Advanced Statistics: Safe Harbor
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 | -0.024 | ||||
| SD | 0.039 | ||||
| Sharpe ratio (Glass type estimate) | -0.612 | ||||
| Sharpe ratio (Hedges UMVUE) | -0.603 | ||||
| df | 56.000 | ||||
| t | -1.333 | ||||
| p | 0.906 | ||||
| Lowerbound of 95% confidence interval for Sharpe Ratio | -1.515 | ||||
| Upperbound of 95% confidence interval for Sharpe Ratio | 0.297 | ||||
| Lowerbound of 95% CI (Gibbons, Hedeker & Davis approximation) | -1.510 | ||||
| Upperbound of 95% CI (Gibbons, Hedeker & Davis approximation) | 0.303 | ||||
| Statistics related to Sortino ratio | |||||
| Sortino ratio | -0.955 | ||||
| Upside Potential Ratio | 1.280 | ||||
| Upside part of mean | 0.032 | ||||
| Downside part of mean | -0.056 | ||||
| Upside SD | 0.030 | ||||
| Downside SD | 0.025 | ||||
| N nonnegative terms | 7.000 | ||||
| N negative terms | 50.000 | ||||
| Statistics related to linear regression on benchmark | |||||
| N of observations | 57.000 | ||||
| Mean of predictor | 0.389 | ||||
| Mean of criterion | -0.024 | ||||
| SD of predictor | 0.299 | ||||
| SD of criterion | 0.039 | ||||
| Covariance | -0.001 | ||||
| r | -0.101 | ||||
| b (slope, estimate of beta) | -0.013 | ||||
| a (intercept, estimate of alpha) | -0.019 | ||||
| Mean Square Error | 0.002 | ||||
| DF error | 55.000 | ||||
| t(b) | -0.753 | ||||
| p(b) | 0.773 | ||||
| t(a) | -0.975 | ||||
| p(a) | 0.833 | ||||
| Lowerbound of 95% confidence interval for beta | -0.048 | ||||
| Upperbound of 95% confidence interval for beta | 0.022 | ||||
| Lowerbound of 95% confidence interval for alpha | -0.057 | ||||
| Upperbound of 95% confidence interval for alpha | 0.020 | ||||
| Treynor index (mean / b) | 1.809 | ||||
| Jensen alpha (a) | -0.019 | ||||
| Ratio statistics of excess log return rates | |||||
| Statistics related to Sharpe ratio | |||||
| Mean | -0.024 | ||||
| SD | 0.038 | ||||
| Sharpe ratio (Glass type estimate) | -0.635 | ||||
| Sharpe ratio (Hedges UMVUE) | -0.627 | ||||
| df | 56.000 | ||||
| t | -1.385 | ||||
| p | 0.914 | ||||
| Lowerbound of 95% confidence interval for Sharpe Ratio | -1.540 | ||||
| Upperbound of 95% confidence interval for Sharpe Ratio | 0.274 | ||||
| Lowerbound of 95% CI (Gibbons, Hedeker & Davis approximation) | -1.534 | ||||
| Upperbound of 95% CI (Gibbons, Hedeker & Davis approximation) | 0.280 | ||||
| Statistics related to Sortino ratio | |||||
| Sortino ratio | -0.975 | ||||
| Upside Potential Ratio | 1.249 | ||||
| Upside part of mean | 0.031 | ||||
| Downside part of mean | -0.056 | ||||
| Upside SD | 0.030 | ||||
| Downside SD | 0.025 | ||||
| N nonnegative terms | 7.000 | ||||
| N negative terms | 50.000 | ||||
| Statistics related to linear regression on benchmark | |||||
| N of observations | 57.000 | ||||
| Mean of predictor | 0.342 | ||||
| Mean of criterion | -0.024 | ||||
| SD of predictor | 0.280 | ||||
| SD of criterion | 0.038 | ||||
| Covariance | -0.001 | ||||
| r | -0.104 | ||||
| b (slope, estimate of beta) | -0.014 | ||||
| a (intercept, estimate of alpha) | -0.020 | ||||
| Mean Square Error | 0.001 | ||||
| DF error | 55.000 | ||||
| t(b) | -0.773 | ||||
| p(b) | 0.779 | ||||
| t(a) | -1.041 | ||||
| p(a) | 0.849 | ||||
| Lowerbound of 95% confidence interval for beta | -0.051 | ||||
| Upperbound of 95% confidence interval for beta | 0.023 | ||||
| Lowerbound of 95% confidence interval for alpha | -0.057 | ||||
| Upperbound of 95% confidence interval for alpha | 0.018 | ||||
| Treynor index (mean / b) | 1.718 | ||||
| Jensen alpha (a) | -0.020 | ||||
| Risk estimates for a one-period unit investment (parametric) | |||||
| assuming log normal returns and losses (using central moments from Sharpe statistics) | |||||
| VaR(95%) | 0.020 | ||||
| Expected Shortfall on VaR | 0.025 | ||||
| assuming Pareto losses only (using partial moments from Sortino statistics) | |||||
| VaR(95%) | 0.014 | ||||
| Expected Shortfall on VaR | 0.021 | ||||
| ORDER STATISTICS | |||||
| Quartiles of return rates | |||||
| Number of observations | 57.000 | ||||
| Minimum | 0.975 | ||||
| Quartile 1 | 1.000 | ||||
| Median | 1.000 | ||||
| Quartile 3 | 1.000 | ||||
| Maximum | 1.051 | ||||
| Mean of quarter 1 | 0.994 | ||||
| Mean of quarter 2 | 1.000 | ||||
| Mean of quarter 3 | 1.000 | ||||
| Mean of quarter 4 | 1.013 | ||||
| Inter Quartile Range | 0.000 | ||||
| Number outliers low | 7.000 | ||||
| Percentage of outliers low | 0.123 | ||||
| Mean of outliers low | 0.988 | ||||
| Number of outliers high | 10.000 | ||||
| Percentage of outliers high | 0.175 | ||||
| Mean of outliers high | 1.018 | ||||
| Risk estimates for a one-period unit investment (based on Extreme Value Theory) | |||||
| Extreme Value Index (moments method) | -10.818 | ||||
| VaR(95%) (moments method) | 0.000 | ||||
| Expected Shortfall (moments method) | 0.000 | ||||
| Extreme Value Index (regression method) | -1.327 | ||||
| VaR(95%) (regression method) | 0.016 | ||||
| Expected Shortfall (regression method) | 0.020 | ||||
| DRAW DOWN STATISTICS | |||||
| Quartiles of draw downs | |||||
| Number of observations | 2.000 | ||||
| Minimum | 0.007 | ||||
| Quartile 1 | 0.021 | ||||
| Median | 0.036 | ||||
| Quartile 3 | 0.050 | ||||
| Maximum | 0.065 | ||||
| Mean of quarter 1 | 0.007 | ||||
| Mean of quarter 2 | NA | ||||
| Mean of quarter 3 | NA | ||||
| Mean of quarter 4 | 0.065 | ||||
| Inter Quartile Range | 0.029 | ||||
| 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 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) | 0.021 | ||||
| Compounded annual return (geometric extrapolation) | 0.020 | ||||
| Calmar ratio (compounded annual return / max draw down) | 0.304 | ||||
| Compounded annual return / average of 25% largest draw downs | 0.304 | ||||
| Compounded annual return / Expected Shortfall lognormal | 0.805 | ||||
| ANALYSIS BASED ON DAILY VALUES, FULL HISTORY (Back) | |||||
| RATIO STATISTICS | |||||
| Ratio statistics of excess return rates | |||||
| Statistics related to Sharpe ratio | |||||
| Mean | -0.021 | ||||
| SD | 0.080 | ||||
| Sharpe ratio (Glass type estimate) | -0.266 | ||||
| Sharpe ratio (Hedges UMVUE) | -0.266 | ||||
| df | 1250.000 | ||||
| t | -0.582 | ||||
| p | 0.508 | ||||
| Lowerbound of 95% confidence interval for Sharpe Ratio | -1.163 | ||||
| Upperbound of 95% confidence interval for Sharpe Ratio | 0.631 | ||||
| Lowerbound of 95% CI (Gibbons, Hedeker & Davis approximation) | -1.163 | ||||
| Upperbound of 95% CI (Gibbons, Hedeker & Davis approximation) | 0.631 | ||||
| Statistics related to Sortino ratio | |||||
| Sortino ratio | -0.405 | ||||
| Upside Potential Ratio | 2.401 | ||||
| Upside part of mean | 0.127 | ||||
| Downside part of mean | -0.148 | ||||
| Upside SD | 0.060 | ||||
| Downside SD | 0.053 | ||||
| N nonnegative terms | 76.000 | ||||
| N negative terms | 1175.000 | ||||
| Statistics related to linear regression on benchmark | |||||
| N of observations | 1251.000 | ||||
| Mean of predictor | 0.396 | ||||
| Mean of criterion | -0.021 | ||||
| SD of predictor | 0.309 | ||||
| SD of criterion | 0.080 | ||||
| Covariance | -0.002 | ||||
| r | -0.094 | ||||
| b (slope, estimate of beta) | -0.024 | ||||
| a (intercept, estimate of alpha) | -0.012 | ||||
| Mean Square Error | 0.006 | ||||
| DF error | 1249.000 | ||||
| t(b) | -3.344 | ||||
| p(b) | 0.560 | ||||
| t(a) | -0.318 | ||||
| p(a) | 0.506 | ||||
| Lowerbound of 95% confidence interval for beta | -0.039 | ||||
| Upperbound of 95% confidence interval for beta | -0.010 | ||||
| Lowerbound of 95% confidence interval for alpha | -0.084 | ||||
| Upperbound of 95% confidence interval for alpha | 0.060 | ||||
| Treynor index (mean / b) | 0.874 | ||||
| Jensen alpha (a) | -0.012 | ||||
| Ratio statistics of excess log return rates | |||||
| Statistics related to Sharpe ratio | |||||
| Mean | -0.025 | ||||
| SD | 0.080 | ||||
| Sharpe ratio (Glass type estimate) | -0.307 | ||||
| Sharpe ratio (Hedges UMVUE) | -0.307 | ||||
| df | 1250.000 | ||||
| t | -0.672 | ||||
| p | 0.509 | ||||
| Lowerbound of 95% confidence interval for Sharpe Ratio | -1.204 | ||||
| Upperbound of 95% confidence interval for Sharpe Ratio | 0.590 | ||||
| Lowerbound of 95% CI (Gibbons, Hedeker & Davis approximation) | -1.204 | ||||
| Upperbound of 95% CI (Gibbons, Hedeker & Davis approximation) | 0.590 | ||||
| Statistics related to Sortino ratio | |||||
| Sortino ratio | -0.449 | ||||
| Upside Potential Ratio | 2.285 | ||||
| Upside part of mean | 0.125 | ||||
| Downside part of mean | -0.149 | ||||
| Upside SD | 0.058 | ||||
| Downside SD | 0.055 | ||||
| N nonnegative terms | 76.000 | ||||
| N negative terms | 1175.000 | ||||
| Statistics related to linear regression on benchmark | |||||
| N of observations | 1251.000 | ||||
| Mean of predictor | 0.348 | ||||
| Mean of criterion | -0.025 | ||||
| SD of predictor | 0.311 | ||||
| SD of criterion | 0.080 | ||||
| Covariance | -0.002 | ||||
| r | -0.093 | ||||
| b (slope, estimate of beta) | -0.024 | ||||
| a (intercept, estimate of alpha) | -0.016 | ||||
| Mean Square Error | 0.006 | ||||
| DF error | 1249.000 | ||||
| t(b) | -3.307 | ||||
| p(b) | 0.559 | ||||
| t(a) | -0.445 | ||||
| p(a) | 0.508 | ||||
| Lowerbound of 95% confidence interval for beta | -0.038 | ||||
| Upperbound of 95% confidence interval for beta | -0.010 | ||||
| Lowerbound of 95% confidence interval for alpha | -0.088 | ||||
| Upperbound of 95% confidence interval for alpha | 0.055 | ||||
| Treynor index (mean / b) | 1.027 | ||||
| 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%) | 0.008 | ||||
| Expected Shortfall on VaR | 0.010 | ||||
| assuming Pareto losses only (using partial moments from Sortino statistics) | |||||
| VaR(95%) | 0.002 | ||||
| Expected Shortfall on VaR | 0.004 | ||||
| ORDER STATISTICS | |||||
| Quartiles of return rates | |||||
| Number of observations | 1251.000 | ||||
| Minimum | 0.906 | ||||
| Quartile 1 | 1.000 | ||||
| Median | 1.000 | ||||
| Quartile 3 | 1.000 | ||||
| Maximum | 1.109 | ||||
| Mean of quarter 1 | 0.998 | ||||
| Mean of quarter 2 | 1.000 | ||||
| Mean of quarter 3 | 1.000 | ||||
| Mean of quarter 4 | 1.002 | ||||
| Inter Quartile Range | 0.000 | ||||
| Number outliers low | 89.000 | ||||
| Percentage of outliers low | 0.071 | ||||
| Mean of outliers low | 0.994 | ||||
| Number of outliers high | 91.000 | ||||
| Percentage of outliers high | 0.073 | ||||
| Mean of outliers high | 1.007 | ||||
| Risk estimates for a one-period unit investment (based on Extreme Value Theory) | |||||
| Extreme Value Index (moments method) | 0.265 | ||||
| VaR(95%) (moments method) | 0.001 | ||||
| Expected Shortfall (moments method) | 0.003 | ||||
| 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 | 5.000 | ||||
| Minimum | 0.000 | ||||
| Quartile 1 | 0.005 | ||||
| Median | 0.015 | ||||
| Quartile 3 | 0.078 | ||||
| Maximum | 0.100 | ||||
| Mean of quarter 1 | 0.002 | ||||
| Mean of quarter 2 | 0.015 | ||||
| Mean of quarter 3 | 0.078 | ||||
| Mean of quarter 4 | 0.100 | ||||
| Inter Quartile Range | 0.073 | ||||
| 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 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) | 0.020 | ||||
| Compounded annual return (geometric extrapolation) | 0.020 | ||||
| Calmar ratio (compounded annual return / max draw down) | 0.196 | ||||
| Compounded annual return / average of 25% largest draw downs | 0.196 | ||||
| Compounded annual return / Expected Shortfall lognormal | 1.931 | ||||
| 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 | 1.000 | ||||
| Mean of criterion | -0.044 | ||||
| SD of predictor | 0.372 | ||||
| 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 | 0.928 | ||||
| Mean of criterion | -0.044 | ||||
| SD of predictor | 0.378 | ||||
| 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) | -8699748216742079.000 | ||||
| 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) | 461919049223677534930632576073728.000 | ||||
| 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 | ||||