 

goldorak


Total Posts: 1091 
Joined: Nov 2004 


Do you know that conditional correlation, in this case conditional to returns being higher than a certain threshold in absolute value (ie high volatility periods), increases with threshold increasing? In R so everybody can follow:
x=rnorm(10000);y=rnorm(10000);rho=0.6;z=rho*x+sqrt(1rho^2)*y;condcors=rep(0,7);thresholds=c(0,0.1,0.5,1,1.5,2,2.5);for (i in seq_along(thresholds)) {condcors[i]=cor(x[abs(x)>thresholds[i]],z[abs(x)>thresholds[i]])};plot(thresholds,condcors)
People in finance tend to mix the concept of "everything is falling together" which means "all averages are negative" with the correlation of returns they use in their portfolio constructions which ignores the means by definition. To control diversification of the averages is clearly a different job from managing random fluctuations around the means.

If you are not living on the edge you are taking up too much space. 


goldorak


Total Posts: 1091 
Joined: Nov 2004 


And I think these fin"tech" will definitely be innovative the day they charge a fixed fee for their advice.

If you are not living on the edge you are taking up too much space. 




>Do you know that conditional correlation, in this case conditional to >returns being higher than a certain threshold in absolute value Yes, but one should not mix the _simulated_ _normal_ random variables (exaustively specified by their correlation) and the real returns (not normal in tails and with more complicated dependence).
Look at your code: z=rho*x+sqrt(1rho^2)*y So x and y contribute to z. Obviously, given that abs(x) is large, its contribution to z is much stronger than that of y (unless abs(y) is large too, but since x and y are independent, this happens relatively rare).
The dependence of stock returns is more complicated. As I already said, tails are not normal. The second aspect: I would say that the factors, which drive the stock returns are not (always) independent, moreover, their (inter)dependence depends on market regime.
Once again, have a look at this figure:
The conditional correlation (better to say "conditional interdependence") crearly depends not only on abs(.) but also on sign(.)
I may agree that speaking about correlations and "falling together" may is probably not the best way from mathematical point of view (better would be speaking about Clayton Copula) but don't forget, I write for mere mortals :)
>And I think these fin"tech" will definitely be innovative >the day they charge a fixed fee for their advice. I agree. But so far it is not the case.

www.yetanotherquant.com  Knowledge rather than Hope: A Book for Retail Investors and Mathematical Finance Students 


goldorak


Total Posts: 1091 
Joined: Nov 2004 


Did you rescale returns to some kind of common fixed volatility reference?
I would add that these ellipses are definitely missleading as they tend to attract the reader's eyes to "prove" a point, distracting from the data point at (0.15,0.1). Setting different colors to datapoints exceeding a given threshold would be a fair representation of fact.
This plot is more an illustration of a negative correlation between returns and volatility.
I just did a plot of AMZN vs YHOO returns in the 19982000 period. Well, it looks like the result is the exact opposite of your plot with negative returns clustering above the regression line and positive returns clustering below. Pretty coherent with the positive correlation between returns and volatility that used to prevail back then.
I am a mortal though

If you are not living on the edge you are taking up too much space. 



goldorak


Total Posts: 1091 
Joined: Nov 2004 


I don't know what is your current status with regulators, but beware of BaFin before writing this in a publicly accessible blog post without any disclaimer. Just my 2c.
> But if you are willing to learn and have some time, we can offer you a better alternative! If you have a large sum to invest, please contact us for a personal consultation.

If you are not living on the edge you are taking up too much space. 



Well, according to my experience they are more correlated when they fall. Anyway, I wrote a comment (http://www.letyourmoneygrow.com/2016/09/16/strippingdowntheroboadvisorssparrowbrainsinside/#comment4) with link to this discussion and encourage my readers to check themselves, who is right.
>I don't know what is your current status with regulators, but beware >of BaFin before writing this in a publicly accessible blog post without >any disclaimer. Just my 2c. Yes, many thanks for this point. I checked and "Die Honorarberatung über Vermögensanlagen ist ab dem 1. August 2014 durch das Honoraranlagenberatungsgesetz geregelt und erlaubnispflichtig. " (from 1. Aug. 2014 one needs a license for such activity). So I removed it from the post for a while :)

www.yetanotherquant.com  Knowledge rather than Hope: A Book for Retail Investors and Mathematical Finance Students 




W.r.t. condition correlation, in most markets this is almost always an artifact of high market volatility relative to idiosyncratic vol. Correlation increases monotonically sublinearly with both beta and the ratio of market vol to idio vol.
Market volatility is much more regime sensitive and varies to a much greater degree than average beta or average idio vol. I feel like most of the time the intuition behind the phrase "correlations go to one" is wrong. It really doesn't have anything to do with stocks moving more in response to the market (beta). It also isn't stockspecific information becoming irrelevant (idio vol). Rather the noise from market volatility rises to the point where it's overwhelming the nonperturbed stockspecific information.
Saying that diversification stops working is misleading. Diversification still reduces risk by the same magnitude both in high and low correlation environments. But in the former high market volatility makes this risk reduction seem small in comparison. It's a little like saying that aspirin stops working when you're shot in the knee cap. Aspirin still delivers the same amount of painrelief, but you have bigger problems than just a headache.

Good questions outrank easy answers.
Paul Samuelson 



EspressoLover, >Aspirin still delivers the same amount of painrelief, but you have >bigger problems than just a headache Isn't it what I say?: "But please understand the message correctly: I am not telling you that the diversification is useless, I merely emphasize that its positive effect should not be overestimated". 
www.yetanotherquant.com  Knowledge rather than Hope: A Book for Retail Investors and Mathematical Finance Students 




BTW, I think this discussion is a good soil for my next article. I still insist that (at least in German market, which I observe daily for more than 10 years) they fall together. And that something like Clayton Copula is a more appropriate tool than a (symmetric) correlation coefficient.
However, without data we operate opinions, with data we operate arguments. But we must be careful: we are not going to scrutinize the correlation coefficients, conditioned on the amplitude and the sign of returns, we are going to scrutinize the strength of (inter)dependences between stock returns (conditioned on the amplitude and the sign of returns).
I don't know (yet) how to define this interdependence in the best way, but one idea of mine is as follows: 1) define the thresholds between "normal" and "extrem" returns (for DAX I would say extreme is everything outside of +/3%) 2) look at how many stocks fall (and how strong they fall), given DAX return is less than 3 % 2a) analogously look at how many stocks grow (and how strong they grow), given DAX return > 3 % 3) If there is a difference in amplitude and number of stocks (significant both visually and in the sense of formal statistical tests) then the asymmetry of stock interdependence is proven... and we should check whether the same works for DowJones. 4) the next step is to evaluate the limits of diversification more precisely.
And last but not least, a small R script to begin with library(quantmod) #get DAX daily OHLC data from yahoo.finance (fix from/to for reproducibility) getSymbols("^GDAXI", from="20070102", to="20160917") dailyDaxRets = as.numeric(ClCl(GDAXI)) dailyDaxRets = dailyDaxRets[which(!is.na(dailyDaxRets))] #remove 1st "n/a" element kmClust = kmeans(dailyDaxRets, centers=3) #higly positive, normal and highly negative returns colorz = c("red", "green", "blue" ) plot(dailyDaxRets, col = colorz[kmClust$cluster]) #my experience says the normal returns are between +/3%, decide yourself for it or for kmeans abline(h=0.03) abline(h=0.03)

www.yetanotherquant.com  Knowledge rather than Hope: A Book for Retail Investors and Mathematical Finance Students 


goldorak


Total Posts: 1091 
Joined: Nov 2004 


finanzmaster, you need to work on data with a modicum of stationarity. You need to decide yourself on a model, clean your data for non stationarity and then start analyzing it. For example, returns as such do not mean anything. A far better concept would be to work at least with quantiles. Just simply admit a gaussian distribution with mean zero (at daily level this is OK for most assets), predict volatility for time t based on information up to time t1, and determine what quantile the actual return at time t is based on a gaussian with second moment equivalent to what you forecasted. A scatter plot of the respective quantiles would be far more informative than what you did in the scatter plot below based on absolute returns.
No one cares about the absolute level of returns (OK, I admit, lots of dumb people out there, so let's say "no one with a few grey cells left"). A stock can go up and down +/ 60% logreturn every day as long as it is a regular behavior. What you care about is what quantile the occurrence belongs to. A +/ 60% logreturn can prove pretty painful when you are used to +/1% ones.
Finally, I do not comment on batch analysis anymore. I have seen way too many clever people saying great things about the past and failing miserably in the future. That kind of analysis looked great back in 1996 and could have been acceptable in 2006, not anymore in 2016.

If you are not living on the edge you are taking up too much space. 




"But if you are willing to learn and have some time, we can offer you a better alternative!"
The link in the original post is a load of rubbish, and blatant advertising for the firm posting it. finanzmaster, are you the author of the post you linked to? If so, then




Maggette


Total Posts: 1348 
Joined: Jun 2007 


"Finally, I do not comment on batch analysis anymore. I have seen way too many clever people saying great things about the past and failing miserably in the future. That kind of analysis looked great back in 1996 and could have been acceptable in 2006, not anymore in 2016."
So you would recommend a more "online" approach? But don't I have to start somewhere? Just to get a selecion of strategies that I am willing to tets online? 
Ich kam hierher und sah dich und deine Leute lächeln,
und sagte mir: Maggette, scheiss auf den small talk,
lass lieber deine Fäuste sprechen...




goldorak


Total Posts: 1091 
Joined: Nov 2004 


Of course, the one single important thing in a backtest is exactly when would you have selected a strategy and applied it, when would you have stopped using it, etc...
Why not start with the minimum number of data points required by your strategy?

If you are not living on the edge you are taking up too much space. 



> finanzmaster, are you the author of the post you linked to? Yes, I am! Do you run a roboadviser?! ;)
>we can offer you a better alternative! And yes, we can (my portfolio "Somewhat better than DUCKS" vs. DAX): https://goo.gl/GZJXW3 (here is the complete transaction history: https://www.wikifolio.com/de/de/wikifolio/999ducks)

www.yetanotherquant.com  Knowledge rather than Hope: A Book for Retail Investors and Mathematical Finance Students 



 

goldorak


Total Posts: 1091 
Joined: Nov 2004 


I am still remembering a sanguine assistant saying to me, when I was a student: "Where the f... are your confidence interval?"
The sanguine myself is still asking: "Where the phuck is the modicum of stationarization of return before you start any analysis?".
It's just a blog, I know. But still. Older sisters have to show example. Otherwise little brothers keep their wrongdoing habits ans misconceptions for life.

If you are not living on the edge you are taking up too much space. 




>I am still remembering a sanguine assistant saying to me, when I was a student: >"Where the f... are your confidence interval?" Here it is! :) We see that for 21 of 27 stocks the correlations, conditioned on exreme DAX ups and downs do differ.
Alternative hypothesis is that they don't and 21 of 27 is just a random outcome. To be even stricter let us talk about 21 of 30 since I disregarded 3 stocks with missing data. But even in this case the probability to get 21 (or more) of 30 is less than 1% pbinom(21,30,0.5) # N_TRIALS = 1e6 arr = array(0, dim=N_TRIALS) for(i in 1:N_TRIALS) { arr[i] = rbinom(1, 30, 0.5) } hist(arr) quantile(arr, 0.99)
So together they do fall stronger than they grow!
Another issue is the confidence intervals for the estimated correlated coefficients. Here I completely agree, as they say in Russia: the precision is plus/minus bast shoe. Moreover, if we try to calculate with them straigtforwardly in a Markowitzlike stile, we risk to get an absurd "optimal" portfolio.
>It's just a blog, I know. Yes, so far it is, but IMO it is much more scientific than any empirical study, published in peerreviewed journals, which does not provide the source code and data. I think after the Rogoff and Reinhard case it is clear that irreproducible paper is not the research result, it is a (potentially misleading) advertisment.
Moreover, I (subjectively) feel a strong trend to superficialness in nowadays web (10 years ago what they wrote was much more insightful). But I try to be an exception and treat my readers without mathematical arrogance but also don't simplify more than it is possible. The feedback to my book has shown that my target group of (pro)actively thinking and willing to learn retail investors is likely less than 1%. But even if it is 0.01%, it is still 10000 persons just in USA (where every 2. household invests). I will be quite happy if I help 10000 people to grow or at least not to lose their money. And I am grateful if you help me to help :)
http://www.letyourmoneygrow.com/mission/ 
www.yetanotherquant.com  Knowledge rather than Hope: A Book for Retail Investors and Mathematical Finance Students 

