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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
 Mean0.094
 SD0.319
 Sharpe ratio (Glass type estimate) 0.295
 Sharpe ratio (Hedges UMVUE)0.276
 df12.000
 t0.307
 p0.456
 Lowerbound of 95% confidence interval for Sharpe Ratio-1.598
 Upperbound of 95% confidence interval for Sharpe Ratio2.176
 Lowerbound of 95% CI (Gibbons, Hedeker & Davis approximation)-1.610
 Upperbound of 95% CI (Gibbons, Hedeker & Davis approximation)2.162
Statistics related to Sortino ratio
 Sortino ratio0.662
 Upside Potential Ratio2.389
 Upside part of mean0.340
 Downside part of mean-0.245
 Upside SD0.273
 Downside SD0.142
 N nonnegative terms3.000
 N negative terms10.000
Statistics related to linear regression on benchmark
 N of observations13.000
 Mean of predictor0.361
 Mean of criterion0.094
 SD of predictor0.217
 SD of criterion0.319
 Covariance0.003
 r0.047
 b (slope, estimate of beta)0.069
 a (intercept, estimate of alpha)0.069
 Mean Square Error0.111
 DF error11.000
 t(b)0.155
 p(b)0.440
 t(a)0.194
 p(a)0.425
 Lowerbound of 95% confidence interval for beta-0.907
 Upperbound of 95% confidence interval for beta1.044
 Lowerbound of 95% confidence interval for alpha-0.718
 Upperbound of 95% confidence interval for alpha0.857
 Treynor index (mean / b)1.367
 Jensen alpha (a)0.069
Ratio statistics of excess log return rates
Statistics related to Sharpe ratio
 Mean0.051
 SD0.296
 Sharpe ratio (Glass type estimate) 0.173
 Sharpe ratio (Hedges UMVUE)0.162
 df12.000
 t0.180
 p0.474
 Lowerbound of 95% confidence interval for Sharpe Ratio-1.715
 Upperbound of 95% confidence interval for Sharpe Ratio2.054
 Lowerbound of 95% CI (Gibbons, Hedeker & Davis approximation)-1.722
 Upperbound of 95% CI (Gibbons, Hedeker & Davis approximation)2.046
Statistics related to Sortino ratio
 Sortino ratio0.344
 Upside Potential Ratio2.056
 Upside part of mean0.307
 Downside part of mean-0.255
 Upside SD0.243
 Downside SD0.149
 N nonnegative terms3.000
 N negative terms10.000
Statistics related to linear regression on benchmark
 N of observations13.000
 Mean of predictor0.335
 Mean of criterion0.051
 SD of predictor0.204
 SD of criterion0.296
 Covariance0.004
 r0.061
 b (slope, estimate of beta)0.088
 a (intercept, estimate of alpha)0.022
 Mean Square Error0.095
 DF error11.000
 t(b)0.203
 p(b)0.422
 t(a)0.066
 p(a)0.474
 Lowerbound of 95% confidence interval for beta-0.872
 Upperbound of 95% confidence interval for beta1.049
 Lowerbound of 95% confidence interval for alpha-0.706
 Upperbound of 95% confidence interval for alpha0.749
 Treynor index (mean / b)0.580
 Jensen alpha (a)0.022
Risk estimates for a one-period unit investment (parametric)
assuming log normal returns and losses (using central moments from Sharpe statistics)
 VaR(95%)0.127
 Expected Shortfall on VaR0.158
assuming Pareto losses only (using partial moments from Sortino statistics)
 VaR(95%)0.061
 Expected Shortfall on VaR0.112
ORDER STATISTICS
Quartiles of return rates
 Number of observations13.000
 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 41.126
 Inter Quartile Range0.000
 Number outliers low3.000
 Percentage of outliers low0.231
 Mean of outliers low0.924
 Number of outliers high3.000
 Percentage of outliers high0.231
 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)0.125
 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)0.100
 Compounded annual return (geometric extrapolation)0.100
 Calmar ratio (compounded annual return / max draw down)0.673
 Compounded annual return / average of 25% largest draw downs0.673
 Compounded annual return / Expected Shortfall lognormal0.634
ANALYSIS BASED ON DAILY VALUES, FULL HISTORY (Back)
RATIO STATISTICS
Ratio statistics of excess return rates
Statistics related to Sharpe ratio
 Mean0.069
 SD0.206
 Sharpe ratio (Glass type estimate) 0.333
 Sharpe ratio (Hedges UMVUE)0.333
 df387.000
 t0.354
 p0.362
 Lowerbound of 95% confidence interval for Sharpe Ratio-1.512
 Upperbound of 95% confidence interval for Sharpe Ratio2.179
 Lowerbound of 95% CI (Gibbons, Hedeker & Davis approximation)-1.513
 Upperbound of 95% CI (Gibbons, Hedeker & Davis approximation)2.178
Statistics related to Sortino ratio
 Sortino ratio0.475
 Upside Potential Ratio5.229
 Upside part of mean0.757
 Downside part of mean-0.688
 Upside SD0.146
 Downside SD0.145
 N nonnegative terms54.000
 N negative terms334.000
Statistics related to linear regression on benchmark
 N of observations388.000
 Mean of predictor0.344
 Mean of criterion0.069
 SD of predictor0.180
 SD of criterion0.206
 Covariance-0.000
 r-0.006
 b (slope, estimate of beta)-0.006
 a (intercept, estimate of alpha)0.071
 Mean Square Error0.043
 DF error386.000
 t(b)-0.109
 p(b)0.543
 t(a)0.363
 p(a)0.358
 Lowerbound of 95% confidence interval for beta-0.121
 Upperbound of 95% confidence interval for beta0.108
 Lowerbound of 95% confidence interval for alpha-0.313
 Upperbound of 95% confidence interval for alpha0.455
 Treynor index (mean / b)-10.827
 Jensen alpha (a)0.071
Ratio statistics of excess log return rates
Statistics related to Sharpe ratio
 Mean0.048
 SD0.206
 Sharpe ratio (Glass type estimate) 0.230
 Sharpe ratio (Hedges UMVUE)0.230
 df387.000
 t0.245
 p0.403
 Lowerbound of 95% confidence interval for Sharpe Ratio-1.615
 Upperbound of 95% confidence interval for Sharpe Ratio2.076
 Lowerbound of 95% CI (Gibbons, Hedeker & Davis approximation)-1.616
 Upperbound of 95% CI (Gibbons, Hedeker & Davis approximation)2.075
Statistics related to Sortino ratio
 Sortino ratio0.322
 Upside Potential Ratio5.052
 Upside part of mean0.746
 Downside part of mean-0.699
 Upside SD0.144
 Downside SD0.148
 N nonnegative terms54.000
 N negative terms334.000
Statistics related to linear regression on benchmark
 N of observations388.000
 Mean of predictor0.328
 Mean of criterion0.048
 SD of predictor0.180
 SD of criterion0.206
 Covariance-0.000
 r-0.005
 b (slope, estimate of beta)-0.005
 a (intercept, estimate of alpha)0.049
 Mean Square Error0.043
 DF error386.000
 t(b)-0.089
 p(b)0.536
 t(a)0.252
 p(a)0.401
 Lowerbound of 95% confidence interval for beta-0.120
 Upperbound of 95% confidence interval for beta0.110
 Lowerbound of 95% confidence interval for alpha-0.335
 Upperbound of 95% confidence interval for alpha0.433
 Treynor index (mean / b)-9.106
 Jensen alpha (a)0.049
Risk estimates for a one-period unit investment (parametric)
assuming log normal returns and losses (using central moments from Sharpe statistics)
 VaR(95%)0.018
 Expected Shortfall on VaR0.023
assuming Pareto losses only (using partial moments from Sortino statistics)
 VaR(95%)0.006
 Expected Shortfall on VaR0.014
ORDER STATISTICS
Quartiles of return rates
 Number of observations388.000
 Minimum0.946
 Quartile 11.000
 Median1.000
 Quartile 31.000
 Maximum1.071
 Mean of quarter 10.992
 Mean of quarter 21.000
 Mean of quarter 31.000
 Mean of quarter 41.009
 Inter Quartile Range0.000
 Number outliers low43.000
 Percentage of outliers low0.111
 Mean of outliers low0.983
 Number of outliers high54.000
 Percentage of outliers high0.139
 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)0.006
 Expected Shortfall (regression method)0.016
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)0.096
 Compounded annual return (geometric extrapolation)0.096
 Calmar ratio (compounded annual return / max draw down)0.378
 Compounded annual return / average of 25% largest draw downs0.378
 Compounded annual return / Expected Shortfall lognormal4.254
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 predictor0.606
 Mean of criterion-0.044
 SD of predictor0.204
 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 predictor0.585
 Mean of criterion-0.044
 SD of predictor0.203
 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)-5529045479546133.000
 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)6896265712889180620242739527680.000
 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