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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
 Mean0.084
 SD0.219
 Sharpe ratio (Glass type estimate) 0.381
 Sharpe ratio (Hedges UMVUE)0.380
 df342.000
 t0.380
 p0.352
 Lowerbound of 95% confidence interval for Sharpe Ratio-1.582
 Upperbound of 95% confidence interval for Sharpe Ratio2.344
 Lowerbound of 95% CI (Gibbons, Hedeker & Davis approximation)-1.583
 Upperbound of 95% CI (Gibbons, Hedeker & Davis approximation)2.343
Statistics related to Sortino ratio
 Sortino ratio0.543
 Upside Potential Ratio5.561
 Upside part of mean0.856
 Downside part of mean-0.772
 Upside SD0.156
 Downside SD0.154
 N nonnegative terms54.000
 N negative terms289.000
Statistics related to linear regression on benchmark
 N of observations343.000
 Mean of predictor0.351
 Mean of criterion0.084
 SD of predictor0.178
 SD of criterion0.219
 Covariance-0.000
 r-0.006
 b (slope, estimate of beta)-0.007
 a (intercept, estimate of alpha)0.086
 Mean Square Error0.048
 DF error341.000
 t(b)-0.111
 p(b)0.544
 t(a)0.389
 p(a)0.349
 Lowerbound of 95% confidence interval for beta-0.139
 Upperbound of 95% confidence interval for beta0.124
 Lowerbound of 95% confidence interval for alpha-0.349
 Upperbound of 95% confidence interval for alpha0.521
 Treynor index (mean / b)-11.221
 Jensen alpha (a)0.086
Ratio statistics of excess log return rates
Statistics related to Sharpe ratio
 Mean0.060
 SD0.219
 Sharpe ratio (Glass type estimate) 0.271
 Sharpe ratio (Hedges UMVUE)0.271
 df342.000
 t0.271
 p0.393
 Lowerbound of 95% confidence interval for Sharpe Ratio-1.692
 Upperbound of 95% confidence interval for Sharpe Ratio2.234
 Lowerbound of 95% CI (Gibbons, Hedeker & Davis approximation)-1.692
 Upperbound of 95% CI (Gibbons, Hedeker & Davis approximation)2.234
Statistics related to Sortino ratio
 Sortino ratio0.379
 Upside Potential Ratio5.374
 Upside part of mean0.844
 Downside part of mean-0.784
 Upside SD0.153
 Downside SD0.157
 N nonnegative terms54.000
 N negative terms289.000
Statistics related to linear regression on benchmark
 N of observations343.000
 Mean of predictor0.335
 Mean of criterion0.060
 SD of predictor0.177
 SD of criterion0.219
 Covariance-0.000
 r-0.005
 b (slope, estimate of beta)-0.006
 a (intercept, estimate of alpha)0.062
 Mean Square Error0.048
 DF error341.000
 t(b)-0.091
 p(b)0.536
 t(a)0.278
 p(a)0.390
 Lowerbound of 95% confidence interval for beta-0.138
 Upperbound of 95% confidence interval for beta0.126
 Lowerbound of 95% confidence interval for alpha-0.373
 Upperbound of 95% confidence interval for alpha0.497
 Treynor index (mean / b)-9.722
 Jensen alpha (a)0.062
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 observations343.000
 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 low0.125
 Mean of outliers low0.983
 Number of outliers high54.000
 Percentage of outliers high0.157
 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)0.109
 Compounded annual return (geometric extrapolation)0.109
 Calmar ratio (compounded annual return / max draw down)0.430
 Compounded annual return / average of 25% largest draw downs0.430
 Compounded annual return / Expected Shortfall lognormal4.560
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 predictor0.672
 Mean of criterion-0.044
 SD of predictor0.209
 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 predictor0.650
 Mean of criterion-0.044
 SD of predictor0.208
 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)-5517563296307240.000
 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)5809001290491913676904311291904.000
 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