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Advanced Statistics: Will Oli Forex

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-0.090
 SD0.565
 Sharpe ratio (Glass type estimate) -0.159
 Sharpe ratio (Hedges UMVUE)-0.134
 df5.000
 t-0.112
 p0.543
 Lowerbound of 95% confidence interval for Sharpe Ratio-2.925
 Upperbound of 95% confidence interval for Sharpe Ratio2.622
 Lowerbound of 95% CI (Gibbons, Hedeker & Davis approximation)-2.907
 Upperbound of 95% CI (Gibbons, Hedeker & Davis approximation)2.639
Statistics related to Sortino ratio
 Sortino ratio-0.219
 Upside Potential Ratio1.498
 Upside part of mean0.614
 Downside part of mean-0.704
 Upside SD0.315
 Downside SD0.410
 N nonnegative terms2.000
 N negative terms4.000
Statistics related to linear regression on benchmark
 N of observations6.000
 Mean of predictor0.037
 Mean of criterion-0.090
 SD of predictor0.133
 SD of criterion0.565
 Covariance-0.060
 r-0.790
 b (slope, estimate of beta)-3.344
 a (intercept, estimate of alpha)0.034
 Mean Square Error0.150
 DF error4.000
 t(b)-2.575
 p(b)0.969
 t(a)0.062
 p(a)0.477
 Lowerbound of 95% confidence interval for beta-6.951
 Upperbound of 95% confidence interval for beta0.263
 Lowerbound of 95% confidence interval for alpha-1.494
 Upperbound of 95% confidence interval for alpha1.563
 Treynor index (mean / b)0.027
 Jensen alpha (a)0.034
Ratio statistics of excess log return rates
Statistics related to Sharpe ratio
 Mean-0.236
 SD0.608
 Sharpe ratio (Glass type estimate) -0.389
 Sharpe ratio (Hedges UMVUE)-0.327
 df5.000
 t-0.275
 p0.603
 Lowerbound of 95% confidence interval for Sharpe Ratio-3.152
 Upperbound of 95% confidence interval for Sharpe Ratio2.411
 Lowerbound of 95% CI (Gibbons, Hedeker & Davis approximation)-3.106
 Upperbound of 95% CI (Gibbons, Hedeker & Davis approximation)2.452
Statistics related to Sortino ratio
 Sortino ratio-0.495
 Upside Potential Ratio1.188
 Upside part of mean0.567
 Downside part of mean-0.804
 Upside SD0.290
 Downside SD0.478
 N nonnegative terms2.000
 N negative terms4.000
Statistics related to linear regression on benchmark
 N of observations6.000
 Mean of predictor0.029
 Mean of criterion-0.236
 SD of predictor0.135
 SD of criterion0.608
 Covariance-0.062
 r-0.762
 b (slope, estimate of beta)-3.434
 a (intercept, estimate of alpha)-0.135
 Mean Square Error0.194
 DF error4.000
 t(b)-2.353
 p(b)0.961
 t(a)-0.217
 p(a)0.581
 Lowerbound of 95% confidence interval for beta-7.487
 Upperbound of 95% confidence interval for beta0.619
 Lowerbound of 95% confidence interval for alpha-1.867
 Upperbound of 95% confidence interval for alpha1.597
 Treynor index (mean / b)0.069
 Jensen alpha (a)-0.135
Risk estimates for a one-period unit investment (parametric)
assuming log normal returns and losses (using central moments from Sharpe statistics)
 VaR(95%)0.265
 Expected Shortfall on VaR0.316
assuming Pareto losses only (using partial moments from Sortino statistics)
 VaR(95%)0.161
 Expected Shortfall on VaR0.301
ORDER STATISTICS
Quartiles of return rates
 Number of observations6.000
 Minimum0.720
 Quartile 10.959
 Median0.998
 Quartile 31.092
 Maximum1.192
 Mean of quarter 10.833
 Mean of quarter 20.996
 Mean of quarter 31.000
 Mean of quarter 41.157
 Inter Quartile Range0.133
 Number outliers low1.000
 Percentage of outliers low0.167
 Mean of outliers low0.720
 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 observations2.000
 Minimum0.053
 Quartile 10.110
 Median0.168
 Quartile 30.226
 Maximum0.283
 Mean of quarter 10.053
 Mean of quarter 2NA
 Mean of quarter 3NA
 Mean of quarter 40.283
 Inter Quartile Range0.115
 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)-0.183
 Compounded annual return (geometric extrapolation)-0.175
 Calmar ratio (compounded annual return / max draw down)-0.618
 Compounded annual return / average of 25% largest draw downs-0.618
 Compounded annual return / Expected Shortfall lognormal-0.554
ANALYSIS BASED ON DAILY VALUES, FULL HISTORY (Back)
RATIO STATISTICS
Ratio statistics of excess return rates
Statistics related to Sharpe ratio
 Mean0.009
 SD0.670
 Sharpe ratio (Glass type estimate) 0.014
 Sharpe ratio (Hedges UMVUE)0.014
 df195.000
 t0.010
 p0.500
 Lowerbound of 95% confidence interval for Sharpe Ratio-2.583
 Upperbound of 95% confidence interval for Sharpe Ratio2.610
 Lowerbound of 95% CI (Gibbons, Hedeker & Davis approximation)-2.583
 Upperbound of 95% CI (Gibbons, Hedeker & Davis approximation)2.610
Statistics related to Sortino ratio
 Sortino ratio0.020
 Upside Potential Ratio6.785
 Upside part of mean3.086
 Downside part of mean-3.077
 Upside SD0.489
 Downside SD0.455
 N nonnegative terms43.000
 N negative terms153.000
Statistics related to linear regression on benchmark
 N of observations196.000
 Mean of predictor0.307
 Mean of criterion0.009
 SD of predictor0.177
 SD of criterion0.670
 Covariance-0.011
 r-0.094
 b (slope, estimate of beta)-0.354
 a (intercept, estimate of alpha)0.118
 Mean Square Error0.447
 DF error194.000
 t(b)-1.309
 p(b)0.547
 t(a)0.133
 p(a)0.495
 Lowerbound of 95% confidence interval for beta-0.886
 Upperbound of 95% confidence interval for beta0.179
 Lowerbound of 95% confidence interval for alpha-1.637
 Upperbound of 95% confidence interval for alpha1.872
 Treynor index (mean / b)-0.026
 Jensen alpha (a)0.118
Ratio statistics of excess log return rates
Statistics related to Sharpe ratio
 Mean-0.213
 SD0.668
 Sharpe ratio (Glass type estimate) -0.319
 Sharpe ratio (Hedges UMVUE)-0.317
 df195.000
 t-0.241
 p0.511
 Lowerbound of 95% confidence interval for Sharpe Ratio-2.915
 Upperbound of 95% confidence interval for Sharpe Ratio2.278
 Lowerbound of 95% CI (Gibbons, Hedeker & Davis approximation)-2.914
 Upperbound of 95% CI (Gibbons, Hedeker & Davis approximation)2.279
Statistics related to Sortino ratio
 Sortino ratio-0.446
 Upside Potential Ratio6.232
 Upside part of mean2.974
 Downside part of mean-3.187
 Upside SD0.465
 Downside SD0.477
 N nonnegative terms43.000
 N negative terms153.000
Statistics related to linear regression on benchmark
 N of observations196.000
 Mean of predictor0.291
 Mean of criterion-0.213
 SD of predictor0.177
 SD of criterion0.668
 Covariance-0.011
 r-0.092
 b (slope, estimate of beta)-0.347
 a (intercept, estimate of alpha)-0.112
 Mean Square Error0.445
 DF error194.000
 t(b)-1.282
 p(b)0.546
 t(a)-0.126
 p(a)0.505
 Lowerbound of 95% confidence interval for beta-0.880
 Upperbound of 95% confidence interval for beta0.187
 Lowerbound of 95% confidence interval for alpha-1.862
 Upperbound of 95% confidence interval for alpha1.638
 Treynor index (mean / b)0.614
 Jensen alpha (a)-0.112
Risk estimates for a one-period unit investment (parametric)
assuming log normal returns and losses (using central moments from Sharpe statistics)
 VaR(95%)0.058
 Expected Shortfall on VaR0.072
assuming Pareto losses only (using partial moments from Sortino statistics)
 VaR(95%)0.027
 Expected Shortfall on VaR0.055
ORDER STATISTICS
Quartiles of return rates
 Number of observations196.000
 Minimum0.858
 Quartile 10.999
 Median1.000
 Quartile 31.000
 Maximum1.170
 Mean of quarter 10.965
 Mean of quarter 21.000
 Mean of quarter 31.000
 Mean of quarter 41.036
 Inter Quartile Range0.001
 Number outliers low47.000
 Percentage of outliers low0.240
 Mean of outliers low0.963
 Number of outliers high41.000
 Percentage of outliers high0.209
 Mean of outliers high1.043
Risk estimates for a one-period unit investment (based on Extreme Value Theory)
 Extreme Value Index (moments method)0.350
 VaR(95%) (moments method)0.011
 Expected Shortfall (moments method)0.023
 Extreme Value Index (regression method)0.058
 VaR(95%) (regression method)0.033
 Expected Shortfall (regression method)0.055
DRAW DOWN STATISTICS
Quartiles of draw downs
 Number of observations6.000
 Minimum0.002
 Quartile 10.040
 Median0.099
 Quartile 30.255
 Maximum0.357
 Mean of quarter 10.018
 Mean of quarter 20.057
 Mean of quarter 30.141
 Mean of quarter 40.325
 Inter Quartile Range0.215
 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)-0.161
 Compounded annual return (geometric extrapolation)-0.155
 Calmar ratio (compounded annual return / max draw down)-0.435
 Compounded annual return / average of 25% largest draw downs-0.478
 Compounded annual return / Expected Shortfall lognormal-2.155
ANALYSIS BASED ON DAILY VALUES, LAST 6 MONTHS (Back)
RATIO STATISTICS
Ratio statistics of excess return rates
Statistics related to Sharpe ratio
 Mean0.009
 SD0.702
 Sharpe ratio (Glass type estimate) 0.013
 Sharpe ratio (Hedges UMVUE)0.013
 df171.000
 t0.009
 p0.500
 Lowerbound of 95% confidence interval for Sharpe Ratio-2.759
 Upperbound of 95% confidence interval for Sharpe Ratio2.785
 Lowerbound of 95% CI (Gibbons, Hedeker & Davis approximation)-2.759
 Upperbound of 95% CI (Gibbons, Hedeker & Davis approximation)2.785
Statistics related to Sortino ratio
 Sortino ratio0.020
 Upside Potential Ratio6.816
 Upside part of mean3.227
 Downside part of mean-3.218
 Upside SD0.515
 Downside SD0.474
 N nonnegative terms36.000
 N negative terms136.000
Statistics related to linear regression on benchmark
 N of observations172.000
 Mean of predictor0.296
 Mean of criterion0.009
 SD of predictor0.186
 SD of criterion0.702
 Covariance-0.012
 r-0.090
 b (slope, estimate of beta)-0.339
 a (intercept, estimate of alpha)0.110
 Mean Square Error0.491
 DF error170.000
 t(b)-1.174
 p(b)0.545
 t(a)0.110
 p(a)0.496
 Lowerbound of 95% confidence interval for beta-0.908
 Upperbound of 95% confidence interval for beta0.231
 Lowerbound of 95% confidence interval for alpha-1.855
 Upperbound of 95% confidence interval for alpha2.074
 Treynor index (mean / b)-0.027
 Jensen alpha (a)0.110
Ratio statistics of excess log return rates
Statistics related to Sharpe ratio
 Mean-0.234
 SD0.700
 Sharpe ratio (Glass type estimate) -0.335
 Sharpe ratio (Hedges UMVUE)-0.333
 df171.000
 t-0.237
 p0.512
 Lowerbound of 95% confidence interval for Sharpe Ratio-3.107
 Upperbound of 95% confidence interval for Sharpe Ratio2.438
 Lowerbound of 95% CI (Gibbons, Hedeker & Davis approximation)-3.105
 Upperbound of 95% CI (Gibbons, Hedeker & Davis approximation)2.439
Statistics related to Sortino ratio
 Sortino ratio-0.471
 Upside Potential Ratio6.240
 Upside part of mean3.103
 Downside part of mean-3.337
 Upside SD0.490
 Downside SD0.497
 N nonnegative terms36.000
 N negative terms136.000
Statistics related to linear regression on benchmark
 N of observations172.000
 Mean of predictor0.279
 Mean of criterion-0.234
 SD of predictor0.185
 SD of criterion0.700
 Covariance-0.011
 r-0.088
 b (slope, estimate of beta)-0.331
 a (intercept, estimate of alpha)-0.142
 Mean Square Error0.489
 DF error170.000
 t(b)-1.146
 p(b)0.544
 t(a)-0.143
 p(a)0.505
 Lowerbound of 95% confidence interval for beta-0.901
 Upperbound of 95% confidence interval for beta0.239
 Lowerbound of 95% confidence interval for alpha-2.100
 Upperbound of 95% confidence interval for alpha1.816
 Treynor index (mean / b)0.708
 Jensen alpha (a)-0.142
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%)0.028
 Expected Shortfall on VaR0.058
ORDER STATISTICS
Quartiles of return rates
 Number of observations172.000
 Minimum0.858
 Quartile 11.000
 Median1.000
 Quartile 31.000
 Maximum1.170
 Mean of quarter 10.963
 Mean of quarter 21.000
 Mean of quarter 31.000
 Mean of quarter 41.038
 Inter Quartile Range0.000
 Number outliers low43.000
 Percentage of outliers low0.250
 Mean of outliers low0.963
 Number of outliers high36.000
 Percentage of outliers high0.209
 Mean of outliers high1.045
Risk estimates for a one-period unit investment (based on Extreme Value Theory)
 Extreme Value Index (moments method)-1.234
 VaR(95%) (moments method)0.005
 Expected Shortfall (moments method)0.005
 Extreme Value Index (regression method)-0.103
 VaR(95%) (regression method)0.038
 Expected Shortfall (regression method)0.057
DRAW DOWN STATISTICS
Quartiles of draw downs
 Number of observations5.000
 Minimum0.002
 Quartile 10.057
 Median0.095
 Quartile 30.293
 Maximum0.357
 Mean of quarter 10.030
 Mean of quarter 20.095
 Mean of quarter 30.293
 Mean of quarter 40.357
 Inter Quartile Range0.235
 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)-0.182
 Compounded annual return (geometric extrapolation)-0.173
 Calmar ratio (compounded annual return / max draw down)-0.485
 Compounded annual return / average of 25% largest draw downs-0.485
 Compounded annual return / Expected Shortfall lognormal-2.298