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
 Mean0.063
 SD0.358
 Sharpe ratio (Glass type estimate) 0.176
 Sharpe ratio (Hedges UMVUE)0.173
 df58.000
 t0.389
 p0.349
 Lowerbound of 95% confidence interval for Sharpe Ratio-0.710
 Upperbound of 95% confidence interval for Sharpe Ratio1.059
 Lowerbound of 95% CI (Gibbons, Hedeker & Davis approximation)-0.711
 Upperbound of 95% CI (Gibbons, Hedeker & Davis approximation)1.058
Statistics related to Sortino ratio
 Sortino ratio0.209
 Upside Potential Ratio1.107
 Upside part of mean0.333
 Downside part of mean-0.270
 Upside SD0.189
 Downside SD0.301
 N nonnegative terms33.000
 N negative terms26.000
Statistics related to linear regression on benchmark
 N of observations59.000
 Mean of predictor0.195
 Mean of criterion0.063
 SD of predictor0.179
 SD of criterion0.358
 Covariance0.001
 r0.018
 b (slope, estimate of beta)0.036
 a (intercept, estimate of alpha)0.056
 Mean Square Error0.130
 DF error57.000
 t(b)0.136
 p(b)0.446
 t(a)0.327
 p(a)0.372
 Lowerbound of 95% confidence interval for beta-0.493
 Upperbound of 95% confidence interval for beta0.565
 Lowerbound of 95% confidence interval for alpha-0.286
 Upperbound of 95% confidence interval for alpha0.398
 Treynor index (mean / b)1.747
 Jensen alpha (a)0.056
Ratio statistics of excess log return rates
Statistics related to Sharpe ratio
 Mean-0.024
 SD0.462
 Sharpe ratio (Glass type estimate) -0.053
 Sharpe ratio (Hedges UMVUE)-0.052
 df58.000
 t-0.117
 p0.546
 Lowerbound of 95% confidence interval for Sharpe Ratio-0.936
 Upperbound of 95% confidence interval for Sharpe Ratio0.832
 Lowerbound of 95% CI (Gibbons, Hedeker & Davis approximation)-0.936
 Upperbound of 95% CI (Gibbons, Hedeker & Davis approximation)0.832
Statistics related to Sortino ratio
 Sortino ratio-0.057
 Upside Potential Ratio0.746
 Upside part of mean0.316
 Downside part of mean-0.340
 Upside SD0.175
 Downside SD0.423
 N nonnegative terms33.000
 N negative terms26.000
Statistics related to linear regression on benchmark
 N of observations59.000
 Mean of predictor0.178
 Mean of criterion-0.024
 SD of predictor0.175
 SD of criterion0.462
 Covariance-0.002
 r-0.021
 b (slope, estimate of beta)-0.056
 a (intercept, estimate of alpha)-0.014
 Mean Square Error0.217
 DF error57.000
 t(b)-0.161
 p(b)0.564
 t(a)-0.065
 p(a)0.526
 Lowerbound of 95% confidence interval for beta-0.755
 Upperbound of 95% confidence interval for beta0.642
 Lowerbound of 95% confidence interval for alpha-0.453
 Upperbound of 95% confidence interval for alpha0.424
 Treynor index (mean / b)0.431
 Jensen alpha (a)-0.014
Risk estimates for a one-period unit investment (parametric)
assuming log normal returns and losses (using central moments from Sharpe statistics)
 VaR(95%)0.199
 Expected Shortfall on VaR0.241
assuming Pareto losses only (using partial moments from Sortino statistics)
 VaR(95%)0.045
 Expected Shortfall on VaR0.107
ORDER STATISTICS
Quartiles of return rates
 Number of observations59.000
 Minimum0.429
 Quartile 10.997
 Median1.012
 Quartile 31.035
 Maximum1.250
 Mean of quarter 10.917
 Mean of quarter 21.003
 Mean of quarter 31.022
 Mean of quarter 41.094
 Inter Quartile Range0.038
 Number outliers low3.000
 Percentage of outliers low0.051
 Mean of outliers low0.681
 Number of outliers high5.000
 Percentage of outliers high0.085
 Mean of outliers high1.161
Risk estimates for a one-period unit investment (based on Extreme Value Theory)
 Extreme Value Index (moments method)1.182
 VaR(95%) (moments method)0.054
 Expected Shortfall (moments method)NA
 Extreme Value Index (regression method)0.987
 VaR(95%) (regression method)0.054
 Expected Shortfall (regression method)4.759
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)0.021
 Compounded annual return (geometric extrapolation)0.020
 Calmar ratio (compounded annual return / max draw down)0.028
 Compounded annual return / average of 25% largest draw downs0.072
 Compounded annual return / Expected Shortfall lognormal0.083
ANALYSIS BASED ON DAILY VALUES, FULL HISTORY (Back)
RATIO STATISTICS
Ratio statistics of excess return rates
Statistics related to Sharpe ratio
 Mean0.009
 SD0.253
 Sharpe ratio (Glass type estimate) 0.035
 Sharpe ratio (Hedges UMVUE)0.035
 df1715.000
 t0.079
 p0.499
 Lowerbound of 95% confidence interval for Sharpe Ratio-0.842
 Upperbound of 95% confidence interval for Sharpe Ratio0.913
 Lowerbound of 95% CI (Gibbons, Hedeker & Davis approximation)-0.842
 Upperbound of 95% CI (Gibbons, Hedeker & Davis approximation)0.913
Statistics related to Sortino ratio
 Sortino ratio0.044
 Upside Potential Ratio4.172
 Upside part of mean0.844
 Downside part of mean-0.835
 Upside SD0.153
 Downside SD0.202
 N nonnegative terms522.000
 N negative terms1194.000
Statistics related to linear regression on benchmark
 N of observations1716.000
 Mean of predictor0.182
 Mean of criterion0.009
 SD of predictor0.198
 SD of criterion0.253
 Covariance-0.001
 r-0.020
 b (slope, estimate of beta)-0.026
 a (intercept, estimate of alpha)0.014
 Mean Square Error0.064
 DF error1714.000
 t(b)-0.845
 p(b)0.510
 t(a)0.120
 p(a)0.499
 Lowerbound of 95% confidence interval for beta-0.087
 Upperbound of 95% confidence interval for beta0.034
 Lowerbound of 95% confidence interval for alpha-0.209
 Upperbound of 95% confidence interval for alpha0.237
 Treynor index (mean / b)-0.343
 Jensen alpha (a)0.014
Ratio statistics of excess log return rates
Statistics related to Sharpe ratio
 Mean-0.025
 SD0.262
 Sharpe ratio (Glass type estimate) -0.094
 Sharpe ratio (Hedges UMVUE)-0.094
 df1715.000
 t-0.209
 p0.503
 Lowerbound of 95% confidence interval for Sharpe Ratio-0.971
 Upperbound of 95% confidence interval for Sharpe Ratio0.784
 Lowerbound of 95% CI (Gibbons, Hedeker & Davis approximation)-0.971
 Upperbound of 95% CI (Gibbons, Hedeker & Davis approximation)0.784
Statistics related to Sortino ratio
 Sortino ratio-0.114
 Upside Potential Ratio3.848
 Upside part of mean0.832
 Downside part of mean-0.857
 Upside SD0.148
 Downside SD0.216
 N nonnegative terms522.000
 N negative terms1194.000
Statistics related to linear regression on benchmark
 N of observations1716.000
 Mean of predictor0.162
 Mean of criterion-0.025
 SD of predictor0.198
 SD of criterion0.262
 Covariance-0.001
 r-0.022
 b (slope, estimate of beta)-0.030
 a (intercept, estimate of alpha)-0.020
 Mean Square Error0.069
 DF error1714.000
 t(b)-0.930
 p(b)0.511
 t(a)-0.168
 p(a)0.502
 Lowerbound of 95% confidence interval for beta-0.092
 Upperbound of 95% confidence interval for beta0.033
 Lowerbound of 95% confidence interval for alpha-0.250
 Upperbound of 95% confidence interval for alpha0.211
 Treynor index (mean / b)0.828
 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%)0.023
 Expected Shortfall on VaR0.029
assuming Pareto losses only (using partial moments from Sortino statistics)
 VaR(95%)0.007
 Expected Shortfall on VaR0.015
ORDER STATISTICS
Quartiles of return rates
 Number of observations1716.000
 Minimum0.810
 Quartile 10.999
 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 41.010
 Inter Quartile Range0.002
 Number outliers low223.000
 Percentage of outliers low0.130
 Mean of outliers low0.984
 Number of outliers high248.000
 Percentage of outliers high0.145
 Mean of outliers high1.015
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)0.037
 Extreme Value Index (regression method)0.547
 VaR(95%) (regression method)0.006
 Expected Shortfall (regression method)0.017
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)0.020
 Compounded annual return (geometric extrapolation)0.020
 Calmar ratio (compounded annual return / max draw down)0.028
 Compounded annual return / average of 25% largest draw downs0.211
 Compounded annual return / Expected Shortfall lognormal0.682
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 predictor0.024
 Mean of criterion-0.044
 SD of predictor0.237
 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 predictor-0.004
 Mean of criterion-0.044
 SD of predictor0.238
 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)-5595542393563694.000
 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)68522104017818115893868000968704.000
 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
 Mean0.063
 SD0.358
 Sharpe ratio (Glass type estimate) 0.176
 Sharpe ratio (Hedges UMVUE)0.173
 df58.000
 t0.389
 p0.349
 Lowerbound of 95% confidence interval for Sharpe Ratio-0.710
 Upperbound of 95% confidence interval for Sharpe Ratio1.059
 Lowerbound of 95% CI (Gibbons, Hedeker & Davis approximation)-0.711
 Upperbound of 95% CI (Gibbons, Hedeker & Davis approximation)1.058
Statistics related to Sortino ratio
 Sortino ratio0.209
 Upside Potential Ratio1.107
 Upside part of mean0.333
 Downside part of mean-0.270
 Upside SD0.189
 Downside SD0.301
 N nonnegative terms33.000
 N negative terms26.000
Statistics related to linear regression on benchmark
 N of observations59.000
 Mean of predictor0.195
 Mean of criterion0.063
 SD of predictor0.179
 SD of criterion0.358
 Covariance0.001
 r0.018
 b (slope, estimate of beta)0.036
 a (intercept, estimate of alpha)0.056
 Mean Square Error0.130
 DF error57.000
 t(b)0.136
 p(b)0.446
 t(a)0.327
 p(a)0.372
 Lowerbound of 95% confidence interval for beta-0.493
 Upperbound of 95% confidence interval for beta0.565
 Lowerbound of 95% confidence interval for alpha-0.286
 Upperbound of 95% confidence interval for alpha0.398
 Treynor index (mean / b)1.747
 Jensen alpha (a)0.056
Ratio statistics of excess log return rates
Statistics related to Sharpe ratio
 Mean-0.024
 SD0.462
 Sharpe ratio (Glass type estimate) -0.053
 Sharpe ratio (Hedges UMVUE)-0.052
 df58.000
 t-0.117
 p0.546
 Lowerbound of 95% confidence interval for Sharpe Ratio-0.936
 Upperbound of 95% confidence interval for Sharpe Ratio0.832
 Lowerbound of 95% CI (Gibbons, Hedeker & Davis approximation)-0.936
 Upperbound of 95% CI (Gibbons, Hedeker & Davis approximation)0.832
Statistics related to Sortino ratio
 Sortino ratio-0.057
 Upside Potential Ratio0.746
 Upside part of mean0.316
 Downside part of mean-0.340
 Upside SD0.175
 Downside SD0.423
 N nonnegative terms33.000
 N negative terms26.000
Statistics related to linear regression on benchmark
 N of observations59.000
 Mean of predictor0.178
 Mean of criterion-0.024
 SD of predictor0.175
 SD of criterion0.462
 Covariance-0.002
 r-0.021
 b (slope, estimate of beta)-0.056
 a (intercept, estimate of alpha)-0.014
 Mean Square Error0.217
 DF error57.000
 t(b)-0.161
 p(b)0.564
 t(a)-0.065
 p(a)0.526
 Lowerbound of 95% confidence interval for beta-0.755
 Upperbound of 95% confidence interval for beta0.642
 Lowerbound of 95% confidence interval for alpha-0.453
 Upperbound of 95% confidence interval for alpha0.424
 Treynor index (mean / b)0.431
 Jensen alpha (a)-0.014
Risk estimates for a one-period unit investment (parametric)
assuming log normal returns and losses (using central moments from Sharpe statistics)
 VaR(95%)0.199
 Expected Shortfall on VaR0.241
assuming Pareto losses only (using partial moments from Sortino statistics)
 VaR(95%)0.045
 Expected Shortfall on VaR0.107
ORDER STATISTICS
Quartiles of return rates
 Number of observations59.000
 Minimum0.429
 Quartile 10.997
 Median1.012
 Quartile 31.035
 Maximum1.250
 Mean of quarter 10.917
 Mean of quarter 21.003
 Mean of quarter 31.022
 Mean of quarter 41.094
 Inter Quartile Range0.038
 Number outliers low3.000
 Percentage of outliers low0.051
 Mean of outliers low0.681
 Number of outliers high5.000
 Percentage of outliers high0.085
 Mean of outliers high1.161
Risk estimates for a one-period unit investment (based on Extreme Value Theory)
 Extreme Value Index (moments method)1.182
 VaR(95%) (moments method)0.054
 Expected Shortfall (moments method)NA
 Extreme Value Index (regression method)0.987
 VaR(95%) (regression method)0.054
 Expected Shortfall (regression method)4.759
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)0.021
 Compounded annual return (geometric extrapolation)0.020
 Calmar ratio (compounded annual return / max draw down)0.028
 Compounded annual return / average of 25% largest draw downs0.072
 Compounded annual return / Expected Shortfall lognormal0.083
ANALYSIS BASED ON DAILY VALUES, FULL HISTORY (Back)
RATIO STATISTICS
Ratio statistics of excess return rates
Statistics related to Sharpe ratio
 Mean0.009
 SD0.253
 Sharpe ratio (Glass type estimate) 0.035
 Sharpe ratio (Hedges UMVUE)0.035
 df1715.000
 t0.079
 p0.499
 Lowerbound of 95% confidence interval for Sharpe Ratio-0.842
 Upperbound of 95% confidence interval for Sharpe Ratio0.913
 Lowerbound of 95% CI (Gibbons, Hedeker & Davis approximation)-0.842
 Upperbound of 95% CI (Gibbons, Hedeker & Davis approximation)0.913
Statistics related to Sortino ratio
 Sortino ratio0.044
 Upside Potential Ratio4.172
 Upside part of mean0.844
 Downside part of mean-0.835
 Upside SD0.153
 Downside SD0.202
 N nonnegative terms522.000
 N negative terms1194.000
Statistics related to linear regression on benchmark
 N of observations1716.000
 Mean of predictor0.182
 Mean of criterion0.009
 SD of predictor0.198
 SD of criterion0.253
 Covariance-0.001
 r-0.020
 b (slope, estimate of beta)-0.026
 a (intercept, estimate of alpha)0.014
 Mean Square Error0.064
 DF error1714.000
 t(b)-0.845
 p(b)0.510
 t(a)0.120
 p(a)0.499
 Lowerbound of 95% confidence interval for beta-0.087
 Upperbound of 95% confidence interval for beta0.034
 Lowerbound of 95% confidence interval for alpha-0.209
 Upperbound of 95% confidence interval for alpha0.237
 Treynor index (mean / b)-0.343
 Jensen alpha (a)0.014
Ratio statistics of excess log return rates
Statistics related to Sharpe ratio
 Mean-0.025
 SD0.262
 Sharpe ratio (Glass type estimate) -0.094
 Sharpe ratio (Hedges UMVUE)-0.094
 df1715.000
 t-0.209
 p0.503
 Lowerbound of 95% confidence interval for Sharpe Ratio-0.971
 Upperbound of 95% confidence interval for Sharpe Ratio0.784
 Lowerbound of 95% CI (Gibbons, Hedeker & Davis approximation)-0.971
 Upperbound of 95% CI (Gibbons, Hedeker & Davis approximation)0.784
Statistics related to Sortino ratio
 Sortino ratio-0.114
 Upside Potential Ratio3.848
 Upside part of mean0.832
 Downside part of mean-0.857
 Upside SD0.148
 Downside SD0.216
 N nonnegative terms522.000
 N negative terms1194.000
Statistics related to linear regression on benchmark
 N of observations1716.000
 Mean of predictor0.162
 Mean of criterion-0.025
 SD of predictor0.198
 SD of criterion0.262
 Covariance-0.001
 r-0.022
 b (slope, estimate of beta)-0.030
 a (intercept, estimate of alpha)-0.020
 Mean Square Error0.069
 DF error1714.000
 t(b)-0.930
 p(b)0.511
 t(a)-0.168
 p(a)0.502
 Lowerbound of 95% confidence interval for beta-0.092
 Upperbound of 95% confidence interval for beta0.033
 Lowerbound of 95% confidence interval for alpha-0.250
 Upperbound of 95% confidence interval for alpha0.211
 Treynor index (mean / b)0.828
 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%)0.023
 Expected Shortfall on VaR0.029
assuming Pareto losses only (using partial moments from Sortino statistics)
 VaR(95%)0.007
 Expected Shortfall on VaR0.015
ORDER STATISTICS
Quartiles of return rates
 Number of observations1716.000
 Minimum0.810
 Quartile 10.999
 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 41.010
 Inter Quartile Range0.002
 Number outliers low223.000
 Percentage of outliers low0.130
 Mean of outliers low0.984
 Number of outliers high248.000
 Percentage of outliers high0.145
 Mean of outliers high1.015
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)0.037
 Extreme Value Index (regression method)0.547
 VaR(95%) (regression method)0.006
 Expected Shortfall (regression method)0.017
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)0.020
 Compounded annual return (geometric extrapolation)0.020
 Calmar ratio (compounded annual return / max draw down)0.028
 Compounded annual return / average of 25% largest draw downs0.211
 Compounded annual return / Expected Shortfall lognormal0.682
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 predictor0.024
 Mean of criterion-0.044
 SD of predictor0.237
 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 predictor-0.004
 Mean of criterion-0.044
 SD of predictor0.238
 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)-5595542393563694.000
 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)68522104017818115893868000968704.000
 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