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
 Mean0.061
 SD0.199
 Sharpe ratio (Glass type estimate) 0.305
 Sharpe ratio (Hedges UMVUE)0.305
 df417.000
 t0.337
 p0.368
 Lowerbound of 95% confidence interval for Sharpe Ratio-1.473
 Upperbound of 95% confidence interval for Sharpe Ratio2.083
 Lowerbound of 95% CI (Gibbons, Hedeker & Davis approximation)-1.473
 Upperbound of 95% CI (Gibbons, Hedeker & Davis approximation)2.083
Statistics related to Sortino ratio
 Sortino ratio0.435
 Upside Potential Ratio5.037
 Upside part of mean0.702
 Downside part of mean-0.642
 Upside SD0.141
 Downside SD0.139
 N nonnegative terms54.000
 N negative terms364.000
Statistics related to linear regression on benchmark
 N of observations418.000
 Mean of predictor0.331
 Mean of criterion0.061
 SD of predictor0.181
 SD of criterion0.199
 Covariance-0.000
 r-0.005
 b (slope, estimate of beta)-0.006
 a (intercept, estimate of alpha)0.063
 Mean Square Error0.040
 DF error416.000
 t(b)-0.106
 p(b)0.542
 t(a)0.345
 p(a)0.365
 Lowerbound of 95% confidence interval for beta-0.112
 Upperbound of 95% confidence interval for beta0.100
 Lowerbound of 95% confidence interval for alpha-0.294
 Upperbound of 95% confidence interval for alpha0.419
 Treynor index (mean / b)-10.629
 Jensen alpha (a)0.063
Ratio statistics of excess log return rates
Statistics related to Sharpe ratio
 Mean0.041
 SD0.199
 Sharpe ratio (Glass type estimate) 0.206
 Sharpe ratio (Hedges UMVUE)0.206
 df417.000
 t0.227
 p0.410
 Lowerbound of 95% confidence interval for Sharpe Ratio-1.572
 Upperbound of 95% confidence interval for Sharpe Ratio1.984
 Lowerbound of 95% CI (Gibbons, Hedeker & Davis approximation)-1.572
 Upperbound of 95% CI (Gibbons, Hedeker & Davis approximation)1.984
Statistics related to Sortino ratio
 Sortino ratio0.288
 Upside Potential Ratio4.868
 Upside part of mean0.693
 Downside part of mean-0.652
 Upside SD0.138
 Downside SD0.142
 N nonnegative terms54.000
 N negative terms364.000
Statistics related to linear regression on benchmark
 N of observations418.000
 Mean of predictor0.314
 Mean of criterion0.041
 SD of predictor0.181
 SD of criterion0.199
 Covariance-0.000
 r-0.004
 b (slope, estimate of beta)-0.005
 a (intercept, estimate of alpha)0.042
 Mean Square Error0.040
 DF error416.000
 t(b)-0.087
 p(b)0.535
 t(a)0.234
 p(a)0.408
 Lowerbound of 95% confidence interval for beta-0.111
 Upperbound of 95% confidence interval for beta0.101
 Lowerbound of 95% confidence interval for alpha-0.314
 Upperbound of 95% confidence interval for alpha0.399
 Treynor index (mean / b)-8.741
 Jensen alpha (a)0.042
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 VaR0.022
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 observations418.000
 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 low0.103
 Mean of outliers low0.983
 Number of outliers high54.000
 Percentage of outliers high0.129
 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)0.006
 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)0.089
 Compounded annual return (geometric extrapolation)0.089
 Calmar ratio (compounded annual return / max draw down)0.349
 Compounded annual return / average of 25% largest draw downs0.349
 Compounded annual return / Expected Shortfall lognormal4.081
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 predictor0.315
 Mean of criterion-0.044
 SD of predictor0.170
 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 predictor0.301
 Mean of criterion-0.044
 SD of predictor0.170
 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)-5570056946937649.000
 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)69801120065818192995751240400896.000
 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