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Advanced Statistics: YM Superior

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
 Mean0.764
 SD2.139
 Sharpe ratio (Glass type estimate) 0.357
 Sharpe ratio (Hedges UMVUE)0.353
 df71.000
 t0.875
 p0.192
 Lowerbound of 95% confidence interval for Sharpe Ratio-0.446
 Upperbound of 95% confidence interval for Sharpe Ratio1.158
 Lowerbound of 95% CI (Gibbons, Hedeker & Davis approximation)-0.449
 Upperbound of 95% CI (Gibbons, Hedeker & Davis approximation)1.156
Statistics related to Sortino ratio
 Sortino ratio2.089
 Upside Potential Ratio2.934
 Upside part of mean1.073
 Downside part of mean-0.309
 Upside SD2.104
 Downside SD0.366
 N nonnegative terms6.000
 N negative terms66.000
Statistics related to linear regression on benchmark
 N of observations72.000
 Mean of predictor0.007
 Mean of criterion0.764
 SD of predictor0.206
 SD of criterion2.139
 Covariance-0.068
 r-0.154
 b (slope, estimate of beta)-1.597
 a (intercept, estimate of alpha)0.776
 Mean Square Error4.530
 DF error70.000
 t(b)-1.303
 p(b)0.902
 t(a)0.893
 p(a)0.187
 Lowerbound of 95% confidence interval for beta-4.041
 Upperbound of 95% confidence interval for beta0.847
 Lowerbound of 95% confidence interval for alpha-0.957
 Upperbound of 95% confidence interval for alpha2.509
 Treynor index (mean / b)-0.479
 Jensen alpha (a)0.776
Ratio statistics of excess log return rates
Statistics related to Sharpe ratio
 Mean0.072
 SD0.950
 Sharpe ratio (Glass type estimate) 0.075
 Sharpe ratio (Hedges UMVUE)0.075
 df71.000
 t0.185
 p0.427
 Lowerbound of 95% confidence interval for Sharpe Ratio-0.725
 Upperbound of 95% confidence interval for Sharpe Ratio0.875
 Lowerbound of 95% CI (Gibbons, Hedeker & Davis approximation)-0.726
 Upperbound of 95% CI (Gibbons, Hedeker & Davis approximation)0.875
Statistics related to Sortino ratio
 Sortino ratio0.132
 Upside Potential Ratio0.909
 Upside part of mean0.492
 Downside part of mean-0.420
 Upside SD0.774
 Downside SD0.541
 N nonnegative terms6.000
 N negative terms66.000
Statistics related to linear regression on benchmark
 N of observations72.000
 Mean of predictor-0.014
 Mean of criterion0.072
 SD of predictor0.212
 SD of criterion0.950
 Covariance-0.030
 r-0.149
 b (slope, estimate of beta)-0.669
 a (intercept, estimate of alpha)0.062
 Mean Square Error0.896
 DF error70.000
 t(b)-1.263
 p(b)0.895
 t(a)0.161
 p(a)0.436
 Lowerbound of 95% confidence interval for beta-1.726
 Upperbound of 95% confidence interval for beta0.387
 Lowerbound of 95% confidence interval for alpha-0.709
 Upperbound of 95% confidence interval for alpha0.833
 Treynor index (mean / b)-0.107
 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%)0.359
 Expected Shortfall on VaR0.426
assuming Pareto losses only (using partial moments from Sortino statistics)
 VaR(95%)0.085
 Expected Shortfall on VaR0.185
ORDER STATISTICS
Quartiles of return rates
 Number of observations72.000
 Minimum0.383
 Quartile 11.000
 Median1.000
 Quartile 31.000
 Maximum6.112
 Mean of quarter 10.910
 Mean of quarter 21.000
 Mean of quarter 31.000
 Mean of quarter 41.359
 Inter Quartile Range0.000
 Number outliers low5.000
 Percentage of outliers low0.069
 Mean of outliers low0.678
 Number of outliers high6.000
 Percentage of outliers high0.083
 Mean of outliers high2.077
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)-0.818
 VaR(95%) (regression method)0.194
 Expected Shortfall (regression method)0.367
DRAW DOWN STATISTICS
Quartiles of draw downs
 Number of observations3.000
 Minimum0.035
 Quartile 10.196
 Median0.358
 Quartile 30.596
 Maximum0.834
 Mean of quarter 10.035
 Mean of quarter 20.358
 Mean of quarter 3NA
 Mean of quarter 40.834
 Inter Quartile Range0.400
 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)0.167
 Compounded annual return (geometric extrapolation)0.123
 Calmar ratio (compounded annual return / max draw down)0.147
 Compounded annual return / average of 25% largest draw downs0.147
 Compounded annual return / Expected Shortfall lognormal0.288
ANALYSIS BASED ON DAILY VALUES, FULL HISTORY (Back)
RATIO STATISTICS
Ratio statistics of excess return rates
Statistics related to Sharpe ratio
 Mean0.456
 SD1.028
 Sharpe ratio (Glass type estimate) 0.444
 Sharpe ratio (Hedges UMVUE)0.443
 df2083.000
 t1.092
 p0.137
 Lowerbound of 95% confidence interval for Sharpe Ratio-0.353
 Upperbound of 95% confidence interval for Sharpe Ratio1.240
 Lowerbound of 95% CI (Gibbons, Hedeker & Davis approximation)-0.353
 Upperbound of 95% CI (Gibbons, Hedeker & Davis approximation)1.240
Statistics related to Sortino ratio
 Sortino ratio0.978
 Upside Potential Ratio3.571
 Upside part of mean1.664
 Downside part of mean-1.208
 Upside SD0.916
 Downside SD0.466
 N nonnegative terms102.000
 N negative terms1982.000
Statistics related to linear regression on benchmark
 N of observations2084.000
 Mean of predictor0.029
 Mean of criterion0.456
 SD of predictor0.250
 SD of criterion1.028
 Covariance-0.012
 r-0.047
 b (slope, estimate of beta)-0.192
 a (intercept, estimate of alpha)0.462
 Mean Square Error1.055
 DF error2082.000
 t(b)-2.126
 p(b)0.983
 t(a)1.106
 p(a)0.134
 Lowerbound of 95% confidence interval for beta-0.368
 Upperbound of 95% confidence interval for beta-0.015
 Lowerbound of 95% confidence interval for alpha-0.357
 Upperbound of 95% confidence interval for alpha1.280
 Treynor index (mean / b)-2.379
 Jensen alpha (a)0.462
Ratio statistics of excess log return rates
Statistics related to Sharpe ratio
 Mean0.071
 SD0.839
 Sharpe ratio (Glass type estimate) 0.084
 Sharpe ratio (Hedges UMVUE)0.084
 df2083.000
 t0.207
 p0.418
 Lowerbound of 95% confidence interval for Sharpe Ratio-0.712
 Upperbound of 95% confidence interval for Sharpe Ratio0.880
 Lowerbound of 95% CI (Gibbons, Hedeker & Davis approximation)-0.712
 Upperbound of 95% CI (Gibbons, Hedeker & Davis approximation)0.880
Statistics related to Sortino ratio
 Sortino ratio0.126
 Upside Potential Ratio2.535
 Upside part of mean1.417
 Downside part of mean-1.346
 Upside SD0.626
 Downside SD0.559
 N nonnegative terms102.000
 N negative terms1982.000
Statistics related to linear regression on benchmark
 N of observations2084.000
 Mean of predictor-0.002
 Mean of criterion0.071
 SD of predictor0.250
 SD of criterion0.839
 Covariance-0.011
 r-0.054
 b (slope, estimate of beta)-0.182
 a (intercept, estimate of alpha)0.070
 Mean Square Error0.703
 DF error2082.000
 t(b)-2.474
 p(b)0.993
 t(a)0.206
 p(a)0.418
 Lowerbound of 95% confidence interval for beta-0.326
 Upperbound of 95% confidence interval for beta-0.038
 Lowerbound of 95% confidence interval for alpha-0.598
 Upperbound of 95% confidence interval for alpha0.738
 Treynor index (mean / b)-0.388
 Jensen alpha (a)0.070
Risk estimates for a one-period unit investment (parametric)
assuming log normal returns and losses (using central moments from Sharpe statistics)
 VaR(95%)0.072
 Expected Shortfall on VaR0.089
assuming Pareto losses only (using partial moments from Sortino statistics)
 VaR(95%)0.012
 Expected Shortfall on VaR0.027
ORDER STATISTICS
Quartiles of return rates
 Number of observations2084.000
 Minimum0.521
 Quartile 11.000
 Median1.000
 Quartile 31.000
 Maximum2.832
 Mean of quarter 10.986
 Mean of quarter 21.000
 Mean of quarter 31.000
 Mean of quarter 41.019
 Inter Quartile Range0.000
 Number outliers low96.000
 Percentage of outliers low0.046
 Mean of outliers low0.926
 Number of outliers high102.000
 Percentage of outliers high0.049
 Mean of outliers high1.099
Risk estimates for a one-period unit investment (based on Extreme Value Theory)
 Extreme Value Index (moments method)-0.652
 VaR(95%) (moments method)0.000
 Expected Shortfall (moments method)0.003
 Extreme Value Index (regression method)0.264
 VaR(95%) (regression method)-0.002
 Expected Shortfall (regression method)NA
DRAW DOWN STATISTICS
Quartiles of draw downs
 Number of observations9.000
 Minimum0.020
 Quartile 10.036
 Median0.102
 Quartile 30.147
 Maximum0.918
 Mean of quarter 10.026
 Mean of quarter 20.072
 Mean of quarter 30.136
 Mean of quarter 40.660
 Inter Quartile Range0.111
 Number outliers low0.000
 Percentage of outliers low0.000
 Mean of outliers lowNA
 Number of outliers high2.000
 Percentage of outliers high0.222
 Mean of outliers high0.660
Risk estimates based on draw downs (based on Extreme Value Theory)
 Extreme Value Index (moments method)-4.003
 VaR(95%) (moments method)0.407
 Expected Shortfall (moments method)0.407
 Extreme Value Index (regression method)0.014
 VaR(95%) (regression method)1.068
 Expected Shortfall (regression method)1.596
COMBINED STATISTICS
 Annualized return (arithmetic extrapolation)0.165
 Compounded annual return (geometric extrapolation)0.121
 Calmar ratio (compounded annual return / max draw down)0.132
 Compounded annual return / average of 25% largest draw downs0.184
 Compounded annual return / Expected Shortfall lognormal1.367
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 predictor0.560
 Mean of criterion-0.044
 SD of predictor0.197
 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 predictor0.540
 Mean of criterion-0.044
 SD of predictor0.196
 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)-5534171842241089.000
 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)16018834193793046876848560013312.000
 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