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Advanced Statistics: OS Long Only 2

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-0.130
 SD0.229
 Sharpe ratio (Glass type estimate) -0.567
 Sharpe ratio (Hedges UMVUE)-0.543
 df18.000
 t-0.714
 p0.583
 Lowerbound of 95% confidence interval for Sharpe Ratio-2.128
 Upperbound of 95% confidence interval for Sharpe Ratio1.009
 Lowerbound of 95% CI (Gibbons, Hedeker & Davis approximation)-2.111
 Upperbound of 95% CI (Gibbons, Hedeker & Davis approximation)1.024
Statistics related to Sortino ratio
 Sortino ratio-0.635
 Upside Potential Ratio0.599
 Upside part of mean0.122
 Downside part of mean-0.252
 Upside SD0.096
 Downside SD0.204
 N nonnegative terms7.000
 N negative terms12.000
Statistics related to linear regression on benchmark
 N of observations19.000
 Mean of predictor0.089
 Mean of criterion-0.130
 SD of predictor0.149
 SD of criterion0.229
 Covariance0.016
 r0.463
 b (slope, estimate of beta)0.712
 a (intercept, estimate of alpha)-0.193
 Mean Square Error0.044
 DF error17.000
 t(b)2.156
 p(b)0.216
 t(a)-1.147
 p(a)0.669
 Lowerbound of 95% confidence interval for beta0.015
 Upperbound of 95% confidence interval for beta1.408
 Lowerbound of 95% confidence interval for alpha-0.548
 Upperbound of 95% confidence interval for alpha0.162
 Treynor index (mean / b)-0.182
 Jensen alpha (a)-0.193
Ratio statistics of excess log return rates
Statistics related to Sharpe ratio
 Mean-0.157
 SD0.245
 Sharpe ratio (Glass type estimate) -0.643
 Sharpe ratio (Hedges UMVUE)-0.615
 df18.000
 t-0.809
 p0.594
 Lowerbound of 95% confidence interval for Sharpe Ratio-2.205
 Upperbound of 95% confidence interval for Sharpe Ratio0.938
 Lowerbound of 95% CI (Gibbons, Hedeker & Davis approximation)-2.186
 Upperbound of 95% CI (Gibbons, Hedeker & Davis approximation)0.955
Statistics related to Sortino ratio
 Sortino ratio-0.700
 Upside Potential Ratio0.523
 Upside part of mean0.118
 Downside part of mean-0.275
 Upside SD0.091
 Downside SD0.225
 N nonnegative terms7.000
 N negative terms12.000
Statistics related to linear regression on benchmark
 N of observations19.000
 Mean of predictor0.078
 Mean of criterion-0.157
 SD of predictor0.150
 SD of criterion0.245
 Covariance0.017
 r0.472
 b (slope, estimate of beta)0.770
 a (intercept, estimate of alpha)-0.217
 Mean Square Error0.049
 DF error17.000
 t(b)2.210
 p(b)0.211
 t(a)-1.217
 p(a)0.678
 Lowerbound of 95% confidence interval for beta0.035
 Upperbound of 95% confidence interval for beta1.506
 Lowerbound of 95% confidence interval for alpha-0.594
 Upperbound of 95% confidence interval for alpha0.159
 Treynor index (mean / b)-0.204
 Jensen alpha (a)-0.217
Risk estimates for a one-period unit investment (parametric)
assuming log normal returns and losses (using central moments from Sharpe statistics)
 VaR(95%)0.121
 Expected Shortfall on VaR0.147
assuming Pareto losses only (using partial moments from Sortino statistics)
 VaR(95%)0.055
 Expected Shortfall on VaR0.117
ORDER STATISTICS
Quartiles of return rates
 Number of observations19.000
 Minimum0.812
 Quartile 11.000
 Median1.000
 Quartile 31.008
 Maximum1.116
 Mean of quarter 10.928
 Mean of quarter 21.000
 Mean of quarter 31.004
 Mean of quarter 41.041
 Inter Quartile Range0.008
 Number outliers low2.000
 Percentage of outliers low0.105
 Mean of outliers low0.822
 Number of outliers high3.000
 Percentage of outliers high0.158
 Mean of outliers high1.062
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)0.222
 VaR(95%) (regression method)0.055
 Expected Shortfall (regression method)0.114
DRAW DOWN STATISTICS
Quartiles of draw downs
 Number of observations2.000
 Minimum0.003
 Quartile 10.083
 Median0.163
 Quartile 30.243
 Maximum0.323
 Mean of quarter 10.003
 Mean of quarter 2NA
 Mean of quarter 3NA
 Mean of quarter 40.323
 Inter Quartile Range0.160
 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)-0.107
 Calmar ratio (compounded annual return / max draw down)-0.331
 Compounded annual return / average of 25% largest draw downs-0.331
 Compounded annual return / Expected Shortfall lognormal-0.731
ANALYSIS BASED ON DAILY VALUES, FULL HISTORY (Back)
RATIO STATISTICS
Ratio statistics of excess return rates
Statistics related to Sharpe ratio
 Mean-0.140
 SD0.161
 Sharpe ratio (Glass type estimate) -0.872
 Sharpe ratio (Hedges UMVUE)-0.870
 df561.000
 t-1.114
 p0.867
 Lowerbound of 95% confidence interval for Sharpe Ratio-2.405
 Upperbound of 95% confidence interval for Sharpe Ratio0.663
 Lowerbound of 95% CI (Gibbons, Hedeker & Davis approximation)-2.405
 Upperbound of 95% CI (Gibbons, Hedeker & Davis approximation)0.664
Statistics related to Sortino ratio
 Sortino ratio-1.009
 Upside Potential Ratio3.635
 Upside part of mean0.506
 Downside part of mean-0.646
 Upside SD0.081
 Downside SD0.139
 N nonnegative terms143.000
 N negative terms419.000
Statistics related to linear regression on benchmark
 N of observations562.000
 Mean of predictor0.192
 Mean of criterion-0.140
 SD of predictor0.211
 SD of criterion0.161
 Covariance0.012
 r0.349
 b (slope, estimate of beta)0.267
 a (intercept, estimate of alpha)-0.192
 Mean Square Error0.023
 DF error560.000
 t(b)8.817
 p(b)0.000
 t(a)-1.619
 p(a)0.947
 Lowerbound of 95% confidence interval for beta0.207
 Upperbound of 95% confidence interval for beta0.326
 Lowerbound of 95% confidence interval for alpha-0.424
 Upperbound of 95% confidence interval for alpha0.041
 Treynor index (mean / b)-0.527
 Jensen alpha (a)-0.192
Ratio statistics of excess log return rates
Statistics related to Sharpe ratio
 Mean-0.154
 SD0.164
 Sharpe ratio (Glass type estimate) -0.935
 Sharpe ratio (Hedges UMVUE)-0.934
 df561.000
 t-1.195
 p0.884
 Lowerbound of 95% confidence interval for Sharpe Ratio-2.469
 Upperbound of 95% confidence interval for Sharpe Ratio0.600
 Lowerbound of 95% CI (Gibbons, Hedeker & Davis approximation)-2.468
 Upperbound of 95% CI (Gibbons, Hedeker & Davis approximation)0.601
Statistics related to Sortino ratio
 Sortino ratio-1.071
 Upside Potential Ratio3.502
 Upside part of mean0.503
 Downside part of mean-0.656
 Upside SD0.080
 Downside SD0.144
 N nonnegative terms143.000
 N negative terms419.000
Statistics related to linear regression on benchmark
 N of observations562.000
 Mean of predictor0.170
 Mean of criterion-0.154
 SD of predictor0.211
 SD of criterion0.164
 Covariance0.012
 r0.350
 b (slope, estimate of beta)0.272
 a (intercept, estimate of alpha)-0.200
 Mean Square Error0.024
 DF error560.000
 t(b)8.834
 p(b)0.000
 t(a)-1.656
 p(a)0.951
 Lowerbound of 95% confidence interval for beta0.212
 Upperbound of 95% confidence interval for beta0.333
 Lowerbound of 95% confidence interval for alpha-0.437
 Upperbound of 95% confidence interval for alpha0.037
 Treynor index (mean / b)-0.565
 Jensen alpha (a)-0.200
Risk estimates for a one-period unit investment (parametric)
assuming log normal returns and losses (using central moments from Sharpe statistics)
 VaR(95%)0.015
 Expected Shortfall on VaR0.019
assuming Pareto losses only (using partial moments from Sortino statistics)
 VaR(95%)0.005
 Expected Shortfall on VaR0.012
ORDER STATISTICS
Quartiles of return rates
 Number of observations562.000
 Minimum0.916
 Quartile 11.000
 Median1.000
 Quartile 31.000
 Maximum1.034
 Mean of quarter 10.993
 Mean of quarter 21.000
 Mean of quarter 31.000
 Mean of quarter 41.006
 Inter Quartile Range0.000
 Number outliers low118.000
 Percentage of outliers low0.210
 Mean of outliers low0.992
 Number of outliers high126.000
 Percentage of outliers high0.224
 Mean of outliers high1.007
Risk estimates for a one-period unit investment (based on Extreme Value Theory)
 Extreme Value Index (moments method)0.670
 VaR(95%) (moments method)0.004
 Expected Shortfall (moments method)0.016
 Extreme Value Index (regression method)0.472
 VaR(95%) (regression method)0.005
 Expected Shortfall (regression method)0.014
DRAW DOWN STATISTICS
Quartiles of draw downs
 Number of observations17.000
 Minimum0.000
 Quartile 10.004
 Median0.016
 Quartile 30.026
 Maximum0.381
 Mean of quarter 10.002
 Mean of quarter 20.010
 Mean of quarter 30.022
 Mean of quarter 40.129
 Inter Quartile Range0.022
 Number outliers low0.000
 Percentage of outliers low0.000
 Mean of outliers lowNA
 Number of outliers high1.000
 Percentage of outliers high0.059
 Mean of outliers high0.381
Risk estimates based on draw downs (based on Extreme Value Theory)
 Extreme Value Index (moments method)0.920
 VaR(95%) (moments method)0.122
 Expected Shortfall (moments method)1.575
 Extreme Value Index (regression method)1.795
 VaR(95%) (regression method)0.154
 Expected Shortfall (regression method)NA
COMBINED STATISTICS
 Annualized return (arithmetic extrapolation)-0.100
 Compounded annual return (geometric extrapolation)-0.104
 Calmar ratio (compounded annual return / max draw down)-0.273
 Compounded annual return / average of 25% largest draw downs-0.803
 Compounded annual return / Expected Shortfall lognormal-5.601
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) -2603.134
 Sharpe ratio (Hedges UMVUE)-2591.700
 df171.000
 t-1840.693
 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)-2866.389
 Upperbound of 95% CI (Gibbons, Hedeker & Davis approximation)-2317.010
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 predictor0.495
 Mean of criterion-0.044
 SD of predictor0.182
 SD of criterion0.000
 Covariance-0.000
 r-0.063
 b (slope, estimate of beta)-0.000
 a (intercept, estimate of alpha)-0.044
 Mean Square Error0.000
 DF error170.000
 t(b)-0.827
 p(b)0.532
 t(a)-1819.423
 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)7499.475
 Jensen alpha (a)-0.044
Ratio statistics of excess log return rates
Statistics related to Sharpe ratio
 Mean-0.044
 SD0.000
 Sharpe ratio (Glass type estimate) -2602.952
 Sharpe ratio (Hedges UMVUE)-2591.518
 df171.000
 t-1840.565
 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)-2866.188
 Upperbound of 95% CI (Gibbons, Hedeker & Davis approximation)-2316.848
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 predictor0.478
 Mean of criterion-0.044
 SD of predictor0.182
 SD of criterion0.000
 Covariance-0.000
 r-0.063
 b (slope, estimate of beta)-0.000
 a (intercept, estimate of alpha)-0.044
 Mean Square Error0.000
 DF error170.000
 t(b)-0.830
 p(b)0.532
 t(a)-1820.525
 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)7463.313
 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 low1.000
 Percentage of outliers low0.006
 Mean of outliers low1.000
 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
 Minimum0.000
 Quartile 10.000
 Median0.000
 Quartile 30.000
 Maximum0.000
 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)-0.000
 Compounded annual return (geometric extrapolation)-0.000
 Calmar ratio (compounded annual return / max draw down)-2.000
 Compounded annual return / average of 25% largest draw downsNA
 Compounded annual return / Expected Shortfall lognormal-0.184