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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-0.691
 SD0.657
 Sharpe ratio (Glass type estimate) -1.052
 Sharpe ratio (Hedges UMVUE)-1.048
 df187.000
 t-0.778
 p0.536
 Lowerbound of 95% confidence interval for Sharpe Ratio-3.704
 Upperbound of 95% confidence interval for Sharpe Ratio1.603
 Lowerbound of 95% CI (Gibbons, Hedeker & Davis approximation)-3.701
 Upperbound of 95% CI (Gibbons, Hedeker & Davis approximation)1.606
Statistics related to Sortino ratio
 Sortino ratio-1.460
 Upside Potential Ratio5.753
 Upside part of mean2.724
 Downside part of mean-3.415
 Upside SD0.454
 Downside SD0.473
 N nonnegative terms70.000
 N negative terms118.000
Statistics related to linear regression on benchmark
 N of observations188.000
 Mean of predictor0.329
 Mean of criterion-0.691
 SD of predictor0.124
 SD of criterion0.657
 Covariance-0.008
 r-0.100
 b (slope, estimate of beta)-0.532
 a (intercept, estimate of alpha)-0.516
 Mean Square Error0.430
 DF error186.000
 t(b)-1.372
 p(b)0.550
 t(a)-0.576
 p(a)0.521
 Lowerbound of 95% confidence interval for beta-1.296
 Upperbound of 95% confidence interval for beta0.233
 Lowerbound of 95% confidence interval for alpha-2.283
 Upperbound of 95% confidence interval for alpha1.251
 Treynor index (mean / b)1.300
 Jensen alpha (a)-0.516
Ratio statistics of excess log return rates
Statistics related to Sharpe ratio
 Mean-0.906
 SD0.657
 Sharpe ratio (Glass type estimate) -1.380
 Sharpe ratio (Hedges UMVUE)-1.374
 df187.000
 t-1.020
 p0.547
 Lowerbound of 95% confidence interval for Sharpe Ratio-4.033
 Upperbound of 95% confidence interval for Sharpe Ratio1.277
 Lowerbound of 95% CI (Gibbons, Hedeker & Davis approximation)-4.029
 Upperbound of 95% CI (Gibbons, Hedeker & Davis approximation)1.281
Statistics related to Sortino ratio
 Sortino ratio-1.811
 Upside Potential Ratio5.256
 Upside part of mean2.629
 Downside part of mean-3.535
 Upside SD0.426
 Downside SD0.500
 N nonnegative terms70.000
 N negative terms118.000
Statistics related to linear regression on benchmark
 N of observations188.000
 Mean of predictor0.322
 Mean of criterion-0.906
 SD of predictor0.123
 SD of criterion0.657
 Covariance-0.008
 r-0.102
 b (slope, estimate of beta)-0.544
 a (intercept, estimate of alpha)-0.731
 Mean Square Error0.429
 DF error186.000
 t(b)-1.401
 p(b)0.551
 t(a)-0.817
 p(a)0.530
 Lowerbound of 95% confidence interval for beta-1.310
 Upperbound of 95% confidence interval for beta0.222
 Lowerbound of 95% confidence interval for alpha-2.496
 Upperbound of 95% confidence interval for alpha1.034
 Treynor index (mean / b)1.666
 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%)0.059
 Expected Shortfall on VaR0.073
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 observations188.000
 Minimum0.837
 Quartile 10.992
 Median1.000
 Quartile 31.006
 Maximum1.228
 Mean of quarter 10.962
 Mean of quarter 20.998
 Mean of quarter 31.001
 Mean of quarter 41.031
 Inter Quartile Range0.014
 Number outliers low23.000
 Percentage of outliers low0.122
 Mean of outliers low0.939
 Number of outliers high16.000
 Percentage of outliers high0.085
 Mean of outliers high1.066
Risk estimates for a one-period unit investment (based on Extreme Value Theory)
 Extreme Value Index (moments method)0.471
 VaR(95%) (moments method)0.031
 Expected Shortfall (moments method)0.071
 Extreme Value Index (regression method)0.057
 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)-0.687
 Compounded annual return (geometric extrapolation)-0.578
 Calmar ratio (compounded annual return / max draw down)-1.020
 Compounded annual return / average of 25% largest draw downs-1.020
 Compounded annual return / Expected Shortfall lognormal-7.936
ANALYSIS BASED ON DAILY VALUES, LAST 6 MONTHS (Back)
RATIO STATISTICS
Ratio statistics of excess return rates
Statistics related to Sharpe ratio
 Mean-0.668
 SD0.683
 Sharpe ratio (Glass type estimate) -0.978
 Sharpe ratio (Hedges UMVUE)-0.973
 df171.000
 t-0.691
 p0.534
 Lowerbound of 95% confidence interval for Sharpe Ratio-3.750
 Upperbound of 95% confidence interval for Sharpe Ratio1.797
 Lowerbound of 95% CI (Gibbons, Hedeker & Davis approximation)-3.747
 Upperbound of 95% CI (Gibbons, Hedeker & Davis approximation)1.800
Statistics related to Sortino ratio
 Sortino ratio-1.360
 Upside Potential Ratio5.820
 Upside part of mean2.860
 Downside part of mean-3.528
 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 predictor0.264
 Mean of criterion-0.668
 SD of predictor0.121
 SD of criterion0.683
 Covariance-0.008
 r-0.096
 b (slope, estimate of beta)-0.541
 a (intercept, estimate of alpha)-0.525
 Mean Square Error0.465
 DF error170.000
 t(b)-1.256
 p(b)0.548
 t(a)-0.541
 p(a)0.521
 Lowerbound of 95% confidence interval for beta-1.391
 Upperbound of 95% confidence interval for beta0.309
 Lowerbound of 95% confidence interval for alpha-2.443
 Upperbound of 95% confidence interval for alpha1.392
 Treynor index (mean / b)1.235
 Jensen alpha (a)-0.525
Ratio statistics of excess log return rates
Statistics related to Sharpe ratio
 Mean-0.900
 SD0.683
 Sharpe ratio (Glass type estimate) -1.318
 Sharpe ratio (Hedges UMVUE)-1.313
 df171.000
 t-0.932
 p0.545
 Lowerbound of 95% confidence interval for Sharpe Ratio-4.092
 Upperbound of 95% confidence interval for Sharpe Ratio1.459
 Lowerbound of 95% CI (Gibbons, Hedeker & Davis approximation)-4.088
 Upperbound of 95% CI (Gibbons, Hedeker & Davis approximation)1.463
Statistics related to Sortino ratio
 Sortino ratio-1.734
 Upside Potential Ratio5.308
 Upside part of mean2.757
 Downside part of mean-3.657
 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 predictor0.257
 Mean of criterion-0.900
 SD of predictor0.121
 SD of criterion0.683
 Covariance-0.008
 r-0.098
 b (slope, estimate of beta)-0.557
 a (intercept, estimate of alpha)-0.758
 Mean Square Error0.465
 DF error170.000
 t(b)-1.290
 p(b)0.549
 t(a)-0.781
 p(a)0.530
 Lowerbound of 95% confidence interval for beta-1.408
 Upperbound of 95% confidence interval for beta0.295
 Lowerbound of 95% confidence interval for alpha-2.673
 Upperbound of 95% confidence interval for alpha1.158
 Treynor index (mean / b)1.618
 Jensen alpha (a)-0.758
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
 Minimum0.008
 Quartile 10.033
 Median0.058
 Quartile 30.304
 Maximum0.549
 Mean of quarter 10.008
 Mean of quarter 20.058
 Mean of quarter 3NA
 Mean of quarter 40.549
 Inter Quartile Range0.271
 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)-0.697
 Compounded annual return (geometric extrapolation)-0.575
 Calmar ratio (compounded annual return / max draw down)-1.048
 Compounded annual return / average of 25% largest draw downs-1.048
 Compounded annual return / Expected Shortfall lognormal-7.622