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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
 Mean0.119
 SD0.349
 Sharpe ratio (Glass type estimate) 0.342
 Sharpe ratio (Hedges UMVUE)0.315
 df10.000
 t0.327
 p0.375
 Lowerbound of 95% confidence interval for Sharpe Ratio-1.719
 Upperbound of 95% confidence interval for Sharpe Ratio2.386
 Lowerbound of 95% CI (Gibbons, Hedeker & Davis approximation)-1.737
 Upperbound of 95% CI (Gibbons, Hedeker & Davis approximation)2.367
Statistics related to Sortino ratio
 Sortino ratio0.772
 Upside Potential Ratio2.599
 Upside part of mean0.401
 Downside part of mean-0.282
 Upside SD0.297
 Downside SD0.154
 N nonnegative terms3.000
 N negative terms8.000
Statistics related to linear regression on benchmark
 N of observations11.000
 Mean of predictor0.394
 Mean of criterion0.119
 SD of predictor0.236
 SD of criterion0.349
 Covariance0.003
 r0.041
 b (slope, estimate of beta)0.061
 a (intercept, estimate of alpha)0.095
 Mean Square Error0.135
 DF error9.000
 t(b)0.124
 p(b)0.452
 t(a)0.221
 p(a)0.415
 Lowerbound of 95% confidence interval for beta-1.053
 Upperbound of 95% confidence interval for beta1.175
 Lowerbound of 95% confidence interval for alpha-0.878
 Upperbound of 95% confidence interval for alpha1.068
 Treynor index (mean / b)1.955
 Jensen alpha (a)0.095
Ratio statistics of excess log return rates
Statistics related to Sharpe ratio
 Mean0.069
 SD0.324
 Sharpe ratio (Glass type estimate) 0.212
 Sharpe ratio (Hedges UMVUE)0.195
 df10.000
 t0.203
 p0.422
 Lowerbound of 95% confidence interval for Sharpe Ratio-1.843
 Upperbound of 95% confidence interval for Sharpe Ratio2.256
 Lowerbound of 95% CI (Gibbons, Hedeker & Davis approximation)-1.854
 Upperbound of 95% CI (Gibbons, Hedeker & Davis approximation)2.244
Statistics related to Sortino ratio
 Sortino ratio0.424
 Upside Potential Ratio2.236
 Upside part of mean0.362
 Downside part of mean-0.294
 Upside SD0.264
 Downside SD0.162
 N nonnegative terms3.000
 N negative terms8.000
Statistics related to linear regression on benchmark
 N of observations11.000
 Mean of predictor0.363
 Mean of criterion0.069
 SD of predictor0.222
 SD of criterion0.324
 Covariance0.004
 r0.057
 b (slope, estimate of beta)0.084
 a (intercept, estimate of alpha)0.038
 Mean Square Error0.116
 DF error9.000
 t(b)0.172
 p(b)0.434
 t(a)0.096
 p(a)0.463
 Lowerbound of 95% confidence interval for beta-1.014
 Upperbound of 95% confidence interval for beta1.181
 Lowerbound of 95% confidence interval for alpha-0.861
 Upperbound of 95% confidence interval for alpha0.937
 Treynor index (mean / b)0.822
 Jensen alpha (a)0.038
Risk estimates for a one-period unit investment (parametric)
assuming log normal returns and losses (using central moments from Sharpe statistics)
 VaR(95%)0.138
 Expected Shortfall on VaR0.170
assuming Pareto losses only (using partial moments from Sortino statistics)
 VaR(95%)0.068
 Expected Shortfall on VaR0.121
ORDER STATISTICS
Quartiles of return rates
 Number of observations11.000
 Minimum0.888
 Quartile 10.980
 Median1.000
 Quartile 31.009
 Maximum1.276
 Mean of quarter 10.924
 Mean of quarter 21.000
 Mean of quarter 31.000
 Mean of quarter 41.126
 Inter Quartile Range0.029
 Number outliers low2.000
 Percentage of outliers low0.182
 Mean of outliers low0.906
 Number of outliers high2.000
 Percentage of outliers high0.182
 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)0.126
 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)0.119
 Compounded annual return (geometric extrapolation)0.119
 Calmar ratio (compounded annual return / max draw down)0.803
 Compounded annual return / average of 25% largest draw downs0.803
 Compounded annual return / Expected Shortfall lognormal0.700
ANALYSIS BASED ON DAILY VALUES, FULL HISTORY (Back)
RATIO STATISTICS
Ratio statistics of excess return rates
Statistics related to Sharpe ratio
 Mean0.093
 SD0.227
 Sharpe ratio (Glass type estimate) 0.409
 Sharpe ratio (Hedges UMVUE)0.409
 df318.000
 t0.394
 p0.347
 Lowerbound of 95% confidence interval for Sharpe Ratio-1.626
 Upperbound of 95% confidence interval for Sharpe Ratio2.445
 Lowerbound of 95% CI (Gibbons, Hedeker & Davis approximation)-1.627
 Upperbound of 95% CI (Gibbons, Hedeker & Davis approximation)2.444
Statistics related to Sortino ratio
 Sortino ratio0.583
 Upside Potential Ratio5.767
 Upside part of mean0.920
 Downside part of mean-0.827
 Upside SD0.162
 Downside SD0.160
 N nonnegative terms54.000
 N negative terms265.000
Statistics related to linear regression on benchmark
 N of observations319.000
 Mean of predictor0.379
 Mean of criterion0.093
 SD of predictor0.180
 SD of criterion0.227
 Covariance-0.000
 r-0.006
 b (slope, estimate of beta)-0.008
 a (intercept, estimate of alpha)0.096
 Mean Square Error0.052
 DF error317.000
 t(b)-0.115
 p(b)0.546
 t(a)0.404
 p(a)0.343
 Lowerbound of 95% confidence interval for beta-0.148
 Upperbound of 95% confidence interval for beta0.131
 Lowerbound of 95% confidence interval for alpha-0.372
 Upperbound of 95% confidence interval for alpha0.564
 Treynor index (mean / b)-11.465
 Jensen alpha (a)0.096
Ratio statistics of excess log return rates
Statistics related to Sharpe ratio
 Mean0.067
 SD0.228
 Sharpe ratio (Glass type estimate) 0.296
 Sharpe ratio (Hedges UMVUE)0.295
 df318.000
 t0.285
 p0.388
 Lowerbound of 95% confidence interval for Sharpe Ratio-1.740
 Upperbound of 95% confidence interval for Sharpe Ratio2.331
 Lowerbound of 95% CI (Gibbons, Hedeker & Davis approximation)-1.740
 Upperbound of 95% CI (Gibbons, Hedeker & Davis approximation)2.331
Statistics related to Sortino ratio
 Sortino ratio0.413
 Upside Potential Ratio5.572
 Upside part of mean0.907
 Downside part of mean-0.840
 Upside SD0.158
 Downside SD0.163
 N nonnegative terms54.000
 N negative terms265.000
Statistics related to linear regression on benchmark
 N of observations319.000
 Mean of predictor0.362
 Mean of criterion0.067
 SD of predictor0.180
 SD of criterion0.228
 Covariance-0.000
 r-0.005
 b (slope, estimate of beta)-0.007
 a (intercept, estimate of alpha)0.070
 Mean Square Error0.052
 DF error317.000
 t(b)-0.094
 p(b)0.537
 t(a)0.293
 p(a)0.385
 Lowerbound of 95% confidence interval for beta-0.146
 Upperbound of 95% confidence interval for beta0.133
 Lowerbound of 95% confidence interval for alpha-0.399
 Upperbound of 95% confidence interval for alpha0.538
 Treynor index (mean / b)-10.081
 Jensen alpha (a)0.070
Risk estimates for a one-period unit investment (parametric)
assuming log normal returns and losses (using central moments from Sharpe statistics)
 VaR(95%)0.020
 Expected Shortfall on VaR0.025
assuming Pareto losses only (using partial moments from Sortino statistics)
 VaR(95%)0.007
 Expected Shortfall on VaR0.016
ORDER STATISTICS
Quartiles of return rates
 Number of observations319.000
 Minimum0.946
 Quartile 11.000
 Median1.000
 Quartile 31.000
 Maximum1.071
 Mean of quarter 10.991
 Mean of quarter 21.000
 Mean of quarter 31.000
 Mean of quarter 41.011
 Inter Quartile Range0.000
 Number outliers low43.000
 Percentage of outliers low0.135
 Mean of outliers low0.983
 Number of outliers high54.000
 Percentage of outliers high0.169
 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)0.008
 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)0.117
 Compounded annual return (geometric extrapolation)0.118
 Calmar ratio (compounded annual return / max draw down)0.464
 Compounded annual return / average of 25% largest draw downs0.464
 Compounded annual return / Expected Shortfall lognormal4.752
ANALYSIS BASED ON DAILY VALUES, LAST 6 MONTHS (Back)
RATIO STATISTICS
Ratio statistics of excess return rates
Statistics related to Sharpe ratio
 Mean-0.231
 SD0.108
 Sharpe ratio (Glass type estimate) -2.129
 Sharpe ratio (Hedges UMVUE)-2.119
 df171.000
 t-1.505
 p0.573
 Lowerbound of 95% confidence interval for Sharpe Ratio-4.907
 Upperbound of 95% confidence interval for Sharpe Ratio0.655
 Lowerbound of 95% CI (Gibbons, Hedeker & Davis approximation)-4.900
 Upperbound of 95% CI (Gibbons, Hedeker & Davis approximation)0.662
Statistics related to Sortino ratio
 Sortino ratio-2.397
 Upside Potential Ratio1.326
 Upside part of mean0.128
 Downside part of mean-0.359
 Upside SD0.051
 Downside SD0.096
 N nonnegative terms6.000
 N negative terms166.000
Statistics related to linear regression on benchmark
 N of observations172.000
 Mean of predictor0.729
 Mean of criterion-0.231
 SD of predictor0.208
 SD of criterion0.108
 Covariance-0.002
 r-0.067
 b (slope, estimate of beta)-0.035
 a (intercept, estimate of alpha)-0.205
 Mean Square Error0.012
 DF error170.000
 t(b)-0.880
 p(b)0.534
 t(a)-1.314
 p(a)0.550
 Lowerbound of 95% confidence interval for beta-0.114
 Upperbound of 95% confidence interval for beta0.044
 Lowerbound of 95% confidence interval for alpha-0.514
 Upperbound of 95% confidence interval for alpha0.103
 Treynor index (mean / b)6.570
 Jensen alpha (a)-0.205
Ratio statistics of excess log return rates
Statistics related to Sharpe ratio
 Mean-0.237
 SD0.110
 Sharpe ratio (Glass type estimate) -2.159
 Sharpe ratio (Hedges UMVUE)-2.150
 df171.000
 t-1.527
 p0.574
 Lowerbound of 95% confidence interval for Sharpe Ratio-4.938
 Upperbound of 95% confidence interval for Sharpe Ratio0.625
 Lowerbound of 95% CI (Gibbons, Hedeker & Davis approximation)-4.931
 Upperbound of 95% CI (Gibbons, Hedeker & Davis approximation)0.631
Statistics related to Sortino ratio
 Sortino ratio-2.415
 Upside Potential Ratio1.290
 Upside part of mean0.126
 Downside part of mean-0.363
 Upside SD0.050
 Downside SD0.098
 N nonnegative terms6.000
 N negative terms166.000
Statistics related to linear regression on benchmark
 N of observations172.000
 Mean of predictor0.707
 Mean of criterion-0.237
 SD of predictor0.207
 SD of criterion0.110
 Covariance-0.002
 r-0.068
 b (slope, estimate of beta)-0.036
 a (intercept, estimate of alpha)-0.212
 Mean Square Error0.012
 DF error170.000
 t(b)-0.885
 p(b)0.534
 t(a)-1.340
 p(a)0.551
 Lowerbound of 95% confidence interval for beta-0.116
 Upperbound of 95% confidence interval for beta0.044
 Lowerbound of 95% confidence interval for alpha-0.523
 Upperbound of 95% confidence interval for alpha0.100
 Treynor index (mean / b)6.609
 Jensen alpha (a)-0.212
Risk estimates for a one-period unit investment (parametric)
assuming log normal returns and losses (using central moments from Sharpe statistics)
 VaR(95%)0.010
 Expected Shortfall on VaR0.013
assuming Pareto losses only (using partial moments from Sortino statistics)
 VaR(95%)0.004
 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 41.002
 Inter Quartile Range0.000
 Number outliers low10.000
 Percentage of outliers low0.058
 Mean of outliers low0.984
 Number of outliers high6.000
 Percentage of outliers high0.035
 Mean of outliers high1.011
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)-0.013
 VaR(95%) (regression method)0.002
 Expected Shortfall (regression method)0.012
DRAW DOWN STATISTICS
Quartiles of draw downs
 Number of observations1.000
 Minimum0.143
 Quartile 10.143
 Median0.143
 Quartile 30.143
 Maximum0.143
 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)-0.184
 Compounded annual return (geometric extrapolation)-0.175
 Calmar ratio (compounded annual return / max draw down)-1.228
 Compounded annual return / average of 25% largest draw downsNA
 Compounded annual return / Expected Shortfall lognormal-13.700