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Advanced Statistics: Sinersys

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-1.936
 SD0.812
 Sharpe ratio (Glass type estimate) -2.385
 Sharpe ratio (Hedges UMVUE)-1.726
 df3.000
 t-1.377
 p0.869
 Lowerbound of 95% confidence interval for Sharpe Ratio-6.096
 Upperbound of 95% confidence interval for Sharpe Ratio1.605
 Lowerbound of 95% CI (Gibbons, Hedeker & Davis approximation)-5.391
 Upperbound of 95% CI (Gibbons, Hedeker & Davis approximation)1.939
Statistics related to Sortino ratio
 Sortino ratio-2.160
 Upside Potential Ratio0.109
 Upside part of mean0.098
 Downside part of mean-2.034
 Upside SD0.056
 Downside SD0.896
 N nonnegative terms1.000
 N negative terms3.000
Statistics related to linear regression on benchmark
 N of observations4.000
 Mean of predictor0.111
 Mean of criterion-1.936
 SD of predictor0.216
 SD of criterion0.812
 Covariance-0.036
 r-0.204
 b (slope, estimate of beta)-0.768
 a (intercept, estimate of alpha)-1.850
 Mean Square Error0.947
 DF error2.000
 t(b)-0.295
 p(b)0.602
 t(a)-1.082
 p(a)0.804
 Lowerbound of 95% confidence interval for beta-11.955
 Upperbound of 95% confidence interval for beta10.420
 Lowerbound of 95% confidence interval for alpha-9.207
 Upperbound of 95% confidence interval for alpha5.507
 Treynor index (mean / b)2.522
 Jensen alpha (a)-1.850
Ratio statistics of excess log return rates
Statistics related to Sharpe ratio
 Mean-2.510
 SD1.084
 Sharpe ratio (Glass type estimate) -2.315
 Sharpe ratio (Hedges UMVUE)-1.675
 df3.000
 t-1.337
 p0.863
 Lowerbound of 95% confidence interval for Sharpe Ratio-6.003
 Upperbound of 95% confidence interval for Sharpe Ratio1.648
 Lowerbound of 95% CI (Gibbons, Hedeker & Davis approximation)-5.325
 Upperbound of 95% CI (Gibbons, Hedeker & Davis approximation)1.975
Statistics related to Sortino ratio
 Sortino ratio-2.119
 Upside Potential Ratio0.081
 Upside part of mean0.096
 Downside part of mean-2.606
 Upside SD0.055
 Downside SD1.185
 N nonnegative terms1.000
 N negative terms3.000
Statistics related to linear regression on benchmark
 N of observations4.000
 Mean of predictor0.093
 Mean of criterion-2.510
 SD of predictor0.218
 SD of criterion1.084
 Covariance-0.063
 r-0.265
 b (slope, estimate of beta)-1.316
 a (intercept, estimate of alpha)-2.388
 Mean Square Error1.640
 DF error2.000
 t(b)-0.389
 p(b)0.633
 t(a)-1.066
 p(a)0.801
 Lowerbound of 95% confidence interval for beta-15.875
 Upperbound of 95% confidence interval for beta13.243
 Lowerbound of 95% confidence interval for alpha-12.026
 Upperbound of 95% confidence interval for alpha7.250
 Treynor index (mean / b)1.908
 Jensen alpha (a)-2.388
Risk estimates for a one-period unit investment (parametric)
assuming log normal returns and losses (using central moments from Sharpe statistics)
 VaR(95%)0.515
 Expected Shortfall on VaR0.572
assuming Pareto losses only (using partial moments from Sortino statistics)
 VaR(95%)0.478
 Expected Shortfall on VaR0.715
ORDER STATISTICS
Quartiles of return rates
 Number of observations4.000
 Minimum0.524
 Quartile 10.738
 Median0.904
 Quartile 31.009
 Maximum1.036
 Mean of quarter 10.524
 Mean of quarter 20.809
 Mean of quarter 31.000
 Mean of quarter 41.036
 Inter Quartile Range0.271
 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 observations1.000
 Minimum0.576
 Quartile 10.576
 Median0.576
 Quartile 30.576
 Maximum0.576
 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)-1.681
 Compounded annual return (geometric extrapolation)-0.915
 Calmar ratio (compounded annual return / max draw down)-1.589
 Compounded annual return / average of 25% largest draw downsNA
 Compounded annual return / Expected Shortfall lognormal-1.600
ANALYSIS BASED ON DAILY VALUES, FULL HISTORY (Back)
RATIO STATISTICS
Ratio statistics of excess return rates
Statistics related to Sharpe ratio
 Mean-2.061
 SD0.542
 Sharpe ratio (Glass type estimate) -3.799
 Sharpe ratio (Hedges UMVUE)-3.777
 df129.000
 t-2.335
 p0.627
 Lowerbound of 95% confidence interval for Sharpe Ratio-7.014
 Upperbound of 95% confidence interval for Sharpe Ratio-0.570
 Lowerbound of 95% CI (Gibbons, Hedeker & Davis approximation)-6.998
 Upperbound of 95% CI (Gibbons, Hedeker & Davis approximation)-0.555
Statistics related to Sortino ratio
 Sortino ratio-4.206
 Upside Potential Ratio2.442
 Upside part of mean1.196
 Downside part of mean-3.257
 Upside SD0.254
 Downside SD0.490
 N nonnegative terms19.000
 N negative terms111.000
Statistics related to linear regression on benchmark
 N of observations130.000
 Mean of predictor0.455
 Mean of criterion-2.061
 SD of predictor0.210
 SD of criterion0.542
 Covariance0.002
 r0.019
 b (slope, estimate of beta)0.050
 a (intercept, estimate of alpha)-2.084
 Mean Square Error0.296
 DF error128.000
 t(b)0.219
 p(b)0.490
 t(a)-2.336
 p(a)0.601
 Lowerbound of 95% confidence interval for beta-0.401
 Upperbound of 95% confidence interval for beta0.501
 Lowerbound of 95% confidence interval for alpha-3.848
 Upperbound of 95% confidence interval for alpha-0.319
 Treynor index (mean / b)-41.322
 Jensen alpha (a)-2.084
Ratio statistics of excess log return rates
Statistics related to Sharpe ratio
 Mean-2.219
 SD0.559
 Sharpe ratio (Glass type estimate) -3.969
 Sharpe ratio (Hedges UMVUE)-3.946
 df129.000
 t-2.440
 p0.633
 Lowerbound of 95% confidence interval for Sharpe Ratio-7.186
 Upperbound of 95% confidence interval for Sharpe Ratio-0.737
 Lowerbound of 95% CI (Gibbons, Hedeker & Davis approximation)-7.170
 Upperbound of 95% CI (Gibbons, Hedeker & Davis approximation)-0.721
Statistics related to Sortino ratio
 Sortino ratio-4.316
 Upside Potential Ratio2.267
 Upside part of mean1.165
 Downside part of mean-3.385
 Upside SD0.245
 Downside SD0.514
 N nonnegative terms19.000
 N negative terms111.000
Statistics related to linear regression on benchmark
 N of observations130.000
 Mean of predictor0.433
 Mean of criterion-2.219
 SD of predictor0.210
 SD of criterion0.559
 Covariance0.002
 r0.019
 b (slope, estimate of beta)0.050
 a (intercept, estimate of alpha)-2.241
 Mean Square Error0.315
 DF error128.000
 t(b)0.211
 p(b)0.491
 t(a)-2.439
 p(a)0.605
 Lowerbound of 95% confidence interval for beta-0.416
 Upperbound of 95% confidence interval for beta0.515
 Lowerbound of 95% confidence interval for alpha-4.058
 Upperbound of 95% confidence interval for alpha-0.423
 Treynor index (mean / b)-44.636
 Jensen alpha (a)-2.241
Risk estimates for a one-period unit investment (parametric)
assuming log normal returns and losses (using central moments from Sharpe statistics)
 VaR(95%)0.054
 Expected Shortfall on VaR0.066
assuming Pareto losses only (using partial moments from Sortino statistics)
 VaR(95%)0.030
 Expected Shortfall on VaR0.062
ORDER STATISTICS
Quartiles of return rates
 Number of observations130.000
 Minimum0.881
 Quartile 10.997
 Median1.000
 Quartile 31.000
 Maximum1.088
 Mean of quarter 10.963
 Mean of quarter 21.000
 Mean of quarter 31.000
 Mean of quarter 41.014
 Inter Quartile Range0.003
 Number outliers low26.000
 Percentage of outliers low0.200
 Mean of outliers low0.955
 Number of outliers high16.000
 Percentage of outliers high0.123
 Mean of outliers high1.028
Risk estimates for a one-period unit investment (based on Extreme Value Theory)
 Extreme Value Index (moments method)0.978
 VaR(95%) (moments method)0.024
 Expected Shortfall (moments method)1.241
 Extreme Value Index (regression method)-0.058
 VaR(95%) (regression method)0.031
 Expected Shortfall (regression method)0.046
DRAW DOWN STATISTICS
Quartiles of draw downs
 Number of observations1.000
 Minimum0.576
 Quartile 10.576
 Median0.576
 Quartile 30.576
 Maximum0.576
 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)-1.483
 Compounded annual return (geometric extrapolation)-0.886
 Calmar ratio (compounded annual return / max draw down)-1.539
 Compounded annual return / average of 25% largest draw downsNA
 Compounded annual return / Expected Shortfall lognormal-13.375