Advanced Statistics: KOT
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 | -0.020 | ||||
| SD | 0.076 | ||||
| Sharpe ratio (Glass type estimate) | -0.267 | ||||
| Sharpe ratio (Hedges UMVUE) | -0.263 | ||||
| df | 50.000 | ||||
| t | -0.550 | ||||
| p | 0.708 | ||||
| Lowerbound of 95% confidence interval for Sharpe Ratio | -1.218 | ||||
| Upperbound of 95% confidence interval for Sharpe Ratio | 0.687 | ||||
| Lowerbound of 95% CI (Gibbons, Hedeker & Davis approximation) | -1.215 | ||||
| Upperbound of 95% CI (Gibbons, Hedeker & Davis approximation) | 0.689 | ||||
| Statistics related to Sortino ratio | |||||
| Sortino ratio | -0.392 | ||||
| Upside Potential Ratio | 1.376 | ||||
| Upside part of mean | 0.072 | ||||
| Downside part of mean | -0.092 | ||||
| Upside SD | 0.055 | ||||
| Downside SD | 0.052 | ||||
| N nonnegative terms | 11.000 | ||||
| N negative terms | 40.000 | ||||
| Statistics related to linear regression on benchmark | |||||
| N of observations | 51.000 | ||||
| Mean of predictor | 0.384 | ||||
| Mean of criterion | -0.020 | ||||
| SD of predictor | 0.270 | ||||
| SD of criterion | 0.076 | ||||
| Covariance | -0.001 | ||||
| r | -0.046 | ||||
| b (slope, estimate of beta) | -0.013 | ||||
| a (intercept, estimate of alpha) | -0.015 | ||||
| Mean Square Error | 0.006 | ||||
| DF error | 49.000 | ||||
| t(b) | -0.321 | ||||
| p(b) | 0.625 | ||||
| t(a) | -0.381 | ||||
| p(a) | 0.647 | ||||
| Lowerbound of 95% confidence interval for beta | -0.094 | ||||
| Upperbound of 95% confidence interval for beta | 0.068 | ||||
| Lowerbound of 95% confidence interval for alpha | -0.097 | ||||
| Upperbound of 95% confidence interval for alpha | 0.066 | ||||
| Treynor index (mean / b) | 1.571 | ||||
| Jensen alpha (a) | -0.015 | ||||
| Ratio statistics of excess log return rates | |||||
| Statistics related to Sharpe ratio | |||||
| Mean | -0.023 | ||||
| SD | 0.076 | ||||
| Sharpe ratio (Glass type estimate) | -0.305 | ||||
| Sharpe ratio (Hedges UMVUE) | -0.300 | ||||
| df | 50.000 | ||||
| t | -0.629 | ||||
| p | 0.734 | ||||
| Lowerbound of 95% confidence interval for Sharpe Ratio | -1.256 | ||||
| Upperbound of 95% confidence interval for Sharpe Ratio | 0.649 | ||||
| Lowerbound of 95% CI (Gibbons, Hedeker & Davis approximation) | -1.253 | ||||
| Upperbound of 95% CI (Gibbons, Hedeker & Davis approximation) | 0.652 | ||||
| Statistics related to Sortino ratio | |||||
| Sortino ratio | -0.435 | ||||
| Upside Potential Ratio | 1.314 | ||||
| Upside part of mean | 0.070 | ||||
| Downside part of mean | -0.093 | ||||
| Upside SD | 0.054 | ||||
| Downside SD | 0.053 | ||||
| N nonnegative terms | 11.000 | ||||
| N negative terms | 40.000 | ||||
| Statistics related to linear regression on benchmark | |||||
| N of observations | 51.000 | ||||
| Mean of predictor | 0.344 | ||||
| Mean of criterion | -0.023 | ||||
| SD of predictor | 0.255 | ||||
| SD of criterion | 0.076 | ||||
| Covariance | -0.001 | ||||
| r | -0.043 | ||||
| b (slope, estimate of beta) | -0.013 | ||||
| a (intercept, estimate of alpha) | -0.019 | ||||
| Mean Square Error | 0.006 | ||||
| DF error | 49.000 | ||||
| t(b) | -0.300 | ||||
| p(b) | 0.617 | ||||
| t(a) | -0.471 | ||||
| p(a) | 0.680 | ||||
| Lowerbound of 95% confidence interval for beta | -0.098 | ||||
| Upperbound of 95% confidence interval for beta | 0.073 | ||||
| Lowerbound of 95% confidence interval for alpha | -0.099 | ||||
| Upperbound of 95% confidence interval for alpha | 0.061 | ||||
| Treynor index (mean / b) | 1.822 | ||||
| Jensen alpha (a) | -0.019 | ||||
| Risk estimates for a one-period unit investment (parametric) | |||||
| assuming log normal returns and losses (using central moments from Sharpe statistics) | |||||
| VaR(95%) | 0.037 | ||||
| Expected Shortfall on VaR | 0.046 | ||||
| assuming Pareto losses only (using partial moments from Sortino statistics) | |||||
| VaR(95%) | 0.023 | ||||
| Expected Shortfall on VaR | 0.042 | ||||
| ORDER STATISTICS | |||||
| Quartiles of return rates | |||||
| Number of observations | 51.000 | ||||
| Minimum | 0.931 | ||||
| Quartile 1 | 1.000 | ||||
| Median | 1.000 | ||||
| Quartile 3 | 1.000 | ||||
| Maximum | 1.080 | ||||
| Mean of quarter 1 | 0.981 | ||||
| Mean of quarter 2 | 1.000 | ||||
| Mean of quarter 3 | 1.000 | ||||
| Mean of quarter 4 | 1.027 | ||||
| Inter Quartile Range | 0.000 | ||||
| Number outliers low | 10.000 | ||||
| Percentage of outliers low | 0.196 | ||||
| Mean of outliers low | 0.975 | ||||
| Number of outliers high | 12.000 | ||||
| Percentage of outliers high | 0.235 | ||||
| Mean of outliers high | 1.029 | ||||
| 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) | -0.142 | ||||
| VaR(95%) (regression method) | 0.028 | ||||
| Expected Shortfall (regression method) | 0.044 | ||||
| DRAW DOWN STATISTICS | |||||
| Quartiles of draw downs | |||||
| Number of observations | 1.000 | ||||
| Minimum | 0.087 | ||||
| Quartile 1 | 0.087 | ||||
| Median | 0.087 | ||||
| Quartile 3 | 0.087 | ||||
| Maximum | 0.087 | ||||
| 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 | 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) | 0.022 | ||||
| Compounded annual return (geometric extrapolation) | 0.021 | ||||
| Calmar ratio (compounded annual return / max draw down) | 0.242 | ||||
| Compounded annual return / average of 25% largest draw downs | NA | ||||
| Compounded annual return / Expected Shortfall lognormal | 0.458 | ||||
| ANALYSIS BASED ON DAILY VALUES, FULL HISTORY (Back) | |||||
| RATIO STATISTICS | |||||
| Ratio statistics of excess return rates | |||||
| Statistics related to Sharpe ratio | |||||
| Mean | -0.022 | ||||
| SD | 0.056 | ||||
| Sharpe ratio (Glass type estimate) | -0.384 | ||||
| Sharpe ratio (Hedges UMVUE) | -0.384 | ||||
| df | 1116.000 | ||||
| t | -0.793 | ||||
| p | 0.512 | ||||
| Lowerbound of 95% confidence interval for Sharpe Ratio | -1.333 | ||||
| Upperbound of 95% confidence interval for Sharpe Ratio | 0.565 | ||||
| Lowerbound of 95% CI (Gibbons, Hedeker & Davis approximation) | -1.333 | ||||
| Upperbound of 95% CI (Gibbons, Hedeker & Davis approximation) | 0.565 | ||||
| Statistics related to Sortino ratio | |||||
| Sortino ratio | -0.535 | ||||
| Upside Potential Ratio | 4.263 | ||||
| Upside part of mean | 0.173 | ||||
| Downside part of mean | -0.194 | ||||
| Upside SD | 0.039 | ||||
| Downside SD | 0.040 | ||||
| N nonnegative terms | 174.000 | ||||
| N negative terms | 943.000 | ||||
| Statistics related to linear regression on benchmark | |||||
| N of observations | 1117.000 | ||||
| Mean of predictor | 0.402 | ||||
| Mean of criterion | -0.022 | ||||
| SD of predictor | 0.293 | ||||
| SD of criterion | 0.056 | ||||
| Covariance | -0.000 | ||||
| r | -0.004 | ||||
| b (slope, estimate of beta) | -0.001 | ||||
| a (intercept, estimate of alpha) | -0.021 | ||||
| Mean Square Error | 0.003 | ||||
| DF error | 1115.000 | ||||
| t(b) | -0.132 | ||||
| p(b) | 0.503 | ||||
| t(a) | -0.779 | ||||
| p(a) | 0.515 | ||||
| Lowerbound of 95% confidence interval for beta | -0.012 | ||||
| Upperbound of 95% confidence interval for beta | 0.011 | ||||
| Lowerbound of 95% confidence interval for alpha | -0.075 | ||||
| Upperbound of 95% confidence interval for alpha | 0.032 | ||||
| Treynor index (mean / b) | 28.466 | ||||
| Jensen alpha (a) | -0.021 | ||||
| Ratio statistics of excess log return rates | |||||
| Statistics related to Sharpe ratio | |||||
| Mean | -0.023 | ||||
| SD | 0.056 | ||||
| Sharpe ratio (Glass type estimate) | -0.412 | ||||
| Sharpe ratio (Hedges UMVUE) | -0.412 | ||||
| df | 1116.000 | ||||
| t | -0.850 | ||||
| p | 0.513 | ||||
| Lowerbound of 95% confidence interval for Sharpe Ratio | -1.361 | ||||
| Upperbound of 95% confidence interval for Sharpe Ratio | 0.538 | ||||
| Lowerbound of 95% CI (Gibbons, Hedeker & Davis approximation) | -1.361 | ||||
| Upperbound of 95% CI (Gibbons, Hedeker & Davis approximation) | 0.538 | ||||
| Statistics related to Sortino ratio | |||||
| Sortino ratio | -0.569 | ||||
| Upside Potential Ratio | 4.208 | ||||
| Upside part of mean | 0.172 | ||||
| Downside part of mean | -0.195 | ||||
| Upside SD | 0.039 | ||||
| Downside SD | 0.041 | ||||
| N nonnegative terms | 174.000 | ||||
| N negative terms | 943.000 | ||||
| Statistics related to linear regression on benchmark | |||||
| N of observations | 1117.000 | ||||
| Mean of predictor | 0.358 | ||||
| Mean of criterion | -0.023 | ||||
| SD of predictor | 0.299 | ||||
| SD of criterion | 0.056 | ||||
| Covariance | -0.000 | ||||
| r | -0.004 | ||||
| b (slope, estimate of beta) | -0.001 | ||||
| a (intercept, estimate of alpha) | -0.023 | ||||
| Mean Square Error | 0.003 | ||||
| DF error | 1115.000 | ||||
| t(b) | -0.121 | ||||
| p(b) | 0.502 | ||||
| t(a) | -0.839 | ||||
| p(a) | 0.516 | ||||
| Lowerbound of 95% confidence interval for beta | -0.012 | ||||
| Upperbound of 95% confidence interval for beta | 0.010 | ||||
| Lowerbound of 95% confidence interval for alpha | -0.077 | ||||
| Upperbound of 95% confidence interval for alpha | 0.031 | ||||
| Treynor index (mean / b) | 33.894 | ||||
| Jensen alpha (a) | -0.023 | ||||
| Risk estimates for a one-period unit investment (parametric) | |||||
| assuming log normal returns and losses (using central moments from Sharpe statistics) | |||||
| VaR(95%) | 0.006 | ||||
| Expected Shortfall on VaR | 0.007 | ||||
| assuming Pareto losses only (using partial moments from Sortino statistics) | |||||
| VaR(95%) | 0.002 | ||||
| Expected Shortfall on VaR | 0.005 | ||||
| ORDER STATISTICS | |||||
| Quartiles of return rates | |||||
| Number of observations | 1117.000 | ||||
| Minimum | 0.969 | ||||
| Quartile 1 | 1.000 | ||||
| Median | 1.000 | ||||
| Quartile 3 | 1.000 | ||||
| Maximum | 1.023 | ||||
| Mean of quarter 1 | 0.998 | ||||
| Mean of quarter 2 | 1.000 | ||||
| Mean of quarter 3 | 1.000 | ||||
| Mean of quarter 4 | 1.003 | ||||
| Inter Quartile Range | 0.000 | ||||
| Number outliers low | 168.000 | ||||
| Percentage of outliers low | 0.150 | ||||
| Mean of outliers low | 0.996 | ||||
| Number of outliers high | 179.000 | ||||
| Percentage of outliers high | 0.160 | ||||
| Mean of outliers high | 1.004 | ||||
| Risk estimates for a one-period unit investment (based on Extreme Value Theory) | |||||
| Extreme Value Index (moments method) | 0.242 | ||||
| VaR(95%) (moments method) | 0.002 | ||||
| Expected Shortfall (moments method) | 0.004 | ||||
| Extreme Value Index (regression method) | 0.110 | ||||
| VaR(95%) (regression method) | 0.003 | ||||
| Expected Shortfall (regression method) | 0.006 | ||||
| DRAW DOWN STATISTICS | |||||
| Quartiles of draw downs | |||||
| Number of observations | 15.000 | ||||
| Minimum | 0.000 | ||||
| Quartile 1 | 0.001 | ||||
| Median | 0.003 | ||||
| Quartile 3 | 0.009 | ||||
| Maximum | 0.109 | ||||
| Mean of quarter 1 | 0.001 | ||||
| Mean of quarter 2 | 0.002 | ||||
| Mean of quarter 3 | 0.005 | ||||
| Mean of quarter 4 | 0.047 | ||||
| Inter Quartile Range | 0.007 | ||||
| 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 | 0.133 | ||||
| Mean of outliers high | 0.081 | ||||
| Risk estimates based on draw downs (based on Extreme Value Theory) | |||||
| Extreme Value Index (moments method) | 0.049 | ||||
| VaR(95%) (moments method) | 0.032 | ||||
| Expected Shortfall (moments method) | 0.049 | ||||
| Extreme Value Index (regression method) | 0.750 | ||||
| VaR(95%) (regression method) | 0.086 | ||||
| Expected Shortfall (regression method) | 0.410 | ||||
| COMBINED STATISTICS | |||||
| Annualized return (arithmetic extrapolation) | 0.022 | ||||
| Compounded annual return (geometric extrapolation) | 0.021 | ||||
| Calmar ratio (compounded annual return / max draw down) | 0.193 | ||||
| Compounded annual return / average of 25% largest draw downs | 0.443 | ||||
| Compounded annual return / Expected Shortfall lognormal | 2.899 | ||||
| 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 | 1.032 | ||||
| Mean of criterion | -0.044 | ||||
| SD of predictor | 0.464 | ||||
| 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 | 0.923 | ||||
| Mean of criterion | -0.044 | ||||
| SD of predictor | 0.467 | ||||
| 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) | -8734446199760959.000 | ||||
| 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) | -143882556570004909848985671303168.000 | ||||
| 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 | ||||