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Market Risk, Model Smash

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Submitted by Salil Mehta of Statistical Ideas

Market Risk, Model Smash

Seeing the market crash from a few weeks ago, it is clear how quickly the market can ferociously hurdle in front of one's risk models. Risk models that failed to safeguard against risk when it mattered the most.  Models that left many large hedge funds hemorrhaging - top funds which by definition were supposed to protect their investors in the August tumult.  Instead when markets broke bad, a lot of things "went wrong"; and stayed that way.  

In this article, we explore a number of the large U.S. market crashes since the mid-20th century, and show how the recent bust compares.  We learn why relying on tail risk models whose approximations presume to work consecutively at all times, can lead to failure.  The key for investors (if they must be active) is to always remain vigilant.  Professor Nassim Taleb recently expressed it nicely:

The *only* way to survive is to panic & overreact early, particularly [as] those who "don't panic" end up panicking & overreacting late.

And there were many who wound up in panic in recent weeks.  Expeditiously selling at a loss, under record volume on August 24 (China's Black Monday).  Let's first consider what an overall market crash look like.  We quickly show a symmetrical V-shaped illustration here.  This illustration also shows a rise in fear on the way down, with peak panic near the bottom (the orange star), then followed by up-moves that mirror the previous down-moves.  We will need to review this overall shape in a future article.  But for now we discuss simply the left side of the illustration (the solid brown down-arrows).

In developing upon the numerous ways in which a market crash can occur, we apply a non-parametric probability approach that explores an initial brutal decline.  Then a peak in market fear, and then an "aftermath".  We'll also tabulate and focus our attention on 10 largest crashes since 1950.  Each one we measure up against these 3 crash patterns below.

Of course we can debate to some extent over what the 10 largest crashes are, but that would be losing the forest through the trees.  It's more important that we simply agree on a respectable overlap of what constitutes a decent sample of market busts, and when the peak jitters were felt by investors and observants.  Now for fun, which of the following 3 patterns do you think generally represents the nature of these large crashes?

A. a slow collapse into maximum fear, then followed by a torrid fall
 
B. a rapid drop into maximum fear, then subsiding into a slow and chaotic recovery with retests
 
C. a straightforward drop terminating in maximum fear, then a shallow and jerky rebound back (perhaps temporarily) to "stability"
 
Most would erroneously assume (and this is also how it is generally portrayed by business leaders through the media) that market crashes frequently occur in the order shown.  That is, more are of pattern A than of pattern C.  We'll see however, even if counter-intuitive, that the precise reverse has been true.
 
We show below, the 10 large market wrecks, in addition to the recent August 24.  We use a probability template as well that shows vertically compounded day of "greater severity" price moves versus the previous day (example follows the 11 graphs here).  If a daily market move is not more severe in direction (lacks acceleration), then we shift the data to the right.  We start each time graph where markets were previously quite stable, and terminate each graph at the first equal period of stability.  And we use the same lightly shaded boxes, similar to those shown above, to show the market price changes in relation to the time of ultimate scare (the performance of which we bold below).
 
June 23, 1950:
 

September 26, 1955:

 

May 28, 1962:

 

 

October 19, 1987:

 

October 13, 1989:

October 27, 1997:

August 31, 1998:

 

April 14, 2000:

October 15, 2008:

August 8, 2011:

August 24, 2015:

 
 
So in the first case of 1950, the returns prior to August 26 of that year were:

August 21 +0.9% 
August 22 +0.8% (positive price move though less severe versus +0.9% so shift up and to the right)
August 23 -0.1% (negative price move is a directional change so shift to the right)
August 26 -5.5% (negative price move and more severe versus -0.1% so just show it vertically below the August 23 result)
Etc.

Again this is not meant to show (by the visual scale) the actual distances traveled in percentage points.  But it gives us a non-parametric feel for the direction (and the colored bars green and red show the magnitude) of the daily price movements.  Even including the horizontal shifting of the price changes, one can see whether there is extraordinary acceleration or deceleration in price changes.

Now in the table below we encapsulate the statistics for the daily prices changes and time duration before (first shaded box in the graph), as well as after (everything after the first shaded box in the graph) the time of ultimate panic.  We also state which of the 3 market crash styles noted previously apply.

1950: crash of -4% over 4 days; then -3% over following 5 days.  Pattern A
1955: crash of -6% over 2 days; then +1% over following 7 days.  Pattern B
1962: crash of -14% over 5 days; then +5% over following 7 days.  Pattern C
1987: crash of -35% over 8 days; then +9% over following 20 days.  Pattern C
1989: crash of -7% over 2 days; then +2% over following 2 days.  Pattern C
1997: crash of -10% over 3 days; then +7% over following 6 days.  Pattern C
1998: crash of -13% over 4 days; then +3% over following 2 days.  Pattern C
2000: crash of -10% over 3 days; then +6% over following 4 days.  Pattern C
2008: crash of -27% over 15 days; then -2% over following 46 days.  Pattern B
2011: crash of -14% over 5 days; then +6% over following 7 days.  Pattern C
2015: crash of -10% over 4 days; then +5% over following 4 days.  Pattern B

Notice that the 10 initial crashes account for a total of only 157 trading days (~1% of the days!)  We also witness the frequency of these crashes as roughly once every 6-7 years (about the duration of an economic cycle).  Also note that you can not simply take the ratios of the price changes over time, in order to measure "speed" of changes, since the second box (when applicable) and the balance of the price graph have been combined into one.

What's more important for our probability investigation here is that we can visually see that of the 10 initial crashes, only one most fits pattern A.  While 2 fit pattern B, and 7 fit pattern C.  We then created a probability matrix to show the categorical placement of the data above.  For example for the 10 years, up through the day of ultimate fear, we see the following:

                                less severe   more severe
daily price increase        15%             0%
daily price decrease        51%            33%

And following this day of paramount scare:

                                less severe   more severe
daily price increase        46%             8%
daily price decrease       34%            11%

 

Now repeating this exercise for the recent August 2015 crash alone, here are the statistics, through the day of ultimate fear:

                               less severe   more severe
daily price increase          0%             0%        
daily price decrease        25%            75%

 

And following this day of paramount scare:

                               less severe   more severe
daily price increase         75%             0%           
daily price decrease        25%             0%
 
?2-test shows that the recent 2015 crash (so far) looks slightly (<25% probability) similar to the 2 pattern B years of 1955 and 2008.  We state "so far" because we are clearly not yet in a stabile period, similar to what we finally saw from prior crashes, though the likelihood is strong at this point that the pattern B identified is firm.  Again this is the pattern where there is severe market turmoil, then subsiding into a rather mediocre recovery with multiple retests.

Additionally the ?2-test strongly evidences that the probability matrix results thusfar (>95% probability) are quite different from the 7 crashes that make up pattern C (either before peak fear, after peak fear, or combined).  Noting again that this is the pattern that few people above would a priori feel represents how crashes "normally" occur.  Yet it account for roughly 2/3 of the crashes we've discussed here.  Meaning no one type of hedge can cheaply and universally protect from all crashes since they vary in styles.

Given the large portion of crashes -particularly in the past decade- which do not fit the typical mold for how risk models would anticipate market crashes to occur, relying on them at all times is imprudent.  Understand that market tail risk models can change in this period, subsequent top maximum jitters.  Eventually when it wreaks havoc, it is sometimes too late to appropriately hedge or know how to speculate in order to stay long with leverage in the hopes for spike in rebound days.  We may see this all unfold again, at a later point, but instead with bonds.  Then we'll again overly exposed funds and investors, in a hysteria once more.

 

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Sat, 09/12/2015 - 18:44 | 6540443 TheEndIsNear
TheEndIsNear's picture

Risk models cannot take into account the irrational human political aspects and insanity of the Fed and the PPT.

Sat, 09/12/2015 - 19:50 | 6540613 CPL
CPL's picture

Math-Hulk smash puny overleveraged ponzi fiat based economies with no value established to the underlying requirements?

Sat, 09/12/2015 - 18:57 | 6540479 ebworthen
ebworthen's picture

Okay, there has to be a dead cat and bounching involved.

Think of the # of headlines this past 8 months that had "not since Lehman" or "not since 2007".

Sat, 09/12/2015 - 19:04 | 6540502 buzzsaw99
buzzsaw99's picture

there is no risk for the tbtf. all prices are set by the central banks.

Sat, 09/12/2015 - 19:06 | 6540509 FreedomGuy
FreedomGuy's picture

So, hard socialist Jeremy Corbyn wins in Britain. Bernie Sanders is leading the Democrat party nomination.

Show me the economic graphs for those things.

Sat, 09/12/2015 - 20:39 | 6540586 Yen Cross
Yen Cross's picture

   What indicies, are these risk models based on?

   Are they just a global macro risk compilation? [a collective of the macro markets year by year]

 Trying to compare risk models based on China for instance,30 years ago, would pretty heavily skew the results.

 Not just the % of the annual moves, but also how those moves were calculated.

 Just ask the BLS. ;-)

 Tylers "swirl-o-gram" risk profiling chat is probably an better indicator.

 It tracks real time risk and sentiment. The Dow Flashing down 1000 points when it's trading 20-30% rich is impressive, but the algos front running the bid, is a bigger story.

 I'll gladly sell you back the position you wanted to purchase, 3~miliseconds ago, because you can't get filled by anyone else.

 Front running, and purchasing orders for the "blink of an eye", and then offloading the order to the original buyer at a higher fill price.

 Efficient Markets!? lol

Sat, 09/12/2015 - 20:45 | 6540750 KashNCarry
KashNCarry's picture

Banks have become almost impenetrable conglomerates attached to Wall Street speculative arbitrage activities and casino-type derivative bets... TBTF wants all bets covered by the FED, backed up by taxpayers.  It is a parasitic system.

Economist Michael Hudson in his new book 'Killing The Host; How Financial Parasites And Debt Destroy the Global Economy' points out how "...A century ago socialists and other Progressive Era reformers advanced an evolutionary theory by which economies would achieve their maximm potential by subordinating the post-feudal rentier class - landlords and bankers - to serve industry, labor and the common weal. Reforms along these lines have been defeated by intellectual deception and often outright violence by the vested interests Pinochet-Chile-style to prevent the kind of evolution that classical free market economists hoped to see - reforms that would check financial, property and monopoly interests.

    So we are brought back to the fact that in nature, parasites survive best by keeping their host alive and thriving. Acting too selfishly starves the host, putting the free luncher in danger.  That is why natural selection favors more positive forms of symbiosis, with mutual gains for host and rider alike. But as the volume of savings mounts up in the form of interest-bearing debt owed by industry and agriculture, households and governments, the financial sector tends to act in an increasingly shortsighted and destructive ways.  For all its positive contributions, today's high (and low) finance rarely leaves the economy enough tangible capital to reproduce, much less to feed the insatiable exponential dynamics of compound interest and predatory asset stripping.

    In nature, parasites tend to kill hosts that are dying, using their substance as food for the intruder's own progeny.  The economic analogy takes hold when financial managers use depreciation allowances for stock buybacks or to pay out as dividends instead of repplenishing and updating their plant and equipment. Tangible capital investment, research and development and employment are cut back to provide purely financial returns,  When creditors demand austerity programs to squeeze out "what is owed," enabling their loans and investments to keep growing exponentially, they starve the industrial economy and create a demographic, political and social crisis..."

 

The path to self destruction comes along with carving up today's global economy in one of the greatest oligarchic takeovers in the history of civilization. Future generations will revile the memory of us...

Sat, 09/12/2015 - 23:20 | 6541120 KashNCarry
KashNCarry's picture

On a side note Hudson adds that, "...Michael Perlman reminds me that most biological parasites that steer their hosts along a suicidal path only do so in order to pass their progeny into new hosts. But today's financial parasites threaten to destroy the host economy without having any alternatives. Their short-termism also is destroying the global environment, education systems, and is dismantling infrastructure.  The ensuing crash may leave financial parasites with no new worlds to colonize, destroying the host and its rider together..."

Sun, 09/13/2015 - 12:14 | 6542222 mvsjcl
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Some might argue that that is the long-term goal, not merely a confluence of short-term consequences.

Sat, 09/12/2015 - 20:57 | 6540780 SHsparx
SHsparx's picture

Market manipulation renders this numbers hookum.

Sat, 09/12/2015 - 21:08 | 6540808 scatha
scatha's picture

I love all those para-psychological economic models they are OK but with one problem. They do not exist in reality. It is not about fear, panic, exuberance, ecstasy etc.

All of that nonsense is to explain the grunt why he was robbed blind at this cesspool of corruption as are the so-called markets run by the plunge protection teams (absent from market models, so is margin debt), protecting cronies against the orchestrated surge and preprogrammed plunge which MSM propaganda calls crashes but what they actually are, manifestations of the credit extension/contraction cycles programmed by world CBs on orders of Wall Street plutocrats who own them.

The financial markets are absolutely detached, not only from mainstream economy but also detached from any shred of reality or sanity even in financial terms such as mathematical tautologies i.e. equations or rule of conservation.

The accounting art (not science) used by the markets only loosely resembles arithmetical manipulation but in fact it is a total fabrication with false ordering, ratings, valuation, and indexing which are useless since they are not invariant between two different states of the market. Such as in monetary terms inflows and outflows do not match (asymmetry) i.e. non-invariant. 

 

This mathematical fact is paper over with fallacy of wealth creation/destruction from thin air just by magic of the stock price increase/decrease which in most cases is due to some inside trading lies proliferated by Boomberg and other factories of pornographic news bringing thousands simultaneous orgasms to sadomasochistic audience seeking relief from their utter confusion and desperation unable or unwilling to understand that they were being raped.

Even those imperfect measures of the market fundamentals that supposedly underlies the stock valuation, EPS, top Line, bottom line, productivity etc., are hopelessly misinterpreted and became completely useless since they apply only to economic scenarios of ever increasing demand (SSE) supported by growth of overall economy and continuous increase of standard of living of the population through “undeclared ”mechanisms of redistribution of the profits (understood on Wall Street as somebody else's profits). Is this the economy we are dealing with now? Of course not, and hence all of it is just useless shit.

Some basics of the “real” markets are concisely put here:

https://contrarianopinion.wordpress.com/2015/01/29/invisible-hand-and-other-paranoid-delusions/

and on the real economy:

 

https://contrarianopinion.wordpress.com/economy-update/

 

Sun, 09/13/2015 - 02:24 | 6541394 foolish banker
foolish banker's picture

The simplicity of Mathematics is INDICATIVE of what will happen regardless of patterns, it is certain. 

This leads again to SAME question of WHEN. 

Sun, 09/13/2015 - 09:20 | 6541774 shovelhead
shovelhead's picture

Sooner or later.

Sun, 09/13/2015 - 07:18 | 6541636 EurGold
Sun, 09/13/2015 - 09:12 | 6541763 shovelhead
shovelhead's picture

No mention of the point within the crash when the projectile diarrhea hits?

I have always found that to be a useful metric in measuring fear.

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