Advanced Statistics: Parcours US Stars
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 | 0.025 | ||||
| SD | 0.097 | ||||
| Sharpe ratio (Glass type estimate) | 0.259 | ||||
| Sharpe ratio (Hedges UMVUE) | 0.257 | ||||
| df | 90.000 | ||||
| t | 0.713 | ||||
| p | 0.239 | ||||
| Lowerbound of 95% confidence interval for Sharpe Ratio | -0.455 | ||||
| Upperbound of 95% confidence interval for Sharpe Ratio | 0.971 | ||||
| Lowerbound of 95% CI (Gibbons, Hedeker & Davis approximation) | -0.456 | ||||
| Upperbound of 95% CI (Gibbons, Hedeker & Davis approximation) | 0.969 | ||||
| Statistics related to Sortino ratio | |||||
| Sortino ratio | 0.533 | ||||
| Upside Potential Ratio | 2.265 | ||||
| Upside part of mean | 0.107 | ||||
| Downside part of mean | -0.082 | ||||
| Upside SD | 0.085 | ||||
| Downside SD | 0.047 | ||||
| N nonnegative terms | 29.000 | ||||
| N negative terms | 62.000 | ||||
| Statistics related to linear regression on benchmark | |||||
| N of observations | 91.000 | ||||
| Mean of predictor | 0.192 | ||||
| Mean of criterion | 0.025 | ||||
| SD of predictor | 0.216 | ||||
| SD of criterion | 0.097 | ||||
| Covariance | 0.003 | ||||
| r | 0.121 | ||||
| b (slope, estimate of beta) | 0.055 | ||||
| a (intercept, estimate of alpha) | 0.015 | ||||
| Mean Square Error | 0.009 | ||||
| DF error | 89.000 | ||||
| t(b) | 1.150 | ||||
| p(b) | 0.127 | ||||
| t(a) | 0.403 | ||||
| p(a) | 0.344 | ||||
| Lowerbound of 95% confidence interval for beta | -0.040 | ||||
| Upperbound of 95% confidence interval for beta | 0.149 | ||||
| Lowerbound of 95% confidence interval for alpha | -0.058 | ||||
| Upperbound of 95% confidence interval for alpha | 0.087 | ||||
| Treynor index (mean / b) | 0.462 | ||||
| Jensen alpha (a) | 0.015 | ||||
| Ratio statistics of excess log return rates | |||||
| Statistics related to Sharpe ratio | |||||
| Mean | 0.021 | ||||
| SD | 0.094 | ||||
| Sharpe ratio (Glass type estimate) | 0.220 | ||||
| Sharpe ratio (Hedges UMVUE) | 0.218 | ||||
| df | 90.000 | ||||
| t | 0.606 | ||||
| p | 0.273 | ||||
| Lowerbound of 95% confidence interval for Sharpe Ratio | -0.493 | ||||
| Upperbound of 95% confidence interval for Sharpe Ratio | 0.932 | ||||
| Lowerbound of 95% CI (Gibbons, Hedeker & Davis approximation) | -0.494 | ||||
| Upperbound of 95% CI (Gibbons, Hedeker & Davis approximation) | 0.931 | ||||
| Statistics related to Sortino ratio | |||||
| Sortino ratio | 0.429 | ||||
| Upside Potential Ratio | 2.150 | ||||
| Upside part of mean | 0.103 | ||||
| Downside part of mean | -0.083 | ||||
| Upside SD | 0.080 | ||||
| Downside SD | 0.048 | ||||
| N nonnegative terms | 29.000 | ||||
| N negative terms | 62.000 | ||||
| Statistics related to linear regression on benchmark | |||||
| N of observations | 91.000 | ||||
| Mean of predictor | 0.169 | ||||
| Mean of criterion | 0.021 | ||||
| SD of predictor | 0.204 | ||||
| SD of criterion | 0.094 | ||||
| Covariance | 0.003 | ||||
| r | 0.139 | ||||
| b (slope, estimate of beta) | 0.064 | ||||
| a (intercept, estimate of alpha) | 0.010 | ||||
| Mean Square Error | 0.009 | ||||
| DF error | 89.000 | ||||
| t(b) | 1.328 | ||||
| p(b) | 0.094 | ||||
| t(a) | 0.282 | ||||
| p(a) | 0.389 | ||||
| Lowerbound of 95% confidence interval for beta | -0.032 | ||||
| Upperbound of 95% confidence interval for beta | 0.160 | ||||
| Lowerbound of 95% confidence interval for alpha | -0.059 | ||||
| Upperbound of 95% confidence interval for alpha | 0.079 | ||||
| Treynor index (mean / b) | 0.322 | ||||
| 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%) | 0.042 | ||||
| Expected Shortfall on VaR | 0.053 | ||||
| assuming Pareto losses only (using partial moments from Sortino statistics) | |||||
| VaR(95%) | 0.019 | ||||
| Expected Shortfall on VaR | 0.035 | ||||
| ORDER STATISTICS | |||||
| Quartiles of return rates | |||||
| Number of observations | 91.000 | ||||
| Minimum | 0.949 | ||||
| Quartile 1 | 1.000 | ||||
| Median | 1.000 | ||||
| Quartile 3 | 1.010 | ||||
| Maximum | 1.163 | ||||
| Mean of quarter 1 | 0.982 | ||||
| Mean of quarter 2 | 1.000 | ||||
| Mean of quarter 3 | 1.003 | ||||
| Mean of quarter 4 | 1.038 | ||||
| Inter Quartile Range | 0.010 | ||||
| Number outliers low | 10.000 | ||||
| Percentage of outliers low | 0.110 | ||||
| Mean of outliers low | 0.966 | ||||
| Number of outliers high | 14.000 | ||||
| Percentage of outliers high | 0.154 | ||||
| Mean of outliers high | 1.051 | ||||
| Risk estimates for a one-period unit investment (based on Extreme Value Theory) | |||||
| Extreme Value Index (moments method) | -0.792 | ||||
| VaR(95%) (moments method) | 0.005 | ||||
| Expected Shortfall (moments method) | 0.005 | ||||
| Extreme Value Index (regression method) | -0.447 | ||||
| VaR(95%) (regression method) | 0.021 | ||||
| Expected Shortfall (regression method) | 0.028 | ||||
| DRAW DOWN STATISTICS | |||||
| Quartiles of draw downs | |||||
| Number of observations | 13.000 | ||||
| Minimum | 0.001 | ||||
| Quartile 1 | 0.004 | ||||
| Median | 0.009 | ||||
| Quartile 3 | 0.029 | ||||
| Maximum | 0.131 | ||||
| Mean of quarter 1 | 0.003 | ||||
| Mean of quarter 2 | 0.009 | ||||
| Mean of quarter 3 | 0.022 | ||||
| Mean of quarter 4 | 0.077 | ||||
| Inter Quartile Range | 0.024 | ||||
| Number outliers low | 0.000 | ||||
| Percentage of outliers low | 0.000 | ||||
| Mean of outliers low | NA | ||||
| Number of outliers high | 1.000 | ||||
| Percentage of outliers high | 0.077 | ||||
| Mean of outliers high | 0.131 | ||||
| Risk estimates based on draw downs (based on Extreme Value Theory) | |||||
| Extreme Value Index (moments method) | -0.278 | ||||
| VaR(95%) (moments method) | 0.068 | ||||
| Expected Shortfall (moments method) | 0.084 | ||||
| Extreme Value Index (regression method) | 0.621 | ||||
| VaR(95%) (regression method) | 0.115 | ||||
| Expected Shortfall (regression method) | 0.328 | ||||
| COMBINED STATISTICS | |||||
| Annualized return (arithmetic extrapolation) | 0.083 | ||||
| Compounded annual return (geometric extrapolation) | 0.067 | ||||
| Calmar ratio (compounded annual return / max draw down) | 0.509 | ||||
| Compounded annual return / average of 25% largest draw downs | 0.869 | ||||
| Compounded annual return / Expected Shortfall lognormal | 1.270 | ||||
| ANALYSIS BASED ON DAILY VALUES, FULL HISTORY (Back) | |||||
| RATIO STATISTICS | |||||
| Ratio statistics of excess return rates | |||||
| Statistics related to Sharpe ratio | |||||
| Mean | 0.023 | ||||
| SD | 0.078 | ||||
| Sharpe ratio (Glass type estimate) | 0.299 | ||||
| Sharpe ratio (Hedges UMVUE) | 0.299 | ||||
| df | 1997.000 | ||||
| t | 0.825 | ||||
| p | 0.488 | ||||
| Lowerbound of 95% confidence interval for Sharpe Ratio | -0.411 | ||||
| Upperbound of 95% confidence interval for Sharpe Ratio | 1.009 | ||||
| Lowerbound of 95% CI (Gibbons, Hedeker & Davis approximation) | -0.411 | ||||
| Upperbound of 95% CI (Gibbons, Hedeker & Davis approximation) | 1.009 | ||||
| Statistics related to Sortino ratio | |||||
| Sortino ratio | 0.462 | ||||
| Upside Potential Ratio | 6.427 | ||||
| Upside part of mean | 0.324 | ||||
| Downside part of mean | -0.301 | ||||
| Upside SD | 0.059 | ||||
| Downside SD | 0.050 | ||||
| N nonnegative terms | 635.000 | ||||
| N negative terms | 1363.000 | ||||
| Statistics related to linear regression on benchmark | |||||
| N of observations | 1998.000 | ||||
| Mean of predictor | 0.208 | ||||
| Mean of criterion | 0.023 | ||||
| SD of predictor | 0.227 | ||||
| SD of criterion | 0.078 | ||||
| Covariance | 0.003 | ||||
| r | 0.188 | ||||
| b (slope, estimate of beta) | 0.064 | ||||
| a (intercept, estimate of alpha) | 0.010 | ||||
| Mean Square Error | 0.006 | ||||
| DF error | 1996.000 | ||||
| t(b) | 8.542 | ||||
| p(b) | 0.406 | ||||
| t(a) | 0.356 | ||||
| p(a) | 0.496 | ||||
| Lowerbound of 95% confidence interval for beta | 0.050 | ||||
| Upperbound of 95% confidence interval for beta | 0.079 | ||||
| Lowerbound of 95% confidence interval for alpha | -0.045 | ||||
| Upperbound of 95% confidence interval for alpha | 0.064 | ||||
| Treynor index (mean / b) | 0.361 | ||||
| Jensen alpha (a) | 0.010 | ||||
| Ratio statistics of excess log return rates | |||||
| Statistics related to Sharpe ratio | |||||
| Mean | 0.020 | ||||
| SD | 0.078 | ||||
| Sharpe ratio (Glass type estimate) | 0.261 | ||||
| Sharpe ratio (Hedges UMVUE) | 0.260 | ||||
| df | 1997.000 | ||||
| t | 0.719 | ||||
| p | 0.490 | ||||
| Lowerbound of 95% confidence interval for Sharpe Ratio | -0.449 | ||||
| Upperbound of 95% confidence interval for Sharpe Ratio | 0.970 | ||||
| Lowerbound of 95% CI (Gibbons, Hedeker & Davis approximation) | -0.449 | ||||
| Upperbound of 95% CI (Gibbons, Hedeker & Davis approximation) | 0.970 | ||||
| Statistics related to Sortino ratio | |||||
| Sortino ratio | 0.398 | ||||
| Upside Potential Ratio | 6.333 | ||||
| Upside part of mean | 0.322 | ||||
| Downside part of mean | -0.302 | ||||
| Upside SD | 0.059 | ||||
| Downside SD | 0.051 | ||||
| N nonnegative terms | 635.000 | ||||
| N negative terms | 1363.000 | ||||
| Statistics related to linear regression on benchmark | |||||
| N of observations | 1998.000 | ||||
| Mean of predictor | 0.182 | ||||
| Mean of criterion | 0.020 | ||||
| SD of predictor | 0.227 | ||||
| SD of criterion | 0.078 | ||||
| Covariance | 0.003 | ||||
| r | 0.188 | ||||
| b (slope, estimate of beta) | 0.064 | ||||
| a (intercept, estimate of alpha) | 0.009 | ||||
| Mean Square Error | 0.006 | ||||
| DF error | 1996.000 | ||||
| t(b) | 8.571 | ||||
| p(b) | 0.406 | ||||
| t(a) | 0.308 | ||||
| p(a) | 0.497 | ||||
| Lowerbound of 95% confidence interval for beta | 0.050 | ||||
| Upperbound of 95% confidence interval for beta | 0.079 | ||||
| Lowerbound of 95% confidence interval for alpha | -0.046 | ||||
| Upperbound of 95% confidence interval for alpha | 0.063 | ||||
| Treynor index (mean / b) | 0.315 | ||||
| Jensen alpha (a) | 0.009 | ||||
| Risk estimates for a one-period unit investment (parametric) | |||||
| assuming log normal returns and losses (using central moments from Sharpe statistics) | |||||
| VaR(95%) | 0.008 | ||||
| Expected Shortfall on VaR | 0.010 | ||||
| assuming Pareto losses only (using partial moments from Sortino statistics) | |||||
| VaR(95%) | 0.003 | ||||
| Expected Shortfall on VaR | 0.007 | ||||
| ORDER STATISTICS | |||||
| Quartiles of return rates | |||||
| Number of observations | 1998.000 | ||||
| Minimum | 0.952 | ||||
| Quartile 1 | 1.000 | ||||
| Median | 1.000 | ||||
| Quartile 3 | 1.001 | ||||
| Maximum | 1.042 | ||||
| Mean of quarter 1 | 0.996 | ||||
| Mean of quarter 2 | 1.000 | ||||
| Mean of quarter 3 | 1.000 | ||||
| Mean of quarter 4 | 1.005 | ||||
| Inter Quartile Range | 0.001 | ||||
| Number outliers low | 256.000 | ||||
| Percentage of outliers low | 0.128 | ||||
| Mean of outliers low | 0.993 | ||||
| Number of outliers high | 238.000 | ||||
| Percentage of outliers high | 0.119 | ||||
| Mean of outliers high | 1.008 | ||||
| Risk estimates for a one-period unit investment (based on Extreme Value Theory) | |||||
| Extreme Value Index (moments method) | 0.309 | ||||
| VaR(95%) (moments method) | 0.003 | ||||
| Expected Shortfall (moments method) | 0.006 | ||||
| Extreme Value Index (regression method) | 0.200 | ||||
| VaR(95%) (regression method) | 0.004 | ||||
| Expected Shortfall (regression method) | 0.007 | ||||
| DRAW DOWN STATISTICS | |||||
| Quartiles of draw downs | |||||
| Number of observations | 64.000 | ||||
| Minimum | 0.000 | ||||
| Quartile 1 | 0.002 | ||||
| Median | 0.006 | ||||
| Quartile 3 | 0.016 | ||||
| Maximum | 0.135 | ||||
| Mean of quarter 1 | 0.001 | ||||
| Mean of quarter 2 | 0.004 | ||||
| Mean of quarter 3 | 0.010 | ||||
| Mean of quarter 4 | 0.048 | ||||
| Inter Quartile Range | 0.013 | ||||
| Number outliers low | 0.000 | ||||
| Percentage of outliers low | 0.000 | ||||
| Mean of outliers low | NA | ||||
| Number of outliers high | 9.000 | ||||
| Percentage of outliers high | 0.141 | ||||
| Mean of outliers high | 0.068 | ||||
| Risk estimates based on draw downs (based on Extreme Value Theory) | |||||
| Extreme Value Index (moments method) | 0.344 | ||||
| VaR(95%) (moments method) | 0.046 | ||||
| Expected Shortfall (moments method) | 0.085 | ||||
| Extreme Value Index (regression method) | 0.142 | ||||
| VaR(95%) (regression method) | 0.051 | ||||
| Expected Shortfall (regression method) | 0.079 | ||||
| COMBINED STATISTICS | |||||
| Annualized return (arithmetic extrapolation) | 0.083 | ||||
| Compounded annual return (geometric extrapolation) | 0.066 | ||||
| Calmar ratio (compounded annual return / max draw down) | 0.490 | ||||
| Compounded annual return / average of 25% largest draw downs | 1.393 | ||||
| Compounded annual return / Expected Shortfall lognormal | 6.789 | ||||
| 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 | 1.161 | ||||
| Mean of criterion | -0.044 | ||||
| SD of predictor | 0.427 | ||||
| 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 | 1.069 | ||||
| Mean of criterion | -0.044 | ||||
| SD of predictor | 0.423 | ||||
| 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) | -8693442059456148.000 | ||||
| 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) | -98737742463056661048452536336384.000 | ||||
| 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 | ||||