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Advanced Statistics: Super Oil

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
 Mean-0.641
 SD0.624
 Sharpe ratio (Glass type estimate) -1.027
 Sharpe ratio (Hedges UMVUE)-1.005
 df35.000
 t-1.779
 p0.958
 Lowerbound of 95% confidence interval for Sharpe Ratio-2.177
 Upperbound of 95% confidence interval for Sharpe Ratio0.137
 Lowerbound of 95% CI (Gibbons, Hedeker & Davis approximation)-2.161
 Upperbound of 95% CI (Gibbons, Hedeker & Davis approximation)0.151
Statistics related to Sortino ratio
 Sortino ratio-1.032
 Upside Potential Ratio0.216
 Upside part of mean0.134
 Downside part of mean-0.775
 Upside SD0.166
 Downside SD0.621
 N nonnegative terms3.000
 N negative terms33.000
Statistics related to linear regression on benchmark
 N of observations36.000
 Mean of predictor0.037
 Mean of criterion-0.641
 SD of predictor0.267
 SD of criterion0.624
 Covariance-0.034
 r-0.206
 b (slope, estimate of beta)-0.481
 a (intercept, estimate of alpha)-0.623
 Mean Square Error0.384
 DF error34.000
 t(b)-1.227
 p(b)0.886
 t(a)-1.740
 p(a)0.955
 Lowerbound of 95% confidence interval for beta-1.277
 Upperbound of 95% confidence interval for beta0.315
 Lowerbound of 95% confidence interval for alpha-1.351
 Upperbound of 95% confidence interval for alpha0.105
 Treynor index (mean / b)1.333
 Jensen alpha (a)-0.623
Ratio statistics of excess log return rates
Statistics related to Sharpe ratio
 Mean-1.013
 SD0.988
 Sharpe ratio (Glass type estimate) -1.026
 Sharpe ratio (Hedges UMVUE)-1.004
 df35.000
 t-1.777
 p0.958
 Lowerbound of 95% confidence interval for Sharpe Ratio-2.175
 Upperbound of 95% confidence interval for Sharpe Ratio0.138
 Lowerbound of 95% CI (Gibbons, Hedeker & Davis approximation)-2.159
 Upperbound of 95% CI (Gibbons, Hedeker & Davis approximation)0.152
Statistics related to Sortino ratio
 Sortino ratio-1.007
 Upside Potential Ratio0.121
 Upside part of mean0.122
 Downside part of mean-1.135
 Upside SD0.150
 Downside SD1.006
 N nonnegative terms3.000
 N negative terms33.000
Statistics related to linear regression on benchmark
 N of observations36.000
 Mean of predictor0.000
 Mean of criterion-1.013
 SD of predictor0.282
 SD of criterion0.988
 Covariance-0.045
 r-0.161
 b (slope, estimate of beta)-0.564
 a (intercept, estimate of alpha)-1.013
 Mean Square Error0.978
 DF error34.000
 t(b)-0.953
 p(b)0.826
 t(a)-1.774
 p(a)0.958
 Lowerbound of 95% confidence interval for beta-1.767
 Upperbound of 95% confidence interval for beta0.639
 Lowerbound of 95% confidence interval for alpha-2.174
 Upperbound of 95% confidence interval for alpha0.147
 Treynor index (mean / b)1.797
 Jensen alpha (a)-1.013
Risk estimates for a one-period unit investment (parametric)
assuming log normal returns and losses (using central moments from Sharpe statistics)
 VaR(95%)0.425
 Expected Shortfall on VaR0.487
assuming Pareto losses only (using partial moments from Sortino statistics)
 VaR(95%)0.214
 Expected Shortfall on VaR0.436
ORDER STATISTICS
Quartiles of return rates
 Number of observations36.000
 Minimum0.286
 Quartile 11.000
 Median1.000
 Quartile 31.000
 Maximum1.238
 Mean of quarter 10.755
 Mean of quarter 21.000
 Mean of quarter 31.000
 Mean of quarter 41.046
 Inter Quartile Range0.000
 Number outliers low8.000
 Percentage of outliers low0.222
 Mean of outliers low0.724
 Number of outliers high3.000
 Percentage of outliers high0.083
 Mean of outliers high1.138
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)0.625
 VaR(95%) (regression method)0.159
 Expected Shortfall (regression method)0.579
DRAW DOWN STATISTICS
Quartiles of draw downs
 Number of observations1.000
 Minimum0.953
 Quartile 10.953
 Median0.953
 Quartile 30.953
 Maximum0.953
 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 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)-0.315
 Compounded annual return (geometric extrapolation)-0.621
 Calmar ratio (compounded annual return / max draw down)-0.651
 Compounded annual return / average of 25% largest draw downsNA
 Compounded annual return / Expected Shortfall lognormal-1.275
ANALYSIS BASED ON DAILY VALUES, FULL HISTORY (Back)
RATIO STATISTICS
Ratio statistics of excess return rates
Statistics related to Sharpe ratio
 Mean-0.753
 SD0.668
 Sharpe ratio (Glass type estimate) -1.127
 Sharpe ratio (Hedges UMVUE)-1.126
 df1053.000
 t-1.972
 p0.539
 Lowerbound of 95% confidence interval for Sharpe Ratio-2.247
 Upperbound of 95% confidence interval for Sharpe Ratio-0.006
 Lowerbound of 95% CI (Gibbons, Hedeker & Davis approximation)-2.247
 Upperbound of 95% CI (Gibbons, Hedeker & Davis approximation)-0.005
Statistics related to Sortino ratio
 Sortino ratio-1.434
 Upside Potential Ratio2.198
 Upside part of mean1.154
 Downside part of mean-1.906
 Upside SD0.415
 Downside SD0.525
 N nonnegative terms79.000
 N negative terms975.000
Statistics related to linear regression on benchmark
 N of observations1054.000
 Mean of predictor0.107
 Mean of criterion-0.753
 SD of predictor0.314
 SD of criterion0.668
 Covariance0.010
 r0.049
 b (slope, estimate of beta)0.104
 a (intercept, estimate of alpha)-0.764
 Mean Square Error0.446
 DF error1052.000
 t(b)1.596
 p(b)0.475
 t(a)-2.002
 p(a)0.531
 Lowerbound of 95% confidence interval for beta-0.024
 Upperbound of 95% confidence interval for beta0.233
 Lowerbound of 95% confidence interval for alpha-1.513
 Upperbound of 95% confidence interval for alpha-0.015
 Treynor index (mean / b)-7.205
 Jensen alpha (a)-0.764
Ratio statistics of excess log return rates
Statistics related to Sharpe ratio
 Mean-0.993
 SD0.708
 Sharpe ratio (Glass type estimate) -1.402
 Sharpe ratio (Hedges UMVUE)-1.401
 df1053.000
 t-2.455
 p0.548
 Lowerbound of 95% confidence interval for Sharpe Ratio-2.523
 Upperbound of 95% confidence interval for Sharpe Ratio-0.281
 Lowerbound of 95% CI (Gibbons, Hedeker & Davis approximation)-2.523
 Upperbound of 95% CI (Gibbons, Hedeker & Davis approximation)-0.280
Statistics related to Sortino ratio
 Sortino ratio-1.651
 Upside Potential Ratio1.792
 Upside part of mean1.078
 Downside part of mean-2.071
 Upside SD0.377
 Downside SD0.601
 N nonnegative terms79.000
 N negative terms975.000
Statistics related to linear regression on benchmark
 N of observations1054.000
 Mean of predictor0.057
 Mean of criterion-0.993
 SD of predictor0.314
 SD of criterion0.708
 Covariance0.010
 r0.046
 b (slope, estimate of beta)0.103
 a (intercept, estimate of alpha)-0.999
 Mean Square Error0.501
 DF error1052.000
 t(b)1.483
 p(b)0.477
 t(a)-2.471
 p(a)0.538
 Lowerbound of 95% confidence interval for beta-0.033
 Upperbound of 95% confidence interval for beta0.239
 Lowerbound of 95% confidence interval for alpha-1.792
 Upperbound of 95% confidence interval for alpha-0.206
 Treynor index (mean / b)-9.645
 Jensen alpha (a)-0.999
Risk estimates for a one-period unit investment (parametric)
assuming log normal returns and losses (using central moments from Sharpe statistics)
 VaR(95%)0.064
 Expected Shortfall on VaR0.078
assuming Pareto losses only (using partial moments from Sortino statistics)
 VaR(95%)0.018
 Expected Shortfall on VaR0.041
ORDER STATISTICS
Quartiles of return rates
 Number of observations1054.000
 Minimum0.570
 Quartile 11.000
 Median1.000
 Quartile 31.000
 Maximum1.332
 Mean of quarter 10.978
 Mean of quarter 21.000
 Mean of quarter 31.000
 Mean of quarter 41.013
 Inter Quartile Range0.000
 Number outliers low95.000
 Percentage of outliers low0.090
 Mean of outliers low0.940
 Number of outliers high79.000
 Percentage of outliers high0.075
 Mean of outliers high1.045
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 observations3.000
 Minimum0.043
 Quartile 10.054
 Median0.066
 Quartile 30.510
 Maximum0.953
 Mean of quarter 10.043
 Mean of quarter 20.066
 Mean of quarter 3NA
 Mean of quarter 40.953
 Inter Quartile Range0.455
 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)-0.309
 Compounded annual return (geometric extrapolation)-0.613
 Calmar ratio (compounded annual return / max draw down)-0.643
 Compounded annual return / average of 25% largest draw downs-0.643
 Compounded annual return / Expected Shortfall lognormal-7.827
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 predictor0.682
 Mean of criterion-0.044
 SD of predictor0.300
 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 predictor0.637
 Mean of criterion-0.044
 SD of predictor0.297
 SD of criterion0.000
 Covariance0.000
 r0.000
 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)-5558445082394382.000
 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)-38417928134430601537620119912448.000
 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