonic pattern with upper-tail dependency. For example we notice a severe clustering at
the 100th percentile of more VIX and VVIX, and not as much at the
0th percentile, or any other corner.
Notice we had many top-most VIX readings during the GFC [chart in upper
left quadrant], and many top-most VVIX readings in the coronavirus sell-off
[chart in the lower right quadrant].
Additionally we’ll note the times we saw the highest joint closings for VIX
and VVIX below. Notice the vast majority
of them all clustered during March 2020?
Outside of this the events were more sporadic, and none at all during September
2008!
Date VVIX VIX
10/27/2008 135 80
5/20/2010 145 46
8/8/2011 135 48
3/9/2020 137 54
3/10/2020 139 47
3/11/2020 147 54
3/12/2020 155 75
3/13/2020 171 58
3/16/2020 208 83
3/17/2020 194 76
3/18/2020 181 76
3/19/2020 182 72
3/20/2020 187 66
3/23/2020 168 62
3/24/2020 172 62
3/25/2020 172 64
3/26/2020 170 61
3/27/2020 169 66
3/30/2020 158 57
3/31/2020 153 54
4/1/2020 157 57
4/2/2020 147 51
4/3/2020 144 47
4/6/2020 143 45
4/7/2020 134 47
4/21/2020 132 45
Officially
August 5 didn’t officially make this cut since the VVX closed at 173, but the
VIX again “only” closed at 39 [the intra-day high of 66 is also not comparable
across this series since it occurred as noted pre-market, where calculations
were only first recorded in 2016.] But
it’s close enough and we blackened the data on the chart above on the lower
right quadrant where we see it is just the left [slight below 96%’ile VIX] of
the top-right most cluster of VVIX and VIX readings. Incidentally a joint 96%’ile event is for the
most part a (1-.96)*(1-.96), or extreme 0.2% event. Or seeing a once every couple year phenomenon.
It
suggests to me that we see multiple statistics concerning sudden market strains,
and not all related to a recession [which we assume has to be dependently
interconnected most times]. Note these
levels from 2022, as well, which were high but still not that high. Of course at the center of this market
meltdown was the weak July employment report, a weakening reading which some
market participants believe may not be an isolated case. We still need to see these upcoming readings,
next released in September and October, to get a sense of overall economic
direction. As a result, there could still
easily be continued panic and a revisiting of market volatility if in fact the
economic readings continue to soften heading into the November election.
For
now though it was sad to see retail investors panic into this unknown, earlier
this month. Novices flooding towards safety
and unclear if the information they were seeing was reasonable changes or not. I have long suspected AI-hyped NVDA stock was
in a bubble of its own making, and due for a market meltdown. I too had to take advantage of this period,
but after a couple of very strong down days I could only count my overwhelming
blessings. On Monday evening that day I terminated
my put options sensing things had come in too far too fast, and likely due for
at least some back and forth from this point forward. Along with the continued uncertainty, which I
believe will define the markets for the coming months. My entire portfolio is now at an all-time
high, while a 60/40 passive stock and bond index is down a few percent from their
July 2024 peak.
Institutional pensions,
and conferences
Switching
gears slightly to the topic of copulas, and the trick in measuring market
changing models, we have explored this topic in the context of institutional liabilities
and fiscal reserves. My customized liability
modeling work in this space is in a draft peer-review article currently under
revision. However I did speak at the
start of an important industry conference over this summer, about my modeling
and the ramifications for investing against institutional liabilities. Particularly with the changing market, labor,
and mortality landscape. And the
uncertainty in newer asset classes at this point in the post-coronavirus cycle.
It was well received, and a long-time friend, Skybridge CEO Anthony Scaramucci
also keynoted shortly afterwards at this conference [and at one point he highlighted
to the audience my statistical polling strength!]
copula narratives
This
summer I released my new book, copula narratives [copula narratives: mehta, salil]. 120 pages and 25 thousand words. It has been a top 25 science book release: a
super-category subsuming all commercial subcategories of ethics and technology,
probability, statistics, and math! We
spent years putting together the nuances of the different modeling methods and differentiating
between short-view statistics [news events that could receive help from this
type of modeling analysis], and the long-view models [news which we should
examine through this lens and at times in fact do if people know to do it.]
New books,
projects, credentials
In
this last section we’ll note our release other versions of this book, for
example an audio and e-book variation, both at a discount about Labor Day [along with my previous books still top ranked in mathematics]. So
please follow [Salil Mehta:
books, biography, latest update] for new information on that. Additionally I am close to completing math
with mira 👶🏻, a 140-page at-home exercises and solutions. This will be our book aimed at pre-K through 2nd
grade, or children aged 3 through 7.
This has been a multi-year project in coaching my baby daughter Mira on
the mechanics of simple math and the higher-level probability concepts to think
about. Doled out in small weekly sample problems
and lessons.
For
example what does it mean to have a small amount at higher odds, or a large
amount at lower odds? Or how do you assess
two statistics, one at a current point in time and another at a distant point
in time? What does it mean to think
about insurance on multiple things at the same time [e.g., wanting a higher allowance
but a parent losing a job, at the same time]?
All topics that are not covered in the closed-theoretical cases of
elementary school math, though still important to see through in life. For example, solving a division between two
given numbers: as if the world is going to be that easy and never having to
know all the shocking things that people still don’t know they got wrong in
their assumptions, for example during the 2016 election.
Some
of the examples of statistics ideas for children were given during my STEAM
[STEM] week presentation at Mira’s👶🏻 school [https://sites.google.com/site/statisticalideas/mira-school-talk]. Where I charged our children to think bigger:
“You’re at the launching pad of your life; You’re unbound by other
people’s passions”.
And
another item we are working on is a 2025 product for children’s coding and logic
development [mira👶
coding (from:salilstatistics) - Search]. This is taking initial steps to learn how to
think through a problem and solve it programmatically, to show an answer. Coding involves a different analytical tool
kit than probability, and statistical math, and this work is a step to
complement the gamification of software such as MIT’s scratch, in order to think
through many more applications and ideas.
Finally
we’ll note we have been completing the American fellowship actuary exams in
order to enjoy staying on the cutting edge of mathematics, an exam level 94% of
actuaries fail to get to. A topic of copula narratives. Our recent exam was a near highest score to
boot. What started as a highly productive
and positive year, will hopefully continue that way!
salil statistics [10k+ books sold, 36m reads, 1/4m follows]
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