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## AT-THE-MONEY IMPLIED VOLATILITY

Studies of the volatility surface have focused on at-the-money implied volatility time behaviour in terms of decay rates being slower than $1/T$.  Empirically, however, even power law $T^{-\alpha}$ may not be quite right.  The graph below shows an example from the stock USO, volatility surface of 2015-04-06.  The black line is log(implied volatility) and the green line is the fit of a cubic polynomial.  If only the linear term is significant, then a power law is sufficient.  However, the red line is the best fit by a linear function (R^2=0.716) and the green line which seems quite accurate (R^2=0.9915) is a cubic polynomial fit.  If the linear fit were sufficient we would have decay $ATMIV(T) = T^{-0.19}$ which is what would result from a power law long memory effect.  The cubic fit is $log(ATMIV) \sim -0.99 -0.22 T -0.04 T^3 -0.0017 T^2$.  The quadratic term is insignificant:

> summary(model)

Call:
lm(formula = x ~ poly(log(t), 3))

Residuals:
1 2 3 4 5 6 7
-0.0005498 0.0060277 -0.0103279 -0.0034048 0.0088524 0.0021038 -0.0030762
8
0.0003747

Coefficients:
Estimate Std. Error t value Pr(>|t|)
(Intercept) -0.992963 0.002780 -357.196 3.69e-10 ***
poly(log(t), 3)1 -0.220855 0.007863 -28.089 9.56e-06 ***
poly(log(t), 3)2 -0.001724 0.007863 -0.219 0.83720
poly(log(t), 3)3 -0.040101 0.007863 -5.100 0.00698 **

Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1

Residual standard error: 0.007863 on 4 degrees of freedom
Multiple R-squared: 0.9951, Adjusted R-squared: 0.9915
F-statistic: 271.7 on 3 and 4 DF, p-value: 4.465e-05

## THE ZULF STOCHASTIC VOLATILITY MODEL VERSUS OPTIONS MARKET MAKERS: FIRST GLIMPSE OF UNIVERSALITY

### zulfikar.ahmed@gmail.com<zulfikar.ahmed@gmail.com>

5:09 AM (2 hours ago)
 to harrington, jharris, jhp, jhricko_4, jianjunp, jinha, jjbrehm, jlind, jlondon, jlw, jmateo, jmerseth, jmetcalf, jmg, jmogel, joel, joelms, john.aldrich, john.beatty, johncrawford53, jose.oliveira, josesoto, josue, jpadgett, jpbalz

I was introduced to the issue of long memory at Gresham Investment Management where Benoit Mandelbrot had advised the principals; this was around a decade ago.  It took me a decade to understand what long memory in option prices means concretely to produce closed form stochastic volatility models from these extending Heston/Bates and the affine models.  Research papers on the topic goes back to 2000-2005 but a concrete closed form model that actually outperforms affine type models with jumps in price and volatility was new.  We are now looking into the issue of whether these models are able to consistently and universally make profits from mispricings of the market makers in liquid options.  This is not a hard problem if one wants to produce a trading strategy for a single option by hammering together something reasonable.  It is a hard problem if one wants to produce a system that is able to profit against the market makers’ mispricing universally.

To this end, I have produced a system that can produce tradeable strategies with a few tunable parameters.  The idea of the strategies is the combination of a VOLATILITY/VOLATILITY SURFACE PREDICTION with an ARBITRAGE OF MARKET MAKER MISPRICING.

One can use arbitrarily sophisticated methods for volatility and volatility surface prediction.  I use an ARFIMA model to predict the log(return^2) volatility of the underlying and a LASSO prediction of the multivariate time series of the 9 parameters of the Zulf SV model.  The LASSO model does not croak when the lookback period is small which is the reason I use it rather than a basic non-regularized linear model; empirically I found that an 80/20 mix of historical average of parameters and LASSO prediction produces better forecasts.  This part is not particularly optimal but it is not the central problem.

More important is the problem of the understanding what is the PRICE THRESHOLD of mispricing.  Here we have results that are far more nontrivial:  we find that the ERROR OF FITTING VOLATILITY SURFACES is the key part of the price threshold we should use.  So the objective function used to fit the volatility surfaces is sqrt(sum(ModelCallPx-MarketCallPx)^2/N) which is the average dollar mispricing per surface.  The best surface fits produces a minimal error of this type which we then use to decide the mispricing level.  This mispricing level seems to be central to actually systematically profiting from the option markets despite a big bid-ask spread!

Let me repeat this a few times so this is clear.  The POWER of the ZULF STOCHASTIC VOLATILITY model is not just that it fits the call prices better than other popular models (like Bates which is better than Heston adding jumps to prices and volatility) but that for 2015 for some of the liquid options the ERROR OF FIT can be used to define nontrivial MISPRICING THRESHOLDS with systematic good performance despite wide bid-ask spreads.  Let’s take a look at some graphs without any stop losses to appreciate the importance of this result.

Ok these graphs may not look pretty but they have no stoplosses or other artificial smoothing.  Now I know from a great deal of experience that it is not hard to produce strategies that are winners 65% of the times.  These are strategies with 80-90% winners (which is not as easy).

Both of these are produced by tuning the three parameters; the mispricing threshold is defined as CONST*ErrorOfVolSurfaceFit for the calibration of that day.  This is actually what produces the reasonable results above in backtests.  Second is a pair of VOLATILITY DIRECTION thresholds which essentially ensures that one does not short the option when the expected volatility is to rise.  This is also crucial:  we want to only do trades consistent with the volatility prediction.  Profitability of a volatility surface prediction strategy in these cases depends on making sure that one does not do ‘full delta hedging’ which means that they are not viable by shorting options when the volatility is expected to rise.

Finally, here is a harder example:  EEM where the results are not as clean but you can see that this problem of producing universal results is a tractable problem at least for 2015.

Of course if I put in a stop loss these would look much  better but that’s not so useful because we want to understand what’s driving the profits; we want universal results over all liquid options because we believe that the Zulf SV model is the best option pricing model in the world and is much better than whatever the option market makers are doing.  My explanation for why this works is precisely because the ERROR OF FITS of the volatility surface is used as thresholds (modulo a constant in [1,5] say).  In fact you can play around with fixed constant thresholds which is what I did till I realized the above and find that the results are much less steady.  On the problematic side, the universality I would like to see does not come without tuning the constants for each stock.

The code attached shows you the details of what produces these results — the valuation code is in cmlf.pyx and the details of the arbitrage strategy in predVSParamsStrategy.R.

I would like to propose to the world that:  STOCHASTIC VOLATILITY MODELS formalized is a SOLVED PROBLEM.  A hard nontrivial problem is the problem of optimal implementation of stochastic volatility models to somehow force arbitrage-freeness.  In other words thus far, this problem has been in the domain of PRACTICE while in fact, this seems to me to be as nontrivial a theoretical issue as the SV models themselves.  Who knows?  Maybe this is the equivalent of Google’s search engine problem ….
The attached files besides some of the code (for which you will need actual historical options data though) as well as files marked *-ret.txt which are extracted returns, *-vsps.txt which is the detailed output of the volatility surface prediction strategy that used PRECALIBRATED ZULF MODEL parameters all in the fill All-calibrations.txt.  But you can examine the takeArbitragePositions and other functions in the R code to verify that these are serious strategies.
11 Attachments

## IOWA: WE ARE BORE

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## DAILY STOCK RETURNS ARE NOT MARTINGALES: UNIVERSALITY OF UNEATEN FREE LUNCHES

 Inbox x

### zulfikar.ahmed@gmail.com<zulfikar.ahmed@gmail.com>

8:31 PM (14 hours ago)

 to harrington, jharris, jhp, jhricko_4, jianjunp, jinha, jjbrehm, jlind, jlondon, jlw, jmateo, jmerseth, jmetcalf, jmg, jmogel, joel, joelms, john.aldrich, john.beatty, johncrawford53, jose.oliveira, josesoto, josue, jpadgett, jpbalz
Today I would like to announce a concrete measurement of free lunch in US Equities.
The fundamental significance is that:

(a)  ARBITRAGE OPPORTUNITIES ARE NOT ANOMALOUS BUT UNIVERSAL

(b) OUR FUNDAMENTAL MODELS OF THE MARKETS ARE MISSING KEY FEATURES
As George Soros keeps repeating, there is no equilibrium in the market.  The lack of equilibrium in the market is sufficiently bad that arbitrage is UNIVERSAL.  The idea that arbitrage removes the profit opportunities is false.  And the work below is not particularly deep or complicated; it may be true that deep and complicated methods can yield profitable strategies but the importance of the following is that in fact SIMPLE EASY strategies can do this as well and the latter are more important to understand how we don’t understand the financial markets at all and all our fundamental theories are sort of missing glaring large problems.

Recall that finance theory has a fundamental pillar:  the Fundamental Theorem of Asset Pricing, the equivalence of No Free Lunch and Martingales.  All of option pricing theory is built on this pillar.  Option values are well-defined only because the underlying return process can be assumed to be a MARTINGALE.  (This is well-known from Harrison-Pliska late 1970s to Delbaen-Schachermayer mid 1990s).
So this is a beautiful academic theory which is almost universally wrong in equities markets.  How to see this?  Very simple.  An AR(1) or AR(2) process is not going to be a martingale generally: if x_t = b*x_{t-1} + noise, then obviously E[x_t] = b*E[x_{t-1}] with white noise and unless b=1 we don’t have a martingale; the same with AR(2).

So the fundamental empirical issue is whether returns are AR(1) or AR(2) with any statistical significance.  For this, grab daily returns from Jan-2007 to Apr-2017 and record the autocorrelations at lags 1 and 2.  The results are that in 403 stocks 68.98% have either lag 1 or lag 2 autocorrelations significantly greater than the 95% confidence interval.

Here is an actual list of tickers with ‘**’ marked next to the tickers with autocorrelation that crosses the significance threshold.  The interpretation is that the financial theory of no arbitrage models are not good models of the markets.  That the theoretical models do not match the markets is not so interesting.  What is interesting is that this is true with strong enough statistical significance for 70% of a random pool of stocks (these stocks are the ones used by sector indices so they are liquid large companies).
Before considering the data, let’s emphasize that this is not a peripheral issue: the fundamental models of the markets and the fundamental ways in which we think about the behaviour of the markets seriously (Black-Scholes and other option pricing etc) are wrong not in anomalous situations but almost UNIVERSALLY.  Now you could say, well quant hedge funds and technical traders know all this.  The problem is that this is not only an issue of making profits; it’s an issue for the world because how will we have any regulation of stable markets etc. if we PROFESSIONALISE a theory of markets that is just completely not matching empirical behaviour?
As for reproducing these results, rather trivial using some of the functions in my code.

symbols<-c(XLESymbols,XLFSymbols,XLVSymbols,XLFSymbols,XLBSymbols,XLISymbols,XLESymbols,XLUSymbols,XLYSymbols,XLKSymbols)

R<-constructComponentRets(symbols,as.Date(‘2007-01-01’))
R[is.na(R)]<-0

AllStocks<-matrix(0,403,2) # to hold 2 lag autocorrelations
for (k in 1:403){
AllStocks[k]<-acf(coredata(R[,k]))$acf[2:3] } for (k in 1:403){ ci<-qnorm((1+0.95)/2)/sqrt(length(index(R)));x<-AllStocksAcf[k,];condition<-(abs(x[1])>ci || abs(x[2])>ci);if(condition){c<-c+1}; disp(paste(symbols[k],x[1],x[2],ifelse(condition,’**’,”),ci))} HES -0.0382046321294291 -0.0570669865098722 ** 0.0377825479458521 CVX -0.0997064687533108 -0.0573128819839226 ** 0.0377825479458521 COP -0.0456617159454092 -0.0586681694691485 ** 0.0377825479458521 OXY -0.0817297336229358 -0.0674534813906045 ** 0.0377825479458521 XOM -0.154390931073284 -0.0937170896373303 ** 0.0377825479458521 TOT -0.0410477829041835 -0.0726442007287631 ** 0.0377825479458521 APC -0.0191200093891514 -0.0486279651769037 ** 0.0377825479458521 RDS-A -0.0492678418517147 -0.0694310181399589 ** 0.0377825479458521 BP -0.0373603425230508 -0.063366917972029 ** 0.0377825479458521 MRO -0.0290751816452744 -0.0529267122907142 ** 0.0377825479458521 MPC 0.017306189764944 0.0449958365717394 ** 0.0377825479458521 VLO -0.00345941128970282 -0.0602516199610069 ** 0.0377825479458521 SUN 0.0852300471426968 -0.00491511937371354 ** 0.0377825479458521 EC -0.0869753722946993 0.0287433678424457 ** 0.0377825479458521 NBL -0.0502316224336053 -0.0471790215190326 ** 0.0377825479458521 PBR 0.00342045429725232 -0.0508831766577323 ** 0.0377825479458521 PSX 0.0692399362629805 0.0115581213823195 ** 0.0377825479458521 PTR -0.0582862510082401 -0.0126595761879041 ** 0.0377825479458521 STO -0.0731744314134723 -0.0378427683283295 ** 0.0377825479458521 SU 0.00296420149908658 -0.0204177001582495 0.0377825479458521 XOI -0.0825226884489279 -0.0714079178125618 ** 0.0377825479458521 USO -0.0504181271525021 0.00401645415989441 ** 0.0377825479458521 UWTI -0.011906902707701 0.0027545420837071 0.0377825479458521 UCO -0.00928451932284817 0.0112879344467586 0.0377825479458521 XLE -0.0882425761390582 -0.0674070863899576 ** 0.0377825479458521 OIL -0.0355705914571595 0.0190243100411833 0.0377825479458521 DWTI -0.0554859100583393 0.023015554550779 ** 0.0377825479458521 SCO 0.00853833435477296 -0.0258144935527226 0.0377825479458521 DBO -0.0512506061901174 0.00897109753967469 ** 0.0377825479458521 VDE -0.0876993157109045 -0.0545651107028085 ** 0.0377825479458521 DIG -0.0879856196103714 -0.0604525070847256 ** 0.0377825479458521 BRK-B -0.0181581035348482 0.00552981244741128 0.0377825479458521 JPM -0.112168793611472 0.00382949994664429 ** 0.0377825479458521 WFC -0.123560698020111 0.0265080557183556 ** 0.0377825479458521 BAC -0.0375718266905737 0.0755510549179119 ** 0.0377825479458521 C 0.00215537806265875 -0.00117259389287589 0.0377825479458521 GS -0.0488775328831961 -0.0135121943728409 ** 0.0377825479458521 USB -0.107830473836386 0.0341711076492987 ** 0.0377825479458521 CB -0.0901844998495054 -0.0985386278446791 ** 0.0377825479458521 MS 0.00227834951905075 -0.0920449700517052 ** 0.0377825479458521 AXP -0.104327766762045 -0.0162314701226256 ** 0.0377825479458521 ICE -0.0811525508138042 -0.0378088620567959 ** 0.0377825479458521 BBT -0.136991907923339 0.0280298699401075 ** 0.0377825479458521 TRV -0.20168222412595 -0.0437715964556488 ** 0.0377825479458521 SPGI -0.00645881348352848 -0.0335211126805885 0.0377825479458521 AON -0.113506441431514 -0.0262821934708995 ** 0.0377825479458521 AFL -0.203097367224819 0.10711590165834 ** 0.0377825479458521 ALL -0.109974287818419 -0.0204586085995221 ** 0.0377825479458521 STT -0.146763172622148 -0.0299751300500908 ** 0.0377825479458521 STI -0.0612653830209914 0.0213140855465753 ** 0.0377825479458521 DFS -0.0836161625072747 -0.00547529490921607 ** 0.0377825479458521 RF -0.00810885842382611 -0.073715591613829 ** 0.0377825479458521 PFG -0.0477039562119986 -0.0497092833824634 ** 0.0377825479458521 TROW -0.123655292200166 -0.0457198993648533 ** 0.0377825479458521 WLTW -0.0372185135152648 -0.0824654326904595 ** 0.0377825479458521 LNC -0.0462211872989022 -0.00166199148230785 ** 0.0377825479458521 BEN -0.0523441200109036 -0.0424716019423321 ** 0.0377825479458521 HBAN -0.082539241511326 0.0504037793277749 ** 0.0377825479458521 L -0.15931989931682 0.00298517418800225 ** 0.0377825479458521 IVZ -0.113467825133864 -0.00714649451463555 ** 0.0377825479458521 CMA -0.0724396726661677 -0.00314028752852232 ** 0.0377825479458521 CINF -0.174034521842851 -0.0751836604271167 ** 0.0377825479458521 UNM -0.156895756787395 -0.0334000841127673 ** 0.0377825479458521 XL -0.0171271951898044 -0.0163243178916789 0.0377825479458521 AJG -0.0910118583535343 0.00217679533424188 ** 0.0377825479458521 ETFC -0.00508780255018044 -0.00809512138027311 0.0377825479458521 RJF -0.0797183553944291 -0.0157614629957661 ** 0.0377825479458521 AMG -0.0563830729562557 0.0341842130634544 ** 0.0377825479458521 LUK -0.047614023063904 0.00217716302892084 ** 0.0377825479458521 TMK -0.111065929777258 0.0326710381984407 ** 0.0377825479458521 ZION -0.0281758159340018 0.00889686303588805 0.0377825479458521 NDAQ -0.0338723081842863 0.00430166275574087 0.0377825479458521 CBOE -0.0532537993511472 0.066195481651599 ** 0.0377825479458521 PBCT -0.130790709218224 -0.0454650521456619 ** 0.0377825479458521 AIZ -0.0949937122321678 0.000423970731246187 ** 0.0377825479458521 NAVI 0.0547632105906803 0.0330805652408505 ** 0.0377825479458521 JNJ -0.0705479102171742 -0.0749617669508772 ** 0.0377825479458521 PFE -0.0604774784203281 -0.0646646879796013 ** 0.0377825479458521 MRK -0.0360385149769978 -0.0423564396973475 ** 0.0377825479458521 UNH -0.0322104907641962 -0.018225202635997 0.0377825479458521 AMGN -0.0619744906445128 -0.0276969578720048 ** 0.0377825479458521 MDT -0.0282306594652347 -0.00794701675692433 0.0377825479458521 ABBV -0.0202318682760407 -0.0301784190704243 0.0377825479458521 CELG -0.0761989024754419 -0.0171393343629497 ** 0.0377825479458521 BMY -0.0349873636658062 -0.047243117143378 ** 0.0377825479458521 GILD -0.043055382010135 -0.0319339234783084 ** 0.0377825479458521 AGN 0.00800492609498722 -0.0634554591660675 ** 0.0377825479458521 LLY -0.0925796969205498 -0.0610658275521083 ** 0.0377825479458521 ABT -0.0436711636308865 -0.0367701499610535 ** 0.0377825479458521 TMO -0.045253239357858 -0.0742932176438085 ** 0.0377825479458521 BIIB -0.0516766500998773 -0.0414792434760039 ** 0.0377825479458521 DHR -0.0509380626989889 -0.0551173706319112 ** 0.0377825479458521 AET -0.0516364732727262 -0.0410965909283735 ** 0.0377825479458521 ANTM -0.00403706396644323 -0.0326105923903629 0.0377825479458521 ESRX -0.0304436837274782 -0.00411197397349527 0.0377825479458521 SYK -0.00850273679748132 -0.0403472314022265 ** 0.0377825479458521 CAN -0.000376070668059349 -0.000374494309213882 0.0377825479458521 ZTS -0.0999795753546863 -0.0391137763119649 ** 0.0377825479458521 ILMN 0.0188985722345515 -0.0192753169943724 0.0377825479458521 HCA 0.0234777239235045 -0.0115960909011663 0.0377825479458521 ZBH 0.0152673975591984 -0.0571768089057087 ** 0.0377825479458521 INCY -0.021587829604441 0.0258937453428128 0.0377825479458521 EW -0.00571564799539204 -0.0286290905299879 0.0377825479458521 BCR 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0.0265080557183556 ** 0.0377825479458521 BAC -0.0375718266905737 0.0755510549179119 ** 0.0377825479458521 C 0.00215537806265875 -0.00117259389287589 0.0377825479458521 GS -0.0488775328831961 -0.0135121943728409 ** 0.0377825479458521 USB -0.107830473836386 0.0341711076492987 ** 0.0377825479458521 CB -0.0901844998495054 -0.0985386278446791 ** 0.0377825479458521 MS 0.00227834951905075 -0.0920449700517052 ** 0.0377825479458521 AXP -0.104327766762045 -0.0162314701226256 ** 0.0377825479458521 ICE -0.0811525508138042 -0.0378088620567959 ** 0.0377825479458521 BBT -0.136991907923339 0.0280298699401075 ** 0.0377825479458521 TRV -0.20168222412595 -0.0437715964556488 ** 0.0377825479458521 SPGI -0.00645881348352848 -0.0335211126805885 0.0377825479458521 AON -0.113506441431514 -0.0262821934708995 ** 0.0377825479458521 AFL -0.203097367224819 0.10711590165834 ** 0.0377825479458521 ALL -0.109974287818419 -0.0204586085995221 ** 0.0377825479458521 STT -0.146763172622148 -0.0299751300500908 ** 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-0.0471271970062459 ** 0.0377825479458521 ECL -0.123055887638274 -0.0535958188047616 ** 0.0377825479458521 PPG -0.0633282488831463 -0.0040491947167132 ** 0.0377825479458521 APD -0.0316480402673555 -0.0405969407828967 ** 0.0377825479458521 SHW -0.0785716358774839 -0.0512791442029955 ** 0.0377825479458521 LYB 0.0561451545093441 -0.000588850046618275 ** 0.0377825479458521 IP -0.0105610870308756 0.00995591710051536 0.0377825479458521 NUE -0.0873056229943715 -0.0475370688748524 ** 0.0377825479458521 NEM -0.0507198195580616 -0.041630987947113 ** 0.0377825479458521 FCX 0.00486664807471653 0.000560967869591787 0.0377825479458521 VMC 0.0437786853909507 -0.0344001785221484 ** 0.0377825479458521 MLM 0.0549278795827485 -0.0488336695194519 ** 0.0377825479458521 WRK 0.0629294383727902 -0.0345431185655866 ** 0.0377825479458521 BLL -0.0334548891170788 0.000796125617868546 0.0377825479458521 ALB -0.0264145512298628 -0.00625238608542115 0.0377825479458521 EMN -0.0202267607402485 0.0322732327992862 0.0377825479458521 IFF -0.119842547097384 -0.00827610696392747 ** 0.0377825479458521 FMC -0.0370767959951041 -0.0593281817912048 ** 0.0377825479458521 MOS 0.00406965753756472 -0.0522120992517892 ** 0.0377825479458521 SEE -0.057037025303748 0.00294223646290396 ** 0.0377825479458521 AVY -0.0382560831005411 -0.014865793751329 ** 0.0377825479458521 CF -0.00819915657977258 -0.0267796065409429 0.0377825479458521 GE -0.023244578854324 0.0265384987529405 0.0377825479458521 MMM -0.0702718177889118 -0.0387309779906187 ** 0.0377825479458521 BA 0.0109590179775202 -0.0287398438093762 0.0377825479458521 HON -0.0383693902394317 -0.0272233879393427 ** 0.0377825479458521 UNP -0.0244316450475462 -0.0381671014056369 ** 0.0377825479458521 UTX -0.0693525798275395 -0.043820747096321 ** 0.0377825479458521 UPS -0.0279300747189551 -0.045113354050877 ** 0.0377825479458521 LMT -0.10038530660541 0.0158725195527435 ** 0.0377825479458521 CAT -0.000321459155340597 0.0116655936661756 0.0377825479458521 GD -0.066642353961703 0.0298917423438843 ** 0.0377825479458521 LUV -0.0901347145252602 0.0454966469916919 ** 0.0377825479458521 DE -0.00694818710365999 -0.0313505790363351 0.0377825479458521 DAL 0.0144097754301961 -0.00334060868464342 0.0377825479458521 WM -0.0469326014292097 -0.074509016455177 ** 0.0377825479458521 PCAR -0.0412887481161378 -0.0261495888811545 ** 0.0377825479458521 PH -0.0125301405818139 -0.011895799768956 0.0377825479458521 ROK -0.0184318353080831 -0.0335231906937113 0.0377825479458521 EFX -0.0550905181828341 -0.0251152608541793 ** 0.0377825479458521 AAL 0.0344720678576242 0.0229593629250087 0.0377825479458521 IR -0.0310847587221513 -0.0338572346488253 0.0377825479458521 ROP -0.0675634268257082 -0.077704067828192 ** 0.0377825479458521 FTV 0.0488513543420545 -0.0159982194050378 ** 0.0377825479458521 SWK -0.0162788373629927 -0.0372662185725849 0.0377825479458521 UAL 0.0690880093261351 -0.019119551896606 ** 0.0377825479458521 COL -0.0527101601588631 -0.00192083825188458 ** 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-0.0262108069085176 0.000100646928523548 0.0377825479458521 R -0.033569790585108 0.0260183957056704 0.0377825479458521 ALLE 0.071791978139639 0.00209361954650035 ** 0.0377825479458521 SRCL -0.0454391900416325 -0.0214081211354089 ** 0.0377825479458521 JEC -0.032378232182086 -0.0268039320627433 0.0377825479458521 FLS -0.0223722352739972 -0.0409351498246482 ** 0.0377825479458521 PWR -0.0271993063028937 -0.029467008401664 0.0377825479458521 HES -0.0382046321294291 -0.0570669865098722 ** 0.0377825479458521 CVX -0.0997064687533108 -0.0573128819839226 ** 0.0377825479458521 COP -0.0456617159454092 -0.0586681694691485 ** 0.0377825479458521 OXY -0.0817297336229358 -0.0674534813906045 ** 0.0377825479458521 XOM -0.154390931073284 -0.0937170896373303 ** 0.0377825479458521 TOT -0.0410477829041835 -0.0726442007287631 ** 0.0377825479458521 APC -0.0191200093891514 -0.0486279651769037 ** 0.0377825479458521 RDS-A -0.0492678418517147 -0.0694310181399589 ** 0.0377825479458521 BP -0.0373603425230508 -0.063366917972029 ** 0.0377825479458521 MRO -0.0290751816452744 -0.0529267122907142 ** 0.0377825479458521 MPC 0.017306189764944 0.0449958365717394 ** 0.0377825479458521 VLO -0.00345941128970282 -0.0602516199610069 ** 0.0377825479458521 SUN 0.0852300471426968 -0.00491511937371354 ** 0.0377825479458521 EC -0.0869753722946993 0.0287433678424457 ** 0.0377825479458521 NBL -0.0502316224336053 -0.0471790215190326 ** 0.0377825479458521 PBR 0.00342045429725232 -0.0508831766577323 ** 0.0377825479458521 PSX 0.0692399362629805 0.0115581213823195 ** 0.0377825479458521 PTR -0.0582862510082401 -0.0126595761879041 ** 0.0377825479458521 STO -0.0731744314134723 -0.0378427683283295 ** 0.0377825479458521 SU 0.00296420149908658 -0.0204177001582495 0.0377825479458521 XOI -0.0825226884489279 -0.0714079178125618 ** 0.0377825479458521 USO -0.0504181271525021 0.00401645415989441 ** 0.0377825479458521 UWTI -0.011906902707701 0.0027545420837071 0.0377825479458521 UCO -0.00928451932284817 0.0112879344467586 0.0377825479458521 XLE -0.0882425761390582 -0.0674070863899576 ** 0.0377825479458521 OIL -0.0355705914571595 0.0190243100411833 0.0377825479458521 DWTI -0.0554859100583393 0.023015554550779 ** 0.0377825479458521 SCO 0.00853833435477296 -0.0258144935527226 0.0377825479458521 DBO -0.0512136079127417 0.00906204028306875 ** 0.0377825479458521 VDE -0.0876327799129898 -0.0546057355975147 ** 0.0377825479458521 DIG -0.0880309307891684 -0.0603871584630796 ** 0.0377825479458521 NEE -0.0733644460612461 -0.0636552503166962 ** 0.0377825479458521 DUK -0.00997790236373513 -0.00529897668985917 0.0377825479458521 SO -0.101100910020167 -0.0692341551544639 ** 0.0377825479458521 D -0.049134974763487 -0.0348094820916262 ** 0.0377825479458521 PCG -0.150077912840686 -0.0219647497342976 ** 0.0377825479458521 EXC -0.077282663522739 -0.0274691854350439 ** 0.0377825479458521 AEP -0.0980825075902536 -0.0518454974809491 ** 0.0377825479458521 SRE -0.104596811864245 -0.0279970190959245 ** 0.0377825479458521 EIX -0.11419085298171 -0.0222443605371055 ** 0.0377825479458521 PPL -0.0887592909810332 -0.0523912137241822 ** 0.0377825479458521 ED -0.0887189918161469 -0.0335470296467105 ** 0.0377825479458521 PEG -0.0747726744199105 -0.0481296763548322 ** 0.0377825479458521 XEL -0.128560310954468 -0.0666299802112818 ** 0.0377825479458521 WEC -0.0602435785132331 -0.026441505233539 ** 0.0377825479458521 ES -0.0874314508122689 0.00353755086428073 ** 0.0377825479458521 DTE -0.104562167411666 -0.00966464871970302 ** 0.0377825479458521 AWK -0.102357501708293 -0.0285113646928926 ** 0.0377825479458521 FE -0.0898835455866787 -0.043179874198026 ** 0.0377825479458521 ETR -0.0652079121330536 -0.059541223895436 ** 0.0377825479458521 AEE -0.0653698480558247 -0.0338633264007653 ** 0.0377825479458521 CMS -0.0499171452392984 -0.016127889320154 ** 0.0377825479458521 CNP -0.0825241291207523 -0.00834062045595049 ** 0.0377825479458521 PNW -0.0425099176115307 -0.050167351202929 ** 0.0377825479458521 SCG -0.0911646488712884 -0.0270481278238912 ** 0.0377825479458521 LNT -0.0612268912250421 -0.00413924863994639 ** 0.0377825479458521 NI -0.0434609243051964 0.00455012747456402 ** 0.0377825479458521 AES -0.105010621208799 -0.0170512227879755 ** 0.0377825479458521 NRG -0.00531926383708485 -0.0442995171959506 ** 0.0377825479458521 AMZN -0.0173431941000491 -0.0572909606926886 ** 0.0377825479458521 HD 0.0102997620394902 -0.0391140195542885 ** 0.0377825479458521 CMCSA -0.0431592089011311 -0.0305526266988228 ** 0.0377825479458521 DIS -0.0654052775183216 -0.058509299824095 ** 0.0377825479458521 MCD -0.0555431302523456 -0.0725231924649655 ** 0.0377825479458521 PCLN -0.0634494242545721 0.0107554334704399 ** 0.0377825479458521 SBUX -0.0264840118856933 0.0090282981493281 0.0377825479458521 TWX -0.0276886333570597 0.0475769380678315 ** 0.0377825479458521 NKE -0.0216340279756836 -0.0173834102817006 0.0377825479458521 LOW 0.00066872888024115 -0.0369036794774796 0.0377825479458521 CTH 0.00884617050635157 0.031890535278314 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0.0377825479458521 HPE -0.000804264442916011 -0.0231348550563911 0.0377825479458521 HPQ -0.0360843351027379 0.0147814912109553 0.0377825479458521 ADI -0.0655377705885021 -0.0358863802046437 ** 0.0377825479458521 INTU -0.108884882393872 -0.0263511428856961 ** 0.0377825479458521 MU 0.0318149385111538 -0.0160916287943178 0.0377825479458521 EA -0.0336118016826927 -0.00514166746900812 0.0377825479458521 FIS -0.0812943583264354 -0.0112350596925837 ** 0.0377825479458521 TEL 0.00724522081214939 -0.00775073214442354 0.0377825479458521 WDC -0.0515400539007221 0.0280207141144566 ** 0.0377825479458521 FISV -0.074437487088425 0.0109475265441429 ** 0.0377825479458521 GLW 0.00763746872466257 -0.0129224858793486 0.0377825479458521 APH -0.0392022437248607 -0.036309484092678 ** 0.0377825479458521 LRCX -0.0334379596094094 0.00255912866730621 0.0377825479458521 DXC -0.0293386065707787 -0.0145935713427751 0.0377825479458521 SYMC -0.0797656290360084 -0.0529522028888647 ** 0.0377825479458521 PAYX -0.0646406762666813 -0.026688358675993 ** 0.0377825479458521 SWKS -0.0311550181384956 0.00181505128643426 0.0377825479458521 ADSK -0.029390239780121 0.0021139564698393 0.0377825479458521 LVLT -0.00353992109011977 0.00457491426518462 0.0377825479458521 MCHP -0.0378250201132974 0.00321766232223941 ** 0.0377825479458521 KLAC -0.031161212161505 0.0196804003024459 0.0377825479458521 RHT -0.0152496632208506 -0.0216184711568318 0.0377825479458521 STX 0.0153258023156781 0.0334379162904983 0.0377825479458521 Attachments area ### M ## MY REACTION TO MY SISTER’S SUICIDE My sister committed suicide yesterday. I am so shocked that even my grief cannot express itself. Unlike when my father died in 2005 and my reaction was an anguished cry this event leaves me drained of all feeling with periodic waves of a feeling of infinite loss so destabilizing for my psyche that I am too fearful to feel the loss. Unfortunately, I can no longer believe with any conviction that there is eternal life somewhere. She was a beautiful tortured soul. I wish I did not have a trainwreck life and thus somehow be in a more financially secure and stable situation since I believe that I could have done something to avoid this situation but nothing brings home my powerlessness in this situation. Grief so tremendous hides within that I cannot face it. ## ON THE SHOULDERS OF GIANTS: DOES GOLDMAN SACHS KNOW FINANCE? ### zulfikar.ahmed@gmail.com<zulfikar.ahmed@gmail.com> 8:48 PM (10 hours ago)  to harrington, jharris, jhp, jhricko_4, jianjunp, jinha, jjbrehm, jlind, jlondon, jlw, jmateo, jmerseth, jmetcalf, jmg, jmogel, joel, joelms, john.aldrich, john.beatty, johncrawford53, jose.oliveira, josesoto, josue, jpadgett, jpbalz Ladies and Gentlemen, We are in the PRESCIENTIFIC era of finance. The preeminent financial services companies of the world, such as Goldman Sachs, doesn’t know finance. What do I mean by this? Being lazy, I refer you to the book by George Soros, ‘The Alchemy of Finance’ because why repeat good work already done. He will explain to you why financial markets are not like natural phenomena studied in physics because thinking participants affect the system being studied. So Goldman Sachs does not know finance. Neither do economists at Yale and Harvard. The academics are still confused from 1970s championing random walks (which was postulated by Bachelier in 1900 in the more sophisticated continuous time Brownian motion). Then the 1990s they are slowly talking about behavioral finance which unfortunately is in a messy state where no one has clear quantitative models that can be used. Now Soros is a genius of first order but his theory of reflexivity is quite elaborate and not quite quantitative in usable forms. I have been thinking about finance since 1995 from my first job at Lehman and it is becoming clearer to me that this is actually completely open terrain. Consider volatility. No one really knows what volatility is. I mean it’s easy to compute standard deviation of returns and define this as volatility but there is a way in which the WORD means something more and something deeper about, well the measure of volatile-ity. Well, if you want to measure volatile-ity, standard deviation of returns is a pretty stupid measure. So Mandelbrot brought into the fray the beautiful empirical observation of long memory in the markets. This is interesting because long memory originally was discovered in hydrology, with measurements of water levels of Nile. To make a long story short, standard deviation volatility (say proxied by return^2) has long memory. There are many studies about this. I FINALLY realized today that long memory of volatility is the totally wrong thing to consider. The right thing to consider is the long memory of the VOLUME OF TRADE. In particular if you take say the percent of total shares being traded (volume/shares outstanding) for stocks, you can see the long memory of this quantity directly say by calculating the autocorrelation sequence at different lags. THIS is the right object for long memory. In other words, the total volume traded has long memory, and this is a direct measurement while it SO HAPPENS that volume and the standard deviation of returns volatility HAPPEN to be correlated and so it is a CONSEQUENCE that there is long memory of volatility. The volume traded has long memory and this is the deeper issue because whatever we mean by volatility is happening under the volume or behind it. Yes yes Goldman folks know this but they don’t know finance anyway because there are no clear models that include reflexivity phenomena that figure as doctrine in any investment bank. Besides, they cannot break out of the religions that they earn their living on, which are completely wrong things. The first thing we need to understand from Soros is that various disequilibria that are the fundamental features of financial markets find their most basic examples in the volume series concretely. Soros’ concepts are based not on equilibrium prices (which he explains are meaningless) and on a reflexivity of two tendencies (he borrows heavily from Hegelian dialectics of thesis/antithesis) he calls the cognitive function and the participative function of market participants. The first place to look for this is of course VOLUME TRADED. So we immediately find that the long memory effects are all to be found here as well. So to the extent that Goldman Sachs does not explicitly model the markets with these sorts of features (they can’t because they sell index funds etc.) they don’t know finance. First I will share with you my latest great discovery, which I can say without much fake humility is absolute genius: even the most ELEMENTARY use of quantitative measures of reflexivity ideas leads very quickly to the discovery that almost EVERY oil stock (and probably much of the equities markets) has NEGATIVE autocorrelation at 1 day lag which while not super strong is strong enough that we can generate extremely good mean reversion strategies for them without doing pairs. So while I had a slightly more involved Alpha for Every Sector strategies before, here is a concrete and deeper example of how to produce alpha for every stock in the oil sector (XLE components) using mean reversion and trend following. The period is 2007-2017 and it is quite good in almost every single stock in the oil sector. So that’s the first great discovery, that alpha is quite common although it takes a bit of care to get the quantitative strategy to be in good order (see the R code for details; you will need the code in the attached file to get this to work in your machine): meanRev4<-function(rets,volchanges){ n<-length(rets); vRef<-rep(0,n) v<-rep(0,n) updown<-1 lastChange<-10000 for(k in 302:n){ lastChange<-lastChange+1 q<-quantile(volchanges,c(0.5,0.5)) CVRef<-cumsum(vRef) CV<-cumsum(v) CVRefSmooth<-savgol(CVRef,301,forder=3,dorder=0) avgVeryLong<-mean(CVRef[(k-30):(k-1)]) avgLong<-mean(CVRef[(k-5):(k-1)]) avgShort<-CVRef[k-1] actualAvgLong<-mean(CV[(k-5):(k-1)]) actualAvgShort<-CV[k-1] #if (avgLong>1.005*avgShort && lastChange>0){ # updown<- -1 # lastChange<-0 #} #if (avgLong<0.995*avgShort && lastChange>0){ # updown<- 1 # lastChange<-0 #} updown<- -sign(CVRefSmooth[k-1]-CVRefSmooth[k-2]) #if (abs(avgLong-avgShort)<0.0005){ # updown<- 0 # lastChange<-0 #} if( volchanges[k-1]>q[2] || volchanges[k-1]<q[1] ){ vRef[k]<- -sign(rets[k-1])*rets[k] v[k]<-updown*vRef[k] if (v[k]< -0.02) { v[k]<- -0.02 } } } list(v=v,vRef=vRef) } performanceTrendFollowingMeanReversion<-function( symbols,startDate ) { R<-constructComponentRets(symbols,startDate) V<-constructVolumeChanges(symbols,startDate) R[is.na(R)]<-0 V[is.na(V)]<-0 dts<-index(R) multiseries<-NULL nsymb<-length(symbols) for (ns in 1:nsymb){ x<-meanRev4(coredata(R[,ns]),coredata(V[,ns])) multiseries<-cbind(multiseries,x$v)
}
df<-data.frame(multiseries,index=dts)
names(df)<-symbols
matplot( df,type=c(‘l’))
legend(‘topleft’,legend=1:nsymb,col=1:nsymb,pch=1)
df
}
Now the second consequence of the problem of Goldman Sachs (and therefore the rest of the industry) not knowing finance.  Just as Bill Gates understood that no one knew software in 1970s we must understand that despite a century of theory of finance since Bachelier and some fancy models, no one actually knows finance because the two fundamental directions (fundamental/technicals) are inadequate to have any real clue about what is going on in the actual reality.  The answer is that someone (if not me someone at least) should start a TECHNOLOGY STARTUP that does this right: the only way that any serious WIDESPREAD OPEN understanding/use of finance can take shape is if we can COMMODITIZE QUANTITATIVE MODELS directly in retail so that actual models are easy to extract and EXECUTE in the markets.  Finance cannot be understood without quantitative models being accessible for RETAIL USE WORLDWIDE and the right vehicle for this is a technology company that provides this sort of service.  The correct quantitative models of the markets should not be considered material for the cognoscenti.  It should be provided as a retail service more or less how Google and Yahoo provide stock data but with ease of EXECUTION of strategies that are solid by anyone anywhere.  This is a big idea in the sense that such a company will probably make the entire financial services investment banks obsolete in time.  Just as Bill Gates understood that it was SOFTWARE that was more important than hardware, we must understand that in the situation where no one knows any finance, the first company to provide PUBLIC OPEN ACCURATE MODELS that show clear alpha and which can be executed conveniently by anyone anywhere in the world will be the company that redefines all financial markets.  The idea is that in the case where no one knows finance (and I don’t want to waste time arguing this since I can cite Soros’ book) the first technology company that makes concrete open easily accessible STANDARD for models of markets which can be USED easily and UNDERSTOOD easily and which which are OPEN and robust etc. will define for posterity what finance is.  Alpha in the markets are ubiquitous but it is quite a bit of work to build the models for the first time by hand.
The individual stock strategies are quite good alpha so check them out by running the code.  The Alchemy of Finance must be accessible to seven billion of this planet in a concrete manner.  A technology company is the right way to do this.  It will succeed if done properly more than Google and Facebook.
For sector strategies, I got decent results by machine learning.  Some of those graphs are attached.  This is original work so unpolished.  QUANTITATION of reflexivity ideas may seem at first glance like technicals/chartist strategies but this is not the right way to think about this.  The chartists’ concepts and viewpoint are not the right way to consider the issues of what is happening in the markets.  Soros’ ideas are much more serious but at the same time, we need some concrete simple results that are clear and compelling.  Alpha in the stock markets should be UNDERSTOOD, should be GLOBALLY PUBLIC, should be available to everyone in the world to trade.  Until this happens, this is a great way to establish a great new company; later on we can understand whether a true science of finance has a chance of emerging.  Soros is saying that this will be forever impossible in a sense but on the other hand, we can’t be sure until we try.

Financial markets should be available to everyone with convenient ways of trading without having to get a Masters in Finance.  This is a great opportunity to transform the entire structure of global finance as well as a path to addressing some subtler issues such as VOLATILITY STORMS and other deeper instabilities.  Academic ways of dealing with these is not going to be effective.  We don’t know what volatility is; how will we be able to quell volatility storms (which I coined but you can probably make sense of these from Soros’ theory).

12 Attachments

## WHICH MACHINE LEARNING ALGORITHM PREDICTS PRICE CHANGES BEST?

Even with a spread that has an autoregressive AR(1), prediction much better than 50% is hard with standard machine learning strategies.  For technology sector XLK, I created minimal lag 1 autocorrelation portfolios per day then I use variables 6 days of lagged returns of the chosen spread, the correlation, the long memory parameter for volatility, the acf.  The prediction accuracy by machine learning algorithm is:

Nearest Neighbors 0.501735250372
Linear SVM 0.5096678235
RBF SVM 0.506197322757
Gaussian Process 0.506693108577
Decision Tree 0.491819533961
Random Forest 0.513634110064
Neural Net 0.513138324244
Naive Bayes 0.489340604859
QDA 0.523549826475

So in this group quadratic discriminant analysis does best but none of these predictions are particularly spectacular.  The code:

import pandas.io.data as web
import pandas as pd
import numpy as np
import sys
import pykalman
from datetime import datetime,timedelta
from math import isnan
import matplotlib.pyplot as plt
import statsmodels.api as sm
from sklearn import linear_model
from sklearn.neural_network import MLPClassifier
from sklearn.model_selection import train_test_split
from sklearn.preprocessing import StandardScaler
from sklearn.datasets import make_moons, make_circles, make_classification
from sklearn.neural_network import MLPClassifier
from sklearn.neighbors import KNeighborsClassifier
from sklearn.svm import SVC
from sklearn.gaussian_process import GaussianProcessClassifier
from sklearn.gaussian_process.kernels import RBF
from sklearn.tree import DecisionTreeClassifier
from sklearn.ensemble import RandomForestClassifier, AdaBoostClassifier
from sklearn.naive_bayes import GaussianNB
from sklearn.discriminant_analysis import QuadraticDiscriminantAnalysis
import warnings
warnings.filterwarnings("ignore")

Sectornames=["XLY",
"XLP",
"XLE",
"XLF",
"XLV",
"XLI",
"XLB",
"XLRE",
"XLK",
"XLU"]
sectors=["Consumer Discretionary",
"Consumer Staples",
"Energy",
"Financials",
"Health Care",
"Industrial",
"Materials",
"Real Estate",
"Technology",
"Utilities"]

XLBSymbols=["DOW",
"DD",
"MON",
"PX",
"ECL",
"PPG",
"APD",
"SHW",
"LYB",
"IP",
"NUE",
"NEM",
"FCX",
"VMC",
"MLM",
"WRK",
"BLL",
"ALB",
"EMN",
"IFF",
"FMC",
"MOS",
"SEE",
"AVY",
"CF"]

XLUSymbols=["NEE",
"DUK",
"SO",
"D",
"PCG",
"EXC",
"AEP",
"SRE",
"EIX",
"PPL",
"ED",
"PEG",
"XEL",
"WEC",
"ES",
"DTE",
"AWK",
"FE",
"ETR",
"AEE",
"CMS",
"CNP",
"PNW",
"SCG",
"LNT",
"NI",
"AES",
"NRG"]

XLKSymbols=["AAPL",
"MSFT",
"FB",
"GOOGL",
"T",
"INTC",
"V",
"CSCO",
"VZ",
"PYPL",
"AMAT",
"YHOO",
"EBAY",
"ATVI",
"HPE",
"HPQ",
"INTU",
"MU",
"EA",
"FIS",
"TEL",
"WDC",
"FISV",
"GLW",
"APH",
"LRCX",
"DXC",
"SYMC",
"PAYX",
"SWKS",
"LVLT",
"MCHP",
"KLAC",
"RHT",
"STX"]

XLRESymbols=["SPG",
"AMT",
"CCI",
"PSA",
"EQIX",
"PLD",
"HCN",
"WY",
"AVB",
"EQR",
"VTR",
"BXP",
"VNO",
"DLR",
"O",
"ESS",
"HCP",
"HST",
"GGP",
"MAA",
"AIV"]

XLBymbols=["DOW",
"DD",
"MON",
"PX",
"ECL",
"PPG",
"APD",
"SHW",
"LYB",
"IP",
"NUE",
"NEM",
"FCX",
"VMC",
"MLM",
"WRK",
"BLL",
"ALB",
"EMN",
"IFF",
"FMC",
"MOS",
"SEE",
"AVY",
"CF"]

XLISymbols=["GE",
"MMM",
"BA",
"HON",
"UNP",
"UTX",
"UPS",
"LMT",
"CAT",
"GD",
"LUV",
"DE",
"DAL",
"WM",
"PCAR",
"PH",
"ROK",
"EFX",
"AAL",
"IR",
"ROP",
"FTV",
"SWK",
"UAL",
"COL",
"GWW",
"TXT",
"DOV",
"FAST",
"RSG",
"FLR",
"PNR",
"URI",
"EXPD",
"SNA",
"KSU",
"FBHS",
"XYL",
"RHI",
"JBHT",
"AYI",
"R",
"ALLE",
"SRCL",
"JEC",
"FLS",
"PWR"]

XLVSymbols=["JNJ",
"PFE",
"MRK",
"UNH",
"AMGN",
"MDT",
"ABBV",
"CELG",
"BMY",
"GILD",
"AGN",
"LLY",
"ABT",
"TMO",
"BIIB",
"DHR",
"AET",
"ANTM",
"ESRX",
"SYK",
"CAN",
"ZTS",
"ILMN",
"HCA",
"ZBH",
"INCY",
"EW",
"BCR",
"MYL",
"CERN",
"HOLX",
"UHS",
"DVA",
"PRGO",
"COO",
"VAR",
"EVHC",
"PKI",
"MNK",
"PDCO"]

XLPSymbols=["PG",
"PM",
"KO",
"MO",
"WMT",
"PEP",
"CVS",
"COST",
"WBA",
"CL",
"TAP",
"EL",
"DPS",
"MNST",
"K",
"CLX",
"CAG",
"MJN",
"SJM",
"HSY",
"CPB",
"MKC",
"HRL",
"CHD",
"WFM",
"BF-B",
"COTY"]

XLFSymbols=["BRK-B",
"JPM",
"WFC",
"BAC",
"C",
"GS",
"USB",
"CB",
"MS",
"AXP",
"ICE",
"BBT",
"TRV",
"SPGI",
"AON",
"AFL",
"ALL",
"STT",
"STI",
"DFS",
"RF",
"PFG",
"TROW",
"WLTW",
"LNC",
"BEN",
"HBAN",
"L",
"IVZ",
"CMA",
"CINF",
"UNM",
"XL",
"AJG",
"ETFC",
"RJF",
"AMG",
"LUK",
"TMK",
"ZION",
"NDAQ",
"CBOE",
"PBCT",
"AIZ",
"NAVI"]

XLESymbols=["HES",
"CVX",
"COP",
"OXY",
"XOM",
"TOT",
"APC",
"RDS-A",
"BP",
"MRO",
"MPC",
"VLO",
"SUN",
"EC",
"NBL",
"PBR",
"PSX",
"PTR",
"STO",
"SU",
"XOI",
"USO",
"UWTI",
"UCO",
"XLE",
"OIL",
"DWTI",
"SCO",
"DBO",
"VDE",
"DIG"]

XLYSymbols=["AMZN",
"HD",
"CMCSA",
"DIS",
"MCD",
"PCLN",
"SBUX",
"TWX",
"NKE",
"LOW",
"CTH",
"NFLX",
"TJX",
"GM",
"F",
"FOXA",
"TGT",
"MAR",
"CBS",
"ROST",
"CCL",
"ORLY",
"NWL",
"YUM",
"DLPH",
"AZO",
"OMC",
"DLTR",
"VEC",
"DG",
"ULTA",
"RCL",
"EXPE",
"VIAB",
"FOX",
"MHK",
"DISH",
"GPC",
"BBY",
"CMG",
"WHR",
"DHI",
"COH",
"HOG",
"HAS",
"KMX",
"AAP",
"LEN",
"DRI",
"TIF",
"IPG",
"FL",
"TSCO",
"WYNN",
"GT",
"M",
"WYN",
"MAT",
"LKQ",
"BBBY",
"GRMN",
"TGNA",
"JWN",
"HRB",
"NWSA",
"TRIP",
"SIG",
"DISCA",
"RL",
"UAA",
"UA",
"AN",
"NWS"]

import re
sectorTicker=sys.argv[1]

def ret_ser(symbols,D,start,end):
X=D[symbols].loc[start:end]
R=np.diff(np.log(X))
R[np.isnan(R)]=0
return R

def print_full(x):
pd.set_option('display.max_rows',len(x))
print(x)
pd.reset_option('display.max_rows')

def create_sector_strat_df( fName):
print fName
#regex=re.compile(r'.*(\d{4}-\d{2}-\d{2}) portA: ([^ ]+) portB: ([^ ]+) acf: ([^ ]+) d: ([^ ]+) cor: ([^ ]+) pr: ([^ ]*) dir: ([^ ]+) rc: ([^ ]+) rf: ([^ ]+) rp1: ([^ ]+) rp2: ([^ ]+) rp3: ([^ ]) rp4: ([^ ]+) rp5: ([^ ]+) rp6: ([^ ]+)\".*')
regex = re.compile(r'.*(\d{4}-\d{2}-\d{2}) portA: ([^ ]+) portB: ([^ ]+) acf: ([^ ]+) d: ([^ ]+) cor: ([^ ]+) pr: ([^ ]*) dir: ([^ ]+) rc: ([^ ]+) rf: ([^ ]+) rp1: ([^ ]+) rp2: ([^ ]+) rp3: ([^ ]+) rp4: ([^ ]+) rp5: ([^ ]+) rp6: ([^ \"]+).*')
colNames = ['date','acf','d','cor','pr','dir','rc','rf','rp1','rp2','rp3','rp4','rp5','rp6']
df = pd.DataFrame( columns=colNames)
df.set_index(['date'],inplace=True)
with open(fName) as f:
for line in f:
m=regex.match(line)

if m:
date = datetime.strptime(m.group(1),'%Y-%m-%d')
portA = m.group(2)
portB = m.group(3)
acf = m.group(4)
d = m.group(5)
cor = m.group(6)
pr = m.group(7)
dir = m.group(8)
rc = m.group(9)
rf = m.group(10)
rp1 = m.group(11)
rp2 = m.group(12)
rp3 = m.group(13)
rp4 = m.group(14)
rp5 = m.group(15)
rp6 = m.group(16)

data = [[date,float(acf),float(d),float(cor),float(pr),float(dir),float(rc),
float(rf),float(rp1),float(rp2),float(rp3),float(rp4),float(rp5),float(rp6)]]
#print data
ndf = pd.DataFrame( data, columns=colNames)
df = df.append(ndf)
return df

names = ["Nearest Neighbors", "Linear SVM", "RBF SVM", "Gaussian Process",
"Decision Tree", "Random Forest", "Neural Net", "AdaBoost",
"Naive Bayes", "QDA"]

classifiers = [
KNeighborsClassifier(3),
SVC(kernel="linear",C=0.0001),
SVC(kernel="rbf",gamma=0.1),
GaussianProcessClassifier(1.0*RBF(1.0),warm_start=True),
DecisionTreeClassifier(max_depth=10),
RandomForestClassifier(max_depth=10,n_estimators=10,max_features=1),
MLPClassifier(alpha=10),
GaussianNB(),

D = create_sector_strat_df( '%s.out' % sectorTicker)
D = D.dropna()
n=len(D.index)
Dp = D.ix[:,D.columns != 'date']
Dx = Dp.ix[:,Dp.columns != 'rf']
Dy = Dp['rf']

for name, clf in zip(names,classifiers):
correct = 0
total = 0
lookback = 40
for k in range( lookback,n-1):
xtrain = Dx.iloc[(k-lookback):k].as_matrix()
ytrain = np.sign(Dy.iloc[(k-lookback):k].as_matrix())

model = clf
model.fit(xtrain,ytrain)
#print'score=', model.score(xtrain, ytrain)

xtest = Dx.iloc[k+1].as_matrix()
#print xtest
yactual = Dy.iloc[k+1]

predicted= model.predict(xtest)

total = total + 1

if np.sign(yactual) == np.sign(predicted[0]):
correct = correct + 1

print name, float(correct)/float(total)