Advanced Statistics: Buzo Principle

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
 Mean0.056
 SD0.346
 Sharpe ratio (Glass type estimate) 0.162
 Sharpe ratio (Hedges UMVUE)0.160
 df62.000
 t0.371
 p0.356
 Lowerbound of 95% confidence interval for Sharpe Ratio-0.695
 Upperbound of 95% confidence interval for Sharpe Ratio1.017
 Lowerbound of 95% CI (Gibbons, Hedeker & Davis approximation)-0.696
 Upperbound of 95% CI (Gibbons, Hedeker & Davis approximation)1.016
Statistics related to Sortino ratio
 Sortino ratio0.192
 Upside Potential Ratio1.071
 Upside part of mean0.312
 Downside part of mean-0.256
 Upside SD0.183
 Downside SD0.291
 N nonnegative terms33.000
 N negative terms30.000
Statistics related to linear regression on benchmark
 N of observations63.000
 Mean of predictor0.212
 Mean of criterion0.056
 SD of predictor0.181
 SD of criterion0.346
 Covariance0.001
 r0.015
 b (slope, estimate of beta)0.029
 a (intercept, estimate of alpha)0.050
 Mean Square Error0.122
 DF error61.000
 t(b)0.117
 p(b)0.454
 t(a)0.311
 p(a)0.379
 Lowerbound of 95% confidence interval for beta-0.460
 Upperbound of 95% confidence interval for beta0.518
 Lowerbound of 95% confidence interval for alpha-0.272
 Upperbound of 95% confidence interval for alpha0.372
 Treynor index (mean / b)1.957
 Jensen alpha (a)0.050
Ratio statistics of excess log return rates
Statistics related to Sharpe ratio
 Mean-0.026
 SD0.447
 Sharpe ratio (Glass type estimate) -0.057
 Sharpe ratio (Hedges UMVUE)-0.056
 df62.000
 t-0.131
 p0.552
 Lowerbound of 95% confidence interval for Sharpe Ratio-0.912
 Upperbound of 95% confidence interval for Sharpe Ratio0.798
 Lowerbound of 95% CI (Gibbons, Hedeker & Davis approximation)-0.912
 Upperbound of 95% CI (Gibbons, Hedeker & Davis approximation)0.799
Statistics related to Sortino ratio
 Sortino ratio-0.062
 Upside Potential Ratio0.722
 Upside part of mean0.296
 Downside part of mean-0.321
 Upside SD0.169
 Downside SD0.410
 N nonnegative terms33.000
 N negative terms30.000
Statistics related to linear regression on benchmark
 N of observations63.000
 Mean of predictor0.194
 Mean of criterion-0.026
 SD of predictor0.177
 SD of criterion0.447
 Covariance-0.002
 r-0.021
 b (slope, estimate of beta)-0.053
 a (intercept, estimate of alpha)-0.015
 Mean Square Error0.203
 DF error61.000
 t(b)-0.163
 p(b)0.564
 t(a)-0.074
 p(a)0.530
 Lowerbound of 95% confidence interval for beta-0.698
 Upperbound of 95% confidence interval for beta0.593
 Lowerbound of 95% confidence interval for alpha-0.428
 Upperbound of 95% confidence interval for alpha0.397
 Treynor index (mean / b)0.487
 Jensen alpha (a)-0.015
Risk estimates for a one-period unit investment (parametric)
assuming log normal returns and losses (using central moments from Sharpe statistics)
 VaR(95%)0.193
 Expected Shortfall on VaR0.234
assuming Pareto losses only (using partial moments from Sortino statistics)
 VaR(95%)0.045
 Expected Shortfall on VaR0.106
ORDER STATISTICS
Quartiles of return rates
 Number of observations63.000
 Minimum0.429
 Quartile 11.000
 Median1.008
 Quartile 31.033
 Maximum1.250
 Mean of quarter 10.923
 Mean of quarter 21.001
 Mean of quarter 31.020
 Mean of quarter 41.090
 Inter Quartile Range0.033
 Number outliers low3.000
 Percentage of outliers low0.048
 Mean of outliers low0.681
 Number of outliers high8.000
 Percentage of outliers high0.127
 Mean of outliers high1.133
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)0.787
 VaR(95%) (regression method)0.051
 Expected Shortfall (regression method)0.314
DRAW DOWN STATISTICS
Quartiles of draw downs
 Number of observations11.000
 Minimum0.006
 Quartile 10.018
 Median0.040
 Quartile 30.044
 Maximum0.703
 Mean of quarter 10.010
 Mean of quarter 20.030
 Mean of quarter 30.042
 Mean of quarter 40.276
 Inter Quartile Range0.026
 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 high0.703
Risk estimates based on draw downs (based on Extreme Value Theory)
 Extreme Value Index (moments method)1.030
 VaR(95%) (moments method)0.248
 Expected Shortfall (moments method)NA
 Extreme Value Index (regression method)3.283
 VaR(95%) (regression method)1.059
 Expected Shortfall (regression method)NA
COMBINED STATISTICS
 Annualized return (arithmetic extrapolation)0.019
 Compounded annual return (geometric extrapolation)0.019
 Calmar ratio (compounded annual return / max draw down)0.027
 Compounded annual return / average of 25% largest draw downs0.068
 Compounded annual return / Expected Shortfall lognormal0.080
ANALYSIS BASED ON DAILY VALUES, FULL HISTORY (Back)
RATIO STATISTICS
Ratio statistics of excess return rates
Statistics related to Sharpe ratio
 Mean0.006
 SD0.247
 Sharpe ratio (Glass type estimate) 0.025
 Sharpe ratio (Hedges UMVUE)0.025
 df1809.000
 t0.058
 p0.499
 Lowerbound of 95% confidence interval for Sharpe Ratio-0.829
 Upperbound of 95% confidence interval for Sharpe Ratio0.880
 Lowerbound of 95% CI (Gibbons, Hedeker & Davis approximation)-0.829
 Upperbound of 95% CI (Gibbons, Hedeker & Davis approximation)0.880
Statistics related to Sortino ratio
 Sortino ratio0.031
 Upside Potential Ratio4.062
 Upside part of mean0.800
 Downside part of mean-0.794
 Upside SD0.149
 Downside SD0.197
 N nonnegative terms522.000
 N negative terms1288.000
Statistics related to linear regression on benchmark
 N of observations1810.000
 Mean of predictor0.210
 Mean of criterion0.006
 SD of predictor0.200
 SD of criterion0.247
 Covariance-0.001
 r-0.020
 b (slope, estimate of beta)-0.024
 a (intercept, estimate of alpha)0.011
 Mean Square Error0.061
 DF error1808.000
 t(b)-0.843
 p(b)0.510
 t(a)0.105
 p(a)0.499
 Lowerbound of 95% confidence interval for beta-0.081
 Upperbound of 95% confidence interval for beta0.032
 Lowerbound of 95% confidence interval for alpha-0.200
 Upperbound of 95% confidence interval for alpha0.223
 Treynor index (mean / b)-0.253
 Jensen alpha (a)0.011
Ratio statistics of excess log return rates
Statistics related to Sharpe ratio
 Mean-0.026
 SD0.255
 Sharpe ratio (Glass type estimate) -0.100
 Sharpe ratio (Hedges UMVUE)-0.100
 df1809.000
 t-0.230
 p0.503
 Lowerbound of 95% confidence interval for Sharpe Ratio-0.955
 Upperbound of 95% confidence interval for Sharpe Ratio0.754
 Lowerbound of 95% CI (Gibbons, Hedeker & Davis approximation)-0.955
 Upperbound of 95% CI (Gibbons, Hedeker & Davis approximation)0.754
Statistics related to Sortino ratio
 Sortino ratio-0.122
 Upside Potential Ratio3.747
 Upside part of mean0.789
 Downside part of mean-0.815
 Upside SD0.144
 Downside SD0.211
 N nonnegative terms522.000
 N negative terms1288.000
Statistics related to linear regression on benchmark
 N of observations1810.000
 Mean of predictor0.191
 Mean of criterion-0.026
 SD of predictor0.199
 SD of criterion0.255
 Covariance-0.001
 r-0.022
 b (slope, estimate of beta)-0.028
 a (intercept, estimate of alpha)-0.020
 Mean Square Error0.065
 DF error1808.000
 t(b)-0.926
 p(b)0.511
 t(a)-0.182
 p(a)0.502
 Lowerbound of 95% confidence interval for beta-0.087
 Upperbound of 95% confidence interval for beta0.031
 Lowerbound of 95% confidence interval for alpha-0.239
 Upperbound of 95% confidence interval for alpha0.198
 Treynor index (mean / b)0.919
 Jensen alpha (a)-0.020
Risk estimates for a one-period unit investment (parametric)
assuming log normal returns and losses (using central moments from Sharpe statistics)
 VaR(95%)0.022
 Expected Shortfall on VaR0.028
assuming Pareto losses only (using partial moments from Sortino statistics)
 VaR(95%)0.006
 Expected Shortfall on VaR0.015
ORDER STATISTICS
Quartiles of return rates
 Number of observations1810.000
 Minimum0.810
 Quartile 11.000
 Median1.000
 Quartile 31.001
 Maximum1.158
 Mean of quarter 10.991
 Mean of quarter 21.000
 Mean of quarter 31.000
 Mean of quarter 41.009
 Inter Quartile Range0.001
 Number outliers low281.000
 Percentage of outliers low0.155
 Mean of outliers low0.987
 Number of outliers high312.000
 Percentage of outliers high0.172
 Mean of outliers high1.013
Risk estimates for a one-period unit investment (based on Extreme Value Theory)
 Extreme Value Index (moments method)0.817
 VaR(95%) (moments method)0.006
 Expected Shortfall (moments method)0.036
 Extreme Value Index (regression method)0.547
 VaR(95%) (regression method)0.006
 Expected Shortfall (regression method)0.016
DRAW DOWN STATISTICS
Quartiles of draw downs
 Number of observations71.000
 Minimum0.000
 Quartile 10.003
 Median0.008
 Quartile 30.023
 Maximum0.703
 Mean of quarter 10.001
 Mean of quarter 20.005
 Mean of quarter 30.016
 Mean of quarter 40.093
 Inter Quartile Range0.020
 Number outliers low0.000
 Percentage of outliers low0.000
 Mean of outliers lowNA
 Number of outliers high11.000
 Percentage of outliers high0.155
 Mean of outliers high0.134
Risk estimates based on draw downs (based on Extreme Value Theory)
 Extreme Value Index (moments method)0.721
 VaR(95%) (moments method)0.089
 Expected Shortfall (moments method)0.338
 Extreme Value Index (regression method)0.541
 VaR(95%) (regression method)0.064
 Expected Shortfall (regression method)0.146
COMBINED STATISTICS
 Annualized return (arithmetic extrapolation)0.019
 Compounded annual return (geometric extrapolation)0.019
 Calmar ratio (compounded annual return / max draw down)0.026
 Compounded annual return / average of 25% largest draw downs0.200
 Compounded annual return / Expected Shortfall lognormal0.663
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 predictor0.182
 Mean of criterion-0.044
 SD of predictor0.261
 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 predictor0.148
 Mean of criterion-0.044
 SD of predictor0.261
 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)-5592900207261204.000
 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)-36580919067216844343179334385664.000
 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

Advanced Statistics: Buzo Principle

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
 Mean0.056
 SD0.346
 Sharpe ratio (Glass type estimate) 0.162
 Sharpe ratio (Hedges UMVUE)0.160
 df62.000
 t0.371
 p0.356
 Lowerbound of 95% confidence interval for Sharpe Ratio-0.695
 Upperbound of 95% confidence interval for Sharpe Ratio1.017
 Lowerbound of 95% CI (Gibbons, Hedeker & Davis approximation)-0.696
 Upperbound of 95% CI (Gibbons, Hedeker & Davis approximation)1.016
Statistics related to Sortino ratio
 Sortino ratio0.192
 Upside Potential Ratio1.071
 Upside part of mean0.312
 Downside part of mean-0.256
 Upside SD0.183
 Downside SD0.291
 N nonnegative terms33.000
 N negative terms30.000
Statistics related to linear regression on benchmark
 N of observations63.000
 Mean of predictor0.212
 Mean of criterion0.056
 SD of predictor0.181
 SD of criterion0.346
 Covariance0.001
 r0.015
 b (slope, estimate of beta)0.029
 a (intercept, estimate of alpha)0.050
 Mean Square Error0.122
 DF error61.000
 t(b)0.117
 p(b)0.454
 t(a)0.311
 p(a)0.379
 Lowerbound of 95% confidence interval for beta-0.460
 Upperbound of 95% confidence interval for beta0.518
 Lowerbound of 95% confidence interval for alpha-0.272
 Upperbound of 95% confidence interval for alpha0.372
 Treynor index (mean / b)1.957
 Jensen alpha (a)0.050
Ratio statistics of excess log return rates
Statistics related to Sharpe ratio
 Mean-0.026
 SD0.447
 Sharpe ratio (Glass type estimate) -0.057
 Sharpe ratio (Hedges UMVUE)-0.056
 df62.000
 t-0.131
 p0.552
 Lowerbound of 95% confidence interval for Sharpe Ratio-0.912
 Upperbound of 95% confidence interval for Sharpe Ratio0.798
 Lowerbound of 95% CI (Gibbons, Hedeker & Davis approximation)-0.912
 Upperbound of 95% CI (Gibbons, Hedeker & Davis approximation)0.799
Statistics related to Sortino ratio
 Sortino ratio-0.062
 Upside Potential Ratio0.722
 Upside part of mean0.296
 Downside part of mean-0.321
 Upside SD0.169
 Downside SD0.410
 N nonnegative terms33.000
 N negative terms30.000
Statistics related to linear regression on benchmark
 N of observations63.000
 Mean of predictor0.194
 Mean of criterion-0.026
 SD of predictor0.177
 SD of criterion0.447
 Covariance-0.002
 r-0.021
 b (slope, estimate of beta)-0.053
 a (intercept, estimate of alpha)-0.015
 Mean Square Error0.203
 DF error61.000
 t(b)-0.163
 p(b)0.564
 t(a)-0.074
 p(a)0.530
 Lowerbound of 95% confidence interval for beta-0.698
 Upperbound of 95% confidence interval for beta0.593
 Lowerbound of 95% confidence interval for alpha-0.428
 Upperbound of 95% confidence interval for alpha0.397
 Treynor index (mean / b)0.487
 Jensen alpha (a)-0.015
Risk estimates for a one-period unit investment (parametric)
assuming log normal returns and losses (using central moments from Sharpe statistics)
 VaR(95%)0.193
 Expected Shortfall on VaR0.234
assuming Pareto losses only (using partial moments from Sortino statistics)
 VaR(95%)0.045
 Expected Shortfall on VaR0.106
ORDER STATISTICS
Quartiles of return rates
 Number of observations63.000
 Minimum0.429
 Quartile 11.000
 Median1.008
 Quartile 31.033
 Maximum1.250
 Mean of quarter 10.923
 Mean of quarter 21.001
 Mean of quarter 31.020
 Mean of quarter 41.090
 Inter Quartile Range0.033
 Number outliers low3.000
 Percentage of outliers low0.048
 Mean of outliers low0.681
 Number of outliers high8.000
 Percentage of outliers high0.127
 Mean of outliers high1.133
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)0.787
 VaR(95%) (regression method)0.051
 Expected Shortfall (regression method)0.314
DRAW DOWN STATISTICS
Quartiles of draw downs
 Number of observations11.000
 Minimum0.006
 Quartile 10.018
 Median0.040
 Quartile 30.044
 Maximum0.703
 Mean of quarter 10.010
 Mean of quarter 20.030
 Mean of quarter 30.042
 Mean of quarter 40.276
 Inter Quartile Range0.026
 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 high0.703
Risk estimates based on draw downs (based on Extreme Value Theory)
 Extreme Value Index (moments method)1.030
 VaR(95%) (moments method)0.248
 Expected Shortfall (moments method)NA
 Extreme Value Index (regression method)3.283
 VaR(95%) (regression method)1.059
 Expected Shortfall (regression method)NA
COMBINED STATISTICS
 Annualized return (arithmetic extrapolation)0.019
 Compounded annual return (geometric extrapolation)0.019
 Calmar ratio (compounded annual return / max draw down)0.027
 Compounded annual return / average of 25% largest draw downs0.068
 Compounded annual return / Expected Shortfall lognormal0.080
ANALYSIS BASED ON DAILY VALUES, FULL HISTORY (Back)
RATIO STATISTICS
Ratio statistics of excess return rates
Statistics related to Sharpe ratio
 Mean0.006
 SD0.247
 Sharpe ratio (Glass type estimate) 0.025
 Sharpe ratio (Hedges UMVUE)0.025
 df1809.000
 t0.058
 p0.499
 Lowerbound of 95% confidence interval for Sharpe Ratio-0.829
 Upperbound of 95% confidence interval for Sharpe Ratio0.880
 Lowerbound of 95% CI (Gibbons, Hedeker & Davis approximation)-0.829
 Upperbound of 95% CI (Gibbons, Hedeker & Davis approximation)0.880
Statistics related to Sortino ratio
 Sortino ratio0.031
 Upside Potential Ratio4.062
 Upside part of mean0.800
 Downside part of mean-0.794
 Upside SD0.149
 Downside SD0.197
 N nonnegative terms522.000
 N negative terms1288.000
Statistics related to linear regression on benchmark
 N of observations1810.000
 Mean of predictor0.210
 Mean of criterion0.006
 SD of predictor0.200
 SD of criterion0.247
 Covariance-0.001
 r-0.020
 b (slope, estimate of beta)-0.024
 a (intercept, estimate of alpha)0.011
 Mean Square Error0.061
 DF error1808.000
 t(b)-0.843
 p(b)0.510
 t(a)0.105
 p(a)0.499
 Lowerbound of 95% confidence interval for beta-0.081
 Upperbound of 95% confidence interval for beta0.032
 Lowerbound of 95% confidence interval for alpha-0.200
 Upperbound of 95% confidence interval for alpha0.223
 Treynor index (mean / b)-0.253
 Jensen alpha (a)0.011
Ratio statistics of excess log return rates
Statistics related to Sharpe ratio
 Mean-0.026
 SD0.255
 Sharpe ratio (Glass type estimate) -0.100
 Sharpe ratio (Hedges UMVUE)-0.100
 df1809.000
 t-0.230
 p0.503
 Lowerbound of 95% confidence interval for Sharpe Ratio-0.955
 Upperbound of 95% confidence interval for Sharpe Ratio0.754
 Lowerbound of 95% CI (Gibbons, Hedeker & Davis approximation)-0.955
 Upperbound of 95% CI (Gibbons, Hedeker & Davis approximation)0.754
Statistics related to Sortino ratio
 Sortino ratio-0.122
 Upside Potential Ratio3.747
 Upside part of mean0.789
 Downside part of mean-0.815
 Upside SD0.144
 Downside SD0.211
 N nonnegative terms522.000
 N negative terms1288.000
Statistics related to linear regression on benchmark
 N of observations1810.000
 Mean of predictor0.191
 Mean of criterion-0.026
 SD of predictor0.199
 SD of criterion0.255
 Covariance-0.001
 r-0.022
 b (slope, estimate of beta)-0.028
 a (intercept, estimate of alpha)-0.020
 Mean Square Error0.065
 DF error1808.000
 t(b)-0.926
 p(b)0.511
 t(a)-0.182
 p(a)0.502
 Lowerbound of 95% confidence interval for beta-0.087
 Upperbound of 95% confidence interval for beta0.031
 Lowerbound of 95% confidence interval for alpha-0.239
 Upperbound of 95% confidence interval for alpha0.198
 Treynor index (mean / b)0.919
 Jensen alpha (a)-0.020
Risk estimates for a one-period unit investment (parametric)
assuming log normal returns and losses (using central moments from Sharpe statistics)
 VaR(95%)0.022
 Expected Shortfall on VaR0.028
assuming Pareto losses only (using partial moments from Sortino statistics)
 VaR(95%)0.006
 Expected Shortfall on VaR0.015
ORDER STATISTICS
Quartiles of return rates
 Number of observations1810.000
 Minimum0.810
 Quartile 11.000
 Median1.000
 Quartile 31.001
 Maximum1.158
 Mean of quarter 10.991
 Mean of quarter 21.000
 Mean of quarter 31.000
 Mean of quarter 41.009
 Inter Quartile Range0.001
 Number outliers low281.000
 Percentage of outliers low0.155
 Mean of outliers low0.987
 Number of outliers high312.000
 Percentage of outliers high0.172
 Mean of outliers high1.013
Risk estimates for a one-period unit investment (based on Extreme Value Theory)
 Extreme Value Index (moments method)0.817
 VaR(95%) (moments method)0.006
 Expected Shortfall (moments method)0.036
 Extreme Value Index (regression method)0.547
 VaR(95%) (regression method)0.006
 Expected Shortfall (regression method)0.016
DRAW DOWN STATISTICS
Quartiles of draw downs
 Number of observations71.000
 Minimum0.000
 Quartile 10.003
 Median0.008
 Quartile 30.023
 Maximum0.703
 Mean of quarter 10.001
 Mean of quarter 20.005
 Mean of quarter 30.016
 Mean of quarter 40.093
 Inter Quartile Range0.020
 Number outliers low0.000
 Percentage of outliers low0.000
 Mean of outliers lowNA
 Number of outliers high11.000
 Percentage of outliers high0.155
 Mean of outliers high0.134
Risk estimates based on draw downs (based on Extreme Value Theory)
 Extreme Value Index (moments method)0.721
 VaR(95%) (moments method)0.089
 Expected Shortfall (moments method)0.338
 Extreme Value Index (regression method)0.541
 VaR(95%) (regression method)0.064
 Expected Shortfall (regression method)0.146
COMBINED STATISTICS
 Annualized return (arithmetic extrapolation)0.019
 Compounded annual return (geometric extrapolation)0.019
 Calmar ratio (compounded annual return / max draw down)0.026
 Compounded annual return / average of 25% largest draw downs0.200
 Compounded annual return / Expected Shortfall lognormal0.663
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 predictor0.182
 Mean of criterion-0.044
 SD of predictor0.261
 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 predictor0.148
 Mean of criterion-0.044
 SD of predictor0.261
 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)-5592900207261204.000
 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)-36580919067216844343179334385664.000
 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