Find System by Name

Wait

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
 Mean0.077
 SD0.382
 Sharpe ratio (Glass type estimate) 0.203
 Sharpe ratio (Hedges UMVUE)0.200
 df51.000
 t0.422
 p0.338
 Lowerbound of 95% confidence interval for Sharpe Ratio-0.741
 Upperbound of 95% confidence interval for Sharpe Ratio1.144
 Lowerbound of 95% CI (Gibbons, Hedeker & Davis approximation)-0.743
 Upperbound of 95% CI (Gibbons, Hedeker & Davis approximation)1.142
Statistics related to Sortino ratio
 Sortino ratio0.241
 Upside Potential Ratio1.179
 Upside part of mean0.378
 Downside part of mean-0.301
 Upside SD0.201
 Downside SD0.321
 N nonnegative terms33.000
 N negative terms19.000
Statistics related to linear regression on benchmark
 N of observations52.000
 Mean of predictor0.215
 Mean of criterion0.077
 SD of predictor0.187
 SD of criterion0.382
 Covariance0.001
 r0.016
 b (slope, estimate of beta)0.032
 a (intercept, estimate of alpha)0.070
 Mean Square Error0.148
 DF error50.000
 t(b)0.110
 p(b)0.456
 t(a)0.360
 p(a)0.360
 Lowerbound of 95% confidence interval for beta-0.549
 Upperbound of 95% confidence interval for beta0.613
 Lowerbound of 95% confidence interval for alpha-0.322
 Upperbound of 95% confidence interval for alpha0.463
 Treynor index (mean / b)2.424
 Jensen alpha (a)0.070
Ratio statistics of excess log return rates
Statistics related to Sharpe ratio
 Mean-0.022
 SD0.493
 Sharpe ratio (Glass type estimate) -0.044
 Sharpe ratio (Hedges UMVUE)-0.043
 df51.000
 t-0.091
 p0.536
 Lowerbound of 95% confidence interval for Sharpe Ratio-0.985
 Upperbound of 95% confidence interval for Sharpe Ratio0.898
 Lowerbound of 95% CI (Gibbons, Hedeker & Davis approximation)-0.985
 Upperbound of 95% CI (Gibbons, Hedeker & Davis approximation)0.898
Statistics related to Sortino ratio
 Sortino ratio-0.048
 Upside Potential Ratio0.795
 Upside part of mean0.359
 Downside part of mean-0.380
 Upside SD0.187
 Downside SD0.451
 N nonnegative terms33.000
 N negative terms19.000
Statistics related to linear regression on benchmark
 N of observations52.000
 Mean of predictor0.196
 Mean of criterion-0.022
 SD of predictor0.183
 SD of criterion0.493
 Covariance-0.002
 r-0.022
 b (slope, estimate of beta)-0.060
 a (intercept, estimate of alpha)-0.010
 Mean Square Error0.247
 DF error50.000
 t(b)-0.158
 p(b)0.562
 t(a)-0.039
 p(a)0.516
 Lowerbound of 95% confidence interval for beta-0.827
 Upperbound of 95% confidence interval for beta0.706
 Lowerbound of 95% confidence interval for alpha-0.513
 Upperbound of 95% confidence interval for alpha0.493
 Treynor index (mean / b)0.359
 Jensen alpha (a)-0.010
Risk estimates for a one-period unit investment (parametric)
assuming log normal returns and losses (using central moments from Sharpe statistics)
 VaR(95%)0.210
 Expected Shortfall on VaR0.255
assuming Pareto losses only (using partial moments from Sortino statistics)
 VaR(95%)0.044
 Expected Shortfall on VaR0.107
ORDER STATISTICS
Quartiles of return rates
 Number of observations52.000
 Minimum0.429
 Quartile 10.992
 Median1.016
 Quartile 31.043
 Maximum1.250
 Mean of quarter 10.906
 Mean of quarter 21.006
 Mean of quarter 31.027
 Mean of quarter 41.102
 Inter Quartile Range0.051
 Number outliers low2.000
 Percentage of outliers low0.038
 Mean of outliers low0.561
 Number of outliers high5.000
 Percentage of outliers high0.096
 Mean of outliers high1.161
Risk estimates for a one-period unit investment (based on Extreme Value Theory)
 Extreme Value Index (moments method)1.082
 VaR(95%) (moments method)0.066
 Expected Shortfall (moments method)NA
 Extreme Value Index (regression method)1.083
 VaR(95%) (regression method)0.061
 Expected Shortfall (regression method)NA
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)0.023
 Compounded annual return (geometric extrapolation)0.023
 Calmar ratio (compounded annual return / max draw down)0.032
 Compounded annual return / average of 25% largest draw downs0.082
 Compounded annual return / Expected Shortfall lognormal0.089
ANALYSIS BASED ON DAILY VALUES, FULL HISTORY (Back)
RATIO STATISTICS
Ratio statistics of excess return rates
Statistics related to Sharpe ratio
 Mean0.016
 SD0.270
 Sharpe ratio (Glass type estimate) 0.060
 Sharpe ratio (Hedges UMVUE)0.060
 df1508.000
 t0.126
 p0.498
 Lowerbound of 95% confidence interval for Sharpe Ratio-0.876
 Upperbound of 95% confidence interval for Sharpe Ratio0.996
 Lowerbound of 95% CI (Gibbons, Hedeker & Davis approximation)-0.876
 Upperbound of 95% CI (Gibbons, Hedeker & Davis approximation)0.996
Statistics related to Sortino ratio
 Sortino ratio0.075
 Upside Potential Ratio4.449
 Upside part of mean0.959
 Downside part of mean-0.943
 Upside SD0.163
 Downside SD0.216
 N nonnegative terms522.000
 N negative terms987.000
Statistics related to linear regression on benchmark
 N of observations1509.000
 Mean of predictor0.218
 Mean of criterion0.016
 SD of predictor0.194
 SD of criterion0.270
 Covariance-0.001
 r-0.022
 b (slope, estimate of beta)-0.031
 a (intercept, estimate of alpha)0.023
 Mean Square Error0.073
 DF error1507.000
 t(b)-0.867
 p(b)0.514
 t(a)0.178
 p(a)0.497
 Lowerbound of 95% confidence interval for beta-0.101
 Upperbound of 95% confidence interval for beta0.039
 Lowerbound of 95% confidence interval for alpha-0.231
 Upperbound of 95% confidence interval for alpha0.277
 Treynor index (mean / b)-0.522
 Jensen alpha (a)0.023
Ratio statistics of excess log return rates
Statistics related to Sharpe ratio
 Mean-0.022
 SD0.280
 Sharpe ratio (Glass type estimate) -0.078
 Sharpe ratio (Hedges UMVUE)-0.078
 df1508.000
 t-0.164
 p0.502
 Lowerbound of 95% confidence interval for Sharpe Ratio-1.014
 Upperbound of 95% confidence interval for Sharpe Ratio0.857
 Lowerbound of 95% CI (Gibbons, Hedeker & Davis approximation)-1.014
 Upperbound of 95% CI (Gibbons, Hedeker & Davis approximation)0.857
Statistics related to Sortino ratio
 Sortino ratio-0.095
 Upside Potential Ratio4.104
 Upside part of mean0.946
 Downside part of mean-0.968
 Upside SD0.158
 Downside SD0.231
 N nonnegative terms522.000
 N negative terms987.000
Statistics related to linear regression on benchmark
 N of observations1509.000
 Mean of predictor0.200
 Mean of criterion-0.022
 SD of predictor0.194
 SD of criterion0.280
 Covariance-0.001
 r-0.025
 b (slope, estimate of beta)-0.035
 a (intercept, estimate of alpha)-0.015
 Mean Square Error0.078
 DF error1507.000
 t(b)-0.952
 p(b)0.516
 t(a)-0.111
 p(a)0.502
 Lowerbound of 95% confidence interval for beta-0.108
 Upperbound of 95% confidence interval for beta0.037
 Lowerbound of 95% confidence interval for alpha-0.277
 Upperbound of 95% confidence interval for alpha0.247
 Treynor index (mean / b)0.621
 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%)0.025
 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 observations1509.000
 Minimum0.810
 Quartile 10.999
 Median1.000
 Quartile 31.002
 Maximum1.158
 Mean of quarter 10.990
 Mean of quarter 21.000
 Mean of quarter 31.000
 Mean of quarter 41.011
 Inter Quartile Range0.004
 Number outliers low137.000
 Percentage of outliers low0.091
 Mean of outliers low0.977
 Number of outliers high164.000
 Percentage of outliers high0.109
 Mean of outliers high1.020
Risk estimates for a one-period unit investment (based on Extreme Value Theory)
 Extreme Value Index (moments method)0.830
 VaR(95%) (moments method)0.008
 Expected Shortfall (moments method)0.052
 Extreme Value Index (regression method)0.569
 VaR(95%) (regression method)0.007
 Expected Shortfall (regression method)0.019
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)0.023
 Compounded annual return (geometric extrapolation)0.022
 Calmar ratio (compounded annual return / max draw down)0.032
 Compounded annual return / average of 25% largest draw downs0.240
 Compounded annual return / Expected Shortfall lognormal0.729
ANALYSIS BASED ON DAILY VALUES, LAST 6 MONTHS (Back)
RATIO STATISTICS
Ratio statistics of excess return rates
Statistics related to Sharpe ratio
 Mean-2.179
 SD0.647
 Sharpe ratio (Glass type estimate) -3.366
 Sharpe ratio (Hedges UMVUE)-3.351
 df171.000
 t-2.380
 p0.613
 Lowerbound of 95% confidence interval for Sharpe Ratio-6.155
 Upperbound of 95% confidence interval for Sharpe Ratio-0.566
 Lowerbound of 95% CI (Gibbons, Hedeker & Davis approximation)-6.145
 Upperbound of 95% CI (Gibbons, Hedeker & Davis approximation)-0.556
Statistics related to Sortino ratio
 Sortino ratio-3.699
 Upside Potential Ratio2.005
 Upside part of mean1.181
 Downside part of mean-3.360
 Upside SD0.289
 Downside SD0.589
 N nonnegative terms20.000
 N negative terms152.000
Statistics related to linear regression on benchmark
 N of observations172.000
 Mean of predictor0.622
 Mean of criterion-2.179
 SD of predictor0.174
 SD of criterion0.647
 Covariance-0.007
 r-0.062
 b (slope, estimate of beta)-0.229
 a (intercept, estimate of alpha)-2.037
 Mean Square Error0.420
 DF error170.000
 t(b)-0.806
 p(b)0.531
 t(a)-2.182
 p(a)0.583
 Lowerbound of 95% confidence interval for beta-0.790
 Upperbound of 95% confidence interval for beta0.332
 Lowerbound of 95% confidence interval for alpha-3.879
 Upperbound of 95% confidence interval for alpha-0.194
 Treynor index (mean / b)9.520
 Jensen alpha (a)-2.037
Ratio statistics of excess log return rates
Statistics related to Sharpe ratio
 Mean-2.410
 SD0.682
 Sharpe ratio (Glass type estimate) -3.533
 Sharpe ratio (Hedges UMVUE)-3.517
 df171.000
 t-2.498
 p0.619
 Lowerbound of 95% confidence interval for Sharpe Ratio-6.325
 Upperbound of 95% confidence interval for Sharpe Ratio-0.731
 Lowerbound of 95% CI (Gibbons, Hedeker & Davis approximation)-6.314
 Upperbound of 95% CI (Gibbons, Hedeker & Davis approximation)-0.721
Statistics related to Sortino ratio
 Sortino ratio-3.790
 Upside Potential Ratio1.796
 Upside part of mean1.142
 Downside part of mean-3.552
 Upside SD0.274
 Downside SD0.636
 N nonnegative terms20.000
 N negative terms152.000
Statistics related to linear regression on benchmark
 N of observations172.000
 Mean of predictor0.607
 Mean of criterion-2.410
 SD of predictor0.174
 SD of criterion0.682
 Covariance-0.007
 r-0.062
 b (slope, estimate of beta)-0.243
 a (intercept, estimate of alpha)-2.263
 Mean Square Error0.466
 DF error170.000
 t(b)-0.808
 p(b)0.531
 t(a)-2.303
 p(a)0.587
 Lowerbound of 95% confidence interval for beta-0.835
 Upperbound of 95% confidence interval for beta0.350
 Lowerbound of 95% confidence interval for alpha-4.202
 Upperbound of 95% confidence interval for alpha-0.323
 Treynor index (mean / b)9.936
 Jensen alpha (a)-2.263
Risk estimates for a one-period unit investment (parametric)
assuming log normal returns and losses (using central moments from Sharpe statistics)
 VaR(95%)0.065
 Expected Shortfall on VaR0.079
assuming Pareto losses only (using partial moments from Sortino statistics)
 VaR(95%)0.032
 Expected Shortfall on VaR0.067
ORDER STATISTICS
Quartiles of return rates
 Number of observations172.000
 Minimum0.810
 Quartile 11.000
 Median1.000
 Quartile 31.000
 Maximum1.158
 Mean of quarter 10.961
 Mean of quarter 21.000
 Mean of quarter 31.000
 Mean of quarter 41.014
 Inter Quartile Range0.000
 Number outliers low38.000
 Percentage of outliers low0.221
 Mean of outliers low0.956
 Number of outliers high20.000
 Percentage of outliers high0.116
 Mean of outliers high1.030
Risk estimates for a one-period unit investment (based on Extreme Value Theory)
 Extreme Value Index (moments method)0.394
 VaR(95%) (moments method)0.006
 Expected Shortfall (moments method)0.014
 Extreme Value Index (regression method)-0.159
 VaR(95%) (regression method)0.035
 Expected Shortfall (regression method)0.054
DRAW DOWN STATISTICS
Quartiles of draw downs
 Number of observations2.000
 Minimum0.002
 Quartile 10.177
 Median0.352
 Quartile 30.528
 Maximum0.703
 Mean of quarter 10.002
 Mean of quarter 2NA
 Mean of quarter 3NA
 Mean of quarter 40.703
 Inter Quartile Range0.351
 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)-1.387
 Compounded annual return (geometric extrapolation)-0.906
 Calmar ratio (compounded annual return / max draw down)-1.289
 Compounded annual return / average of 25% largest draw downs-1.289
 Compounded annual return / Expected Shortfall lognormal-11.407