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Advanced Statistics: Bravo Tango

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
 SD0.448
 Sharpe ratio (Glass type estimate) 0.474
 Sharpe ratio (Hedges UMVUE)0.412
 df6.000
 t0.362
 p0.365
 Lowerbound of 95% confidence interval for Sharpe Ratio-2.124
 Upperbound of 95% confidence interval for Sharpe Ratio3.035
 Lowerbound of 95% CI (Gibbons, Hedeker & Davis approximation)-2.165
 Upperbound of 95% CI (Gibbons, Hedeker & Davis approximation)2.989
Statistics related to Sortino ratio
 Sortino ratio1.100
 Upside Potential Ratio3.262
 Upside part of mean0.631
 Downside part of mean-0.418
 Upside SD0.372
 Downside SD0.193
 N nonnegative terms3.000
 N negative terms4.000
Statistics related to linear regression on benchmark
 N of observations7.000
 Mean of predictor-0.015
 Mean of criterion0.213
 SD of predictor0.132
 SD of criterion0.448
 Covariance0.016
 r0.269
 b (slope, estimate of beta)0.913
 a (intercept, estimate of alpha)0.227
 Mean Square Error0.224
 DF error5.000
 t(b)0.624
 p(b)0.280
 t(a)0.366
 p(a)0.365
 Lowerbound of 95% confidence interval for beta-2.850
 Upperbound of 95% confidence interval for beta4.677
 Lowerbound of 95% confidence interval for alpha-1.366
 Upperbound of 95% confidence interval for alpha1.819
 Treynor index (mean / b)0.233
 Jensen alpha (a)0.227
Ratio statistics of excess log return rates
Statistics related to Sharpe ratio
 Mean0.133
 SD0.417
 Sharpe ratio (Glass type estimate) 0.319
 Sharpe ratio (Hedges UMVUE)0.277
 df6.000
 t0.244
 p0.408
 Lowerbound of 95% confidence interval for Sharpe Ratio-2.266
 Upperbound of 95% confidence interval for Sharpe Ratio2.878
 Lowerbound of 95% CI (Gibbons, Hedeker & Davis approximation)-2.294
 Upperbound of 95% CI (Gibbons, Hedeker & Davis approximation)2.848
Statistics related to Sortino ratio
 Sortino ratio0.656
 Upside Potential Ratio2.807
 Upside part of mean0.569
 Downside part of mean-0.436
 Upside SD0.331
 Downside SD0.203
 N nonnegative terms3.000
 N negative terms4.000
Statistics related to linear regression on benchmark
 N of observations7.000
 Mean of predictor-0.023
 Mean of criterion0.133
 SD of predictor0.133
 SD of criterion0.417
 Covariance0.014
 r0.244
 b (slope, estimate of beta)0.767
 a (intercept, estimate of alpha)0.150
 Mean Square Error0.196
 DF error5.000
 t(b)0.563
 p(b)0.299
 t(a)0.259
 p(a)0.403
 Lowerbound of 95% confidence interval for beta-2.734
 Upperbound of 95% confidence interval for beta4.267
 Lowerbound of 95% confidence interval for alpha-1.342
 Upperbound of 95% confidence interval for alpha1.643
 Treynor index (mean / b)0.173
 Jensen alpha (a)0.150
Risk estimates for a one-period unit investment (parametric)
assuming log normal returns and losses (using central moments from Sharpe statistics)
 VaR(95%)0.170
 Expected Shortfall on VaR0.210
assuming Pareto losses only (using partial moments from Sortino statistics)
 VaR(95%)0.087
 Expected Shortfall on VaR0.141
ORDER STATISTICS
Quartiles of return rates
 Number of observations7.000
 Minimum0.888
 Quartile 10.942
 Median1.000
 Quartile 31.052
 Maximum1.276
 Mean of quarter 10.906
 Mean of quarter 20.980
 Mean of quarter 31.018
 Mean of quarter 41.180
 Inter Quartile Range0.110
 Number outliers low0.000
 Percentage of outliers low0.000
 Mean of outliers lowNA
 Number of outliers high1.000
 Percentage of outliers high0.143
 Mean of outliers high1.276
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 observations2.000
 Minimum0.076
 Quartile 10.094
 Median0.112
 Quartile 30.130
 Maximum0.148
 Mean of quarter 10.076
 Mean of quarter 2NA
 Mean of quarter 3NA
 Mean of quarter 40.148
 Inter Quartile Range0.036
 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)0.186
 Compounded annual return (geometric extrapolation)0.194
 Calmar ratio (compounded annual return / max draw down)1.304
 Compounded annual return / average of 25% largest draw downs1.304
 Compounded annual return / Expected Shortfall lognormal0.920
ANALYSIS BASED ON DAILY VALUES, FULL HISTORY (Back)
RATIO STATISTICS
Ratio statistics of excess return rates
Statistics related to Sharpe ratio
 Mean0.150
 SD0.270
 Sharpe ratio (Glass type estimate) 0.553
 Sharpe ratio (Hedges UMVUE)0.551
 df225.000
 t0.448
 p0.327
 Lowerbound of 95% confidence interval for Sharpe Ratio-1.866
 Upperbound of 95% confidence interval for Sharpe Ratio2.971
 Lowerbound of 95% CI (Gibbons, Hedeker & Davis approximation)-1.867
 Upperbound of 95% CI (Gibbons, Hedeker & Davis approximation)2.970
Statistics related to Sortino ratio
 Sortino ratio0.789
 Upside Potential Ratio6.851
 Upside part of mean1.299
 Downside part of mean-1.149
 Upside SD0.192
 Downside SD0.190
 N nonnegative terms54.000
 N negative terms172.000
Statistics related to linear regression on benchmark
 N of observations226.000
 Mean of predictor0.263
 Mean of criterion0.150
 SD of predictor0.169
 SD of criterion0.270
 Covariance-0.000
 r-0.007
 b (slope, estimate of beta)-0.011
 a (intercept, estimate of alpha)0.152
 Mean Square Error0.073
 DF error224.000
 t(b)-0.101
 p(b)0.540
 t(a)0.454
 p(a)0.325
 Lowerbound of 95% confidence interval for beta-0.222
 Upperbound of 95% confidence interval for beta0.200
 Lowerbound of 95% confidence interval for alpha-0.508
 Upperbound of 95% confidence interval for alpha0.813
 Treynor index (mean / b)-13.849
 Jensen alpha (a)0.152
Ratio statistics of excess log return rates
Statistics related to Sharpe ratio
 Mean0.113
 SD0.270
 Sharpe ratio (Glass type estimate) 0.418
 Sharpe ratio (Hedges UMVUE)0.417
 df225.000
 t0.339
 p0.367
 Lowerbound of 95% confidence interval for Sharpe Ratio-2.001
 Upperbound of 95% confidence interval for Sharpe Ratio2.836
 Lowerbound of 95% CI (Gibbons, Hedeker & Davis approximation)-2.001
 Upperbound of 95% CI (Gibbons, Hedeker & Davis approximation)2.835
Statistics related to Sortino ratio
 Sortino ratio0.585
 Upside Potential Ratio6.620
 Upside part of mean1.281
 Downside part of mean-1.168
 Upside SD0.188
 Downside SD0.193
 N nonnegative terms54.000
 N negative terms172.000
Statistics related to linear regression on benchmark
 N of observations226.000
 Mean of predictor0.249
 Mean of criterion0.113
 SD of predictor0.168
 SD of criterion0.270
 Covariance-0.000
 r-0.006
 b (slope, estimate of beta)-0.009
 a (intercept, estimate of alpha)0.115
 Mean Square Error0.073
 DF error224.000
 t(b)-0.083
 p(b)0.533
 t(a)0.344
 p(a)0.366
 Lowerbound of 95% confidence interval for beta-0.221
 Upperbound of 95% confidence interval for beta0.203
 Lowerbound of 95% confidence interval for alpha-0.546
 Upperbound of 95% confidence interval for alpha0.776
 Treynor index (mean / b)-12.643
 Jensen alpha (a)0.115
Risk estimates for a one-period unit investment (parametric)
assuming log normal returns and losses (using central moments from Sharpe statistics)
 VaR(95%)0.023
 Expected Shortfall on VaR0.029
assuming Pareto losses only (using partial moments from Sortino statistics)
 VaR(95%)0.010
 Expected Shortfall on VaR0.021
ORDER STATISTICS
Quartiles of return rates
 Number of observations226.000
 Minimum0.946
 Quartile 11.000
 Median1.000
 Quartile 31.000
 Maximum1.071
 Mean of quarter 10.987
 Mean of quarter 21.000
 Mean of quarter 31.000
 Mean of quarter 41.015
 Inter Quartile Range0.000
 Number outliers low43.000
 Percentage of outliers low0.190
 Mean of outliers low0.983
 Number of outliers high54.000
 Percentage of outliers high0.239
 Mean of outliers high1.016
Risk estimates for a one-period unit investment (based on Extreme Value Theory)
 Extreme Value Index (moments method)-0.843
 VaR(95%) (moments method)0.002
 Expected Shortfall (moments method)0.002
 Extreme Value Index (regression method)0.136
 VaR(95%) (regression method)0.011
 Expected Shortfall (regression method)0.021
DRAW DOWN STATISTICS
Quartiles of draw downs
 Number of observations5.000
 Minimum0.001
 Quartile 10.002
 Median0.014
 Quartile 30.143
 Maximum0.254
 Mean of quarter 10.002
 Mean of quarter 20.014
 Mean of quarter 30.143
 Mean of quarter 40.254
 Inter Quartile Range0.141
 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)0.166
 Compounded annual return (geometric extrapolation)0.170
 Calmar ratio (compounded annual return / max draw down)0.670
 Compounded annual return / average of 25% largest draw downs0.670
 Compounded annual return / Expected Shortfall lognormal5.809
ANALYSIS BASED ON DAILY VALUES, LAST 6 MONTHS (Back)
RATIO STATISTICS
Ratio statistics of excess return rates
Statistics related to Sharpe ratio
 Mean0.468
 SD0.280
 Sharpe ratio (Glass type estimate) 1.669
 Sharpe ratio (Hedges UMVUE)1.662
 df171.000
 t1.180
 p0.443
 Lowerbound of 95% confidence interval for Sharpe Ratio-1.111
 Upperbound of 95% confidence interval for Sharpe Ratio4.444
 Lowerbound of 95% CI (Gibbons, Hedeker & Davis approximation)-1.116
 Upperbound of 95% CI (Gibbons, Hedeker & Davis approximation)4.439
Statistics related to Sortino ratio
 Sortino ratio2.527
 Upside Potential Ratio8.277
 Upside part of mean1.533
 Downside part of mean-1.065
 Upside SD0.211
 Downside SD0.185
 N nonnegative terms47.000
 N negative terms125.000
Statistics related to linear regression on benchmark
 N of observations172.000
 Mean of predictor0.323
 Mean of criterion0.468
 SD of predictor0.182
 SD of criterion0.280
 Covariance0.001
 r0.027
 b (slope, estimate of beta)0.041
 a (intercept, estimate of alpha)0.455
 Mean Square Error0.079
 DF error170.000
 t(b)0.349
 p(b)0.487
 t(a)1.138
 p(a)0.457
 Lowerbound of 95% confidence interval for beta-0.192
 Upperbound of 95% confidence interval for beta0.274
 Lowerbound of 95% confidence interval for alpha-0.334
 Upperbound of 95% confidence interval for alpha1.243
 Treynor index (mean / b)11.341
 Jensen alpha (a)0.455
Ratio statistics of excess log return rates
Statistics related to Sharpe ratio
 Mean0.429
 SD0.280
 Sharpe ratio (Glass type estimate) 1.530
 Sharpe ratio (Hedges UMVUE)1.524
 df171.000
 t1.082
 p0.448
 Lowerbound of 95% confidence interval for Sharpe Ratio-1.248
 Upperbound of 95% confidence interval for Sharpe Ratio4.305
 Lowerbound of 95% CI (Gibbons, Hedeker & Davis approximation)-1.253
 Upperbound of 95% CI (Gibbons, Hedeker & Davis approximation)4.300
Statistics related to Sortino ratio
 Sortino ratio2.266
 Upside Potential Ratio7.990
 Upside part of mean1.511
 Downside part of mean-1.083
 Upside SD0.207
 Downside SD0.189
 N nonnegative terms47.000
 N negative terms125.000
Statistics related to linear regression on benchmark
 N of observations172.000
 Mean of predictor0.306
 Mean of criterion0.429
 SD of predictor0.181
 SD of criterion0.280
 Covariance0.001
 r0.029
 b (slope, estimate of beta)0.044
 a (intercept, estimate of alpha)0.415
 Mean Square Error0.079
 DF error170.000
 t(b)0.375
 p(b)0.486
 t(a)1.041
 p(a)0.460
 Lowerbound of 95% confidence interval for beta-0.189
 Upperbound of 95% confidence interval for beta0.278
 Lowerbound of 95% confidence interval for alpha-0.372
 Upperbound of 95% confidence interval for alpha1.202
 Treynor index (mean / b)9.660
 Jensen alpha (a)0.415
Risk estimates for a one-period unit investment (parametric)
assuming log normal returns and losses (using central moments from Sharpe statistics)
 VaR(95%)0.023
 Expected Shortfall on VaR0.029
assuming Pareto losses only (using partial moments from Sortino statistics)
 VaR(95%)0.009
 Expected Shortfall on VaR0.019
ORDER STATISTICS
Quartiles of return rates
 Number of observations172.000
 Minimum0.946
 Quartile 11.000
 Median1.000
 Quartile 31.002
 Maximum1.071
 Mean of quarter 10.988
 Mean of quarter 21.000
 Mean of quarter 31.000
 Mean of quarter 41.018
 Inter Quartile Range0.002
 Number outliers low23.000
 Percentage of outliers low0.134
 Mean of outliers low0.978
 Number of outliers high37.000
 Percentage of outliers high0.215
 Mean of outliers high1.020
Risk estimates for a one-period unit investment (based on Extreme Value Theory)
 Extreme Value Index (moments method)0.007
 VaR(95%) (moments method)0.002
 Expected Shortfall (moments method)0.003
 Extreme Value Index (regression method)0.362
 VaR(95%) (regression method)0.008
 Expected Shortfall (regression method)0.020
DRAW DOWN STATISTICS
Quartiles of draw downs
 Number of observations9.000
 Minimum0.001
 Quartile 10.007
 Median0.021
 Quartile 30.044
 Maximum0.215
 Mean of quarter 10.003
 Mean of quarter 20.018
 Mean of quarter 30.033
 Mean of quarter 40.179
 Inter Quartile Range0.037
 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 high0.179
Risk estimates based on draw downs (based on Extreme Value Theory)
 Extreme Value Index (moments method)-21.259
 VaR(95%) (moments method)0.107
 Expected Shortfall (moments method)0.107
 Extreme Value Index (regression method)-1.463
 VaR(95%) (regression method)0.271
 Expected Shortfall (regression method)0.282
COMBINED STATISTICS
 Annualized return (arithmetic extrapolation)0.533
 Compounded annual return (geometric extrapolation)0.604
 Calmar ratio (compounded annual return / max draw down)2.814
 Compounded annual return / average of 25% largest draw downs3.379
 Compounded annual return / Expected Shortfall lognormal20.521