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Advanced Statistics: Stellar--not supp. since 08.22.08

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-0.031
 SD0.093
 Sharpe ratio (Glass type estimate) -0.332
 Sharpe ratio (Hedges UMVUE)-0.325
 df41.000
 t-0.620
 p0.731
 Lowerbound of 95% confidence interval for Sharpe Ratio-1.380
 Upperbound of 95% confidence interval for Sharpe Ratio0.720
 Lowerbound of 95% CI (Gibbons, Hedeker & Davis approximation)-1.376
 Upperbound of 95% CI (Gibbons, Hedeker & Davis approximation)0.725
Statistics related to Sortino ratio
 Sortino ratio-0.463
 Upside Potential Ratio0.850
 Upside part of mean0.056
 Downside part of mean-0.087
 Upside SD0.064
 Downside SD0.066
 N nonnegative terms4.000
 N negative terms38.000
Statistics related to linear regression on benchmark
 N of observations42.000
 Mean of predictor0.034
 Mean of criterion-0.031
 SD of predictor0.273
 SD of criterion0.093
 Covariance0.002
 r0.073
 b (slope, estimate of beta)0.025
 a (intercept, estimate of alpha)-0.032
 Mean Square Error0.009
 DF error40.000
 t(b)0.463
 p(b)0.323
 t(a)-0.631
 p(a)0.734
 Lowerbound of 95% confidence interval for beta-0.083
 Upperbound of 95% confidence interval for beta0.133
 Lowerbound of 95% confidence interval for alpha-0.133
 Upperbound of 95% confidence interval for alpha0.070
 Treynor index (mean / b)-1.239
 Jensen alpha (a)-0.032
Ratio statistics of excess log return rates
Statistics related to Sharpe ratio
 Mean-0.035
 SD0.093
 Sharpe ratio (Glass type estimate) -0.376
 Sharpe ratio (Hedges UMVUE)-0.369
 df41.000
 t-0.703
 p0.757
 Lowerbound of 95% confidence interval for Sharpe Ratio-1.424
 Upperbound of 95% confidence interval for Sharpe Ratio0.677
 Lowerbound of 95% CI (Gibbons, Hedeker & Davis approximation)-1.420
 Upperbound of 95% CI (Gibbons, Hedeker & Davis approximation)0.682
Statistics related to Sortino ratio
 Sortino ratio-0.503
 Upside Potential Ratio0.784
 Upside part of mean0.054
 Downside part of mean-0.089
 Upside SD0.061
 Downside SD0.069
 N nonnegative terms4.000
 N negative terms38.000
Statistics related to linear regression on benchmark
 N of observations42.000
 Mean of predictor-0.005
 Mean of criterion-0.035
 SD of predictor0.286
 SD of criterion0.093
 Covariance0.002
 r0.077
 b (slope, estimate of beta)0.025
 a (intercept, estimate of alpha)-0.035
 Mean Square Error0.009
 DF error40.000
 t(b)0.491
 p(b)0.313
 t(a)-0.694
 p(a)0.754
 Lowerbound of 95% confidence interval for beta-0.078
 Upperbound of 95% confidence interval for beta0.129
 Lowerbound of 95% confidence interval for alpha-0.136
 Upperbound of 95% confidence interval for alpha0.066
 Treynor index (mean / b)-1.386
 Jensen alpha (a)-0.035
Risk estimates for a one-period unit investment (parametric)
assuming log normal returns and losses (using central moments from Sharpe statistics)
 VaR(95%)0.046
 Expected Shortfall on VaR0.056
assuming Pareto losses only (using partial moments from Sortino statistics)
 VaR(95%)0.024
 Expected Shortfall on VaR0.048
ORDER STATISTICS
Quartiles of return rates
 Number of observations42.000
 Minimum0.900
 Quartile 10.998
 Median1.000
 Quartile 31.001
 Maximum1.108
 Mean of quarter 10.983
 Mean of quarter 20.999
 Mean of quarter 31.001
 Mean of quarter 41.021
 Inter Quartile Range0.003
 Number outliers low2.000
 Percentage of outliers low0.048
 Mean of outliers low0.920
 Number of outliers high4.000
 Percentage of outliers high0.095
 Mean of outliers high1.053
Risk estimates for a one-period unit investment (based on Extreme Value Theory)
 Extreme Value Index (moments method)1.283
 VaR(95%) (moments method)0.011
 Expected Shortfall (moments method)NA
 Extreme Value Index (regression method)2.151
 VaR(95%) (regression method)0.006
 Expected Shortfall (regression method)NA
DRAW DOWN STATISTICS
Quartiles of draw downs
 Number of observations1.000
 Minimum0.154
 Quartile 10.154
 Median0.154
 Quartile 30.154
 Maximum0.154
 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)0.009
 Compounded annual return (geometric extrapolation)0.009
 Calmar ratio (compounded annual return / max draw down)0.060
 Compounded annual return / average of 25% largest draw downsNA
 Compounded annual return / Expected Shortfall lognormal0.163
ANALYSIS BASED ON DAILY VALUES, FULL HISTORY (Back)
RATIO STATISTICS
Ratio statistics of excess return rates
Statistics related to Sharpe ratio
 Mean-0.026
 SD0.132
 Sharpe ratio (Glass type estimate) -0.195
 Sharpe ratio (Hedges UMVUE)-0.194
 df1208.000
 t-0.365
 p0.505
 Lowerbound of 95% confidence interval for Sharpe Ratio-1.240
 Upperbound of 95% confidence interval for Sharpe Ratio0.851
 Lowerbound of 95% CI (Gibbons, Hedeker & Davis approximation)-1.240
 Upperbound of 95% CI (Gibbons, Hedeker & Davis approximation)0.851
Statistics related to Sortino ratio
 Sortino ratio-0.296
 Upside Potential Ratio2.484
 Upside part of mean0.215
 Downside part of mean-0.240
 Upside SD0.099
 Downside SD0.087
 N nonnegative terms267.000
 N negative terms942.000
Statistics related to linear regression on benchmark
 N of observations1209.000
 Mean of predictor0.060
 Mean of criterion-0.026
 SD of predictor0.307
 SD of criterion0.132
 Covariance0.003
 r0.073
 b (slope, estimate of beta)0.031
 a (intercept, estimate of alpha)-0.027
 Mean Square Error0.017
 DF error1207.000
 t(b)2.541
 p(b)0.454
 t(a)-0.392
 p(a)0.507
 Lowerbound of 95% confidence interval for beta0.007
 Upperbound of 95% confidence interval for beta0.055
 Lowerbound of 95% confidence interval for alpha-0.165
 Upperbound of 95% confidence interval for alpha0.110
 Treynor index (mean / b)-0.820
 Jensen alpha (a)-0.027
Ratio statistics of excess log return rates
Statistics related to Sharpe ratio
 Mean-0.034
 SD0.131
 Sharpe ratio (Glass type estimate) -0.261
 Sharpe ratio (Hedges UMVUE)-0.261
 df1208.000
 t-0.489
 p0.507
 Lowerbound of 95% confidence interval for Sharpe Ratio-1.306
 Upperbound of 95% confidence interval for Sharpe Ratio0.785
 Lowerbound of 95% CI (Gibbons, Hedeker & Davis approximation)-1.306
 Upperbound of 95% CI (Gibbons, Hedeker & Davis approximation)0.785
Statistics related to Sortino ratio
 Sortino ratio-0.380
 Upside Potential Ratio2.334
 Upside part of mean0.210
 Downside part of mean-0.244
 Upside SD0.095
 Downside SD0.090
 N nonnegative terms267.000
 N negative terms942.000
Statistics related to linear regression on benchmark
 N of observations1209.000
 Mean of predictor0.012
 Mean of criterion-0.034
 SD of predictor0.307
 SD of criterion0.131
 Covariance0.003
 r0.073
 b (slope, estimate of beta)0.031
 a (intercept, estimate of alpha)-0.035
 Mean Square Error0.017
 DF error1207.000
 t(b)2.556
 p(b)0.453
 t(a)-0.496
 p(a)0.509
 Lowerbound of 95% confidence interval for beta0.007
 Upperbound of 95% confidence interval for beta0.055
 Lowerbound of 95% confidence interval for alpha-0.172
 Upperbound of 95% confidence interval for alpha0.102
 Treynor index (mean / b)-1.093
 Jensen alpha (a)-0.035
Risk estimates for a one-period unit investment (parametric)
assuming log normal returns and losses (using central moments from Sharpe statistics)
 VaR(95%)0.012
 Expected Shortfall on VaR0.015
assuming Pareto losses only (using partial moments from Sortino statistics)
 VaR(95%)0.002
 Expected Shortfall on VaR0.005
ORDER STATISTICS
Quartiles of return rates
 Number of observations1209.000
 Minimum0.884
 Quartile 11.000
 Median1.000
 Quartile 31.000
 Maximum1.115
 Mean of quarter 10.998
 Mean of quarter 21.000
 Mean of quarter 31.000
 Mean of quarter 41.003
 Inter Quartile Range0.000
 Number outliers low108.000
 Percentage of outliers low0.089
 Mean of outliers low0.994
 Number of outliers high104.000
 Percentage of outliers high0.086
 Mean of outliers high1.007
Risk estimates for a one-period unit investment (based on Extreme Value Theory)
 Extreme Value Index (moments method)1.206
 VaR(95%) (moments method)0.001
 Expected Shortfall (moments method)NA
 Extreme Value Index (regression method)0.780
 VaR(95%) (regression method)0.000
 Expected Shortfall (regression method)0.010
DRAW DOWN STATISTICS
Quartiles of draw downs
 Number of observations6.000
 Minimum0.003
 Quartile 10.011
 Median0.018
 Quartile 30.107
 Maximum0.232
 Mean of quarter 10.006
 Mean of quarter 20.017
 Mean of quarter 30.020
 Mean of quarter 40.184
 Inter Quartile Range0.096
 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)0.010
 Compounded annual return (geometric extrapolation)0.010
 Calmar ratio (compounded annual return / max draw down)0.042
 Compounded annual return / average of 25% largest draw downs0.053
 Compounded annual return / Expected Shortfall lognormal0.674
ANALYSIS BASED ON DAILY VALUES, LAST 6 MONTHS (Back)
RATIO STATISTICS
Ratio statistics of excess return rates
Statistics related to Sharpe ratio
 Mean-0.043
 SD0.008
 Sharpe ratio (Glass type estimate) -5.439
 Sharpe ratio (Hedges UMVUE)-5.415
 df171.000
 t-3.846
 p0.677
 Lowerbound of 95% confidence interval for Sharpe Ratio-8.263
 Upperbound of 95% confidence interval for Sharpe Ratio-2.601
 Lowerbound of 95% CI (Gibbons, Hedeker & Davis approximation)-8.246
 Upperbound of 95% CI (Gibbons, Hedeker & Davis approximation)-2.585
Statistics related to Sortino ratio
 Sortino ratio-6.723
 Upside Potential Ratio4.656
 Upside part of mean0.030
 Downside part of mean-0.072
 Upside SD0.005
 Downside SD0.006
 N nonnegative terms45.000
 N negative terms127.000
Statistics related to linear regression on benchmark
 N of observations172.000
 Mean of predictor0.603
 Mean of criterion-0.043
 SD of predictor0.287
 SD of criterion0.008
 Covariance-0.000
 r-0.014
 b (slope, estimate of beta)-0.000
 a (intercept, estimate of alpha)-0.042
 Mean Square Error0.000
 DF error170.000
 t(b)-0.180
 p(b)0.507
 t(a)-3.791
 p(a)0.640
 Lowerbound of 95% confidence interval for beta-0.005
 Upperbound of 95% confidence interval for beta0.004
 Lowerbound of 95% confidence interval for alpha-0.064
 Upperbound of 95% confidence interval for alpha-0.020
 Treynor index (mean / b)113.057
 Jensen alpha (a)-0.042
Ratio statistics of excess log return rates
Statistics related to Sharpe ratio
 Mean-0.043
 SD0.008
 Sharpe ratio (Glass type estimate) -5.444
 Sharpe ratio (Hedges UMVUE)-5.420
 df171.000
 t-3.850
 p0.677
 Lowerbound of 95% confidence interval for Sharpe Ratio-8.268
 Upperbound of 95% confidence interval for Sharpe Ratio-2.605
 Lowerbound of 95% CI (Gibbons, Hedeker & Davis approximation)-8.251
 Upperbound of 95% CI (Gibbons, Hedeker & Davis approximation)-2.590
Statistics related to Sortino ratio
 Sortino ratio-6.725
 Upside Potential Ratio4.651
 Upside part of mean0.030
 Downside part of mean-0.072
 Upside SD0.005
 Downside SD0.006
 N nonnegative terms45.000
 N negative terms127.000
Statistics related to linear regression on benchmark
 N of observations172.000
 Mean of predictor0.561
 Mean of criterion-0.043
 SD of predictor0.286
 SD of criterion0.008
 Covariance-0.000
 r-0.013
 b (slope, estimate of beta)-0.000
 a (intercept, estimate of alpha)-0.042
 Mean Square Error0.000
 DF error170.000
 t(b)-0.165
 p(b)0.506
 t(a)-3.800
 p(a)0.640
 Lowerbound of 95% confidence interval for beta-0.004
 Upperbound of 95% confidence interval for beta0.004
 Lowerbound of 95% confidence interval for alpha-0.065
 Upperbound of 95% confidence interval for alpha-0.020
 Treynor index (mean / b)122.944
 Jensen alpha (a)-0.042
Risk estimates for a one-period unit investment (parametric)
assuming log normal returns and losses (using central moments from Sharpe statistics)
 VaR(95%)0.001
 Expected Shortfall on VaR0.001
assuming Pareto losses only (using partial moments from Sortino statistics)
 VaR(95%)0.001
 Expected Shortfall on VaR0.001
ORDER STATISTICS
Quartiles of return rates
 Number of observations172.000
 Minimum0.998
 Quartile 11.000
 Median1.000
 Quartile 31.000
 Maximum1.003
 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 low8.000
 Percentage of outliers low0.047
 Mean of outliers low0.999
 Number of outliers high8.000
 Percentage of outliers high0.047
 Mean of outliers high1.001
Risk estimates for a one-period unit investment (based on Extreme Value Theory)
 Extreme Value Index (moments method)-0.782
 VaR(95%) (moments method)-0.001
 Expected Shortfall (moments method)NA
 Extreme Value Index (regression method)0.715
 VaR(95%) (regression method)0.001
 Expected Shortfall (regression method)0.001
DRAW DOWN STATISTICS
Quartiles of draw downs
 Number of observations7.000
 Minimum0.000
 Quartile 10.000
 Median0.000
 Quartile 30.002
 Maximum0.006
 Mean of quarter 10.000
 Mean of quarter 20.000
 Mean of quarter 30.000
 Mean of quarter 40.005
 Inter Quartile Range0.002
 Number outliers low0.000
 Percentage of outliers low0.000
 Mean of outliers lowNA
 Number of outliers high1.000
 Percentage of outliers high0.143
 Mean of outliers high0.006
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)0.001
 Compounded annual return (geometric extrapolation)0.001
 Calmar ratio (compounded annual return / max draw down)0.223
 Compounded annual return / average of 25% largest draw downs0.281
 Compounded annual return / Expected Shortfall lognormal1.361