EWMA Durchschnitt
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"How to calculate the exponentially weighted moving ave Simple % Continuously Return Compounded Return Population variance Sample variance Simple variance: 1. Assume average daily return 2. Replace m-1 with m i i i1 S u ln S i i1 i i1 S S u S m 2 2 n n i i1 1 (u u) m 1 2 n variance rate perday m m ostrecentm observations u the m ean/average ofalldaily returns (u m 2 n i1 1 m m 2 2 n n i i1 1 (u u) m
Transcript of EWMA Durchschnitt
"How to calculate the exponentially weighted moving average (EWMA)"Simple % ContinuouslyReturn CompoundedReturnPopulation varianceSample varianceSimple variance:1. Assume average daily return is 02. Replace m-1 with m| |= |\ .iii 1Su lnS=i i 1ii 1S SuSo== m2 2n n ii 11(u u )m 12ni variance rat e per daymmostrecentm observat ionsut he mean/ average of all daily ret urns (u )o ===m2 2n n ii 11umo==m2 2n n ii 11(u u )mo== "How to calculate the exponentially weighted moving average (EWMA)"Simple variance:1. Assume average daily return is 0| |= |\ .iii 1Su lnS2ni variance rat e per daymmostrecentm observat ionsut he mean/ average of all daily ret urns (u )o ===m2 2n n ii 11umo==Exponentially Weighted Moving Average (EWMA)Simple % given that lambda is less than oneReturnVariance Weight , day 1ContinuouslyCompounded Weight, day 2ReturnWeight, day 3Simple Weight, day 4VarianceWeight, day 5(Generic)WeightedVariancealphas sum to one(they are weights)weights decline exponentiallym2 2n n ii 11umo==2 2 2n n 1 n 1(1 )u o o = + | |= |\ .iii 1Su lnS=i i 1ii 1S SuSm2 2n i n ii 1u o o==Exponentially Weighted Moving Average (EWMA)given that lambda is less than oneVariance Weight , day 1Weight, day 2Weight, day 3Weight, day 4Weight, day 5weights decline exponentially 0(1 ) 2 2 2n n 1 n 1(1 )u o o = + 1(1 ) 2(1 ) 3(1 ) 4(1 ) Google (GOOG) - Daily Stock Prices Lambda () = Adj. PeriodPrice Return Return^2 Equal WeightDate Close( ) ( 2 )Weight( o )25-Aug-06 $373.26 -0.126% 0.00016% 0.196% 6.00%24-Aug-06 373.73 0.080% 0.00006% 0.196% 5.64%23-Aug-06 373.43 -1.293% 0.01672% 0.196% 5.30%22-Aug-06 378.29 0.262% 0.00069% 0.196% 4.98%21-Aug-06 377.3 -1.593% 0.02539% 0.196% 4.68%2 Years (500+ days) collapsed (Data>Group) below18-Aug-06 383.36 -0.634% 0.00403% 0.196% 4.40%17-Aug-06 385.8 -0.496% 0.00246% 0.196% 4.14%16-Aug-06 387.72 1.756% 0.03085% 0.196% 3.89%15-Aug-06 380.97 3.076% 0.09461% 0.196% 3.66%14-Aug-06 369.43 0.252% 0.00064% 0.196% 3.44%11-Aug-06 368.5 -1.535% 0.02356% 0.196% 3.23%10-Aug-06 374.2 -0.730% 0.00532% 0.196% 3.04%9-Aug-06 376.94 -1.071% 0.01148% 0.196% 2.86%8-Aug-06 381 0.804% 0.00646% 0.196% 2.68%7-Aug-06 377.95 1.091% 0.01190% 0.196% 2.52%4-Aug-06 373.85 -0.411% 0.00169% 0.196% 2.37%3-Aug-06 375.39 2.198% 0.04830% 0.196% 2.23%2-Aug-06 367.23 -2.230% 0.04971% 0.196% 2.10%1-Aug-06 375.51 -2.911% 0.08471% 0.196% 1.97%31-Jul-06 386.6 -0.392% 0.00154% 0.196% 1.85%28-Jul-06 388.12 1.485% 0.02204% 0.196% 1.74%27-Jul-06 382.4 -0.807% 0.00652% 0.196% 1.64%26-Jul-06 385.5 -0.996% 0.00993% 0.196% 1.54%25-Jul-06 389.36 -0.395% 0.00156% 0.196% 1.45%24-Jul-06 390.9 0.202% 0.00041% 0.196% 1.36%21-Jul-06 390.11 0.769% 0.00592% 0.196% 1.28%20-Jul-06 387.12 -3.023% 0.09137% 0.196% 1.20%19-Jul-06 399 -1.010% 0.01020% 0.196% 1.13%18-Jul-06 403.05 -1.194% 0.01425% 0.196% 1.06%17-Jul-06 407.89 1.082% 0.01171% 0.196% 1.00%14-Jul-06 403.5 -1.312% 0.01722% 0.196% 0.94%13-Jul-06 408.83 -2.039% 0.04156% 0.196% 0.88%12-Jul-06 417.25 -1.737% 0.03016% 0.196% 0.83%11-Jul-06 424.56 1.509% 0.02278% 0.196% 0.78%10-Jul-06 418.2 -0.537% 0.00288% 0.196% 0.73%7-Jul-06 420.45 -0.650% 0.00422% 0.196% 0.69%6-Jul-06 423.19 0.410% 0.00168% 0.196% 0.65%5-Jul-06 421.46 -0.412% 0.00170% 0.196% 0.61%3-Jul-06 423.2 0.919% 0.00844% 0.196% 0.57%30-Jun-06 419.33 0.363% 0.00132% 0.196% 0.54%29-Jun-06 417.81 2.840% 0.08067% 0.196% 0.50%28-Jun-06 406.11 0.938% 0.00879% 0.196% 0.47%27-Jun-06 402.32 -0.471% 0.00222% 0.196% 0.45%26-Jun-06 404.22 -0.158% 0.00025% 0.196% 0.42%23-Jun-06 404.86 1.220% 0.01489% 0.196% 0.39%22-Jun-06 399.95 -0.544% 0.00295% 0.196% 0.37%21-Jun-06 402.13 3.791% 0.14373% 0.196% 0.35%20-Jun-06 387.17 -0.250% 0.00063% 0.196% 0.33%19-Jun-06 388.14 -0.657% 0.00432% 0.196% 0.31%16-Jun-06 390.7 -0.077% 0.00006% 0.196% 0.29%15-Jun-06 391 1.705% 0.02907% 0.196% 0.27%14-Jun-06 384.39 -0.553% 0.00305% 0.196% 0.26%13-Jun-06 386.52 1.297% 0.01682% 0.196% 0.24%12-Jun-06 381.54 -1.310% 0.01715% 0.196% 0.23%9-Jun-06 386.57 -1.726% 0.02979% 0.196% 0.21%8-Jun-06 393.3 1.741% 0.03033% 0.196% 0.20%7-Jun-06 386.51 -0.896% 0.00803% 0.196% 0.19%6-Jun-06 389.99 4.069% 0.16556% 0.196% 0.18%5-Jun-06 374.44 -1.326% 0.01760% 0.196% 0.17%2-Jun-06 379.44 -0.835% 0.00697% 0.196% 0.16%1-Jun-06 382.62 2.863% 0.08198% 0.196% 0.15%31-May-06 371.82 -0.032% 0.00001% 0.196% 0.14%30-May-06 371.94 -2.499% 0.06243% 0.196% 0.13%26-May-06 381.35 -0.429% 0.00184% 0.196% 0.12%25-May-06 382.99 0.455% 0.00207% 0.196% 0.11%24-May-06 381.25 1.498% 0.02245% 0.196% 0.11%23-May-06 375.58 1.240% 0.01539% 0.196% 0.10%22-May-06 370.95 0.251% 0.00063% 0.196% 0.09%19-May-06 370.02 -0.262% 0.00069% 0.196% 0.09%18-May-06 370.99 -0.942% 0.00887% 0.196% 0.08%17-May-06 374.5 0.858% 0.00736% 0.196% 0.08%16-May-06 371.3 -1.311% 0.01719% 0.196% 0.07%15-May-06 376.2 0.552% 0.00304% 0.196% 0.07%12-May-06 374.13 -3.382% 0.11439% 0.196% 0.07%11-May-06 387 -4.046% 0.16372% 0.196% 0.06%10-May-06 402.98 -1.434% 0.02056% 0.196% 0.06%9-May-06 408.8 3.490% 0.12178% 0.196% 0.05%8-May-06 394.78 0.122% 0.00015% 0.196% 0.05%5-May-06 394.3 -0.114% 0.00013% 0.196% 0.05%4-May-06 394.75 0.147% 0.00022% 0.196% 0.05%3-May-06 394.17 -0.160% 0.00026% 0.196% 0.04%2-May-06 394.8 -1.033% 0.01067% 0.196% 0.04%1-May-06 398.9 -4.663% 0.21741% 0.196% 0.04%28-Apr-06 417.94 -0.499% 0.00249% 0.196% 0.04%27-Apr-06 420.03 -1.404% 0.01972% 0.196% 0.03%26-Apr-06 425.97 -0.279% 0.00078% 0.196% 0.03%25-Apr-06 427.16 -3.075% 0.09457% 0.196% 0.03%24-Apr-06 440.5 0.775% 0.00600% 0.196% 0.03%21-Apr-06 437.1 5.188% 0.26919% 0.196% 0.03%20-Apr-06 415 1.090% 0.01189% 0.196% 0.02%19-Apr-06 410.5 1.537% 0.02361% 0.196% 0.02%18-Apr-06 404.24 -0.636% 0.00405% 0.196% 0.02%17-Apr-06 406.82 1.152% 0.01327% 0.196% 0.02%13-Apr-06 402.16 -1.674% 0.02803% 0.196% 0.02%12-Apr-06 408.95 -0.173% 0.00030% 0.196% 0.02%11-Apr-06 409.66 -1.627% 0.02647% 0.196% 0.02%10-Apr-06 416.38 2.485% 0.06176% 0.196% 0.02%7-Apr-06 406.16 -1.228% 0.01509% 0.196% 0.01%6-Apr-06 411.18 0.779% 0.00607% 0.196% 0.01%5-Apr-06 407.99 0.899% 0.00808% 0.196% 0.01%4-Apr-06 404.34 3.688% 0.13601% 0.196% 0.01%3-Apr-06 389.7 -0.077% 0.00006% 0.196% 0.01%31-Mar-06 390 0.401% 0.00161% 0.196% 0.01%30-Mar-06 388.44 -1.670% 0.02788% 0.196% 0.01%29-Mar-06 394.98 4.606% 0.21215% 0.196% 0.01%28-Mar-06 377.2 2.011% 0.04044% 0.196% 0.01%27-Mar-06 369.69 1.058% 0.01119% 0.196% 0.01%24-Mar-06 365.8 6.760% 0.45694% 0.196% 0.01%23-Mar-06 341.89 0.490% 0.00240% 0.196% 0.01%22-Mar-06 340.22 0.088% 0.00008% 0.196% 0.01%21-Mar-06 339.92 -2.404% 0.05778% 0.196% 0.01%20-Mar-06 348.19 2.442% 0.05964% 0.196% 0.01%17-Mar-06 339.79 0.301% 0.00090% 0.196% 0.01%16-Mar-06 338.77 -1.677% 0.02813% 0.196% 0.01%15-Mar-06 344.5 -1.915% 0.03666% 0.196% 0.01%14-Mar-06 351.16 4.098% 0.16794% 0.196% 0.00%13-Mar-06 337.06 -0.130% 0.00017% 0.196% 0.00%10-Mar-06 337.5 -1.616% 0.02613% 0.196% 0.00%9-Mar-06 343 -3.123% 0.09752% 0.196% 0.00%8-Mar-06 353.88 -2.943% 0.08662% 0.196% 0.00%7-Mar-06 364.45 -0.997% 0.00993% 0.196% 0.00%6-Mar-06 368.1 -2.702% 0.07298% 0.196% 0.00%3-Mar-06 378.18 0.459% 0.00210% 0.196% 0.00%2-Mar-06 376.45 3.144% 0.09882% 0.196% 0.00%1-Mar-06 364.8 0.599% 0.00359% 0.196% 0.00%28-Feb-06 362.62 -7.377% 0.54413% 0.196% 0.00%27-Feb-06 390.38 3.381% 0.11435% 0.196% 0.00%24-Feb-06 377.4 -0.177% 0.00031% 0.196% 0.00%23-Feb-06 378.07 3.384% 0.11452% 0.196% 0.00%22-Feb-06 365.49 -0.301% 0.00090% 0.196% 0.00%21-Feb-06 366.59 -0.587% 0.00345% 0.196% 0.00%17-Feb-06 368.75 0.623% 0.00388% 0.196% 0.00%16-Feb-06 366.46 6.797% 0.46197% 0.196% 0.00%15-Feb-06 342.38 -0.274% 0.00075% 0.196% 0.00%14-Feb-06 343.32 -0.691% 0.00477% 0.196% 0.00%13-Feb-06 345.7 -4.776% 0.22807% 0.196% 0.00%10-Feb-06 362.61 1.065% 0.01133% 0.196% 0.00%9-Feb-06 358.77 -2.833% 0.08027% 0.196% 0.00%8-Feb-06 369.08 0.315% 0.00099% 0.196% 0.00%7-Feb-06 367.92 -4.564% 0.20828% 0.196% 0.00%6-Feb-06 385.1 0.926% 0.00858% 0.196% 0.00%3-Feb-06 381.55 -3.727% 0.13893% 0.196% 0.00%2-Feb-06 396.04 -1.439% 0.02071% 0.196% 0.00%1-Feb-06 401.78 -7.405% 0.54830% 0.196% 0.00%31-Jan-06 432.66 1.359% 0.01847% 0.196% 0.00%30-Jan-06 426.82 -1.551% 0.02404% 0.196% 0.00%27-Jan-06 433.49 -0.180% 0.00032% 0.196% 0.00%26-Jan-06 434.27 0.293% 0.00086% 0.196% 0.00%25-Jan-06 433 -2.290% 0.05244% 0.196% 0.00%24-Jan-06 443.03 3.568% 0.12733% 0.196% 0.00%23-Jan-06 427.5 6.784% 0.46024% 0.196% 0.00%20-Jan-06 399.46 -8.856% 0.78429% 0.196% 0.00%19-Jan-06 436.45 -1.920% 0.03686% 0.196% 0.00%18-Jan-06 444.91 -4.869% 0.23710% 0.196% 0.00%17-Jan-06 467.11 0.184% 0.00034% 0.196% 0.00%13-Jan-06 466.25 0.564% 0.00318% 0.196% 0.00%12-Jan-06 463.63 -1.711% 0.02927% 0.196% 0.00%11-Jan-06 471.63 0.397% 0.00158% 0.196% 0.00%10-Jan-06 469.76 0.611% 0.00373% 0.196% 0.00%9-Jan-06 466.9 0.266% 0.00071% 0.196% 0.00%6-Jan-06 465.66 3.146% 0.09895% 0.196% 0.00%5-Jan-06 451.24 1.339% 0.01792% 0.196% 0.00%4-Jan-06 445.24 2.274% 0.05171% 0.196% 0.00%3-Jan-06 435.23 4.793% 0.22976% 0.196% 0.00%30-Dec-05 414.86 -1.267% 0.01605% 0.196% 0.00%29-Dec-05 420.15 -1.545% 0.02386% 0.196% 0.00%28-Dec-05 426.69 0.482% 0.00232% 0.196% 0.00%27-Dec-05 424.64 -1.470% 0.02162% 0.196% 0.00%23-Dec-05 430.93 -0.257% 0.00066% 0.196% 0.00%22-Dec-05 432.04 1.330% 0.01770% 0.196% 0.00%21-Dec-05 426.33 -0.797% 0.00635% 0.196% 0.00%20-Dec-05 429.74 1.203% 0.01448% 0.196% 0.00%19-Dec-05 424.6 -1.299% 0.01686% 0.196% 0.00%16-Dec-05 430.15 1.783% 0.03178% 0.196% 0.00%15-Dec-05 422.55 0.853% 0.00728% 0.196% 0.00%14-Dec-05 418.96 0.351% 0.00124% 0.196% 0.00%13-Dec-05 417.49 1.176% 0.01382% 0.196% 0.00%12-Dec-05 412.61 0.830% 0.00689% 0.196% 0.00%9-Dec-05 409.2 -0.354% 0.00125% 0.196% 0.00%8-Dec-05 410.65 1.578% 0.02491% 0.196% 0.00%7-Dec-05 404.22 -0.079% 0.00006% 0.196% 0.00%6-Dec-05 404.54 -0.323% 0.00105% 0.196% 0.00%5-Dec-05 405.85 -2.878% 0.08283% 0.196% 0.00%2-Dec-05 417.7 0.868% 0.00753% 0.196% 0.00%1-Dec-05 414.09 2.242% 0.05026% 0.196% 0.00%30-Nov-05 404.91 0.339% 0.00115% 0.196% 0.00%29-Nov-05 403.54 -4.823% 0.23262% 0.196% 0.00%28-Nov-05 423.48 -1.206% 0.01456% 0.196% 0.00%25-Nov-05 428.62 1.353% 0.01830% 0.196% 0.00%23-Nov-05 422.86 1.523% 0.02319% 0.196% 0.00%22-Nov-05 416.47 1.722% 0.02965% 0.196% 0.00%21-Nov-05 409.36 2.261% 0.05110% 0.196% 0.00%18-Nov-05 400.21 -0.806% 0.00650% 0.196% 0.00%17-Nov-05 403.45 1.322% 0.01749% 0.196% 0.00%16-Nov-05 398.15 1.353% 0.01830% 0.196% 0.00%15-Nov-05 392.8 -1.056% 0.01115% 0.196% 0.00%14-Nov-05 396.97 1.669% 0.02785% 0.196% 0.00%11-Nov-05 390.4 -0.179% 0.00032% 0.196% 0.00%10-Nov-05 391.1 3.103% 0.09629% 0.196% 0.00%9-Nov-05 379.15 -2.796% 0.07817% 0.196% 0.00%8-Nov-05 389.9 -1.307% 0.01709% 0.196% 0.00%7-Nov-05 395.03 1.171% 0.01372% 0.196% 0.00%4-Nov-05 390.43 1.154% 0.01332% 0.196% 0.00%3-Nov-05 385.95 1.638% 0.02683% 0.196% 0.00%2-Nov-05 379.68 0.079% 0.00006% 0.196% 0.00%1-Nov-05 379.38 1.927% 0.03713% 0.196% 0.00%31-Oct-05 372.14 3.826% 0.14640% 0.196% 0.00%28-Oct-05 358.17 1.437% 0.02065% 0.196% 0.00%27-Oct-05 353.06 -0.672% 0.00451% 0.196% 0.00%26-Oct-05 355.44 2.429% 0.05901% 0.196% 0.00%25-Oct-05 346.91 -0.500% 0.00250% 0.196% 0.00%24-Oct-05 348.65 2.542% 0.06460% 0.196% 0.00%21-Oct-05 339.9 11.426% 1.30551% 0.196% 0.00%20-Oct-05 303.2 -1.798% 0.03232% 0.196% 0.00%19-Oct-05 308.7 1.771% 0.03138% 0.196% 0.00%18-Oct-05 303.28 -0.566% 0.00320% 0.196% 0.00%17-Oct-05 305 2.948% 0.08690% 0.196% 0.00%14-Oct-05 296.14 -0.438% 0.00192% 0.196% 0.00%13-Oct-05 297.44 -1.180% 0.01392% 0.196% 0.00%12-Oct-05 300.97 -1.690% 0.02857% 0.196% 0.00%11-Oct-05 306.1 -1.476% 0.02177% 0.196% 0.00%10-Oct-05 310.65 -0.750% 0.00563% 0.196% 0.00%7-Oct-05 312.99 0.077% 0.00006% 0.196% 0.00%6-Oct-05 312.75 0.654% 0.00428% 0.196% 0.00%5-Oct-05 310.71 -0.093% 0.00009% 0.196% 0.00%4-Oct-05 311 -2.439% 0.05951% 0.196% 0.00%3-Oct-05 318.68 0.699% 0.00489% 0.196% 0.00%30-Sep-05 316.46 2.185% 0.04775% 0.196% 0.00%29-Sep-05 309.62 1.176% 0.01383% 0.196% 0.00%28-Sep-05 306 -2.562% 0.06562% 0.196% 0.00%27-Sep-05 313.94 -0.108% 0.00012% 0.196% 0.00%26-Sep-05 314.28 -0.343% 0.00118% 0.196% 0.00%23-Sep-05 315.36 1.273% 0.01621% 0.196% 0.00%22-Sep-05 311.37 -0.170% 0.00029% 0.196% 0.00%21-Sep-05 311.9 1.288% 0.01658% 0.196% 0.00%20-Sep-05 307.91 1.347% 0.01815% 0.196% 0.00%19-Sep-05 303.79 1.189% 0.01413% 0.196% 0.00%16-Sep-05 300.2 -0.803% 0.00645% 0.196% 0.00%15-Sep-05 302.62 -0.125% 0.00016% 0.196% 0.00%14-Sep-05 303 -2.824% 0.07977% 0.196% 0.00%13-Sep-05 311.68 0.624% 0.00390% 0.196% 0.00%12-Sep-05 309.74 3.499% 0.12242% 0.196% 0.00%9-Sep-05 299.09 1.245% 0.01550% 0.196% 0.00%8-Sep-05 295.39 0.176% 0.00031% 0.196% 0.00%7-Sep-05 294.87 2.667% 0.07112% 0.196% 0.00%6-Sep-05 287.11 -0.466% 0.00217% 0.196% 0.00%2-Sep-05 288.45 0.766% 0.00586% 0.196% 0.00%1-Sep-05 286.25 0.087% 0.00008% 0.196% 0.00%31-Aug-05 286 -0.443% 0.00196% 0.196% 0.00%30-Aug-05 287.27 -0.410% 0.00168% 0.196% 0.00%29-Aug-05 288.45 1.703% 0.02899% 0.196% 0.00%26-Aug-05 283.58 0.350% 0.00122% 0.196% 0.00%25-Aug-05 282.59 0.007% 0.00000% 0.196% 0.00%24-Aug-05 282.57 1.064% 0.01132% 0.196% 0.00%23-Aug-05 279.58 2.012% 0.04050% 0.196% 0.00%22-Aug-05 274.01 -2.163% 0.04676% 0.196% 0.00%19-Aug-05 280 0.004% 0.00000% 0.196% 0.00%18-Aug-05 279.99 -1.809% 0.03271% 0.196% 0.00%17-Aug-05 285.1 -0.193% 0.00037% 0.196% 0.00%16-Aug-05 285.65 0.579% 0.00336% 0.196% 0.00%15-Aug-05 284 -1.994% 0.03976% 0.196% 0.00%12-Aug-05 289.72 1.976% 0.03906% 0.196% 0.00%11-Aug-05 284.05 -0.572% 0.00327% 0.196% 0.00%10-Aug-05 285.68 -2.041% 0.04165% 0.196% 0.00%9-Aug-05 291.57 0.110% 0.00012% 0.196% 0.00%8-Aug-05 291.25 -0.377% 0.00142% 0.196% 0.00%5-Aug-05 292.35 -1.824% 0.03325% 0.196% 0.00%4-Aug-05 297.73 0.145% 0.00021% 0.196% 0.00%3-Aug-05 297.3 -0.634% 0.00402% 0.196% 0.00%2-Aug-05 299.19 2.566% 0.06585% 0.196% 0.00%1-Aug-05 291.61 1.329% 0.01766% 0.196% 0.00%29-Jul-05 287.76 -1.975% 0.03901% 0.196% 0.00%28-Jul-05 293.5 -1.162% 0.01350% 0.196% 0.00%27-Jul-05 296.93 0.283% 0.00080% 0.196% 0.00%26-Jul-05 296.09 0.081% 0.00007% 0.196% 0.00%25-Jul-05 295.85 -2.190% 0.04795% 0.196% 0.00%22-Jul-05 302.4 -3.745% 0.14026% 0.196% 0.00%21-Jul-05 313.94 0.620% 0.00384% 0.196% 0.00%20-Jul-05 312 0.675% 0.00456% 0.196% 0.00%19-Jul-05 309.9 3.400% 0.11561% 0.196% 0.00%18-Jul-05 299.54 -0.549% 0.00302% 0.196% 0.00%15-Jul-05 301.19 0.100% 0.00010% 0.196% 0.00%14-Jul-05 300.89 0.677% 0.00458% 0.196% 0.00%13-Jul-05 298.86 2.398% 0.05748% 0.196% 0.00%12-Jul-05 291.78 -0.537% 0.00288% 0.196% 0.00%11-Jul-05 293.35 -0.977% 0.00954% 0.196% 0.00%8-Jul-05 296.23 0.233% 0.00054% 0.196% 0.00%7-Jul-05 295.54 1.370% 0.01876% 0.196% 0.00%6-Jul-05 291.52 -1.427% 0.02037% 0.196% 0.00%5-Jul-05 295.71 1.520% 0.02310% 0.196% 0.00%1-Jul-05 291.25 -0.991% 0.00982% 0.196% 0.00%30-Jun-05 294.15 0.487% 0.00237% 0.196% 0.00%29-Jun-05 292.72 -3.121% 0.09741% 0.196% 0.00%28-Jun-05 302 -0.693% 0.00480% 0.196% 0.00%27-Jun-05 304.1 2.278% 0.05191% 0.196% 0.00%24-Jun-05 297.25 2.569% 0.06601% 0.196% 0.00%23-Jun-05 289.71 0.142% 0.00020% 0.196% 0.00%22-Jun-05 289.3 0.506% 0.00256% 0.196% 0.00%21-Jun-05 287.84 0.397% 0.00157% 0.196% 0.00%20-Jun-05 286.7 2.258% 0.05097% 0.196% 0.00%17-Jun-05 280.3 1.026% 0.01052% 0.196% 0.00%16-Jun-05 277.44 0.956% 0.00914% 0.196% 0.00%15-Jun-05 274.8 -1.284% 0.01648% 0.196% 0.00%14-Jun-05 278.35 -1.568% 0.02460% 0.196% 0.00%13-Jun-05 282.75 0.088% 0.00008% 0.196% 0.00%10-Jun-05 282.5 -1.340% 0.01795% 0.196% 0.00%9-Jun-05 286.31 2.386% 0.05692% 0.196% 0.00%8-Jun-05 279.56 -4.737% 0.22435% 0.196% 0.00%7-Jun-05 293.12 0.747% 0.00557% 0.196% 0.00%6-Jun-05 290.94 3.740% 0.13987% 0.196% 0.00%3-Jun-05 280.26 -2.690% 0.07234% 0.196% 0.00%2-Jun-05 287.9 -0.035% 0.00001% 0.196% 0.00%1-Jun-05 288 3.797% 0.14416% 0.196% 0.00%31-May-05 277.27 4.150% 0.17219% 0.196% 0.00%27-May-05 266 2.590% 0.06706% 0.196% 0.00%26-May-05 259.2 -0.619% 0.00383% 0.196% 0.00%25-May-05 260.81 1.861% 0.03465% 0.196% 0.00%24-May-05 256 0.215% 0.00046% 0.196% 0.00%23-May-05 255.45 5.570% 0.31027% 0.196% 0.00%20-May-05 241.61 1.011% 0.01022% 0.196% 0.00%19-May-05 239.18 0.008% 0.00000% 0.196% 0.00%18-May-05 239.16 2.554% 0.06521% 0.196% 0.00%17-May-05 233.13 0.896% 0.00803% 0.196% 0.00%16-May-05 231.05 0.786% 0.00619% 0.196% 0.00%13-May-05 229.24 0.227% 0.00052% 0.196% 0.00%12-May-05 228.72 -1.117% 0.01249% 0.196% 0.00%11-May-05 231.29 1.520% 0.02312% 0.196% 0.00%10-May-05 227.8 0.784% 0.00615% 0.196% 0.00%9-May-05 226.02 -0.881% 0.00776% 0.196% 0.00%6-May-05 228.02 0.457% 0.00209% 0.196% 0.00%5-May-05 226.98 -0.667% 0.00445% 0.196% 0.00%4-May-05 228.5 1.016% 0.01032% 0.196% 0.00%3-May-05 226.19 1.739% 0.03025% 0.196% 0.00%2-May-05 222.29 1.036% 0.01072% 0.196% 0.00%29-Apr-05 220 0.250% 0.00063% 0.196% 0.00%28-Apr-05 219.45 -0.150% 0.00023% 0.196% 0.00%27-Apr-05 219.78 0.470% 0.00221% 0.196% 0.00%26-Apr-05 218.75 -2.162% 0.04673% 0.196% 0.00%25-Apr-05 223.53 3.515% 0.12353% 0.196% 0.00%22-Apr-05 215.81 5.520% 0.30471% 0.196% 0.00%21-Apr-05 204.22 3.043% 0.09257% 0.196% 0.00%20-Apr-05 198.1 3.441% 0.11838% 0.196% 0.00%19-Apr-05 191.4 2.342% 0.05484% 0.196% 0.00%18-Apr-05 186.97 1.059% 0.01122% 0.196% 0.00%15-Apr-05 185 -3.427% 0.11745% 0.196% 0.00%14-Apr-05 191.45 -0.770% 0.00593% 0.196% 0.00%13-Apr-05 192.93 -0.532% 0.00284% 0.196% 0.00%12-Apr-05 193.96 0.377% 0.00142% 0.196% 0.00%11-Apr-05 193.23 0.613% 0.00375% 0.196% 0.00%8-Apr-05 192.05 -0.886% 0.00786% 0.196% 0.00%7-Apr-05 193.76 2.371% 0.05622% 0.196% 0.00%6-Apr-05 189.22 0.344% 0.00118% 0.196% 0.00%5-Apr-05 188.57 1.755% 0.03079% 0.196% 0.00%4-Apr-05 185.29 2.874% 0.08262% 0.196% 0.00%1-Apr-05 180.04 -0.261% 0.00068% 0.196% 0.00%31-Mar-05 180.51 0.033% 0.00001% 0.196% 0.00%30-Mar-05 180.45 0.489% 0.00239% 0.196% 0.00%29-Mar-05 179.57 -1.025% 0.01051% 0.196% 0.00%28-Mar-05 181.42 1.203% 0.01448% 0.196% 0.00%24-Mar-05 179.25 0.151% 0.00023% 0.196% 0.00%23-Mar-05 178.98 0.213% 0.00045% 0.196% 0.00%22-Mar-05 178.6 -1.269% 0.01609% 0.196% 0.00%21-Mar-05 180.88 0.465% 0.00217% 0.196% 0.00%18-Mar-05 180.04 0.417% 0.00174% 0.196% 0.00%17-Mar-05 179.29 2.080% 0.04325% 0.196% 0.00%16-Mar-05 175.6 -1.700% 0.02889% 0.196% 0.00%15-Mar-05 178.61 2.048% 0.04193% 0.196% 0.00%14-Mar-05 174.99 -1.593% 0.02538% 0.196% 0.00%11-Mar-05 177.8 -1.219% 0.01485% 0.196% 0.00%10-Mar-05 179.98 -0.758% 0.00575% 0.196% 0.00%9-Mar-05 181.35 -2.101% 0.04413% 0.196% 0.00%8-Mar-05 185.2 -1.930% 0.03727% 0.196% 0.00%7-Mar-05 188.81 1.553% 0.02413% 0.196% 0.00%4-Mar-05 185.9 -0.595% 0.00354% 0.196% 0.00%3-Mar-05 187.01 0.983% 0.00967% 0.196% 0.00%2-Mar-05 185.18 -0.474% 0.00225% 0.196% 0.00%1-Mar-05 186.06 -1.032% 0.01065% 0.196% 0.00%28-Feb-05 187.99 1.134% 0.01286% 0.196% 0.00%25-Feb-05 185.87 -1.612% 0.02598% 0.196% 0.00%24-Feb-05 188.89 -2.644% 0.06988% 0.196% 0.00%23-Feb-05 193.95 1.339% 0.01793% 0.196% 0.00%22-Feb-05 191.37 -3.381% 0.11428% 0.196% 0.00%18-Feb-05 197.95 0.025% 0.00001% 0.196% 0.00%17-Feb-05 197.9 -0.257% 0.00066% 0.196% 0.00%16-Feb-05 198.41 1.616% 0.02611% 0.196% 0.00%15-Feb-05 195.23 1.154% 0.01332% 0.196% 0.00%14-Feb-05 192.99 2.939% 0.08639% 0.196% 0.00%11-Feb-05 187.4 -0.309% 0.00095% 0.196% 0.00%10-Feb-05 187.98 -1.897% 0.03599% 0.196% 0.00%9-Feb-05 191.58 -3.619% 0.13096% 0.196% 0.00%8-Feb-05 198.64 1.323% 0.01749% 0.196% 0.00%7-Feb-05 196.03 -4.162% 0.17318% 0.196% 0.00%4-Feb-05 204.36 -3.131% 0.09804% 0.196% 0.00%3-Feb-05 210.86 2.351% 0.05528% 0.196% 0.00%2-Feb-05 205.96 7.071% 0.49996% 0.196% 0.00%1-Feb-05 191.9 -1.920% 0.03686% 0.196% 0.00%31-Jan-05 195.62 2.736% 0.07487% 0.196% 0.00%28-Jan-05 190.34 1.194% 0.01427% 0.196% 0.00%27-Jan-05 188.08 -0.615% 0.00378% 0.196% 0.00%26-Jan-05 189.24 6.619% 0.43809% 0.196% 0.00%25-Jan-05 177.12 -2.012% 0.04049% 0.196% 0.00%24-Jan-05 180.72 -4.098% 0.16795% 0.196% 0.00%21-Jan-05 188.28 -2.952% 0.08712% 0.196% 0.00%20-Jan-05 193.92 -1.728% 0.02986% 0.196% 0.00%19-Jan-05 197.3 -3.290% 0.10827% 0.196% 0.00%18-Jan-05 203.9 1.946% 0.03788% 0.196% 0.00%14-Jan-05 199.97 2.348% 0.05512% 0.196% 0.00%13-Jan-05 195.33 -0.026% 0.00001% 0.196% 0.00%12-Jan-05 195.38 0.946% 0.00895% 0.196% 0.00%11-Jan-05 193.54 -0.782% 0.00612% 0.196% 0.00%10-Jan-05 195.06 0.622% 0.00387% 0.196% 0.00%7-Jan-05 193.85 2.772% 0.07685% 0.196% 0.00%6-Jan-05 188.55 -2.597% 0.06742% 0.196% 0.00%5-Jan-05 193.51 -0.510% 0.00260% 0.196% 0.00%4-Jan-05 194.5 -4.134% 0.17093% 0.196% 0.00%3-Jan-05 202.71 5.017% 0.25175% 0.196% 0.00%31-Dec-04 192.79 -2.464% 0.06073% 0.196% 0.00%30-Dec-04 197.6 2.407% 0.05795% 0.196% 0.00%29-Dec-04 192.9 0.073% 0.00005% 0.196% 0.00%28-Dec-04 192.76 0.442% 0.00195% 0.196% 0.00%27-Dec-04 191.91 2.112% 0.04459% 0.196% 0.00%23-Dec-04 187.9 0.855% 0.00731% 0.196% 0.00%22-Dec-04 186.3 1.378% 0.01899% 0.196% 0.00%21-Dec-04 183.75 -0.689% 0.00474% 0.196% 0.00%20-Dec-04 185.02 2.706% 0.07324% 0.196% 0.00%17-Dec-04 180.08 2.025% 0.04101% 0.196% 0.00%16-Dec-04 176.47 -1.858% 0.03453% 0.196% 0.00%15-Dec-04 179.78 0.608% 0.00370% 0.196% 0.00%14-Dec-04 178.69 4.721% 0.22288% 0.196% 0.00%13-Dec-04 170.45 -0.702% 0.00492% 0.196% 0.00%10-Dec-04 171.65 -1.032% 0.01064% 0.196% 0.00%9-Dec-04 173.43 2.009% 0.04037% 0.196% 0.00%8-Dec-04 169.98 -0.849% 0.00722% 0.196% 0.00%7-Dec-04 171.43 -2.796% 0.07815% 0.196% 0.00%6-Dec-04 176.29 -2.305% 0.05311% 0.196% 0.00%3-Dec-04 180.4 0.556% 0.00309% 0.196% 0.00%2-Dec-04 179.4 -0.312% 0.00097% 0.196% 0.00%1-Dec-04 179.96 -1.116% 0.01246% 0.196% 0.00%30-Nov-04 181.98 0.512% 0.00263% 0.196% 0.00%29-Nov-04 181.05 0.921% 0.00848% 0.196% 0.00%26-Nov-04 179.39 2.615% 0.06837% 0.196% 0.00%24-Nov-04 174.76 4.231% 0.17902% 0.196% 0.00%23-Nov-04 167.52 1.455% 0.02117% 0.196% 0.00%22-Nov-04 165.1 -2.571% 0.06611% 0.196% 0.00%19-Nov-04 169.4 1.104% 0.01219% 0.196% 0.00%18-Nov-04 167.54 -2.918% 0.08512% 0.196% 0.00%17-Nov-04 172.5 -0.023% 0.00001% 0.196% 0.00%16-Nov-04 172.54 -6.902% 0.47643% 0.196% 0.00%15-Nov-04 184.87 1.565% 0.02448% 0.196% 0.00%12-Nov-04 182 -0.559% 0.00312% 0.196% 0.00%11-Nov-04 183.02 8.647% 0.74762% 0.196% 0.00%10-Nov-04 167.86 -0.499% 0.00249% 0.196% 0.00%9-Nov-04 168.7 -2.257% 0.05092% 0.196% 0.00%8-Nov-04 172.55 1.872% 0.03504% 0.196% 0.00%5-Nov-04 169.35 -8.677% 0.75282% 0.196% 0.00%4-Nov-04 184.7 -3.704% 0.13721% 0.196% 0.00%3-Nov-04 191.67 -1.656% 0.02742% 0.196% 0.00%2-Nov-04 194.87 -0.594% 0.00352% 0.196% 0.00%1-Nov-04 196.03 2.788% 0.07773% 0.196% 0.00%29-Oct-04 190.64 -1.386% 0.01920% 0.196% 0.00%28-Oct-04 193.3 3.866% 0.14944% 0.196% 0.00%27-Oct-04 185.97 2.268% 0.05143% 0.196% 0.00%26-Oct-04 181.8 -3.034% 0.09204% 0.196% 0.00%25-Oct-04 187.4 8.325% 0.69312% 0.196% 0.00%22-Oct-04 172.43 14.350% 2.05917% 0.196% 0.00%21-Oct-04 149.38 6.136% 0.37647% 0.196% 0.00%20-Oct-04 140.49 -5.167% 0.26698% 0.196% 0.00%19-Oct-04 147.94 -0.821% 0.00674% 0.196% 0.00%18-Oct-04 149.16 3.444% 0.11863% 0.196% 0.00%15-Oct-04 144.11 1.475% 0.02176% 0.196% 0.00%14-Oct-04 142 0.778% 0.00605% 0.196% 0.00%13-Oct-04 140.9 2.515% 0.06327% 0.196% 0.00%12-Oct-04 137.4 1.570% 0.02464% 0.196% 0.00%11-Oct-04 135.26 -1.810% 0.03275% 0.196% 0.00%8-Oct-04 137.73 -0.810% 0.00656% 0.196% 0.00%7-Oct-04 138.85 1.283% 0.01646% 0.196% 0.00%6-Oct-04 137.08 -0.937% 0.00877% 0.196% 0.00%5-Oct-04 138.37 2.421% 0.05862% 0.196% 0.00%4-Oct-04 135.06 1.853% 0.03435% 0.196% 0.00%1-Oct-04 132.58 2.273% 0.05168% 0.196% 0.00%30-Sep-04 129.6 -1.136% 0.01289% 0.196% 0.00%29-Sep-04 131.08 3.272% 0.10708% 0.196% 0.00%28-Sep-04 126.86 7.020% 0.49278% 0.196% 0.00%27-Sep-04 118.26 -1.319% 0.01739% 0.196% 0.00%24-Sep-04 119.83 -0.823% 0.00677% 0.196% 0.00%23-Sep-04 120.82 2.040% 0.04162% 0.196% 0.00%22-Sep-04 118.38 0.457% 0.00209% 0.196% 0.00%21-Sep-04 117.84 -1.282% 0.01643% 0.196% 0.00%20-Sep-04 119.36 1.579% 0.02494% 0.196% 0.00%17-Sep-04 117.49 3.042% 0.09253% 0.196% 0.00%16-Sep-04 113.97 1.744% 0.03040% 0.196% 0.00%15-Sep-04 112 0.456% 0.00208% 0.196% 0.00%14-Sep-04 111.49 3.644% 0.13282% 0.196% 0.00%13-Sep-04 107.5 2.039% 0.04159% 0.196% 0.00%10-Sep-04 105.33 2.909% 0.08463% 0.196% 0.00%9-Sep-04 102.31 0.010% 0.00000% 0.196% 0.00%8-Sep-04 102.3 0.706% 0.00499% 0.196% 0.00%7-Sep-04 101.58 1.558% 0.02426% 0.196% 0.00%3-Sep-04 100.01 -1.489% 0.02216% 0.196% 0.00%2-Sep-04 101.51 1.249% 0.01560% 0.196% 0.00%1-Sep-04 100.25 -2.093% 0.04379% 0.196% 0.00%31-Aug-04 102.37 0.352% 0.00124% 0.196% 0.00%30-Aug-04 102.01 -3.978% 0.15826% 0.196% 0.00%27-Aug-04 106.15 -1.644% 0.02704% 0.196% 0.00%26-Aug-04 107.91 1.786% 0.03189% 0.196% 0.00%25-Aug-04 106 1.072% 0.01149% 0.196% 0.00%24-Aug-04 104.87 -4.229% 0.17884% 0.196% 0.00%23-Aug-04 109.4 1.001% 0.01003% 0.196% 0.00%20-Aug-04 108.31 7.643% 0.58420% 0.196% 0.00%19-Aug-04 100.34 100% 100%Sum as of Aug 25thVariance on 24thRecursive EWMA2 2 2n n 1 n 1(1 )u o o = + | |= |\ .iii 1Su lnS94.0%(RiskMetrics)oReturn^2( o2 )0.000010%0.000004%0.000886%0.000034%0.001189%2 Years (500+ days) collapsed (Data>Group) below0.000177%0.000102%0.001200%0.003460%0.000022%0.000761%0.000162%0.000328%0.000173%0.000300%0.000040%0.001077%0.001042%0.001669%0.000029%0.000384%0.000107%0.000153%0.000023%0.000006%0.000076%0.001097%0.000115%0.000151%0.000117%0.000161%0.000366%0.000250%0.000177%0.000021%0.000029%| |= |\ .iii 1Su lnS=i i 1ii 1S SuSo== m2 2n n ii 11(u u )m 12ni variance rat e per daymmostrecentm observat ionsut he mean/ average of all daily ret urns (u )o ===m2 2n n ii 11umo==m2 2n n ii 11(u u )mo== m2 2n n ii 11umo==0.000011%0.000010%0.000048%0.000007%0.000407%0.000042%0.000010%0.000001%0.000059%0.000011%0.000501%0.000002%0.000013%0.000000%0.000079%0.000008%0.000040%0.000039%0.000063%0.000061%0.000015%0.000292%0.000029%0.000011%0.000120%0.000000%0.000081%0.000002%0.000002%0.000024%0.000016%0.000001%0.000001%0.000007%0.000006%0.000013%0.000002%0.000075%0.000101%0.000012%0.000066%0.000000%0.000000%0.000000%m2 2n n ii 11umo==0.000000%0.000004%0.000082%0.000001%0.000007%0.000000%0.000028%0.000002%0.000070%0.000003%0.000005%0.000001%0.000003%0.000005%0.000000%0.000004%0.000010%0.000002%0.000001%0.000001%0.000017%0.000000%0.000000%0.000003%0.000020%0.000004%0.000001%0.000037%0.000000%0.000000%0.000004%0.000004%0.000000%0.000002%0.000002%0.000008%0.000000%0.000001%0.000004%0.000003%0.000000%0.000002%0.000000%0.000003%m2 2n n ii 11umo==0.000000%0.000014%0.000003%0.000000%0.000002%0.000000%0.000000%0.000000%0.000008%0.000000%0.000000%0.000003%0.000000%0.000001%0.000000%0.000002%0.000000%0.000001%0.000000%0.000005%0.000000%0.000000%0.000000%0.000000%0.000000%0.000001%0.000003%0.000004%0.000000%0.000001%0.000000%0.000000%0.000000%0.000000%0.000000%0.000000%0.000000%0.000000%0.000000%0.000001%0.000000%0.000000%0.000000%0.000000%m2 2n n ii 11umo==0.000000%0.000000%0.000000%0.000000%0.000000%0.000000%0.000000%0.000000%0.000000%0.000000%0.000000%0.000000%0.000000%0.000000%0.000000%0.000000%0.000000%0.000000%0.000000%0.000000%0.000000%0.000000%0.000000%0.000000%0.000000%0.000000%0.000000%0.000000%0.000000%0.000000%0.000000%0.000000%0.000000%0.000000%0.000000%0.000000%0.000000%0.000000%0.000000%0.000000%0.000000%0.000000%0.000000%0.000000%m2 2n n ii 11umo==0.000000%0.000000%0.000000%0.000000%0.000000%0.000000%0.000000%0.000000%0.000000%0.000000%0.000000%0.000000%0.000000%0.000000%0.000000%0.000000%0.000000%0.000000%0.000000%0.000000%0.000000%0.000000%0.000000%0.000000%0.000000%0.000000%0.000000%0.000000%0.000000%0.000000%0.000000%0.000000%0.000000%0.000000%0.000000%0.000000%0.000000%0.000000%0.000000%0.000000%0.000000%0.000000%0.000000%0.000000%m2 2n n ii 11umo==0.000000%0.000000%0.000000%0.000000%0.000000%0.000000%0.000000%0.000000%0.000000%0.000000%0.000000%0.000000%0.000000%0.000000%0.000000%0.000000%0.000000%0.000000%0.000000%0.000000%0.000000%0.000000%0.000000%0.000000%0.000000%0.000000%0.000000%0.000000%0.000000%0.000000%0.000000%0.000000%0.000000%0.000000%0.000000%0.000000%0.000000%0.000000%0.000000%0.000000%0.000000%0.000000%0.000000%0.000000%m2 2n n ii 11umo==0.000000%0.000000%0.000000%0.000000%0.000000%0.000000%0.000000%0.000000%0.000000%0.000000%0.000000%0.000000%0.000000%0.000000%0.000000%0.000000%0.000000%0.000000%0.000000%0.000000%0.000000%0.000000%0.000000%0.000000%0.000000%0.000000%0.000000%0.000000%0.000000%0.000000%0.000000%0.000000%0.000000%0.000000%0.000000%0.000000%0.000000%0.000000%0.000000%0.000000%0.000000%0.000000%0.000000%0.000000%m2 2n n ii 11umo==0.000000%0.000000%0.000000%0.000000%0.000000%0.000000%0.000000%0.000000%0.000000%0.000000%0.000000%0.000000%0.000000%0.000000%0.000000%0.000000%0.000000%0.000000%0.000000%0.000000%0.000000%0.000000%0.000000%0.000000%0.000000%0.000000%0.000000%0.000000%0.000000%0.000000%0.000000%0.000000%0.000000%0.000000%0.000000%0.000000%0.000000%0.000000%0.000000%0.000000%0.000000%0.000000%0.000000%0.000000%m2 2n n ii 11umo==0.000000%0.000000%0.000000%0.000000%0.000000%0.000000%0.000000%0.000000%0.000000%0.000000%0.000000%0.000000%0.000000%0.000000%0.000000%0.000000%0.000000%0.000000%0.000000%0.000000%0.000000%0.000000%0.000000%0.000000%0.000000%0.000000%0.000000%0.000000%0.000000%0.000000%0.000000%0.000000%0.000000%0.000000%0.000000%0.000000%0.000000%0.000000%0.000000%0.000000%0.000000%0.000000%0.000000%0.000000%m2 2n n ii 11umo==0.000000%0.000000%0.000000%0.000000%0.000000%0.000000%0.000000%0.000000%0.000000%0.000000%0.000000%0.000000%0.000000%0.000000%0.000000%0.000000%0.000000%0.000000%0.000000%0.000000%0.000000%0.000000%0.000000%0.000000%0.000000%0.000000%0.000000%0.000000%0.000000%0.000000%0.000000%0.000000%0.000000%0.000000%0.000000%0.000000%0.000000%0.000000%0.000000%0.000000%0.000000%0.000000%0.000000%0.000000%m2 2n n ii 11umo==0.000000%0.000000%0.000000%0.000000%0.000000%0.000000%0.000000%0.000000%0.000000%0.000000%0.000000%0.000000%0.000000%0.000000%0.000000%0.000000%0.000000%0.000000%0.000000%0.000000%0.000000%0.000000%0.000000%0.000000%0.000000%0.000000%0.000000%0.000000%0.000000%0.000000%0.000000%0.000000%0.000000%0.018581373165%0.019757%0.018581373165%2 2 2n n 1 n 1(1 )u o o = + m2 2n n ii 11umo==| |= |\ .iii 1Su lnS=i i 1ii 1S SuSo== m2 2n n ii 11(u u )m 12ni variance rat e per daymmostrecentm observat ionsut he mean/ average of all daily ret urns (u )o ===m2 2n n ii 11umo==m2 2n n ii 11(u u )mo== m2 2n n ii 11umo==m2 2n n ii 11umo==m2 2n n ii 11umo==m2 2n n ii 11umo==m2 2n n ii 11umo==m2 2n n ii 11umo==m2 2n n ii 11umo==m2 2n n ii 11umo==m2 2n n ii 11umo==m2 2n n ii 11umo==m2 2n n ii 11umo==m2 2n n ii 11umo==
