Factors that influence the volatility of stock prices

Generally, boosting is sequential process, which is represented by tree, that grows with information from previous tree, where trees grow after each other. Boosting convert week predictors, which are slightly better than random ones, in strong predictors. But, it is difficult to create appropriate classes of predictors and classifiers has misclassification errors. XGBoost can solve both classification and regression problem. In order to solve regression problem, XGBoost can use two methods. The first one is usage of booster - “gbtree” parameter, which is a tree, that grows one after each other and aim to reduce misclassification rate, using subsequent iterative process. The second method is usage of booster - “gblinear” parameter. In gblimear method, XGBoost make generalized linear model and optimizes it using L1 or L2 regularization. It also can optimize through gradient descent: it optimize the loss function(RSS minimal) by finding appropriate coefficients' weights. Than, iteratively, models are comprised on the basis of residuals of previous model. XGBoost parameters can be divided into general, booster and learning task parameters. General parameters control the type of a booster: booster is gbtree or gblinear. Gbtree parameters are: nrounds(number of iterations, obtained using cross-valodation), eta(learning rate), gamma(regularization), max_depth(complexity of the model), min_child_weight(control overfitting), colsample_bytree(number of sample by tree), lambda and alpha(from elastic net). Gblinear parameters are: nrounds, alpha and lambda. As we consider regression, evaluation metrics will be captured by Mean Absolute Error and Root Mean Squared Error. We will use linear model for prediction of volatility: a linear combination of possible predictors. Also, we will use ranking score, in order to determine the most important features. Our objective function contains the trainng and testing set:



where L - is traing loss function, Щ - is regularization term, that control overfitting and и - set of parameters. The trade-off between L(и) and Щ(и) refers to bias-variance tradeoff in machine learning. What is tree in xgboost? Tree is a real score, associated with each leaf of different feauture. Single tree does not provide a full picture for prediction, that is why each tree is combined in set of CART: classification and regression trees. Random forest and boosted tree are similar in terms of model, which can be represented in terms of trees:

The difference is in the way, we train that trees. In order to determine, how well is predictive power of our model in training set, we will consider the loss function, captured by Mean Squared Error:

At very first stage, all parameters are set by default:

Number of iterations are 100 or 200, complexity of the model is given by c(10, 15, 20, 25), to control overfitting we use sequence of (0.5, 0.9, length.out = 5), learning rate is 0.1, gamma=0, number of sample by tree is = 1, and number of subsample is 1.

Then cross-validation allows to find relevant nrounds, alpha, eta, max_depth. At the next stage, we obtain prediction for volatility and compare it with observed volatility. We expect to have different results obtained from gbtrees and gblinear, because of parameters use, which affect accuracy and prediction outcome.

Our aim to use XGBoost for regularization purpose and check it's performace. Firstly, I apply XGBoost for whole model with full number of possible predictors. Our variables is transformed in matrix form as it required by package: using “xgboost” package, it is divivded into training and testing values. Our training set is the sample from first till 659^th observation. Testing set starts from 660^th till the end of sample. Also we specify cross-validation method by setting train control function.

Then we find the best parameters values using grid search, using defaults values for parameters. Finding appropriate hyperparameters is cruicial, as xgboost can give very different results for different values of parameters. Using “caret” package, we apply train function for xgbtree method. It allows to find best values of hyperparameters (“xgb_modelABS$bestTune”). Let us consider, case of absolute returns as proxy for volatility. It gives the following values for hyperparameters:

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nrounds	max_depth	eta	gamma	colsample_bytree	min_child_weight	subsample
200	15	0.1	0	0.6	1	1

Then we predict our xgb model. Root Mean Squared Error of model is 0.006. is 0.853. is large, which tells us that 85% of variation in response variable is explained by variation in predictors. Let us look at the plot of actual actual volatility with predicted:

Applying XGBoost, for model with dependent variable as absolute returns, shows good predictive power.

If we consider squared returns as proxy for volatility, results for hyperparameters are:

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nrounds	max_depth	eta	gamma	colsample_bytree	min_child_weight	subsample
200	10	0.1	0	0.8	1	1

The root mean square error of the test data is 0.001 and the of the test data is 0.527. It is lower than in absolute returns case. Loss function is almost zero, but predictive power is worse than in absolute returns case. However, still, as we can see from the following plot it does predict volatility reasonable, expecially for small values. It fails to predict big values for volatility, in other words, it does not predict big shocks.

For Range Based Proxy, results are much more worse. Value for hyperparameters are:

nrounds	max_depth	eta	gamma	colsample_bytree	min_child_weight	subsample
100	10	0.1	0	0.7	1	1

If we focus on weekly variance as a proxy for volatility, XGBoost gave us the following results: best values for hyperparameters:

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nrounds	max_depth	eta	gamma	colsample_bytree	min_child_weight	subsample
200	10	0.1	0	0.7	1	1

RMSE = 0, but is low and equal to 0.326. And the following plot is:

Overall, XGboost suggest, that if we choose absolute returns, as proxy for voaltility, our model is a good predictor, however such good model performance is not observed in other types of proxy. But it could be said, that in other, except absolute returns proxy, cases: weekly variance and squared returns as proxy, model performance is middle-quality, as average is around 30/40%. But in case of Range-Based proxy, Xgboost totally incapable in prediction of volatility, as is too low. Low volatility is predicted by all four cases better, than high volatility, which can suggest that high volatility shocks are not predictable at all.

The Xgboost has internal setup, that allows to find importance scores that bring each variable. We can find the most important variables in the models.

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Variable	Score
196: ME5PRIOR2	0.2724
199: BIGHiPRIOR	0.1979
197: ME5PRIOR3	0.1338
195: BIGLoPRIOR	0.1272
191: ME4PRIOR2	0.0638
174: THREEFY5	0.0248
102:BAMLC7A0C1015Y	0.0241
15: DTP30A28	0.0238
194: ME4PRIOR5	0.02
7: CAD1MTD156N	0.0084
22: GBP6MTD156N	0.0083
192: ME4PRIOR3	0.0071
190: ME4PRIOR1	0.0062
198: ME5PRIOR4	0.0059
175: SMALLLoPRIOR	0.0058
41: SMB	0.0054
184: ME2PRIOR5	0.0041
55: TYCSD678FRBCLE	0.0038
176: ME1PRIOR2	0.0029
153: T5YIE	0.0025

Absolute returns case , suggest that the variable that brings the biggest score 0.272440 is one of the 25 portfolios formed on size and book-to-market ratio: ME5PRIOR2 portfolio. If we pay attention to the list of top 20 important variables of the xgb model, we will found out that almost half of important variables are Fama-French portfolios of different book-to-market ratio and size. So, we can conclude that change in returns of different Fama-French portfolios has considerable impact on volatility proxy: absolute returns. Beside Fama-French portfolios, Fitted Yield on a 5 Year Zero Coupon Bond appears to bring some score(0.024842), ICE BofAML US Corporate 10-15 Year Effective Yield(0.024140), 30-Year 3-5/8% Treasury Inflation-Indexed Bond Yield(0.023809), 1-Month London Interbank Offered Rate (LIBOR) in Canadian dollar(0.008496) and 6-Month London Interbank Offered Rate (LIBOR) in British pound(0.008340). Only very few score brings 5-year Treasury Constant Maturity minus Federal Funds Rate and contributions to the Cleveland Financial Stress Index: Treasury Yield Curve.

Variable	Score
303: WILL5000IND	0.2361
309: WILLSMLCAPVAL	0.1619
116: BAMLH0A2HYBSYTW	0.0741
126: RPMBSD	0.0547
242: BAMLEMFSFCRPIOAS	0.0544
315: RU3000VPR	0.0509
299: DDFUELUSGULF	0.0378
10: CHF1MTD156N	0.0314
46: DPCREDIT	0.0313
7: GBP1MTD156N	0.0207
254: BAMLCC1A013YTRIV	0.0166
52: CMRKTSD678FRBCLE	0.0151
215: VXOCLS	0.012
15: DTP30A28	0.0116
80: DSWP4	0.0106
187: ME3PRIOR3	0.0081
229: BAMLEM4BRRBLCRPIEY	0.0077
33: EURONTD156N	0.0076
174: THREEFY5	0.0072
289: RMIDGRTR	0.0071

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Range-Based proxy case, is mentioned above as not appropriate xgboost model, because of low prediction power. But, anyway, let us look for variable importance. The variable with the highest score(0.236155) is Wilshire 5000 Total Market Index. The next is Wilshire US Small-Cap Value Total Market Index with score 0.161926 and the following is ICE BofAML US High Yield B Semi-Annual Yield to Worst with score 0.074110. Repurchase Agreements: Mortgage-Backed Securities Purchased by the Federal Reserve in the Temporary Open Market Operations is also considered as important variable with score 0.054779 but does not appear in other three cases as well as some other less important vatiables, so we can conclude, that these results are unreliable and are due to bad xgboost volatility prediction, if proxy chosen is Range-Based. The plot of variable importance:

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Variable	Score
115: BAMLH0A1HYBBSYTW	0.1159
191: ME4PRIOR2	0.1098
100: THREEFY5	0.1008
102: BAMLC7A0C1015Y	0.0991
304: WILLLRGCAP	0.088
346: NASDAQCOM	0.0492
217: NASDAQCOM	0.039
329: USDBRL	0.0388
195: BIGLoPRIOR	0.0339
264: BAMLHYH0A1BBTRIV	0.0334
119: AAAFF	0.0286
116: BAMLH0A2HYBSYTW	0.0286
197: ME5PRIOR3	0.0279
276: RU1000GTR	0.0271
103: BAMLC1A0C13YEY	0.0253
344: WILL5000INDFC	0.0207
10: CHF1MTD156N	0.02
181: ME2PRIOR2	0.0195
331: USDINR	0.0166
190: ME4PRIOR1	0.0143

If we consider case with weekly variance as proxy for volatility, we will notice, that the most important variable in terms of score contributed is ICE BofAML Public Sector Issuers Emerging Markets Corporate Plus Sub-Index Effective Yield(0.11569). This variable does already appear in absolute returns case, as well as some of Fama-French portfolios. New variables, that appear in weekly variance case, are Wilshire US Large-Cap Total Market Index(0.08802), NASDAQ 100 Index(0.04916) and Moody's Seasoned Aaa Corporate Bond Minus Federal Funds Rate(0.02860). Fitted Yield on a 5 Year Zero Coupon Bond is considered to be important also and have score of 0.10089. As in case of Range - Based proxy, it also consider 1-Month London Interbank Offered Rate (LIBOR) in Swiss franc as important feature, although with not big score, only 2%.

The corresponding graph is the following:



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Variable	Score
7: CAD1MTD156N	0.2464
197: ME5PRIOR3	0.1414
174: THREEFY5	0.1125
195: BIGLoPRIOR	0.10799
196: ME5PRIOR2	0.1056
102: BAMLC7A0C1015Y	0.0546
199: BIGHiPRIOR	0.0449
42: HML	0.0283
192: ME4PRIOR3	0.0278
189: ME3PRIOR5	0.0174
352: RUMIDCAPPR	0.0162
191: ME4PRIOR2	0.0159
313: RU2500TR	0.0131
108: BAMLC2A0C35Y	0.0103
111: BAMLC4A0C710Y	0.009
194: ME4PRIOR5	0.0077
198: ME5PRIOR4	0.0053
190: ME4PRIOR1	0.0045
188: ME3PRIOR4	0.0043
301: DEXVZUS	0.0043



The last case is when proxy chosen is squared returns. As it was expected, there are lots of important variables, that were already captured in absolute returns case. Overall, squared return case has shown best performance after absolute returns case, so summing results from both cases will bring us valuable information about really important features. Top 5 variables in squared returns case was mentioned in absolute returns case. The most important variable is 1-Month London Interbank Offered Rate (LIBOR), Canadian dollar, with score 0.246414. Fama - French portfolios returns are considered as important variables with scores 0.141350, 0.107986, 0.044841, etc. ICE BofAML US Corporate 10-15 Year Effective Yield goes further and has score 0.054500. There are some new variables, such that Russell 2500 Total Market Index with score 0.013094.

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XGboost make inconsistemt results, due to choice of different proxies. As we can see above, the model predicts well the dependent variable - absolute returns, and not bad - squared returns. So, it is reasonable to make inference about variables importance by looking at tables one and four. With no doubt, Xgboost consider Fama-French portfolio returns(especially BIGLoPRIOR, ME5PRIOR2, ME5PRIOR2) as one of the most important factors, from our dataset, that affect volatility. Another factors, that are, probably, important in predictiong real volatility is 1-Month London Interbank Offered Rate (LIBOR) in Canadian dollar and ICE BofAML US Corporate 10-15 Year Effective Yield.

GARCH vs XGBoost

One of the most popular types of models, that are used for predicting volatility is GARCH(Generalized Autoregressive Conditionally Heteroskedastic).It is more parsimonious version of ARCH model.

GARCH accounts for volatility clustering and volatility mean reversion. Volatility clustering is the phenomenon, that is associated with the fact that during some periods of time volatility is unusually high, and during other - low. We can examine these stylized fact by looking at plots of different proxies for volatility, obtained using returns on SPDR® S&P 500 Exchange Traded Fund from 1993 year.

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We can observe, that, though absolute return proxy is much more volatile, than other proxies, there is obvious existence of volatility clustering. For example, during the period of June 2003 - December 2006 there was a period of low volatility and no shock was observable. From these plots we can see that periods of high volatility were during 1998 - 2002 and at 2008, which are associated with Dot-com bubble and Credit Crunch correspondingly.

We will use GARCH(1;1) to predict volatility using rolling window, because it is the most widely used extension of ARCH - type model and in some cases it performs better than other model. “Rugarch” package in R was used to estimate GARCH model. Our in-sample contains of 656 observations and out-sample - 659 observations. Here are volatility(sigma) n-ahead forecasts for n: from 1 to 10.

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T+N	Sigma: 2018-04-02
T+1	0.03126217
T+2	0.03123286
T+3	0.03120393
T+4	0.03117535
T+5	0.03114714
T+6	0.03111928
T+7	0.03109178
T+8	0.03106462
T+9	0.03103781
T+10	0.03101134



Next stage is to evaluate GARCH performance by comparing it with XGBoost via Diebold Mariano test. Diebold Mariano test evaluate performance of corresponding models via comparing its loss function. We use “Forecast” package in R and calculate corresponding loss functions(difference between squared realized and squared predicted sigma) as input to perform DM-test. Both models gave list of predicted sigma for our rolling window and actual volatility is obtained through using proxies. Null hypothesis states that difference between forecast errors is zero and non of the model is better than another. Alternative hypothesis is that difference is positive: so Xgboost is better than GARCH in predicting volatility.

If proxy is absolute returns, Diebold - Mariano statistics is -2.6094. DM-statistics is compared with N(0;1) for 99% confidence level. On the basis of above statistics we conclude that GARCH outperform Xgboost in-sample if proxy used is absolute returns. But, If we use squared returns as proxy, and compare Xgboost based on squared return proxy as dependent variable with GARCH, we will found out that DM-stat is 6.8115, which states that Xgboost overperform GARCH model. In case of Range - Based proxy result is the same as in case of absolute returns: GARCH overperformes Xgboost and DM - statistics is -4.0937. However, if proxy - weekly variance, than DM - statistics is 6.8115 and we conclude that Xgboost predict better than GARCH in case of following proxy. The results are the same for both methods of Xgboost: tree and linear.

Overall, result of Diabold - Mariano test results are very uncertain. Absolute returns proxy Xgboost model have the biggest prediction power among other Xgboost models, that we have considered. But, it came out, that GARCH model perform better. As it was expected GARCH overperform XGboost in case of Range-Based proxy, as Xgboost model have too low predictive power. XGboost model in weekly variance proxy case predict better than GARCH, even if have around 30%. It means, that either variance proxy is certainly not relevant proxy for volatility or that both models are not reliable. Squared returns case XGBoost model predict better than GARCH according to Diabold - Mariano test.



Conclusion:

We do not expect models to give similar results, so it is not surprisingly, that models give different and inconclusive results about volatility predictors. What is more, chosen proxies may not fully and accurately track the real volatility behavior, as it is unobservable. So, we can not say for sure which method of regularization and fitting model is appropriate. It we assume that absolute returns is a true proxy for volatility, than GARCH(1;1) is the best model for predicting volatility compared to XGBoost. XGBoost has high predictive power but GARCH due to Diebold Mariano test overperform it, and so, we conclude that GARCH is the best. Least Angle Regression results is not very different from XGboost in terms of variables selection: we can see different Fama-French portfolios' returns, ICE BofAML indices: only those which are associated with US market, as indices of Asian market for instance do not appear to be significant. Also, there were 1-Month London Interbank Offered Rate (LIBOR) in Canadian dollar and British pounds almost in all four models we have considered. In case of squared returns as dependent variable, results of all methods are not very different from results of absolute returns proxy case. However, we can see that weekly variance proxy behaves very different from that proxies, because estimation results differs much. As for squared returns, XGBoost predict better than GARCH, predictive power is not bad, so it is reasonable to rely on results obtained from XGBoost. LARS and Elastic net/Lasso/Ridge features selection methods, overall, do not contradict XGBoost, as variables which we pointed out above, have significant coefficient in those models. However, it is not expected different models to give same results, because of different technical issues: especially, practice shows that elastic net/lasso/alpha often give very different results if there is variation in some parameters.

What we understand for sure, that there are variables that are able to predict volatility. For better investigation, we should consider longer time span. Also, we will do better, if use variables selected by Elastic net/LASSO/Ridge in XGBoost analysis. There are also variables, that we have omitted, but which may be good volatility predictors. Also, there are other methods of future selection, that we do not cover. So, for more complex investigation should be done in order to find predictors for volatility. These field of quantitative finance is in progress: new and more complicative methods of feature selection are being developed.



Appendix

1)Lasso/ElasticNet/Ridge for model with Range - Based proxy.

...

ALPHA	0	0.1	0.2	0.3	0.4	0.5	0.6	0.7	0.8	0.9	1
INTERCEPT	2.15928483246391	10.0839487185343	1.84442022285079	2.3554661822759	14.7762693870226	3.60974675501633	12.1017226855176	8.08158278589657	1.65939449295081	1.54006959455379	1.30298093551891
GBP12MD156N	-0.0119421014688941	-0.0450448593089435	-0.0240594868419793	0	0	-0.0345298726585922	-0.0142745050238663	-0.108900389956637	-0.0250185555545981	-0.0208113407995364	-0.00682765276639955
JPY12MD156N	-0.133466625704626	-0.416690998813696	-0.121299665155315	-0.133797857564033	-0.89809438595451	-0.118627426164606	-0.582412767792062	-0.302601644311395	-0.108643990102628	-0.0814632078464557	0
CHF12MD156N	0	0	0	0	0.153035097990261	0	0.0277669297935811	0	0	0	0
AUD1MTD156N	0	0	0	0	0	-0.0424855531001031	-0.00774693063649866	0	0	0	0
GBP1MTD156N	0	0	0	0	-0.000716537455901797	0	0	0	0	0	0
CAD1MTD156N	0	0	0	0	0.0757949013206743	0	0.00686028240143209	0	0	0	0
EUR1MTD156N	0.0364024229738082	0.107539971673762	0.0185536497925789	0.0433215601155012	0.0564899096492468	0.0790919966791045	0.0762170959881627	0.0900237312570269	0.0112288763438682	0.000410524493667655	0
USD1WKD156N	0	0.0100724719422269	0	0	0	0	0.00041844070784975	0.0192420640019986	0	0	0
USD2MTD156N	0	0.00483645830671032	0	0	0	0	0	0	0	0	0
USD2WKD156N	0	0.197362821884349	0	0	0.244227651689422	0	0.180217104939055	0.096932748811904	0	0	0
CPFF	0.546668251251374	0.0361016166080762	0.539147248982866	0.547164069214296	-0.474963643399769	0.507129345505199	-0.0544456019815717	0.195497212478746	0.534594934860194	0.523287023223096	0.524587777975796
AUD3MTD156N	-0.117218395072685	-0.121591675904449	-0.112187342686684	-0.118911540948816	-0.131146355832748	-0.0708870033802646	-0.126591299439071	-0.115295352402454	-0.110230195681587	-0.106858999878187	-0.0950945862189301
CHF3MTD156N	0	0	0	0	0	0	0.00238761905211329	0	0	0	0
GBP6MTD156N	-0.012535826547416	-0.0344897583100546	-0.00091543850520022	-0.0258884515586919	-0.117645072902446	-0.040201686914083	-0.0878535362401986	-0.00993490536576895	-0.000165595331511364	0	0
JPY6MTD156N	0	0	-0.0149077075442441	0	-0.0113265512729014	-0.0728653230461107	0	0	-0.0298802940393335	-0.0574791881243042	-0.106311456167958
USD9MTD156N	0	0	0	0	-0.115131696591681	0	0	0	0	0	0
DDISCRT	0	0	0	0	0.1865803931891	0	0	0	0	0	0
EFFR	0	0.020411000698235	0	0	0.000203160969658635	0.0206849098056921	0.0107054428703931	0.0575945754883136	0	0	0
AB2140AAVOL	0	0	0	0	0.00051416052474144	0	0	0	0	0	0
CADONTD156N	0	0	0	0	-0.112757941501928	0	0	0	0	0	0
EURONTD156N	0	-0.114874354545085	0	0	-0.156857726681721	0	-0.114115298339615	-0.020719884963661	0	0	0
JPYONTD156N	0.625213468484874	1.98872727489712	0.601390031166572	0.664975623846019	2.90219416617608	1.1961165433958	2.36006241110394	1.78842189111397	0.578262229854957	0.554099316453313	0.305126722948084
FIN4180AAAMT	0	0.00019431951050602	0	0	0.000301954507569242	0	0.000250936267558457	0.000123241179925382	0	0	0
USD5MTD156N	0	0	0	0	-0.00106291459351865	0	0	0	0	0	0
NONFIN59AAAMT	-0.000187355615254542	-0.000347270809702276	-0.000144103998979666	-0.000209711892922807	0	-0.000365941112161528	-0.000297311729826143	-0.000364359928187222	-0.000119298407106444	-9.53656246371963e-05	-1.30866177483674e-05
T10YIE	0	-0.757983068261287	0	-0.0464046608769355	-0.589053676461718	-0.32650340838817	-0.697343943632037	-0.727371939015994	0	0	0
EFFR	0	0.0507351190429168	0	0	0.137344322772005	0.0117527257468634	0.101083694137166	0.00330856212769497	0	0	0
SMB	0	-0.40238886494654	0	-0.00285508867751996	-0.665581374472426	-0.162679916842869	-0.543703280852577	-0.363183115656326	0	0	0
HML	0.0872591416773536	0.288987789585824	0.0801694352240779	0.0915751779406145	0.324904477071558	0.239868129252645	0.292550801563542	0.296943889345038	0.0761937547642682	0.0668433471041755	0.00883987708389486
RMW	0	0.0837809404991009	0	0	0.143299420266988	0	0.112771931584418	0.0335557140650671	0	0	0
CMA	0	0.172677045673741	0	0	0.234486447195353	0	0.209003677912421	0.0948430138860737	0	0	0
DPCREDIT	0	0	0	0	0.298967213289492	0	0.0883291877272428	0	0	0	0
TEDRATE	0.468428428617831	0.0884327496533104	0.515196805811578	0.444285849109968	0	0.417970015005296	0	0.256741637271776	0.537427835594738	0.553761559811197	0.604581203995833
DPRIME	-0.0713840741514156	-1.66387059470678	-0.0321501631813677	-0.0927051346389134	-3.33437846900426	-0.178818426359899	-2.30439063858386	-1.01992754174097	-0.00883430109285057	0	0
USD12MD156N	0	-0.0371943457497702	0	0	-0.0691243883555335	-0.011709859342908	-0.0601465001423364	-0.0221449830014686	0	0	0
CMRKTSD678FRBCLE	0	-0.0145270409821792	0	0	-0.0316537101082235	0	-0.0157152631350434	-0.0106949900204734	0	0	0
CPTBSD678FRBCLE	0	0.136352660400078	0	0	0.185625671250174	0	0.141251942963797	0.115336308831224	0	0	0
IBLSD678FRBCLE	-0.0283530660796975	-0.129168530788995	-0.0169514305765776	-0.0339102855848429	-0.0931099782739649	-0.0879813628219778	-0.109888147082574	-0.118469171423293	-0.00787412376885099	0	0
TYCSD678FRBCLE	0	0	0	0	0.18579461912438	0	0.0420267470602946	0	0	0	0
USD1MTD156N	0	0.942311035748107	0	0	2.10421156055845	0	1.42031841810957	0.363999244694396	0	0	0
USD3MTD156N	0	0	0	0	0.242638005746417	0	0.0994816026028619	0	0	0	0
MKT4180MKTAMT	0	-3.69100056148388e-05	0	0	-6.2532909233504e-05	0	-4.65433151750015e-05	-2.27740645473129e-05	0	0	0
DCPN30	0	0	0	0	0	0.00549543237643811	0	0	0	0	0
DCD1M	0	0	0	0	-0.0705372293809908	0	0	0	0	0	0
DED1	0	0	0	0	0	0	0	0.00291063009043979	0	0	0
DSWP2	0	0	0	0	-0.0512843752410452	-0.00347273809445766	-0.0517927553952399	0	0	0	0
RIFSPPFAAD01NB	0	0	0	0	0.171339699133334	0	0.000712534889723664	0	0	0	0
DSWP30	0	0	0	0	0.0213327859021876	0	0	0	0	0	0
DED3	0	0	0	0	0.0289530352828422	0	0	0	0	0	0
T3MFF	0	0	0	0	-0.289939055196588	0	0	0	0	0	0
DSWP3	-0.00885395706867963	-0.0958656712180046	-0.0136441473603381	-0.00140554246076807	-0.135302089723387	-0.0291044674473774	-0.0718743824044025	-0.0780225788330798	-0.0141120224654849	-0.0156702117184908	-0.0218319405503367
DSWP4	-0.0242941220443889	0	-0.0150803161517583	-0.0336345848129172	0	-0.0313193997123039	0	0	-0.0129845385949195	-0.00917377538487387	0
T5YFF	0	-0.771756607959469	0	0	-1.43717203580132	-0.018948780695014	-1.09224645467311	-0.647774392857231	-0.00629106152283764	-0.00181025197836284	0
DCD6M	0	0	0	0	-0.0635519240769501	0	0	0	0	0	0
T6MFF	0	0.215339727274474	0	0	0.689838156350735	0	0.219449049378595	0.264315967371277	0	0	0
DSWP7	0	0	0	0	0	-0.000770269013829032	0	0	0	0	0
DFII7	0	0	0	0	0.00208084981499502	0	0	0	0	0	0
RIFSPPNA2P2D30NB	0	0	0	0	-0.0863300657387924	0	0	0	0	0	0
RIFSPPNA2P2D90NB	0.0103740888738469	0.00307346933845113	0.00246402022618417	0.0139246945284403	0.0232663713572916	0.030059388302254	0.00109657384634657	0.0088451065670007	0	0	0
VXTYN	0.00836352293254236	0.0396182577390735	0.0053810121014454	0.0102365206012293	0.0482872120032063	0.0239700643835563	0.0440578867692023	0.0369918538504509	0.00370927448129844	0.00243077161904971	0.000503645092983215
THREEFF1	0	0	0	0	-0.0174776383920416	0	-0.0325454184224569	0	0	0	0
THREEFY10	0	-0.141598663602275	0	0	0	-0.0108944092574402	-0.0495918301171896	-0.109491457472832	0	0	0
BAMLC7A0C1015YEY	0	-0.0136789146290153	0	0	-0.0653039180623953	0	-0.0228378691897224	0	0	0	0
BAMLC7A0C1015Y	0	-0.274604162677786	0	0	-0.239083985800543	0	-0.33997543760862	-0.179831748193038	0	0	0
BAMLC1A0C13Y	0	-0.0542262813018759	0	0	-0.241019307078092	0	-0.125654165034679	0	0	0	0
BAMLC8A0C15PY	0	0.405053260807537	0	0	0.859177611348779	0	0.622720999095138	0.0769004310544115	0	0	0
BAMLH0A2HYBSYTW	0.0255310008006152	0.033512992709844	0.0247169606218582	0.025915824619199	0.038768637271607	0.0230690654684705	0.0361049364432506	0.0327034556851663	0.0241527181084012	0.0234341059298833	0.0194464814638679
BAMLH0A3HYCSYTW	-0.00137624384349411	-0.00280166748009713	-0.00115089643618764	-0.00149486337660995	-0.00303707597195386	-0.0017146252692666	-0.00291188217674017	-0.00276124179991054	-0.00101677973165178	-0.000878297833575345	-0.000210362427479268
AAAFF	0	0	0	0	0.24632592382038	0	0.0813731000941014	0	0	0	0
BAAFF	0	0	0	0	0	-0.00374506581994504	0	0	0	0	0
RIFSPPNAAD90NB	0.0171799082244207	0	0.0272626256102508	0.0102603984028481	0	0	0	0	0.0272266784799045	0.0223891359027014	0.0239609269935556
RPONTSYD	0	0.00202901239180228	0	0	0.00366058295810601	0.000291214156557859	0.00321701385549196	0.00132197038030395	0	0	0
RPMBSD	0.00117342754639051	0.00239130842508333	0.000970662910722819	0.00125320812284034	0.00283192133420789	0.00179198828687527	0.00265458188859346	0.00217135537436896	0.000845798646494399	0.000723497328619788	0.00045033354458999
MKT59MKTAMT	0	0	0	0	-2.0728547644992e-17	6.49797704502532e-18	0	0	0	0	0
DLTIIT	0	0	0	0	-0.40469159391943	0	-0.153310009993695	0	0	0	0
DCPF2M	0	0	0	0	0.0881202332553344	0.00408287611652141	0	0	0	0	0
DTP10J19	0	0.273843641468256	0	0	0.538372746238056	0	0.493969180138427	0.122768673062095	0	0	0
THREEFYTP3	0	2.76987318690114	0	0	5.65189322230595	0.166057133765765	4.01183217778241	2.22437316889332	0	0	0
DTP10L17	0	0.237769950525272	0

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