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Advanced Statistics: constantine

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
 Mean0.363
 SD0.765
 Sharpe ratio (Glass type estimate) 0.474
 Sharpe ratio (Hedges UMVUE)0.465
 df41.000
 t0.887
 p0.190
 Lowerbound of 95% confidence interval for Sharpe Ratio-0.582
 Upperbound of 95% confidence interval for Sharpe Ratio1.524
 Lowerbound of 95% CI (Gibbons, Hedeker & Davis approximation)-0.587
 Upperbound of 95% CI (Gibbons, Hedeker & Davis approximation)1.518
Statistics related to Sortino ratio
 Sortino ratio0.815
 Upside Potential Ratio2.266
 Upside part of mean1.008
 Downside part of mean-0.646
 Upside SD0.620
 Downside SD0.445
 N nonnegative terms21.000
 N negative terms21.000
Statistics related to linear regression on benchmark
 N of observations42.000
 Mean of predictor0.001
 Mean of criterion0.363
 SD of predictor0.285
 SD of criterion0.765
 Covariance-0.057
 r-0.261
 b (slope, estimate of beta)-0.702
 a (intercept, estimate of alpha)0.363
 Mean Square Error0.559
 DF error40.000
 t(b)-1.712
 p(b)0.953
 t(a)0.909
 p(a)0.184
 Lowerbound of 95% confidence interval for beta-1.531
 Upperbound of 95% confidence interval for beta0.127
 Lowerbound of 95% confidence interval for alpha-0.444
 Upperbound of 95% confidence interval for alpha1.171
 Treynor index (mean / b)-0.516
 Jensen alpha (a)0.363
Ratio statistics of excess log return rates
Statistics related to Sharpe ratio
 Mean0.067
 SD0.806
 Sharpe ratio (Glass type estimate) 0.083
 Sharpe ratio (Hedges UMVUE)0.081
 df41.000
 t0.154
 p0.439
 Lowerbound of 95% confidence interval for Sharpe Ratio-0.966
 Upperbound of 95% confidence interval for Sharpe Ratio1.130
 Lowerbound of 95% CI (Gibbons, Hedeker & Davis approximation)-0.967
 Upperbound of 95% CI (Gibbons, Hedeker & Davis approximation)1.129
Statistics related to Sortino ratio
 Sortino ratio0.107
 Upside Potential Ratio1.383
 Upside part of mean0.863
 Downside part of mean-0.797
 Upside SD0.495
 Downside SD0.624
 N nonnegative terms21.000
 N negative terms21.000
Statistics related to linear regression on benchmark
 N of observations42.000
 Mean of predictor-0.041
 Mean of criterion0.067
 SD of predictor0.300
 SD of criterion0.806
 Covariance-0.061
 r-0.253
 b (slope, estimate of beta)-0.680
 a (intercept, estimate of alpha)0.039
 Mean Square Error0.623
 DF error40.000
 t(b)-1.652
 p(b)0.947
 t(a)0.091
 p(a)0.464
 Lowerbound of 95% confidence interval for beta-1.512
 Upperbound of 95% confidence interval for beta0.152
 Lowerbound of 95% confidence interval for alpha-0.815
 Upperbound of 95% confidence interval for alpha0.892
 Treynor index (mean / b)-0.098
 Jensen alpha (a)0.039
Risk estimates for a one-period unit investment (parametric)
assuming log normal returns and losses (using central moments from Sharpe statistics)
 VaR(95%)0.314
 Expected Shortfall on VaR0.375
assuming Pareto losses only (using partial moments from Sortino statistics)
 VaR(95%)0.122
 Expected Shortfall on VaR0.255
ORDER STATISTICS
Quartiles of return rates
 Number of observations42.000
 Minimum0.377
 Quartile 10.935
 Median1.005
 Quartile 31.106
 Maximum1.841
 Mean of quarter 10.816
 Mean of quarter 20.984
 Mean of quarter 31.052
 Mean of quarter 41.281
 Inter Quartile Range0.171
 Number outliers low2.000
 Percentage of outliers low0.048
 Mean of outliers low0.513
 Number of outliers high3.000
 Percentage of outliers high0.071
 Mean of outliers high1.557
Risk estimates for a one-period unit investment (based on Extreme Value Theory)
 Extreme Value Index (moments method)0.662
 VaR(95%) (moments method)0.211
 Expected Shortfall (moments method)0.651
 Extreme Value Index (regression method)1.094
 VaR(95%) (regression method)0.192
 Expected Shortfall (regression method)NA
DRAW DOWN STATISTICS
Quartiles of draw downs
 Number of observations3.000
 Minimum0.025
 Quartile 10.198
 Median0.370
 Quartile 30.563
 Maximum0.755
 Mean of quarter 10.025
 Mean of quarter 20.370
 Mean of quarter 3NA
 Mean of quarter 40.755
 Inter Quartile Range0.365
 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)0.135
 Compounded annual return (geometric extrapolation)0.117
 Calmar ratio (compounded annual return / max draw down)0.155
 Compounded annual return / average of 25% largest draw downs0.155
 Compounded annual return / Expected Shortfall lognormal0.311
ANALYSIS BASED ON DAILY VALUES, FULL HISTORY (Back)
RATIO STATISTICS
Ratio statistics of excess return rates
Statistics related to Sharpe ratio
 Mean0.322
 SD0.651
 Sharpe ratio (Glass type estimate) 0.495
 Sharpe ratio (Hedges UMVUE)0.495
 df1228.000
 t0.935
 p0.487
 Lowerbound of 95% confidence interval for Sharpe Ratio-0.542
 Upperbound of 95% confidence interval for Sharpe Ratio1.532
 Lowerbound of 95% CI (Gibbons, Hedeker & Davis approximation)-0.543
 Upperbound of 95% CI (Gibbons, Hedeker & Davis approximation)1.532
Statistics related to Sortino ratio
 Sortino ratio0.684
 Upside Potential Ratio7.375
 Upside part of mean3.475
 Downside part of mean-3.153
 Upside SD0.449
 Downside SD0.471
 N nonnegative terms555.000
 N negative terms674.000
Statistics related to linear regression on benchmark
 N of observations1229.000
 Mean of predictor0.063
 Mean of criterion0.322
 SD of predictor0.304
 SD of criterion0.651
 Covariance-0.035
 r-0.179
 b (slope, estimate of beta)-0.383
 a (intercept, estimate of alpha)0.346
 Mean Square Error0.411
 DF error1227.000
 t(b)-6.362
 p(b)0.613
 t(a)1.022
 p(a)0.481
 Lowerbound of 95% confidence interval for beta-0.501
 Upperbound of 95% confidence interval for beta-0.265
 Lowerbound of 95% confidence interval for alpha-0.319
 Upperbound of 95% confidence interval for alpha1.012
 Treynor index (mean / b)-0.841
 Jensen alpha (a)0.346
Ratio statistics of excess log return rates
Statistics related to Sharpe ratio
 Mean0.097
 SD0.686
 Sharpe ratio (Glass type estimate) 0.141
 Sharpe ratio (Hedges UMVUE)0.141
 df1228.000
 t0.267
 p0.496
 Lowerbound of 95% confidence interval for Sharpe Ratio-0.896
 Upperbound of 95% confidence interval for Sharpe Ratio1.178
 Lowerbound of 95% CI (Gibbons, Hedeker & Davis approximation)-0.896
 Upperbound of 95% CI (Gibbons, Hedeker & Davis approximation)1.178
Statistics related to Sortino ratio
 Sortino ratio0.180
 Upside Potential Ratio6.292
 Upside part of mean3.381
 Downside part of mean-3.284
 Upside SD0.425
 Downside SD0.537
 N nonnegative terms555.000
 N negative terms674.000
Statistics related to linear regression on benchmark
 N of observations1229.000
 Mean of predictor0.017
 Mean of criterion0.097
 SD of predictor0.304
 SD of criterion0.686
 Covariance-0.036
 r-0.172
 b (slope, estimate of beta)-0.389
 a (intercept, estimate of alpha)0.103
 Mean Square Error0.456
 DF error1227.000
 t(b)-6.127
 p(b)0.609
 t(a)0.290
 p(a)0.495
 Lowerbound of 95% confidence interval for beta-0.513
 Upperbound of 95% confidence interval for beta-0.264
 Lowerbound of 95% confidence interval for alpha-0.598
 Upperbound of 95% confidence interval for alpha0.805
 Treynor index (mean / b)-0.249
 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%)0.059
 Expected Shortfall on VaR0.073
assuming Pareto losses only (using partial moments from Sortino statistics)
 VaR(95%)0.022
 Expected Shortfall on VaR0.047
ORDER STATISTICS
Quartiles of return rates
 Number of observations1229.000
 Minimum0.603
 Quartile 10.990
 Median1.000
 Quartile 31.012
 Maximum1.321
 Mean of quarter 10.967
 Mean of quarter 20.997
 Mean of quarter 31.004
 Mean of quarter 41.036
 Inter Quartile Range0.022
 Number outliers low55.000
 Percentage of outliers low0.045
 Mean of outliers low0.918
 Number of outliers high65.000
 Percentage of outliers high0.053
 Mean of outliers high1.080
Risk estimates for a one-period unit investment (based on Extreme Value Theory)
 Extreme Value Index (moments method)0.243
 VaR(95%) (moments method)0.029
 Expected Shortfall (moments method)0.047
 Extreme Value Index (regression method)0.151
 VaR(95%) (regression method)0.029
 Expected Shortfall (regression method)0.044
DRAW DOWN STATISTICS
Quartiles of draw downs
 Number of observations12.000
 Minimum0.001
 Quartile 10.048
 Median0.117
 Quartile 30.168
 Maximum0.788
 Mean of quarter 10.017
 Mean of quarter 20.091
 Mean of quarter 30.147
 Mean of quarter 40.479
 Inter Quartile Range0.120
 Number outliers low0.000
 Percentage of outliers low0.000
 Mean of outliers lowNA
 Number of outliers high2.000
 Percentage of outliers high0.167
 Mean of outliers high0.627
Risk estimates based on draw downs (based on Extreme Value Theory)
 Extreme Value Index (moments method)-8.811
 VaR(95%) (moments method)0.426
 Expected Shortfall (moments method)0.426
 Extreme Value Index (regression method)-0.821
 VaR(95%) (regression method)0.873
 Expected Shortfall (regression method)0.997
COMBINED STATISTICS
 Annualized return (arithmetic extrapolation)0.183
 Compounded annual return (geometric extrapolation)0.151
 Calmar ratio (compounded annual return / max draw down)0.192
 Compounded annual return / average of 25% largest draw downs0.316
 Compounded annual return / Expected Shortfall lognormal2.070
ANALYSIS BASED ON DAILY VALUES, LAST 6 MONTHS (Back)
RATIO STATISTICS
Ratio statistics of excess return rates
Statistics related to Sharpe ratio
 Mean0.424
 SD0.408
 Sharpe ratio (Glass type estimate) 1.039
 Sharpe ratio (Hedges UMVUE)1.035
 df171.000
 t0.735
 p0.464
 Lowerbound of 95% confidence interval for Sharpe Ratio-1.736
 Upperbound of 95% confidence interval for Sharpe Ratio3.812
 Lowerbound of 95% CI (Gibbons, Hedeker & Davis approximation)-1.739
 Upperbound of 95% CI (Gibbons, Hedeker & Davis approximation)3.809
Statistics related to Sortino ratio
 Sortino ratio1.624
 Upside Potential Ratio11.613
 Upside part of mean3.035
 Downside part of mean-2.610
 Upside SD0.313
 Downside SD0.261
 N nonnegative terms83.000
 N negative terms89.000
Statistics related to linear regression on benchmark
 N of observations172.000
 Mean of predictor0.644
 Mean of criterion0.424
 SD of predictor0.277
 SD of criterion0.408
 Covariance-0.042
 r-0.370
 b (slope, estimate of beta)-0.544
 a (intercept, estimate of alpha)0.775
 Mean Square Error0.145
 DF error170.000
 t(b)-5.185
 p(b)0.685
 t(a)1.429
 p(a)0.446
 Lowerbound of 95% confidence interval for beta-0.752
 Upperbound of 95% confidence interval for beta-0.337
 Lowerbound of 95% confidence interval for alpha-0.296
 Upperbound of 95% confidence interval for alpha1.846
 Treynor index (mean / b)-0.779
 Jensen alpha (a)0.775
Ratio statistics of excess log return rates
Statistics related to Sharpe ratio
 Mean0.342
 SD0.407
 Sharpe ratio (Glass type estimate) 0.840
 Sharpe ratio (Hedges UMVUE)0.837
 df171.000
 t0.594
 p0.471
 Lowerbound of 95% confidence interval for Sharpe Ratio-1.934
 Upperbound of 95% confidence interval for Sharpe Ratio3.612
 Lowerbound of 95% CI (Gibbons, Hedeker & Davis approximation)-1.937
 Upperbound of 95% CI (Gibbons, Hedeker & Davis approximation)3.610
Statistics related to Sortino ratio
 Sortino ratio1.286
 Upside Potential Ratio11.241
 Upside part of mean2.986
 Downside part of mean-2.645
 Upside SD0.307
 Downside SD0.266
 N nonnegative terms83.000
 N negative terms89.000
Statistics related to linear regression on benchmark
 N of observations172.000
 Mean of predictor0.606
 Mean of criterion0.342
 SD of predictor0.277
 SD of criterion0.407
 Covariance-0.042
 r-0.372
 b (slope, estimate of beta)-0.546
 a (intercept, estimate of alpha)0.672
 Mean Square Error0.143
 DF error170.000
 t(b)-5.230
 p(b)0.686
 t(a)1.248
 p(a)0.452
 Lowerbound of 95% confidence interval for beta-0.753
 Upperbound of 95% confidence interval for beta-0.340
 Lowerbound of 95% confidence interval for alpha-0.392
 Upperbound of 95% confidence interval for alpha1.737
 Treynor index (mean / b)-0.625
 Jensen alpha (a)0.672
Risk estimates for a one-period unit investment (parametric)
assuming log normal returns and losses (using central moments from Sharpe statistics)
 VaR(95%)0.034
 Expected Shortfall on VaR0.043
assuming Pareto losses only (using partial moments from Sortino statistics)
 VaR(95%)0.018
 Expected Shortfall on VaR0.033
ORDER STATISTICS
Quartiles of return rates
 Number of observations172.000
 Minimum0.953
 Quartile 10.990
 Median1.000
 Quartile 31.012
 Maximum1.061
 Mean of quarter 10.975
 Mean of quarter 20.995
 Mean of quarter 31.005
 Mean of quarter 41.030
 Inter Quartile Range0.021
 Number outliers low5.000
 Percentage of outliers low0.029
 Mean of outliers low0.955
 Number of outliers high8.000
 Percentage of outliers high0.047
 Mean of outliers high1.053
Risk estimates for a one-period unit investment (based on Extreme Value Theory)
 Extreme Value Index (moments method)-0.883
 VaR(95%) (moments method)0.024
 Expected Shortfall (moments method)0.026
 Extreme Value Index (regression method)-0.565
 VaR(95%) (regression method)0.024
 Expected Shortfall (regression method)0.028
DRAW DOWN STATISTICS
Quartiles of draw downs
 Number of observations7.000
 Minimum0.002
 Quartile 10.006
 Median0.010
 Quartile 30.111
 Maximum0.180
 Mean of quarter 10.002
 Mean of quarter 20.010
 Mean of quarter 30.102
 Mean of quarter 40.150
 Inter Quartile Range0.105
 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)0.425
 Compounded annual return (geometric extrapolation)0.471
 Calmar ratio (compounded annual return / max draw down)2.610
 Compounded annual return / average of 25% largest draw downs3.137
 Compounded annual return / Expected Shortfall lognormal10.885