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Advanced Statistics: FXCould1

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-0.103
 SD0.042
 Sharpe ratio (Glass type estimate) -2.475
 Sharpe ratio (Hedges UMVUE)-2.081
 df5.000
 t-1.750
 p0.930
 Lowerbound of 95% confidence interval for Sharpe Ratio-5.531
 Upperbound of 95% confidence interval for Sharpe Ratio0.764
 Lowerbound of 95% CI (Gibbons, Hedeker & Davis approximation)-5.138
 Upperbound of 95% CI (Gibbons, Hedeker & Davis approximation)0.976
Statistics related to Sortino ratio
 Sortino ratio-2.135
 Upside Potential Ratio0.000
 Upside part of mean0.000
 Downside part of mean-0.103
 Upside SD0.000
 Downside SD0.048
 N nonnegative terms0.000
 N negative terms6.000
Statistics related to linear regression on benchmark
 N of observations6.000
 Mean of predictor0.237
 Mean of criterion-0.103
 SD of predictor0.165
 SD of criterion0.042
 Covariance-0.001
 r-0.153
 b (slope, estimate of beta)-0.039
 a (intercept, estimate of alpha)-0.094
 Mean Square Error0.002
 DF error4.000
 t(b)-0.309
 p(b)0.614
 t(a)-1.314
 p(a)0.870
 Lowerbound of 95% confidence interval for beta-0.385
 Upperbound of 95% confidence interval for beta0.308
 Lowerbound of 95% confidence interval for alpha-0.292
 Upperbound of 95% confidence interval for alpha0.104
 Treynor index (mean / b)2.668
 Jensen alpha (a)-0.094
Ratio statistics of excess log return rates
Statistics related to Sharpe ratio
 Mean-0.104
 SD0.042
 Sharpe ratio (Glass type estimate) -2.457
 Sharpe ratio (Hedges UMVUE)-2.066
 df5.000
 t-1.738
 p0.929
 Lowerbound of 95% confidence interval for Sharpe Ratio-5.509
 Upperbound of 95% confidence interval for Sharpe Ratio0.776
 Lowerbound of 95% CI (Gibbons, Hedeker & Davis approximation)-5.119
 Upperbound of 95% CI (Gibbons, Hedeker & Davis approximation)0.987
Statistics related to Sortino ratio
 Sortino ratio-2.126
 Upside Potential Ratio0.000
 Upside part of mean0.000
 Downside part of mean-0.104
 Upside SD0.000
 Downside SD0.049
 N nonnegative terms0.000
 N negative terms6.000
Statistics related to linear regression on benchmark
 N of observations6.000
 Mean of predictor0.222
 Mean of criterion-0.104
 SD of predictor0.163
 SD of criterion0.042
 Covariance-0.001
 r-0.159
 b (slope, estimate of beta)-0.041
 a (intercept, estimate of alpha)-0.095
 Mean Square Error0.002
 DF error4.000
 t(b)-0.322
 p(b)0.618
 t(a)-1.318
 p(a)0.871
 Lowerbound of 95% confidence interval for beta-0.396
 Upperbound of 95% confidence interval for beta0.313
 Lowerbound of 95% confidence interval for alpha-0.294
 Upperbound of 95% confidence interval for alpha0.105
 Treynor index (mean / b)2.524
 Jensen alpha (a)-0.095
Risk estimates for a one-period unit investment (parametric)
assuming log normal returns and losses (using central moments from Sharpe statistics)
 VaR(95%)0.028
 Expected Shortfall on VaR0.033
assuming Pareto losses only (using partial moments from Sortino statistics)
 VaR(95%)0.028
 Expected Shortfall on VaR0.043
ORDER STATISTICS
Quartiles of return rates
 Number of observations6.000
 Minimum0.971
 Quartile 11.000
 Median1.000
 Quartile 31.000
 Maximum1.000
 Mean of quarter 10.985
 Mean of quarter 21.000
 Mean of quarter 31.000
 Mean of quarter 41.000
 Inter Quartile Range0.000
 Number outliers low1.000
 Percentage of outliers low0.167
 Mean of outliers low0.971
 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
 Minimum0.029
 Quartile 10.029
 Median0.029
 Quartile 30.029
 Maximum0.029
 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)-0.059
 Compounded annual return (geometric extrapolation)-0.058
 Calmar ratio (compounded annual return / max draw down)-1.971
 Compounded annual return / average of 25% largest draw downsNA
 Compounded annual return / Expected Shortfall lognormal-1.745
ANALYSIS BASED ON DAILY VALUES, FULL HISTORY (Back)
RATIO STATISTICS
Ratio statistics of excess return rates
Statistics related to Sharpe ratio
 Mean-0.102
 SD0.036
 Sharpe ratio (Glass type estimate) -2.800
 Sharpe ratio (Hedges UMVUE)-2.788
 df174.000
 t-1.997
 p0.575
 Lowerbound of 95% confidence interval for Sharpe Ratio-5.560
 Upperbound of 95% confidence interval for Sharpe Ratio-0.032
 Lowerbound of 95% CI (Gibbons, Hedeker & Davis approximation)-5.551
 Upperbound of 95% CI (Gibbons, Hedeker & Davis approximation)-0.024
Statistics related to Sortino ratio
 Sortino ratio-2.970
 Upside Potential Ratio0.841
 Upside part of mean0.029
 Downside part of mean-0.131
 Upside SD0.013
 Downside SD0.034
 N nonnegative terms3.000
 N negative terms172.000
Statistics related to linear regression on benchmark
 N of observations175.000
 Mean of predictor0.352
 Mean of criterion-0.102
 SD of predictor0.189
 SD of criterion0.036
 Covariance0.000
 r0.017
 b (slope, estimate of beta)0.003
 a (intercept, estimate of alpha)-0.103
 Mean Square Error0.001
 DF error173.000
 t(b)0.222
 p(b)0.489
 t(a)-2.004
 p(a)0.596
 Lowerbound of 95% confidence interval for beta-0.026
 Upperbound of 95% confidence interval for beta0.032
 Lowerbound of 95% confidence interval for alpha-0.205
 Upperbound of 95% confidence interval for alpha-0.002
 Treynor index (mean / b)-31.367
 Jensen alpha (a)-0.103
Ratio statistics of excess log return rates
Statistics related to Sharpe ratio
 Mean-0.103
 SD0.037
 Sharpe ratio (Glass type estimate) -2.802
 Sharpe ratio (Hedges UMVUE)-2.790
 df174.000
 t-1.999
 p0.575
 Lowerbound of 95% confidence interval for Sharpe Ratio-5.562
 Upperbound of 95% confidence interval for Sharpe Ratio-0.035
 Lowerbound of 95% CI (Gibbons, Hedeker & Davis approximation)-5.554
 Upperbound of 95% CI (Gibbons, Hedeker & Davis approximation)-0.027
Statistics related to Sortino ratio
 Sortino ratio-2.969
 Upside Potential Ratio0.832
 Upside part of mean0.029
 Downside part of mean-0.131
 Upside SD0.013
 Downside SD0.035
 N nonnegative terms3.000
 N negative terms172.000
Statistics related to linear regression on benchmark
 N of observations175.000
 Mean of predictor0.334
 Mean of criterion-0.103
 SD of predictor0.189
 SD of criterion0.037
 Covariance0.000
 r0.016
 b (slope, estimate of beta)0.003
 a (intercept, estimate of alpha)-0.104
 Mean Square Error0.001
 DF error173.000
 t(b)0.216
 p(b)0.490
 t(a)-2.005
 p(a)0.596
 Lowerbound of 95% confidence interval for beta-0.026
 Upperbound of 95% confidence interval for beta0.032
 Lowerbound of 95% confidence interval for alpha-0.206
 Upperbound of 95% confidence interval for alpha-0.002
 Treynor index (mean / b)-32.174
 Jensen alpha (a)-0.104
Risk estimates for a one-period unit investment (parametric)
assuming log normal returns and losses (using central moments from Sharpe statistics)
 VaR(95%)0.004
 Expected Shortfall on VaR0.004
assuming Pareto losses only (using partial moments from Sortino statistics)
 VaR(95%)0.001
 Expected Shortfall on VaR0.003
ORDER STATISTICS
Quartiles of return rates
 Number of observations175.000
 Minimum0.984
 Quartile 11.000
 Median1.000
 Quartile 31.000
 Maximum1.008
 Mean of quarter 10.999
 Mean of quarter 21.000
 Mean of quarter 31.000
 Mean of quarter 41.000
 Inter Quartile Range0.000
 Number outliers low4.000
 Percentage of outliers low0.023
 Mean of outliers low0.989
 Number of outliers high3.000
 Percentage of outliers high0.017
 Mean of outliers high1.005
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)-1.448
 VaR(95%) (regression method)-0.024
 Expected Shortfall (regression method)NA
DRAW DOWN STATISTICS
Quartiles of draw downs
 Number of observations2.000
 Minimum0.004
 Quartile 10.011
 Median0.018
 Quartile 30.025
 Maximum0.032
 Mean of quarter 10.004
 Mean of quarter 2NA
 Mean of quarter 3NA
 Mean of quarter 40.032
 Inter Quartile Range0.014
 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)-0.058
 Compounded annual return (geometric extrapolation)-0.057
 Calmar ratio (compounded annual return / max draw down)-1.753
 Compounded annual return / average of 25% largest draw downs-1.753
 Compounded annual return / Expected Shortfall lognormal-13.056
ANALYSIS BASED ON DAILY VALUES, LAST 6 MONTHS (Back)
RATIO STATISTICS
Ratio statistics of excess return rates
Statistics related to Sharpe ratio
 Mean-0.101
 SD0.036
 Sharpe ratio (Glass type estimate) -2.796
 Sharpe ratio (Hedges UMVUE)-2.784
 df171.000
 t-1.977
 p0.595
 Lowerbound of 95% confidence interval for Sharpe Ratio-5.579
 Upperbound of 95% confidence interval for Sharpe Ratio-0.004
 Lowerbound of 95% CI (Gibbons, Hedeker & Davis approximation)-5.571
 Upperbound of 95% CI (Gibbons, Hedeker & Davis approximation)0.004
Statistics related to Sortino ratio
 Sortino ratio-2.955
 Upside Potential Ratio0.702
 Upside part of mean0.024
 Downside part of mean-0.125
 Upside SD0.013
 Downside SD0.034
 N nonnegative terms2.000
 N negative terms170.000
Statistics related to linear regression on benchmark
 N of observations172.000
 Mean of predictor0.364
 Mean of criterion-0.101
 SD of predictor0.191
 SD of criterion0.036
 Covariance0.000
 r0.020
 b (slope, estimate of beta)0.004
 a (intercept, estimate of alpha)-0.102
 Mean Square Error0.001
 DF error170.000
 t(b)0.265
 p(b)0.490
 t(a)-1.988
 p(a)0.575
 Lowerbound of 95% confidence interval for beta-0.025
 Upperbound of 95% confidence interval for beta0.033
 Lowerbound of 95% confidence interval for alpha-0.204
 Upperbound of 95% confidence interval for alpha-0.001
 Treynor index (mean / b)-26.203
 Jensen alpha (a)-0.102
Ratio statistics of excess log return rates
Statistics related to Sharpe ratio
 Mean-0.102
 SD0.036
 Sharpe ratio (Glass type estimate) -2.798
 Sharpe ratio (Hedges UMVUE)-2.785
 df171.000
 t-1.978
 p0.595
 Lowerbound of 95% confidence interval for Sharpe Ratio-5.581
 Upperbound of 95% confidence interval for Sharpe Ratio-0.006
 Lowerbound of 95% CI (Gibbons, Hedeker & Davis approximation)-5.573
 Upperbound of 95% CI (Gibbons, Hedeker & Davis approximation)0.002
Statistics related to Sortino ratio
 Sortino ratio-2.953
 Upside Potential Ratio0.695
 Upside part of mean0.024
 Downside part of mean-0.126
 Upside SD0.013
 Downside SD0.034
 N nonnegative terms2.000
 N negative terms170.000
Statistics related to linear regression on benchmark
 N of observations172.000
 Mean of predictor0.346
 Mean of criterion-0.102
 SD of predictor0.190
 SD of criterion0.036
 Covariance0.000
 r0.020
 b (slope, estimate of beta)0.004
 a (intercept, estimate of alpha)-0.103
 Mean Square Error0.001
 DF error170.000
 t(b)0.259
 p(b)0.490
 t(a)-1.989
 p(a)0.575
 Lowerbound of 95% confidence interval for beta-0.025
 Upperbound of 95% confidence interval for beta0.033
 Lowerbound of 95% confidence interval for alpha-0.205
 Upperbound of 95% confidence interval for alpha-0.001
 Treynor index (mean / b)-26.777
 Jensen alpha (a)-0.103
Risk estimates for a one-period unit investment (parametric)
assuming log normal returns and losses (using central moments from Sharpe statistics)
 VaR(95%)0.004
 Expected Shortfall on VaR0.004
assuming Pareto losses only (using partial moments from Sortino statistics)
 VaR(95%)0.001
 Expected Shortfall on VaR0.003
ORDER STATISTICS
Quartiles of return rates
 Number of observations172.000
 Minimum0.984
 Quartile 11.000
 Median1.000
 Quartile 31.000
 Maximum1.008
 Mean of quarter 10.999
 Mean of quarter 21.000
 Mean of quarter 31.000
 Mean of quarter 41.000
 Inter Quartile Range0.000
 Number outliers low3.000
 Percentage of outliers low0.017
 Mean of outliers low0.986
 Number of outliers high2.000
 Percentage of outliers high0.012
 Mean of outliers high1.006
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)-2.163
 VaR(95%) (regression method)-0.089
 Expected Shortfall (regression method)NA
DRAW DOWN STATISTICS
Quartiles of draw downs
 Number of observations1.000
 Minimum0.032
 Quartile 10.032
 Median0.032
 Quartile 30.032
 Maximum0.032
 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)-0.057
 Compounded annual return (geometric extrapolation)-0.056
 Calmar ratio (compounded annual return / max draw down)-1.725
 Compounded annual return / average of 25% largest draw downsNA
 Compounded annual return / Expected Shortfall lognormal-12.948