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Advanced Statistics: bmrtrading

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
 Mean-0.690
 SD0.823
 Sharpe ratio (Glass type estimate) -0.838
 Sharpe ratio (Hedges UMVUE)-0.757
 df8.000
 t-0.726
 p0.756
 Lowerbound of 95% confidence interval for Sharpe Ratio-3.112
 Upperbound of 95% confidence interval for Sharpe Ratio1.486
 Lowerbound of 95% CI (Gibbons, Hedeker & Davis approximation)-3.050
 Upperbound of 95% CI (Gibbons, Hedeker & Davis approximation)1.537
Statistics related to Sortino ratio
 Sortino ratio-0.904
 Upside Potential Ratio0.639
 Upside part of mean0.487
 Downside part of mean-1.177
 Upside SD0.245
 Downside SD0.762
 N nonnegative terms4.000
 N negative terms5.000
Statistics related to linear regression on benchmark
 N of observations9.000
 Mean of predictor0.060
 Mean of criterion-0.690
 SD of predictor0.098
 SD of criterion0.823
 Covariance0.002
 r0.027
 b (slope, estimate of beta)0.231
 a (intercept, estimate of alpha)-0.703
 Mean Square Error0.773
 DF error7.000
 t(b)0.072
 p(b)0.472
 t(a)-0.681
 p(a)0.741
 Lowerbound of 95% confidence interval for beta-7.303
 Upperbound of 95% confidence interval for beta7.765
 Lowerbound of 95% confidence interval for alpha-3.146
 Upperbound of 95% confidence interval for alpha1.739
 Treynor index (mean / b)-2.991
 Jensen alpha (a)-0.703
Ratio statistics of excess log return rates
Statistics related to Sharpe ratio
 Mean-1.233
 SD1.220
 Sharpe ratio (Glass type estimate) -1.010
 Sharpe ratio (Hedges UMVUE)-0.912
 df8.000
 t-0.875
 p0.796
 Lowerbound of 95% confidence interval for Sharpe Ratio-3.296
 Upperbound of 95% confidence interval for Sharpe Ratio1.334
 Lowerbound of 95% CI (Gibbons, Hedeker & Davis approximation)-3.219
 Upperbound of 95% CI (Gibbons, Hedeker & Davis approximation)1.395
Statistics related to Sortino ratio
 Sortino ratio-1.043
 Upside Potential Ratio0.388
 Upside part of mean0.458
 Downside part of mean-1.691
 Upside SD0.228
 Downside SD1.183
 N nonnegative terms4.000
 N negative terms5.000
Statistics related to linear regression on benchmark
 N of observations9.000
 Mean of predictor0.055
 Mean of criterion-1.233
 SD of predictor0.097
 SD of criterion1.220
 Covariance0.016
 r0.137
 b (slope, estimate of beta)1.727
 a (intercept, estimate of alpha)-1.328
 Mean Square Error1.670
 DF error7.000
 t(b)0.366
 p(b)0.363
 t(a)-0.877
 p(a)0.795
 Lowerbound of 95% confidence interval for beta-9.431
 Upperbound of 95% confidence interval for beta12.885
 Lowerbound of 95% confidence interval for alpha-4.910
 Upperbound of 95% confidence interval for alpha2.254
 Treynor index (mean / b)-0.714
 Jensen alpha (a)-1.328
Risk estimates for a one-period unit investment (parametric)
assuming log normal returns and losses (using central moments from Sharpe statistics)
 VaR(95%)0.495
 Expected Shortfall on VaR0.560
assuming Pareto losses only (using partial moments from Sortino statistics)
 VaR(95%)0.240
 Expected Shortfall on VaR0.482
ORDER STATISTICS
Quartiles of return rates
 Number of observations9.000
 Minimum0.367
 Quartile 10.943
 Median0.995
 Quartile 31.070
 Maximum1.177
 Mean of quarter 10.717
 Mean of quarter 20.993
 Mean of quarter 31.050
 Mean of quarter 41.140
 Inter Quartile Range0.127
 Number outliers low1.000
 Percentage of outliers low0.111
 Mean of outliers low0.367
 Number of outliers high0.000
 Percentage of outliers high0.000
 Mean of outliers highNA
Risk estimates for a one-period unit investment (based on Extreme Value Theory)
 Extreme Value Index (moments method)-0.845
 VaR(95%) (moments method)0.211
 Expected Shortfall (moments method)0.239
 Extreme Value Index (regression method)1.226
 VaR(95%) (regression method)0.862
 Expected Shortfall (regression method)NA
DRAW DOWN STATISTICS
Quartiles of draw downs
 Number of observations2.000
 Minimum0.015
 Quartile 10.188
 Median0.362
 Quartile 30.536
 Maximum0.709
 Mean of quarter 10.015
 Mean of quarter 2NA
 Mean of quarter 3NA
 Mean of quarter 40.709
 Inter Quartile Range0.347
 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)-0.787
 Compounded annual return (geometric extrapolation)-0.695
 Calmar ratio (compounded annual return / max draw down)-0.981
 Compounded annual return / average of 25% largest draw downs-0.981
 Compounded annual return / Expected Shortfall lognormal-1.241
ANALYSIS BASED ON DAILY VALUES, FULL HISTORY (Back)
RATIO STATISTICS
Ratio statistics of excess return rates
Statistics related to Sharpe ratio
 Mean-0.785
 SD0.804
 Sharpe ratio (Glass type estimate) -0.976
 Sharpe ratio (Hedges UMVUE)-0.974
 df280.000
 t-0.882
 p0.811
 Lowerbound of 95% confidence interval for Sharpe Ratio-3.145
 Upperbound of 95% confidence interval for Sharpe Ratio1.195
 Lowerbound of 95% CI (Gibbons, Hedeker & Davis approximation)-3.144
 Upperbound of 95% CI (Gibbons, Hedeker & Davis approximation)1.197
Statistics related to Sortino ratio
 Sortino ratio-1.190
 Upside Potential Ratio3.845
 Upside part of mean2.536
 Downside part of mean-3.321
 Upside SD0.459
 Downside SD0.659
 N nonnegative terms105.000
 N negative terms176.000
Statistics related to linear regression on benchmark
 N of observations281.000
 Mean of predictor0.251
 Mean of criterion-0.785
 SD of predictor0.146
 SD of criterion0.804
 Covariance-0.009
 r-0.078
 b (slope, estimate of beta)-0.428
 a (intercept, estimate of alpha)-0.677
 Mean Square Error0.645
 DF error279.000
 t(b)-1.303
 p(b)0.903
 t(a)-0.759
 p(a)0.776
 Lowerbound of 95% confidence interval for beta-1.075
 Upperbound of 95% confidence interval for beta0.219
 Lowerbound of 95% confidence interval for alpha-2.434
 Upperbound of 95% confidence interval for alpha1.079
 Treynor index (mean / b)1.833
 Jensen alpha (a)-0.677
Ratio statistics of excess log return rates
Statistics related to Sharpe ratio
 Mean-1.136
 SD0.857
 Sharpe ratio (Glass type estimate) -1.325
 Sharpe ratio (Hedges UMVUE)-1.321
 df280.000
 t-1.197
 p0.884
 Lowerbound of 95% confidence interval for Sharpe Ratio-3.495
 Upperbound of 95% confidence interval for Sharpe Ratio0.848
 Lowerbound of 95% CI (Gibbons, Hedeker & Davis approximation)-3.493
 Upperbound of 95% CI (Gibbons, Hedeker & Davis approximation)0.850
Statistics related to Sortino ratio
 Sortino ratio-1.532
 Upside Potential Ratio3.289
 Upside part of mean2.439
 Downside part of mean-3.574
 Upside SD0.431
 Downside SD0.741
 N nonnegative terms105.000
 N negative terms176.000
Statistics related to linear regression on benchmark
 N of observations281.000
 Mean of predictor0.240
 Mean of criterion-1.136
 SD of predictor0.146
 SD of criterion0.857
 Covariance-0.009
 r-0.076
 b (slope, estimate of beta)-0.444
 a (intercept, estimate of alpha)-1.029
 Mean Square Error0.733
 DF error279.000
 t(b)-1.265
 p(b)0.897
 t(a)-1.082
 p(a)0.860
 Lowerbound of 95% confidence interval for beta-1.135
 Upperbound of 95% confidence interval for beta0.247
 Lowerbound of 95% confidence interval for alpha-2.901
 Upperbound of 95% confidence interval for alpha0.843
 Treynor index (mean / b)2.558
 Jensen alpha (a)-1.029
Risk estimates for a one-period unit investment (parametric)
assuming log normal returns and losses (using central moments from Sharpe statistics)
 VaR(95%)0.076
 Expected Shortfall on VaR0.094
assuming Pareto losses only (using partial moments from Sortino statistics)
 VaR(95%)0.025
 Expected Shortfall on VaR0.056
ORDER STATISTICS
Quartiles of return rates
 Number of observations281.000
 Minimum0.692
 Quartile 10.999
 Median1.000
 Quartile 31.003
 Maximum1.221
 Mean of quarter 10.962
 Mean of quarter 21.000
 Mean of quarter 31.001
 Mean of quarter 41.029
 Inter Quartile Range0.004
 Number outliers low46.000
 Percentage of outliers low0.164
 Mean of outliers low0.943
 Number of outliers high40.000
 Percentage of outliers high0.142
 Mean of outliers high1.046
Risk estimates for a one-period unit investment (based on Extreme Value Theory)
 Extreme Value Index (moments method)1.645
 VaR(95%) (moments method)0.021
 Expected Shortfall (moments method)NA
 Extreme Value Index (regression method)0.875
 VaR(95%) (regression method)0.022
 Expected Shortfall (regression method)0.218
DRAW DOWN STATISTICS
Quartiles of draw downs
 Number of observations20.000
 Minimum0.000
 Quartile 10.002
 Median0.007
 Quartile 30.048
 Maximum0.720
 Mean of quarter 10.001
 Mean of quarter 20.003
 Mean of quarter 30.018
 Mean of quarter 40.256
 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 high0.150
 Mean of outliers high0.365
Risk estimates based on draw downs (based on Extreme Value Theory)
 Extreme Value Index (moments method)0.452
 VaR(95%) (moments method)0.237
 Expected Shortfall (moments method)0.521
 Extreme Value Index (regression method)1.006
 VaR(95%) (regression method)0.378
 Expected Shortfall (regression method)NA
COMBINED STATISTICS
 Annualized return (arithmetic extrapolation)-0.722
 Compounded annual return (geometric extrapolation)-0.664
 Calmar ratio (compounded annual return / max draw down)-0.923
 Compounded annual return / average of 25% largest draw downs-2.597
 Compounded annual return / Expected Shortfall lognormal-7.084
ANALYSIS BASED ON DAILY VALUES, LAST 6 MONTHS (Back)
RATIO STATISTICS
Ratio statistics of excess return rates
Statistics related to Sharpe ratio
 Mean-1.800
 SD0.879
 Sharpe ratio (Glass type estimate) -2.046
 Sharpe ratio (Hedges UMVUE)-2.037
 df171.000
 t-1.447
 p0.570
 Lowerbound of 95% confidence interval for Sharpe Ratio-4.824
 Upperbound of 95% confidence interval for Sharpe Ratio0.737
 Lowerbound of 95% CI (Gibbons, Hedeker & Davis approximation)-4.818
 Upperbound of 95% CI (Gibbons, Hedeker & Davis approximation)0.743
Statistics related to Sortino ratio
 Sortino ratio-2.311
 Upside Potential Ratio3.004
 Upside part of mean2.340
 Downside part of mean-4.139
 Upside SD0.414
 Downside SD0.779
 N nonnegative terms60.000
 N negative terms112.000
Statistics related to linear regression on benchmark
 N of observations172.000
 Mean of predictor0.364
 Mean of criterion-1.800
 SD of predictor0.165
 SD of criterion0.879
 Covariance-0.010
 r-0.068
 b (slope, estimate of beta)-0.360
 a (intercept, estimate of alpha)-1.669
 Mean Square Error0.774
 DF error170.000
 t(b)-0.883
 p(b)0.534
 t(a)-1.332
 p(a)0.551
 Lowerbound of 95% confidence interval for beta-1.163
 Upperbound of 95% confidence interval for beta0.444
 Lowerbound of 95% confidence interval for alpha-4.143
 Upperbound of 95% confidence interval for alpha0.805
 Treynor index (mean / b)5.005
 Jensen alpha (a)-1.669
Ratio statistics of excess log return rates
Statistics related to Sharpe ratio
 Mean-2.237
 SD0.960
 Sharpe ratio (Glass type estimate) -2.329
 Sharpe ratio (Hedges UMVUE)-2.319
 df171.000
 t-1.647
 p0.579
 Lowerbound of 95% confidence interval for Sharpe Ratio-5.108
 Upperbound of 95% confidence interval for Sharpe Ratio0.457
 Lowerbound of 95% CI (Gibbons, Hedeker & Davis approximation)-5.101
 Upperbound of 95% CI (Gibbons, Hedeker & Davis approximation)0.464
Statistics related to Sortino ratio
 Sortino ratio-2.538
 Upside Potential Ratio2.563
 Upside part of mean2.259
 Downside part of mean-4.496
 Upside SD0.393
 Downside SD0.881
 N nonnegative terms60.000
 N negative terms112.000
Statistics related to linear regression on benchmark
 N of observations172.000
 Mean of predictor0.350
 Mean of criterion-2.237
 SD of predictor0.165
 SD of criterion0.960
 Covariance-0.011
 r-0.068
 b (slope, estimate of beta)-0.393
 a (intercept, estimate of alpha)-2.099
 Mean Square Error0.924
 DF error170.000
 t(b)-0.883
 p(b)0.534
 t(a)-1.534
 p(a)0.558
 Lowerbound of 95% confidence interval for beta-1.273
 Upperbound of 95% confidence interval for beta0.486
 Lowerbound of 95% confidence interval for alpha-4.800
 Upperbound of 95% confidence interval for alpha0.602
 Treynor index (mean / b)5.684
 Jensen alpha (a)-2.099
Risk estimates for a one-period unit investment (parametric)
assuming log normal returns and losses (using central moments from Sharpe statistics)
 VaR(95%)0.088
 Expected Shortfall on VaR0.107
assuming Pareto losses only (using partial moments from Sortino statistics)
 VaR(95%)0.032
 Expected Shortfall on VaR0.071
ORDER STATISTICS
Quartiles of return rates
 Number of observations172.000
 Minimum0.692
 Quartile 11.000
 Median1.000
 Quartile 31.003
 Maximum1.160
 Mean of quarter 10.952
 Mean of quarter 21.000
 Mean of quarter 31.001
 Mean of quarter 41.027
 Inter Quartile Range0.003
 Number outliers low31.000
 Percentage of outliers low0.180
 Mean of outliers low0.934
 Number of outliers high29.000
 Percentage of outliers high0.169
 Mean of outliers high1.037
Risk estimates for a one-period unit investment (based on Extreme Value Theory)
 Extreme Value Index (moments method)1.168
 VaR(95%) (moments method)0.009
 Expected Shortfall (moments method)NA
 Extreme Value Index (regression method)0.754
 VaR(95%) (regression method)0.032
 Expected Shortfall (regression method)0.178
DRAW DOWN STATISTICS
Quartiles of draw downs
 Number of observations8.000
 Minimum0.001
 Quartile 10.002
 Median0.002
 Quartile 30.023
 Maximum0.720
 Mean of quarter 10.001
 Mean of quarter 20.002
 Mean of quarter 30.010
 Mean of quarter 40.379
 Inter Quartile Range0.022
 Number outliers low0.000
 Percentage of outliers low0.000
 Mean of outliers lowNA
 Number of outliers high1.000
 Percentage of outliers high0.125
 Mean of outliers high0.720
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)-1.332
 Compounded annual return (geometric extrapolation)-0.888
 Calmar ratio (compounded annual return / max draw down)-1.234
 Compounded annual return / average of 25% largest draw downs-2.346
 Compounded annual return / Expected Shortfall lognormal-8.305