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Advanced Statistics: Kingda Forex (20x)

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
 Mean0.213
 SD0.165
 Sharpe ratio (Glass type estimate) 1.290
 Sharpe ratio (Hedges UMVUE)1.258
 df30.000
 t2.074
 p0.023
 Lowerbound of 95% confidence interval for Sharpe Ratio0.018
 Upperbound of 95% confidence interval for Sharpe Ratio2.542
 Lowerbound of 95% CI (Gibbons, Hedeker & Davis approximation)-0.002
 Upperbound of 95% CI (Gibbons, Hedeker & Davis approximation)2.518
Statistics related to Sortino ratio
 Sortino ratio2.954
 Upside Potential Ratio4.455
 Upside part of mean0.321
 Downside part of mean-0.108
 Upside SD0.158
 Downside SD0.072
 N nonnegative terms21.000
 N negative terms10.000
Statistics related to linear regression on benchmark
 N of observations31.000
 Mean of predictor0.078
 Mean of criterion0.213
 SD of predictor0.140
 SD of criterion0.165
 Covariance0.005
 r0.234
 b (slope, estimate of beta)0.274
 a (intercept, estimate of alpha)0.191
 Mean Square Error0.027
 DF error29.000
 t(b)1.294
 p(b)0.103
 t(a)1.862
 p(a)0.036
 Lowerbound of 95% confidence interval for beta-0.159
 Upperbound of 95% confidence interval for beta0.707
 Lowerbound of 95% confidence interval for alpha-0.019
 Upperbound of 95% confidence interval for alpha0.401
 Treynor index (mean / b)0.776
 Jensen alpha (a)0.191
Ratio statistics of excess log return rates
Statistics related to Sharpe ratio
 Mean0.197
 SD0.160
 Sharpe ratio (Glass type estimate) 1.237
 Sharpe ratio (Hedges UMVUE)1.205
 df30.000
 t1.987
 p0.028
 Lowerbound of 95% confidence interval for Sharpe Ratio-0.032
 Upperbound of 95% confidence interval for Sharpe Ratio2.485
 Lowerbound of 95% CI (Gibbons, Hedeker & Davis approximation)-0.052
 Upperbound of 95% CI (Gibbons, Hedeker & Davis approximation)2.462
Statistics related to Sortino ratio
 Sortino ratio2.668
 Upside Potential Ratio4.157
 Upside part of mean0.308
 Downside part of mean-0.110
 Upside SD0.150
 Downside SD0.074
 N nonnegative terms21.000
 N negative terms10.000
Statistics related to linear regression on benchmark
 N of observations31.000
 Mean of predictor0.068
 Mean of criterion0.197
 SD of predictor0.141
 SD of criterion0.160
 Covariance0.005
 r0.236
 b (slope, estimate of beta)0.268
 a (intercept, estimate of alpha)0.179
 Mean Square Error0.025
 DF error29.000
 t(b)1.310
 p(b)0.100
 t(a)1.807
 p(a)0.041
 Lowerbound of 95% confidence interval for beta-0.151
 Upperbound of 95% confidence interval for beta0.688
 Lowerbound of 95% confidence interval for alpha-0.024
 Upperbound of 95% confidence interval for alpha0.382
 Treynor index (mean / b)0.736
 Jensen alpha (a)0.179
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 VaR0.075
assuming Pareto losses only (using partial moments from Sortino statistics)
 VaR(95%)0.015
 Expected Shortfall on VaR0.034
ORDER STATISTICS
Quartiles of return rates
 Number of observations31.000
 Minimum0.928
 Quartile 10.995
 Median1.014
 Quartile 31.041
 Maximum1.133
 Mean of quarter 10.971
 Mean of quarter 21.006
 Mean of quarter 31.025
 Mean of quarter 41.085
 Inter Quartile Range0.046
 Number outliers low0.000
 Percentage of outliers low0.000
 Mean of outliers lowNA
 Number of outliers high2.000
 Percentage of outliers high0.065
 Mean of outliers high1.129
Risk estimates for a one-period unit investment (based on Extreme Value Theory)
 Extreme Value Index (moments method)-0.342
 VaR(95%) (moments method)0.019
 Expected Shortfall (moments method)0.024
 Extreme Value Index (regression method)-0.444
 VaR(95%) (regression method)0.032
 Expected Shortfall (regression method)0.039
DRAW DOWN STATISTICS
Quartiles of draw downs
 Number of observations7.000
 Minimum0.005
 Quartile 10.019
 Median0.021
 Quartile 30.049
 Maximum0.073
 Mean of quarter 10.011
 Mean of quarter 20.021
 Mean of quarter 30.032
 Mean of quarter 40.070
 Inter Quartile Range0.031
 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)0.335
 Compounded annual return (geometric extrapolation)0.273
 Calmar ratio (compounded annual return / max draw down)3.729
 Compounded annual return / average of 25% largest draw downs3.905
 Compounded annual return / Expected Shortfall lognormal3.618
ANALYSIS BASED ON DAILY VALUES, FULL HISTORY (Back)
RATIO STATISTICS
Ratio statistics of excess return rates
Statistics related to Sharpe ratio
 Mean0.213
 SD0.182
 Sharpe ratio (Glass type estimate) 1.170
 Sharpe ratio (Hedges UMVUE)1.169
 df893.000
 t1.886
 p0.030
 Lowerbound of 95% confidence interval for Sharpe Ratio-0.047
 Upperbound of 95% confidence interval for Sharpe Ratio2.387
 Lowerbound of 95% CI (Gibbons, Hedeker & Davis approximation)-0.048
 Upperbound of 95% CI (Gibbons, Hedeker & Davis approximation)2.386
Statistics related to Sortino ratio
 Sortino ratio1.810
 Upside Potential Ratio7.375
 Upside part of mean0.868
 Downside part of mean-0.655
 Upside SD0.139
 Downside SD0.118
 N nonnegative terms308.000
 N negative terms586.000
Statistics related to linear regression on benchmark
 N of observations894.000
 Mean of predictor0.086
 Mean of criterion0.213
 SD of predictor0.172
 SD of criterion0.182
 Covariance0.001
 r0.028
 b (slope, estimate of beta)0.030
 a (intercept, estimate of alpha)0.211
 Mean Square Error0.033
 DF error892.000
 t(b)0.834
 p(b)0.202
 t(a)1.863
 p(a)0.031
 Lowerbound of 95% confidence interval for beta-0.040
 Upperbound of 95% confidence interval for beta0.099
 Lowerbound of 95% confidence interval for alpha-0.011
 Upperbound of 95% confidence interval for alpha0.433
 Treynor index (mean / b)7.209
 Jensen alpha (a)0.211
Ratio statistics of excess log return rates
Statistics related to Sharpe ratio
 Mean0.197
 SD0.181
 Sharpe ratio (Glass type estimate) 1.085
 Sharpe ratio (Hedges UMVUE)1.084
 df893.000
 t1.749
 p0.040
 Lowerbound of 95% confidence interval for Sharpe Ratio-0.132
 Upperbound of 95% confidence interval for Sharpe Ratio2.301
 Lowerbound of 95% CI (Gibbons, Hedeker & Davis approximation)-0.133
 Upperbound of 95% CI (Gibbons, Hedeker & Davis approximation)2.301
Statistics related to Sortino ratio
 Sortino ratio1.642
 Upside Potential Ratio7.175
 Upside part of mean0.859
 Downside part of mean-0.662
 Upside SD0.136
 Downside SD0.120
 N nonnegative terms308.000
 N negative terms586.000
Statistics related to linear regression on benchmark
 N of observations894.000
 Mean of predictor0.071
 Mean of criterion0.197
 SD of predictor0.172
 SD of criterion0.181
 Covariance0.001
 r0.028
 b (slope, estimate of beta)0.029
 a (intercept, estimate of alpha)0.195
 Mean Square Error0.033
 DF error892.000
 t(b)0.831
 p(b)0.203
 t(a)1.729
 p(a)0.042
 Lowerbound of 95% confidence interval for beta-0.040
 Upperbound of 95% confidence interval for beta0.098
 Lowerbound of 95% confidence interval for alpha-0.026
 Upperbound of 95% confidence interval for alpha0.415
 Treynor index (mean / b)6.722
 Jensen alpha (a)0.195
Risk estimates for a one-period unit investment (parametric)
assuming log normal returns and losses (using central moments from Sharpe statistics)
 VaR(95%)0.015
 Expected Shortfall on VaR0.019
assuming Pareto losses only (using partial moments from Sortino statistics)
 VaR(95%)0.005
 Expected Shortfall on VaR0.011
ORDER STATISTICS
Quartiles of return rates
 Number of observations894.000
 Minimum0.946
 Quartile 11.000
 Median1.000
 Quartile 31.002
 Maximum1.090
 Mean of quarter 10.993
 Mean of quarter 21.000
 Mean of quarter 31.000
 Mean of quarter 41.010
 Inter Quartile Range0.002
 Number outliers low121.000
 Percentage of outliers low0.135
 Mean of outliers low0.987
 Number of outliers high131.000
 Percentage of outliers high0.147
 Mean of outliers high1.015
Risk estimates for a one-period unit investment (based on Extreme Value Theory)
 Extreme Value Index (moments method)0.366
 VaR(95%) (moments method)0.004
 Expected Shortfall (moments method)0.008
 Extreme Value Index (regression method)0.153
 VaR(95%) (regression method)0.008
 Expected Shortfall (regression method)0.015
DRAW DOWN STATISTICS
Quartiles of draw downs
 Number of observations36.000
 Minimum0.000
 Quartile 10.004
 Median0.013
 Quartile 30.037
 Maximum0.111
 Mean of quarter 10.002
 Mean of quarter 20.007
 Mean of quarter 30.025
 Mean of quarter 40.076
 Inter Quartile Range0.033
 Number outliers low0.000
 Percentage of outliers low0.000
 Mean of outliers lowNA
 Number of outliers high4.000
 Percentage of outliers high0.111
 Mean of outliers high0.103
Risk estimates based on draw downs (based on Extreme Value Theory)
 Extreme Value Index (moments method)-0.358
 VaR(95%) (moments method)0.082
 Expected Shortfall (moments method)0.096
 Extreme Value Index (regression method)-1.510
 VaR(95%) (regression method)0.063
 Expected Shortfall (regression method)0.064
COMBINED STATISTICS
 Annualized return (arithmetic extrapolation)0.334
 Compounded annual return (geometric extrapolation)0.272
 Calmar ratio (compounded annual return / max draw down)2.450
 Compounded annual return / average of 25% largest draw downs3.587
 Compounded annual return / Expected Shortfall lognormal14.030
ANALYSIS BASED ON DAILY VALUES, LAST 6 MONTHS (Back)
RATIO STATISTICS
Ratio statistics of excess return rates
Statistics related to Sharpe ratio
 Mean0.251
 SD0.176
 Sharpe ratio (Glass type estimate) 1.424
 Sharpe ratio (Hedges UMVUE)1.418
 df171.000
 t1.007
 p0.451
 Lowerbound of 95% confidence interval for Sharpe Ratio-1.354
 Upperbound of 95% confidence interval for Sharpe Ratio4.198
 Lowerbound of 95% CI (Gibbons, Hedeker & Davis approximation)-1.358
 Upperbound of 95% CI (Gibbons, Hedeker & Davis approximation)4.194
Statistics related to Sortino ratio
 Sortino ratio2.350
 Upside Potential Ratio7.927
 Upside part of mean0.847
 Downside part of mean-0.596
 Upside SD0.140
 Downside SD0.107
 N nonnegative terms71.000
 N negative terms101.000
Statistics related to linear regression on benchmark
 N of observations172.000
 Mean of predictor0.255
 Mean of criterion0.251
 SD of predictor0.119
 SD of criterion0.176
 Covariance0.002
 r0.085
 b (slope, estimate of beta)0.125
 a (intercept, estimate of alpha)0.219
 Mean Square Error0.031
 DF error170.000
 t(b)1.110
 p(b)0.458
 t(a)0.874
 p(a)0.467
 Lowerbound of 95% confidence interval for beta-0.098
 Upperbound of 95% confidence interval for beta0.348
 Lowerbound of 95% confidence interval for alpha-0.276
 Upperbound of 95% confidence interval for alpha0.715
 Treynor index (mean / b)2.004
 Jensen alpha (a)0.219
Ratio statistics of excess log return rates
Statistics related to Sharpe ratio
 Mean0.236
 SD0.175
 Sharpe ratio (Glass type estimate) 1.350
 Sharpe ratio (Hedges UMVUE)1.344
 df171.000
 t0.955
 p0.454
 Lowerbound of 95% confidence interval for Sharpe Ratio-1.427
 Upperbound of 95% confidence interval for Sharpe Ratio4.124
 Lowerbound of 95% CI (Gibbons, Hedeker & Davis approximation)-1.431
 Upperbound of 95% CI (Gibbons, Hedeker & Davis approximation)4.120
Statistics related to Sortino ratio
 Sortino ratio2.174
 Upside Potential Ratio7.724
 Upside part of mean0.838
 Downside part of mean-0.602
 Upside SD0.137
 Downside SD0.108
 N nonnegative terms71.000
 N negative terms101.000
Statistics related to linear regression on benchmark
 N of observations172.000
 Mean of predictor0.247
 Mean of criterion0.236
 SD of predictor0.119
 SD of criterion0.175
 Covariance0.002
 r0.081
 b (slope, estimate of beta)0.118
 a (intercept, estimate of alpha)0.207
 Mean Square Error0.030
 DF error170.000
 t(b)1.056
 p(b)0.460
 t(a)0.832
 p(a)0.468
 Lowerbound of 95% confidence interval for beta-0.103
 Upperbound of 95% confidence interval for beta0.339
 Lowerbound of 95% confidence interval for alpha-0.284
 Upperbound of 95% confidence interval for alpha0.697
 Treynor index (mean / b)1.996
 Jensen alpha (a)0.207
Risk estimates for a one-period unit investment (parametric)
assuming log normal returns and losses (using central moments from Sharpe statistics)
 VaR(95%)0.015
 Expected Shortfall on VaR0.019
assuming Pareto losses only (using partial moments from Sortino statistics)
 VaR(95%)0.004
 Expected Shortfall on VaR0.010
ORDER STATISTICS
Quartiles of return rates
 Number of observations172.000
 Minimum0.956
 Quartile 11.000
 Median1.000
 Quartile 31.002
 Maximum1.076
 Mean of quarter 10.993
 Mean of quarter 21.000
 Mean of quarter 31.001
 Mean of quarter 41.009
 Inter Quartile Range0.002
 Number outliers low22.000
 Percentage of outliers low0.128
 Mean of outliers low0.988
 Number of outliers high25.000
 Percentage of outliers high0.145
 Mean of outliers high1.014
Risk estimates for a one-period unit investment (based on Extreme Value Theory)
 Extreme Value Index (moments method)-0.405
 VaR(95%) (moments method)0.003
 Expected Shortfall (moments method)0.004
 Extreme Value Index (regression method)0.229
 VaR(95%) (regression method)0.006
 Expected Shortfall (regression method)0.013
DRAW DOWN STATISTICS
Quartiles of draw downs
 Number of observations8.000
 Minimum0.002
 Quartile 10.012
 Median0.018
 Quartile 30.033
 Maximum0.068
 Mean of quarter 10.005
 Mean of quarter 20.015
 Mean of quarter 30.024
 Mean of quarter 40.056
 Inter Quartile Range0.021
 Number outliers low0.000
 Percentage of outliers low0.000
 Mean of outliers lowNA
 Number of outliers high1.000
 Percentage of outliers high0.125
 Mean of outliers high0.068
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)0.300
 Compounded annual return (geometric extrapolation)0.323
 Calmar ratio (compounded annual return / max draw down)4.721
 Compounded annual return / average of 25% largest draw downs5.739
 Compounded annual return / Expected Shortfall lognormal17.401