Advanced Statistics: Tango
Advanced Statistics module contributed by Jules Ellis, C2 Member. Jules has written a very helpful guide for these statistics. | |||||
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| ANALYSIS BASED ON MONTHLY VALUES, FULL HISTORY (Back) | |||||
| RATIO STATISTICS | |||||
| Ratio statistics of excess return rates | |||||
| Statistics related to Sharpe ratio | |||||
| Mean | 0.065 | ||||
| SD | 0.226 | ||||
| Sharpe ratio (Glass type estimate) | 0.285 | ||||
| Sharpe ratio (Hedges UMVUE) | 0.283 | ||||
| df | 94.000 | ||||
| t | 0.803 | ||||
| p | 0.212 | ||||
| Lowerbound of 95% confidence interval for Sharpe Ratio | -0.413 | ||||
| Upperbound of 95% confidence interval for Sharpe Ratio | 0.982 | ||||
| Lowerbound of 95% CI (Gibbons, Hedeker & Davis approximation) | -0.415 | ||||
| Upperbound of 95% CI (Gibbons, Hedeker & Davis approximation) | 0.981 | ||||
| Statistics related to Sortino ratio | |||||
| Sortino ratio | 0.340 | ||||
| Upside Potential Ratio | 1.191 | ||||
| Upside part of mean | 0.226 | ||||
| Downside part of mean | -0.161 | ||||
| Upside SD | 0.122 | ||||
| Downside SD | 0.190 | ||||
| N nonnegative terms | 38.000 | ||||
| N negative terms | 57.000 | ||||
| Statistics related to linear regression on benchmark | |||||
| N of observations | 95.000 | ||||
| Mean of predictor | 0.123 | ||||
| Mean of criterion | 0.065 | ||||
| SD of predictor | 0.216 | ||||
| SD of criterion | 0.226 | ||||
| Covariance | 0.020 | ||||
| r | 0.406 | ||||
| b (slope, estimate of beta) | 0.425 | ||||
| a (intercept, estimate of alpha) | 0.012 | ||||
| Mean Square Error | 0.043 | ||||
| DF error | 93.000 | ||||
| t(b) | 4.287 | ||||
| p(b) | 0.000 | ||||
| t(a) | 0.166 | ||||
| p(a) | 0.434 | ||||
| Lowerbound of 95% confidence interval for beta | 0.228 | ||||
| Upperbound of 95% confidence interval for beta | 0.621 | ||||
| Lowerbound of 95% confidence interval for alpha | -0.136 | ||||
| Upperbound of 95% confidence interval for alpha | 0.161 | ||||
| Treynor index (mean / b) | 0.152 | ||||
| Jensen alpha (a) | 0.012 | ||||
| Ratio statistics of excess log return rates | |||||
| Statistics related to Sharpe ratio | |||||
| Mean | 0.032 | ||||
| SD | 0.276 | ||||
| Sharpe ratio (Glass type estimate) | 0.115 | ||||
| Sharpe ratio (Hedges UMVUE) | 0.114 | ||||
| df | 94.000 | ||||
| t | 0.324 | ||||
| p | 0.373 | ||||
| Lowerbound of 95% confidence interval for Sharpe Ratio | -0.582 | ||||
| Upperbound of 95% confidence interval for Sharpe Ratio | 0.812 | ||||
| Lowerbound of 95% CI (Gibbons, Hedeker & Davis approximation) | -0.583 | ||||
| Upperbound of 95% CI (Gibbons, Hedeker & Davis approximation) | 0.811 | ||||
| Statistics related to Sortino ratio | |||||
| Sortino ratio | 0.128 | ||||
| Upside Potential Ratio | 0.879 | ||||
| Upside part of mean | 0.218 | ||||
| Downside part of mean | -0.186 | ||||
| Upside SD | 0.117 | ||||
| Downside SD | 0.248 | ||||
| N nonnegative terms | 38.000 | ||||
| N negative terms | 57.000 | ||||
| Statistics related to linear regression on benchmark | |||||
| N of observations | 95.000 | ||||
| Mean of predictor | 0.098 | ||||
| Mean of criterion | 0.032 | ||||
| SD of predictor | 0.222 | ||||
| SD of criterion | 0.276 | ||||
| Covariance | 0.025 | ||||
| r | 0.402 | ||||
| b (slope, estimate of beta) | 0.499 | ||||
| a (intercept, estimate of alpha) | -0.017 | ||||
| Mean Square Error | 0.064 | ||||
| DF error | 93.000 | ||||
| t(b) | 4.239 | ||||
| p(b) | 0.000 | ||||
| t(a) | -0.188 | ||||
| p(a) | 0.575 | ||||
| Lowerbound of 95% confidence interval for beta | 0.265 | ||||
| Upperbound of 95% confidence interval for beta | 0.732 | ||||
| Lowerbound of 95% confidence interval for alpha | -0.198 | ||||
| Upperbound of 95% confidence interval for alpha | 0.163 | ||||
| Treynor index (mean / b) | 0.064 | ||||
| Jensen alpha (a) | -0.017 | ||||
| Risk estimates for a one-period unit investment (parametric) | |||||
| assuming log normal returns and losses (using central moments from Sharpe statistics) | |||||
| VaR(95%) | 0.120 | ||||
| Expected Shortfall on VaR | 0.149 | ||||
| assuming Pareto losses only (using partial moments from Sortino statistics) | |||||
| VaR(95%) | 0.034 | ||||
| Expected Shortfall on VaR | 0.077 | ||||
| ORDER STATISTICS | |||||
| Quartiles of return rates | |||||
| Number of observations | 95.000 | ||||
| Minimum | 0.521 | ||||
| Quartile 1 | 1.000 | ||||
| Median | 1.000 | ||||
| Quartile 3 | 1.034 | ||||
| Maximum | 1.140 | ||||
| Mean of quarter 1 | 0.955 | ||||
| Mean of quarter 2 | 1.000 | ||||
| Mean of quarter 3 | 1.014 | ||||
| Mean of quarter 4 | 1.067 | ||||
| Inter Quartile Range | 0.034 | ||||
| Number outliers low | 6.000 | ||||
| Percentage of outliers low | 0.063 | ||||
| Mean of outliers low | 0.849 | ||||
| Number of outliers high | 6.000 | ||||
| Percentage of outliers high | 0.063 | ||||
| Mean of outliers high | 1.105 | ||||
| Risk estimates for a one-period unit investment (based on Extreme Value Theory) | |||||
| Extreme Value Index (moments method) | 1.373 | ||||
| VaR(95%) (moments method) | 0.008 | ||||
| Expected Shortfall (moments method) | NA | ||||
| Extreme Value Index (regression method) | 0.642 | ||||
| VaR(95%) (regression method) | 0.036 | ||||
| Expected Shortfall (regression method) | 0.149 | ||||
| DRAW DOWN STATISTICS | |||||
| Quartiles of draw downs | |||||
| Number of observations | 9.000 | ||||
| Minimum | 0.000 | ||||
| Quartile 1 | 0.003 | ||||
| Median | 0.013 | ||||
| Quartile 3 | 0.055 | ||||
| Maximum | 0.479 | ||||
| Mean of quarter 1 | 0.001 | ||||
| Mean of quarter 2 | 0.009 | ||||
| Mean of quarter 3 | 0.054 | ||||
| Mean of quarter 4 | 0.375 | ||||
| Inter Quartile Range | 0.053 | ||||
| Number outliers low | 0.000 | ||||
| Percentage of outliers low | 0.000 | ||||
| Mean of outliers low | NA | ||||
| Number of outliers high | 2.000 | ||||
| Percentage of outliers high | 0.222 | ||||
| Mean of outliers high | 0.375 | ||||
| Risk estimates based on draw downs (based on Extreme Value Theory) | |||||
| Extreme Value Index (moments method) | -19.381 | ||||
| VaR(95%) (moments method) | 0.164 | ||||
| Expected Shortfall (moments method) | 0.164 | ||||
| Extreme Value Index (regression method) | -1.056 | ||||
| VaR(95%) (regression method) | 0.588 | ||||
| Expected Shortfall (regression method) | 0.637 | ||||
| COMBINED STATISTICS | |||||
| Annualized return (arithmetic extrapolation) | 0.104 | ||||
| Compounded annual return (geometric extrapolation) | 0.079 | ||||
| Calmar ratio (compounded annual return / max draw down) | 0.164 | ||||
| Compounded annual return / average of 25% largest draw downs | 0.210 | ||||
| Compounded annual return / Expected Shortfall lognormal | 0.529 | ||||
| ANALYSIS BASED ON DAILY VALUES, FULL HISTORY (Back) | |||||
| RATIO STATISTICS | |||||
| Ratio statistics of excess return rates | |||||
| Statistics related to Sharpe ratio | |||||
| Mean | 0.216 | ||||
| SD | 0.616 | ||||
| Sharpe ratio (Glass type estimate) | 0.351 | ||||
| Sharpe ratio (Hedges UMVUE) | 0.351 | ||||
| df | 2091.000 | ||||
| t | 0.993 | ||||
| p | 0.161 | ||||
| Lowerbound of 95% confidence interval for Sharpe Ratio | -0.342 | ||||
| Upperbound of 95% confidence interval for Sharpe Ratio | 1.045 | ||||
| Lowerbound of 95% CI (Gibbons, Hedeker & Davis approximation) | -0.343 | ||||
| Upperbound of 95% CI (Gibbons, Hedeker & Davis approximation) | 1.045 | ||||
| Statistics related to Sortino ratio | |||||
| Sortino ratio | 0.560 | ||||
| Upside Potential Ratio | 3.962 | ||||
| Upside part of mean | 1.531 | ||||
| Downside part of mean | -1.315 | ||||
| Upside SD | 0.480 | ||||
| Downside SD | 0.386 | ||||
| N nonnegative terms | 642.000 | ||||
| N negative terms | 1450.000 | ||||
| Statistics related to linear regression on benchmark | |||||
| N of observations | 2092.000 | ||||
| Mean of predictor | 0.232 | ||||
| Mean of criterion | 0.216 | ||||
| SD of predictor | 0.535 | ||||
| SD of criterion | 0.616 | ||||
| Covariance | 0.142 | ||||
| r | 0.430 | ||||
| b (slope, estimate of beta) | 0.496 | ||||
| a (intercept, estimate of alpha) | 0.101 | ||||
| Mean Square Error | 0.309 | ||||
| DF error | 2090.000 | ||||
| t(b) | 21.803 | ||||
| p(b) | 0.000 | ||||
| t(a) | 0.515 | ||||
| p(a) | 0.303 | ||||
| Lowerbound of 95% confidence interval for beta | 0.451 | ||||
| Upperbound of 95% confidence interval for beta | 0.540 | ||||
| Lowerbound of 95% confidence interval for alpha | -0.285 | ||||
| Upperbound of 95% confidence interval for alpha | 0.488 | ||||
| Treynor index (mean / b) | 0.437 | ||||
| Jensen alpha (a) | 0.101 | ||||
| Ratio statistics of excess log return rates | |||||
| Statistics related to Sharpe ratio | |||||
| Mean | 0.031 | ||||
| SD | 0.614 | ||||
| Sharpe ratio (Glass type estimate) | 0.051 | ||||
| Sharpe ratio (Hedges UMVUE) | 0.051 | ||||
| df | 2091.000 | ||||
| t | 0.143 | ||||
| p | 0.443 | ||||
| Lowerbound of 95% confidence interval for Sharpe Ratio | -0.643 | ||||
| Upperbound of 95% confidence interval for Sharpe Ratio | 0.744 | ||||
| Lowerbound of 95% CI (Gibbons, Hedeker & Davis approximation) | -0.643 | ||||
| Upperbound of 95% CI (Gibbons, Hedeker & Davis approximation) | 0.744 | ||||
| Statistics related to Sortino ratio | |||||
| Sortino ratio | 0.068 | ||||
| Upside Potential Ratio | 3.132 | ||||
| Upside part of mean | 1.439 | ||||
| Downside part of mean | -1.408 | ||||
| Upside SD | 0.406 | ||||
| Downside SD | 0.459 | ||||
| N nonnegative terms | 642.000 | ||||
| N negative terms | 1450.000 | ||||
| Statistics related to linear regression on benchmark | |||||
| N of observations | 2092.000 | ||||
| Mean of predictor | 0.090 | ||||
| Mean of criterion | 0.031 | ||||
| SD of predictor | 0.532 | ||||
| SD of criterion | 0.614 | ||||
| Covariance | 0.139 | ||||
| r | 0.426 | ||||
| b (slope, estimate of beta) | 0.492 | ||||
| a (intercept, estimate of alpha) | -0.013 | ||||
| Mean Square Error | 0.308 | ||||
| DF error | 2090.000 | ||||
| t(b) | 21.527 | ||||
| p(b) | 0.000 | ||||
| t(a) | -0.068 | ||||
| p(a) | 0.527 | ||||
| Lowerbound of 95% confidence interval for beta | 0.447 | ||||
| Upperbound of 95% confidence interval for beta | 0.536 | ||||
| Lowerbound of 95% confidence interval for alpha | -0.399 | ||||
| Upperbound of 95% confidence interval for alpha | 0.372 | ||||
| Treynor index (mean / b) | 0.063 | ||||
| Jensen alpha (a) | -0.013 | ||||
| Risk estimates for a one-period unit investment (parametric) | |||||
| assuming log normal returns and losses (using central moments from Sharpe statistics) | |||||
| VaR(95%) | 0.060 | ||||
| Expected Shortfall on VaR | 0.075 | ||||
| assuming Pareto losses only (using partial moments from Sortino statistics) | |||||
| VaR(95%) | 0.014 | ||||
| Expected Shortfall on VaR | 0.031 | ||||
| ORDER STATISTICS | |||||
| Quartiles of return rates | |||||
| Number of observations | 2092.000 | ||||
| Minimum | 0.512 | ||||
| Quartile 1 | 1.000 | ||||
| Median | 1.000 | ||||
| Quartile 3 | 1.002 | ||||
| Maximum | 1.786 | ||||
| Mean of quarter 1 | 0.980 | ||||
| Mean of quarter 2 | 1.000 | ||||
| Mean of quarter 3 | 1.000 | ||||
| Mean of quarter 4 | 1.023 | ||||
| Inter Quartile Range | 0.002 | ||||
| Number outliers low | 344.000 | ||||
| Percentage of outliers low | 0.164 | ||||
| Mean of outliers low | 0.971 | ||||
| Number of outliers high | 416.000 | ||||
| Percentage of outliers high | 0.199 | ||||
| Mean of outliers high | 1.029 | ||||
| Risk estimates for a one-period unit investment (based on Extreme Value Theory) | |||||
| Extreme Value Index (moments method) | 1.265 | ||||
| VaR(95%) (moments method) | 0.009 | ||||
| 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 observations | 28.000 | ||||
| Minimum | 0.000 | ||||
| Quartile 1 | 0.005 | ||||
| Median | 0.033 | ||||
| Quartile 3 | 0.127 | ||||
| Maximum | 0.513 | ||||
| Mean of quarter 1 | 0.002 | ||||
| Mean of quarter 2 | 0.011 | ||||
| Mean of quarter 3 | 0.080 | ||||
| Mean of quarter 4 | 0.288 | ||||
| Inter Quartile Range | 0.122 | ||||
| Number outliers low | 0.000 | ||||
| Percentage of outliers low | 0.000 | ||||
| Mean of outliers low | NA | ||||
| Number of outliers high | 3.000 | ||||
| Percentage of outliers high | 0.107 | ||||
| Mean of outliers high | 0.399 | ||||
| Risk estimates based on draw downs (based on Extreme Value Theory) | |||||
| Extreme Value Index (moments method) | -1.528 | ||||
| VaR(95%) (moments method) | 0.296 | ||||
| Expected Shortfall (moments method) | 0.307 | ||||
| Extreme Value Index (regression method) | 0.014 | ||||
| VaR(95%) (regression method) | 0.345 | ||||
| Expected Shortfall (regression method) | 0.479 | ||||
| COMBINED STATISTICS | |||||
| Annualized return (arithmetic extrapolation) | 0.103 | ||||
| Compounded annual return (geometric extrapolation) | 0.078 | ||||
| Calmar ratio (compounded annual return / max draw down) | 0.152 | ||||
| Compounded annual return / average of 25% largest draw downs | 0.270 | ||||
| Compounded annual return / Expected Shortfall lognormal | 1.039 | ||||
| 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 | ||||
| SD | 0.000 | ||||
| Sharpe ratio (Glass type estimate) | NA | ||||
| Sharpe ratio (Hedges UMVUE) | NA | ||||
| df | NA | ||||
| t | NA | ||||
| p | NA | ||||
| Lowerbound of 95% confidence interval for Sharpe Ratio | NA | ||||
| Upperbound of 95% confidence interval for Sharpe Ratio | NA | ||||
| 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 | -16.186 | ||||
| Upside Potential Ratio | 0.000 | ||||
| Upside part of mean | 0.000 | ||||
| Downside part of mean | -0.044 | ||||
| Upside SD | 0.000 | ||||
| Downside SD | 0.003 | ||||
| N nonnegative terms | 0.000 | ||||
| N negative terms | 131.000 | ||||
| Statistics related to linear regression on benchmark | |||||
| N of observations | 131.000 | ||||
| Mean of predictor | 0.826 | ||||
| Mean of criterion | -0.044 | ||||
| SD of predictor | 0.562 | ||||
| SD of criterion | 0.000 | ||||
| Covariance | 0.000 | ||||
| r | NA | ||||
| b (slope, estimate of beta) | NA | ||||
| a (intercept, estimate of alpha) | NA | ||||
| Mean Square Error | NA | ||||
| DF error | NA | ||||
| t(b) | NA | ||||
| p(b) | NA | ||||
| t(a) | NA | ||||
| p(a) | NA | ||||
| Lowerbound of 95% confidence interval for beta | NA | ||||
| Upperbound of 95% confidence interval for beta | NA | ||||
| Lowerbound of 95% confidence interval for alpha | NA | ||||
| Upperbound of 95% confidence interval for alpha | NA | ||||
| Treynor index (mean / b) | NA | ||||
| Jensen alpha (a) | NA | ||||
| Ratio statistics of excess log return rates | |||||
| Statistics related to Sharpe ratio | |||||
| Mean | -0.044 | ||||
| SD | 0.000 | ||||
| Sharpe ratio (Glass type estimate) | -12492933348697024.000 | ||||
| Sharpe ratio (Hedges UMVUE) | -12420719861132300.000 | ||||
| df | 130.000 | ||||
| t | -8833837887775228.000 | ||||
| p | 1.000 | ||||
| Lowerbound of 95% confidence interval for Sharpe Ratio | NA | ||||
| Upperbound of 95% confidence interval for Sharpe Ratio | NA | ||||
| Lowerbound of 95% CI (Gibbons, Hedeker & Davis approximation) | -13930479873814932.000 | ||||
| Upperbound of 95% CI (Gibbons, Hedeker & Davis approximation) | -10910959848449668.000 | ||||
| Statistics related to Sortino ratio | |||||
| Sortino ratio | -16.186 | ||||
| Upside Potential Ratio | 0.000 | ||||
| Upside part of mean | 0.000 | ||||
| Downside part of mean | -0.044 | ||||
| Upside SD | 0.000 | ||||
| Downside SD | 0.003 | ||||
| N nonnegative terms | 0.000 | ||||
| N negative terms | 131.000 | ||||
| Statistics related to linear regression on benchmark | |||||
| N of observations | 131.000 | ||||
| Mean of predictor | 0.664 | ||||
| Mean of criterion | -0.044 | ||||
| SD of predictor | 0.575 | ||||
| SD of criterion | 0.000 | ||||
| Covariance | -0.000 | ||||
| r | -0.000 | ||||
| b (slope, estimate of beta) | -0.000 | ||||
| a (intercept, estimate of alpha) | -0.044 | ||||
| Mean Square Error | 0.000 | ||||
| DF error | 129.000 | ||||
| t(b) | -0.000 | ||||
| p(b) | 0.500 | ||||
| t(a) | -8777320509851700.000 | ||||
| p(a) | 1.000 | ||||
| Lowerbound of 95% confidence interval for beta | -0.000 | ||||
| Upperbound of 95% confidence interval for beta | 0.000 | ||||
| Lowerbound of 95% confidence interval for alpha | -0.044 | ||||
| Upperbound of 95% confidence interval for alpha | -0.044 | ||||
| Treynor index (mean / b) | 266624175450774720090735833513984.000 | ||||
| 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 VaR | 0.000 | ||||
| assuming Pareto losses only (using partial moments from Sortino statistics) | |||||
| VaR(95%) | 0.000 | ||||
| Expected Shortfall on VaR | 0.000 | ||||
| ORDER STATISTICS | |||||
| Quartiles of return rates | |||||
| Number of observations | 131.000 | ||||
| Minimum | 1.000 | ||||
| Quartile 1 | 1.000 | ||||
| Median | 1.000 | ||||
| Quartile 3 | 1.000 | ||||
| Maximum | 1.000 | ||||
| Mean of quarter 1 | 1.000 | ||||
| Mean of quarter 2 | 1.000 | ||||
| Mean of quarter 3 | 1.000 | ||||
| Mean of quarter 4 | 1.000 | ||||
| Inter Quartile Range | 0.000 | ||||
| Number outliers low | 0.000 | ||||
| Percentage of outliers low | 0.000 | ||||
| Mean of outliers low | NA | ||||
| Number of outliers high | 0.000 | ||||
| Percentage of outliers high | 0.000 | ||||
| Mean of outliers high | NA | ||||
| 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 observations | 0.000 | ||||
| Minimum | NA | ||||
| Quartile 1 | NA | ||||
| Median | NA | ||||
| Quartile 3 | NA | ||||
| Maximum | NA | ||||
| Mean of quarter 1 | NA | ||||
| Mean of quarter 2 | NA | ||||
| Mean of quarter 3 | NA | ||||
| Mean of quarter 4 | NA | ||||
| Inter Quartile Range | 0.000 | ||||
| Number outliers low | 0.000 | ||||
| Percentage of outliers low | NA | ||||
| Mean of outliers low | NA | ||||
| Number of outliers high | 0.000 | ||||
| Percentage of outliers high | NA | ||||
| Mean of outliers high | NA | ||||
| 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 downs | NA | ||||
| Compounded annual return / Expected Shortfall lognormal | 0.000 | ||||