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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
 Mean0.156
 SD0.389
 Sharpe ratio (Glass type estimate) 0.399
 Sharpe ratio (Hedges UMVUE)0.361
 df8.000
 t0.346
 p0.369
 Lowerbound of 95% confidence interval for Sharpe Ratio-1.884
 Upperbound of 95% confidence interval for Sharpe Ratio2.659
 Lowerbound of 95% CI (Gibbons, Hedeker & Davis approximation)-1.909
 Upperbound of 95% CI (Gibbons, Hedeker & Davis approximation)2.631
Statistics related to Sortino ratio
 Sortino ratio0.912
 Upside Potential Ratio2.875
 Upside part of mean0.490
 Downside part of mean-0.335
 Upside SD0.328
 Downside SD0.171
 N nonnegative terms3.000
 N negative terms6.000
Statistics related to linear regression on benchmark
 N of observations9.000
 Mean of predictor0.378
 Mean of criterion0.156
 SD of predictor0.263
 SD of criterion0.389
 Covariance0.005
 r0.044
 b (slope, estimate of beta)0.066
 a (intercept, estimate of alpha)0.131
 Mean Square Error0.173
 DF error7.000
 t(b)0.118
 p(b)0.455
 t(a)0.249
 p(a)0.405
 Lowerbound of 95% confidence interval for beta-1.257
 Upperbound of 95% confidence interval for beta1.389
 Lowerbound of 95% confidence interval for alpha-1.110
 Upperbound of 95% confidence interval for alpha1.371
 Treynor index (mean / b)2.361
 Jensen alpha (a)0.131
Ratio statistics of excess log return rates
Statistics related to Sharpe ratio
 Mean0.094
 SD0.362
 Sharpe ratio (Glass type estimate) 0.259
 Sharpe ratio (Hedges UMVUE)0.234
 df8.000
 t0.224
 p0.414
 Lowerbound of 95% confidence interval for Sharpe Ratio-2.016
 Upperbound of 95% confidence interval for Sharpe Ratio2.518
 Lowerbound of 95% CI (Gibbons, Hedeker & Davis approximation)-2.032
 Upperbound of 95% CI (Gibbons, Hedeker & Davis approximation)2.500
Statistics related to Sortino ratio
 Sortino ratio0.523
 Upside Potential Ratio2.474
 Upside part of mean0.443
 Downside part of mean-0.349
 Upside SD0.292
 Downside SD0.179
 N nonnegative terms3.000
 N negative terms6.000
Statistics related to linear regression on benchmark
 N of observations9.000
 Mean of predictor0.343
 Mean of criterion0.094
 SD of predictor0.247
 SD of criterion0.362
 Covariance0.005
 r0.061
 b (slope, estimate of beta)0.089
 a (intercept, estimate of alpha)0.063
 Mean Square Error0.149
 DF error7.000
 t(b)0.161
 p(b)0.438
 t(a)0.131
 p(a)0.450
 Lowerbound of 95% confidence interval for beta-1.216
 Upperbound of 95% confidence interval for beta1.394
 Lowerbound of 95% confidence interval for alpha-1.082
 Upperbound of 95% confidence interval for alpha1.208
 Treynor index (mean / b)1.056
 Jensen alpha (a)0.063
Risk estimates for a one-period unit investment (parametric)
assuming log normal returns and losses (using central moments from Sharpe statistics)
 VaR(95%)0.151
 Expected Shortfall on VaR0.187
assuming Pareto losses only (using partial moments from Sortino statistics)
 VaR(95%)0.076
 Expected Shortfall on VaR0.132
ORDER STATISTICS
Quartiles of return rates
 Number of observations9.000
 Minimum0.888
 Quartile 10.959
 Median1.000
 Quartile 31.018
 Maximum1.276
 Mean of quarter 10.924
 Mean of quarter 21.000
 Mean of quarter 31.009
 Mean of quarter 41.180
 Inter Quartile Range0.059
 Number outliers low0.000
 Percentage of outliers low0.000
 Mean of outliers lowNA
 Number of outliers high1.000
 Percentage of outliers high0.111
 Mean of outliers high1.276
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)0.130
 Expected Shortfall (regression method)0.139
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)0.145
 Compounded annual return (geometric extrapolation)0.148
 Calmar ratio (compounded annual return / max draw down)0.994
 Compounded annual return / average of 25% largest draw downs0.994
 Compounded annual return / Expected Shortfall lognormal0.790
ANALYSIS BASED ON DAILY VALUES, FULL HISTORY (Back)
RATIO STATISTICS
Ratio statistics of excess return rates
Statistics related to Sharpe ratio
 Mean0.109
 SD0.241
 Sharpe ratio (Glass type estimate) 0.455
 Sharpe ratio (Hedges UMVUE)0.454
 df284.000
 t0.414
 p0.340
 Lowerbound of 95% confidence interval for Sharpe Ratio-1.699
 Upperbound of 95% confidence interval for Sharpe Ratio2.608
 Lowerbound of 95% CI (Gibbons, Hedeker & Davis approximation)-1.700
 Upperbound of 95% CI (Gibbons, Hedeker & Davis approximation)2.607
Statistics related to Sortino ratio
 Sortino ratio0.648
 Upside Potential Ratio6.101
 Upside part of mean1.030
 Downside part of mean-0.921
 Upside SD0.171
 Downside SD0.169
 N nonnegative terms54.000
 N negative terms231.000
Statistics related to linear regression on benchmark
 N of observations285.000
 Mean of predictor0.354
 Mean of criterion0.109
 SD of predictor0.188
 SD of criterion0.241
 Covariance-0.000
 r-0.006
 b (slope, estimate of beta)-0.008
 a (intercept, estimate of alpha)0.112
 Mean Square Error0.058
 DF error283.000
 t(b)-0.106
 p(b)0.542
 t(a)0.422
 p(a)0.337
 Lowerbound of 95% confidence interval for beta-0.158
 Upperbound of 95% confidence interval for beta0.142
 Lowerbound of 95% confidence interval for alpha-0.412
 Upperbound of 95% confidence interval for alpha0.636
 Treynor index (mean / b)-13.598
 Jensen alpha (a)0.112
Ratio statistics of excess log return rates
Statistics related to Sharpe ratio
 Mean0.081
 SD0.241
 Sharpe ratio (Glass type estimate) 0.335
 Sharpe ratio (Hedges UMVUE)0.334
 df284.000
 t0.305
 p0.380
 Lowerbound of 95% confidence interval for Sharpe Ratio-1.819
 Upperbound of 95% confidence interval for Sharpe Ratio2.488
 Lowerbound of 95% CI (Gibbons, Hedeker & Davis approximation)-1.820
 Upperbound of 95% CI (Gibbons, Hedeker & Davis approximation)2.487
Statistics related to Sortino ratio
 Sortino ratio0.468
 Upside Potential Ratio5.895
 Upside part of mean1.016
 Downside part of mean-0.935
 Upside SD0.168
 Downside SD0.172
 N nonnegative terms54.000
 N negative terms231.000
Statistics related to linear regression on benchmark
 N of observations285.000
 Mean of predictor0.336
 Mean of criterion0.081
 SD of predictor0.187
 SD of criterion0.241
 Covariance-0.000
 r-0.005
 b (slope, estimate of beta)-0.007
 a (intercept, estimate of alpha)0.083
 Mean Square Error0.058
 DF error283.000
 t(b)-0.087
 p(b)0.534
 t(a)0.311
 p(a)0.378
 Lowerbound of 95% confidence interval for beta-0.157
 Upperbound of 95% confidence interval for beta0.144
 Lowerbound of 95% confidence interval for alpha-0.441
 Upperbound of 95% confidence interval for alpha0.607
 Treynor index (mean / b)-12.196
 Jensen alpha (a)0.083
Risk estimates for a one-period unit investment (parametric)
assuming log normal returns and losses (using central moments from Sharpe statistics)
 VaR(95%)0.021
 Expected Shortfall on VaR0.026
assuming Pareto losses only (using partial moments from Sortino statistics)
 VaR(95%)0.008
 Expected Shortfall on VaR0.018
ORDER STATISTICS
Quartiles of return rates
 Number of observations285.000
 Minimum0.946
 Quartile 11.000
 Median1.000
 Quartile 31.000
 Maximum1.071
 Mean of quarter 10.990
 Mean of quarter 21.000
 Mean of quarter 31.000
 Mean of quarter 41.012
 Inter Quartile Range0.000
 Number outliers low43.000
 Percentage of outliers low0.151
 Mean of outliers low0.983
 Number of outliers high54.000
 Percentage of outliers high0.189
 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)0.009
 Expected Shortfall (regression method)0.019
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)0.131
 Compounded annual return (geometric extrapolation)0.133
 Calmar ratio (compounded annual return / max draw down)0.523
 Compounded annual return / average of 25% largest draw downs0.523
 Compounded annual return / Expected Shortfall lognormal5.069
ANALYSIS BASED ON DAILY VALUES, LAST 6 MONTHS (Back)
RATIO STATISTICS
Ratio statistics of excess return rates
Statistics related to Sharpe ratio
 Mean-0.027
 SD0.119
 Sharpe ratio (Glass type estimate) -0.230
 Sharpe ratio (Hedges UMVUE)-0.229
 df171.000
 t-0.162
 p0.508
 Lowerbound of 95% confidence interval for Sharpe Ratio-3.001
 Upperbound of 95% confidence interval for Sharpe Ratio2.543
 Lowerbound of 95% CI (Gibbons, Hedeker & Davis approximation)-3.001
 Upperbound of 95% CI (Gibbons, Hedeker & Davis approximation)2.543
Statistics related to Sortino ratio
 Sortino ratio-0.284
 Upside Potential Ratio3.475
 Upside part of mean0.335
 Downside part of mean-0.362
 Upside SD0.070
 Downside SD0.096
 N nonnegative terms18.000
 N negative terms154.000
Statistics related to linear regression on benchmark
 N of observations172.000
 Mean of predictor0.636
 Mean of criterion-0.027
 SD of predictor0.215
 SD of criterion0.119
 Covariance-0.002
 r-0.066
 b (slope, estimate of beta)-0.037
 a (intercept, estimate of alpha)-0.004
 Mean Square Error0.014
 DF error170.000
 t(b)-0.865
 p(b)0.533
 t(a)-0.024
 p(a)0.501
 Lowerbound of 95% confidence interval for beta-0.120
 Upperbound of 95% confidence interval for beta0.047
 Lowerbound of 95% confidence interval for alpha-0.341
 Upperbound of 95% confidence interval for alpha0.333
 Treynor index (mean / b)0.747
 Jensen alpha (a)-0.004
Ratio statistics of excess log return rates
Statistics related to Sharpe ratio
 Mean-0.035
 SD0.120
 Sharpe ratio (Glass type estimate) -0.287
 Sharpe ratio (Hedges UMVUE)-0.286
 df171.000
 t-0.203
 p0.510
 Lowerbound of 95% confidence interval for Sharpe Ratio-3.059
 Upperbound of 95% confidence interval for Sharpe Ratio2.485
 Lowerbound of 95% CI (Gibbons, Hedeker & Davis approximation)-3.058
 Upperbound of 95% CI (Gibbons, Hedeker & Davis approximation)2.486
Statistics related to Sortino ratio
 Sortino ratio-0.352
 Upside Potential Ratio3.389
 Upside part of mean0.332
 Downside part of mean-0.367
 Upside SD0.069
 Downside SD0.098
 N nonnegative terms18.000
 N negative terms154.000
Statistics related to linear regression on benchmark
 N of observations172.000
 Mean of predictor0.613
 Mean of criterion-0.035
 SD of predictor0.215
 SD of criterion0.120
 Covariance-0.002
 r-0.067
 b (slope, estimate of beta)-0.037
 a (intercept, estimate of alpha)-0.012
 Mean Square Error0.014
 DF error170.000
 t(b)-0.871
 p(b)0.533
 t(a)-0.068
 p(a)0.503
 Lowerbound of 95% confidence interval for beta-0.122
 Upperbound of 95% confidence interval for beta0.047
 Lowerbound of 95% confidence interval for alpha-0.352
 Upperbound of 95% confidence interval for alpha0.328
 Treynor index (mean / b)0.925
 Jensen alpha (a)-0.012
Risk estimates for a one-period unit investment (parametric)
assuming log normal returns and losses (using central moments from Sharpe statistics)
 VaR(95%)0.011
 Expected Shortfall on VaR0.013
assuming Pareto losses only (using partial moments from Sortino statistics)
 VaR(95%)0.003
 Expected Shortfall on VaR0.008
ORDER STATISTICS
Quartiles of return rates
 Number of observations172.000
 Minimum0.958
 Quartile 11.000
 Median1.000
 Quartile 31.000
 Maximum1.029
 Mean of quarter 10.996
 Mean of quarter 21.000
 Mean of quarter 31.000
 Mean of quarter 41.004
 Inter Quartile Range0.000
 Number outliers low14.000
 Percentage of outliers low0.081
 Mean of outliers low0.988
 Number of outliers high18.000
 Percentage of outliers high0.105
 Mean of outliers high1.009
Risk estimates for a one-period unit investment (based on Extreme Value Theory)
 Extreme Value Index (moments method)0.819
 VaR(95%) (moments method)0.001
 Expected Shortfall (moments method)0.006
 Extreme Value Index (regression method)1.037
 VaR(95%) (regression method)0.001
 Expected Shortfall (regression method)NA
DRAW DOWN STATISTICS
Quartiles of draw downs
 Number of observations3.000
 Minimum0.001
 Quartile 10.002
 Median0.002
 Quartile 30.072
 Maximum0.143
 Mean of quarter 10.001
 Mean of quarter 20.002
 Mean of quarter 3NA
 Mean of quarter 40.143
 Inter Quartile Range0.071
 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)0.010
 Compounded annual return (geometric extrapolation)0.010
 Calmar ratio (compounded annual return / max draw down)0.067
 Compounded annual return / average of 25% largest draw downs0.067
 Compounded annual return / Expected Shortfall lognormal0.713