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Advanced Statistics: eminialerts

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
 Mean0.186
 SD0.437
 Sharpe ratio (Glass type estimate) 0.426
 Sharpe ratio (Hedges UMVUE)0.417
 df37.000
 t0.757
 p0.227
 Lowerbound of 95% confidence interval for Sharpe Ratio-0.683
 Upperbound of 95% confidence interval for Sharpe Ratio1.528
 Lowerbound of 95% CI (Gibbons, Hedeker & Davis approximation)-0.689
 Upperbound of 95% CI (Gibbons, Hedeker & Davis approximation)1.522
Statistics related to Sortino ratio
 Sortino ratio0.895
 Upside Potential Ratio2.585
 Upside part of mean0.537
 Downside part of mean-0.351
 Upside SD0.381
 Downside SD0.208
 N nonnegative terms19.000
 N negative terms19.000
Statistics related to linear regression on benchmark
 N of observations38.000
 Mean of predictor0.071
 Mean of criterion0.186
 SD of predictor0.139
 SD of criterion0.437
 Covariance-0.022
 r-0.364
 b (slope, estimate of beta)-1.141
 a (intercept, estimate of alpha)0.267
 Mean Square Error0.170
 DF error36.000
 t(b)-2.348
 p(b)0.988
 t(a)1.140
 p(a)0.131
 Lowerbound of 95% confidence interval for beta-2.127
 Upperbound of 95% confidence interval for beta-0.156
 Lowerbound of 95% confidence interval for alpha-0.208
 Upperbound of 95% confidence interval for alpha0.742
 Treynor index (mean / b)-0.163
 Jensen alpha (a)0.267
Ratio statistics of excess log return rates
Statistics related to Sharpe ratio
 Mean0.104
 SD0.394
 Sharpe ratio (Glass type estimate) 0.265
 Sharpe ratio (Hedges UMVUE)0.259
 df37.000
 t0.471
 p0.320
 Lowerbound of 95% confidence interval for Sharpe Ratio-0.840
 Upperbound of 95% confidence interval for Sharpe Ratio1.366
 Lowerbound of 95% CI (Gibbons, Hedeker & Davis approximation)-0.844
 Upperbound of 95% CI (Gibbons, Hedeker & Davis approximation)1.362
Statistics related to Sortino ratio
 Sortino ratio0.454
 Upside Potential Ratio2.081
 Upside part of mean0.479
 Downside part of mean-0.374
 Upside SD0.315
 Downside SD0.230
 N nonnegative terms19.000
 N negative terms19.000
Statistics related to linear regression on benchmark
 N of observations38.000
 Mean of predictor0.061
 Mean of criterion0.104
 SD of predictor0.140
 SD of criterion0.394
 Covariance-0.018
 r-0.328
 b (slope, estimate of beta)-0.924
 a (intercept, estimate of alpha)0.161
 Mean Square Error0.143
 DF error36.000
 t(b)-2.085
 p(b)0.978
 t(a)0.752
 p(a)0.229
 Lowerbound of 95% confidence interval for beta-1.823
 Upperbound of 95% confidence interval for beta-0.025
 Lowerbound of 95% confidence interval for alpha-0.273
 Upperbound of 95% confidence interval for alpha0.595
 Treynor index (mean / b)-0.113
 Jensen alpha (a)0.161
Risk estimates for a one-period unit investment (parametric)
assuming log normal returns and losses (using central moments from Sharpe statistics)
 VaR(95%)0.164
 Expected Shortfall on VaR0.202
assuming Pareto losses only (using partial moments from Sortino statistics)
 VaR(95%)0.067
 Expected Shortfall on VaR0.132
ORDER STATISTICS
Quartiles of return rates
 Number of observations38.000
 Minimum0.748
 Quartile 10.966
 Median1.007
 Quartile 31.054
 Maximum1.583
 Mean of quarter 10.911
 Mean of quarter 20.983
 Mean of quarter 31.025
 Mean of quarter 41.154
 Inter Quartile Range0.089
 Number outliers low2.000
 Percentage of outliers low0.053
 Mean of outliers low0.781
 Number of outliers high2.000
 Percentage of outliers high0.053
 Mean of outliers high1.408
Risk estimates for a one-period unit investment (based on Extreme Value Theory)
 Extreme Value Index (moments method)0.470
 VaR(95%) (moments method)0.098
 Expected Shortfall (moments method)0.205
 Extreme Value Index (regression method)0.510
 VaR(95%) (regression method)0.090
 Expected Shortfall (regression method)0.190
DRAW DOWN STATISTICS
Quartiles of draw downs
 Number of observations1.000
 Minimum0.521
 Quartile 10.521
 Median0.521
 Quartile 30.521
 Maximum0.521
 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)0.189
 Compounded annual return (geometric extrapolation)0.160
 Calmar ratio (compounded annual return / max draw down)0.307
 Compounded annual return / average of 25% largest draw downsNA
 Compounded annual return / Expected Shortfall lognormal0.793
ANALYSIS BASED ON DAILY VALUES, FULL HISTORY (Back)
RATIO STATISTICS
Ratio statistics of excess return rates
Statistics related to Sharpe ratio
 Mean0.136
 SD0.303
 Sharpe ratio (Glass type estimate) 0.450
 Sharpe ratio (Hedges UMVUE)0.449
 df1096.000
 t0.803
 p0.488
 Lowerbound of 95% confidence interval for Sharpe Ratio-0.648
 Upperbound of 95% confidence interval for Sharpe Ratio1.547
 Lowerbound of 95% CI (Gibbons, Hedeker & Davis approximation)-0.648
 Upperbound of 95% CI (Gibbons, Hedeker & Davis approximation)1.547
Statistics related to Sortino ratio
 Sortino ratio0.640
 Upside Potential Ratio7.113
 Upside part of mean1.515
 Downside part of mean-1.378
 Upside SD0.215
 Downside SD0.213
 N nonnegative terms383.000
 N negative terms714.000
Statistics related to linear regression on benchmark
 N of observations1097.000
 Mean of predictor0.074
 Mean of criterion0.136
 SD of predictor0.179
 SD of criterion0.303
 Covariance-0.002
 r-0.037
 b (slope, estimate of beta)-0.063
 a (intercept, estimate of alpha)0.141
 Mean Square Error0.092
 DF error1095.000
 t(b)-1.238
 p(b)0.524
 t(a)0.830
 p(a)0.484
 Lowerbound of 95% confidence interval for beta-0.163
 Upperbound of 95% confidence interval for beta0.037
 Lowerbound of 95% confidence interval for alpha-0.192
 Upperbound of 95% confidence interval for alpha0.474
 Treynor index (mean / b)-2.155
 Jensen alpha (a)0.141
Ratio statistics of excess log return rates
Statistics related to Sharpe ratio
 Mean0.090
 SD0.305
 Sharpe ratio (Glass type estimate) 0.295
 Sharpe ratio (Hedges UMVUE)0.295
 df1096.000
 t0.526
 p0.492
 Lowerbound of 95% confidence interval for Sharpe Ratio-0.803
 Upperbound of 95% confidence interval for Sharpe Ratio1.392
 Lowerbound of 95% CI (Gibbons, Hedeker & Davis approximation)-0.803
 Upperbound of 95% CI (Gibbons, Hedeker & Davis approximation)1.392
Statistics related to Sortino ratio
 Sortino ratio0.407
 Upside Potential Ratio6.751
 Upside part of mean1.492
 Downside part of mean-1.402
 Upside SD0.210
 Downside SD0.221
 N nonnegative terms383.000
 N negative terms714.000
Statistics related to linear regression on benchmark
 N of observations1097.000
 Mean of predictor0.057
 Mean of criterion0.090
 SD of predictor0.180
 SD of criterion0.305
 Covariance-0.002
 r-0.038
 b (slope, estimate of beta)-0.065
 a (intercept, estimate of alpha)0.094
 Mean Square Error0.093
 DF error1095.000
 t(b)-1.262
 p(b)0.524
 t(a)0.548
 p(a)0.489
 Lowerbound of 95% confidence interval for beta-0.165
 Upperbound of 95% confidence interval for beta0.036
 Lowerbound of 95% confidence interval for alpha-0.241
 Upperbound of 95% confidence interval for alpha0.429
 Treynor index (mean / b)-1.389
 Jensen alpha (a)0.094
Risk estimates for a one-period unit investment (parametric)
assuming log normal returns and losses (using central moments from Sharpe statistics)
 VaR(95%)0.026
 Expected Shortfall on VaR0.033
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 observations1097.000
 Minimum0.841
 Quartile 10.997
 Median1.000
 Quartile 31.004
 Maximum1.120
 Mean of quarter 10.985
 Mean of quarter 20.999
 Mean of quarter 31.001
 Mean of quarter 41.017
 Inter Quartile Range0.007
 Number outliers low92.000
 Percentage of outliers low0.084
 Mean of outliers low0.969
 Number of outliers high106.000
 Percentage of outliers high0.097
 Mean of outliers high1.031
Risk estimates for a one-period unit investment (based on Extreme Value Theory)
 Extreme Value Index (moments method)0.544
 VaR(95%) (moments method)0.013
 Expected Shortfall (moments method)0.033
 Extreme Value Index (regression method)0.423
 VaR(95%) (regression method)0.013
 Expected Shortfall (regression method)0.026
DRAW DOWN STATISTICS
Quartiles of draw downs
 Number of observations12.000
 Minimum0.000
 Quartile 10.004
 Median0.026
 Quartile 30.047
 Maximum0.544
 Mean of quarter 10.001
 Mean of quarter 20.016
 Mean of quarter 30.037
 Mean of quarter 40.233
 Inter Quartile Range0.042
 Number outliers low0.000
 Percentage of outliers low0.000
 Mean of outliers lowNA
 Number of outliers high1.000
 Percentage of outliers high0.083
 Mean of outliers high0.544
Risk estimates based on draw downs (based on Extreme Value Theory)
 Extreme Value Index (moments method)0.286
 VaR(95%) (moments method)0.163
 Expected Shortfall (moments method)0.317
 Extreme Value Index (regression method)2.030
 VaR(95%) (regression method)0.547
 Expected Shortfall (regression method)NA
COMBINED STATISTICS
 Annualized return (arithmetic extrapolation)0.167
 Compounded annual return (geometric extrapolation)0.143
 Calmar ratio (compounded annual return / max draw down)0.263
 Compounded annual return / average of 25% largest draw downs0.615
 Compounded annual return / Expected Shortfall lognormal4.332
ANALYSIS BASED ON DAILY VALUES, LAST 6 MONTHS (Back)
RATIO STATISTICS
Ratio statistics of excess return rates
Statistics related to Sharpe ratio
 Mean0.545
 SD0.439
 Sharpe ratio (Glass type estimate) 1.242
 Sharpe ratio (Hedges UMVUE)1.237
 df171.000
 t0.879
 p0.457
 Lowerbound of 95% confidence interval for Sharpe Ratio-1.534
 Upperbound of 95% confidence interval for Sharpe Ratio4.016
 Lowerbound of 95% CI (Gibbons, Hedeker & Davis approximation)-1.538
 Upperbound of 95% CI (Gibbons, Hedeker & Davis approximation)4.012
Statistics related to Sortino ratio
 Sortino ratio1.902
 Upside Potential Ratio9.387
 Upside part of mean2.690
 Downside part of mean-2.145
 Upside SD0.332
 Downside SD0.287
 N nonnegative terms71.000
 N negative terms101.000
Statistics related to linear regression on benchmark
 N of observations172.000
 Mean of predictor0.308
 Mean of criterion0.545
 SD of predictor0.113
 SD of criterion0.439
 Covariance0.000
 r0.010
 b (slope, estimate of beta)0.039
 a (intercept, estimate of alpha)0.533
 Mean Square Error0.194
 DF error170.000
 t(b)0.130
 p(b)0.495
 t(a)0.848
 p(a)0.468
 Lowerbound of 95% confidence interval for beta-0.549
 Upperbound of 95% confidence interval for beta0.627
 Lowerbound of 95% confidence interval for alpha-0.708
 Upperbound of 95% confidence interval for alpha1.775
 Treynor index (mean / b)14.048
 Jensen alpha (a)0.533
Ratio statistics of excess log return rates
Statistics related to Sharpe ratio
 Mean0.450
 SD0.437
 Sharpe ratio (Glass type estimate) 1.029
 Sharpe ratio (Hedges UMVUE)1.024
 df171.000
 t0.727
 p0.465
 Lowerbound of 95% confidence interval for Sharpe Ratio-1.747
 Upperbound of 95% confidence interval for Sharpe Ratio3.801
 Lowerbound of 95% CI (Gibbons, Hedeker & Davis approximation)-1.750
 Upperbound of 95% CI (Gibbons, Hedeker & Davis approximation)3.798
Statistics related to Sortino ratio
 Sortino ratio1.525
 Upside Potential Ratio8.945
 Upside part of mean2.637
 Downside part of mean-2.187
 Upside SD0.322
 Downside SD0.295
 N nonnegative terms71.000
 N negative terms101.000
Statistics related to linear regression on benchmark
 N of observations172.000
 Mean of predictor0.302
 Mean of criterion0.450
 SD of predictor0.113
 SD of criterion0.437
 Covariance0.000
 r0.004
 b (slope, estimate of beta)0.016
 a (intercept, estimate of alpha)0.445
 Mean Square Error0.192
 DF error170.000
 t(b)0.055
 p(b)0.498
 t(a)0.710
 p(a)0.473
 Lowerbound of 95% confidence interval for beta-0.570
 Upperbound of 95% confidence interval for beta0.603
 Lowerbound of 95% confidence interval for alpha-0.792
 Upperbound of 95% confidence interval for alpha1.681
 Treynor index (mean / b)27.684
 Jensen alpha (a)0.445
Risk estimates for a one-period unit investment (parametric)
assuming log normal returns and losses (using central moments from Sharpe statistics)
 VaR(95%)0.037
 Expected Shortfall on VaR0.046
assuming Pareto losses only (using partial moments from Sortino statistics)
 VaR(95%)0.016
 Expected Shortfall on VaR0.033
ORDER STATISTICS
Quartiles of return rates
 Number of observations172.000
 Minimum0.908
 Quartile 10.995
 Median1.000
 Quartile 31.008
 Maximum1.120
 Mean of quarter 10.976
 Mean of quarter 20.999
 Mean of quarter 31.003
 Mean of quarter 41.029
 Inter Quartile Range0.013
 Number outliers low13.000
 Percentage of outliers low0.076
 Mean of outliers low0.951
 Number of outliers high17.000
 Percentage of outliers high0.099
 Mean of outliers high1.048
Risk estimates for a one-period unit investment (based on Extreme Value Theory)
 Extreme Value Index (moments method)0.448
 VaR(95%) (moments method)0.021
 Expected Shortfall (moments method)0.046
 Extreme Value Index (regression method)0.344
 VaR(95%) (regression method)0.021
 Expected Shortfall (regression method)0.040
DRAW DOWN STATISTICS
Quartiles of draw downs
 Number of observations9.000
 Minimum0.005
 Quartile 10.011
 Median0.025
 Quartile 30.043
 Maximum0.202
 Mean of quarter 10.008
 Mean of quarter 20.022
 Mean of quarter 30.035
 Mean of quarter 40.149
 Inter Quartile Range0.032
 Number outliers low0.000
 Percentage of outliers low0.000
 Mean of outliers lowNA
 Number of outliers high2.000
 Percentage of outliers high0.222
 Mean of outliers high0.149
Risk estimates based on draw downs (based on Extreme Value Theory)
 Extreme Value Index (moments method)-3.225
 VaR(95%) (moments method)0.109
 Expected Shortfall (moments method)0.109
 Extreme Value Index (regression method)0.019
 VaR(95%) (regression method)0.233
 Expected Shortfall (regression method)0.342
COMBINED STATISTICS
 Annualized return (arithmetic extrapolation)0.560
 Compounded annual return (geometric extrapolation)0.638
 Calmar ratio (compounded annual return / max draw down)3.165
 Compounded annual return / average of 25% largest draw downs4.295
 Compounded annual return / Expected Shortfall lognormal13.825