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Advanced Statistics: WSS_AustralianDollar

Advanced Statistics module contributed by Jules Ellis, C2 Member.

Jules has written a very helpful guide for these statistics.

MonthlyDaily (all)Daily (last 6 mo.)
ANALYSIS BASED ON MONTHLY VALUES, FULL HISTORY (Back)
RATIO STATISTICS
Ratio statistics of excess return rates
Statistics related to Sharpe ratio
 Mean0.352
 SD0.509
 Sharpe ratio (Glass type estimate) 0.693
 Sharpe ratio (Hedges UMVUE)0.655
 df14.000
 t0.774
 p0.399
 Lowerbound of 95% confidence interval for Sharpe Ratio-1.091
 Upperbound of 95% confidence interval for Sharpe Ratio2.452
 Lowerbound of 95% CI (Gibbons, Hedeker & Davis approximation)-1.115
 Upperbound of 95% CI (Gibbons, Hedeker & Davis approximation)2.424
Statistics related to Sortino ratio
 Sortino ratio1.858
 Upside Potential Ratio3.806
 Upside part of mean0.721
 Downside part of mean-0.369
 Upside SD0.465
 Downside SD0.190
 N nonnegative terms6.000
 N negative terms9.000
Statistics related to linear regression on benchmark
 N of observations15.000
 Mean of predictor0.020
 Mean of criterion0.352
 SD of predictor0.218
 SD of criterion0.509
 Covariance0.022
 r0.194
 b (slope, estimate of beta)0.453
 a (intercept, estimate of alpha)0.343
 Mean Square Error0.268
 DF error13.000
 t(b)0.714
 p(b)0.377
 t(a)0.741
 p(a)0.373
 Lowerbound of 95% confidence interval for beta-0.918
 Upperbound of 95% confidence interval for beta1.824
 Lowerbound of 95% confidence interval for alpha-0.657
 Upperbound of 95% confidence interval for alpha1.344
 Treynor index (mean / b)0.777
 Jensen alpha (a)0.343
Ratio statistics of excess log return rates
Statistics related to Sharpe ratio
 Mean0.244
 SD0.457
 Sharpe ratio (Glass type estimate) 0.533
 Sharpe ratio (Hedges UMVUE)0.504
 df14.000
 t0.596
 p0.421
 Lowerbound of 95% confidence interval for Sharpe Ratio-1.240
 Upperbound of 95% confidence interval for Sharpe Ratio2.288
 Lowerbound of 95% CI (Gibbons, Hedeker & Davis approximation)-1.259
 Upperbound of 95% CI (Gibbons, Hedeker & Davis approximation)2.267
Statistics related to Sortino ratio
 Sortino ratio1.217
 Upside Potential Ratio3.150
 Upside part of mean0.631
 Downside part of mean-0.387
 Upside SD0.400
 Downside SD0.200
 N nonnegative terms6.000
 N negative terms9.000
Statistics related to linear regression on benchmark
 N of observations15.000
 Mean of predictor-0.004
 Mean of criterion0.244
 SD of predictor0.228
 SD of criterion0.457
 Covariance0.026
 r0.251
 b (slope, estimate of beta)0.503
 a (intercept, estimate of alpha)0.246
 Mean Square Error0.211
 DF error13.000
 t(b)0.937
 p(b)0.342
 t(a)0.598
 p(a)0.396
 Lowerbound of 95% confidence interval for beta-0.657
 Upperbound of 95% confidence interval for beta1.663
 Lowerbound of 95% confidence interval for alpha-0.641
 Upperbound of 95% confidence interval for alpha1.132
 Treynor index (mean / b)0.484
 Jensen alpha (a)0.246
Risk estimates for a one-period unit investment (parametric)
assuming log normal returns and losses (using central moments from Sharpe statistics)
 VaR(95%)0.179
 Expected Shortfall on VaR0.222
assuming Pareto losses only (using partial moments from Sortino statistics)
 VaR(95%)0.080
 Expected Shortfall on VaR0.140
ORDER STATISTICS
Quartiles of return rates
 Number of observations15.000
 Minimum0.878
 Quartile 10.964
 Median1.000
 Quartile 31.031
 Maximum1.393
 Mean of quarter 10.904
 Mean of quarter 20.988
 Mean of quarter 31.006
 Mean of quarter 41.227
 Inter Quartile Range0.067
 Number outliers low0.000
 Percentage of outliers low0.000
 Mean of outliers lowNA
 Number of outliers high3.000
 Percentage of outliers high0.200
 Mean of outliers high1.285
Risk estimates for a one-period unit investment (based on Extreme Value Theory)
 Extreme Value Index (moments method)-40.225
 VaR(95%) (moments method)0.088
 Expected Shortfall (moments method)NA
 Extreme Value Index (regression method)-3.587
 VaR(95%) (regression method)0.174
 Expected Shortfall (regression method)0.174
DRAW DOWN STATISTICS
Quartiles of draw downs
 Number of observations3.000
 Minimum0.117
 Quartile 10.118
 Median0.118
 Quartile 30.151
 Maximum0.184
 Mean of quarter 10.117
 Mean of quarter 20.118
 Mean of quarter 3NA
 Mean of quarter 40.184
 Inter Quartile Range0.033
 Number outliers low0.000
 Percentage of outliers low0.000
 Mean of outliers lowNA
 Number of outliers high0.000
 Percentage of outliers high0.000
 Mean of outliers highNA
Risk estimates based on draw downs (based on Extreme Value Theory)
 Extreme Value Index (moments method)NA
 VaR(95%) (moments method)NA
 Expected Shortfall (moments method)NA
 Extreme Value Index (regression method)NA
 VaR(95%) (regression method)NA
 Expected Shortfall (regression method)NA
COMBINED STATISTICS
 Annualized return (arithmetic extrapolation)0.346
 Compounded annual return (geometric extrapolation)0.333
 Calmar ratio (compounded annual return / max draw down)1.814
 Compounded annual return / average of 25% largest draw downs1.814
 Compounded annual return / Expected Shortfall lognormal1.503
ANALYSIS BASED ON DAILY VALUES, FULL HISTORY (Back)
RATIO STATISTICS
Ratio statistics of excess return rates
Statistics related to Sharpe ratio
 Mean0.285
 SD0.324
 Sharpe ratio (Glass type estimate) 0.880
 Sharpe ratio (Hedges UMVUE)0.879
 df446.000
 t1.003
 p0.158
 Lowerbound of 95% confidence interval for Sharpe Ratio-0.841
 Upperbound of 95% confidence interval for Sharpe Ratio2.600
 Lowerbound of 95% CI (Gibbons, Hedeker & Davis approximation)-0.842
 Upperbound of 95% CI (Gibbons, Hedeker & Davis approximation)2.599
Statistics related to Sortino ratio
 Sortino ratio1.308
 Upside Potential Ratio9.357
 Upside part of mean2.040
 Downside part of mean-1.755
 Upside SD0.240
 Downside SD0.218
 N nonnegative terms178.000
 N negative terms269.000
Statistics related to linear regression on benchmark
 N of observations447.000
 Mean of predictor0.139
 Mean of criterion0.285
 SD of predictor0.232
 SD of criterion0.324
 Covariance0.005
 r0.068
 b (slope, estimate of beta)0.095
 a (intercept, estimate of alpha)0.272
 Mean Square Error0.105
 DF error445.000
 t(b)1.438
 p(b)0.076
 t(a)0.957
 p(a)0.169
 Lowerbound of 95% confidence interval for beta-0.035
 Upperbound of 95% confidence interval for beta0.225
 Lowerbound of 95% confidence interval for alpha-0.286
 Upperbound of 95% confidence interval for alpha0.830
 Treynor index (mean / b)2.998
 Jensen alpha (a)0.272
Ratio statistics of excess log return rates
Statistics related to Sharpe ratio
 Mean0.233
 SD0.324
 Sharpe ratio (Glass type estimate) 0.718
 Sharpe ratio (Hedges UMVUE)0.716
 df446.000
 t0.818
 p0.207
 Lowerbound of 95% confidence interval for Sharpe Ratio-1.003
 Upperbound of 95% confidence interval for Sharpe Ratio2.437
 Lowerbound of 95% CI (Gibbons, Hedeker & Davis approximation)-1.004
 Upperbound of 95% CI (Gibbons, Hedeker & Davis approximation)2.437
Statistics related to Sortino ratio
 Sortino ratio1.044
 Upside Potential Ratio9.029
 Upside part of mean2.012
 Downside part of mean-1.779
 Upside SD0.235
 Downside SD0.223
 N nonnegative terms178.000
 N negative terms269.000
Statistics related to linear regression on benchmark
 N of observations447.000
 Mean of predictor0.112
 Mean of criterion0.233
 SD of predictor0.232
 SD of criterion0.324
 Covariance0.005
 r0.071
 b (slope, estimate of beta)0.100
 a (intercept, estimate of alpha)0.221
 Mean Square Error0.105
 DF error445.000
 t(b)1.508
 p(b)0.066
 t(a)0.780
 p(a)0.218
 Lowerbound of 95% confidence interval for beta-0.030
 Upperbound of 95% confidence interval for beta0.230
 Lowerbound of 95% confidence interval for alpha-0.337
 Upperbound of 95% confidence interval for alpha0.780
 Treynor index (mean / b)2.335
 Jensen alpha (a)0.221
Risk estimates for a one-period unit investment (parametric)
assuming log normal returns and losses (using central moments from Sharpe statistics)
 VaR(95%)0.028
 Expected Shortfall on VaR0.035
assuming Pareto losses only (using partial moments from Sortino statistics)
 VaR(95%)0.013
 Expected Shortfall on VaR0.026
ORDER STATISTICS
Quartiles of return rates
 Number of observations447.000
 Minimum0.917
 Quartile 10.994
 Median1.000
 Quartile 31.007
 Maximum1.064
 Mean of quarter 10.981
 Mean of quarter 20.999
 Mean of quarter 31.002
 Mean of quarter 41.022
 Inter Quartile Range0.013
 Number outliers low22.000
 Percentage of outliers low0.049
 Mean of outliers low0.959
 Number of outliers high36.000
 Percentage of outliers high0.081
 Mean of outliers high1.039
Risk estimates for a one-period unit investment (based on Extreme Value Theory)
 Extreme Value Index (moments method)0.141
 VaR(95%) (moments method)0.016
 Expected Shortfall (moments method)0.025
 Extreme Value Index (regression method)0.112
 VaR(95%) (regression method)0.017
 Expected Shortfall (regression method)0.025
DRAW DOWN STATISTICS
Quartiles of draw downs
 Number of observations16.000
 Minimum0.004
 Quartile 10.017
 Median0.034
 Quartile 30.063
 Maximum0.324
 Mean of quarter 10.007
 Mean of quarter 20.026
 Mean of quarter 30.046
 Mean of quarter 40.213
 Inter Quartile Range0.046
 Number outliers low0.000
 Percentage of outliers low0.000
 Mean of outliers lowNA
 Number of outliers high3.000
 Percentage of outliers high0.188
 Mean of outliers high0.255
Risk estimates based on draw downs (based on Extreme Value Theory)
 Extreme Value Index (moments method)-15.004
 VaR(95%) (moments method)0.186
 Expected Shortfall (moments method)0.186
 Extreme Value Index (regression method)-0.835
 VaR(95%) (regression method)0.236
 Expected Shortfall (regression method)0.261
COMBINED STATISTICS
 Annualized return (arithmetic extrapolation)0.333
 Compounded annual return (geometric extrapolation)0.319
 Calmar ratio (compounded annual return / max draw down)0.983
 Compounded annual return / average of 25% largest draw downs1.493
 Compounded annual return / Expected Shortfall lognormal9.175
ANALYSIS BASED ON DAILY VALUES, LAST 6 MONTHS (Back)
RATIO STATISTICS
Ratio statistics of excess return rates
Statistics related to Sharpe ratio
 Mean-0.354
 SD0.138
 Sharpe ratio (Glass type estimate) -2.567
 Sharpe ratio (Hedges UMVUE)-2.556
 df171.000
 t-1.815
 p0.587
 Lowerbound of 95% confidence interval for Sharpe Ratio-5.349
 Upperbound of 95% confidence interval for Sharpe Ratio0.222
 Lowerbound of 95% CI (Gibbons, Hedeker & Davis approximation)-5.341
 Upperbound of 95% CI (Gibbons, Hedeker & Davis approximation)0.229
Statistics related to Sortino ratio
 Sortino ratio-3.258
 Upside Potential Ratio4.695
 Upside part of mean0.510
 Downside part of mean-0.863
 Upside SD0.086
 Downside SD0.109
 N nonnegative terms39.000
 N negative terms133.000
Statistics related to linear regression on benchmark
 N of observations172.000
 Mean of predictor0.366
 Mean of criterion-0.354
 SD of predictor0.200
 SD of criterion0.138
 Covariance0.007
 r0.238
 b (slope, estimate of beta)0.164
 a (intercept, estimate of alpha)-0.414
 Mean Square Error0.018
 DF error170.000
 t(b)3.193
 p(b)0.381
 t(a)-2.169
 p(a)0.582
 Lowerbound of 95% confidence interval for beta0.063
 Upperbound of 95% confidence interval for beta0.265
 Lowerbound of 95% confidence interval for alpha-0.790
 Upperbound of 95% confidence interval for alpha-0.037
 Treynor index (mean / b)-2.157
 Jensen alpha (a)-0.414
Ratio statistics of excess log return rates
Statistics related to Sharpe ratio
 Mean-0.363
 SD0.138
 Sharpe ratio (Glass type estimate) -2.637
 Sharpe ratio (Hedges UMVUE)-2.626
 df171.000
 t-1.865
 p0.590
 Lowerbound of 95% confidence interval for Sharpe Ratio-5.419
 Upperbound of 95% confidence interval for Sharpe Ratio0.152
 Lowerbound of 95% CI (Gibbons, Hedeker & Davis approximation)-5.411
 Upperbound of 95% CI (Gibbons, Hedeker & Davis approximation)0.160
Statistics related to Sortino ratio
 Sortino ratio-3.318
 Upside Potential Ratio4.621
 Upside part of mean0.506
 Downside part of mean-0.869
 Upside SD0.085
 Downside SD0.109
 N nonnegative terms39.000
 N negative terms133.000
Statistics related to linear regression on benchmark
 N of observations172.000
 Mean of predictor0.346
 Mean of criterion-0.363
 SD of predictor0.199
 SD of criterion0.138
 Covariance0.007
 r0.238
 b (slope, estimate of beta)0.164
 a (intercept, estimate of alpha)-0.420
 Mean Square Error0.018
 DF error170.000
 t(b)3.190
 p(b)0.381
 t(a)-2.204
 p(a)0.583
 Lowerbound of 95% confidence interval for beta0.063
 Upperbound of 95% confidence interval for beta0.266
 Lowerbound of 95% confidence interval for alpha-0.796
 Upperbound of 95% confidence interval for alpha-0.044
 Treynor index (mean / b)-2.213
 Jensen alpha (a)-0.420
Risk estimates for a one-period unit investment (parametric)
assuming log normal returns and losses (using central moments from Sharpe statistics)
 VaR(95%)0.013
 Expected Shortfall on VaR0.016
assuming Pareto losses only (using partial moments from Sortino statistics)
 VaR(95%)0.007
 Expected Shortfall on VaR0.015
ORDER STATISTICS
Quartiles of return rates
 Number of observations172.000
 Minimum0.974
 Quartile 10.999
 Median1.000
 Quartile 31.000
 Maximum1.042
 Mean of quarter 10.990
 Mean of quarter 21.000
 Mean of quarter 31.000
 Mean of quarter 41.006
 Inter Quartile Range0.001
 Number outliers low38.000
 Percentage of outliers low0.221
 Mean of outliers low0.989
 Number of outliers high34.000
 Percentage of outliers high0.198
 Mean of outliers high1.008
Risk estimates for a one-period unit investment (based on Extreme Value Theory)
 Extreme Value Index (moments method)-0.514
 VaR(95%) (moments method)0.004
 Expected Shortfall (moments method)0.005
 Extreme Value Index (regression method)-0.372
 VaR(95%) (regression method)0.009
 Expected Shortfall (regression method)0.012
DRAW DOWN STATISTICS
Quartiles of draw downs
 Number of observations2.000
 Minimum0.006
 Quartile 10.057
 Median0.108
 Quartile 30.158
 Maximum0.209
 Mean of quarter 10.006
 Mean of quarter 2NA
 Mean of quarter 3NA
 Mean of quarter 40.209
 Inter Quartile Range0.101
 Number outliers low0.000
 Percentage of outliers low0.000
 Mean of outliers lowNA
 Number of outliers high0.000
 Percentage of outliers high0.000
 Mean of outliers highNA
Risk estimates based on draw downs (based on Extreme Value Theory)
 Extreme Value Index (moments method)NA
 VaR(95%) (moments method)NA
 Expected Shortfall (moments method)NA
 Extreme Value Index (regression method)NA
 VaR(95%) (regression method)NA
 Expected Shortfall (regression method)NA
COMBINED STATISTICS
 Annualized return (arithmetic extrapolation)-0.295
 Compounded annual return (geometric extrapolation)-0.273
 Calmar ratio (compounded annual return / max draw down)-1.310
 Compounded annual return / average of 25% largest draw downs-1.310
 Compounded annual return / Expected Shortfall lognormal-16.832