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Advanced Statistics: system

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-0.068
 SD0.444
 Sharpe ratio (Glass type estimate) -0.154
 Sharpe ratio (Hedges UMVUE)-0.148
 df20.000
 t-0.203
 p0.523
 Lowerbound of 95% confidence interval for Sharpe Ratio-1.634
 Upperbound of 95% confidence interval for Sharpe Ratio1.330
 Lowerbound of 95% CI (Gibbons, Hedeker & Davis approximation)-1.630
 Upperbound of 95% CI (Gibbons, Hedeker & Davis approximation)1.334
Statistics related to Sortino ratio
 Sortino ratio-0.243
 Upside Potential Ratio1.862
 Upside part of mean0.524
 Downside part of mean-0.592
 Upside SD0.331
 Downside SD0.281
 N nonnegative terms9.000
 N negative terms12.000
Statistics related to linear regression on benchmark
 N of observations21.000
 Mean of predictor0.072
 Mean of criterion-0.068
 SD of predictor0.199
 SD of criterion0.444
 Covariance-0.073
 r-0.828
 b (slope, estimate of beta)-1.846
 a (intercept, estimate of alpha)0.064
 Mean Square Error0.065
 DF error19.000
 t(b)-6.434
 p(b)0.958
 t(a)0.332
 p(a)0.452
 Lowerbound of 95% confidence interval for beta-2.447
 Upperbound of 95% confidence interval for beta-1.246
 Lowerbound of 95% confidence interval for alpha-0.342
 Upperbound of 95% confidence interval for alpha0.471
 Treynor index (mean / b)0.037
 Jensen alpha (a)0.064
Ratio statistics of excess log return rates
Statistics related to Sharpe ratio
 Mean-0.159
 SD0.432
 Sharpe ratio (Glass type estimate) -0.367
 Sharpe ratio (Hedges UMVUE)-0.353
 df20.000
 t-0.486
 p0.554
 Lowerbound of 95% confidence interval for Sharpe Ratio-1.849
 Upperbound of 95% confidence interval for Sharpe Ratio1.123
 Lowerbound of 95% CI (Gibbons, Hedeker & Davis approximation)-1.839
 Upperbound of 95% CI (Gibbons, Hedeker & Davis approximation)1.132
Statistics related to Sortino ratio
 Sortino ratio-0.517
 Upside Potential Ratio1.550
 Upside part of mean0.476
 Downside part of mean-0.635
 Upside SD0.293
 Downside SD0.307
 N nonnegative terms9.000
 N negative terms12.000
Statistics related to linear regression on benchmark
 N of observations21.000
 Mean of predictor0.053
 Mean of criterion-0.159
 SD of predictor0.197
 SD of criterion0.432
 Covariance-0.072
 r-0.849
 b (slope, estimate of beta)-1.865
 a (intercept, estimate of alpha)-0.060
 Mean Square Error0.055
 DF error19.000
 t(b)-6.991
 p(b)0.965
 t(a)-0.337
 p(a)0.549
 Lowerbound of 95% confidence interval for beta-2.424
 Upperbound of 95% confidence interval for beta-1.307
 Lowerbound of 95% confidence interval for alpha-0.432
 Upperbound of 95% confidence interval for alpha0.313
 Treynor index (mean / b)0.085
 Jensen alpha (a)-0.060
Risk estimates for a one-period unit investment (parametric)
assuming log normal returns and losses (using central moments from Sharpe statistics)
 VaR(95%)0.196
 Expected Shortfall on VaR0.236
assuming Pareto losses only (using partial moments from Sortino statistics)
 VaR(95%)0.124
 Expected Shortfall on VaR0.206
ORDER STATISTICS
Quartiles of return rates
 Number of observations21.000
 Minimum0.781
 Quartile 10.950
 Median0.972
 Quartile 31.051
 Maximum1.335
 Mean of quarter 10.866
 Mean of quarter 20.966
 Mean of quarter 31.017
 Mean of quarter 41.170
 Inter Quartile Range0.101
 Number outliers low1.000
 Percentage of outliers low0.048
 Mean of outliers low0.781
 Number of outliers high2.000
 Percentage of outliers high0.095
 Mean of outliers high1.279
Risk estimates for a one-period unit investment (based on Extreme Value Theory)
 Extreme Value Index (moments method)-5.578
 VaR(95%) (moments method)0.112
 Expected Shortfall (moments method)0.112
 Extreme Value Index (regression method)-0.960
 VaR(95%) (regression method)0.191
 Expected Shortfall (regression method)0.208
DRAW DOWN STATISTICS
Quartiles of draw downs
 Number of observations2.000
 Minimum0.092
 Quartile 10.168
 Median0.243
 Quartile 30.318
 Maximum0.394
 Mean of quarter 10.092
 Mean of quarter 2NA
 Mean of quarter 3NA
 Mean of quarter 40.394
 Inter Quartile Range0.151
 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)-0.104
 Compounded annual return (geometric extrapolation)-0.108
 Calmar ratio (compounded annual return / max draw down)-0.275
 Compounded annual return / average of 25% largest draw downs-0.275
 Compounded annual return / Expected Shortfall lognormal-0.459
ANALYSIS BASED ON DAILY VALUES, FULL HISTORY (Back)
RATIO STATISTICS
Ratio statistics of excess return rates
Statistics related to Sharpe ratio
 Mean-0.140
 SD0.353
 Sharpe ratio (Glass type estimate) -0.397
 Sharpe ratio (Hedges UMVUE)-0.396
 df606.000
 t-0.527
 p0.701
 Lowerbound of 95% confidence interval for Sharpe Ratio-1.872
 Upperbound of 95% confidence interval for Sharpe Ratio1.079
 Lowerbound of 95% CI (Gibbons, Hedeker & Davis approximation)-1.872
 Upperbound of 95% CI (Gibbons, Hedeker & Davis approximation)1.080
Statistics related to Sortino ratio
 Sortino ratio-0.561
 Upside Potential Ratio8.333
 Upside part of mean2.079
 Downside part of mean-2.219
 Upside SD0.249
 Downside SD0.249
 N nonnegative terms260.000
 N negative terms347.000
Statistics related to linear regression on benchmark
 N of observations607.000
 Mean of predictor0.088
 Mean of criterion-0.140
 SD of predictor0.200
 SD of criterion0.353
 Covariance-0.036
 r-0.516
 b (slope, estimate of beta)-0.908
 a (intercept, estimate of alpha)-0.060
 Mean Square Error0.091
 DF error605.000
 t(b)-14.803
 p(b)1.000
 t(a)-0.262
 p(a)0.603
 Lowerbound of 95% confidence interval for beta-1.029
 Upperbound of 95% confidence interval for beta-0.788
 Lowerbound of 95% confidence interval for alpha-0.507
 Upperbound of 95% confidence interval for alpha0.388
 Treynor index (mean / b)0.154
 Jensen alpha (a)-0.060
Ratio statistics of excess log return rates
Statistics related to Sharpe ratio
 Mean-0.202
 SD0.352
 Sharpe ratio (Glass type estimate) -0.573
 Sharpe ratio (Hedges UMVUE)-0.572
 df606.000
 t-0.761
 p0.777
 Lowerbound of 95% confidence interval for Sharpe Ratio-2.048
 Upperbound of 95% confidence interval for Sharpe Ratio0.903
 Lowerbound of 95% CI (Gibbons, Hedeker & Davis approximation)-2.048
 Upperbound of 95% CI (Gibbons, Hedeker & Davis approximation)0.904
Statistics related to Sortino ratio
 Sortino ratio-0.793
 Upside Potential Ratio8.046
 Upside part of mean2.048
 Downside part of mean-2.250
 Upside SD0.244
 Downside SD0.255
 N nonnegative terms260.000
 N negative terms347.000
Statistics related to linear regression on benchmark
 N of observations607.000
 Mean of predictor0.068
 Mean of criterion-0.202
 SD of predictor0.201
 SD of criterion0.352
 Covariance-0.036
 r-0.515
 b (slope, estimate of beta)-0.904
 a (intercept, estimate of alpha)-0.140
 Mean Square Error0.091
 DF error605.000
 t(b)-14.766
 p(b)1.000
 t(a)-0.616
 p(a)0.731
 Lowerbound of 95% confidence interval for beta-1.024
 Upperbound of 95% confidence interval for beta-0.783
 Lowerbound of 95% confidence interval for alpha-0.587
 Upperbound of 95% confidence interval for alpha0.307
 Treynor index (mean / b)0.223
 Jensen alpha (a)-0.140
Risk estimates for a one-period unit investment (parametric)
assuming log normal returns and losses (using central moments from Sharpe statistics)
 VaR(95%)0.031
 Expected Shortfall on VaR0.039
assuming Pareto losses only (using partial moments from Sortino statistics)
 VaR(95%)0.016
 Expected Shortfall on VaR0.031
ORDER STATISTICS
Quartiles of return rates
 Number of observations607.000
 Minimum0.923
 Quartile 10.992
 Median1.000
 Quartile 31.008
 Maximum1.094
 Mean of quarter 10.977
 Mean of quarter 20.997
 Mean of quarter 31.002
 Mean of quarter 41.022
 Inter Quartile Range0.015
 Number outliers low38.000
 Percentage of outliers low0.063
 Mean of outliers low0.958
 Number of outliers high32.000
 Percentage of outliers high0.053
 Mean of outliers high1.045
Risk estimates for a one-period unit investment (based on Extreme Value Theory)
 Extreme Value Index (moments method)0.025
 VaR(95%) (moments method)0.019
 Expected Shortfall (moments method)0.027
 Extreme Value Index (regression method)-0.073
 VaR(95%) (regression method)0.022
 Expected Shortfall (regression method)0.030
DRAW DOWN STATISTICS
Quartiles of draw downs
 Number of observations11.000
 Minimum0.000
 Quartile 10.012
 Median0.043
 Quartile 30.100
 Maximum0.445
 Mean of quarter 10.004
 Mean of quarter 20.024
 Mean of quarter 30.070
 Mean of quarter 40.242
 Inter Quartile Range0.089
 Number outliers low0.000
 Percentage of outliers low0.000
 Mean of outliers lowNA
 Number of outliers high1.000
 Percentage of outliers high0.091
 Mean of outliers high0.445
Risk estimates based on draw downs (based on Extreme Value Theory)
 Extreme Value Index (moments method)0.064
 VaR(95%) (moments method)0.250
 Expected Shortfall (moments method)0.362
 Extreme Value Index (regression method)1.808
 VaR(95%) (regression method)0.494
 Expected Shortfall (regression method)NA
COMBINED STATISTICS
 Annualized return (arithmetic extrapolation)-0.138
 Compounded annual return (geometric extrapolation)-0.146
 Calmar ratio (compounded annual return / max draw down)-0.328
 Compounded annual return / average of 25% largest draw downs-0.603
 Compounded annual return / Expected Shortfall lognormal-3.747
ANALYSIS BASED ON DAILY VALUES, LAST 6 MONTHS (Back)
RATIO STATISTICS
Ratio statistics of excess return rates
Statistics related to Sharpe ratio
 Mean-0.458
 SD0.332
 Sharpe ratio (Glass type estimate) -1.382
 Sharpe ratio (Hedges UMVUE)-1.376
 df171.000
 t-0.977
 p0.547
 Lowerbound of 95% confidence interval for Sharpe Ratio-4.156
 Upperbound of 95% confidence interval for Sharpe Ratio1.395
 Lowerbound of 95% CI (Gibbons, Hedeker & Davis approximation)-4.152
 Upperbound of 95% CI (Gibbons, Hedeker & Davis approximation)1.399
Statistics related to Sortino ratio
 Sortino ratio-1.884
 Upside Potential Ratio6.656
 Upside part of mean1.620
 Downside part of mean-2.078
 Upside SD0.225
 Downside SD0.243
 N nonnegative terms66.000
 N negative terms106.000
Statistics related to linear regression on benchmark
 N of observations172.000
 Mean of predictor0.261
 Mean of criterion-0.458
 SD of predictor0.124
 SD of criterion0.332
 Covariance-0.017
 r-0.416
 b (slope, estimate of beta)-1.109
 a (intercept, estimate of alpha)-0.169
 Mean Square Error0.091
 DF error170.000
 t(b)-5.968
 p(b)0.708
 t(a)-0.392
 p(a)0.515
 Lowerbound of 95% confidence interval for beta-1.476
 Upperbound of 95% confidence interval for beta-0.742
 Lowerbound of 95% confidence interval for alpha-1.018
 Upperbound of 95% confidence interval for alpha0.681
 Treynor index (mean / b)0.413
 Jensen alpha (a)-0.169
Ratio statistics of excess log return rates
Statistics related to Sharpe ratio
 Mean-0.513
 SD0.331
 Sharpe ratio (Glass type estimate) -1.549
 Sharpe ratio (Hedges UMVUE)-1.542
 df171.000
 t-1.095
 p0.553
 Lowerbound of 95% confidence interval for Sharpe Ratio-4.323
 Upperbound of 95% confidence interval for Sharpe Ratio1.230
 Lowerbound of 95% CI (Gibbons, Hedeker & Davis approximation)-4.318
 Upperbound of 95% CI (Gibbons, Hedeker & Davis approximation)1.235
Statistics related to Sortino ratio
 Sortino ratio-2.062
 Upside Potential Ratio6.408
 Upside part of mean1.595
 Downside part of mean-2.108
 Upside SD0.219
 Downside SD0.249
 N nonnegative terms66.000
 N negative terms106.000
Statistics related to linear regression on benchmark
 N of observations172.000
 Mean of predictor0.253
 Mean of criterion-0.513
 SD of predictor0.124
 SD of criterion0.331
 Covariance-0.017
 r-0.419
 b (slope, estimate of beta)-1.119
 a (intercept, estimate of alpha)-0.230
 Mean Square Error0.091
 DF error170.000
 t(b)-6.013
 p(b)0.709
 t(a)-0.535
 p(a)0.521
 Lowerbound of 95% confidence interval for beta-1.486
 Upperbound of 95% confidence interval for beta-0.751
 Lowerbound of 95% confidence interval for alpha-1.078
 Upperbound of 95% confidence interval for alpha0.618
 Treynor index (mean / b)0.459
 Jensen alpha (a)-0.230
Risk estimates for a one-period unit investment (parametric)
assuming log normal returns and losses (using central moments from Sharpe statistics)
 VaR(95%)0.030
 Expected Shortfall on VaR0.038
assuming Pareto losses only (using partial moments from Sortino statistics)
 VaR(95%)0.016
 Expected Shortfall on VaR0.031
ORDER STATISTICS
Quartiles of return rates
 Number of observations172.000
 Minimum0.923
 Quartile 10.994
 Median1.000
 Quartile 31.005
 Maximum1.094
 Mean of quarter 10.979
 Mean of quarter 20.997
 Mean of quarter 31.001
 Mean of quarter 41.018
 Inter Quartile Range0.012
 Number outliers low14.000
 Percentage of outliers low0.081
 Mean of outliers low0.962
 Number of outliers high9.000
 Percentage of outliers high0.052
 Mean of outliers high1.042
Risk estimates for a one-period unit investment (based on Extreme Value Theory)
 Extreme Value Index (moments method)0.295
 VaR(95%) (moments method)0.020
 Expected Shortfall (moments method)0.034
 Extreme Value Index (regression method)0.201
 VaR(95%) (regression method)0.022
 Expected Shortfall (regression method)0.036
DRAW DOWN STATISTICS
Quartiles of draw downs
 Number of observations3.000
 Minimum0.002
 Quartile 10.007
 Median0.011
 Quartile 30.115
 Maximum0.218
 Mean of quarter 10.002
 Mean of quarter 20.011
 Mean of quarter 3NA
 Mean of quarter 40.218
 Inter Quartile Range0.108
 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)-0.418
 Compounded annual return (geometric extrapolation)-0.375
 Calmar ratio (compounded annual return / max draw down)-1.716
 Compounded annual return / average of 25% largest draw downs-1.716
 Compounded annual return / Expected Shortfall lognormal-9.960