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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
 Mean0.106
 SD0.333
 Sharpe ratio (Glass type estimate) 0.317
 Sharpe ratio (Hedges UMVUE)0.295
 df11.000
 t0.317
 p0.379
 Lowerbound of 95% confidence interval for Sharpe Ratio-1.654
 Upperbound of 95% confidence interval for Sharpe Ratio2.274
 Lowerbound of 95% CI (Gibbons, Hedeker & Davis approximation)-1.669
 Upperbound of 95% CI (Gibbons, Hedeker & Davis approximation)2.259
Statistics related to Sortino ratio
 Sortino ratio0.714
 Upside Potential Ratio2.488
 Upside part of mean0.368
 Downside part of mean-0.262
 Upside SD0.284
 Downside SD0.148
 N nonnegative terms3.000
 N negative terms9.000
Statistics related to linear regression on benchmark
 N of observations12.000
 Mean of predictor0.370
 Mean of criterion0.106
 SD of predictor0.226
 SD of criterion0.333
 Covariance0.003
 r0.045
 b (slope, estimate of beta)0.067
 a (intercept, estimate of alpha)0.081
 Mean Square Error0.122
 DF error10.000
 t(b)0.143
 p(b)0.444
 t(a)0.208
 p(a)0.420
 Lowerbound of 95% confidence interval for beta-0.969
 Upperbound of 95% confidence interval for beta1.103
 Lowerbound of 95% confidence interval for alpha-0.786
 Upperbound of 95% confidence interval for alpha0.948
 Treynor index (mean / b)1.585
 Jensen alpha (a)0.081
Ratio statistics of excess log return rates
Statistics related to Sharpe ratio
 Mean0.059
 SD0.309
 Sharpe ratio (Glass type estimate) 0.192
 Sharpe ratio (Hedges UMVUE)0.178
 df11.000
 t0.192
 p0.426
 Lowerbound of 95% confidence interval for Sharpe Ratio-1.774
 Upperbound of 95% confidence interval for Sharpe Ratio2.149
 Lowerbound of 95% CI (Gibbons, Hedeker & Davis approximation)-1.783
 Upperbound of 95% CI (Gibbons, Hedeker & Davis approximation)2.140
Statistics related to Sortino ratio
 Sortino ratio0.382
 Upside Potential Ratio2.141
 Upside part of mean0.332
 Downside part of mean-0.273
 Upside SD0.253
 Downside SD0.155
 N nonnegative terms3.000
 N negative terms9.000
Statistics related to linear regression on benchmark
 N of observations12.000
 Mean of predictor0.342
 Mean of criterion0.059
 SD of predictor0.213
 SD of criterion0.309
 Covariance0.004
 r0.060
 b (slope, estimate of beta)0.087
 a (intercept, estimate of alpha)0.029
 Mean Square Error0.105
 DF error10.000
 t(b)0.190
 p(b)0.426
 t(a)0.082
 p(a)0.468
 Lowerbound of 95% confidence interval for beta-0.933
 Upperbound of 95% confidence interval for beta1.107
 Lowerbound of 95% confidence interval for alpha-0.771
 Upperbound of 95% confidence interval for alpha0.830
 Treynor index (mean / b)0.680
 Jensen alpha (a)0.029
Risk estimates for a one-period unit investment (parametric)
assuming log normal returns and losses (using central moments from Sharpe statistics)
 VaR(95%)0.132
 Expected Shortfall on VaR0.164
assuming Pareto losses only (using partial moments from Sortino statistics)
 VaR(95%)0.064
 Expected Shortfall on VaR0.116
ORDER STATISTICS
Quartiles of return rates
 Number of observations12.000
 Minimum0.888
 Quartile 10.990
 Median1.000
 Quartile 31.005
 Maximum1.276
 Mean of quarter 10.924
 Mean of quarter 21.000
 Mean of quarter 31.000
 Mean of quarter 41.126
 Inter Quartile Range0.015
 Number outliers low3.000
 Percentage of outliers low0.250
 Mean of outliers low0.924
 Number of outliers high2.000
 Percentage of outliers high0.167
 Mean of outliers high1.180
Risk estimates for a one-period unit investment (based on Extreme Value Theory)
 Extreme Value Index (moments method)-7.493
 VaR(95%) (moments method)0.079
 Expected Shortfall (moments method)0.079
 Extreme Value Index (regression method)-0.960
 VaR(95%) (regression method)0.124
 Expected Shortfall (regression method)0.137
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)0.109
 Compounded annual return (geometric extrapolation)0.109
 Calmar ratio (compounded annual return / max draw down)0.732
 Compounded annual return / average of 25% largest draw downs0.732
 Compounded annual return / Expected Shortfall lognormal0.665
ANALYSIS BASED ON DAILY VALUES, FULL HISTORY (Back)
RATIO STATISTICS
Ratio statistics of excess return rates
Statistics related to Sharpe ratio
 Mean0.081
 SD0.217
 Sharpe ratio (Glass type estimate) 0.373
 Sharpe ratio (Hedges UMVUE)0.372
 df349.000
 t0.376
 p0.353
 Lowerbound of 95% confidence interval for Sharpe Ratio-1.570
 Upperbound of 95% confidence interval for Sharpe Ratio2.316
 Lowerbound of 95% CI (Gibbons, Hedeker & Davis approximation)-1.571
 Upperbound of 95% CI (Gibbons, Hedeker & Davis approximation)2.316
Statistics related to Sortino ratio
 Sortino ratio0.531
 Upside Potential Ratio5.505
 Upside part of mean0.839
 Downside part of mean-0.758
 Upside SD0.154
 Downside SD0.152
 N nonnegative terms54.000
 N negative terms296.000
Statistics related to linear regression on benchmark
 N of observations350.000
 Mean of predictor0.336
 Mean of criterion0.081
 SD of predictor0.177
 SD of criterion0.217
 Covariance-0.000
 r-0.006
 b (slope, estimate of beta)-0.007
 a (intercept, estimate of alpha)0.083
 Mean Square Error0.047
 DF error348.000
 t(b)-0.109
 p(b)0.544
 t(a)0.385
 p(a)0.350
 Lowerbound of 95% confidence interval for beta-0.137
 Upperbound of 95% confidence interval for beta0.122
 Lowerbound of 95% confidence interval for alpha-0.343
 Upperbound of 95% confidence interval for alpha0.509
 Treynor index (mean / b)-11.220
 Jensen alpha (a)0.083
Ratio statistics of excess log return rates
Statistics related to Sharpe ratio
 Mean0.057
 SD0.217
 Sharpe ratio (Glass type estimate) 0.265
 Sharpe ratio (Hedges UMVUE)0.264
 df349.000
 t0.267
 p0.395
 Lowerbound of 95% confidence interval for Sharpe Ratio-1.679
 Upperbound of 95% confidence interval for Sharpe Ratio2.208
 Lowerbound of 95% CI (Gibbons, Hedeker & Davis approximation)-1.679
 Upperbound of 95% CI (Gibbons, Hedeker & Davis approximation)2.207
Statistics related to Sortino ratio
 Sortino ratio0.369
 Upside Potential Ratio5.320
 Upside part of mean0.827
 Downside part of mean-0.770
 Upside SD0.151
 Downside SD0.155
 N nonnegative terms54.000
 N negative terms296.000
Statistics related to linear regression on benchmark
 N of observations350.000
 Mean of predictor0.320
 Mean of criterion0.057
 SD of predictor0.176
 SD of criterion0.217
 Covariance-0.000
 r-0.005
 b (slope, estimate of beta)-0.006
 a (intercept, estimate of alpha)0.059
 Mean Square Error0.047
 DF error348.000
 t(b)-0.090
 p(b)0.536
 t(a)0.274
 p(a)0.392
 Lowerbound of 95% confidence interval for beta-0.136
 Upperbound of 95% confidence interval for beta0.124
 Lowerbound of 95% confidence interval for alpha-0.367
 Upperbound of 95% confidence interval for alpha0.485
 Treynor index (mean / b)-9.672
 Jensen alpha (a)0.059
Risk estimates for a one-period unit investment (parametric)
assuming log normal returns and losses (using central moments from Sharpe statistics)
 VaR(95%)0.019
 Expected Shortfall on VaR0.024
assuming Pareto losses only (using partial moments from Sortino statistics)
 VaR(95%)0.007
 Expected Shortfall on VaR0.015
ORDER STATISTICS
Quartiles of return rates
 Number of observations350.000
 Minimum0.946
 Quartile 11.000
 Median1.000
 Quartile 31.000
 Maximum1.071
 Mean of quarter 10.992
 Mean of quarter 21.000
 Mean of quarter 31.000
 Mean of quarter 41.010
 Inter Quartile Range0.000
 Number outliers low43.000
 Percentage of outliers low0.123
 Mean of outliers low0.983
 Number of outliers high54.000
 Percentage of outliers high0.154
 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)0.001
 Expected Shortfall (moments method)0.002
 Extreme Value Index (regression method)0.136
 VaR(95%) (regression method)0.007
 Expected Shortfall (regression method)0.017
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)0.107
 Compounded annual return (geometric extrapolation)0.107
 Calmar ratio (compounded annual return / max draw down)0.421
 Compounded annual return / average of 25% largest draw downs0.421
 Compounded annual return / Expected Shortfall lognormal4.508
ANALYSIS BASED ON DAILY VALUES, LAST 6 MONTHS (Back)
RATIO STATISTICS
Ratio statistics of excess return rates
Statistics related to Sharpe ratio
 Mean-0.044
 SD0.000
 Sharpe ratio (Glass type estimate) NA
 Sharpe ratio (Hedges UMVUE)NA
 dfNA
 tNA
 pNA
 Lowerbound of 95% confidence interval for Sharpe RatioNA
 Upperbound of 95% confidence interval for Sharpe RatioNA
 Lowerbound of 95% CI (Gibbons, Hedeker & Davis approximation)NA
 Upperbound of 95% CI (Gibbons, Hedeker & Davis approximation)NA
Statistics related to Sortino ratio
 Sortino ratio-18.547
 Upside Potential Ratio0.000
 Upside part of mean0.000
 Downside part of mean-0.044
 Upside SD0.000
 Downside SD0.002
 N nonnegative terms0.000
 N negative terms172.000
Statistics related to linear regression on benchmark
 N of observations172.000
 Mean of predictor0.638
 Mean of criterion-0.044
 SD of predictor0.210
 SD of criterion0.000
 Covariance0.000
 rNA
 b (slope, estimate of beta)NA
 a (intercept, estimate of alpha)NA
 Mean Square ErrorNA
 DF errorNA
 t(b)NA
 p(b)NA
 t(a)NA
 p(a)NA
 Lowerbound of 95% confidence interval for betaNA
 Upperbound of 95% confidence interval for betaNA
 Lowerbound of 95% confidence interval for alphaNA
 Upperbound of 95% confidence interval for alphaNA
 Treynor index (mean / b)NA
 Jensen alpha (a)NA
Ratio statistics of excess log return rates
Statistics related to Sharpe ratio
 Mean-0.044
 SD0.000
 Sharpe ratio (Glass type estimate) -7936535306446244.000
 Sharpe ratio (Hedges UMVUE)-7901674975671223.000
 df171.000
 t-5611977934314593.000
 p1.000
 Lowerbound of 95% confidence interval for Sharpe RatioNA
 Upperbound of 95% confidence interval for Sharpe RatioNA
 Lowerbound of 95% CI (Gibbons, Hedeker & Davis approximation)-8739115425704417.000
 Upperbound of 95% CI (Gibbons, Hedeker & Davis approximation)-7064234525638030.000
Statistics related to Sortino ratio
 Sortino ratio-18.547
 Upside Potential Ratio0.000
 Upside part of mean0.000
 Downside part of mean-0.044
 Upside SD0.000
 Downside SD0.002
 N nonnegative terms0.000
 N negative terms172.000
Statistics related to linear regression on benchmark
 N of observations172.000
 Mean of predictor0.616
 Mean of criterion-0.044
 SD of predictor0.209
 SD of criterion0.000
 Covariance-0.000
 r-0.000
 b (slope, estimate of beta)-0.000
 a (intercept, estimate of alpha)-0.044
 Mean Square Error0.000
 DF error170.000
 t(b)-0.000
 p(b)0.500
 t(a)-5526047753079328.000
 p(a)1.000
 Lowerbound of 95% confidence interval for beta-0.000
 Upperbound of 95% confidence interval for beta0.000
 Lowerbound of 95% confidence interval for alpha-0.044
 Upperbound of 95% confidence interval for alpha-0.044
 Treynor index (mean / b)6790505766213766304910534508544.000
 Jensen alpha (a)-0.044
Risk estimates for a one-period unit investment (parametric)
assuming log normal returns and losses (using central moments from Sharpe statistics)
 VaR(95%)0.000
 Expected Shortfall on VaR0.000
assuming Pareto losses only (using partial moments from Sortino statistics)
 VaR(95%)0.000
 Expected Shortfall on VaR0.000
ORDER STATISTICS
Quartiles of return rates
 Number of observations172.000
 Minimum1.000
 Quartile 11.000
 Median1.000
 Quartile 31.000
 Maximum1.000
 Mean of quarter 11.000
 Mean of quarter 21.000
 Mean of quarter 31.000
 Mean of quarter 41.000
 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 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 observations0.000
 MinimumNA
 Quartile 1NA
 MedianNA
 Quartile 3NA
 MaximumNA
 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 lowNA
 Mean of outliers lowNA
 Number of outliers high0.000
 Percentage of outliers highNA
 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)0.000
 Compounded annual return (geometric extrapolation)0.000
 Calmar ratio (compounded annual return / max draw down)NA
 Compounded annual return / average of 25% largest draw downsNA
 Compounded annual return / Expected Shortfall lognormal0.000