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Are Short Term Stock Asset Returns Predictable? An Extended Empirical Analysis
Thomas Mazzoni
Diskussionsbeitrag Nr. 449 März 2010
Diskussionsbeiträge der Fakultät für Wirtschaftswissenschaft der FernUniversität in Hagen
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Are Short Term Stock Asset Returns Predictable?An Extended Empirical Analysis
Thomas Mazzoni∗
March 16, 2010
AbstractIn this paper, the question is addressed, whether or not short termstock asset returns are predictable from the knowledge of the past re-turn series. Several methods like Hodrick-Prescott-filtering, Kalman-filtering, GARCH-M, EWMA and non-parametric regression are bench-marked against naive mean predictions. The extended empirical analysisincludes data of several hundred stocks and indexes over the last ten years.The root mean square error of the concerning prediction methods is cal-culated for several rolling windows of different length, in order to assesswhether or not local model fit is favorable.
Keywords: Hodrick-Prescot-Filter; Kalman-Filter; GARCH-Model;Non-Parametric Regression; Maximum-Likelihood Estimation; Nadaraya-Watson-Estimator.
1. Introduction
The question whether or not stock asset returns are predictable is a mostactive and controversially discussed issue since the influential works of Famaand French (1988a,b), Campbell and Shiller (1988) and Poterba and Summers(1988). Subsequent research has focused on middle- and long-term predictabil-ity. Additional variables, beyond the stock asset price and its dividend, wereused to enhance predictive power. An incomplete list includes changes in inter-est rates and yield spreads between short- and long-term interest rates (Keimand Stambaugh, 1986; Campbell, 1987, 1991), book-to-market ratios (Kothariand Shanken, 1997; Pontiff and Schall, 1998), price-earnings ratios (Lamont,1998), consumption-wealth ratios (Lettau and Ludvigson, 2001) and stock mar-ket volatility (Goyal and Santa-Clara, 2003). A comparative survey of aggre-gated stock prediction with financial ratios is provided in Lewellen (2004). Anexcellent review is given in Rey (2003).
Unfortunately, short-term returns are exceedingly difficult to predict for dif-ferent reasons. First, the signal-to-noise ratio is extremely unfavorable for short-term returns or log-returns, respectively. Second, additional variables, like those
∗Thomas Mazzoni, Department for Applied Statistics, University of Hagen, Germany,Tel.: 0049 2331 9872106, Email: [email protected]
1
mentioned in the previous paragraph, usually contribute to the trend of a stockasset over an extended period. Thus, in case of daily returns, their influenceis not detectable and one relies solely on statistical instruments and the infor-mation contained in the observation history. Nonetheless, predicting short-termreturns of stock assets is of great importance for example in risk-managementand related fields.
This paper contributes to the existing literature in that an extended em-pirical analysis of short-term (daily) log-returns of stock assets and indexes isconducted to answer the question, whether or not they are predictable to a cer-tain degree. For this purpose, more than 360 stocks are analyzed over the last10 years. Several statistical prediction methods are applied and benchmarkedagainst each other by assessing their root mean square errors.
The remainder of the paper is organized as follows: Section 2 introducesthe statistical instruments used in this survey. Section 3 provides a detailedanalysis of eight influential stock indexes. Based on the results, an optimizedstudy design is established for the analysis of the 355 stock assets contained inthe indexes. In section 4 the procedure is exercised on thirty DAX stocks. Theresults are summarized in table form. Additional results from the remainingstock assets are provided in appendix B. Section 5 summarizes the findings anddiscusses the implications.
2. Prediction Methods
In this section the prediction methods used in this survey are introduced. Priorto this it is necessary to distinguish between local and global methods. In whatfollows, local methods are understood as prediction methods, which incorporateonly a limited amount of past information. A typical information horizon reaches40 or 100 days into the past. Global methods are prediction methods that rely onthe complete information available; in this case log-return data from 01-January-2000 to 31-January-2010. On the one hand, local methods often experience largevariability in their parameter estimates because of the small sample size. Onthe other hand, structural shifts due to environmental influences can cause themodel parameters themselves to vary over time. Local methods can betteradjust to such structural changes than global ones.
2.1. Mean Prediction
Log-returns, when analyzed with time series methods, generally turn out to bewhite noise processes. Therefore, the mean is the optimal linear predictor. It isalthough the most simple predictor to compute and hence serves as benchmarkin this survey, both locally and globally.
Let xt = logSt be the logarithmic stock asset price at time t. Let further∇ = 1−B be the difference operator and B the usual backward shift operator,then the log-return is ∇xt = xt − xt−1 and its linear local predictor is
∇xt+1 =1K
K−1∑k=0
∇xt−k =xt − xt−K
K. (1)
2
K defines the size of the window for the rolling mean calculation. The globalpredictor is calculated analogously, but the telescoping series yields xT − x1.
Remark: Notice that in case of global prediction future information is in-volved in the prediction at time t < T . This is not a problem if the log-returnprocess is ergodic. In this case the distribution of the predictor is identical tothe distribution of another predictor, using the same amount of information butshifted back into the past by T − t days. Thus, equation (1) applies for theglobal predictor as well with K = T − 1.
2.2. Hodrick-Prescott-Filter
The Hodrick-Prescott-Filter (Hodrick and Prescott, 1997) basically divides atime series into its trend and cyclical component. Let
xt = gt + ct, (2)
again with xt = logSt, gt the growth component, ct the cyclical (noise) com-ponent and t = 1, . . . ,K. Then the HP-Filter is determined by solving theoptimization problem
min{gt}Kt=1
[K∑t=1
(xt − gt)2 + λK−1∑t=2
(∇2gt+1)2]. (3)
Because of the logarithmic transformation the trend of xt can be expected tobe linear. If changes in the trend are only due to random fluctuations, onecan formulate a random walk model for the growth rate ∇gt = ∇gt−1 +∇2gt.It can be shown (for example Reeves et al., 2000) that for ∇2gt ∼ N(0, σ2
g),ct ∼ N(0, σ2
c ), ∇2gt and ct independent and λ = σ2c/σ
2g , minimizing (3) yields
the Maximum-Likelihood estimator for g = (g1, . . . , gK)′
g(λ) = (I + λF′F)−1x, (4a)
with
F =
1 −2 1 0 · · · 00 1 −2 1 · · · 0...
. . . . . . . . ....
0 · · · 0 1 −2 1
. (4b)
In most cases the variances σ2c and σ2
g , and hence λ, will not be known (theymay even not be constant in time, see section 2.4). Remarkably, Schlicht (2005)was able to derive the log-likelihood function for λ
l(λ;x) = − log det[I + λF′F
]−K log
[x′x− x′g(λ)
]+ (K − 2) log λ. (5)
Equation (5) has to be maximized numerically with Newton-Raphson or a similaralgorithm (for an excellent treatment on this subject see Dennis and Schnabel,1983). The first and second derivative with respect to λ is derived analyticallyin appendix A.1.
3
0 20 40 60 80 100
8.80
8.85
8.90
8.95
9.00
9.05
9.10
t
x t,g
t
Λ=10.26
0 5 10 15 20
-0.5
0.0
0.5
Lag
PAC
F
Figure 1: Original and HP-Filtered Logarithmic DJI (left) – Partial SampleAutocorrelation Function for Log-Returns (right)
In figure 1 (left) a portion of the Dow Jones Industrial Average index isshown in logarithmic scale (gray) and HP-Filtered (black). The estimated vari-ance ratio is λ = 10.263. Obviously, the filtered log-return series has partialautocorrelations at lag one and two (figure 1 right), whereas the original log-returns are white noise. The dashed lines indicate the 95% confidence bandunder the white noise hypothesis. The correlation structure of ∇gt is used to fitan AR(p) model, where the model order is selected with BIC (Schwarz, 1978).In this case a AR(2)-model is identified with φ1 = 1.522 and φ2 = −0.629.
The general prediction formula under Hodrick-Prescott-filtering is thus
∇xt+1 = µ+p∑
k=1
(φk∇gt−k+1 − µ), (6a)
withµ =
gt − gt−KK
. (6b)
The HP-prediction is clearly a local method because it involves a (K+1)×(K+1)matrix inversion and the predictor cannot be updated recursively.
2.3. Kalman-Filter
The Kalman-Filter (Kalman, 1960) is a sophisticated estimator for a partiallyor completely unobservable system state, conditioned on an information set pro-vided by a corresponding measurement process. If both, system and measure-ment process, are linear with Gaussian noise, the Kalman-Filter is the optimalestimator. For nonlinear processes, it is still the best linear estimator.
Because the Kalman-Filter is used as local predictor, the variance of the log-return process is assumed locally constant1. Thus, a basic structural state-space
1Prediction methods allowing for time varying variance, even locally, are introduced insections 2.4 and 2.5.
4
model called local linear trend model can be formulated(ytµt
)=(
1 10 1
)(yt−1
µt−1
)+(εtηt
)(7a)
xt =(1 0
)(ytµt
). (7b)
The noise vector is assumed identically and independently N(0,Q)-distributed.The variance of εt can be estimated by the sample variance of ∇xt, Var[εt] =E[(∇xt − µ)2] = σ2. To determine the variance of ηt is a little more involved,because the mean process is unobserved. Because ηt represents the variabilityof the estimated mean, its variance can be estimated by cross validation of µ.Let µ−k be the estimated mean, omitting the k-th log-return. Then the crossvalidated mean estimator is
µ =1K
K∑k=1
µ−k =1
K(K − 1)
K−1∑k=0
∑j 6=k∇xt−j . (8)
It is easy to see that µ is unbiased, because E[µ] = E[µ], and its sample varianceis Var[µ] = σ2/K(K−1), which is an estimator for the variance of ηt. Because ytand µt are assumed mutually independent, the off-diagonal entries of Q vanishand one obtains
Q =
(σ2 00 σ2
K(K−1)
). (9)
The rekursive Kalman-scheme provides an optimal estimator for the unob-served system state. It is convenient to write (7a) and (7b) in vector/matrix-form as yt = Ayt−1 + εt and xt = Hyt, respectively. Let further yt be thesystem state expectation at time t and Pt the state error covariance. Then theoptimal filter is provided by the Kalman-recursions
yt+1|t = Ayt|tPt+1|t = APt|tA′ + Q
(10a)
Kt = Pt|t−1H′(HPt|t−1H′)−1
yt|t = yt|t−1 + Kt(xt −Hyt|t−1)
Pt|t = (I−KtH)Pt|t−1.
(10b)
Finally, the Kalman-Filter has to be initialized with prior state expectation anderror covariance. It is assumed that µ0 = µ and y0 = x1 − µ and therefore,Var[µ0] = Var[y0] = σ2/K. Then the initial prior moments are
y1|0 =(x1
µ
)and P1|0 =
σ2
K
(K + 2 1
1 KK−1
). (11)
Figure 2 illustrates the filtered mean process and log-predictions for the“Deutscher Aktien Index” (DAX) from November-2009 until January-2010.
5
0 10 20 30 40 50 60
-0.4
-0.2
0.0
0.2
0.4
0.6
t
Μ`tt
in%
0 10 20 30 40 50 60
8.60
8.65
8.70
t
y` t+1
t
Figure 2: Filtered Mean Process and 95% HPD-Band for DAX (left) – PredictedLogarithmic DAX and 95% HPD-Band (right)
The Kalman-predicted log-return takes the particularly simple form
∇xt+1 = yt+1|t − xt. (12)
The Kalman-Filter is clearly a local instrument because the variance is assumedconstant. In the next two subsections methods are introduced that do not sufferfrom this restriction.
2.4. GARCH-in-Mean
In this subsection the GARCH-in-Mean-model is introduced. ARCH- andGARCH-models (Engle, 1982; Bollerslev, 1986) are extraordinary successful ineconometrics and finance because they account for heteroscedasticity and otherstylized facts of financial time series (e.g. volatility clustering). This is accom-plished by conditioning the variance on former variances and squared errors.The ARCH-in-Mean model (Engle et al., 1987) involves an additional point ofgreat importance. It relates the expected return to the level of present volatil-ity. This is significant from an economic point of view, because in arbitragepricing theory it is assumed that an agent has to be compensated for the riskhe is taking in form of a risk premium. Thus, GARCH-in-Mean models are thestarting point for GARCH-based option valuation methods (e.g. Duan, 1995;Duan et al., 1999, 2004; Heston and Nandi, 1997, 2000; Mazzoni, 2008). Recentresearch challenges the calibration of option valuation models under the physicalprobability measure (Christoffersen and Jacobs, 2004). Therefore, the results ofthis survey may provide some insights on this topic.
For the empirical analysis a standard GARCH(1,1)-model has been chosenand the risk premium is modeled linearly regarding volatility. The model equa-tions are
∇xt = µ+ λσt + εt (13a)
σ2t = ω + αε2t−1 + βσ2
t−1, (13b)
with εt = σtzt and zt ∼ N(0, 1). The parameters have to be estimated withMaximum-Likelihood. This can cause problems because on the one hand, ML
6
is only asymptotically optimal. In small samples ML-estimates can be seriouslybiased and the distribution of the estimates can suffer from large deviationsfrom normality. On the other hand, in small samples the likelihood-surfacemight be nearly flat, which causes problems in numerical maximization routines.Therefore the model parameters are estimated using the full time series, whichmakes the prediction a global one. Under GARCH-in-Mean, the predictionformula is
∇xt+1 = µ+ λ√ω + αε2t + βσ2
t . (14)
2.5. EWMA
Exponentially Weighted Moving Average (EWMA, McNeil et al., 2005, sect. 4.4)is an easy to calculate alternative to ARCH/GARCH specification. It is alsoable to track changing volatility, but its theoretical rational is not as strong asfor the heteroscedastic models of section 2.4. The variance equation (13b) isreplaced by a simpler version
σ2t = γσ2
t−1 + (1− γ)(∇xt−1)2, (15)
where γ is a persistence parameter, yet to be determined. If it is known, andthe initial value σ2
t−K is approximated, for example by the sample variance, thewhole series σ2
t−K , . . . , σ2t+1 can be calculated. Thus, the parameters in (13a)
can be estimated directly with Generalized Least-Squares (GLS). Let θ = (µ, λ)′
thenθ = (X′WX)−1X′W∇x, (16a)
with
X =
1 σt...
...1 σt−K
and W =
σ2t 0
. . .0 σ2
t−K
. (16b)
The volatility persistence γ can either be obtained by external estimationor be fixed at γ = 0.9, which is a practitioners setting. Figure 3 shows log-returns of the FTSE 100 index of the last ten years. A GARCH-in-Mean modelwas fitted and the local volatility σt was calculated. The upper limit of the95% confidence area in figure 3 is calculated from these GARCH-volatilities.The lower limit is calculated from an EWMA-model with volatility persistenceγ = 0.9. Both limits are virtually symmetric, but the GARCH-estimation ismuch more demanding. Furthermore, the EWMA-method can be used as localpredictor and the corresponding prediction formula is
∇xt+1 = µ+ λ√γσ2
t + (1− γ)(∇xt)2. (17)
2.6. Non-Parametric Regression
The general idea of the non-parametric regression method is to establish a non-linear function for the conditional expectation m(x) = E[∇xt|∇xt−1 = x] and
7
2000 2002 2004 2006 2008 2010
-10
-5
0
5
10
Time
Log
-R
etur
nsin
%
Figure 3: FTSE 100 Log-Returns and Confidence Band – GARCH-in-Mean (upper) andEWMA (lower)
estimate this function from the data under the model
∇xt = m(∇xt−1) + εt, (18)
(cf. Franke et al., 2001, sect. 13.1). The non-linear function m(x) can be ap-proximated by Taylor -series expansion in the neighborhood of an arbitrary ob-servation ∇xt
m(∇xt) ≈p∑j=0
m(j)(x)j!
(∇xt − x)j (19)
and hence, one can formulate a Least-Squares problem of the kind
K−1∑k=0
ε2t−k =K−1∑k=0
(∇xt−k −
p∑j=0
θj(∇xt−k−1 − x)j)2, (20)
with the coefficients θj = m(j)(x)/j!. Notice that (20) is only a local approxi-mation. Thus, the observations have to be weighted according to their distanceto x. This is usually done by using kernel-functions.
Kernel-functions are mainly used in non-parametric density estimation2.Certain characteristics are required by a kernel function, which are already sat-isfied, if a valid probability density function is used as kernel function. In thisapplication, the standard normal density function is used as kernel function,because it is sufficiently efficient compared to the optimal kernel (Silverman,1986, tab. 3.1 on p. 43) and it has smooth derivatives of arbitrary order
Kh(x) =1hφ(xh
). (21)
2For an excellent treatment on this subject see Silverman (1986).
8
The parameter h is the bandwidth or smoothing parameter of the kernel func-tion; its determination has a strong impact on the results of the nonparametricregression. Now the coefficient vector θ(x) can be estimated by solving theoptimization problem
θ = arg minθ
K∑k=1
(∇xt−k+1 −
p∑j=0
θj(∇xt−k − x)j)2Kh(∇xt−k − x). (22)
This optimization problem can be solved by GLS, if the bandwidth of the kernelfunction is determined prior to the estimation procedure. This is usually done bycross validation (e.g. Bhar and Hamori, 2005, sect. 4.5). But if the distributionof the log-returns is assumed locally normal, the optimal bandwidth can becalculated analytically (Silverman, 1986, sect. 3.4.2)
hopt = 5
√4
3Kσ. (23)
Estimating σ and inserting the resulting optimal bandwidth in (22), the opti-mization problem has the solution
θ = (X′WX)−1X′W∇x, (24a)
with
X =
1 ∇xt−1 − x . . . (∇xt−1 − x)p...
.... . .
...1 ∇xt−K − x . . . (∇xt−K − x)p
, ∇x =
∇xt...
∇xt−K+1
and W =
Kh(∇xt−1 − x) 0. . .
0 Kh(∇xt−K − x)
.
(24b)
The desired non-parametric estimator for the conditional expectation is givenby
m(x) = θ0(x). (25)
Notice: for p = 0 the optimization problem, and hence the non-parametricestimator (24a) and (24b), reduces to the ordinary Nadaraya-Watson-estimator(Nadaraya, 1964; Watson, 1964).
In figure 4 non-parametric regression estimates of orders p = 0 (solid black),p = 1 (dashed) and p = 2 (gray) are given. Observe that higher order polynomialfits tend to diverge for peripheral values. This is the case for p = 2 in figure 4left. Divergent behavior of the approximation can be counteracted to a certaindegree by increasing the bandwidth of the kernel function, see figure 4 right.Obviously, the non-parametric regression yields a roughly parabolic structure,which could explain the absence of linear correlation.
Non-parametric regression is clearly a local method and the log-return pre-dictor is
∇xt+1 = m(∇xt). (26)
9
-0.04 -0.02 0.02 0.04Ñxt-1
-0.02
-0.01
0.01
0.02
0.03
E@ÑxtÈÑxt-1D
h=hopt
-0.04 -0.02 0.02 0.04Ñxt-1
0.01
0.02
0.03
E@ÑxtÈÑxt-1D
h=1.5hopt
Figure 4: Non-Parametric Regression of Hang Seng Index
3. Empirical Analysis of Index Returns
In this section, the log-returns of eight representative stock indexes are ana-lyzed. The stock assets contained in each index are analyzed in detail in thenext section. The indexes are Deutscher Aktienindex (DAX), Dow Jones EuroStoxx 50 (STOXX50E), Dow Jones Industrial Average Index (DJI), FinancialTimes Stock Exchange 100 Index (FTSE), Hang Seng Index (HSI), NasdaqCanada (CND), Nasdaq Technology Index (NDXT) and TecDAX (TECDAX).The analyzed log-return data ranges from 01-January-2000 to 31-January-2010,if available3.
Table 1 gives the root mean square error of the applied prediction methodin %. The table is organized as follows:
• Index indicates the analyzed stock index. All abbreviations refer to Wol-fram’s financial and economic database.
• K gives the window size, used in local prediction methods.
• Mean indicates the overall mean value (global) and the ordinary rollingmean (local), respectively.
• The abbreviation HP indicates prediction with the Hodrick-Prescott-Filter. HP(λ) means that the filter was applied with the fixed smoothingparameter λ. This is computationally more convenient because numericalmaximization routines are no longer required.
• KF indicates prediction with the Kalman-Filter.
• EW(γ) indicates prediction with the EWMA method. Volatility persis-tence γ is given in %.
• NR(p) means non-parametric regression. The parameter p indicates theorder of polynomial approximation. For p = 0 the method results in theordinary Nadaraya-Watson-estimator.
• GARCH indicates the prediction with a globally fitted GARCH-in-Meanmodel.
3The TecDAX index gained approval to the Prime Standard of Deutsche Börse AG at24-March-2003. It replaced the Nemax50 index.
10
LocalR
MSE
GlobalR
MSE
Index
KMean
HP
HP(6)
HP(10)
HP(20)
KF
EW(80)
EW(90)
EW(95)
NR(0)
NR(1)
NR(2)
Mean
GARCH
DAX
401.6884
1.8102
1.8168
1.8026
1.7858
1.6901
1.7540
1.7629
1.7613
1.7335
1.8769
7.7156
1.66
701.6695
STOXX50E
401.5758
1.6984
1.7109
1.6975
1.6790
1.5785
1.6319
1.6407
1.6378
1.6089
1.7167
23.3640
1.55
601.5584
DJI
401.3305
1.4279
1.4379
1.4240
1.4070
1.3321
1.3809
1.3821
1.3818
1.3605
1.6544
11.7722
1.31
151.3129
FTSE
401.3548
1.4632
1.4704
1.4572
1.4396
1.3570
1.4128
1.4156
1.4132
1.3948
1.5477
5.0607
1.33
651.3375
HSI
401.7137
1.8475
1.8392
1.8279
1.8118
1.7149
1.8263
1.8290
1.8164
1.7815
2.5769
16.9932
1.69
281.6938
CND
402.2914
2.4423
2.4331
2.4190
2.4030
2.2899
2.4074
2.3952
2.3795
2.3462
3.1807
52.0094
2.2709
2.27
05NDXT
402.1137
2.2806
2.2971
2.2716
2.2399
2.1172
2.2145
2.2180
2.2206
2.1524
2.4040
6.0588
2.09
382.0981
TEC
DAX
401.7523
1.863
1.8652
1.8591
1.8508
1.7527
1.8195
1.814
1.8133
1.8183
2.0185
6.8387
1.73
271.7337
DAX
100
1.6733
1.8163
1.8228
1.8070
1.7872
1.6743
1.7128
1.7167
1.7208
1.7118
1.8093
4.4208
1.66
681.6691
STOXX50E
100
1.4818
1.6162
1.6266
1.6101
1.5918
1.4832
1.5228
1.5269
1.5328
1.5146
2.0347
24.1967
1.47
651.4783
DJI
100
1.3056
1.4189
1.4320
1.4157
1.3970
1.3068
1.3354
1.3400
1.3444
1.3224
1.5263
9.7191
1.30
031.3020
FTSE
100
1.3392
1.4643
1.4729
1.4583
1.4396
1.3407
1.3767
1.3769
1.3801
1.3700
1.6050
6.8907
1.33
421.3354
HSI
100
1.6836
1.8284
1.8288
1.8140
1.7961
1.6841
1.7555
1.7437
1.7387
1.7572
4.6404
53.0186
1.67
631.6768
CND
100
2.2862
2.4517
2.4498
2.4333
2.4139
2.2853
2.3258
2.3248
2.3293
2.3222
3.2307
37.2829
2.2795
2.27
91NDXT
100
2.1649
2.3602
2.3799
2.3503
2.3141
2.1658
2.2219
2.2268
2.2335
2.1876
2.3724
3.2032
2.15
842.1629
TEC
DAX
100
1.7402
1.8659
1.8706
1.8646
1.8554
1.7407
1.7844
1.7841
1.7851
1.7808
2.0986
12.6642
1.73
461.7359
DAX
250
1.6909
1.8517
1.8530
1.8357
1.8138
1.6909
1.7173
1.7176
1.7163
1.7214
2.1478
7.8891
1.68
741.6896
STOXX50E
250
1.4021
1.5388
1.5427
1.5257
1.5062
1.4019
1.4362
1.4328
1.4328
1.4202
1.6333
1.6621
1.39
861.4005
DJI
250
1.3168
1.4373
1.4486
1.4321
1.4125
1.3169
1.3422
1.3411
1.3416
1.3356
1.5753
1.8065
1.31
371.3154
FTSE
250
1.3561
1.4941
1.4996
1.4831
1.4624
1.3564
1.3874
1.3825
1.3826
1.3725
1.4975
2.2697
1.35
341.3545
HSI
250
1.6747
1.8312
1.8328
1.8156
1.7955
1.6745
1.7212
1.7069
1.6980
1.7241
6.3393
86.4545
1.67
081.6715
CND
250
2.3212
2.4910
2.4947
2.4773
2.4557
2.3201
2.3572
2.3631
2.3625
2.3729
3.1625
12.6406
2.3131
2.31
21NDXT
250
2.3515
2.5684
2.5897
2.5562
2.5164
2.3512
2.3882
2.3910
2.3966
2.3733
2.5462
6.3705
2.34
532.3507
TEC
DAX
250
1.7688
1.9034
1.9104
1.9019
1.8904
1.7682
1.7931
1.7945
1.7954
1.8203
2.6563
79.7466
1.76
321.7649
Tab
le1:
Roo
tMeanSq
uare
Errorin
%of
IndexLo
g-ReturnPrediction
11
The minimum root mean square error in % over all prediction methods is indi-cated in boldface.
In particular, each prediction is generated by considering the last K valuesxt, . . . , xt−K and then calculating the one step log-return prediction ∇xt+1. Thisis also done for the global predictors, even if their parameter estimates do notdepend on the rolling window position or size.
Obviously, the global mean provides the best predictor for log-returns inalmost all cases. Its RMSE differs only slightly from the RMSE of the GARCH-in-Mean prediction. Because all root mean square errors are in %, the differenceis roughly O(10−5). Hence, the first surprising result is that using local methodsdoes not seem to enhance prediction quality. Among all local predictors, rollingmean and Kalman-Filter provide the most precise forecasts. Observe furtherthat the RMSE for the Hodrick-Prescott-predictor nearly coincides with theHP-Filter prediction with fixed smoothing parameter λ = 10. Thus, in furthercomputations HP(10) is used to speed up calculations. All EWMA predictionsprovide very similar results. Therefore, only EW(90) will be used in furtheranalysis, because it provides a good average. The non-parametric regressionmethod clearly indicates that higher order Taylor -series expansion is ineffectivein this situation. Only NR(0), which coincides with the Nadaraya-Watson-estimator, generates reasonable RMSEs. Thus, higher order NR-predictors areabandoned in further analysis.
From this first survey it can be concluded that the benefit of local predictionis questionable. Furthermore, it seems that the global mean value is the simplestand most efficient predictor.
4. Empirical Analysis of Stock Asset Returns
In this section the stock assets contained in the “Deutscher Aktien Index” (DAX)are analyzed in detail. A similar analysis was conducted for the stocks containedin the other indexes of section 3. The results are summarized in appendix B, andwill be discussed comprehensively in section 5. The results of local and globallog-return predictions of DAX stocks are summarized in table 2. The organiza-tion of the data is analogous to table 1, with two exceptions. First, smoothing-or persistence-parameters are fixed as indicated in the previous section andtherefore no longer listed, and second, the abbreviation NW now indicates theNadaraya-Watson-prediction method.
Again, the mean prediction is the dominant method. But despite the resultsfor indexes, a smaller RMSE can be achieved by local prediction in roughlyone half of the cases. For some stock assets, the most efficient prediction isaccomplished by the Kalman-Filter, which virtually tracks the changes in thelog-return expectation. Furthermore, in those cases, where the GARCH-in-Mean method appears superior, GARCH-prediction RMSEs are barely smallerthan the corresponding global mean RMSEs.
Some preliminary conclusions can be drawn from this observation. First,obviously market portfolios, or indexes as their proxies, are unaffected by lo-cal trends in the expected log-returns, whereas stock assets may be. Second,
12
Loca
lRM
SEK
=40
Loca
lRM
SEK
=10
0Lo
calR
MSE
K=
250
Glo
balR
MSE
Stoc
kM
ean
HP
KF
EW
MA
NW
Mea
nH
PK
FEW
MA
NW
Mea
nH
PK
FEW
MA
NW
Mea
nG
ARCH
AD
S.D
E3.
7735
3.99
333.
7764
3.85
183.
8086
3.77
384.
0138
3.77
593.
8049
3.80
353.
9075
4.16
023.
9083
3.93
613.
9366
3.89
973.
9466
ALV
.DE
2.68
452.
8746
2.68
802.
8269
2.78
802.
6455
2.85
662.
6467
2.71
422.
7380
2.69
122.
9219
2.69
102.
7368
2.78
802.
6854
2.68
86B
AS.
DE
2.35
462.
5275
2.35
992.
5527
2.37
252.
3423
2.54
282.
3451
2.46
232.
3173
2.33
102.
5455
2.33
162.
3853
2.35
852.
3254
2.33
20B
AY
N.D
E2.
6902
2.88
282.
6960
2.89
762.
8113
2.68
732.
9089
2.68
902.
8537
2.66
742.
6155
2.85
892.
6160
2.66
322.
6253
2.60
912.
6330
BEI.D
E3.
0727
3.23
563.
0739
3.11
503.
1101
3.07
033.
2450
3.07
053.
0781
3.09
693.
1591
3.34
573.
1594
3.16
453.
1656
3.15
424.
0011
BM
W.D
E2.
1269
2.27
772.
1305
2.19
342.
2330
2.05
512.
2285
2.05
692.
0867
2.12
052.
0585
2.23
822.
0589
2.07
672.
1322
2.05
402.
0543
CB
K.D
E3.
2402
3.44
653.
2438
3.38
413.
3113
3.19
553.
4321
3.19
513.
2719
3.24
553.
2358
3.48
493.
2334
3.28
873.
2906
3.22
463.
4090
DA
I.DE
2.34
752.
4922
2.34
792.
4751
2.41
632.
3008
2.47
512.
3031
2.36
692.
3478
2.33
342.
5148
2.33
302.
3796
2.37
342.
3276
2.33
04D
B1.
DE
5.65
285.
9800
5.65
695.
7368
5.68
002.
8094
2.98
372.
8054
2.90
972.
8400
2.81
573.
0342
2.81
362.
8679
2.83
562.
8038
2.96
08D
BK
.DE
2.70
072.
8958
2.70
372.
8189
2.80
802.
6744
2.88
682.
6741
2.74
762.
7655
2.72
932.
9574
2.72
842.
7789
2.87
022.
7208
2.72
24D
PW
.DE
2.46
752.
6191
2.46
942.
7354
2.54
442.
2589
2.43
462.
2614
2.37
342.
3590
2.18
192.
3612
2.18
192.
2352
2.31
862.
1769
2.17
75D
TE.D
E2.
5324
2.72
332.
5364
2.63
142.
5900
2.43
832.
6519
2.44
052.
4951
2.49
572.
3659
2.59
172.
3669
2.40
012.
4000
2.36
212.
3626
EO
AN
.DE
2.57
672.
7669
2.58
372.
8690
2.71
132.
5640
2.78
242.
5670
2.83
542.
7138
2.54
412.
7807
2.54
512.
6046
2.66
002.
5387
2.62
86FM
E.D
E3.
0104
3.19
153.
0138
3.06
693.
0326
2.99
653.
1833
2.99
793.
0188
3.00
633.
0767
3.27
543.
0775
3.08
393.
0925
3.06
993.
0724
FRE3.
DE
3.24
773.
4341
3.24
993.
3138
3.28
473.
2377
3.43
113.
2387
3.26
653.
2639
3.33
153.
5392
3.33
153.
3416
3.35
253.
3234
3.46
60H
EN
3.D
E3.
1154
3.28
583.
1157
3.16
743.
1991
3.11
053.
2927
3.11
113.
1280
3.12
593.
2174
3.41
503.
2178
3.22
283.
2289
3.21
053.
7094
IFX
.DE
4.01
614.
1975
4.01
224.
1376
4.10
194.
0061
4.22
484.
0014
4.05
444.
0851
4.02
684.
2626
4.02
544.
0697
4.07
524.
0181
4.18
17LH
A.D
E2.
0820
2.22
212.
0841
2.18
182.
1396
1.98
632.
1474
1.98
832.
0128
1.98
991.
9051
2.05
951.
9046
1.92
911.
9238
1.89
971.
8996
LIN
.DE
1.95
502.
0973
1.95
812.
0051
1.97
571.
8774
2.03
861.
8789
1.91
891.
8965
1.81
861.
9808
1.81
871.
8540
1.84
191.
8137
1.81
33M
AN
.DE
2.91
913.
1218
2.92
363.
1359
2.96
352.
8709
3.10
782.
8734
3.14
942.
9340
2.52
082.
7356
2.52
002.
5395
2.57
682.
5149
2.51
51M
EO
.DE
2.15
692.
3137
2.15
832.
3072
2.21
522.
0645
2.23
772.
0667
2.15
762.
1448
2.04
072.
2128
2.04
072.
1249
2.15
292.
0360
2.03
82M
RK
.DE
1.95
902.
0925
1.96
052.
0312
1.99
111.
8947
2.05
741.
8965
1.92
191.
9216
1.82
621.
9953
1.82
671.
8397
1.86
981.
8227
1.82
07M
UV
2.D
E2.
0257
2.16
342.
0279
2.13
302.
0633
1.81
171.
9602
1.81
311.
8852
1.86
011.
7226
1.87
781.
7233
1.77
391.
8029
1.71
871.
7186
RW
E.D
E1.
8070
1.93
461.
8092
2.00
401.
9080
1.66
531.
7990
1.66
601.
7606
1.79
061.
6582
1.80
381.
6588
1.70
681.
7697
1.65
601.
6582
SAP.
DE
1.92
092.
0391
1.92
261.
9641
1.96
431.
8371
1.97
321.
8378
1.87
881.
8753
1.71
931.
8599
1.71
991.
7559
1.74
751.
7151
1.76
50SD
F.D
E2.
4995
2.65
782.
5016
2.58
902.
5795
2.47
352.
6578
2.47
372.
5177
2.53
652.
5189
2.72
312.
5192
2.55
092.
5795
2.51
372.
5144
SIE.D
E2.
1927
2.34
132.
1940
2.29
822.
2636
2.14
782.
3258
2.14
922.
2123
2.20
682.
1757
2.36
462.
1756
2.20
952.
2424
2.16
862.
2493
SZG
.DE
2.99
123.
2117
2.99
553.
1138
3.09
472.
9904
3.24
422.
9921
3.08
323.
0422
3.07
533.
3561
3.07
603.
1272
3.15
703.
0738
3.07
60T
KA
.DE
3.03
773.
2372
3.04
253.
3715
3.09
462.
9912
3.21
862.
9934
3.42
513.
0302
3.03
663.
2870
3.03
693.
5320
3.09
123.
0291
3.05
47VO
W3.
DE
2.59
672.
7513
2.59
482.
7760
2.70
692.
5704
2.74
602.
5680
2.67
582.
6936
2.59
472.
7843
2.59
362.
6878
2.74
312.
5874
2.58
38
Tab
le2:
Roo
tMeanSq
uare
Errorin
%of
Log-ReturnPredictionforDeutscher
AktienIndex(D
AX)Stocks
13
there seems to be very little exploitable systematic information to infer from theknowledge of previous log-returns to future log-returns. The GARCH-in-Meanprediction, which associates information about the current volatility with thedesired risk-premium, generates barely more efficient forecasts than the corre-sponding mean prediction, and only for a few stock assets. Only for BASF theincorporation of nonlinear information results in more precise forecasts. Thus,for most stocks the log-return process seems to be a noise process.
5. Summary and Conclusions
Daily log-returns of 355 stock assets and 8 indexes were analyzed over more thanten years. Several non trivial methods were used to calculate a one-step-aheadprediction. The efficiency of the predictions was assessed by the root meansquare error criterium.
In roughly half the cases, the global mean prediction generated the smallestRMSE. The GARCH-in-Mean prediction achieved RMSEs of similar magnitudesin some cases. Especially indexes seem to be dominated by global parameters,whereas stock assets occasionally are better predicted by local methods. Amongall local prediction methods the rolling mean is superior in almost all cases. In asmall number of occasions the Kalman-Filter method generates the best predic-tions. The Nadaraya-Watson-estimator only prevails on very rare exceptions.Other prediction methods seem to be inferior.
What conclusions can be drawn from this analysis? First, short-term stockasset log-returns are modeled adequately by noise processes. The same is trueof indexes. Nonlinear dependencies, if they exist, are obviously of minor impor-tance. As a consequence, knowledge of the past is not instrumental in predictingthe next value of the log-return process. Second, the parameters of those noisemodels have not necessarily to be invariant in time. It is common knowledgethat volatilities are not constant. One possible way to account for this fact math-ematically are GARCH-models. But the results of the current analysis suggestthat expectation values might be subject to local trends as well. This can beinferred from the fact that local prediction methods are successful in roughlyhalf the cases. Third, one would have expected the GARCH-in-Mean predictionto be superior, because it involves well established economic assumptions aboutrisk premia. This is not the case, which is problematic for the arbitrage pricingtheory. GARCH-in-Mean models are used for option valuation (Duan, 1995;Heston and Nandi, 2000; Mazzoni, 2008) in that they are estimated under aphysical probability measure P and subsequently translated into an equivalentmodel with risk-neutral measure Q, under which the option is valuated. Thismight explain why recent approaches to calibrate the model directly under therisk-neutral measure Q are partially more successful (Christoffersen and Jacobs,2004).
The current investigation clearly indicates that daily log-return processes arenot predictable, at least not beyond their mean value. Therefore, they are notsuited for profit-oriented investment strategies. This clearly classifies financialmarkets as risk transfer markets, at least in short term.
14
A. Mathematical Appendix
A.1. Log-Likelihood Derivatives
Let M(λ) = (I + λF′F)−1. For notational convenience, functional argumentsare omitted in what follows. Then the log-likelihood function (5) can be written
l = − log detM−1 −K log[x′(I−M)x
]+ (K − 2) log λ. (27)
The differential of the determinant of an arbitrary quadratic and invertiblematrix A is ddetA = detA · tr
[A−1dA
](cf. Magnus and Neudecker, 2007,
sect. 8.3). In particular, d log detA = tr[A−1dA
]holds. Further, the dif-
ferential of the inverse is dA−1 = −A−1(dA)A−1 (Magnus and Neudecker,2007, sect. 8.4). Observe that M can be expanded into a Taylor -seriesM = I−λF′F+(λF′F)2− . . . and hence, M and F′F commute. Therefore, thederivative of M with respect to λ is −M2F′F. Now the derivative of (27) canbe calculated and one obtains
dl
dλ= −tr
[MF′F
]−K x′M2F′Fx
x′(I−M)x+K − 2λ
. (28)
Because dtrA = tr dA (Magnus and Neudecker, 2007, p. 148), the calculationof the second derivative is straight forward
d2l
dλ2= tr
[(MF′F)2
]+K
(x′M2F′Fxx′(I−M)x
)2
+ 2Kx′M3(F′F)2xx′(I−M)x
− K − 2λ2
. (29)
15
B.
Tab
les
B.1
.R
MSE
ofD
owJo
nes
Euro
Sto
xx50
Index
(ST
OX
X50
E)
Sto
cks
Loca
lRM
SEK
=40
Loca
lRM
SEK
=10
0Lo
calR
MSE
K=
250
Glo
balR
MSE
Stoc
kM
ean
HP
KF
EW
MA
NW
Mea
nH
PK
FEW
MA
NW
Mea
nH
PK
FEW
MA
NW
Mea
nG
ARCH
AB
I.BR
5.77
136.
1225
5.77
245.
9143
5.92
205.
8001
6.17
915.
7991
5.96
306.
0225
5.96
486.
3620
5.96
417.
1517
6.21
105.
9518
6.74
39ACA
.PA
2.62
772.
8167
2.63
122.
7293
2.70
772.
6271
2.85
342.
6295
2.67
782.
6947
2.55
152.
7811
2.55
162.
5737
2.60
682.
5449
2.54
52AG
N.A
S3.
4509
3.68
433.
4548
3.59
783.
5550
3.29
173.
5527
3.29
573.
3650
3.40
383.
3260
3.59
353.
3265
3.37
553.
4430
3.31
723.
4623
AI.P
A3.
3125
3.52
813.
3219
3.89
653.
7945
3.31
473.
5538
3.31
874.
1444
3.76
173.
4294
3.68
483.
4309
4.29
893.
8959
3.42
235.
3999
ALO
.PA
2.95
333.
1702
2.95
783.
0579
3.02
532.
9651
3.21
522.
9676
3.01
353.
0453
2.99
263.
2724
2.99
343.
0325
3.03
982.
9880
2.98
77A
LV.D
E2.
6845
2.87
462.
6880
2.82
692.
7880
2.64
552.
8566
2.64
672.
7142
2.73
802.
6912
2.92
192.
6910
2.73
682.
7880
2.68
542.
6886
BA
S.D
E2.
3546
2.52
752.
3599
2.55
272.
3725
2.34
232.
5428
2.34
512.
4623
2.31
732.
3310
2.54
552.
3316
2.38
532.
3585
2.32
542.
3320
BAY
N.D
E2.
6902
2.88
282.
6960
2.89
762.
8113
2.68
732.
9089
2.68
902.
8537
2.66
742.
6155
2.85
892.
6160
2.66
322.
6253
2.60
912.
6330
BB
VA
.MC
1.93
642.
0548
1.93
612.
0110
1.97
841.
8775
2.01
441.
8788
1.92
131.
8951
1.90
802.
0495
1.90
771.
9338
1.90
731.
9031
1.90
69B
N.P
A2.
3207
2.47
072.
3220
2.40
412.
3537
2.30
362.
4756
2.30
562.
3455
2.33
282.
3825
2.56
682.
3835
2.41
122.
4016
2.37
912.
3964
BN
P.PA
2.44
732.
6121
2.45
122.
5483
2.52
812.
4165
2.59
672.
4166
2.44
992.
4685
2.47
182.
6747
2.47
222.
4927
2.49
582.
4658
2.48
32CA
.PA
1.77
831.
8981
1.78
061.
8476
1.83
541.
6975
1.83
121.
6986
1.75
321.
7552
1.71
011.
8529
1.71
061.
7417
1.77
321.
7072
1.70
74CRG
.IR2.
2364
2.41
192.
2406
2.32
282.
3118
2.22
842.
4326
2.23
092.
2570
2.27
662.
2760
2.50
102.
2773
2.29
752.
3159
2.27
312.
2736
CS.
PA5.
2962
5.64
755.
3146
6.47
905.
3263
5.27
185.
6654
5.28
097.
1877
5.30
415.
4736
5.89
465.
4769
7.54
985.
5002
5.46
226.
0403
DA
I.DE
2.34
752.
4922
2.34
792.
4751
2.41
632.
3008
2.47
512.
3031
2.36
692.
3478
2.33
342.
5148
2.33
302.
3796
2.37
342.
3276
2.33
04D
B1.
DE
5.65
285.
9800
5.65
695.
7368
5.68
002.
8094
2.98
372.
8054
2.90
972.
8400
2.81
573.
0342
2.81
362.
8679
2.83
562.
8038
2.96
08D
BK
.DE
2.70
072.
8958
2.70
372.
8189
2.80
802.
6744
2.88
682.
6741
2.74
762.
7655
2.72
932.
9574
2.72
842.
7789
2.87
022.
7208
2.72
24D
G.P
A3.
1277
3.32
003.
1295
3.20
933.
1654
3.13
453.
3548
3.13
653.
1804
3.16
033.
2405
3.47
403.
2409
3.26
863.
2737
3.23
443.
4804
DT
E.D
E2.
5324
2.72
332.
5364
2.63
142.
5900
2.43
832.
6519
2.44
052.
4951
2.49
572.
3659
2.59
172.
3669
2.40
012.
4000
2.36
212.
3626
EN
EL.
MI
1.54
141.
6477
1.54
321.
6769
1.64
301.
5278
1.65
301.
5292
1.61
901.
6178
1.56
651.
7029
1.56
711.
6348
1.69
581.
5654
1.56
89EN
I.MI
1.72
441.
8477
1.72
701.
8145
1.73
731.
7024
1.84
581.
7037
1.76
281.
7208
1.74
461.
9020
1.74
561.
7834
1.75
401.
7422
1.74
31EO
AN
.DE
2.57
672.
7669
2.58
372.
8690
2.71
132.
5640
2.78
242.
5670
2.83
542.
7138
2.54
412.
7807
2.54
512.
6046
2.66
002.
5387
2.62
86FP
.PA
3.83
304.
0643
3.83
823.
8932
3.85
713.
8403
4.08
433.
8419
3.88
303.
8402
3.98
484.
2485
3.98
584.
0010
3.99
603.
9772
4.35
75FT
E.P
A1.
7132
1.85
391.
7168
1.80
531.
7724
1.56
681.
7061
1.56
801.
6019
1.59
961.
5431
1.69
391.
5435
1.55
461.
5674
1.53
941.
5396
GLE
.PA
2.58
012.
7429
2.58
192.
7151
2.68
452.
5415
2.73
722.
5437
2.59
322.
5820
2.61
062.
8183
2.61
072.
6529
2.63
632.
6057
2.60
89G
.MI
1.67
601.
7734
1.67
611.
7494
1.74
291.
6579
1.77
431.
6589
1.70
491.
7082
1.67
281.
7973
1.67
281.
6950
1.71
541.
6687
1.66
95IB
E.M
C3.
8166
4.03
223.
8174
3.93
883.
8630
3.84
524.
0772
3.84
603.
8767
3.87
843.
9917
4.23
753.
9914
3.99
374.
0220
3.97
994.
3596
16
Loca
lRM
SEK
=40
Loca
lRM
SEK
=10
0Lo
calR
MSE
K=
250
Glo
balR
MSE
Stoc
kM
ean
HP
KF
EW
MA
NW
Mea
nH
PK
FEW
MA
NW
Mea
nH
PK
FEW
MA
NW
Mea
nG
ARCH
ING
A.A
S3.
4984
3.70
223.
4966
3.73
993.
5918
3.37
463.
6180
3.37
753.
5001
3.47
723.
4808
3.73
373.
4798
3.56
743.
5585
3.46
943.
9115
ISP.
MI
2.50
332.
6791
2.50
452.
6310
2.56
512.
4246
2.62
432.
4257
2.47
862.
4660
2.45
712.
6714
2.45
702.
4983
2.49
582.
4504
2.45
39M
C.P
A1.
8439
1.97
151.
8464
1.90
661.
8954
1.79
251.
9410
1.79
391.
8376
1.82
951.
8193
1.98
091.
8196
1.84
421.
8507
1.81
521.
8206
MU
V2.
DE
2.02
572.
1634
2.02
792.
1330
2.06
331.
8117
1.96
021.
8131
1.88
521.
8601
1.72
261.
8778
1.72
331.
7739
1.80
291.
7187
1.71
86O
R.P
A1.
6337
1.75
251.
6360
1.70
411.
6606
1.55
791.
6935
1.55
961.
6144
1.59
151.
5711
1.71
381.
5713
1.59
191.
5733
1.56
751.
5670
PH
IA.A
S2.
7297
2.91
832.
7331
2.83
322.
7925
2.65
112.
8693
2.65
322.
6894
2.67
662.
5629
2.78
532.
5630
2.58
042.
6027
2.55
652.
5570
REP.
MC
1.70
691.
8225
1.70
791.
7920
1.75
701.
6858
1.82
011.
6870
1.73
621.
7442
1.74
191.
8870
1.74
201.
7681
1.75
551.
7375
1.73
74RW
E.D
E1.
8070
1.93
461.
8092
2.00
401.
9080
1.66
531.
7990
1.66
601.
7606
1.79
061.
6582
1.80
381.
6588
1.70
681.
7697
1.65
601.
6582
SAN
.MC
2.17
232.
2934
2.17
262.
2672
2.21
882.
1265
2.26
402.
1266
2.17
702.
1766
2.08
732.
2330
2.08
642.
1092
2.11
352.
0800
2.24
72SA
N.P
A1.
7148
1.84
221.
7181
1.77
571.
7605
1.65
071.
7917
1.65
241.
6880
1.67
781.
6582
1.81
361.
6588
1.68
161.
6673
1.65
441.
6546
SAP.
DE
1.92
092.
0391
1.92
261.
9641
1.96
431.
8371
1.97
321.
8378
1.87
881.
8753
1.71
931.
8599
1.71
991.
7559
1.74
751.
7151
1.76
50SG
O.P
A2.
4859
2.64
312.
4860
2.59
782.
5452
2.41
722.
6160
2.42
112.
4897
2.44
122.
4642
2.66
612.
4646
2.50
702.
5044
2.45
982.
4632
SIE.D
E2.
1927
2.34
132.
1940
2.29
822.
2636
2.14
782.
3258
2.14
922.
2123
2.20
682.
1757
2.36
462.
1756
2.20
952.
2424
2.16
862.
2493
SU.P
A2.
1059
2.25
942.
1086
2.19
852.
1748
2.07
512.
2587
2.07
732.
1369
2.10
312.
1289
2.32
912.
1294
2.16
862.
1477
2.12
442.
1254
TEF.
MC
1.93
182.
0666
1.93
382.
0168
1.98
361.
8886
2.04
031.
8894
1.92
571.
9400
1.79
371.
9550
1.79
421.
8159
1.83
551.
7905
1.79
10T
IT.M
I5.
8648
6.35
625.
8833
6.20
275.
8856
5.30
065.
7710
5.30
685.
3838
5.75
314.
1179
4.62
874.
1200
4.11
454.
3072
4.10
724.
4009
UCG
.MI
2.38
552.
5315
2.38
622.
5191
2.45
082.
3451
2.51
572.
3468
2.41
622.
3812
2.39
202.
5718
2.39
152.
4487
2.43
532.
3857
2.46
55U
L.PA
1.77
911.
9116
1.78
221.
8470
1.83
251.
7825
1.93
381.
7835
1.80
481.
8250
1.83
532.
0021
1.83
551.
8437
1.85
911.
8318
1.83
09U
NA
.AS
1.76
651.
9037
1.76
981.
8734
1.79
911.
7891
1.94
771.
7909
1.84
371.
8346
1.90
882.
0905
1.90
921.
9457
1.93
981.
9043
1.90
59V
IV.P
A1.
7543
1.89
111.
7568
1.82
781.
8053
1.61
691.
7550
1.61
811.
6533
1.65
081.
5668
1.70
691.
5672
1.58
871.
5894
1.56
281.
5636
B.2
.R
MSE
ofD
owJo
nes
Indust
rial
Ave
rage
Index
(DJI
)Sto
cks
Loca
lRM
SEK
=40
Loca
lRM
SEK
=10
0Lo
calR
MSE
K=
250
Glo
balR
MSE
Stoc
kM
ean
HP
KF
EW
MA
NW
Mea
nH
PK
FEW
MA
NW
Mea
nH
PK
FEW
MA
NW
Mea
nG
ARCH
AA
3.01
493.
2228
3.01
783.
1141
3.11
882.
9891
3.23
192.
9912
3.05
583.
0886
2.95
983.
2077
2.95
873.
0249
3.06
762.
9501
2.95
06A
XP
2.78
362.
9831
2.78
682.
9014
2.82
192.
7500
2.98
422.
7519
2.79
372.
7716
2.75
002.
9917
2.75
012.
7872
2.78
292.
7433
2.86
44
17
Loca
lRM
SEK
=40
Loca
lRM
SEK
=10
0Lo
calR
MSE
K=
250
Glo
balR
MSE
Stoc
kM
ean
HP
KF
EW
MA
NW
Mea
nH
PK
FEW
MA
NW
Mea
nH
PK
FEW
MA
NW
Mea
nG
ARCH
BA
2.17
332.
3042
2.17
392.
2501
2.21
822.
1334
2.28
722.
1341
2.17
932.
1636
2.10
472.
2621
2.10
462.
1329
2.13
152.
1003
2.09
96B
AC
3.53
133.
7723
3.53
553.
6699
3.69
073.
5222
3.80
473.
5235
3.56
843.
6685
3.55
163.
8622
3.55
223.
6286
3.74
063.
5436
3.84
02CAT
2.29
142.
4275
2.29
022.
3671
2.36
102.
2436
2.41
322.
2454
2.27
412.
2791
2.22
502.
3969
2.22
452.
2434
2.23
842.
2182
2.21
90CSC
O3.
0387
3.25
743.
0436
3.13
793.
1051
2.97
083.
2188
2.97
273.
0088
3.00
312.
8531
3.10
622.
8535
2.87
002.
8963
2.84
782.
8496
CV
X1.
8139
1.94
361.
8168
1.92
911.
8322
1.78
191.
9327
1.78
371.
8595
1.77
191.
7863
1.94
861.
7873
1.84
951.
7933
1.78
371.
7842
DD
2.02
742.
1611
2.02
912.
1037
2.07
451.
9597
2.11
711.
9615
2.00
011.
9884
1.92
432.
0846
1.92
451.
9508
1.96
351.
9188
1.91
93D
IS2.
2613
2.41
742.
2645
2.35
022.
3062
2.22
922.
4122
2.23
122.
2751
2.26
132.
1877
2.38
022.
1886
2.21
242.
2247
2.18
392.
3119
GE
2.27
202.
4190
2.27
392.
3581
2.34
462.
2387
2.41
342.
2410
2.27
292.
2996
2.23
732.
4176
2.23
732.
2757
2.31
922.
2317
2.23
26H
D2.
4353
2.59
952.
4376
2.50
272.
5065
2.38
692.
5833
2.38
932.
4227
2.44
902.
2124
2.40
582.
2128
2.23
332.
2399
2.20
662.
3126
HPQ
2.68
612.
8699
2.68
942.
7725
2.77
572.
6299
2.83
972.
6318
2.66
002.
7010
2.48
942.
7099
2.49
062.
5069
2.53
472.
4859
2.56
72IB
M1.
9367
2.05
311.
9369
2.00
432.
0072
1.88
912.
0283
1.88
951.
9121
1.92
941.
7524
1.88
821.
7528
1.76
951.
7845
1.74
741.
8124
INT
C2.
9163
3.13
202.
9197
3.03
482.
9633
2.85
053.
0989
2.85
242.
9010
2.90
182.
6918
2.94
192.
6919
2.71
602.
7159
2.68
372.
6843
JNJ
1.40
081.
5048
1.40
321.
4632
1.43
371.
3346
1.45
061.
3354
1.36
921.
3645
1.30
621.
4283
1.30
661.
3350
1.33
171.
3028
1.30
30JP
M3.
0590
3.28
843.
0655
3.20
973.
1703
3.03
553.
3006
3.03
783.
0801
3.10
913.
0350
3.32
603.
0362
3.13
823.
1485
3.02
793.
1598
KFT
1.48
721.
5843
1.48
761.
5593
1.54
231.
4732
1.58
971.
4739
1.50
111.
5163
1.46
231.
5838
1.46
261.
4796
1.49
321.
4576
1.45
80K
O1.
5502
1.66
451.
5532
1.63
861.
6059
1.46
521.
5826
1.46
601.
5176
1.50
941.
3810
1.49
411.
3809
1.43
031.
4316
1.37
661.
3772
MCD
1.76
641.
8910
1.76
871.
8248
1.83
991.
7057
1.84
421.
7061
1.73
931.
7685
1.66
941.
8161
1.66
911.
6871
1.73
081.
6648
1.66
48M
MM
1.64
261.
7592
1.64
441.
6926
1.70
371.
5940
1.72
721.
5953
1.62
491.
6302
1.56
831.
7102
1.56
881.
5817
1.58
881.
5649
1.56
53M
RK
2.09
052.
2271
2.09
292.
1708
2.17
912.
0483
2.20
072.
0490
2.07
042.
1038
2.04
452.
2123
2.04
502.
0545
2.08
432.
0410
2.04
77M
SFT
2.29
342.
4510
2.29
442.
3819
2.35
242.
1932
2.37
302.
1943
2.23
682.
2226
2.07
732.
2666
2.07
792.
0952
2.08
482.
0708
2.07
04PFE
1.87
462.
0157
1.87
761.
9546
1.91
851.
8289
1.98
831.
8304
1.86
101.
8706
1.76
801.
9277
1.76
851.
7987
1.79
771.
7636
1.76
44PG
1.63
051.
7401
1.63
351.
6743
1.66
621.
3681
1.48
201.
3690
1.39
691.
4010
1.30
171.
4216
1.30
231.
3242
1.32
321.
2994
1.33
06T
2.00
942.
1557
2.01
192.
0848
2.05
721.
9469
2.11
031.
9478
1.98
171.
9840
1.89
402.
0660
1.89
471.
9163
1.91
971.
8907
1.89
10T
RV
2.28
262.
4375
2.28
532.
4106
2.35
642.
2216
2.41
272.
2238
2.32
342.
2614
2.20
562.
4092
2.20
632.
2841
2.26
472.
1997
2.20
08U
TX
2.00
562.
1431
2.00
872.
0699
2.05
551.
9436
2.09
901.
9453
1.97
591.
9768
1.91
362.
0739
1.91
401.
9391
1.93
391.
9087
1.91
41V
Z1.
9126
2.04
441.
9140
1.98
511.
9923
1.87
432.
0299
1.87
511.
9121
1.94
911.
7844
1.94
691.
7849
1.80
791.
8432
1.77
991.
7800
WM
T1.
7580
1.89
191.
7607
1.81
681.
7998
1.67
161.
8224
1.67
331.
6954
1.68
991.
5452
1.69
101.
5459
1.56
211.
5624
1.54
141.
5414
XO
M1.
7846
1.92
401.
7888
1.91
221.
8262
1.75
161.
9087
1.75
361.
8361
1.77
801.
7485
1.91
681.
7496
1.81
901.
7770
1.74
601.
7460
18
B.3
.R
MSE
ofFin
anci
alT
imes
Sto
ckExc
han
geIn
dex
(FT
SE)
Sto
cks
Loca
lRM
SEK
=40
Loca
lRM
SEK
=10
0Lo
calR
MSE
K=
250
Glo
balR
MSE
Stoc
kM
ean
HP
KF
EW
MA
NW
Mea
nH
PK
FEW
MA
NW
Mea
nH
PK
FEW
MA
NW
Mea
nG
ARCH
AA
L.L
3.04
093.
2715
3.04
563.
1590
3.15
253.
0263
3.29
943.
0300
3.09
683.
0970
3.12
893.
4245
3.12
943.
1684
3.19
453.
1209
3.27
95A
BF.
L1.
2963
1.38
151.
2978
1.35
791.
3321
1.27
641.
3786
1.27
741.
3127
1.29
531.
2926
1.40
421.
2928
1.30
481.
3095
1.28
921.
2895
AD
M.L
2.29
872.
4574
2.30
232.
4392
2.36
142.
3224
2.51
382.
3238
2.46
602.
3679
2.42
562.
6492
2.42
692.
4891
2.46
402.
4224
2.42
08AG
K.L
2.41
492.
5769
2.41
712.
5278
2.47
452.
3637
2.55
462.
3657
2.40
682.
4056
2.28
702.
4817
2.28
702.
3131
2.31
372.
2810
2.28
12A
MEC.L
2.22
032.
3746
2.22
242.
3315
2.32
062.
2010
2.38
002.
2012
2.25
652.
2689
2.21
922.
4175
2.21
962.
2609
2.29
412.
2144
2.21
52A
NT
O.L
4.61
184.
8808
4.61
594.
6858
4.68
764.
6247
4.93
484.
6285
4.66
194.
6534
4.78
165.
1176
4.78
294.
8097
4.80
454.
7727
5.28
52A
RM
.L4.
0450
4.30
334.
0457
4.16
724.
1136
3.98
894.
3129
3.99
294.
0167
4.02
203.
8289
4.14
033.
8284
3.90
873.
8512
3.81
834.
1647
AU
.L4.
0882
4.30
414.
0869
4.22
054.
1260
3.95
564.
2179
3.95
564.
0329
3.98
063.
4568
3.72
183.
4551
3.49
043.
5026
3.44
173.
5258
AV.L
2.95
693.
1675
2.96
053.
0738
3.02
722.
9008
3.14
092.
9043
2.98
282.
9643
2.97
633.
2351
2.97
753.
0324
3.02
582.
9700
2.97
11A
ZN
.L1.
6631
1.76
961.
6642
1.73
451.
7106
1.61
351.
7370
1.61
481.
6441
1.64
711.
6089
1.74
181.
6092
1.62
541.
6348
1.60
541.
6049
BA
.L1.
9501
2.09
641.
9541
2.03
151.
9887
1.86
902.
0278
1.87
031.
9027
1.87
431.
8328
2.00
191.
8336
1.85
561.
8418
1.83
031.
8307
BA
RC.L
3.53
673.
7523
3.53
953.
7050
3.64
893.
5341
3.76
693.
5347
3.59
783.
6030
3.66
223.
9091
3.66
173.
7234
3.70
483.
6505
3.92
54B
AT
S.L
2.43
402.
6098
2.43
852.
4982
2.47
752.
4348
2.62
602.
4373
2.47
722.
4787
2.50
062.
7084
2.50
152.
5370
2.54
512.
4953
2.84
25B
AY
.L2.
8878
3.08
052.
8894
2.97
222.
9611
2.80
163.
0246
2.80
362.
8411
2.86
022.
8103
3.04
672.
8104
2.84
362.
8558
2.80
422.
8055
BG
.L2.
1106
2.26
502.
1155
2.18
882.
1652
2.08
562.
2635
2.08
792.
1283
2.12
032.
1509
2.34
632.
1515
2.18
102.
1833
2.14
532.
1457
BLN
D.L
2.09
022.
2468
2.09
462.
1889
2.16
712.
0894
2.27
182.
0917
2.12
612.
1045
2.09
822.
2901
2.09
872.
1175
2.12
262.
0947
2.09
46B
LT.L
2.78
142.
9788
2.78
412.
8889
2.83
182.
7646
3.00
322.
7678
2.83
282.
8118
2.84
483.
1070
2.84
582.
8912
2.89
722.
8382
2.83
94B
NZL.
L1.
6484
1.76
791.
6513
1.73
191.
6846
1.65
751.
8006
1.65
871.
6954
1.68
501.
7195
1.88
541.
7201
1.74
871.
7553
1.71
501.
7154
BP.
L1.
6390
1.75
201.
6409
1.72
101.
6746
1.61
111.
7433
1.61
261.
6695
1.64
691.
6448
1.79
391.
6455
1.68
891.
6868
1.64
151.
6417
BRB
Y.L
2.38
602.
5459
2.38
812.
4593
2.42
132.
3609
2.54
512.
3614
2.38
842.
3920
2.34
682.
5471
2.34
682.
3825
2.35
462.
3433
2.34
50B
SY.L
3.51
613.
7513
3.52
974.
2781
3.50
503.
5212
3.78
463.
5265
4.74
623.
5060
1.79
581.
9441
1.79
651.
9799
1.80
521.
7921
1.79
20B
T-A
.L2.
2055
2.36
992.
2094
2.27
902.
2703
2.18
012.
3679
2.18
132.
2179
2.23
342.
0519
2.23
972.
0520
2.07
672.
0827
2.04
822.
0487
CCL.
L2.
1098
2.25
832.
1117
2.21
732.
1846
2.11
402.
2907
2.11
562.
1565
2.17
682.
1611
2.35
242.
1618
2.18
992.
2203
2.15
702.
1594
CN
A.L
1.74
141.
8456
1.74
471.
8434
1.77
971.
7489
1.87
431.
7508
1.78
921.
7877
1.80
831.
9482
1.80
891.
8387
1.86
251.
8051
1.80
58CN
E.L
12.7
6713
.606
12.8
2014
.511
12.7
0312
.895
13.8
2212
.915
15.5
6512
.860
13.4
1714
.404
13.4
2516
.241
13.4
4513
.391
13.1
08CO
B.L
1.64
761.
7505
1.64
861.
7327
1.70
801.
6429
1.76
891.
6445
1.68
851.
6775
1.68
081.
8202
1.68
151.
6977
1.70
451.
6769
1.67
78CPG
.L2.
2083
2.36
652.
2113
2.30
762.
2590
2.19
692.
3786
2.19
872.
2478
2.22
562.
1477
2.33
612.
1480
2.17
762.
1742
2.14
272.
1429
CPI.L
1.63
591.
7611
1.63
971.
6838
1.69
981.
5713
1.70
641.
5729
1.58
661.
6241
1.47
131.
6098
1.47
191.
4836
1.50
181.
4683
1.46
81CW
.L2.
0723
2.21
212.
0744
2.14
512.
1241
1.94
652.
0946
1.94
751.
9831
1.96
711.
8821
2.02
271.
8815
1.90
221.
8949
1.87
501.
8759
19
Loca
lRM
SEK
=40
Loca
lRM
SEK
=10
0Lo
calR
MSE
K=
250
Glo
balR
MSE
Stoc
kM
ean
HP
KF
EW
MA
NW
Mea
nH
PK
FEW
MA
NW
Mea
nH
PK
FEW
MA
NW
Mea
nG
ARCH
DG
E.L
1.30
031.
3979
1.30
251.
3492
1.33
951.
2685
1.38
011.
2698
1.29
761.
2985
1.27
581.
3978
1.27
651.
2970
1.30
611.
2734
1.27
36EM
G.L
3.96
864.
2633
3.97
844.
2214
4.18
304.
0697
4.40
974.
0728
4.21
254.
2583
4.44
124.
8306
4.44
144.
5283
4.59
134.
4274
4.68
70EN
RC.L
5.70
626.
1952
5.71
915.
9252
5.84
635.
8936
6.46
425.
8949
6.00
605.
9777
4.63
675.
0292
4.63
484.
6478
4.65
944.
5828
4.58
08EX
PN
.L2.
4486
2.61
162.
4503
2.55
712.
4873
2.49
352.
7064
2.49
702.
5600
2.54
262.
5965
2.82
322.
5980
2.63
462.
6731
2.59
402.
5941
FRES.
L4.
8129
4.98
524.
7974
4.95
544.
9476
5.06
155.
2475
5.04
755.
1670
5.20
043.
7035
3.94
953.
6986
3.68
303.
7660
3.67
193.
6543
GFS
.L1.
7506
1.87
161.
7524
1.82
751.
7938
1.73
271.
8778
1.73
441.
7738
1.75
791.
6921
1.84
491.
6928
1.71
841.
7090
1.68
791.
6888
GSK
.L1.
6939
1.81
901.
6980
1.78
801.
7569
1.66
911.
8107
1.67
081.
7932
1.70
991.
6563
1.80
771.
6569
1.67
111.
6643
1.65
261.
6502
HM
SO.L
2.41
052.
5624
2.41
442.
5618
2.42
092.
4008
2.58
152.
4026
2.62
362.
3976
2.45
572.
6486
2.45
582.
7011
2.43
752.
4508
2.46
18H
OM
E.L
3.92
614.
1652
3.93
063.
9879
3.97
023.
9996
4.27
884.
0022
4.02
594.
0277
2.97
433.
2206
2.97
532.
9980
3.00
802.
9636
2.96
13H
SBA
.L1.
9403
2.08
231.
9432
2.00
771.
9838
1.92
932.
0939
1.93
081.
9676
1.96
231.
8981
2.06
871.
8983
1.93
121.
9298
1.89
241.
8943
IAP.
L2.
9319
3.14
482.
9372
3.10
383.
0466
2.94
903.
2046
2.95
173.
0710
3.05
423.
0501
3.32
943.
0501
3.13
473.
1573
3.04
113.
2274
IHG
.L2.
5445
2.72
312.
5462
2.61
142.
6138
2.59
142.
8140
2.59
462.
6257
2.63
302.
7823
3.03
092.
7819
2.79
072.
8295
2.77
402.
7754
III.L
2.95
823.
1349
2.95
953.
0857
3.01
302.
9211
3.12
732.
9224
2.96
032.
9679
3.00
303.
2297
3.00
313.
0414
3.05
492.
9969
3.13
91IM
T.L
1.51
611.
6304
1.51
851.
5946
1.52
941.
5004
1.63
191.
5018
1.54
041.
5265
1.53
051.
6761
1.53
111.
5460
1.60
621.
5281
1.52
83IP
R.L
2.13
302.
2532
2.13
422.
2666
2.21
502.
0458
2.19
022.
0473
2.09
352.
0828
2.03
012.
1844
2.03
042.
0559
2.04
662.
0267
2.02
61IS
AT
.L2.
2033
2.35
842.
2065
2.29
562.
3284
2.20
712.
3965
2.20
922.
2620
2.29
912.
2615
2.47
712.
2627
2.28
502.
3330
2.25
682.
2536
ISY
S.L
6.71
117.
0706
6.71
456.
7867
6.87
516.
6651
7.03
716.
6638
6.68
216.
7231
6.78
077.
1837
6.78
016.
7882
6.80
376.
7575
7.65
93IT
RK
.L1.
8461
1.97
391.
8485
1.92
561.
8805
1.83
271.
9862
1.83
351.
9317
1.85
651.
8419
2.00
901.
8423
1.88
621.
8720
1.83
691.
8367
JMAT
.L1.
9899
2.11
521.
9921
2.06
252.
0295
1.96
202.
1082
1.96
362.
0018
1.98
572.
0072
2.16
332.
0068
2.02
912.
0271
2.00
092.
0010
KA
Z.L
4.56
244.
9060
4.56
894.
7499
4.72
254.
6553
5.04
204.
6544
4.73
874.
7556
4.87
885.
2882
4.87
344.
9265
4.97
704.
8572
5.13
72KG
F.L
2.20
262.
3383
2.20
372.
2558
2.27
502.
1975
2.37
342.
2004
2.23
102.
2395
2.27
312.
4631
2.27
362.
2862
2.30
652.
2690
2.26
89LA
ND
.L2.
0351
2.15
032.
0365
2.08
552.
0839
2.04
062.
1820
2.04
252.
0791
2.06
052.
0962
2.24
412.
0959
2.12
432.
1319
2.09
262.
0907
LGEN
.L3.
0096
3.22
593.
0140
3.09
573.
0728
2.93
253.
1784
2.93
642.
9803
2.97
853.
0140
3.27
163.
0146
3.05
333.
0795
3.00
623.
0078
LII.L
2.34
752.
4908
2.35
052.
4144
2.39
802.
3525
2.51
402.
3533
2.38
952.
3879
2.36
582.
5440
2.36
582.
3996
2.39
142.
3613
2.47
11LL
OY
.L3.
5642
3.78
193.
5671
3.80
403.
6664
3.55
373.
8067
3.55
653.
7066
3.66
153.
6241
3.89
293.
6251
3.71
563.
7550
3.61
764.
1650
LMI.L
3.28
733.
4871
3.29
023.
4016
3.38
353.
2843
3.50
713.
2831
3.31
023.
3760
3.38
443.
6407
3.38
443.
4080
3.47
773.
3770
3.37
78LS
E.L
2.62
772.
7821
2.62
992.
7666
2.81
822.
6147
2.79
952.
6157
2.69
752.
7528
2.67
142.
8690
2.67
072.
6995
2.73
882.
6646
2.76
43M
KS.
L2.
1194
2.24
622.
1208
2.18
212.
1542
2.08
472.
2340
2.08
582.
1095
2.10
182.
1284
2.29
022.
1283
2.14
402.
1532
2.12
542.
2717
MRW
.L2.
4790
2.64
872.
4863
2.88
102.
5584
2.45
742.
6493
2.46
003.
1720
2.53
662.
5265
2.74
022.
5279
3.66
952.
6023
2.52
132.
5188
NG
.L1.
6416
1.77
851.
6463
1.80
211.
7553
1.65
791.
8095
1.65
981.
8264
1.77
811.
7404
1.90
931.
7412
1.85
771.
8932
1.73
711.
7378
NX
T.L
2.12
892.
2840
2.13
192.
1847
2.18
312.
1095
2.29
442.
1112
2.13
402.
1434
2.17
022.
3746
2.17
072.
1876
2.20
212.
1672
2.16
84O
ML.
L5.
9519
6.25
695.
9585
6.04
905.
9686
5.96
216.
2996
5.96
716.
0469
6.02
616.
1913
6.55
776.
1937
7.06
566.
2814
6.17
776.
8110
PFC
.L2.
8775
3.09
692.
8832
3.06
652.
9581
2.91
263.
1547
2.91
303.
0002
2.97
702.
9253
3.19
582.
9248
2.96
083.
0066
2.91
502.
9150
20
Loca
lRM
SEK
=40
Loca
lRM
SEK
=10
0Lo
calR
MSE
K=
250
Glo
balR
MSE
Stoc
kM
ean
HP
KF
EW
MA
NW
Mea
nH
PK
FEW
MA
NW
Mea
nH
PK
FEW
MA
NW
Mea
nG
ARCH
PRU
.L3.
0903
3.34
443.
0951
3.21
633.
2075
3.02
263.
3102
3.02
783.
0940
3.11
213.
1075
3.41
033.
1082
3.17
063.
1758
3.09
913.
1022
PSO
N.L
1.60
841.
7304
1.61
101.
6726
1.64
841.
5038
1.62
981.
5049
1.53
941.
5288
1.48
381.
6218
1.48
441.
5002
1.49
971.
4811
1.48
15RB
.L1.
9108
2.06
401.
9141
2.02
991.
9795
1.87
582.
0626
1.87
831.
9496
1.94
831.
7159
1.90
911.
7170
1.72
951.
7553
1.71
121.
7120
RB
S.L
4.48
334.
7036
4.48
344.
6537
4.66
224.
4941
4.76
494.
4964
4.59
164.
7423
4.67
844.
9701
4.67
804.
8068
4.99
604.
6693
5.05
77RD
SA.L
1.88
182.
0071
1.88
342.
0062
1.92
451.
8995
2.05
121.
9008
1.97
581.
9388
1.98
552.
1636
1.98
672.
0462
2.02
181.
9817
1.98
25REL.
L1.
9002
2.03
701.
9027
1.97
531.
9466
1.88
222.
0480
1.88
411.
9189
1.91
471.
8434
2.02
201.
8443
1.85
451.
8537
1.83
891.
8390
REX
.L1.
9099
2.01
501.
9125
1.99
811.
9696
1.89
022.
0144
1.89
161.
9320
1.92
961.
9106
2.04
611.
9117
1.92
881.
9449
1.90
751.
9079
RIO
.L3.
2647
3.49
163.
2720
3.38
733.
3732
3.28
253.
5371
3.28
393.
3537
3.35
693.
3946
3.67
863.
3945
3.43
643.
4815
3.38
583.
3850
RR.L
2.09
082.
2368
2.09
252.
1659
2.15
522.
0679
2.24
442.
0704
2.10
742.
1074
2.05
952.
2469
2.05
992.
0789
2.11
282.
0557
2.05
67RRS.
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1764
3.37
903.
1793
3.27
033.
2433
3.18
163.
4293
3.18
443.
2212
3.25
073.
2289
3.50
103.
2304
3.25
333.
2893
3.22
133.
2191
RSA
.L2.
3939
2.56
272.
3957
2.49
282.
4537
2.21
882.
3983
2.21
862.
2555
2.25
482.
0628
2.26
422.
0637
2.08
662.
0700
2.05
802.
0930
RSL
.L2.
3462
2.51
772.
3555
2.38
142.
3142
1.90
392.
0357
1.90
601.
9192
1.89
051.
7551
1.77
081.
7560
1.77
721.
7829
1.75
081.
7305
SAB
.L2.
0823
2.20
862.
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2.15
502.
1424
2.06
142.
2114
2.06
242.
1035
2.09
552.
1184
2.28
702.
1188
2.14
222.
1448
2.11
452.
1822
SBRY
.L1.
8747
1.99
741.
8772
1.96
021.
9364
1.84
591.
9913
1.84
861.
8874
1.87
681.
8660
2.01
931.
8664
1.87
711.
8841
1.86
271.
8637
SDRC.L
2.70
202.
9015
2.70
892.
9268
2.74
272.
6256
2.85
052.
6282
2.92
112.
6450
2.63
362.
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2.63
452.
8053
2.64
542.
6276
2.62
83SD
R.L
2.58
532.
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2.59
072.
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2.65
192.
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2.72
862.
5185
2.75
732.
5549
2.55
822.
7953
2.55
892.
7151
2.52
812.
5521
2.62
54SG
E.L
1.94
952.
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1.95
292.
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1.98
911.
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1.99
531.
8401
1.86
601.
8746
1.77
111.
9338
1.77
171.
7870
1.79
121.
7671
1.76
79SG
RO
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4583
8.94
738.
4710
8.48
448.
5108
8.84
799.
4139
8.85
058.
9252
8.90
5710
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11.1
5610
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10.5
5210
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10.4
4412
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SHP.
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3497
2.50
712.
3497
2.42
402.
4079
2.31
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5096
2.32
132.
3542
2.38
082.
2167
2.40
832.
2176
2.22
562.
2354
2.21
492.
2155
SL.L
3.17
823.
4196
3.18
453.
3238
3.26
853.
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3.54
233.
2496
3.34
413.
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3.53
623.
8726
3.53
783.
6110
3.69
483.
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3.52
92SM
IN.L
1.97
652.
1076
1.97
792.
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2.04
531.
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2.07
131.
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1.96
441.
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1.90
162.
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1.90
191.
9275
1.94
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1.89
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2.69
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1.89
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1.89
181.
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1.93
961.
8816
2.05
751.
8821
1.89
561.
9124
1.87
681.
8773
SRP.
L1.
8534
1.99
121.
8548
1.93
361.
8897
1.76
161.
9177
1.76
261.
7850
1.78
991.
6648
1.81
911.
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1.67
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6794
1.66
171.
6618
SSE.L
1.43
091.
5465
1.43
511.
5536
1.53
251.
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1.54
521.
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1.63
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5282
1.44
491.
5822
1.44
561.
5719
1.58
061.
4428
1.44
29ST
AN
.L2.
6423
2.83
252.
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2.76
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2.61
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2.61
712.
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2.67
832.
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2.81
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5794
2.63
252.
6738
2.57
152.
6864
SVT
.L1.
6957
1.82
021.
6983
1.74
331.
7317
1.68
721.
8247
1.68
821.
7376
1.71
831.
7316
1.88
361.
7322
1.76
701.
7702
1.72
791.
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TLW
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6609
2.82
202.
6625
2.77
262.
7551
2.64
832.
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2.64
962.
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2.70
742.
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2.90
092.
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2.71
342.
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2.67
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TSC
O.L
1.58
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1.58
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1.63
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1.68
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1.56
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1.54
531.
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1.54
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5618
1.55
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5423
1.54
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T.L
2.42
772.
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2.43
152.
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2.48
192.
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2.55
652.
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2.40
802.
3832
2.37
362.
6001
2.37
442.
3991
2.38
982.
3677
2.41
32U
U.L
1.46
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5764
1.47
211.
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1.52
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1.57
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1.49
381.
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1.43
361.
5663
1.43
411.
4636
1.48
671.
4307
1.43
12V
ED
.L3.
6749
3.91
643.
6772
3.80
843.
8063
3.70
543.
9908
3.70
703.
7918
3.84
253.
8611
4.15
833.
8590
3.91
323.
9923
3.84
874.
0298
VO
D.L
1.88
492.
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1.88
911.
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1.95
931.
8700
2.03
581.
8713
1.96
421.
9181
1.89
752.
0798
1.89
831.
9164
1.90
321.
8936
1.89
44W
OS.
L5.
7584
6.10
705.
7675
6.35
995.
7959
5.75
276.
1594
5.75
986.
4344
5.81
655.
9021
6.34
155.
9047
6.79
405.
8839
5.88
997.
4229
21
Loca
lRM
SEK
=40
Loca
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250
Glo
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ARCH
WPP.
L2.
3404
2.51
562.
3428
2.43
242.
4022
2.32
562.
5351
2.32
782.
3664
2.37
022.
2291
2.43
592.
2293
2.24
482.
2447
2.22
302.
2235
WT
B.L
2.45
992.
6142
2.46
152.
5673
2.51
192.
5050
2.69
912.
5075
2.57
302.
5459
2.68
822.
9100
2.68
812.
7052
2.71
092.
6832
2.68
25X
TA
.L3.
5601
3.82
953.
5676
3.67
873.
6358
3.53
733.
8439
3.54
003.
6051
3.61
963.
6024
3.92
423.
6010
3.64
443.
6837
3.59
233.
7967
B.4
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MSE
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Sen
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dex
(HSI)
Sto
cks
Loca
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Loca
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250
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MA
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0001
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2.17
902.
3373
2.18
162.
2973
2.22
702.
1713
2.35
472.
1725
2.22
742.
1823
2.19
722.
3942
2.19
762.
2276
2.21
832.
1917
2.19
1900
02.H
K1.
2808
1.37
821.
2847
1.42
891.
2821
1.28
391.
3965
1.28
561.
3925
1.29
171.
3216
1.44
481.
3220
1.41
561.
3530
1.31
791.
3175
0003
.HK
1.74
591.
8723
1.74
871.
9167
1.81
301.
7461
1.89
331.
7475
1.90
961.
8214
1.79
851.
9555
1.79
811.
9302
1.88
211.
7921
1.79
1600
04.H
K2.
6051
2.78
892.
6078
2.68
322.
6957
2.57
942.
7948
2.58
122.
6626
2.59
982.
6236
2.84
832.
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2.65
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6455
2.61
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1.92
572.
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1.92
812.
2329
2.11
121.
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2.07
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2.17
872.
1719
2.00
622.
1519
2.00
572.
1380
2.30
331.
9996
2.00
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06.H
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2694
1.37
111.
2728
1.32
981.
3244
1.26
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3813
1.26
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3131
1.32
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3043
1.43
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3051
1.33
101.
3495
1.30
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3017
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1.61
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1.61
331.
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1.73
501.
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1.72
621.
6173
1.67
611.
7133
1.66
691.
7888
1.66
711.
7075
1.76
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6629
1.66
5600
12.H
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3683
2.53
832.
3707
2.50
422.
4285
2.35
432.
5502
2.35
542.
4406
2.38
432.
3721
2.57
012.
3714
2.40
792.
4306
2.36
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3634
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1.84
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1.84
581.
9639
1.90
561.
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1.97
541.
8330
1.89
801.
8875
1.85
832.
0113
1.85
801.
8928
1.86
731.
8531
1.85
2200
16.H
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2560
2.41
612.
2584
2.37
752.
3094
2.24
842.
4311
2.24
872.
3133
2.28
312.
2437
2.42
912.
2426
2.26
652.
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2.23
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2348
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3.09
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2990
3.09
553.
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3.16
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0834
3.30
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3.16
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1184
3.03
073.
2716
3.02
853.
0621
3.03
603.
0180
3.01
7900
19.H
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0846
2.23
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2.20
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2.05
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2.05
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1303
2.07
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2.23
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2.08
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0777
2.05
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2.25
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4033
2.25
532.
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2.35
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2612
2.42
752.
2615
2.34
182.
3804
2.29
782.
4693
2.29
662.
3342
2.35
512.
2905
2.29
2000
66.H
K1.
7555
1.86
341.
7570
1.90
601.
8238
1.74
791.
8778
1.74
871.
8591
1.79
271.
7425
1.88
281.
7424
1.79
161.
7573
1.73
651.
7361
0083
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3.03
993.
2602
3.04
263.
1524
3.13
513.
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3.30
533.
0526
3.10
153.
1196
3.06
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3317
3.06
543.
0900
3.11
283.
0571
3.05
6501
01.H
K2.
6663
2.87
132.
6714
2.75
612.
7328
2.66
332.
8995
2.66
562.
7054
2.70
752.
7373
2.99
922.
7378
2.75
052.
7613
2.73
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7316
0144
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3.07
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2977
3.08
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2400
3.22
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3.33
563.
0783
3.15
703.
2194
3.11
343.
3906
3.11
353.
1518
3.23
353.
1054
3.10
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67.H
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3951
3.53
263.
3882
3.66
583.
4786
3.40
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5784
3.40
043.
5170
3.45
073.
5353
3.71
713.
5335
3.61
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5787
3.52
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5682
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2.81
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2.82
253.
0233
2.93
472.
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3.06
012.
8175
2.93
153.
0002
2.88
003.
1450
2.88
012.
9552
3.08
402.
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2.87
73
22
Loca
lRM
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Loca
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K=
250
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kM
ean
HP
KF
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MA
NW
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nH
PK
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PK
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NW
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2.23
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2.47
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1917
2.37
882.
1935
2.45
852.
4587
2.21
022.
4121
2.21
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2.55
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2053
2.20
6403
30.H
K2.
7637
2.96
792.
7691
2.87
792.
8519
2.75
722.
9961
2.76
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8044
2.81
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7728
3.02
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2.79
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2.76
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2.79
243.
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2.79
662.
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2.89
862.
7663
3.01
032.
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2.83
862.
8533
2.75
563.
0207
2.75
642.
7862
2.79
112.
7502
2.74
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88.H
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5576
2.71
302.
5560
2.66
582.
6090
2.54
062.
7253
2.53
922.
5947
2.56
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2.74
232.
5493
2.56
102.
5622
2.54
432.
5871
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3.01
613.
2441
3.02
323.
1338
3.10
962.
9743
3.22
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9760
3.04
393.
0385
2.95
053.
2286
2.95
102.
9978
2.98
182.
9409
2.93
9806
88.H
K3.
3117
3.56
663.
3178
3.43
723.
4004
3.31
073.
6020
3.31
213.
3672
3.40
033.
3465
3.65
853.
3465
3.36
453.
3914
3.33
733.
3387
0700
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3.28
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5432
3.29
413.
4714
3.37
963.
2887
3.57
973.
2904
3.37
943.
3576
3.33
493.
6642
3.33
623.
3901
3.35
573.
3279
3.32
8507
62.H
K3.
1603
3.41
203.
1660
3.29
123.
2986
3.15
343.
4378
3.15
533.
2074
3.26
283.
0986
3.41
053.
0996
3.12
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1823
3.09
313.
0966
0836
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3.21
763.
4514
3.22
393.
3941
3.32
903.
2068
3.47
363.
2085
3.30
593.
2723
3.19
623.
4952
3.19
753.
2284
3.27
563.
1924
3.19
2408
57.H
K2.
4895
2.65
812.
4903
2.64
502.
6053
2.44
762.
6397
2.44
832.
5133
2.48
502.
4160
2.61
682.
4164
2.45
002.
4494
2.41
122.
4111
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2.95
523.
1569
2.95
613.
1425
3.00
522.
9575
3.19
892.
9589
3.02
092.
9960
3.06
353.
3261
3.06
363.
1026
3.07
483.
0547
3.09
1909
39.H
K2.
9834
3.18
692.
9865
3.22
173.
1878
3.01
083.
2581
3.01
233.
1695
3.19
843.
2301
3.51
583.
2308
3.30
103.
4266
3.22
253.
2565
0941
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2.22
982.
3786
2.23
152.
3238
2.29
272.
2144
2.39
052.
2153
2.24
662.
2558
2.23
962.
4300
2.23
952.
2579
2.25
962.
2347
2.23
4410
88.H
K3.
5177
3.77
183.
5221
3.70
843.
7133
3.56
653.
8632
3.56
813.
7900
3.83
313.
7395
4.06
043.
7379
3.91
844.
0804
3.72
773.
7325
1199
.HK
3.23
773.
4355
3.23
973.
5187
3.34
333.
2242
3.46
103.
2267
3.35
773.
3547
3.29
753.
5489
3.29
773.
4072
3.41
013.
2886
3.38
1113
98.H
K3.
0384
3.26
143.
0419
3.26
703.
2249
3.06
043.
3267
3.06
163.
1844
3.22
213.
2306
3.53
283.
2306
3.28
233.
3702
3.21
793.
2288
2038
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4.19
344.
5035
4.19
654.
4627
4.32
674.
2400
4.61
434.
2428
4.39
774.
2896
4.41
714.
8210
4.41
664.
5511
4.48
554.
4134
4.62
1423
18.H
K3.
0968
3.30
443.
0984
3.31
373.
2177
3.11
433.
3615
3.11
513.
2132
3.17
303.
2653
3.54
503.
2656
3.30
533.
2765
3.25
993.
2614
2388
.HK
2.06
902.
2216
2.07
252.
1731
2.12
992.
0824
2.25
012.
0820
2.14
652.
1202
2.15
472.
3336
2.15
332.
1795
2.16
912.
1467
2.14
7426
00.H
K3.
7029
3.93
853.
7054
3.88
673.
7821
3.69
823.
9664
3.69
773.
7786
3.75
883.
7528
4.03
743.
7499
3.79
463.
8046
3.73
883.
7389
2628
.HK
2.72
072.
9063
2.72
372.
9592
2.91
022.
7145
2.92
972.
7155
2.88
242.
8976
2.79
003.
0361
2.79
112.
8510
2.97
512.
7884
2.81
7033
28.H
K2.
9362
3.13
812.
9386
3.14
633.
0228
2.98
093.
2198
2.98
113.
0827
3.08
943.
1229
3.38
823.
1221
3.16
243.
1647
3.11
273.
1472
3988
.HK
2.76
622.
9783
2.77
022.
9984
2.94
522.
8454
3.09
362.
8459
2.95
593.
0709
3.06
343.
3542
3.06
313.
1342
3.21
253.
0536
3.05
53
23
B.5
.R
MSE
ofN
asdaq
Can
ada
(CN
D)
Sto
cks
Loca
lRM
SEK
=40
Loca
lRM
SEK
=10
0Lo
calR
MSE
K=
250
Glo
balR
MSE
Stoc
kM
ean
HP
KF
EW
MA
NW
Mea
nH
PK
FEW
MA
NW
Mea
nH
PK
FEW
MA
NW
Mea
nGA
RCH
AEZS
5.02
825.
3383
5.03
505.
1472
5.31
425.
0141
5.35
895.
0144
5.07
035.
2406
5.03
335.
4197
5.03
495.
0689
5.15
555.
0224
5.29
92A
LTI
6.49
186.
9475
6.49
966.
8816
6.72
056.
4222
6.95
286.
4266
6.59
706.
5929
6.20
026.
7561
6.20
226.
2581
6.31
966.
1861
6.43
83A
NPI
5.09
715.
4962
5.10
335.
4290
5.36
765.
0457
5.46
905.
0457
5.31
085.
2893
5.10
875.
5624
5.10
735.
2074
5.18
735.
0954
5.90
75B
LDP
4.76
085.
0584
4.76
025.
0783
4.92
314.
6420
4.99
634.
6432
4.80
244.
7198
4.61
374.
9978
4.61
504.
7117
4.72
224.
6034
4.76
45CFK
3.91
904.
1547
3.92
144.
1738
4.05
863.
8791
4.15
523.
8801
4.02
733.
9944
3.70
703.
9977
3.70
793.
7985
3.77
613.
7010
3.77
80CN
IC8.
1544
8.73
758.
1730
8.72
208.
3041
8.08
218.
7547
8.08
898.
8408
8.32
978.
0377
8.77
238.
0398
8.41
808.
3467
8.02
178.
3218
CRM
E3.
8896
4.13
503.
8915
4.09
634.
0734
3.78
234.
0547
3.78
403.
8530
3.89
163.
7414
4.03
763.
7425
3.77
213.
8242
3.73
353.
9737
CSI
Q6.
5372
6.91
986.
5398
6.77
366.
7099
6.63
077.
0742
6.62
916.
7224
6.68
327.
1367
7.61
487.
1285
7.18
247.
1970
7.09
737.
2702
DD
SS6.
1410
6.44
946.
1332
6.43
556.
2495
6.25
266.
6411
6.25
216.
3113
6.28
346.
7220
7.19
296.
7244
6.72
866.
7256
6.71
326.
8791
DRW
I6.
5706
6.86
286.
5693
6.76
966.
8696
5.71
036.
1199
5.70
865.
7457
5.91
964.
4462
4.71
834.
4299
4.42
204.
4471
4.41
364.
5225
DSG
X4.
4363
4.74
614.
4416
4.54
724.
6557
4.17
994.
4937
4.18
034.
2436
4.28
773.
9597
4.28
313.
9604
3.99
634.
0204
3.95
434.
1413
ECG
I7.
1174
7.56
347.
1271
7.37
107.
2313
7.10
777.
6358
7.11
267.
2839
7.18
007.
1687
7.73
927.
1689
7.26
857.
2428
7.15
187.
3959
EX
FO4.
5536
4.82
844.
5546
4.74
814.
7167
4.42
344.
7290
4.42
514.
4922
4.55
993.
9215
4.22
693.
9225
3.95
793.
9906
3.91
923.
9496
FSRV
2.41
202.
5624
2.41
292.
4918
2.46
932.
3885
2.56
732.
3904
2.40
802.
4146
2.39
372.
5772
2.39
272.
4086
2.46
992.
3876
2.38
78G
LGL
5.58
855.
9631
5.58
575.
9413
5.87
375.
7698
6.20
225.
7689
5.91
646.
0606
6.20
226.
7221
6.20
026.
2774
6.57
796.
1754
6.29
82H
YG
S5.
0778
5.40
795.
0778
5.29
905.
2471
4.91
745.
3000
4.91
735.
0338
5.05
054.
6524
5.06
054.
6540
4.68
684.
7629
4.64
194.
7868
IMA
X5.
3152
5.60
385.
3175
5.46
575.
4412
5.31
255.
6470
5.31
185.
4046
5.37
924.
6248
4.98
284.
6241
4.66
294.
7119
4.61
074.
8042
IVA
N5.
6291
5.99
675.
6343
5.85
775.
7242
5.66
996.
0823
5.66
825.
7961
5.76
675.
6539
6.09
905.
6521
5.72
485.
7749
5.63
535.
8017
JCT
CF
3.44
873.
7145
3.45
703.
6744
3.69
523.
4517
3.75
993.
4557
3.54
133.
6308
3.48
673.
8199
3.48
813.
5363
3.62
153.
4782
3.74
77LB
IX7.
0282
7.54
917.
0405
7.34
487.
1391
6.88
997.
4971
6.89
526.
9970
6.95
796.
7528
7.37
826.
7536
6.84
126.
7904
6.73
777.
0456
LMLP
6.25
506.
5856
6.25
436.
5668
6.55
935.
7944
6.18
485.
7966
5.97
975.
9198
5.37
935.
7810
5.38
085.
4921
5.52
545.
3675
5.61
48M
DCA
4.97
235.
2578
4.97
595.
0723
5.07
623.
3547
3.54
423.
3454
3.42
923.
4302
3.33
253.
5624
3.33
013.
3812
3.39
013.
3231
3.33
75M
EO
H2.
9417
3.13
402.
9436
3.04
913.
0145
2.80
313.
0139
2.80
342.
8327
2.87
312.
6383
2.83
862.
6369
2.64
772.
6701
2.62
902.
6299
NEPT
7.32
497.
8394
7.34
087.
5674
7.35
487.
6013
8.19
857.
6043
7.74
107.
7086
8.40
589.
0903
8.40
258.
5077
8.54
788.
3756
8.63
88N
GA
S5.
4801
5.87
685.
4877
5.73
895.
6800
5.18
255.
6113
5.18
725.
3341
5.36
315.
0876
5.52
845.
0885
5.15
785.
2252
5.07
855.
1209
NIC
K3.
2140
3.44
463.
2179
3.33
453.
2537
3.12
803.
3869
3.13
083.
1748
3.16
803.
0719
3.33
003.
0717
3.10
043.
0832
3.06
563.
0663
NY
MX
4.94
035.
2589
4.94
465.
1756
5.08
334.
5576
4.88
954.
5598
4.71
164.
7126
4.17
584.
5260
4.17
774.
2491
4.30
674.
1671
4.29
83O
NCY
5.01
165.
3731
5.01
545.
2556
5.21
354.
6387
5.02
234.
6420
4.74
994.
7640
4.62
455.
0364
4.62
544.
6760
4.68
774.
6131
4.62
98O
PM
R4.
4529
4.70
634.
4502
4.67
934.
5832
4.31
814.
6305
4.32
114.
4248
4.42
924.
2792
4.60
514.
2792
4.33
294.
4186
4.27
224.
5301
24
Loca
lRM
SEK
=40
Loca
lRM
SEK
=10
0Lo
calR
MSE
K=
250
Glo
balR
MSE
Stoc
kM
ean
HP
KF
EW
MA
NW
Mea
nH
PK
FEW
MA
NW
Mea
nH
PK
FEW
MA
NW
Mea
nGA
RCH
OT
EX
3.24
803.
4139
3.24
383.
3559
3.35
013.
0325
3.22
823.
0332
3.07
223.
0764
2.82
203.
0362
2.82
372.
8389
2.85
222.
8191
2.96
90PA
AS
3.66
203.
9097
3.66
703.
7764
3.77
753.
6350
3.92
123.
6384
3.68
263.
7286
3.65
963.
9603
3.66
043.
6897
3.75
153.
6503
3.65
01Q
LTI
3.84
364.
0786
3.84
464.
0177
4.02
493.
7116
3.98
493.
7144
3.82
753.
9343
3.49
813.
7842
3.49
813.
5213
3.65
313.
4914
3.63
62RIM
M4.
8275
5.13
134.
8279
5.02
984.
9278
4.54
494.
8866
4.54
554.
6024
4.62
044.
1522
4.49
754.
1525
4.19
244.
2149
4.14
934.
2785
SSRI
4.14
434.
4012
4.14
644.
2955
4.27
174.
1024
4.39
604.
1043
4.18
614.
1712
4.13
934.
4539
4.14
034.
1803
4.18
864.
1305
4.13
16ST
KL
4.33
194.
5387
4.32
654.
5375
4.47
374.
1569
4.43
614.
1589
4.20
324.
2369
3.93
824.
1970
3.93
823.
9753
3.96
693.
9312
4.10
00SW
IR4.
8136
5.06
094.
8095
4.94
094.
9167
4.80
315.
1032
4.80
154.
8626
4.85
914.
5496
4.86
204.
5478
4.59
264.
6085
4.54
104.
7164
SXCI
3.33
473.
5418
3.33
603.
4725
3.48
663.
3854
3.62
463.
3850
3.45
243.
5062
3.60
333.
8867
3.60
323.
6298
3.69
983.
5958
3.73
76T
ESO
3.57
573.
7934
3.57
713.
6516
3.67
913.
5219
3.76
523.
5201
3.55
523.
6023
3.45
113.
7095
3.45
143.
4784
3.53
623.
4449
3.55
81T
GA
5.62
236.
0506
5.63
505.
8288
5.61
905.
3497
5.83
755.
3554
5.42
435.
3631
5.12
335.
6259
5.12
515.
1786
5.16
935.
1141
5.21
50T
TH
I5.
3936
5.68
115.
3921
5.60
145.
5101
5.55
095.
8559
5.54
385.
6827
5.71
956.
2655
6.61
446.
2613
6.34
146.
4083
6.23
546.
5436
VT
NC
3.30
023.
5047
3.30
383.
4957
3.33
783.
1278
3.34
283.
1271
3.18
183.
1634
3.08
073.
3008
3.08
013.
1270
3.06
393.
0736
3.20
75W
PRT
5.67
436.
0449
5.67
915.
9338
6.05
404.
9333
5.31
424.
9391
4.98
115.
0613
4.21
094.
4954
4.20
234.
2986
4.18
894.
1806
4.13
37
B.6
.R
MSE
ofN
asdaq
Tec
hnol
ogy
Index
(ND
XT
)Sto
cks
Loca
lRM
SEK
=40
Loca
lRM
SEK
=10
0Lo
calR
MSE
K=
250
Glo
balR
MSE
Stoc
kM
ean
HP
KF
EW
MA
NW
Mea
nH
PK
FEW
MA
NW
Mea
nH
PK
FEW
MA
NW
Mea
nG
ARCH
AA
PL
3.37
843.
5765
3.37
893.
4628
3.44
573.
3119
3.53
583.
3111
3.33
213.
3636
2.83
873.
0741
2.83
932.
8560
2.90
382.
8309
2.82
96A
DB
E3.
4449
3.68
953.
4514
3.58
003.
5352
3.29
683.
5585
3.29
713.
3446
3.36
693.
0427
3.29
453.
0432
3.06
513.
1084
3.03
543.
2183
AD
SK3.
0027
3.18
393.
0033
3.09
153.
0543
2.93
823.
1525
2.93
872.
9869
2.97
042.
8366
3.07
602.
8372
2.85
372.
8516
2.83
302.
8751
ALT
R3.
7243
3.99
233.
7305
3.83
053.
8111
3.58
983.
8995
3.59
373.
6429
3.64
643.
2653
3.56
383.
2665
3.27
463.
2989
3.25
773.
3323
AM
AT
3.33
313.
5789
3.33
903.
4840
3.38
273.
2117
3.48
953.
2145
3.26
253.
2488
3.02
063.
2988
3.02
193.
0458
3.04
803.
0135
3.01
36B
IDU
4.17
334.
4806
4.18
014.
3119
4.25
594.
1692
4.49
284.
1674
4.19
434.
2192
4.08
494.
4435
4.08
384.
0968
4.16
644.
0737
4.27
61B
MC
3.23
533.
4158
3.23
293.
3232
3.43
263.
1507
3.36
953.
1508
3.19
883.
3176
2.73
022.
9894
2.73
172.
7493
2.94
952.
7260
2.85
98B
RCM
4.44
264.
7110
4.44
224.
5814
4.56
604.
3115
4.62
774.
3125
4.39
264.
3999
4.12
254.
4553
4.12
214.
1432
4.20
174.
1116
4.11
19CA
3.22
293.
3816
3.21
903.
3977
3.35
033.
1505
3.35
393.
1513
3.21
563.
1956
2.80
423.
0241
2.80
442.
8269
2.88
642.
7971
3.03
15
25
Loca
lRM
SEK
=40
Loca
lRM
SEK
=10
0Lo
calR
MSE
K=
250
Glo
balR
MSE
Stoc
kM
ean
HP
KF
EW
MA
NW
Mea
nH
PK
FEW
MA
NW
Mea
nH
PK
FEW
MA
NW
Mea
nG
ARCH
CERN
3.30
333.
5126
3.30
743.
4360
3.34
073.
1316
3.36
173.
1333
3.16
253.
1895
2.97
613.
2021
2.97
672.
9955
3.02
222.
9690
3.11
19CH
KP
3.74
414.
0043
3.74
943.
9142
3.78
833.
5134
3.80
543.
5167
3.56
243.
5306
3.25
923.
5419
3.26
013.
2699
3.25
583.
2535
3.44
28CSC
O3.
0387
3.25
743.
0436
3.13
793.
1051
2.97
083.
2188
2.97
273.
0088
3.00
312.
8531
3.10
622.
8535
2.87
002.
8963
2.84
782.
8496
CT
SH3.
5093
3.73
423.
5116
3.61
793.
6203
3.34
933.
6289
3.35
183.
3994
3.38
343.
1675
3.44
723.
1683
3.17
193.
1968
3.16
063.
2473
CT
XS
4.15
264.
4234
4.15
564.
3337
4.24
913.
9564
4.23
523.
9550
4.02
944.
0177
3.27
973.
5526
3.27
843.
2979
3.31
273.
2697
3.42
13D
ELL
2.81
623.
0154
2.81
852.
9044
2.86
532.
7605
2.99
992.
7621
2.80
222.
7860
2.56
472.
8039
2.56
542.
5736
2.57
612.
5563
2.55
56G
OO
G2.
4028
2.55
872.
4033
2.52
502.
4588
2.32
002.
4841
2.31
772.
3541
2.37
902.
3364
2.52
682.
3362
2.34
832.
4021
2.33
162.
3329
INFY
3.65
433.
9205
3.65
673.
7599
3.77
083.
4248
3.71
863.
4276
3.46
143.
4872
3.24
243.
5489
3.24
393.
2620
3.27
203.
2383
3.34
54IN
TC
2.91
633.
1320
2.91
973.
0348
2.96
332.
8505
3.09
892.
8524
2.90
102.
9018
2.69
182.
9419
2.69
192.
7160
2.71
592.
6837
2.68
43IN
TU
3.15
933.
3870
3.16
413.
2495
3.24
682.
9506
3.20
122.
9528
2.98
242.
9894
2.71
172.
9802
2.71
352.
7209
2.72
952.
7068
2.80
78K
LAC
3.57
773.
8411
3.58
273.
6827
3.66
483.
4012
3.69
583.
4045
3.44
143.
4477
3.05
503.
3194
3.05
553.
0739
3.07
433.
0473
3.04
66LL
TC
3.16
483.
3982
3.16
943.
2543
3.21
853.
0258
3.29
963.
0296
3.06
753.
0606
2.79
193.
0525
2.79
342.
8047
2.79
732.
7866
2.80
82LO
GI
3.29
023.
5067
3.29
093.
4189
3.35
423.
1936
3.44
843.
1950
3.25
703.
2230
3.02
363.
2837
3.02
433.
0449
3.06
453.
0169
3.05
68LR
CX
3.94
034.
2134
3.94
464.
0923
4.03
613.
7873
4.09
313.
7902
3.83
773.
8169
3.54
873.
8538
3.54
953.
5747
3.57
003.
5403
3.54
05M
CH
P3.
3380
3.59
823.
3455
3.48
403.
4254
3.19
803.
4854
3.20
133.
2360
3.23
022.
9100
3.18
682.
9112
2.93
412.
9518
2.90
312.
9033
MRV
L4.
4276
4.69
374.
4253
4.54
534.
5625
4.27
134.
5955
4.27
244.
3065
4.32
193.
8887
4.25
393.
8889
3.91
293.
9685
3.87
913.
9319
MSF
T2.
2934
2.45
102.
2944
2.38
192.
3524
2.19
322.
3730
2.19
432.
2368
2.22
262.
0773
2.26
662.
0779
2.09
522.
0848
2.07
082.
0704
MX
IM3.
3937
3.63
573.
3983
3.50
973.
5006
3.20
453.
4807
3.20
813.
2474
3.28
702.
9993
3.26
633.
0005
3.01
553.
0376
2.99
282.
9930
NTAP
4.70
244.
9918
4.70
264.
8283
4.83
734.
4818
4.82
404.
4851
4.53
334.
5279
4.22
624.
5757
4.22
504.
2446
4.29
224.
2139
4.35
33N
VD
A4.
7944
5.08
904.
7969
4.98
854.
9427
4.55
404.
8752
4.55
334.
6210
4.63
074.
3583
4.69
114.
3579
4.38
294.
4548
4.34
794.
5447
ORCL
3.08
233.
3196
3.08
803.
1813
3.15
582.
9929
3.25
742.
9955
3.02
653.
0213
2.82
643.
0930
2.82
712.
8443
2.83
702.
8202
2.82
05Q
CO
M3.
2727
3.50
623.
2774
3.41
333.
3318
3.16
203.
4380
3.16
433.
1979
3.22
092.
8849
3.13
772.
8859
2.89
842.
9173
2.87
962.
9314
RIM
M4.
8275
5.13
134.
8279
5.02
984.
9278
4.54
494.
8866
4.54
554.
6024
4.62
044.
1522
4.49
754.
1525
4.19
244.
2149
4.14
934.
2785
SND
K4.
9493
5.23
274.
9508
5.07
395.
1062
4.76
825.
1057
4.77
124.
8176
4.88
384.
5698
4.92
044.
5705
4.60
324.
6207
4.56
194.
7262
STX
3.35
903.
5792
3.36
113.
4593
3.43
993.
3508
3.60
213.
3498
3.40
493.
4162
3.29
323.
5400
3.29
013.
3280
3.33
413.
2812
3.28
05SY
MC
3.34
313.
5913
3.34
823.
4712
3.42
463.
2434
3.51
923.
2452
3.28
213.
2811
3.06
083.
3401
3.06
283.
0748
3.11
593.
0558
3.10
52V
RSN
4.54
254.
8388
4.54
484.
7488
4.66
364.
2942
4.60
714.
2951
4.37
794.
3835
4.07
804.
3923
4.07
804.
1374
4.13
834.
0697
4.06
98X
LNX
3.55
963.
8010
3.56
363.
6580
3.63
463.
4352
3.72
353.
4384
3.47
383.
4804
3.15
683.
4357
3.15
813.
1730
3.19
273.
1503
3.21
68Y
HO
O3.
8845
4.13
613.
8863
3.97
793.
9756
3.81
194.
1085
3.81
303.
8693
3.86
923.
6164
3.92
263.
6173
3.65
923.
6408
3.60
953.
6609
26
B.7. RMSE of Deutscher Aktien Index Technologiewerte (TecDAX) Stocks
Local RMSE K=40 Local RMSE K=100 Local RMSE K=250 Global RMSEStock Mean HP KF EWMA NW Mean HP KF EWMA NW Mean HP KF EWMA NW Mean GARCH
AFX.DE 3.5392 3.7663 3.5415 3.7384 3.6523 3.4838 3.7516 3.4851 3.6194 3.5302 3.4280 3.7157 3.4286 3.5625 3.4708 3.4199 3.5919AIXA.DE 4.6198 4.9326 4.6219 4.7769 4.7389 4.5902 4.9422 4.5907 4.6624 4.6774 4.3861 4.7538 4.3843 4.4054 4.4345 4.3785 4.4429BBZA.DE 4.6712 4.9462 4.6755 4.7593 4.7096 4.5841 4.8672 4.5866 4.6170 4.6296 4.5958 4.8777 4.5948 4.5968 4.5990 4.5854 4.6865BC8.DE 2.8172 3.0101 2.8214 3.0115 2.9472 2.7922 3.0140 2.7936 2.9151 2.9058 2.6558 2.8924 2.6562 2.6881 2.7549 2.6505 2.6501CGY.DE 7.2013 7.6144 7.2032 7.5599 7.6277 7.3208 7.7899 7.3197 7.5549 7.7036 7.7666 8.2997 7.7654 7.8468 8.1310 7.7424 8.2534CTN.DE 5.0805 5.4617 5.0879 5.5148 5.2485 4.8868 5.2995 4.8854 4.9995 5.0194 5.0481 5.5502 5.0476 5.0888 5.0924 5.0285 5.1543DRI.DE 3.6266 3.8675 3.6306 3.7099 3.7179 3.5097 3.7694 3.5097 3.5925 3.5519 3.1912 3.4277 3.1871 3.2270 3.2174 3.1777 3.2688DRW3.DE 2.8466 3.0389 2.8492 3.0039 2.9258 2.6791 2.9008 2.6813 2.7397 2.7061 2.6913 2.9258 2.6907 2.7085 2.7076 2.6847 2.6873EVT.DE 3.4322 3.6369 3.4317 3.5959 3.5725 3.2702 3.5248 3.2720 3.3205 3.3922 3.2622 3.5337 3.2610 3.3091 3.3511 3.2538 3.2529FNTN.DE 5.5412 5.9509 5.5482 5.9630 5.7589 5.4745 5.9207 5.4782 5.8442 5.7662 5.4692 5.9375 5.4685 5.8108 5.8466 5.4528 5.7347JEN.DE 2.7575 2.9205 2.7589 2.8861 2.8635 2.7181 2.9183 2.7194 2.7696 2.8118 2.7231 2.9449 2.7242 2.7606 2.7917 2.7166 2.7159KBC.DE 2.9360 3.1138 2.9411 3.2395 2.9958 2.7291 2.9505 2.7307 2.9295 2.7701 2.5774 2.8058 2.5777 2.6030 2.6047 2.5724 2.6207M5Z.DE 5.1071 5.4400 5.1168 5.4704 5.3316 5.2502 5.6301 5.2523 5.4339 5.4014 5.4288 5.8260 5.4252 5.5073 5.6332 5.4138 5.6080MDG.DE 4.8674 5.1877 4.8710 5.0715 5.0104 4.7738 5.1524 4.7755 4.8935 4.8820 4.4240 4.7961 4.4242 4.4710 4.5530 4.4105 4.6041MOR.DE 4.6842 4.9878 4.6837 5.0227 4.8687 4.5805 4.9435 4.5824 4.7112 4.8627 4.4996 4.8871 4.5009 4.5485 4.8025 4.4944 4.5872NDX1.DE 4.3295 4.5616 4.3279 4.4577 4.3959 4.3015 4.5949 4.3030 4.3898 4.3392 4.3375 4.6633 4.3384 4.3949 4.4277 4.3325 4.7085PFV.DE 2.3376 2.4969 2.3407 2.4623 2.4264 2.1732 2.3543 2.1752 2.2326 2.2360 2.1479 2.3406 2.1484 2.1622 2.1759 2.1421 2.1461PS4.DE 4.0892 4.4007 4.0971 4.3314 4.2685 4.0696 4.4090 4.0706 4.1532 4.1537 4.0647 4.4295 4.0653 4.1081 4.1169 4.0533 4.1565QCE.DE 5.1776 5.5275 5.1838 5.4138 5.3482 5.1327 5.5390 5.1374 5.2167 5.2387 4.8880 5.3208 4.8884 4.9715 5.0369 4.8774 5.1034QSC.DE 4.3442 4.6239 4.3468 4.5156 4.4227 4.3107 4.6388 4.3115 4.3920 4.4053 4.0105 4.3351 4.0102 4.0287 4.0510 4.0061 4.0060R8R.DE 6.2215 6.6091 6.2254 6.4437 6.2776 6.3501 6.8233 6.3545 6.3954 6.4492 6.9128 7.4175 6.9071 6.9379 6.9585 6.8922 7.4137RSI.DE 3.5835 3.8349 3.5885 3.7010 3.6512 3.5626 3.8534 3.5658 3.6170 3.6170 3.4245 3.7117 3.4256 3.4372 3.4454 3.4184 3.5774S92.DE 4.5862 4.8756 4.5886 4.7203 4.7301 4.2304 4.5832 4.2351 4.3540 4.3338 3.5674 3.8756 3.5677 3.6030 3.7022 3.5636 3.5850SM7.DE 3.7562 3.9704 3.7621 3.9305 3.8522 3.8345 4.1042 3.8389 3.8743 3.9150 4.0998 4.3857 4.0986 4.1410 4.2001 4.0897 4.0941SOW.DE 2.7794 2.9808 2.7846 2.8927 2.8314 2.7576 2.9917 2.7591 2.8119 2.7867 2.7379 2.9998 2.7389 2.7693 2.7667 2.7333 2.7340SWV.DE 4.8146 5.1565 4.8220 5.0124 5.0212 4.6755 5.0483 4.6786 4.7809 4.6847 4.1787 4.5257 4.1804 4.2282 4.3159 4.1842 4.2523UTDI.DE 2.8826 3.0855 2.8876 3.0117 2.9396 2.8290 3.0604 2.8305 2.8724 2.8469 2.8236 3.0625 2.8231 2.8585 2.8493 2.8158 2.8169WDI.DE 4.1353 4.4299 4.1420 4.3944 4.2813 4.0102 4.3640 4.0136 4.0806 4.1155 3.7561 4.1044 3.7565 3.8441 3.7764 3.7467 3.7937
27
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29
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Pankratz, Giselher
362
2004 Möglichkeiten der Integration eines Zeitmanagements in das Blueprinting von Dienstleistungsprozessen
Fließ, Sabine Lasshof, Britta Meckel, Monika
363
2004 Controlling im Stadtmarketing - Eine Analyse des Hagener Schaufensterwettbewerbs 2003
Fließ, Sabine Wittko, Ole
364 2004
Ein Tabu Search-Verfahren zur Lösung des Timetabling-Problems an deutschen Grundschulen
Desef, Thorsten Bortfeldt, Andreas Gehring, Hermann
365
2004 Die Bedeutung von Informationen, Garantien und Reputation bei integrativer Leistungserstellung
Prechtl, Anja Völker-Albert, Jan-Hendrik
366
2004 The Influence of Control Systems on Innovation: An empirical Investigation
Littkemann, Jörn Derfuß, Klaus
367
2004 Permit Trading and Stability of International Climate Agreements
Altamirano-Cabrera, Juan-Carlos Finus, Michael
368
2004 Zeitdiskrete vs. zeitstetige Modellierung von Preismechanismen zur Regulierung von Angebots- und Nachfragemengen
Mazzoni, Thomas
369
2004 Marktversagen auf dem Softwaremarkt? Zur Förderung der quelloffenen Softwareentwicklung
Christian Maaß Ewald Scherm
370
2004 Die Konzentration der Forschung als Weg in die Sackgasse? Neo-Institutionalistische Überlegungen zu 10 Jahren Anreizsystemforschung in der deutschsprachigen Betriebswirtschaftslehre
Süß, Stefan Muth, Insa
371
2004 Economic Analysis of Cross-Border Legal Uncertainty: the Example of the European Union
Wagner, Helmut
372
2004 Pension Reforms in the New EU Member States Wagner, Helmut
373
2005 Die Bundestrainer-Scorecard Zur Anwendbarkeit des Balanced Scorecard Konzepts in nicht-ökonomischen Fragestellungen
Eisenberg, David Schulte, Klaus
374
2005 Monetary Policy and Asset Prices: More Bad News for ‚Benign Neglect“
Berger, Wolfram Kißmer, Friedrich Wagner, Helmut
375
2005 Zeitstetige Modellbildung am Beispiel einer volkswirtschaftlichen Produktionsstruktur
Mazzoni, Thomas
376
2005 Economic Valuation of the Environment Endres, Alfred
377
2005 Netzwerkökonomik – Eine vernachlässigte theoretische Perspektive in der Strategie-/Marketingforschung?
Maaß, Christian Scherm, Ewald
378
2005 Diversity management`s diffusion and design: a study of German DAX-companies and Top-50-U.S.-companies in Germany
Süß, Stefan Kleiner, Markus
379
2005 Fiscal Issues in the New EU Member Countries – Prospects and Challenges
Wagner, Helmut
380
2005 Mobile Learning – Modetrend oder wesentlicher Bestandteil lebenslangen Lernens?
Kuszpa, Maciej Scherm, Ewald
381
2005 Zur Berücksichtigung von Unsicherheit in der Theorie der Zentralbankpolitik
Wagner, Helmut
382
2006 Effort, Trade, and Unemployment Altenburg, Lutz Brenken, Anke
383 2006 Do Abatement Quotas Lead to More Successful Climate Coalitions?
Altamirano-Cabrera, Juan-Carlos Finus, Michael Dellink, Rob
384 2006 Continuous-Discrete Unscented Kalman Filtering
Singer, Hermann
385
2006 Informationsbewertung im Spannungsfeld zwischen der Informationstheorie und der Betriebswirtschaftslehre
Reucher, Elmar
386 2006
The Rate Structure Pattern: An Analysis Pattern for the Flexible Parameterization of Charges, Fees and Prices
Pleß, Volker Pankratz, Giselher Bortfeldt, Andreas
387a 2006 On the Relevance of Technical Inefficiencies
Fandel, Günter Lorth, Michael
387b 2006 Open Source und Wettbewerbsstrategie - Theoretische Fundierung und Gestaltung
Maaß, Christian
388
2006 Induktives Lernen bei unvollständigen Daten unter Wahrung des Entropieprinzips
Rödder, Wilhelm
389 2006
Banken als Einrichtungen zur Risikotransformation Bitz, Michael
390 2006 Kapitalerhöhungen börsennotierter Gesellschaften ohne börslichen Bezugsrechtshandel
Terstege, Udo Stark, Gunnar
391
2006 Generalized Gauss-Hermite Filtering Singer, Hermann
392
2006 Das Göteborg Protokoll zur Bekämpfung grenzüberschreitender Luftschadstoffe in Europa: Eine ökonomische und spieltheoretische Evaluierung
Ansel, Wolfgang Finus, Michael
393
2006 Why do monetary policymakers lean with the wind during asset price booms?
Berger, Wolfram Kißmer, Friedrich
394
2006 On Supply Functions of Multi-product Firms with Linear Technologies
Steinrücke, Martin
395
2006 Ein Überblick zur Theorie der Produktionsplanung Steinrücke, Martin
396
2006 Parallel greedy algorithms for packing unequal circles into a strip or a rectangle
Timo Kubach, Bortfeldt, Andreas Gehring, Hermann
397 2006 C&P Software for a cutting problem of a German wood panel manufacturer – a case study
Papke, Tracy Bortfeldt, Andreas Gehring, Hermann
398
2006 Nonlinear Continuous Time Modeling Approaches in Panel Research
Singer, Hermann
399
2006 Auftragsterminierung und Materialflussplanung bei Werkstattfertigung
Steinrücke, Martin
400
2006 Import-Penetration und der Kollaps der Phillips-Kurve Mazzoni, Thomas
401
2006 Bayesian Estimation of Volatility with Moment-Based Nonlinear Stochastic Filters
Grothe, Oliver Singer, Hermann
402
2006 Generalized Gauss-H ermite Filtering for Multivariate Diffusion Processes
Singer, Hermann
403
2007 A Note on Nash Equilibrium in Soccer
Sonnabend, Hendrik Schlepütz, Volker
404
2007 Der Einfluss von Schaufenstern auf die Erwartungen der Konsumenten - eine explorative Studie
Fließ, Sabine Kudermann, Sarah Trell, Esther
405
2007 Die psychologische Beziehung zwischen Unternehmen und freien Mitarbeitern: Eine empirische Untersuchung des Commitments und der arbeitsbezogenen Erwartungen von IT-Freelancern
Süß, Stefan
406 2007 An Alternative Derivation of the Black-Scholes Formula
Zucker, Max Singer, Hermann
407
2007 Computational Aspects of Continuous-Discrete Extended Kalman-Filtering
Mazzoni, Thomas
408 2007 Web 2.0 als Mythos, Symbol und Erwartung
Maaß, Christian Pietsch, Gotthard
409
2007 „Beyond Balanced Growth“: Some Further Results Stijepic, Denis Wagner, Helmut
410
2007 Herausforderungen der Globalisierung für die Entwicklungsländer: Unsicherheit und geldpolitisches Risikomanagement
Wagner, Helmut
411 2007 Graphical Analysis in the New Neoclassical Synthesis
Giese, Guido Wagner, Helmut
412
2007 Monetary Policy and Asset Prices: The Impact of Globalization on Monetary Policy Trade-Offs
Berger, Wolfram Kißmer, Friedrich Knütter, Rolf
413
2007 Entropiebasiertes Data Mining im Produktdesign Rudolph, Sandra Rödder, Wilhelm
414
2007 Game Theoretic Research on the Design of International Environmental Agreements: Insights, Critical Remarks and Future Challenges
Finus, Michael
415 2007 Qualitätsmanagement in Unternehmenskooperationen - Steuerungsmöglichkeiten und Datenintegrationsprobleme
Meschke, Martina
416
2007 Modernisierung im Bund: Akteursanalyse hat Vorrang Pietsch, Gotthard Jamin, Leander
417
2007 Inducing Technical Change by Standard Oriented Evirnonmental Policy: The Role of Information
Endres, Alfred Bertram, Regina Rundshagen, Bianca
418
2007 Der Einfluss des Kontextes auf die Phasen einer SAP-Systemimplementierung
Littkemann, Jörn Eisenberg, David Kuboth, Meike
419
2007 Endogenous in Uncertainty and optimal Monetary Policy
Giese, Guido Wagner, Helmut
420
2008 Stockkeeping and controlling under game theoretic aspects Fandel, Günter Trockel, Jan
421
2008 On Overdissipation of Rents in Contests with Endogenous Intrinsic Motivation
Schlepütz, Volker
422 2008 Maximum Entropy Inference for Mixed Continuous-Discrete Variables
Singer, Hermann
423 2008 Eine Heuristik für das mehrdimensionale Bin Packing Problem
Mack, Daniel Bortfeldt, Andreas
424
2008 Expected A Posteriori Estimation in Financial Applications Mazzoni, Thomas
425
2008 A Genetic Algorithm for the Two-Dimensional Knapsack Problem with Rectangular Pieces
Bortfeldt, Andreas Winter, Tobias
426
2008 A Tree Search Algorithm for Solving the Container Loading Problem
Fanslau, Tobias Bortfeldt, Andreas
427
2008 Dynamic Effects of Offshoring
Stijepic, Denis Wagner, Helmut
428
2008 Der Einfluss von Kostenabweichungen auf das Nash-Gleichgewicht in einem nicht-kooperativen Disponenten-Controller-Spiel
Fandel, Günter Trockel, Jan
429
2008 Fast Analytic Option Valuation with GARCH Mazzoni, Thomas
430
2008 Conditional Gauss-Hermite Filtering with Application to Volatility Estimation
Singer, Hermann
431 2008 Web 2.0 auf dem Prüfstand: Zur Bewertung von Internet-Unternehmen
Christian Maaß Gotthard Pietsch
432
2008 Zentralbank-Kommunikation und Finanzstabilität – Eine Bestandsaufnahme
Knütter, Rolf Mohr, Benjamin
433
2008 Globalization and Asset Prices: Which Trade-Offs Do Central Banks Face in Small Open Economies?
Knütter, Rolf Wagner, Helmut
434 2008 International Policy Coordination and Simple Monetary Policy Rules
Berger, Wolfram Wagner, Helmut
435
2009 Matchingprozesse auf beruflichen Teilarbeitsmärkten Stops, Michael Mazzoni, Thomas
436 2009 Wayfindingprozesse in Parksituationen - eine empirische Analyse
Fließ, Sabine Tetzner, Stefan
437 2009 ENTROPY-DRIVEN PORTFOLIO SELECTION a downside and upside risk framework
Rödder, Wilhelm Gartner, Ivan Ricardo Rudolph, Sandra
438 2009 Consulting Incentives in Contests Schlepütz, Volker
439 2009 A Genetic Algorithm for a Bi-Objective Winner-Determination Problem in a Transportation-Procurement Auction"
Buer, Tobias Pankratz, Giselher
440
2009 Parallel greedy algorithms for packing unequal spheres into a cuboidal strip or a cuboid
Kubach, Timo Bortfeldt, Andreas Tilli, Thomas Gehring, Hermann
441 2009 SEM modeling with singular moment matrices Part I: ML-Estimation of time series
Singer, Hermann
442 2009 SEM modeling with singular moment matrices Part II: ML-Estimation of sampled stochastic differential equations
Singer, Hermann
443 2009 Konsensuale Effizienzbewertung und -verbesserung – Untersuchungen mittels der Data Envelopment Analysis (DEA)
Rödder, Wilhelm Reucher, Elmar
444 2009 Legal Uncertainty – Is Hamonization of Law the Right Answer? A Short Overview
Wagner, Helmut
445
2009 Fast Continuous-Discrete DAF-Filters Mazzoni, Thomas
446 2010 Quantitative Evaluierung von Multi-Level Marketingsystemen
Lorenz, Marina Mazzoni, Thomas
447 2010 Quasi-Continuous Maximum Entropy Distribution Approximation with Kernel Density
Mazzoni, Thomas Reucher, Elmar
448 2010 Solving a Bi-Objective Winner Determination Problem in a Transportation Procurement Auction
Buer, Tobias Pankratz, Giselher
449 2010 Are Short Term Stock Asset Returns Predictable? An Extended Empirical Analysis
Mazzoni, Thomas