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Advanced Statistics: PTQQS 2.0.B

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-0.050
 SD0.512
 Sharpe ratio (Glass type estimate) -0.098
 Sharpe ratio (Hedges UMVUE)-0.093
 df16.000
 t-0.116
 p0.515
 Lowerbound of 95% confidence interval for Sharpe Ratio-1.743
 Upperbound of 95% confidence interval for Sharpe Ratio1.551
 Lowerbound of 95% CI (Gibbons, Hedeker & Davis approximation)-1.740
 Upperbound of 95% CI (Gibbons, Hedeker & Davis approximation)1.554
Statistics related to Sortino ratio
 Sortino ratio-0.118
 Upside Potential Ratio0.931
 Upside part of mean0.393
 Downside part of mean-0.443
 Upside SD0.262
 Downside SD0.422
 N nonnegative terms4.000
 N negative terms13.000
Statistics related to linear regression on benchmark
 N of observations17.000
 Mean of predictor0.096
 Mean of criterion-0.050
 SD of predictor0.197
 SD of criterion0.512
 Covariance0.005
 r0.049
 b (slope, estimate of beta)0.127
 a (intercept, estimate of alpha)-0.062
 Mean Square Error0.279
 DF error15.000
 t(b)0.189
 p(b)0.469
 t(a)-0.138
 p(a)0.523
 Lowerbound of 95% confidence interval for beta-1.302
 Upperbound of 95% confidence interval for beta1.556
 Lowerbound of 95% confidence interval for alpha-1.017
 Upperbound of 95% confidence interval for alpha0.893
 Treynor index (mean / b)-0.393
 Jensen alpha (a)-0.062
Ratio statistics of excess log return rates
Statistics related to Sharpe ratio
 Mean-0.213
 SD0.637
 Sharpe ratio (Glass type estimate) -0.335
 Sharpe ratio (Hedges UMVUE)-0.319
 df16.000
 t-0.399
 p0.550
 Lowerbound of 95% confidence interval for Sharpe Ratio-1.981
 Upperbound of 95% confidence interval for Sharpe Ratio1.321
 Lowerbound of 95% CI (Gibbons, Hedeker & Davis approximation)-1.969
 Upperbound of 95% CI (Gibbons, Hedeker & Davis approximation)1.331
Statistics related to Sortino ratio
 Sortino ratio-0.372
 Upside Potential Ratio0.630
 Upside part of mean0.362
 Downside part of mean-0.575
 Upside SD0.238
 Downside SD0.574
 N nonnegative terms4.000
 N negative terms13.000
Statistics related to linear regression on benchmark
 N of observations17.000
 Mean of predictor0.076
 Mean of criterion-0.213
 SD of predictor0.205
 SD of criterion0.637
 Covariance0.001
 r0.009
 b (slope, estimate of beta)0.027
 a (intercept, estimate of alpha)-0.215
 Mean Square Error0.433
 DF error15.000
 t(b)0.033
 p(b)0.495
 t(a)-0.387
 p(a)0.563
 Lowerbound of 95% confidence interval for beta-1.682
 Upperbound of 95% confidence interval for beta1.735
 Lowerbound of 95% confidence interval for alpha-1.401
 Upperbound of 95% confidence interval for alpha0.970
 Treynor index (mean / b)-8.036
 Jensen alpha (a)-0.215
Risk estimates for a one-period unit investment (parametric)
assuming log normal returns and losses (using central moments from Sharpe statistics)
 VaR(95%)0.274
 Expected Shortfall on VaR0.326
assuming Pareto losses only (using partial moments from Sortino statistics)
 VaR(95%)0.109
 Expected Shortfall on VaR0.235
ORDER STATISTICS
Quartiles of return rates
 Number of observations17.000
 Minimum0.511
 Quartile 11.000
 Median1.000
 Quartile 31.003
 Maximum1.241
 Mean of quarter 10.883
 Mean of quarter 21.000
 Mean of quarter 31.001
 Mean of quarter 41.143
 Inter Quartile Range0.003
 Number outliers low2.000
 Percentage of outliers low0.118
 Mean of outliers low0.708
 Number of outliers high4.000
 Percentage of outliers high0.235
 Mean of outliers high1.143
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)1.051
 VaR(95%) (regression method)0.300
 Expected Shortfall (regression method)NA
DRAW DOWN STATISTICS
Quartiles of draw downs
 Number of observations1.000
 Minimum0.537
 Quartile 10.537
 Median0.537
 Quartile 30.537
 Maximum0.537
 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)-0.151
 Compounded annual return (geometric extrapolation)-0.156
 Calmar ratio (compounded annual return / max draw down)-0.290
 Compounded annual return / average of 25% largest draw downsNA
 Compounded annual return / Expected Shortfall lognormal-0.478
ANALYSIS BASED ON DAILY VALUES, FULL HISTORY (Back)
RATIO STATISTICS
Ratio statistics of excess return rates
Statistics related to Sharpe ratio
 Mean0.036
 SD0.701
 Sharpe ratio (Glass type estimate) 0.051
 Sharpe ratio (Hedges UMVUE)0.051
 df491.000
 t0.061
 p0.476
 Lowerbound of 95% confidence interval for Sharpe Ratio-1.588
 Upperbound of 95% confidence interval for Sharpe Ratio1.690
 Lowerbound of 95% CI (Gibbons, Hedeker & Davis approximation)-1.588
 Upperbound of 95% CI (Gibbons, Hedeker & Davis approximation)1.690
Statistics related to Sortino ratio
 Sortino ratio0.073
 Upside Potential Ratio4.109
 Upside part of mean2.018
 Downside part of mean-1.982
 Upside SD0.499
 Downside SD0.491
 N nonnegative terms42.000
 N negative terms450.000
Statistics related to linear regression on benchmark
 N of observations492.000
 Mean of predictor0.147
 Mean of criterion0.036
 SD of predictor0.220
 SD of criterion0.701
 Covariance-0.012
 r-0.079
 b (slope, estimate of beta)-0.250
 a (intercept, estimate of alpha)0.073
 Mean Square Error0.489
 DF error490.000
 t(b)-1.747
 p(b)0.959
 t(a)0.125
 p(a)0.450
 Lowerbound of 95% confidence interval for beta-0.532
 Upperbound of 95% confidence interval for beta0.031
 Lowerbound of 95% confidence interval for alpha-1.077
 Upperbound of 95% confidence interval for alpha1.222
 Treynor index (mean / b)-0.144
 Jensen alpha (a)0.073
Ratio statistics of excess log return rates
Statistics related to Sharpe ratio
 Mean-0.212
 SD0.708
 Sharpe ratio (Glass type estimate) -0.299
 Sharpe ratio (Hedges UMVUE)-0.299
 df491.000
 t-0.358
 p0.640
 Lowerbound of 95% confidence interval for Sharpe Ratio-1.938
 Upperbound of 95% confidence interval for Sharpe Ratio1.340
 Lowerbound of 95% CI (Gibbons, Hedeker & Davis approximation)-1.938
 Upperbound of 95% CI (Gibbons, Hedeker & Davis approximation)1.340
Statistics related to Sortino ratio
 Sortino ratio-0.396
 Upside Potential Ratio3.562
 Upside part of mean1.905
 Downside part of mean-2.116
 Upside SD0.464
 Downside SD0.535
 N nonnegative terms42.000
 N negative terms450.000
Statistics related to linear regression on benchmark
 N of observations492.000
 Mean of predictor0.123
 Mean of criterion-0.212
 SD of predictor0.221
 SD of criterion0.708
 Covariance-0.013
 r-0.080
 b (slope, estimate of beta)-0.257
 a (intercept, estimate of alpha)-0.180
 Mean Square Error0.500
 DF error490.000
 t(b)-1.777
 p(b)0.962
 t(a)-0.305
 p(a)0.620
 Lowerbound of 95% confidence interval for beta-0.541
 Upperbound of 95% confidence interval for beta0.027
 Lowerbound of 95% confidence interval for alpha-1.342
 Upperbound of 95% confidence interval for alpha0.982
 Treynor index (mean / b)0.824
 Jensen alpha (a)-0.180
Risk estimates for a one-period unit investment (parametric)
assuming log normal returns and losses (using central moments from Sharpe statistics)
 VaR(95%)0.061
 Expected Shortfall on VaR0.076
assuming Pareto losses only (using partial moments from Sortino statistics)
 VaR(95%)0.019
 Expected Shortfall on VaR0.042
ORDER STATISTICS
Quartiles of return rates
 Number of observations492.000
 Minimum0.781
 Quartile 11.000
 Median1.000
 Quartile 31.000
 Maximum1.262
 Mean of quarter 10.977
 Mean of quarter 21.000
 Mean of quarter 31.000
 Mean of quarter 41.024
 Inter Quartile Range0.000
 Number outliers low38.000
 Percentage of outliers low0.077
 Mean of outliers low0.927
 Number of outliers high42.000
 Percentage of outliers high0.085
 Mean of outliers high1.069
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)-0.123
 VaR(95%) (regression method)0.021
 Expected Shortfall (regression method)0.061
DRAW DOWN STATISTICS
Quartiles of draw downs
 Number of observations7.000
 Minimum0.013
 Quartile 10.024
 Median0.043
 Quartile 30.071
 Maximum0.623
 Mean of quarter 10.014
 Mean of quarter 20.038
 Mean of quarter 30.045
 Mean of quarter 40.360
 Inter Quartile Range0.047
 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 high0.623
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)-0.149
 Compounded annual return (geometric extrapolation)-0.155
 Calmar ratio (compounded annual return / max draw down)-0.248
 Compounded annual return / average of 25% largest draw downs-0.429
 Compounded annual return / Expected Shortfall lognormal-2.027
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 predictor0.335
 Mean of criterion-0.044
 SD of predictor0.195
 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 predictor0.316
 Mean of criterion-0.044
 SD of predictor0.194
 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)-5574056293179388.000
 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)23909124472646524271795602718720.000
 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