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
 Mean0.076
 SD0.296
 Sharpe ratio (Glass type estimate) 0.256
 Sharpe ratio (Hedges UMVUE)0.242
 df14.000
 t0.286
 p0.462
 Lowerbound of 95% confidence interval for Sharpe Ratio-1.504
 Upperbound of 95% confidence interval for Sharpe Ratio2.007
 Lowerbound of 95% CI (Gibbons, Hedeker & Davis approximation)-1.513
 Upperbound of 95% CI (Gibbons, Hedeker & Davis approximation)1.997
Statistics related to Sortino ratio
 Sortino ratio0.572
 Upside Potential Ratio2.223
 Upside part of mean0.294
 Downside part of mean-0.219
 Upside SD0.254
 Downside SD0.132
 N nonnegative terms3.000
 N negative terms12.000
Statistics related to linear regression on benchmark
 N of observations15.000
 Mean of predictor0.320
 Mean of criterion0.076
 SD of predictor0.203
 SD of criterion0.296
 Covariance0.003
 r0.053
 b (slope, estimate of beta)0.078
 a (intercept, estimate of alpha)0.051
 Mean Square Error0.094
 DF error13.000
 t(b)0.193
 p(b)0.466
 t(a)0.167
 p(a)0.470
 Lowerbound of 95% confidence interval for beta-0.793
 Upperbound of 95% confidence interval for beta0.949
 Lowerbound of 95% confidence interval for alpha-0.604
 Upperbound of 95% confidence interval for alpha0.706
 Treynor index (mean / b)0.973
 Jensen alpha (a)0.051
Ratio statistics of excess log return rates
Statistics related to Sharpe ratio
 Mean0.039
 SD0.274
 Sharpe ratio (Glass type estimate) 0.141
 Sharpe ratio (Hedges UMVUE)0.133
 df14.000
 t0.157
 p0.479
 Lowerbound of 95% confidence interval for Sharpe Ratio-1.616
 Upperbound of 95% confidence interval for Sharpe Ratio1.892
 Lowerbound of 95% CI (Gibbons, Hedeker & Davis approximation)-1.621
 Upperbound of 95% CI (Gibbons, Hedeker & Davis approximation)1.887
Statistics related to Sortino ratio
 Sortino ratio0.278
 Upside Potential Ratio1.913
 Upside part of mean0.266
 Downside part of mean-0.227
 Upside SD0.226
 Downside SD0.139
 N nonnegative terms3.000
 N negative terms12.000
Statistics related to linear regression on benchmark
 N of observations15.000
 Mean of predictor0.298
 Mean of criterion0.039
 SD of predictor0.191
 SD of criterion0.274
 Covariance0.003
 r0.065
 b (slope, estimate of beta)0.094
 a (intercept, estimate of alpha)0.011
 Mean Square Error0.081
 DF error13.000
 t(b)0.237
 p(b)0.458
 t(a)0.038
 p(a)0.493
 Lowerbound of 95% confidence interval for beta-0.764
 Upperbound of 95% confidence interval for beta0.952
 Lowerbound of 95% confidence interval for alpha-0.595
 Upperbound of 95% confidence interval for alpha0.616
 Treynor index (mean / b)0.411
 Jensen alpha (a)0.011
Risk estimates for a one-period unit investment (parametric)
assuming log normal returns and losses (using central moments from Sharpe statistics)
 VaR(95%)0.119
 Expected Shortfall on VaR0.148
assuming Pareto losses only (using partial moments from Sortino statistics)
 VaR(95%)0.055
 Expected Shortfall on VaR0.104
ORDER STATISTICS
Quartiles of return rates
 Number of observations15.000
 Minimum0.888
 Quartile 11.000
 Median1.000
 Quartile 31.000
 Maximum1.276
 Mean of quarter 10.943
 Mean of quarter 21.000
 Mean of quarter 31.000
 Mean of quarter 41.095
 Inter Quartile Range0.000
 Number outliers low3.000
 Percentage of outliers low0.200
 Mean of outliers low0.924
 Number of outliers high3.000
 Percentage of outliers high0.200
 Mean of outliers high1.126
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)-1.090
 VaR(95%) (regression method)0.122
 Expected Shortfall (regression method)0.135
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)0.087
 Compounded annual return (geometric extrapolation)0.086
 Calmar ratio (compounded annual return / max draw down)0.580
 Compounded annual return / average of 25% largest draw downs0.580
 Compounded annual return / Expected Shortfall lognormal0.583
ANALYSIS BASED ON DAILY VALUES, FULL HISTORY (Back)
RATIO STATISTICS
Ratio statistics of excess return rates
Statistics related to Sharpe ratio
 Mean0.056
 SD0.194
 Sharpe ratio (Glass type estimate) 0.288
 Sharpe ratio (Hedges UMVUE)0.287
 df437.000
 t0.325
 p0.373
 Lowerbound of 95% confidence interval for Sharpe Ratio-1.449
 Upperbound of 95% confidence interval for Sharpe Ratio2.025
 Lowerbound of 95% CI (Gibbons, Hedeker & Davis approximation)-1.450
 Upperbound of 95% CI (Gibbons, Hedeker & Davis approximation)2.024
Statistics related to Sortino ratio
 Sortino ratio0.410
 Upside Potential Ratio4.921
 Upside part of mean0.670
 Downside part of mean-0.614
 Upside SD0.138
 Downside SD0.136
 N nonnegative terms54.000
 N negative terms384.000
Statistics related to linear regression on benchmark
 N of observations438.000
 Mean of predictor0.306
 Mean of criterion0.056
 SD of predictor0.181
 SD of criterion0.194
 Covariance-0.000
 r-0.005
 b (slope, estimate of beta)-0.005
 a (intercept, estimate of alpha)0.057
 Mean Square Error0.038
 DF error436.000
 t(b)-0.102
 p(b)0.540
 t(a)0.332
 p(a)0.370
 Lowerbound of 95% confidence interval for beta-0.106
 Upperbound of 95% confidence interval for beta0.096
 Lowerbound of 95% confidence interval for alpha-0.282
 Upperbound of 95% confidence interval for alpha0.397
 Treynor index (mean / b)-10.689
 Jensen alpha (a)0.057
Ratio statistics of excess log return rates
Statistics related to Sharpe ratio
 Mean0.037
 SD0.194
 Sharpe ratio (Glass type estimate) 0.191
 Sharpe ratio (Hedges UMVUE)0.191
 df437.000
 t0.215
 p0.415
 Lowerbound of 95% confidence interval for Sharpe Ratio-1.546
 Upperbound of 95% confidence interval for Sharpe Ratio1.928
 Lowerbound of 95% CI (Gibbons, Hedeker & Davis approximation)-1.546
 Upperbound of 95% CI (Gibbons, Hedeker & Davis approximation)1.928
Statistics related to Sortino ratio
 Sortino ratio0.267
 Upside Potential Ratio4.755
 Upside part of mean0.661
 Downside part of mean-0.624
 Upside SD0.135
 Downside SD0.139
 N nonnegative terms54.000
 N negative terms384.000
Statistics related to linear regression on benchmark
 N of observations438.000
 Mean of predictor0.289
 Mean of criterion0.037
 SD of predictor0.181
 SD of criterion0.194
 Covariance-0.000
 r-0.004
 b (slope, estimate of beta)-0.004
 a (intercept, estimate of alpha)0.038
 Mean Square Error0.038
 DF error436.000
 t(b)-0.083
 p(b)0.533
 t(a)0.222
 p(a)0.412
 Lowerbound of 95% confidence interval for beta-0.105
 Upperbound of 95% confidence interval for beta0.097
 Lowerbound of 95% confidence interval for alpha-0.301
 Upperbound of 95% confidence interval for alpha0.378
 Treynor index (mean / b)-8.637
 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%)0.017
 Expected Shortfall on VaR0.021
assuming Pareto losses only (using partial moments from Sortino statistics)
 VaR(95%)0.006
 Expected Shortfall on VaR0.013
ORDER STATISTICS
Quartiles of return rates
 Number of observations438.000
 Minimum0.946
 Quartile 11.000
 Median1.000
 Quartile 31.000
 Maximum1.071
 Mean of quarter 10.993
 Mean of quarter 21.000
 Mean of quarter 31.000
 Mean of quarter 41.008
 Inter Quartile Range0.000
 Number outliers low43.000
 Percentage of outliers low0.098
 Mean of outliers low0.983
 Number of outliers high54.000
 Percentage of outliers high0.123
 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)0.005
 Expected Shortfall (regression method)0.015
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)0.085
 Compounded annual return (geometric extrapolation)0.084
 Calmar ratio (compounded annual return / max draw down)0.333
 Compounded annual return / average of 25% largest draw downs0.333
 Compounded annual return / Expected Shortfall lognormal3.976
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 predictor0.239
 Mean of criterion-0.044
 SD of predictor0.168
 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 predictor0.225
 Mean of criterion-0.044
 SD of predictor0.168
 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)-5580977590787060.000
 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)137403835233201733460603223146496.000
 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