Advanced Statistics: Bravo Tango

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
 Mean0.084
 SD0.307
 Sharpe ratio (Glass type estimate) 0.275
 Sharpe ratio (Hedges UMVUE)0.258
 df13.000
 t0.297
 p0.448
 Lowerbound of 95% confidence interval for Sharpe Ratio-1.548
 Upperbound of 95% confidence interval for Sharpe Ratio2.087
 Lowerbound of 95% CI (Gibbons, Hedeker & Davis approximation)-1.559
 Upperbound of 95% CI (Gibbons, Hedeker & Davis approximation)2.076
Statistics related to Sortino ratio
 Sortino ratio0.615
 Upside Potential Ratio2.302
 Upside part of mean0.315
 Downside part of mean-0.231
 Upside SD0.263
 Downside SD0.137
 N nonnegative terms3.000
 N negative terms11.000
Statistics related to linear regression on benchmark
 N of observations14.000
 Mean of predictor0.337
 Mean of criterion0.084
 SD of predictor0.210
 SD of criterion0.307
 Covariance0.003
 r0.051
 b (slope, estimate of beta)0.074
 a (intercept, estimate of alpha)0.059
 Mean Square Error0.102
 DF error12.000
 t(b)0.176
 p(b)0.475
 t(a)0.181
 p(a)0.474
 Lowerbound of 95% confidence interval for beta-0.843
 Upperbound of 95% confidence interval for beta0.992
 Lowerbound of 95% confidence interval for alpha-0.655
 Upperbound of 95% confidence interval for alpha0.773
 Treynor index (mean / b)1.136
 Jensen alpha (a)0.059
Ratio statistics of excess log return rates
Statistics related to Sharpe ratio
 Mean0.044
 SD0.284
 Sharpe ratio (Glass type estimate) 0.156
 Sharpe ratio (Hedges UMVUE)0.147
 df13.000
 t0.169
 p0.470
 Lowerbound of 95% confidence interval for Sharpe Ratio-1.662
 Upperbound of 95% confidence interval for Sharpe Ratio1.969
 Lowerbound of 95% CI (Gibbons, Hedeker & Davis approximation)-1.668
 Upperbound of 95% CI (Gibbons, Hedeker & Davis approximation)1.963
Statistics related to Sortino ratio
 Sortino ratio0.309
 Upside Potential Ratio1.981
 Upside part of mean0.285
 Downside part of mean-0.240
 Upside SD0.234
 Downside SD0.144
 N nonnegative terms3.000
 N negative terms11.000
Statistics related to linear regression on benchmark
 N of observations14.000
 Mean of predictor0.313
 Mean of criterion0.044
 SD of predictor0.198
 SD of criterion0.284
 Covariance0.004
 r0.064
 b (slope, estimate of beta)0.092
 a (intercept, estimate of alpha)0.016
 Mean Square Error0.087
 DF error12.000
 t(b)0.221
 p(b)0.468
 t(a)0.052
 p(a)0.492
 Lowerbound of 95% confidence interval for beta-0.812
 Upperbound of 95% confidence interval for beta0.995
 Lowerbound of 95% confidence interval for alpha-0.644
 Upperbound of 95% confidence interval for alpha0.675
 Treynor index (mean / b)0.485
 Jensen alpha (a)0.016
Risk estimates for a one-period unit investment (parametric)
assuming log normal returns and losses (using central moments from Sharpe statistics)
 VaR(95%)0.123
 Expected Shortfall on VaR0.152
assuming Pareto losses only (using partial moments from Sortino statistics)
 VaR(95%)0.058
 Expected Shortfall on VaR0.108
ORDER STATISTICS
Quartiles of return rates
 Number of observations14.000
 Minimum0.888
 Quartile 11.000
 Median1.000
 Quartile 31.000
 Maximum1.276
 Mean of quarter 10.943
 Mean of quarter 21.000
 Mean of quarter 31.000
 Mean of quarter 41.095
 Inter Quartile Range0.000
 Number outliers low3.000
 Percentage of outliers low0.214
 Mean of outliers low0.924
 Number of outliers high3.000
 Percentage of outliers high0.214
 Mean of outliers high1.126
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)-1.090
 VaR(95%) (regression method)0.123
 Expected Shortfall (regression method)0.136
DRAW DOWN STATISTICS
Quartiles of draw downs
 Number of observations2.000
 Minimum0.076
 Quartile 10.094
 Median0.112
 Quartile 30.130
 Maximum0.148
 Mean of quarter 10.076
 Mean of quarter 2NA
 Mean of quarter 3NA
 Mean of quarter 40.148
 Inter Quartile Range0.036
 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)0.093
 Compounded annual return (geometric extrapolation)0.093
 Calmar ratio (compounded annual return / max draw down)0.623
 Compounded annual return / average of 25% largest draw downs0.623
 Compounded annual return / Expected Shortfall lognormal0.607
ANALYSIS BASED ON DAILY VALUES, FULL HISTORY (Back)
RATIO STATISTICS
Ratio statistics of excess return rates
Statistics related to Sharpe ratio
 Mean0.058
 SD0.196
 Sharpe ratio (Glass type estimate) 0.296
 Sharpe ratio (Hedges UMVUE)0.296
 df427.000
 t0.331
 p0.371
 Lowerbound of 95% confidence interval for Sharpe Ratio-1.461
 Upperbound of 95% confidence interval for Sharpe Ratio2.054
 Lowerbound of 95% CI (Gibbons, Hedeker & Davis approximation)-1.461
 Upperbound of 95% CI (Gibbons, Hedeker & Davis approximation)2.053
Statistics related to Sortino ratio
 Sortino ratio0.422
 Upside Potential Ratio4.978
 Upside part of mean0.686
 Downside part of mean-0.628
 Upside SD0.139
 Downside SD0.138
 N nonnegative terms54.000
 N negative terms374.000
Statistics related to linear regression on benchmark
 N of observations428.000
 Mean of predictor0.304
 Mean of criterion0.058
 SD of predictor0.182
 SD of criterion0.196
 Covariance-0.000
 r-0.005
 b (slope, estimate of beta)-0.005
 a (intercept, estimate of alpha)0.060
 Mean Square Error0.039
 DF error426.000
 t(b)-0.101
 p(b)0.540
 t(a)0.338
 p(a)0.368
 Lowerbound of 95% confidence interval for beta-0.108
 Upperbound of 95% confidence interval for beta0.098
 Lowerbound of 95% confidence interval for alpha-0.288
 Upperbound of 95% confidence interval for alpha0.407
 Treynor index (mean / b)-11.008
 Jensen alpha (a)0.060
Ratio statistics of excess log return rates
Statistics related to Sharpe ratio
 Mean0.039
 SD0.196
 Sharpe ratio (Glass type estimate) 0.198
 Sharpe ratio (Hedges UMVUE)0.198
 df427.000
 t0.221
 p0.412
 Lowerbound of 95% confidence interval for Sharpe Ratio-1.559
 Upperbound of 95% confidence interval for Sharpe Ratio1.956
 Lowerbound of 95% CI (Gibbons, Hedeker & Davis approximation)-1.559
 Upperbound of 95% CI (Gibbons, Hedeker & Davis approximation)1.955
Statistics related to Sortino ratio
 Sortino ratio0.277
 Upside Potential Ratio4.810
 Upside part of mean0.676
 Downside part of mean-0.637
 Upside SD0.137
 Downside SD0.141
 N nonnegative terms54.000
 N negative terms374.000
Statistics related to linear regression on benchmark
 N of observations428.000
 Mean of predictor0.288
 Mean of criterion0.039
 SD of predictor0.181
 SD of criterion0.196
 Covariance-0.000
 r-0.004
 b (slope, estimate of beta)-0.004
 a (intercept, estimate of alpha)0.040
 Mean Square Error0.039
 DF error426.000
 t(b)-0.083
 p(b)0.533
 t(a)0.227
 p(a)0.410
 Lowerbound of 95% confidence interval for beta-0.107
 Upperbound of 95% confidence interval for beta0.099
 Lowerbound of 95% confidence interval for alpha-0.307
 Upperbound of 95% confidence interval for alpha0.388
 Treynor index (mean / b)-8.976
 Jensen alpha (a)0.040
Risk estimates for a one-period unit investment (parametric)
assuming log normal returns and losses (using central moments from Sharpe statistics)
 VaR(95%)0.017
 Expected Shortfall on VaR0.021
assuming Pareto losses only (using partial moments from Sortino statistics)
 VaR(95%)0.006
 Expected Shortfall on VaR0.013
ORDER STATISTICS
Quartiles of return rates
 Number of observations428.000
 Minimum0.946
 Quartile 11.000
 Median1.000
 Quartile 31.000
 Maximum1.071
 Mean of quarter 10.993
 Mean of quarter 21.000
 Mean of quarter 31.000
 Mean of quarter 41.008
 Inter Quartile Range0.000
 Number outliers low43.000
 Percentage of outliers low0.100
 Mean of outliers low0.983
 Number of outliers high54.000
 Percentage of outliers high0.126
 Mean of outliers high1.016
Risk estimates for a one-period unit investment (based on Extreme Value Theory)
 Extreme Value Index (moments method)-0.843
 VaR(95%) (moments method)0.001
 Expected Shortfall (moments method)0.002
 Extreme Value Index (regression method)0.136
 VaR(95%) (regression method)0.005
 Expected Shortfall (regression method)0.015
DRAW DOWN STATISTICS
Quartiles of draw downs
 Number of observations5.000
 Minimum0.001
 Quartile 10.002
 Median0.014
 Quartile 30.143
 Maximum0.254
 Mean of quarter 10.002
 Mean of quarter 20.014
 Mean of quarter 30.143
 Mean of quarter 40.254
 Inter Quartile Range0.141
 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)0.087
 Compounded annual return (geometric extrapolation)0.087
 Calmar ratio (compounded annual return / max draw down)0.341
 Compounded annual return / average of 25% largest draw downs0.341
 Compounded annual return / Expected Shortfall lognormal4.027
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 predictor0.195
 Mean of criterion-0.044
 SD of predictor0.172
 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 predictor0.180
 Mean of criterion-0.044
 SD of predictor0.172
 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)-5586620237671944.000
 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)23977339601330866766702413086720.000
 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