naked capitalism

Yves Smith says:

Kurt,

I am looking for comments from risk management professionals, and trust me, there is a strong consensus on what that means, namely, volatility of returns (as far as I can tell, the notion of defining risk more in accordance with commonsensical notions like avoidance of loss or negative outcomes has not penetrated into practice, as represented by the content of risk management tools).

Doc Holiday says:

I know this doesn’t help anyone and just adds noise, but it has been sitting in storage waiting to be seen:

When the Long Term Capital Investment fund, having the Scholes and Merton in its advisory board, collapsed in 1998, the failure of risk management was traced back to the use of Gaussian distributions in the Black Scholes model. Levy distributions can produce heavier tails needed to model the risks in financial markets more correctly. Since there is no general formula for the densities of Levy distributions, many statistical methods, e.g. maximum likelihood, cannot be easily applied. Using the Wilson-Polchinski renormalization group and generalized Feynman graphs, B. Smii, H. Thaler and I have been able to provide a Borel summable asymptotic expansion for general Levy distributions with a diffusive component and a jump distribution that has all moments. First numerical checks are promising.

In a simple equilibrium model designed to make market external risk tradable, agents exposed to the risk measure their preferences according to exponential utility functions. The equilibrium price of external risk can be described by backward stochastic differential equations (BSDE) with non-Lipschitz generators. In joint work with A. Popier (Ecole Polytechnique, Palaiseau) we investigate a new concept of solutions for BSDE of this type, which we call measure solutions and which corresponds to theconcept of risk-neutral measures in arbitrage theory. We show that strong solutions of BSDE induce measure solutions, and present an algorithm by which measure solutions can be constructed without reference to strong ones.

* Full Disclosure: The author has spaced out where this stuff came from, but it was from the internet and seems related to something that is on topic or someday may be on topic; I have no position in anything and really care less and less every day about most everything.

lewy14 says:

DocH,

Thanks for that. I’m reading Mandelbrot’s book on the (Mis) Behavior of Markets and I’ve been wondering if his statistical approaches are being taken up.

I think the answer hinted at from the citations you provide is “yes, but it’s friggin’ hard stuff.” I’d be very interested to know if folks knew of gentle but formal introductions to this “new financial math”.

And thanks also Yves for this thread; I’ve been thinking that the fashionable calumny heaped on risk managers for their alleged ignorance of non-Gaussian tail risk has been a bit overdone – could they possibly be so ignorant with their “twenty five sigma” utterances, when even a rank dilettante such as myself am familiar with heavy tails?

It seems… well… unlikely…

Steve says:

An alternative to NT is Riccardo Rebonnato. His book Plight of the Fortune Tellers is no more comforting than NT, but comes without NT’s m’as-tu vu attitude. It’s a practitioner’s view of the false promises of VaR. Scholes wrote a brief and prescient critique of VaR in 2000, “Crisis and Risk Management” (Amer. Econ. Review, v. 90, no. 2) that is well worth reading–particularly regarding unmodeled market liquidity risk and non-stationary correlation assumptions.

I don’t believe I’ve ever met a commercial banker who went beyond statistics 101, if even that.

tom says:

Many,many moons ago I was a mortgage underwriter and very briefly worked in a risk managment department for a European Bank assessing the trading books and specific trades for swaps, MBS and so on. We relied heavily on CAPM (by basing our decisions on ’scientific’ meaths) and pure common sense. The traders had a book limit and we made sure they didn’t surpass their limits and that the various books in aggregate didn’t open up gaps in income/cost flows. Very quickly I learnt a career in Risk Management was for fools. A RM takes all the risks and isn’t listened to until something goes arse over tip. That was back in 1990 when I left banking altogether.

Generally top management are aware of the risks they take, even if they don’t know the specifics, but if the bucks are rolling in their risk decision making appartus quickly malfunctions.

trelsco says:

The people trading the complex products generally know the risks are non-normal. Arguably the issue is that it is easier to arbitrage your bank than the market. So unless you have an appropriate incentive structure and finance and risk management functions that are politically strong and on the ball, you will have problems.

Thomas says:

On a side note:

After getting my ph.d. 10 years ago, I also applied for a job with the risk management department of a major European bank. Two days after submitting the application, I received a phone call from their head of risk management, who was all excited, because he had seen on my CV that I had also published an article on VaR used for performance-measurement in banks.

He explained to me that top management had just decided to introduce a scientific and objective way of measuring risk by VaR, to allow top management to make the right decisions. Now they wanted to hire the people to do it. When I cautiously tried to point out the potential problems and pitfalls, and the serious limits of “scientific and objective ways” to quantify risk, they didn’t want to hear it. They wanted somebody to develop a tool to give top management what it wanted. (This particular bank, which shall not be identified, got severely damaged during the crisis and is now on government life-support)

A separate application went to a large reinsurance company, which also invited me for an interview and told me that their CEO had decided to develop a “scientific tool for pricing of all risks, including financial risks”, for the company to use itself, but also to sell it to their insurance clients, so that they can also price their products according to state-of-the-art techniques. Again, I pointed out that whoever uses such “tools” would need an in-depth understanding of what he was doing, an ability to factor in qualitative aspects, as well as a feel for the limits of any quantitative analysis. I was told that I needn’t worry – they only needed somebody to develop a tool, because the CEO thought it was a good idea. (This particular company is still alive, but struggling, and has needed quite a bit of additional funds over the last few years in order to survive)

What struck me in both cases is: Nobody wanted to talk about limitations and caveats. People wanted a scientific, objective, quantatitive method. And spare us the details, because we anyway don’t understand them. With that kind of approach, things just had to go wrong!

(Back then, I got both job offers, but turned down both of them, because it didn’t sound like an attractive proposition to build a model that people would use without wanting to know about the small print.)

fisheryc says:

Yves, thanks to the other qualifed comments, I think you have one answer to your underlying question; Do senior management etc, understand the models. Answer; absolutely not. Bigger question; is it predictive. Answer: absolutely No.

Any of the serious quantitative models rely almost entirely on the “Efficient Market Theory(some form)” for their intellectual existence. The EMT, as we should all know by now, is the luminiferous ether of market movements. It’s a voodoo, no how many IBM super computers they use.

It matters only because some people think it works and therefore make decisions based on the results.

gpp says:

As I see it there are at least the following problems with risk management in banks

(I) Banks have no genuine interest in controlling risk.

The risc control department is the minimal operation that will pass a regulatory audit.
It exists only because otherwise the activities of the bank would be severely curtailed by existing regulations
(at least in Europe).
It has no prestige within the bank (after all it makes no money), people are paid less and often have
to work longer. They have no clout within the bank and dare not interfere with "profitable" trading.
The quant working in risc control hopes that he will be "promoted" to work with the traders.

Suppose for example a group of quants develop an incorrect mathematical model for a financial
instrument that consistently misprices the instrument and leads to incorrect hedges.

The bank now has a difference of opinion with most other banks about what the instrument is worth.
It believes that is knows something others don't know and thus has the opportunity for large profits.
It finds that there is no shortage of counterparties willing to take the other side of a trade.

The positions are hedged and profit and loss computed by marking to the faulty model.
The model shows large profits. The more position size is increased the larger the profit.
Quants, traders and management all get generous bonuses.

Such "profits" cannot be put at risk by the risc control department.
A risc manager raising objections will soon work elsewhere.

This can go on for a couple of years. The bank becomes a large player.
When the situation gets out of hand, some participants are fired but since they are not personally liable
they don't really care. They may have made a lot of money.
If possible the incident will have been hushed up so they will find employment elsewhere.

I have second hand knowledge of one such case at a medium sized bank in Europe.

(II) Formidable mathematical problems.

There is no reason to believe that the past can predict the future.
But even under the optimistic assumption that available data contain all the relevant information about
the future insurmountable mathematical difficulties remain.

The problems go considerably further than "fat tails".
There is also the problem of high dimension — "the curse of dimensionality".

The book of a medium sized bank will contain in excess of ten thousand positions.
The first step in making this a little more manageable is a reduction in dimension.
Instead of modelling each instrument you identify a smaller number of "risc factors" that drive
the returns of the individual instruments.

Many of these risc factors have no economic interpretation (they are abstract mathematical quantities derived from an
eigenvector decomposition of the return covariance matrix) and are thus impossible to understand intuitively.

There are still hundreds of risc factors X_1,…,X_D left.
Assemble the individual risc factors into a vector X=(X_1,…,X_D).
This is a quantity that lives in a very high dimensional space.
The dimension is the number D of risc factors.

You must now find the probability distribution of X in this very high dimensional space.

This is where the Gaussian distribution comes in: it is completely determined by the mean and covariance matrix
and is easy to implement and simulate.

It is VERY HARD to go to other distributions in high dimensional spaces.

You have to collect data and choose a high dimensional distribution consistent with these data.
This is a nontrivial problem.

The simplest (some would say only) reasonable distribution to use is the maximum entropy distribution consistent with the data that
have been collected.
This is the distribution that makes the fewest assumptions other than the constraints imposed by the data
(see "maximum entropy principle").

The Gaussian distribution is the maximum entropy distribution consistent with the means and covariances,
equivalently, the first and second order moments:

E(X_i), E(X_iX_j), 0 < i <= j < D+1.

These are more than D(D+1)/2 constraints (tens of thousands to hundreds of thousands).
Here E denotes the expected value and "constraint" means: the expected values E(X_i), E(X_iX_j)
equal the sample means.

If you want to capture the phenomenon of "fat tails" in a high dimensional space you must go further
and impose constraints on all moments up to order 3:

E(X_i), E(X_iX_j), E(X_iX_jX_k), 0 < i <= j <= k < D+1. (*)

These are millions to hundreds of millions of constraints.
But this is only a minimal approach to the "fat tails" in a high dimensional space.

If you go up to moments of order 4 you have billions of constraints.
Let us list three problems with which we are now faced:

(A) Computation is beyond the ability of current computers.

The maximum entropy distribution satisfying these constraints (*) has a known form but
cannot realistically be computed explicitly.
Even if I were to give it to you explicitly the computational load is too high for
simulating from this distribution.

The same will be true for all other distributions satisfying the contraints:
A distribution satisfying hundreds of millions of constraints will have hundreds of millions of
intricate details (as many terms as constraints) each necessitating computation so that you will
be overwhelmed by the computational load.

Recall that you want to generate at least tens of thousands of samples from this distribution
leading to hundreds of billions to trillions of floating point operations.

(B) Insufficient data to support the constraints

You will typically only have thousands of data points for the risk factors X.
You cannot meaningfully compute hundreds of millions of constraints on the basis
of thousands of data points.

For example: there will be lots of polynomials P of degree 3 in the variables x_1,..,x_d
such that the equation P(X) = 0 is satisfied at each data point X.

For each data point X the condition

0 = P(X) = \sum_{1<=i<=j<=k<=D} a_ijk X_iX_jX_k (the X_i given)

is a linear equation in the coefficients a_ijk and there are a lot more coefficients than there
are data points, that is the a_ijk are the solutions of a system of linear equations
with many more variables than equations — thus there are many such solutions.

Fix such a polynomial P, add all the equations P(X)=0, for each data point X, and divide by the number of
data points to obtain the relation:

\sum_{1<=i<=j<=k<=D} a_ijk E(X_iX_jX_k) = 0.

In other words the sample means E(X_iX_jX_k) computed from an insufficiently large number of data
(fewer data than constraints) satisfy lots of linear relations which the actual expected values of the
moments of the distribution will not in general satisfy — they are simply artifacts of the data paucity.

(C) Impossibility to simulate adequately many scenarios.

But let us disregard all this and assume you can sample from
the distribution of the risc factors X.

You now have to compute the distribution of the portfolio returns R=R(X).
Given a realization of the risc factors X your valuation models compute the portfolio return
R as a function of X.
This function is not given by any explicit formula but rather by a horribly complicated algorithm (input X, output R(X))
applying all your pricing models to the respective positions in your book.

It is safe to say the mathematical properties of the function R=R(X) are not at all well understood.
Often the function R is not continuous (default events,…)
It is a function of hundreds of variables:

R=R(X)=R(X_1,X_2,…,X_D).

After a standard reduction we can assume that 0 < X_j < 1, that is, X lives in the hypercube C of dimension D.
We must now evaluate R at enough points X in the hypercube C to convince ourselves that we have seen everything
that the portfolio can do to us with the correct frequencies.

Since we have no idea how the function R varies over C we need to evaluate R at a very dense subset of points
of C.
An idea might be to choose 10 equidistant points on each edge of the cube, combine these into a grid of points
in C and evaluate R at each grid point.

This grid is not particularly dense.
It contains 10^D points (note D is on the order of 500), that is, by many orders of magnitude more points than
there are elementary particles in the universe.

Since it is infeasible to evaluate R(X) at so many points we choose the points X in C "randomly".
Each evaluation of R(X) evaluates the entire portfolio and so is a considerable computational expense.
We can realistically try for 10000 evaluations.

This is literally nothing in the vastness of the hypercube C.
To make this clear suppose D=500, and you have computed R(X) not at ten thousand but rather at 10 trillion
points X in the hypercube.

To fix a unit of length let's say the hypercube has edges which are one light year long.
I now drop you off in the hypercube C with a telescope that allows you to see everything
within 1 light year of yourself. In particular you can see all the way to each wall of the cube
(but you cannot see the entire wall).

What is the probability q that you will see at least one of points X?
The answer is: q is virtually zero (smaller than 1/10^100)!
With probability practically equal to one you won't see a single one of the ten trillion points X.

By contrast in the three dimensional cube you are very likely to see at least 90% the points X.

Doc Holiday says:

Re1: "Nobody wanted to talk about limitations and caveats. People wanted a scientific, objective, quantatitive method. And spare us the details, because we anyway don't understand them. With that kind of approach, things just had to go wrong! "

> That's it in a nutshell and that comment could be directly shot at Moody's, S&P and Fitch, because they have models built on science which amounts to bullshit voodoo. Governments of the world which are stuffed to the gills with nepotism and inefficiencies then suggest they will regulate things like derivatives and risk, and even medicine and food interactions which they don't understand.

We have the SEC, FTC, FASB, FOMC, Treasury, Congress and 1000's of highly educated monkey's that interact in a dance of chaos, pretending that they understand the risks associated with a few hundred trillion bananas — this global society we have today simply is out of control, because the pirates that abuse power are way ahead on the curves and able to frontrun "intended" regulations related to risks. The same mentality that provides consumers with toxic shit like melamine, in dog food, baby food, candy, etc, are the same producers that provide us with toxic waste shit in the form of derivatives that are based on models that are designed to value shit like gold!

Full disclosure: The author is undergoing stress and has just had cereal with almonds, sunflower seeds, oatmeal, bran flakes and milk. However, this opinion has not been edited and the author has no responsibility for anything and really doesn't give a crap about anything. Furthermore, the author is about to listen to theis: http://www.youtube.com/watch?v=jfO1dzkD-E8

maika13 says:

And now with the link

http://finanalytica.com/

Luke Lea says:

“Using the Wilson-Polchinski renormalization group and generalized Feynman graphs, B. Smii, H. Thaler and I have been able to provide a Borel summable asymptotic expansion for general Levy distributions with a diffusive component and a jump distribution that has all moments.”

Ah, just what we need!

Yves Smith says:

This so far is GREAT, thanks so much! Further comments and elaboration appreciated.

Doc Holiday says:

Garbage analysis input, CDO's and various derivatives output…. and rubes are hired every day, and retarded investors will buy things if the package has attractive packaging and sales reps and those little finger sandwiches with smoked salmon, and don't forget the booze and music; short skirts help too and time, don't forget that you have to rush into things that don't make sense!

STATISTICS IN MEDICINE
Statist. Med. 2007; 26:2919–2936

Re: SUMMARY
When a likelihood ratio is used to measure the strength of evidence for one hypothesis over another, its reliability (i.e. how often it produces misleading evidence) depends on the specification of the working model. When the working model happens to be the ‘true’ or ‘correct’ model, the probability of observing strong misleading evidence is low and controllable. But this is not necessarily the case when the working model is misspecified.

Royall and Tsou (J. R. Stat. Soc., Ser. B 2003; 65:391–404) show how to adjust working models to make them robust to misspecification. Likelihood ratios derived from their ‘robust
adjusted likelihood’ are just as reliable (asymptotically) as if the working model were correctly specified in the first place. In this paper, we apply and extend these ideas to the generalized linear model (GLM) regression setting.

Re: The exponential adjustment factorA/B is simply the ratio of the model-based variance estimate for to the robust variance estimate (sandwich estimator) using the ‘corrected’ data.

To accommodate this type of model failure, we need to only slightly modify how the adjustment factor B is calculated. We do this in the same way that the ‘meat’ of the sandwich estimator is adjusted for clustering.

Also see: The canonical correlation (don't go forgetting those little fuc-ers) obtained as follows: the data are mapped to empirical uniforms and transformed with the inverse function of the Gaussian distribution. The correlation is then computed for the transformed data. The advantage of the canonical measure is that no distribution is assumed for individual risks.Indeed, it can be shown that a misspecification about the marginal distributions (for example to assume Gaussian margins if they are not) leads to a biased estimator of the correlation matrix.

> I have no clue why I have this stuff, but maybe I should start a ponzi scheme, or take over the world?

Doc Holiday says:

I thought I’d make an observation on this and see if anyone has an opinion. It seems to me that it’s interesting that there are ways to calculate and model a treasury yield curve and thus the associated underlying debts and obligations of Treasury, but yet there seems to be no realistic way to model the gaming component of equities which are now highly linked and correlated to Treasury instruments, i.e, it would seem that all these models are broken, and manipulative with falsified inputs and chaotic outputs.

I have to point a finger once again at FASB and the accounting fraud they helped engineer, along with rating agency models that were built with false and misleading data, and Treasury for backing this up, along with FTC, DOJ, Congress and the full collusion support of all wall street entities that thrive on illusions.

The stress tests that have just been superficially biased will do nothing for anyone or any model, so in this half-assed attempt to buy time, where is the relationship between Volcker and Obama in regard to truth, honesty and change? If we allow a group of crooks to continue to falsify data and produce falsified models, we will undermine our society to a point where it will collapse sooner than later.

The concept of nationalizing the banks has to begin ASAP and there must be a massive effort to build an army of financial engineers to examine this systemic collapse. This period of financial terrorism by wall street is a challenge that is essentially an economic war which our president and congress are failing to address; this is Pearl Harbor, this is an attack by a group of people that for all practical purposes is not unlike The Nazis!

See: The Manhattan Project was the project, conducted during World War II primarily by the United States, to develop the first atomic bomb. Formally designated as the Manhattan Engineer District (MED), it refers specifically to the period of the project from 1942–1946 under the control of the U.S. Army Corps of Engineers, under the administration of General Leslie R. Groves. The scientific research was directed by American physicist J. Robert Oppenheimer.

Where is our leadership and why are we not seeing this corruption for what it really is??? We need an army of financial engineers to clean house ASAP!

maika13 says:

economicdarwinism,

I’m not quite sure about the possibility of deriving a closed form expression of the stable distribution VaR or ETL (Expected Tail Loss aka CVaR) but it could be that you’re right, at least for the univariate case.

Still I doubt it’s possible to come up with general closed form solution – and thus to avoid the Monte Carlo simullations – for the cumulative stable VaR or ETL of a portfolio which is made up of multiple positions (risk factors); especially if you impose more complicated dependence structures on the positions (risk factors) like stable t-copula or dependen subordinators where the latter are meant to capture more accurately the dependences in the tails more.

trelsco says:

For a typical investment bank the array of products and valuation techniques is very broad and it is not reasonable to expect senior management to be across them all in any depth. Instead the responsibility of the boards and senior management is to make sure people are managed and incentivised to do the right thing for the firm and its shareholders.

I believe redst8r gets to the point. If you as a senior manager are getting very well rewarded in the short term for taking excessive risk, and everyone else on the street is doing the same thing, what is your motivation to dampen things down?

In my view, there is a large portion of blame for senior management that did not show the leadership and independence to set the structure and incentives of their firms to build long-run firm value. Following the herd was easier, particularly if you are well paid, even if your shareholders lose their shirts.

t says:

Q: Does CFA Training address these Issues?
A: No.

I sat the CFA in ‘02 – ‘04. I don’t know how the syllabus or reaing list (which no-one actually reads) has changed since then, but at the time, it barely mentioned the themes in your post at all.

There was some mention of VAR, a few basic calculations, and a list of disadvantages thereof, like correlations changing over time, but nothing in great detail.

Far more volume of the CFA is taken up with CAPM as the foundation of financial markets, so all that belief in rationality. I’d argue that’s the opposite of what should be taught.