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Advanced Statistics: MORE FX

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-0.773
 SD0.443
 Sharpe ratio (Glass type estimate) -1.746
 Sharpe ratio (Hedges UMVUE)-1.468
 df5.000
 t-1.235
 p0.864
 Lowerbound of 95% confidence interval for Sharpe Ratio-4.638
 Upperbound of 95% confidence interval for Sharpe Ratio1.292
 Lowerbound of 95% CI (Gibbons, Hedeker & Davis approximation)-4.386
 Upperbound of 95% CI (Gibbons, Hedeker & Davis approximation)1.449
Statistics related to Sortino ratio
 Sortino ratio-1.788
 Upside Potential Ratio0.546
 Upside part of mean0.236
 Downside part of mean-1.009
 Upside SD0.162
 Downside SD0.432
 N nonnegative terms3.000
 N negative terms3.000
Statistics related to linear regression on benchmark
 N of observations6.000
 Mean of predictor0.155
 Mean of criterion-0.773
 SD of predictor0.143
 SD of criterion0.443
 Covariance0.004
 r0.067
 b (slope, estimate of beta)0.208
 a (intercept, estimate of alpha)-0.805
 Mean Square Error0.244
 DF error4.000
 t(b)0.134
 p(b)0.450
 t(a)-1.090
 p(a)0.832
 Lowerbound of 95% confidence interval for beta-4.090
 Upperbound of 95% confidence interval for beta4.506
 Lowerbound of 95% confidence interval for alpha-2.856
 Upperbound of 95% confidence interval for alpha1.245
 Treynor index (mean / b)-3.720
 Jensen alpha (a)-0.805
Ratio statistics of excess log return rates
Statistics related to Sharpe ratio
 Mean-0.889
 SD0.474
 Sharpe ratio (Glass type estimate) -1.876
 Sharpe ratio (Hedges UMVUE)-1.577
 df5.000
 t-1.327
 p0.879
 Lowerbound of 95% confidence interval for Sharpe Ratio-4.793
 Upperbound of 95% confidence interval for Sharpe Ratio1.195
 Lowerbound of 95% CI (Gibbons, Hedeker & Davis approximation)-4.516
 Upperbound of 95% CI (Gibbons, Hedeker & Davis approximation)1.362
Statistics related to Sortino ratio
 Sortino ratio-1.855
 Upside Potential Ratio0.466
 Upside part of mean0.223
 Downside part of mean-1.112
 Upside SD0.153
 Downside SD0.479
 N nonnegative terms3.000
 N negative terms3.000
Statistics related to linear regression on benchmark
 N of observations6.000
 Mean of predictor0.146
 Mean of criterion-0.889
 SD of predictor0.143
 SD of criterion0.474
 Covariance0.004
 r0.057
 b (slope, estimate of beta)0.188
 a (intercept, estimate of alpha)-0.916
 Mean Square Error0.280
 DF error4.000
 t(b)0.113
 p(b)0.458
 t(a)-1.166
 p(a)0.846
 Lowerbound of 95% confidence interval for beta-4.414
 Upperbound of 95% confidence interval for beta4.790
 Lowerbound of 95% confidence interval for alpha-3.099
 Upperbound of 95% confidence interval for alpha1.266
 Treynor index (mean / b)-4.727
 Jensen alpha (a)-0.916
Risk estimates for a one-period unit investment (parametric)
assuming log normal returns and losses (using central moments from Sharpe statistics)
 VaR(95%)0.259
 Expected Shortfall on VaR0.299
assuming Pareto losses only (using partial moments from Sortino statistics)
 VaR(95%)0.196
 Expected Shortfall on VaR0.298
ORDER STATISTICS
Quartiles of return rates
 Number of observations6.000
 Minimum0.797
 Quartile 10.826
 Median0.958
 Quartile 31.006
 Maximum1.118
 Mean of quarter 10.798
 Mean of quarter 20.911
 Mean of quarter 31.004
 Mean of quarter 41.062
 Inter Quartile Range0.180
 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 for a one-period unit investment (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
DRAW DOWN STATISTICS
Quartiles of draw downs
 Number of observations1.000
 Minimum0.420
 Quartile 10.420
 Median0.420
 Quartile 30.420
 Maximum0.420
 Mean of quarter 1NA
 Mean of quarter 2NA
 Mean of quarter 3NA
 Mean of quarter 4NA
 Inter Quartile Range0.000
 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)-0.689
 Compounded annual return (geometric extrapolation)-0.570
 Calmar ratio (compounded annual return / max draw down)-1.358
 Compounded annual return / average of 25% largest draw downsNA
 Compounded annual return / Expected Shortfall lognormal-1.909
ANALYSIS BASED ON DAILY VALUES, FULL HISTORY (Back)
RATIO STATISTICS
Ratio statistics of excess return rates
Statistics related to Sharpe ratio
 Mean-0.684
 SD0.654
 Sharpe ratio (Glass type estimate) -1.047
 Sharpe ratio (Hedges UMVUE)-1.043
 df189.000
 t-0.778
 p0.536
 Lowerbound of 95% confidence interval for Sharpe Ratio-3.685
 Upperbound of 95% confidence interval for Sharpe Ratio1.594
 Lowerbound of 95% CI (Gibbons, Hedeker & Davis approximation)-3.682
 Upperbound of 95% CI (Gibbons, Hedeker & Davis approximation)1.596
Statistics related to Sortino ratio
 Sortino ratio-1.453
 Upside Potential Ratio5.723
 Upside part of mean2.695
 Downside part of mean-3.380
 Upside SD0.452
 Downside SD0.471
 N nonnegative terms70.000
 N negative terms120.000
Statistics related to linear regression on benchmark
 N of observations190.000
 Mean of predictor0.364
 Mean of criterion-0.684
 SD of predictor0.126
 SD of criterion0.654
 Covariance-0.008
 r-0.097
 b (slope, estimate of beta)-0.507
 a (intercept, estimate of alpha)-0.500
 Mean Square Error0.425
 DF error188.000
 t(b)-1.341
 p(b)0.549
 t(a)-0.563
 p(a)0.520
 Lowerbound of 95% confidence interval for beta-1.252
 Upperbound of 95% confidence interval for beta0.239
 Lowerbound of 95% confidence interval for alpha-2.252
 Upperbound of 95% confidence interval for alpha1.252
 Treynor index (mean / b)1.351
 Jensen alpha (a)-0.500
Ratio statistics of excess log return rates
Statistics related to Sharpe ratio
 Mean-0.897
 SD0.653
 Sharpe ratio (Glass type estimate) -1.373
 Sharpe ratio (Hedges UMVUE)-1.368
 df189.000
 t-1.021
 p0.547
 Lowerbound of 95% confidence interval for Sharpe Ratio-4.012
 Upperbound of 95% confidence interval for Sharpe Ratio1.269
 Lowerbound of 95% CI (Gibbons, Hedeker & Davis approximation)-4.009
 Upperbound of 95% CI (Gibbons, Hedeker & Davis approximation)1.273
Statistics related to Sortino ratio
 Sortino ratio-1.803
 Upside Potential Ratio5.229
 Upside part of mean2.602
 Downside part of mean-3.499
 Upside SD0.423
 Downside SD0.498
 N nonnegative terms70.000
 N negative terms120.000
Statistics related to linear regression on benchmark
 N of observations190.000
 Mean of predictor0.356
 Mean of criterion-0.897
 SD of predictor0.125
 SD of criterion0.653
 Covariance-0.008
 r-0.099
 b (slope, estimate of beta)-0.517
 a (intercept, estimate of alpha)-0.713
 Mean Square Error0.425
 DF error188.000
 t(b)-1.366
 p(b)0.550
 t(a)-0.803
 p(a)0.529
 Lowerbound of 95% confidence interval for beta-1.265
 Upperbound of 95% confidence interval for beta0.230
 Lowerbound of 95% confidence interval for alpha-2.463
 Upperbound of 95% confidence interval for alpha1.038
 Treynor index (mean / b)1.734
 Jensen alpha (a)-0.713
Risk estimates for a one-period unit investment (parametric)
assuming log normal returns and losses (using central moments from Sharpe statistics)
 VaR(95%)0.059
 Expected Shortfall on VaR0.072
assuming Pareto losses only (using partial moments from Sortino statistics)
 VaR(95%)0.026
 Expected Shortfall on VaR0.054
ORDER STATISTICS
Quartiles of return rates
 Number of observations190.000
 Minimum0.837
 Quartile 10.993
 Median1.000
 Quartile 31.006
 Maximum1.228
 Mean of quarter 10.963
 Mean of quarter 20.998
 Mean of quarter 31.001
 Mean of quarter 41.030
 Inter Quartile Range0.013
 Number outliers low23.000
 Percentage of outliers low0.121
 Mean of outliers low0.939
 Number of outliers high16.000
 Percentage of outliers high0.084
 Mean of outliers high1.066
Risk estimates for a one-period unit investment (based on Extreme Value Theory)
 Extreme Value Index (moments method)0.519
 VaR(95%) (moments method)0.032
 Expected Shortfall (moments method)0.077
 Extreme Value Index (regression method)0.072
 VaR(95%) (regression method)0.031
 Expected Shortfall (regression method)0.048
DRAW DOWN STATISTICS
Quartiles of draw downs
 Number of observations2.000
 Minimum0.013
 Quartile 10.151
 Median0.290
 Quartile 30.428
 Maximum0.567
 Mean of quarter 10.013
 Mean of quarter 2NA
 Mean of quarter 3NA
 Mean of quarter 40.567
 Inter Quartile Range0.277
 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)-0.680
 Compounded annual return (geometric extrapolation)-0.574
 Calmar ratio (compounded annual return / max draw down)-1.013
 Compounded annual return / average of 25% largest draw downs-1.013
 Compounded annual return / Expected Shortfall lognormal-7.925
ANALYSIS BASED ON DAILY VALUES, LAST 6 MONTHS (Back)
RATIO STATISTICS
Ratio statistics of excess return rates
Statistics related to Sharpe ratio
 Mean-0.656
 SD0.683
 Sharpe ratio (Glass type estimate) -0.960
 Sharpe ratio (Hedges UMVUE)-0.956
 df171.000
 t-0.679
 p0.533
 Lowerbound of 95% confidence interval for Sharpe Ratio-3.733
 Upperbound of 95% confidence interval for Sharpe Ratio1.815
 Lowerbound of 95% CI (Gibbons, Hedeker & Davis approximation)-3.730
 Upperbound of 95% CI (Gibbons, Hedeker & Davis approximation)1.818
Statistics related to Sortino ratio
 Sortino ratio-1.336
 Upside Potential Ratio5.821
 Upside part of mean2.860
 Downside part of mean-3.516
 Upside SD0.473
 Downside SD0.491
 N nonnegative terms63.000
 N negative terms109.000
Statistics related to linear regression on benchmark
 N of observations172.000
 Mean of predictor0.307
 Mean of criterion-0.656
 SD of predictor0.124
 SD of criterion0.683
 Covariance-0.008
 r-0.093
 b (slope, estimate of beta)-0.512
 a (intercept, estimate of alpha)-0.499
 Mean Square Error0.466
 DF error170.000
 t(b)-1.217
 p(b)0.546
 t(a)-0.513
 p(a)0.520
 Lowerbound of 95% confidence interval for beta-1.343
 Upperbound of 95% confidence interval for beta0.319
 Lowerbound of 95% confidence interval for alpha-2.421
 Upperbound of 95% confidence interval for alpha1.423
 Treynor index (mean / b)1.281
 Jensen alpha (a)-0.499
Ratio statistics of excess log return rates
Statistics related to Sharpe ratio
 Mean-0.889
 SD0.683
 Sharpe ratio (Glass type estimate) -1.301
 Sharpe ratio (Hedges UMVUE)-1.295
 df171.000
 t-0.920
 p0.545
 Lowerbound of 95% confidence interval for Sharpe Ratio-4.074
 Upperbound of 95% confidence interval for Sharpe Ratio1.476
 Lowerbound of 95% CI (Gibbons, Hedeker & Davis approximation)-4.070
 Upperbound of 95% CI (Gibbons, Hedeker & Davis approximation)1.480
Statistics related to Sortino ratio
 Sortino ratio-1.711
 Upside Potential Ratio5.308
 Upside part of mean2.757
 Downside part of mean-3.645
 Upside SD0.443
 Downside SD0.519
 N nonnegative terms63.000
 N negative terms109.000
Statistics related to linear regression on benchmark
 N of observations172.000
 Mean of predictor0.299
 Mean of criterion-0.889
 SD of predictor0.124
 SD of criterion0.683
 Covariance-0.008
 r-0.095
 b (slope, estimate of beta)-0.526
 a (intercept, estimate of alpha)-0.731
 Mean Square Error0.465
 DF error170.000
 t(b)-1.246
 p(b)0.548
 t(a)-0.752
 p(a)0.529
 Lowerbound of 95% confidence interval for beta-1.358
 Upperbound of 95% confidence interval for beta0.307
 Lowerbound of 95% confidence interval for alpha-2.651
 Upperbound of 95% confidence interval for alpha1.188
 Treynor index (mean / b)1.691
 Jensen alpha (a)-0.731
Risk estimates for a one-period unit investment (parametric)
assuming log normal returns and losses (using central moments from Sharpe statistics)
 VaR(95%)0.061
 Expected Shortfall on VaR0.075
assuming Pareto losses only (using partial moments from Sortino statistics)
 VaR(95%)0.027
 Expected Shortfall on VaR0.056
ORDER STATISTICS
Quartiles of return rates
 Number of observations172.000
 Minimum0.837
 Quartile 10.993
 Median1.000
 Quartile 31.006
 Maximum1.228
 Mean of quarter 10.961
 Mean of quarter 20.999
 Mean of quarter 31.001
 Mean of quarter 41.032
 Inter Quartile Range0.013
 Number outliers low23.000
 Percentage of outliers low0.134
 Mean of outliers low0.939
 Number of outliers high16.000
 Percentage of outliers high0.093
 Mean of outliers high1.066
Risk estimates for a one-period unit investment (based on Extreme Value Theory)
 Extreme Value Index (moments method)0.435
 VaR(95%) (moments method)0.030
 Expected Shortfall (moments method)0.066
 Extreme Value Index (regression method)0.004
 VaR(95%) (regression method)0.033
 Expected Shortfall (regression method)0.049
DRAW DOWN STATISTICS
Quartiles of draw downs
 Number of observations3.000
 Minimum0.002
 Quartile 10.030
 Median0.058
 Quartile 30.304
 Maximum0.549
 Mean of quarter 10.002
 Mean of quarter 20.058
 Mean of quarter 3NA
 Mean of quarter 40.549
 Inter Quartile Range0.274
 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)-0.689
 Compounded annual return (geometric extrapolation)-0.570
 Calmar ratio (compounded annual return / max draw down)-1.039
 Compounded annual return / average of 25% largest draw downs-1.039
 Compounded annual return / Expected Shortfall lognormal-7.558