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Advanced Statistics: Cambist Fund

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-0.484
 SD0.401
 Sharpe ratio (Glass type estimate) -1.205
 Sharpe ratio (Hedges UMVUE)-1.102
 df9.000
 t-1.100
 p0.850
 Lowerbound of 95% confidence interval for Sharpe Ratio-3.390
 Upperbound of 95% confidence interval for Sharpe Ratio1.042
 Lowerbound of 95% CI (Gibbons, Hedeker & Davis approximation)-3.308
 Upperbound of 95% CI (Gibbons, Hedeker & Davis approximation)1.105
Statistics related to Sortino ratio
 Sortino ratio-1.193
 Upside Potential Ratio0.000
 Upside part of mean0.000
 Downside part of mean-0.484
 Upside SD0.000
 Downside SD0.405
 N nonnegative terms0.000
 N negative terms10.000
Statistics related to linear regression on benchmark
 N of observations10.000
 Mean of predictor0.169
 Mean of criterion-0.484
 SD of predictor0.236
 SD of criterion0.401
 Covariance-0.023
 r-0.245
 b (slope, estimate of beta)-0.417
 a (intercept, estimate of alpha)-0.413
 Mean Square Error0.170
 DF error8.000
 t(b)-0.715
 p(b)0.753
 t(a)-0.893
 p(a)0.801
 Lowerbound of 95% confidence interval for beta-1.763
 Upperbound of 95% confidence interval for beta0.929
 Lowerbound of 95% confidence interval for alpha-1.480
 Upperbound of 95% confidence interval for alpha0.654
 Treynor index (mean / b)1.158
 Jensen alpha (a)-0.413
Ratio statistics of excess log return rates
Statistics related to Sharpe ratio
 Mean-0.591
 SD0.500
 Sharpe ratio (Glass type estimate) -1.184
 Sharpe ratio (Hedges UMVUE)-1.082
 df9.000
 t-1.080
 p0.846
 Lowerbound of 95% confidence interval for Sharpe Ratio-3.367
 Upperbound of 95% confidence interval for Sharpe Ratio1.060
 Lowerbound of 95% CI (Gibbons, Hedeker & Davis approximation)-3.286
 Upperbound of 95% CI (Gibbons, Hedeker & Davis approximation)1.123
Statistics related to Sortino ratio
 Sortino ratio-1.174
 Upside Potential Ratio0.000
 Upside part of mean0.000
 Downside part of mean-0.591
 Upside SD0.000
 Downside SD0.504
 N nonnegative terms0.000
 N negative terms10.000
Statistics related to linear regression on benchmark
 N of observations10.000
 Mean of predictor0.143
 Mean of criterion-0.591
 SD of predictor0.232
 SD of criterion0.500
 Covariance-0.029
 r-0.249
 b (slope, estimate of beta)-0.536
 a (intercept, estimate of alpha)-0.515
 Mean Square Error0.263
 DF error8.000
 t(b)-0.728
 p(b)0.756
 t(a)-0.900
 p(a)0.803
 Lowerbound of 95% confidence interval for beta-2.235
 Upperbound of 95% confidence interval for beta1.162
 Lowerbound of 95% confidence interval for alpha-1.834
 Upperbound of 95% confidence interval for alpha0.804
 Treynor index (mean / b)1.102
 Jensen alpha (a)-0.515
Risk estimates for a one-period unit investment (parametric)
assuming log normal returns and losses (using central moments from Sharpe statistics)
 VaR(95%)0.249
 Expected Shortfall on VaR0.292
assuming Pareto losses only (using partial moments from Sortino statistics)
 VaR(95%)0.140
 Expected Shortfall on VaR0.288
ORDER STATISTICS
Quartiles of return rates
 Number of observations10.000
 Minimum0.634
 Quartile 11.000
 Median1.000
 Quartile 31.000
 Maximum1.000
 Mean of quarter 10.878
 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 low0.100
 Mean of outliers low0.634
 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
 Minimum0.366
 Quartile 10.366
 Median0.366
 Quartile 30.366
 Maximum0.366
 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)-0.440
 Compounded annual return (geometric extrapolation)-0.422
 Calmar ratio (compounded annual return / max draw down)-1.151
 Compounded annual return / average of 25% largest draw downsNA
 Compounded annual return / Expected Shortfall lognormal-1.443
ANALYSIS BASED ON DAILY VALUES, FULL HISTORY (Back)
RATIO STATISTICS
Ratio statistics of excess return rates
Statistics related to Sharpe ratio
 Mean-0.516
 SD0.253
 Sharpe ratio (Glass type estimate) -2.035
 Sharpe ratio (Hedges UMVUE)-2.030
 df309.000
 t-1.931
 p0.973
 Lowerbound of 95% confidence interval for Sharpe Ratio-4.104
 Upperbound of 95% confidence interval for Sharpe Ratio0.038
 Lowerbound of 95% CI (Gibbons, Hedeker & Davis approximation)-4.100
 Upperbound of 95% CI (Gibbons, Hedeker & Davis approximation)0.041
Statistics related to Sortino ratio
 Sortino ratio-2.130
 Upside Potential Ratio0.832
 Upside part of mean0.201
 Downside part of mean-0.717
 Upside SD0.079
 Downside SD0.242
 N nonnegative terms7.000
 N negative terms303.000
Statistics related to linear regression on benchmark
 N of observations310.000
 Mean of predictor0.341
 Mean of criterion-0.516
 SD of predictor0.275
 SD of criterion0.253
 Covariance0.001
 r0.020
 b (slope, estimate of beta)0.018
 a (intercept, estimate of alpha)-0.522
 Mean Square Error0.064
 DF error308.000
 t(b)0.346
 p(b)0.365
 t(a)-1.947
 p(a)0.974
 Lowerbound of 95% confidence interval for beta-0.085
 Upperbound of 95% confidence interval for beta0.121
 Lowerbound of 95% confidence interval for alpha-1.049
 Upperbound of 95% confidence interval for alpha0.005
 Treynor index (mean / b)-28.442
 Jensen alpha (a)-0.522
Ratio statistics of excess log return rates
Statistics related to Sharpe ratio
 Mean-0.550
 SD0.266
 Sharpe ratio (Glass type estimate) -2.065
 Sharpe ratio (Hedges UMVUE)-2.060
 df309.000
 t-1.960
 p0.975
 Lowerbound of 95% confidence interval for Sharpe Ratio-4.134
 Upperbound of 95% confidence interval for Sharpe Ratio0.008
 Lowerbound of 95% CI (Gibbons, Hedeker & Davis approximation)-4.131
 Upperbound of 95% CI (Gibbons, Hedeker & Davis approximation)0.011
Statistics related to Sortino ratio
 Sortino ratio-2.147
 Upside Potential Ratio0.774
 Upside part of mean0.198
 Downside part of mean-0.748
 Upside SD0.077
 Downside SD0.256
 N nonnegative terms7.000
 N negative terms303.000
Statistics related to linear regression on benchmark
 N of observations310.000
 Mean of predictor0.303
 Mean of criterion-0.550
 SD of predictor0.276
 SD of criterion0.266
 Covariance0.001
 r0.018
 b (slope, estimate of beta)0.017
 a (intercept, estimate of alpha)-0.555
 Mean Square Error0.071
 DF error308.000
 t(b)0.312
 p(b)0.378
 t(a)-1.972
 p(a)0.975
 Lowerbound of 95% confidence interval for beta-0.091
 Upperbound of 95% confidence interval for beta0.125
 Lowerbound of 95% confidence interval for alpha-1.109
 Upperbound of 95% confidence interval for alpha-0.001
 Treynor index (mean / b)-32.052
 Jensen alpha (a)-0.555
Risk estimates for a one-period unit investment (parametric)
assuming log normal returns and losses (using central moments from Sharpe statistics)
 VaR(95%)0.025
 Expected Shortfall on VaR0.031
assuming Pareto losses only (using partial moments from Sortino statistics)
 VaR(95%)0.007
 Expected Shortfall on VaR0.016
ORDER STATISTICS
Quartiles of return rates
 Number of observations310.000
 Minimum0.870
 Quartile 11.000
 Median1.000
 Quartile 31.000
 Maximum1.046
 Mean of quarter 10.992
 Mean of quarter 21.000
 Mean of quarter 31.000
 Mean of quarter 41.002
 Inter Quartile Range0.000
 Number outliers low12.000
 Percentage of outliers low0.039
 Mean of outliers low0.949
 Number of outliers high7.000
 Percentage of outliers high0.023
 Mean of outliers high1.026
Risk estimates for a one-period unit investment (based on Extreme Value Theory)
 Extreme Value Index (moments method)-7.427
 VaR(95%) (moments method)-0.046
 Expected Shortfall (moments method)NA
 Extreme Value Index (regression method)-0.827
 VaR(95%) (regression method)-0.020
 Expected Shortfall (regression method)NA
DRAW DOWN STATISTICS
Quartiles of draw downs
 Number of observations2.000
 Minimum0.001
 Quartile 10.108
 Median0.215
 Quartile 30.322
 Maximum0.429
 Mean of quarter 10.001
 Mean of quarter 2NA
 Mean of quarter 3NA
 Mean of quarter 40.429
 Inter Quartile Range0.214
 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)-0.406
 Compounded annual return (geometric extrapolation)-0.397
 Calmar ratio (compounded annual return / max draw down)-0.926
 Compounded annual return / average of 25% largest draw downs-0.926
 Compounded annual return / Expected Shortfall lognormal-12.922
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 predictor0.629
 Mean of criterion-0.044
 SD of predictor0.268
 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 predictor0.593
 Mean of criterion-0.044
 SD of predictor0.268
 SD of criterion0.000
 Covariance0.000
 r0.000
 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)-5555914004748505.000
 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)-231756525449348717820757252505600.000
 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