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Advanced Statistics: German Forex - EUR/USD -

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-0.591
 SD0.231
 Sharpe ratio (Glass type estimate) -2.562
 Sharpe ratio (Hedges UMVUE)-2.154
 df5.000
 t-1.811
 p0.935
 Lowerbound of 95% confidence interval for Sharpe Ratio-5.642
 Upperbound of 95% confidence interval for Sharpe Ratio0.704
 Lowerbound of 95% CI (Gibbons, Hedeker & Davis approximation)-5.230
 Upperbound of 95% CI (Gibbons, Hedeker & Davis approximation)0.923
Statistics related to Sortino ratio
 Sortino ratio-2.225
 Upside Potential Ratio0.356
 Upside part of mean0.095
 Downside part of mean-0.686
 Upside SD0.054
 Downside SD0.266
 N nonnegative terms2.000
 N negative terms4.000
Statistics related to linear regression on benchmark
 N of observations6.000
 Mean of predictor0.135
 Mean of criterion-0.591
 SD of predictor0.099
 SD of criterion0.231
 Covariance-0.012
 r-0.543
 b (slope, estimate of beta)-1.263
 a (intercept, estimate of alpha)-0.421
 Mean Square Error0.047
 DF error4.000
 t(b)-1.293
 p(b)0.867
 t(a)-1.260
 p(a)0.862
 Lowerbound of 95% confidence interval for beta-3.976
 Upperbound of 95% confidence interval for beta1.450
 Lowerbound of 95% confidence interval for alpha-1.348
 Upperbound of 95% confidence interval for alpha0.507
 Treynor index (mean / b)0.468
 Jensen alpha (a)-0.421
Ratio statistics of excess log return rates
Statistics related to Sharpe ratio
 Mean-0.629
 SD0.243
 Sharpe ratio (Glass type estimate) -2.584
 Sharpe ratio (Hedges UMVUE)-2.173
 df5.000
 t-1.827
 p0.936
 Lowerbound of 95% confidence interval for Sharpe Ratio-5.670
 Upperbound of 95% confidence interval for Sharpe Ratio0.688
 Lowerbound of 95% CI (Gibbons, Hedeker & Davis approximation)-5.254
 Upperbound of 95% CI (Gibbons, Hedeker & Davis approximation)0.909
Statistics related to Sortino ratio
 Sortino ratio-2.230
 Upside Potential Ratio0.329
 Upside part of mean0.093
 Downside part of mean-0.722
 Upside SD0.053
 Downside SD0.282
 N nonnegative terms2.000
 N negative terms4.000
Statistics related to linear regression on benchmark
 N of observations6.000
 Mean of predictor0.130
 Mean of criterion-0.629
 SD of predictor0.099
 SD of criterion0.243
 Covariance-0.013
 r-0.540
 b (slope, estimate of beta)-1.332
 a (intercept, estimate of alpha)-0.456
 Mean Square Error0.052
 DF error4.000
 t(b)-1.282
 p(b)0.865
 t(a)-1.298
 p(a)0.868
 Lowerbound of 95% confidence interval for beta-4.219
 Upperbound of 95% confidence interval for beta1.554
 Lowerbound of 95% confidence interval for alpha-1.430
 Upperbound of 95% confidence interval for alpha0.519
 Treynor index (mean / b)0.472
 Jensen alpha (a)-0.456
Risk estimates for a one-period unit investment (parametric)
assuming log normal returns and losses (using central moments from Sharpe statistics)
 VaR(95%)0.155
 Expected Shortfall on VaR0.179
assuming Pareto losses only (using partial moments from Sortino statistics)
 VaR(95%)0.142
 Expected Shortfall on VaR0.184
ORDER STATISTICS
Quartiles of return rates
 Number of observations6.000
 Minimum0.857
 Quartile 10.922
 Median0.948
 Quartile 31.002
 Maximum1.040
 Mean of quarter 10.888
 Mean of quarter 20.932
 Mean of quarter 30.963
 Mean of quarter 41.027
 Inter Quartile Range0.079
 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
 Minimum0.264
 Quartile 10.264
 Median0.264
 Quartile 30.264
 Maximum0.264
 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)-0.507
 Compounded annual return (geometric extrapolation)-0.443
 Calmar ratio (compounded annual return / max draw down)-1.677
 Compounded annual return / average of 25% largest draw downsNA
 Compounded annual return / Expected Shortfall lognormal-2.477
ANALYSIS BASED ON DAILY VALUES, FULL HISTORY (Back)
RATIO STATISTICS
Ratio statistics of excess return rates
Statistics related to Sharpe ratio
 Mean-0.550
 SD0.214
 Sharpe ratio (Glass type estimate) -2.573
 Sharpe ratio (Hedges UMVUE)-2.563
 df189.000
 t-1.912
 p0.587
 Lowerbound of 95% confidence interval for Sharpe Ratio-5.219
 Upperbound of 95% confidence interval for Sharpe Ratio0.081
 Lowerbound of 95% CI (Gibbons, Hedeker & Davis approximation)-5.212
 Upperbound of 95% CI (Gibbons, Hedeker & Davis approximation)0.087
Statistics related to Sortino ratio
 Sortino ratio-3.010
 Upside Potential Ratio3.799
 Upside part of mean0.694
 Downside part of mean-1.244
 Upside SD0.114
 Downside SD0.183
 N nonnegative terms37.000
 N negative terms153.000
Statistics related to linear regression on benchmark
 N of observations190.000
 Mean of predictor0.369
 Mean of criterion-0.550
 SD of predictor0.152
 SD of criterion0.214
 Covariance-0.003
 r-0.105
 b (slope, estimate of beta)-0.147
 a (intercept, estimate of alpha)-0.496
 Mean Square Error0.045
 DF error188.000
 t(b)-1.445
 p(b)0.552
 t(a)-1.714
 p(a)0.562
 Lowerbound of 95% confidence interval for beta-0.348
 Upperbound of 95% confidence interval for beta0.054
 Lowerbound of 95% confidence interval for alpha-1.066
 Upperbound of 95% confidence interval for alpha0.075
 Treynor index (mean / b)3.740
 Jensen alpha (a)-0.496
Ratio statistics of excess log return rates
Statistics related to Sharpe ratio
 Mean-0.573
 SD0.217
 Sharpe ratio (Glass type estimate) -2.647
 Sharpe ratio (Hedges UMVUE)-2.637
 df189.000
 t-1.967
 p0.590
 Lowerbound of 95% confidence interval for Sharpe Ratio-5.295
 Upperbound of 95% confidence interval for Sharpe Ratio0.007
 Lowerbound of 95% CI (Gibbons, Hedeker & Davis approximation)-5.287
 Upperbound of 95% CI (Gibbons, Hedeker & Davis approximation)0.014
Statistics related to Sortino ratio
 Sortino ratio-3.065
 Upside Potential Ratio3.676
 Upside part of mean0.688
 Downside part of mean-1.261
 Upside SD0.112
 Downside SD0.187
 N nonnegative terms37.000
 N negative terms153.000
Statistics related to linear regression on benchmark
 N of observations190.000
 Mean of predictor0.357
 Mean of criterion-0.573
 SD of predictor0.151
 SD of criterion0.217
 Covariance-0.003
 r-0.104
 b (slope, estimate of beta)-0.149
 a (intercept, estimate of alpha)-0.520
 Mean Square Error0.047
 DF error188.000
 t(b)-1.439
 p(b)0.552
 t(a)-1.775
 p(a)0.564
 Lowerbound of 95% confidence interval for beta-0.354
 Upperbound of 95% confidence interval for beta0.055
 Lowerbound of 95% confidence interval for alpha-1.098
 Upperbound of 95% confidence interval for alpha0.058
 Treynor index (mean / b)3.842
 Jensen alpha (a)-0.520
Risk estimates for a one-period unit investment (parametric)
assuming log normal returns and losses (using central moments from Sharpe statistics)
 VaR(95%)0.021
 Expected Shortfall on VaR0.025
assuming Pareto losses only (using partial moments from Sortino statistics)
 VaR(95%)0.011
 Expected Shortfall on VaR0.023
ORDER STATISTICS
Quartiles of return rates
 Number of observations190.000
 Minimum0.918
 Quartile 10.998
 Median1.000
 Quartile 31.000
 Maximum1.043
 Mean of quarter 10.986
 Mean of quarter 21.000
 Mean of quarter 31.000
 Mean of quarter 41.008
 Inter Quartile Range0.002
 Number outliers low40.000
 Percentage of outliers low0.211
 Mean of outliers low0.984
 Number of outliers high29.000
 Percentage of outliers high0.153
 Mean of outliers high1.013
Risk estimates for a one-period unit investment (based on Extreme Value Theory)
 Extreme Value Index (moments method)0.265
 VaR(95%) (moments method)0.007
 Expected Shortfall (moments method)0.013
 Extreme Value Index (regression method)0.007
 VaR(95%) (regression method)0.015
 Expected Shortfall (regression method)0.024
DRAW DOWN STATISTICS
Quartiles of draw downs
 Number of observations2.000
 Minimum0.001
 Quartile 10.070
 Median0.140
 Quartile 30.209
 Maximum0.278
 Mean of quarter 10.001
 Mean of quarter 2NA
 Mean of quarter 3NA
 Mean of quarter 40.278
 Inter Quartile Range0.139
 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)-0.459
 Compounded annual return (geometric extrapolation)-0.411
 Calmar ratio (compounded annual return / max draw down)-1.477
 Compounded annual return / average of 25% largest draw downs-1.477
 Compounded annual return / Expected Shortfall lognormal-16.171
ANALYSIS BASED ON DAILY VALUES, LAST 6 MONTHS (Back)
RATIO STATISTICS
Ratio statistics of excess return rates
Statistics related to Sharpe ratio
 Mean-0.603
 SD0.225
 Sharpe ratio (Glass type estimate) -2.686
 Sharpe ratio (Hedges UMVUE)-2.674
 df171.000
 t-1.899
 p0.591
 Lowerbound of 95% confidence interval for Sharpe Ratio-5.468
 Upperbound of 95% confidence interval for Sharpe Ratio0.105
 Lowerbound of 95% CI (Gibbons, Hedeker & Davis approximation)-5.460
 Upperbound of 95% CI (Gibbons, Hedeker & Davis approximation)0.112
Statistics related to Sortino ratio
 Sortino ratio-3.140
 Upside Potential Ratio3.993
 Upside part of mean0.767
 Downside part of mean-1.370
 Upside SD0.120
 Downside SD0.192
 N nonnegative terms37.000
 N negative terms135.000
Statistics related to linear regression on benchmark
 N of observations172.000
 Mean of predictor0.331
 Mean of criterion-0.603
 SD of predictor0.147
 SD of criterion0.225
 Covariance-0.004
 r-0.116
 b (slope, estimate of beta)-0.176
 a (intercept, estimate of alpha)-0.545
 Mean Square Error0.050
 DF error170.000
 t(b)-1.521
 p(b)0.558
 t(a)-1.709
 p(a)0.565
 Lowerbound of 95% confidence interval for beta-0.405
 Upperbound of 95% confidence interval for beta0.053
 Lowerbound of 95% confidence interval for alpha-1.174
 Upperbound of 95% confidence interval for alpha0.084
 Treynor index (mean / b)3.418
 Jensen alpha (a)-0.545
Ratio statistics of excess log return rates
Statistics related to Sharpe ratio
 Mean-0.629
 SD0.228
 Sharpe ratio (Glass type estimate) -2.764
 Sharpe ratio (Hedges UMVUE)-2.752
 df171.000
 t-1.955
 p0.594
 Lowerbound of 95% confidence interval for Sharpe Ratio-5.548
 Upperbound of 95% confidence interval for Sharpe Ratio0.027
 Lowerbound of 95% CI (Gibbons, Hedeker & Davis approximation)-5.539
 Upperbound of 95% CI (Gibbons, Hedeker & Davis approximation)0.035
Statistics related to Sortino ratio
 Sortino ratio-3.198
 Upside Potential Ratio3.863
 Upside part of mean0.760
 Downside part of mean-1.389
 Upside SD0.118
 Downside SD0.197
 N nonnegative terms37.000
 N negative terms135.000
Statistics related to linear regression on benchmark
 N of observations172.000
 Mean of predictor0.320
 Mean of criterion-0.629
 SD of predictor0.147
 SD of criterion0.228
 Covariance-0.004
 r-0.116
 b (slope, estimate of beta)-0.179
 a (intercept, estimate of alpha)-0.572
 Mean Square Error0.051
 DF error170.000
 t(b)-1.517
 p(b)0.558
 t(a)-1.771
 p(a)0.567
 Lowerbound of 95% confidence interval for beta-0.413
 Upperbound of 95% confidence interval for beta0.054
 Lowerbound of 95% confidence interval for alpha-1.209
 Upperbound of 95% confidence interval for alpha0.066
 Treynor index (mean / b)3.505
 Jensen alpha (a)-0.572
Risk estimates for a one-period unit investment (parametric)
assuming log normal returns and losses (using central moments from Sharpe statistics)
 VaR(95%)0.022
 Expected Shortfall on VaR0.027
assuming Pareto losses only (using partial moments from Sortino statistics)
 VaR(95%)0.012
 Expected Shortfall on VaR0.024
ORDER STATISTICS
Quartiles of return rates
 Number of observations172.000
 Minimum0.918
 Quartile 10.998
 Median1.000
 Quartile 31.000
 Maximum1.043
 Mean of quarter 10.985
 Mean of quarter 21.000
 Mean of quarter 31.000
 Mean of quarter 41.009
 Inter Quartile Range0.002
 Number outliers low32.000
 Percentage of outliers low0.186
 Mean of outliers low0.981
 Number of outliers high25.000
 Percentage of outliers high0.145
 Mean of outliers high1.015
Risk estimates for a one-period unit investment (based on Extreme Value Theory)
 Extreme Value Index (moments method)0.068
 VaR(95%) (moments method)0.009
 Expected Shortfall (moments method)0.014
 Extreme Value Index (regression method)-0.008
 VaR(95%) (regression method)0.016
 Expected Shortfall (regression method)0.025
DRAW DOWN STATISTICS
Quartiles of draw downs
 Number of observations2.000
 Minimum0.001
 Quartile 10.070
 Median0.140
 Quartile 30.209
 Maximum0.278
 Mean of quarter 10.001
 Mean of quarter 2NA
 Mean of quarter 3NA
 Mean of quarter 40.278
 Inter Quartile Range0.139
 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)-0.507
 Compounded annual return (geometric extrapolation)-0.443
 Calmar ratio (compounded annual return / max draw down)-1.591
 Compounded annual return / average of 25% largest draw downs-1.591
 Compounded annual return / Expected Shortfall lognormal-16.552