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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
 Mean0.086
 SD0.222
 Sharpe ratio (Glass type estimate) 0.389
 Sharpe ratio (Hedges UMVUE)0.388
 df335.000
 t0.384
 p0.350
 Lowerbound of 95% confidence interval for Sharpe Ratio-1.595
 Upperbound of 95% confidence interval for Sharpe Ratio2.372
 Lowerbound of 95% CI (Gibbons, Hedeker & Davis approximation)-1.595
 Upperbound of 95% CI (Gibbons, Hedeker & Davis approximation)2.371
Statistics related to Sortino ratio
 Sortino ratio0.554
 Upside Potential Ratio5.619
 Upside part of mean0.874
 Downside part of mean-0.788
 Upside SD0.157
 Downside SD0.156
 N nonnegative terms54.000
 N negative terms282.000
Statistics related to linear regression on benchmark
 N of observations336.000
 Mean of predictor0.368
 Mean of criterion0.086
 SD of predictor0.179
 SD of criterion0.222
 Covariance-0.000
 r-0.006
 b (slope, estimate of beta)-0.008
 a (intercept, estimate of alpha)0.089
 Mean Square Error0.049
 DF error334.000
 t(b)-0.114
 p(b)0.545
 t(a)0.394
 p(a)0.347
 Lowerbound of 95% confidence interval for beta-0.141
 Upperbound of 95% confidence interval for beta0.126
 Lowerbound of 95% confidence interval for alpha-0.355
 Upperbound of 95% confidence interval for alpha0.533
 Treynor index (mean / b)-11.202
 Jensen alpha (a)0.089
Ratio statistics of excess log return rates
Statistics related to Sharpe ratio
 Mean0.062
 SD0.222
 Sharpe ratio (Glass type estimate) 0.278
 Sharpe ratio (Hedges UMVUE)0.278
 df335.000
 t0.275
 p0.392
 Lowerbound of 95% confidence interval for Sharpe Ratio-1.705
 Upperbound of 95% confidence interval for Sharpe Ratio2.261
 Lowerbound of 95% CI (Gibbons, Hedeker & Davis approximation)-1.706
 Upperbound of 95% CI (Gibbons, Hedeker & Davis approximation)2.261
Statistics related to Sortino ratio
 Sortino ratio0.389
 Upside Potential Ratio5.429
 Upside part of mean0.862
 Downside part of mean-0.800
 Upside SD0.154
 Downside SD0.159
 N nonnegative terms54.000
 N negative terms282.000
Statistics related to linear regression on benchmark
 N of observations336.000
 Mean of predictor0.352
 Mean of criterion0.062
 SD of predictor0.179
 SD of criterion0.222
 Covariance-0.000
 r-0.005
 b (slope, estimate of beta)-0.006
 a (intercept, estimate of alpha)0.064
 Mean Square Error0.049
 DF error334.000
 t(b)-0.093
 p(b)0.537
 t(a)0.283
 p(a)0.389
 Lowerbound of 95% confidence interval for beta-0.140
 Upperbound of 95% confidence interval for beta0.127
 Lowerbound of 95% confidence interval for alpha-0.380
 Upperbound of 95% confidence interval for alpha0.508
 Treynor index (mean / b)-9.753
 Jensen alpha (a)0.064
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 VaR0.016
ORDER STATISTICS
Quartiles of return rates
 Number of observations336.000
 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 41.010
 Inter Quartile Range0.000
 Number outliers low43.000
 Percentage of outliers low0.128
 Mean of outliers low0.983
 Number of outliers high54.000
 Percentage of outliers high0.161
 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)0.007
 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)0.111
 Compounded annual return (geometric extrapolation)0.111
 Calmar ratio (compounded annual return / max draw down)0.439
 Compounded annual return / average of 25% largest draw downs0.439
 Compounded annual return / Expected Shortfall lognormal4.613
ANALYSIS BASED ON DAILY VALUES, LAST 6 MONTHS (Back)
RATIO STATISTICS
Ratio statistics of excess return rates
Statistics related to Sharpe ratio
 Mean-0.016
 SD0.078
 Sharpe ratio (Glass type estimate) -0.210
 Sharpe ratio (Hedges UMVUE)-0.209
 df171.000
 t-0.149
 p0.507
 Lowerbound of 95% confidence interval for Sharpe Ratio-2.982
 Upperbound of 95% confidence interval for Sharpe Ratio2.562
 Lowerbound of 95% CI (Gibbons, Hedeker & Davis approximation)-2.981
 Upperbound of 95% CI (Gibbons, Hedeker & Davis approximation)2.562
Statistics related to Sortino ratio
 Sortino ratio-0.277
 Upside Potential Ratio1.919
 Upside part of mean0.114
 Downside part of mean-0.130
 Upside SD0.050
 Downside SD0.059
 N nonnegative terms3.000
 N negative terms169.000
Statistics related to linear regression on benchmark
 N of observations172.000
 Mean of predictor0.703
 Mean of criterion-0.016
 SD of predictor0.208
 SD of criterion0.078
 Covariance-0.000
 r-0.021
 b (slope, estimate of beta)-0.008
 a (intercept, estimate of alpha)-0.011
 Mean Square Error0.006
 DF error170.000
 t(b)-0.279
 p(b)0.511
 t(a)-0.096
 p(a)0.504
 Lowerbound of 95% confidence interval for beta-0.065
 Upperbound of 95% confidence interval for beta0.049
 Lowerbound of 95% confidence interval for alpha-0.232
 Upperbound of 95% confidence interval for alpha0.211
 Treynor index (mean / b)2.043
 Jensen alpha (a)-0.011
Ratio statistics of excess log return rates
Statistics related to Sharpe ratio
 Mean-0.019
 SD0.078
 Sharpe ratio (Glass type estimate) -0.248
 Sharpe ratio (Hedges UMVUE)-0.247
 df171.000
 t-0.175
 p0.509
 Lowerbound of 95% confidence interval for Sharpe Ratio-3.019
 Upperbound of 95% confidence interval for Sharpe Ratio2.525
 Lowerbound of 95% CI (Gibbons, Hedeker & Davis approximation)-3.018
 Upperbound of 95% CI (Gibbons, Hedeker & Davis approximation)2.525
Statistics related to Sortino ratio
 Sortino ratio-0.321
 Upside Potential Ratio1.859
 Upside part of mean0.112
 Downside part of mean-0.132
 Upside SD0.050
 Downside SD0.060
 N nonnegative terms3.000
 N negative terms169.000
Statistics related to linear regression on benchmark
 N of observations172.000
 Mean of predictor0.681
 Mean of criterion-0.019
 SD of predictor0.207
 SD of criterion0.078
 Covariance-0.000
 r-0.021
 b (slope, estimate of beta)-0.008
 a (intercept, estimate of alpha)-0.014
 Mean Square Error0.006
 DF error170.000
 t(b)-0.278
 p(b)0.511
 t(a)-0.123
 p(a)0.505
 Lowerbound of 95% confidence interval for beta-0.065
 Upperbound of 95% confidence interval for beta0.049
 Lowerbound of 95% confidence interval for alpha-0.237
 Upperbound of 95% confidence interval for alpha0.209
 Treynor index (mean / b)2.402
 Jensen alpha (a)-0.014
Risk estimates for a one-period unit investment (parametric)
assuming log normal returns and losses (using central moments from Sharpe statistics)
 VaR(95%)0.007
 Expected Shortfall on VaR0.009
assuming Pareto losses only (using partial moments from Sortino statistics)
 VaR(95%)0.001
 Expected Shortfall on VaR0.003
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 10.999
 Mean of quarter 21.000
 Mean of quarter 31.000
 Mean of quarter 41.001
 Inter Quartile Range0.000
 Number outliers low2.000
 Percentage of outliers low0.012
 Mean of outliers low0.978
 Number of outliers high3.000
 Percentage of outliers high0.017
 Mean of outliers high1.019
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)3.545
 VaR(95%) (regression method)-0.000
 Expected Shortfall (regression method)NA
DRAW DOWN STATISTICS
Quartiles of draw downs
 Number of observations2.000
 Minimum0.002
 Quartile 10.012
 Median0.022
 Quartile 30.032
 Maximum0.042
 Mean of quarter 10.002
 Mean of quarter 2NA
 Mean of quarter 3NA
 Mean of quarter 40.042
 Inter Quartile Range0.020
 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)0.025
 Compounded annual return (geometric extrapolation)0.025
 Calmar ratio (compounded annual return / max draw down)0.598
 Compounded annual return / average of 25% largest draw downs0.598
 Compounded annual return / Expected Shortfall lognormal2.848