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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
 Mean0.106
 SD0.333
 Sharpe ratio (Glass type estimate) 0.317
 Sharpe ratio (Hedges UMVUE)0.295
 df11.000
 t0.317
 p0.379
 Lowerbound of 95% confidence interval for Sharpe Ratio-1.654
 Upperbound of 95% confidence interval for Sharpe Ratio2.274
 Lowerbound of 95% CI (Gibbons, Hedeker & Davis approximation)-1.669
 Upperbound of 95% CI (Gibbons, Hedeker & Davis approximation)2.259
Statistics related to Sortino ratio
 Sortino ratio0.714
 Upside Potential Ratio2.488
 Upside part of mean0.368
 Downside part of mean-0.262
 Upside SD0.284
 Downside SD0.148
 N nonnegative terms3.000
 N negative terms9.000
Statistics related to linear regression on benchmark
 N of observations12.000
 Mean of predictor0.370
 Mean of criterion0.106
 SD of predictor0.226
 SD of criterion0.333
 Covariance0.003
 r0.045
 b (slope, estimate of beta)0.067
 a (intercept, estimate of alpha)0.081
 Mean Square Error0.122
 DF error10.000
 t(b)0.143
 p(b)0.444
 t(a)0.208
 p(a)0.420
 Lowerbound of 95% confidence interval for beta-0.969
 Upperbound of 95% confidence interval for beta1.103
 Lowerbound of 95% confidence interval for alpha-0.786
 Upperbound of 95% confidence interval for alpha0.948
 Treynor index (mean / b)1.585
 Jensen alpha (a)0.081
Ratio statistics of excess log return rates
Statistics related to Sharpe ratio
 Mean0.059
 SD0.309
 Sharpe ratio (Glass type estimate) 0.192
 Sharpe ratio (Hedges UMVUE)0.178
 df11.000
 t0.192
 p0.426
 Lowerbound of 95% confidence interval for Sharpe Ratio-1.774
 Upperbound of 95% confidence interval for Sharpe Ratio2.149
 Lowerbound of 95% CI (Gibbons, Hedeker & Davis approximation)-1.783
 Upperbound of 95% CI (Gibbons, Hedeker & Davis approximation)2.140
Statistics related to Sortino ratio
 Sortino ratio0.382
 Upside Potential Ratio2.141
 Upside part of mean0.332
 Downside part of mean-0.273
 Upside SD0.253
 Downside SD0.155
 N nonnegative terms3.000
 N negative terms9.000
Statistics related to linear regression on benchmark
 N of observations12.000
 Mean of predictor0.342
 Mean of criterion0.059
 SD of predictor0.213
 SD of criterion0.309
 Covariance0.004
 r0.060
 b (slope, estimate of beta)0.087
 a (intercept, estimate of alpha)0.029
 Mean Square Error0.105
 DF error10.000
 t(b)0.190
 p(b)0.426
 t(a)0.082
 p(a)0.468
 Lowerbound of 95% confidence interval for beta-0.933
 Upperbound of 95% confidence interval for beta1.107
 Lowerbound of 95% confidence interval for alpha-0.771
 Upperbound of 95% confidence interval for alpha0.830
 Treynor index (mean / b)0.680
 Jensen alpha (a)0.029
Risk estimates for a one-period unit investment (parametric)
assuming log normal returns and losses (using central moments from Sharpe statistics)
 VaR(95%)0.132
 Expected Shortfall on VaR0.164
assuming Pareto losses only (using partial moments from Sortino statistics)
 VaR(95%)0.064
 Expected Shortfall on VaR0.116
ORDER STATISTICS
Quartiles of return rates
 Number of observations12.000
 Minimum0.888
 Quartile 10.990
 Median1.000
 Quartile 31.005
 Maximum1.276
 Mean of quarter 10.924
 Mean of quarter 21.000
 Mean of quarter 31.000
 Mean of quarter 41.126
 Inter Quartile Range0.015
 Number outliers low3.000
 Percentage of outliers low0.250
 Mean of outliers low0.924
 Number of outliers high2.000
 Percentage of outliers high0.167
 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)0.124
 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)0.109
 Compounded annual return (geometric extrapolation)0.109
 Calmar ratio (compounded annual return / max draw down)0.732
 Compounded annual return / average of 25% largest draw downs0.732
 Compounded annual return / Expected Shortfall lognormal0.665
ANALYSIS BASED ON DAILY VALUES, FULL HISTORY (Back)
RATIO STATISTICS
Ratio statistics of excess return rates
Statistics related to Sharpe ratio
 Mean0.077
 SD0.214
 Sharpe ratio (Glass type estimate) 0.361
 Sharpe ratio (Hedges UMVUE)0.360
 df360.000
 t0.370
 p0.356
 Lowerbound of 95% confidence interval for Sharpe Ratio-1.553
 Upperbound of 95% confidence interval for Sharpe Ratio2.274
 Lowerbound of 95% CI (Gibbons, Hedeker & Davis approximation)-1.553
 Upperbound of 95% CI (Gibbons, Hedeker & Davis approximation)2.274
Statistics related to Sortino ratio
 Sortino ratio0.514
 Upside Potential Ratio5.421
 Upside part of mean0.813
 Downside part of mean-0.736
 Upside SD0.152
 Downside SD0.150
 N nonnegative terms54.000
 N negative terms307.000
Statistics related to linear regression on benchmark
 N of observations361.000
 Mean of predictor0.322
 Mean of criterion0.077
 SD of predictor0.180
 SD of criterion0.214
 Covariance-0.000
 r-0.006
 b (slope, estimate of beta)-0.007
 a (intercept, estimate of alpha)0.079
 Mean Square Error0.046
 DF error359.000
 t(b)-0.105
 p(b)0.542
 t(a)0.378
 p(a)0.353
 Lowerbound of 95% confidence interval for beta-0.130
 Upperbound of 95% confidence interval for beta0.116
 Lowerbound of 95% confidence interval for alpha-0.333
 Upperbound of 95% confidence interval for alpha0.492
 Treynor index (mean / b)-11.771
 Jensen alpha (a)0.079
Ratio statistics of excess log return rates
Statistics related to Sharpe ratio
 Mean0.054
 SD0.214
 Sharpe ratio (Glass type estimate) 0.254
 Sharpe ratio (Hedges UMVUE)0.254
 df360.000
 t0.260
 p0.397
 Lowerbound of 95% confidence interval for Sharpe Ratio-1.659
 Upperbound of 95% confidence interval for Sharpe Ratio2.167
 Lowerbound of 95% CI (Gibbons, Hedeker & Davis approximation)-1.660
 Upperbound of 95% CI (Gibbons, Hedeker & Davis approximation)2.167
Statistics related to Sortino ratio
 Sortino ratio0.355
 Upside Potential Ratio5.238
 Upside part of mean0.802
 Downside part of mean-0.748
 Upside SD0.149
 Downside SD0.153
 N nonnegative terms54.000
 N negative terms307.000
Statistics related to linear regression on benchmark
 N of observations361.000
 Mean of predictor0.306
 Mean of criterion0.054
 SD of predictor0.180
 SD of criterion0.214
 Covariance-0.000
 r-0.005
 b (slope, estimate of beta)-0.005
 a (intercept, estimate of alpha)0.056
 Mean Square Error0.046
 DF error359.000
 t(b)-0.086
 p(b)0.534
 t(a)0.267
 p(a)0.395
 Lowerbound of 95% confidence interval for beta-0.129
 Upperbound of 95% confidence interval for beta0.118
 Lowerbound of 95% confidence interval for alpha-0.357
 Upperbound of 95% confidence interval for alpha0.469
 Treynor index (mean / b)-10.095
 Jensen alpha (a)0.056
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 VaR0.023
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 observations361.000
 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 41.010
 Inter Quartile Range0.000
 Number outliers low43.000
 Percentage of outliers low0.119
 Mean of outliers low0.983
 Number of outliers high54.000
 Percentage of outliers high0.150
 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)0.016
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)0.104
 Compounded annual return (geometric extrapolation)0.103
 Calmar ratio (compounded annual return / max draw down)0.407
 Compounded annual return / average of 25% largest draw downs0.407
 Compounded annual return / Expected Shortfall lognormal4.430
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 predictor0.218
 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 predictor0.582
 Mean of criterion-0.044
 SD of predictor0.218
 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)-5538060973364238.000
 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)7665122623386428219886051262464.000
 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