Nacho Oliveras

Day one: Good start: Raphaël is an excel guy.

Nassim, as all #RWRI attendants is a Mathematica guy, @DrCirillo who will pop in tomorrow an R guy.

What is a statistician? It is a kid playing with data.

1/n

We start with a Yahoo Finance extract of the NASDAQ data from 1971 till today...

2/n

First thing to know about data is integration.

We are in the same order of magnitude when we deal with ratios not when we do with differences. 

The H column stays within the same order of magnitude. Volatility increases, but if we takes the logs-return as in J we re-scale.

3/n

Plotting in log scale.

Severe crisis appear now as glitches.

Now we can really compare the volatility, and if covid crisis has been worse than 9/11...

Lessons: 
1) When one deals with time series, it is necessary to re-scale
2) Differentiating the right amount of times...

4/n

Let us look at T-Bills now for a ~15 year period.

It appears quite smooth, with rare exceptions, and returns are quite limited.

But we are not interested as much in the returns as in the change in those returns: that is our signal.

Interest rates are interesting.

5/n

Raphaël tells us how he remembers inflation above 17%, rates at 15%. Bringing these down was very difficult.
Q: Is there a link between the scale of the measure, e.g. bi-weekly change vs daily change?
Yes, depends on the scale. Look at correlations. 
.

6/n

If correlations between successive periods are positively correlated, the returns will look smoother.

This relates with Madelbrot and Fractal BM...

7/n

Back to the market plot.

No obvious correlation, except when there are "rebounds"...

Idea is we get from this course the tools to play with data as kids play with Lego.

We need to differentiate sometimes the same way we differentiate velocity from acceleration...

8/n

Raphaël shares with us a study he did on interest rates: the higher they go the more volatile they get.

This appears true for all countries he studied.

The more the rates will grow, the more the volatility of a bond portfolio will rise.

But let us go back to the NASDAQ. 

9/n

There seems to be 2 sources of Black Swans.

One is unexpected events, the second source is accumulated dynamics (bubbles) that don't form in just one day.

The largest moves of the stock market are negative (top 5 in the last 50 years).

10/n

I column is std deviation, J ratio of J2 and J3.

Log return scales well even with variations like 1987 Black Monday.

The Russian Market had a 95% drop in the 90s. 

Blue plots actual returns, orange log returns.

At -100% it goes to infinity, on the upside almost opposite.
11/n

So in the Russian story, if you invested 100 USD you are left with 5 USD.

The fuel you need to "rebound" to 100 USD is then massive...

12/n

The VC problem can be better grasped by thinking in moments: the cubic (3) of the return on a positive event will dwarf the losses of all other investments that are sterile.

Skew corrects it by the variance, kurtosis measure the contribution of one event to the variance...

13/n

Raphaël plots kurtosis before we will do a short break.

@NonMeek asks him how would this look with a normal distribution.

Raphaël plays with the data and comes up with the graph in the right.

The distribution of the kurtosis is itself skewed, and it often goes negative.
 
14/n

Identifying Fat Tails.

Here the distributions we should know, these function explains how the probability decays.

NNT found an alpha below 1 when he was studying wars: it is difficult to understand phenomenon with no average.

15/n

Whatever the distribution we can use the Maximum Likelihood Method: we multiply the density of probability and try to find the parameter theta that makes some distribution most probable...

16/n

MLE (Maximum Likelihood Estimation) fills tons of books, it is so attractive. 
But this is tricky: in 99% of the cases we will underestimate (when Bezos is not in our sample) and in 1% of the cases we will vastly overestimate (when he is), so we don't really solve the issue.
17/n

What if we apply the "Fat-Tail Parts Magic function"?

This technique would not work well with Gaussian/Exponentials as going to infinity, but works pretty well with the Paretian!

18/n

One technique (Tail Index Hill's Estimator):

If X is Paretian, P will look as an exponential.

Look at the underlined formula: in a way this technique looks like a linear regression...

19/n

Back to the NASDAQ, the biggest positive days were always rebounds.
Raphaël plays with it, gets a nice straight line.
We cannot get the same picture when we apply it to the normal distribution.
Giving you the estimation of the NASDAQ alpha obtained with this Hill estimator.
20/n

Once we have calculated the alpha, we can analyze the CVaR.

Raphaël does so.

21/n

Here the idea is without having Bill Gates in our distribution, anticipating that he exists by the probability distribution. 

Raphaël invites his friend Patrice Kiener to participate with a presentation on "real life application" of these techniques.

22/n

kappa is the Pareto estimator.

If it is below alpha, we have no average, if it is below 2, no variance, if it is below 3 no skew, below 4 no kurtosis...

23/n

Many people before Patrice and Raphaël has tried to find how to determine a distribution, some examples...

24/n

At Raphaël's request, Patrice jumped several slides.

Under Fat Tails, we know that the probability denisty in the middle looks thinner as we can observe here...

25/n

French gold market: very fat tails, 

kappa/alpha almost 4 and almost no kurtosis.

The quantity we will need to cover our investment changes a lot, can double a normal portfolio/Markowitz...

27/n

Société Générale had the Kerviel scandal, Vivendi before had a "Messier" scandal as he made the utilities company run out of money with investments in Hollywood.

The risk of these in the market and the money needed to cover these positions...

28/n

VIX: Fat-Tailed and very asymmetrical.

29/n

Patrice shows as a short clip of the SP500 evolution, Raphaël comments that for the SP500 returns and log returns don't make a big difference.

30/n

Quintile estimation: one manages to do an estimation with 5 data points only. We can estimate the distribution by say knowing what are the values at 99% (and 1%) and 75% (so 25%)...

31/n

The larger the number of factors, the larger the colinearity.

(What @nntaleb  calls "the curse of dimensionality")

What number of factors starts being problematic does not respond to a magic number, as we will see.

We can also have polynomial, or non-linear regression...

32/n

Data is almost never Gaussian, most of the time is a mixture of many things.

Raphaël tells us most of the standard tools assume Gaussian, which is not going to work most of the time as he himself has often tested...

33/n

Raphaël type of joke:

"If the p-square is negative, p is an imaginary number".

This is the type of jokes he would crack at RWRI and only him would laugh at them...

34/n

P-squate at the bottom of this slide, for those who want to get it...

35/n

His data set is stock market (for past decades)...

36/n

This is the more correlated data set Raphael could produce before having a microphone technical issue, so unexpected break...

37/n

Raphael rebooted his laptop and now he is back with us.

38/n

42% is the R squared.

Is this good enough for prediction?

39/n

Raphaël: "I hate VB...".

He will make us hate it as well.

40/n

Raphaël extracted from his data set data up to May 2004, now he will use that to predict the returns of what will come next via linear regression and the fitted error moved by 1 month, so that he will calibrate his model.

42/n

It does not replicate and error is huge.

P-square is negative... If we had predicted 0 we would have bettered the prediction of this model, not even for the subsequent months after May 2004.

43/n

The fact that P-square is negative means that the variance increases by using the model.

Here we shall look for models that increase the P-square rather than the R square.

44/n

Coming to my original question, the first model had 11 factors.

Chances are that removing factors we reduce overfitting.

By the way Raphaël is trying to get a model that has P-square positive (so some predictive value) for real estate based on SP500 values and other data.

45/n

Cross Validation is useful for this

1) Identify which factors matter

2) Decide if we shall include linearity or non-linearity (once we have determined the factors, if trying non-linear regression improves the model)

Cross validation is much more telling than a high R...

46/n

Linear regression can be fooled easily, models that pass the cross validation test not so much.

So the goodness of a fit is measured more by a P-square than by an R-square.

For extreme events, often 1 factor is the one giving the best fit.

We are going to wrap up soon...

47/n

Any 2 factor explanation has a better R-square than a 1 factor, by definition.

But is that true?

fughetabout it!

Raphaël recommends to start with 2 factors and add, to that, to see if that improves the P-square, that is the value we really want to improve.

48/n

Thought experiment to think of the markets for traders: we are in a cheap Thai casino, and we observe one bias in the roulette.
Then the croupier changes, and the bias changes.
So we can observe some patterns, but these are not stable, unless we get to understand the bias...
49/n

of all roulettes done by that manufacturer.

The prediction exercise is the most difficult in the world.
The real way to do it is depict 2 or 3 scenarios, not assigning them particular probabilities, and get positions consequential with those scenarios.

50/n

Raphaël talks about the current situation, and how odd it is that Trump getting covid didn't translate into the markets.

Are we in a metastable equilibrium, in that nothing can really affect the market now? Not sure, but that can be a work hypothesis/scenario.

51/n

What is p values, for instance that a random correlation is of 42%?

The standard for publication is that the p value chances correlation is not random to be 5%. But by definition, if 20 monkeys are searching something one will find such potential "non random" correlation.

52/n

There is a lot of such p-hacking.

"To be a good statistician, you need to understand how your friend works".

For instance, we are fooled by optical illusions. But the optical illusions are the result of our brain interpreting data, without that we are blind.

Day 2 END.

53/53

The LogDensity shows that the Gaussian is the thinner, logit comes next, the fatter tails are the distributions with discontinued trait lines...

16/n

Today is the grande Finale of #RWRIPPP1 with Raphaël Douady.

Sound seems very good and Raphaël in top shape, citing Minsky, Franco his Modigliani, and saying that the Chicago school of economics might have many Nobel prizes but their models are shit.

A promising appetizer.

1/n

I missed the moment, but Raphaël has like 100 internet tabs open.

And he rebooted his laptop yesterday.

We recover the spreadsheet he was using yesterday.

What is a polynomial? It is just adding one regressor, on top of having kappa and beta times x we add x squared.

2/n

Raphaël explaining how to tinker with factors to improve P-square, Werner asking if we can get stuck in a local maximum.

Absoutely! Says Raphaël.

The whole industry is about picking the right risk factors.

3/n

Raphaël tells us that he was reluctant to use cross validation at the begging for being too restrictive/severe, but then he learnt to use P-square as test.

P-values works, but P-square is the most useful (or more difficult to fool than others). But there is no panacea...

4/n

Today, there are even companies specialized in cross validation.

It is complicated to test factors. It needs to be done in different time periods, forms, etc.

But eventually one gets a good factor set.

People do often calculations without thinking what they are doing.

5/n

A good doctor will not ask to do a massive battery of tests, he will ask questions, get to understand the issue, then maybe say you need to take a test for allergen X and then order you just that test.

Someone suggests to try as many factors as possible, Raphaël disagrees.

6/n

We get eventually started with a RWRI slide NNT likes a lot.

Slide says that when we minimize risk (e.g. via diversification), but the measured risk is based on past data, so contains a lot of hidden risk. But objective was decreasing risk, not just measured risk...

7/n

Someone asks if all this models are not Gaussian.

Raphaël partly agrees.

There is an underlying assumption of fat tails.

Raphaël gives an example, a football (rugby) ball, it is elliptical. I did not copy this, sound issue. Also a potato germing, with ramifications...

8/n

Some risk factors, in the extremes, hide huge risk factors, this was the case 2007 and 2008 with mortgages.

Covid is one such factor, that could make blow up entire portfolios.

This is the real question of the "curse of dimensionality" I wrongly mentioned yesterday.

9/n

Dynamics: things build up.

We know a move was 4%.

After the fact, we know the probabilities of the regime: it is more likely this maps a large regime change than a 4x "normal" 1% change...

The are with the yellow line signals a systematic regime change.

11/n

Regression in practice.

Yesterday we regressed real estate with SP500 values and ETF, high covariance.

If I make linear changes to my regressions, we will get the same results as yesterday.

But what if we use polynomial regression?

12/n

Reminder: the big jump maps the 2008 crisis, the real estate market is backtracked 100 months that is ~8 years...

14/n

We improve a lot squaring one regressor: P-square is up to 34%. 

Question: what is a good enough P-square?

34% is a pretty good P-square (not bad, that is French for good).

15/n

It depends on the number of factors.

0.2 with 500 factors might be good, with very few factors something below 0.5 might be bad.

16/n

This what is plotted here is non linear regression.

The advantage of this technique is identifying changes in the regime. We are in the variable space.

Different to non-linear optimization (parameters).

Not the "true" behavior is the brown line (when it drops, it drops).

17/n

Raphaël tells that for phi 2 he uses the median, not the average, and this is a point of discrepancy between him and NNT.
Someone suggests a coffee break (blessed him), Rapaël says 5 more minutes. 
Result of using linear/non linear reg, and penalizing non-linear regressors.

18/n

This is to compensate the risk of overfitting.

If rho is very low, we will have pure linear regression, the higher the regression the more we penalize. Thomas Barrau, one of Raphaël's students in the attendant, has a whole chapter of his PhD thesis to selecting the rho...

19/n

Neighbor giving me bouzouki concert as I prepare to reconnect...

20/n

Polymodels now.

"I never make a statistical calculation if he does not know what he is looking for."

Now he want to see what happens to the portfolio in case of certain events/scenarios happen, or whether to invest or not in a fund.

Every scenario is determined by shifts

21/n

in the risk factors.

We want to identify risks that can hit that we did not identify.

NNT thinks we cannot get hit by risk, if that is the case, we did not see the risk by definition.

Here is where Raphaël slightly disagrees. Sometimes, he tells us, we are a bit blind...

22/n

I won't share the next screen to not put Raphaël in trouble, but he is giving us some interesting examples of factors he has been using recently (equities/bonds/mutual funds in different industries/countries, etc.).

23/n

Observe Raphaëls internet tabs... (PC rebooted yesterday).

He just closed Slack as he was getting repeated notifications from a client.

24/n

Score: not good goes to 0.

Good, can go to infinity.

G is at 1/3, score is 70%

G is 20%, score is 50%, etc. (just to give orders of magnitude).

The brown line is F (best linear regressor).

25/n

Had to answer some call. Let's remove the factors not having good score (down from 200). We calculate the 99% confidence interval and within that interval the worst case scenario.

2 funds, one progresses linearly, one does much quickly. Is SVaR a detector of antifragility?

26/n

Yes, works as a detector.

What is the Long Term Expectation (LTE).

We do some averaging with the scores themselves as weights.

I am sure I would understand all this better if I was allocating any considerable amounts of money to funds as many attendants are doing.

27/n

Surprisingly, non linear factors tend to be more stable than non linear ones.

Polymodel analysis consists in removing a lot of factors that don't improve the model.

28/n

Many clients show up with simulations, often persuaded they are right.

Sometimes they are. Sometimes not.

When we apply this polymodels, that is difficult to hide.

E.g. I had a client that was trading commodities (in theory) but had a position short on LIBOR...

29/n

Those are correlated, but not correlated enough.

They were long gamma in one market, not in other (was not the same gamma).

Raphaël was able to identify a hidden risk by using the polymodel. Opens a round of question, before passing to Bayesian statistics if we have time.

30/n

Then @NonMeek asks what happened to that fund selling gamma.

Raphael says they corrected it.

@NonMeek asks what was his compensation. 

RiskData Inc. is Raphaël's company, he sold that one except the American branch he had created. I understand those were consulting fees.

31/n

The moments have a correspondence with the Pareto parameters.

Potential use? Manage risk (regulation, VCs), Portfolio management, etc.

One of his R packages is public, he recommends we backtrack his data using it.

These distributions change our thinking of volatility.

32/n

Traders ask Patrice uses of this for trading.

Patrice is not a trader, says he can't say but won't be surprised it can be used. He advises institutional clients on the amount of capital needed to cover their positions.

Raphaël makes an observation.

33/n

"When tails get fatter, they get the more symmetric".

Raphaël wraps it up, reminding us to connect tomorrow at the same time for @DrCirillo's presentation.

34/34

Day 2 of #RWRIPPP1 starts with @DrCirillo as promised.

He is an R, and also a Mathematica man...

So the first minutes are spent explaining the datasets and R packages he will be using.

1/n

First (apparently) trivial advice: plot the data.

@DrCirillo tells us he has seen people assuming data was normally distributed working for banks when a simple plot would have shown that the distribution was asymmetric (those people never even bothered plotting the data)...

2/n

Danish Reinsurance Claim Dset
The univariate dataset was collected at Copenhagen Reinsurance and comprise 2167 fire losses over the period 1980 to 1990. They have been adjusted for inflation to reflect 1985 values and are expressed in millions of Danish Krone.
Via @joonya__!

3/n

The multivariate data set is the same data as above but the total claim has been divided into a building loss, a loss of contents and a loss of profits.

We will be using it to illustrate EVT, by the way (Extreme Value Theory).

The bulk (mean, std, etc) of the data isn't...

4/n

the most important part of the data in EVT.

It is important only when we have analyzed the tails.

Long/fat/heavy/thick tails are not the same things, @DrCirillo invites us to see his videos to understand the difference.

5/n

Thin tailed (normal) decays exponentially.
Heavy tailed means that it does not decay exponentially.
Pareto or Lognormal are heavy tailed.
They are better studied not by their moments as we saw yesterday but by the catastrophe principle (both distributions are subexponential).
6/n

There can be functions that behave like a normal distribution around the mean, but not in the tails.

Pasquale Cirillo recommends the book "Modern introduction to probability and statistics".

Pareto is a fat tailed power-law, but Lognormal distribution is not fat tailed.

7/n

This is a Pareto, decays as per the exponent within the circle (alpha).

8/n

Power laws are more general than fat tails.

In order to be fat tailed, one needs a power law component in the tails.

Pareto is an entire power law.

9/n

The problem in EVT is finding the thresholds.

The highlighted formula corresponds to a GP (Generalized Pareto) formulation.

10/n

The first thing is understanding is our distribution is heavy-tailed. If it is, it may be fat-tailed.

If it isn't, it is thin-tailed and then we will look at the moments.

In EVT we don't care about normal as much as by exponentials.

Let us qplot the data...

11/n

The qplot plots data in quintiles (up to ~263).
If data was coming from a standard exponential it would lay over the diagonal line.

It doesn't, we see concavity, this is a clear signal of heavy tails. Convexity is, conversely, a signal of thinner tails than an exponential.

12/n

Edit *Quantiles*

A reminder

Heavy means it decays slower than an exponential, power law tells us how it decays.

Same as "I measure less than 1.9m" or "I am 1.8m tall", the second statement is more precise than the first.

13/n

A question: Are exponential function used for what relates with time?

@DrCirillo: The exponential functions have many uses, not just with what relates to time, but it is often used to processes related with decay.

EVT is not a new theory, it was developed ~100 years ago.

14/n

We often waste time by assuming normality.

Dr Cirillo says he might have bias, but that "Pareto should be the new normal", as most things are not normal.

Let us use a Zipf plot (from Zipf, the scholar who studied the distribution of words in the English language)...

15/n

Zipf maps Paretian for a large part, but not the whole data.

@DrCirillo tells us to be careful of plots, but if we won't observe any linearity at all in the data over the plot, this is a first signal of fat tails (concavity, or some concavity will rule out fat tails).

16/n

Fat tails is a term used very often (marketing, medicine), and often not precisely, but this does not mean that it does not have a precise technical definition.

From J Bold, a reminder.

17/n

"Fat is heavy, but heavy is not necessarily fat. Heavy decays slower than exponential but this doesn’t confirm power law. Fat tails decay via power law".

18/n

When we talk about moments and infinite moments not having mean or variance, this does not mean that we cannot measure the mean or the variance of a sample, which can always be done, but that those values might be meaningless in certain circumstances. For example?

19/n

Our average wealth if we invite Bezos into the room, or if we not.

I ask @DrCirillo how he translates fat tails and heavy tails into Italian, he does so by "coda grassa" and "coda pesante".

20/n

I was slightly interrupted, unfortunately

First plot is data, plot 2 is data squared and p = 3 the cube, etc.

We observe the moments, and see if by the law of large numbers it closes to 0.

Here the moment does not exist (we don't have convergence) certainly for the cube.

21/n

Nor p = 4.

Convergence for the square is even questionable.

Depending on the speed of the convergence , the fatness of the tail.

We can apply this formula, if parameter kappa pointed by Pasquale C. is larger than 10 possibly we do not need EVT.

22/n

What is the alpha of our sample? 

~1.5? The red lines are the 95% confidence intervals.

We don't care if it is 1.47 or 1.49: @DrCirillo recommends to stop at the first decimal: that is informative enough and we have to assume some error anyways.

23/n

Question about the axis.

In that graph y is alpha, on the x axis we have the observations ranked by size.

24/n

If alpha is negative, we can have something that behaves like a power law, but it isn't because it has an upper bound.

The Hill plot we saw yesterday makes only sense if alpha is positive.

25/n

If our alpha was, on the other hand, something like 300, it would not make sense to talk of fat tails, and we would be with all certainty in the thin-tailed domain.

26/n

Recaps of the plots.

The plot with the hand on it is plotting the errors, that are normally distributed as an exponential around one, the last plot shows the stability of the queue in the quantiles (it holds as a power law).

27/n

Software? R, Mathematica, Python?

Each software has its own advantages. This is like discussing if vanilla or chocolate ice cream is better.

@DrCirillo prefers Mathematica is better for symbolic analysis and plots, R for academic purposes, etc.

28/n

A question by @NonMeek: do risk managers in banks like EVT?

Answer: Not so much, but the problem is not the risk analysts, that are aware of these things, as CEOs or regulators. Those would only be interested in meeting the regulations.

Some attendant had a comment...

29/n

Capital requirements increase under EVT.

@DrCirillo says true, but not necessarily dramatically (depends on your modelization), this is more linked to regulation.

Everyone seems to agree, including Raphël, that at the end, it all comes to politics and stubborn regulators.

30/n

It was an excellent session.

We are back with Raphaël now.

What is a linear regression?

Check the independent variables and check the relation, i for time/size, k the factors...

31/n

Some software based on what he developed if I get it correctly here...

32/n

Compensation by % is so rare these days.

Raphaël asks to the other attendants about their experiences.

Someone says customers want to listen to "Santa Claus" stories and sharpe ratios. More to do with human psychology than with technical analysis...

We move on.

33/n

Simple question: if you get a PCR test that turns positive, what are the probabilities you actually have covid?

34/n

PCR has 1% false negatives and 3% false negatives.

This is a good test!

But the amount of people infected is not "symmetric".

35/n

As the bulk of the population is negative, we have a total number of false positives equivalent to the number of true positives, meaning that a positive result translates effectively into a 50% chance of infection.

37/n

Let us assume now two categories.

Imagine for instance A is obese people, B not obese people, or something similar.

38/n

Imagine A is 30% and B 70%.

We select 10 people.

A distribution of 3 obese 7 not is the most likely.

And it falls very quicky from that!

39/n

Column I plotted in orange, the "Bayesian" correction in blue.

This is the basis of Hill or maximum likelihood estimation, as we don't know the probability distribution, we just estimate the likelihoods...

40/n

Dave shared this link he thinks it is brilliant.

41/n

It is much better to be explicit in our hypothesis.

Sometimes we decide that a distribution is Paretian and this is a huge assumption (saying we are in that distribution class).

Raphaël mentions this lecture of his, that I might watch very soon...



42/n

The right way to do things is be truthful about one's priors, and where blind spots are, and if we don't know the alpha (and we are thinking of an epidemic) that we cannot project the number of victims, considering the uncertainty.

43/n

Attendees map, me highlighted.

Sorry to the quants following this that my attention is now being eaten by these things.

44/n

What does Bayes tells us?

Considering the data, the likelihood of the regime in which we are.

Raphaël opens round of questions, not many. 

Is Nassim problem with Bayes generalized?

Raphaël: I don't think he has a problem with it...

@Heinonmatti says @nntaleb said in...

45/n

a debate "F* Bayes!"...

Raphaël: "Va savoir what he wanted to say"...
"He is like you all know".

Someone asks if it is correct to assume Bayes is useful to say that Bayes is useful when we have not enough data.

Raphaël disagrees. We cannot, in practice, get rid of Bayes.

46/n

This is a statistical version of the Gödel problem, even an infinite amount of data will not allow us to get rid of Bayes.
The utility often has a huge sensitivity to the tail of the distribution, and there is a flaw in the whole 20th century not to look at this sensitivity.
47/n

So most of those decision making models were wrong.

Raphaël talks of 2011, it was a period of high turbulence and many of his friends had to close their funds, those who survived got to swing: one needs money to rebound...

48/n

Then @Heinonmatti asks: What do you think of works in complex systems of early warning signals (like increased intercorrelation)?

Raphaël says he does not know about it in depth, but he has talked with regulators about capital requirements for banks and stress testing.

49/n

Raphaël says his model helps identifying risk factors. Then something like the bank CEOs are responsible for their "boat" but responsibility to detect early signals of storms is not theirs, they are inside the "boats", rather in regulators.

50/n

If all "boats" are going to China, then the capital requirements increase.
 
Thomas Barrau asks if that can create self-fulfilling prophecies.

On the contrary, says Raphaël, this is about easing the risks.

Raphaël asks @Heinonmatti about his conference tomorrow.

51/51