Advanced Statistics: Lilac
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 | 0.142 | ||||
| Sharpe ratio (Glass type estimate) | -0.166 | ||||
| Sharpe ratio (Hedges UMVUE) | -0.164 | ||||
| df | 73.000 | ||||
| t | -0.412 | ||||
| p | 0.659 | ||||
| Lowerbound of 95% confidence interval for Sharpe Ratio | -0.955 | ||||
| Upperbound of 95% confidence interval for Sharpe Ratio | 0.624 | ||||
| Lowerbound of 95% CI (Gibbons, Hedeker & Davis approximation) | -0.954 | ||||
| Upperbound of 95% CI (Gibbons, Hedeker & Davis approximation) | 0.625 | ||||
| Statistics related to Sortino ratio | |||||
| Sortino ratio | -0.275 | ||||
| Upside Potential Ratio | 0.832 | ||||
| Upside part of mean | 0.071 | ||||
| Downside part of mean | -0.095 | ||||
| Upside SD | 0.112 | ||||
| Downside SD | 0.085 | ||||
| N nonnegative terms | 3.000 | ||||
| N negative terms | 71.000 | ||||
| Statistics related to linear regression on benchmark | |||||
| N of observations | 74.000 | ||||
| Mean of predictor | 0.234 | ||||
| Mean of criterion | -0.024 | ||||
| SD of predictor | 0.296 | ||||
| SD of criterion | 0.142 | ||||
| Covariance | -0.003 | ||||
| r | -0.075 | ||||
| b (slope, estimate of beta) | -0.036 | ||||
| a (intercept, estimate of alpha) | -0.015 | ||||
| Mean Square Error | 0.020 | ||||
| DF error | 72.000 | ||||
| t(b) | -0.637 | ||||
| p(b) | 0.737 | ||||
| t(a) | -0.258 | ||||
| p(a) | 0.601 | ||||
| Lowerbound of 95% confidence interval for beta | -0.148 | ||||
| Upperbound of 95% confidence interval for beta | 0.076 | ||||
| Lowerbound of 95% confidence interval for alpha | -0.132 | ||||
| Upperbound of 95% confidence interval for alpha | 0.102 | ||||
| Treynor index (mean / b) | 0.656 | ||||
| Jensen alpha (a) | -0.015 | ||||
| Ratio statistics of excess log return rates | |||||
| Statistics related to Sharpe ratio | |||||
| Mean | -0.033 | ||||
| SD | 0.139 | ||||
| Sharpe ratio (Glass type estimate) | -0.238 | ||||
| Sharpe ratio (Hedges UMVUE) | -0.236 | ||||
| df | 73.000 | ||||
| t | -0.592 | ||||
| p | 0.722 | ||||
| Lowerbound of 95% confidence interval for Sharpe Ratio | -1.028 | ||||
| Upperbound of 95% confidence interval for Sharpe Ratio | 0.553 | ||||
| Lowerbound of 95% CI (Gibbons, Hedeker & Davis approximation) | -1.026 | ||||
| Upperbound of 95% CI (Gibbons, Hedeker & Davis approximation) | 0.554 | ||||
| Statistics related to Sortino ratio | |||||
| Sortino ratio | -0.354 | ||||
| Upside Potential Ratio | 0.701 | ||||
| Upside part of mean | 0.065 | ||||
| Downside part of mean | -0.098 | ||||
| Upside SD | 0.102 | ||||
| Downside SD | 0.093 | ||||
| N nonnegative terms | 3.000 | ||||
| N negative terms | 71.000 | ||||
| Statistics related to linear regression on benchmark | |||||
| N of observations | 74.000 | ||||
| Mean of predictor | 0.190 | ||||
| Mean of criterion | -0.033 | ||||
| SD of predictor | 0.288 | ||||
| SD of criterion | 0.139 | ||||
| Covariance | -0.003 | ||||
| r | -0.069 | ||||
| b (slope, estimate of beta) | -0.033 | ||||
| a (intercept, estimate of alpha) | -0.027 | ||||
| Mean Square Error | 0.019 | ||||
| DF error | 72.000 | ||||
| t(b) | -0.590 | ||||
| p(b) | 0.721 | ||||
| t(a) | -0.468 | ||||
| p(a) | 0.679 | ||||
| Lowerbound of 95% confidence interval for beta | -0.146 | ||||
| Upperbound of 95% confidence interval for beta | 0.079 | ||||
| Lowerbound of 95% confidence interval for alpha | -0.140 | ||||
| Upperbound of 95% confidence interval for alpha | 0.087 | ||||
| Treynor index (mean / b) | 0.989 | ||||
| Jensen alpha (a) | -0.027 | ||||
| Risk estimates for a one-period unit investment (parametric) | |||||
| assuming log normal returns and losses (using central moments from Sharpe statistics) | |||||
| VaR(95%) | 0.066 | ||||
| Expected Shortfall on VaR | 0.082 | ||||
| assuming Pareto losses only (using partial moments from Sortino statistics) | |||||
| VaR(95%) | 0.027 | ||||
| Expected Shortfall on VaR | 0.056 | ||||
| ORDER STATISTICS | |||||
| Quartiles of return rates | |||||
| Number of observations | 74.000 | ||||
| Minimum | 0.812 | ||||
| Quartile 1 | 1.000 | ||||
| Median | 1.000 | ||||
| Quartile 3 | 1.000 | ||||
| Maximum | 1.240 | ||||
| Mean of quarter 1 | 0.983 | ||||
| Mean of quarter 2 | 1.000 | ||||
| Mean of quarter 3 | 1.000 | ||||
| Mean of quarter 4 | 1.024 | ||||
| Inter Quartile Range | 0.000 | ||||
| Number outliers low | 6.000 | ||||
| Percentage of outliers low | 0.081 | ||||
| Mean of outliers low | 0.946 | ||||
| Number of outliers high | 5.000 | ||||
| Percentage of outliers high | 0.068 | ||||
| Mean of outliers high | 1.090 | ||||
| Risk estimates for a one-period unit investment (based on Extreme Value Theory) | |||||
| Extreme Value Index (moments method) | -47.351 | ||||
| VaR(95%) (moments method) | 0.000 | ||||
| Expected Shortfall (moments method) | 0.000 | ||||
| Extreme Value Index (regression method) | 0.034 | ||||
| VaR(95%) (regression method) | 0.016 | ||||
| Expected Shortfall (regression method) | 0.072 | ||||
| DRAW DOWN STATISTICS | |||||
| Quartiles of draw downs | |||||
| Number of observations | 2.000 | ||||
| Minimum | 0.050 | ||||
| Quartile 1 | 0.102 | ||||
| Median | 0.153 | ||||
| Quartile 3 | 0.204 | ||||
| Maximum | 0.255 | ||||
| Mean of quarter 1 | 0.050 | ||||
| Mean of quarter 2 | NA | ||||
| Mean of quarter 3 | NA | ||||
| Mean of quarter 4 | 0.255 | ||||
| Inter Quartile Range | 0.102 | ||||
| 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) | 0.011 | ||||
| Compounded annual return (geometric extrapolation) | 0.011 | ||||
| Calmar ratio (compounded annual return / max draw down) | 0.044 | ||||
| Compounded annual return / average of 25% largest draw downs | 0.044 | ||||
| Compounded annual return / Expected Shortfall lognormal | 0.136 | ||||
| ANALYSIS BASED ON DAILY VALUES, FULL HISTORY (Back) | |||||
| RATIO STATISTICS | |||||
| Ratio statistics of excess return rates | |||||
| Statistics related to Sharpe ratio | |||||
| Mean | 0.121 | ||||
| SD | 0.566 | ||||
| Sharpe ratio (Glass type estimate) | 0.214 | ||||
| Sharpe ratio (Hedges UMVUE) | 0.214 | ||||
| df | 1620.000 | ||||
| t | 0.531 | ||||
| p | 0.493 | ||||
| Lowerbound of 95% confidence interval for Sharpe Ratio | -0.574 | ||||
| Upperbound of 95% confidence interval for Sharpe Ratio | 1.002 | ||||
| Lowerbound of 95% CI (Gibbons, Hedeker & Davis approximation) | -0.574 | ||||
| Upperbound of 95% CI (Gibbons, Hedeker & Davis approximation) | 1.002 | ||||
| Statistics related to Sortino ratio | |||||
| Sortino ratio | 0.352 | ||||
| Upside Potential Ratio | 2.670 | ||||
| Upside part of mean | 0.916 | ||||
| Downside part of mean | -0.796 | ||||
| Upside SD | 0.449 | ||||
| Downside SD | 0.343 | ||||
| N nonnegative terms | 64.000 | ||||
| N negative terms | 1557.000 | ||||
| Statistics related to linear regression on benchmark | |||||
| N of observations | 1621.000 | ||||
| Mean of predictor | 0.361 | ||||
| Mean of criterion | 0.121 | ||||
| SD of predictor | 0.556 | ||||
| SD of criterion | 0.566 | ||||
| Covariance | -0.067 | ||||
| r | -0.213 | ||||
| b (slope, estimate of beta) | -0.217 | ||||
| a (intercept, estimate of alpha) | 0.199 | ||||
| Mean Square Error | 0.305 | ||||
| DF error | 1619.000 | ||||
| t(b) | -8.783 | ||||
| p(b) | 0.635 | ||||
| t(a) | 0.895 | ||||
| p(a) | 0.486 | ||||
| Lowerbound of 95% confidence interval for beta | -0.265 | ||||
| Upperbound of 95% confidence interval for beta | -0.169 | ||||
| Lowerbound of 95% confidence interval for alpha | -0.237 | ||||
| Upperbound of 95% confidence interval for alpha | 0.635 | ||||
| Treynor index (mean / b) | -0.557 | ||||
| Jensen alpha (a) | 0.199 | ||||
| Ratio statistics of excess log return rates | |||||
| Statistics related to Sharpe ratio | |||||
| Mean | -0.033 | ||||
| SD | 0.552 | ||||
| Sharpe ratio (Glass type estimate) | -0.060 | ||||
| Sharpe ratio (Hedges UMVUE) | -0.060 | ||||
| df | 1620.000 | ||||
| t | -0.149 | ||||
| p | 0.502 | ||||
| Lowerbound of 95% confidence interval for Sharpe Ratio | -0.848 | ||||
| Upperbound of 95% confidence interval for Sharpe Ratio | 0.728 | ||||
| Lowerbound of 95% CI (Gibbons, Hedeker & Davis approximation) | -0.848 | ||||
| Upperbound of 95% CI (Gibbons, Hedeker & Davis approximation) | 0.728 | ||||
| Statistics related to Sortino ratio | |||||
| Sortino ratio | -0.087 | ||||
| Upside Potential Ratio | 2.178 | ||||
| Upside part of mean | 0.830 | ||||
| Downside part of mean | -0.863 | ||||
| Upside SD | 0.399 | ||||
| Downside SD | 0.381 | ||||
| N nonnegative terms | 64.000 | ||||
| N negative terms | 1557.000 | ||||
| Statistics related to linear regression on benchmark | |||||
| N of observations | 1621.000 | ||||
| Mean of predictor | 0.208 | ||||
| Mean of criterion | -0.033 | ||||
| SD of predictor | 0.553 | ||||
| SD of criterion | 0.552 | ||||
| Covariance | -0.066 | ||||
| r | -0.218 | ||||
| b (slope, estimate of beta) | -0.217 | ||||
| a (intercept, estimate of alpha) | 0.012 | ||||
| Mean Square Error | 0.290 | ||||
| DF error | 1619.000 | ||||
| t(b) | -8.977 | ||||
| p(b) | 0.638 | ||||
| t(a) | 0.056 | ||||
| p(a) | 0.499 | ||||
| Lowerbound of 95% confidence interval for beta | -0.265 | ||||
| Upperbound of 95% confidence interval for beta | -0.170 | ||||
| Lowerbound of 95% confidence interval for alpha | -0.413 | ||||
| Upperbound of 95% confidence interval for alpha | 0.437 | ||||
| Treynor index (mean / b) | 0.152 | ||||
| Jensen alpha (a) | 0.012 | ||||
| Risk estimates for a one-period unit investment (parametric) | |||||
| assuming log normal returns and losses (using central moments from Sharpe statistics) | |||||
| VaR(95%) | 0.055 | ||||
| Expected Shortfall on VaR | 0.068 | ||||
| assuming Pareto losses only (using partial moments from Sortino statistics) | |||||
| VaR(95%) | 0.010 | ||||
| Expected Shortfall on VaR | 0.023 | ||||
| ORDER STATISTICS | |||||
| Quartiles of return rates | |||||
| Number of observations | 1621.000 | ||||
| Minimum | 0.753 | ||||
| Quartile 1 | 1.000 | ||||
| Median | 1.000 | ||||
| Quartile 3 | 1.000 | ||||
| Maximum | 1.352 | ||||
| Mean of quarter 1 | 0.989 | ||||
| Mean of quarter 2 | 1.000 | ||||
| Mean of quarter 3 | 1.000 | ||||
| Mean of quarter 4 | 1.014 | ||||
| Inter Quartile Range | 0.000 | ||||
| Number outliers low | 101.000 | ||||
| Percentage of outliers low | 0.062 | ||||
| Mean of outliers low | 0.954 | ||||
| Number of outliers high | 100.000 | ||||
| Percentage of outliers high | 0.062 | ||||
| Mean of outliers high | 1.057 | ||||
| Risk estimates for a one-period unit investment (based on Extreme Value Theory) | |||||
| Extreme Value Index (moments method) | -4.944 | ||||
| VaR(95%) (moments method) | -0.001 | ||||
| Expected Shortfall (moments method) | NA | ||||
| Extreme Value Index (regression method) | -0.391 | ||||
| VaR(95%) (regression method) | -0.016 | ||||
| Expected Shortfall (regression method) | NA | ||||
| DRAW DOWN STATISTICS | |||||
| Quartiles of draw downs | |||||
| Number of observations | 10.000 | ||||
| Minimum | 0.073 | ||||
| Quartile 1 | 0.104 | ||||
| Median | 0.225 | ||||
| Quartile 3 | 0.269 | ||||
| Maximum | 0.287 | ||||
| Mean of quarter 1 | 0.082 | ||||
| Mean of quarter 2 | 0.169 | ||||
| Mean of quarter 3 | 0.242 | ||||
| Mean of quarter 4 | 0.280 | ||||
| Inter Quartile Range | 0.164 | ||||
| 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) | -1.151 | ||||
| VaR(95%) (moments method) | 0.286 | ||||
| Expected Shortfall (moments method) | 0.287 | ||||
| Extreme Value Index (regression method) | 0.296 | ||||
| VaR(95%) (regression method) | 0.288 | ||||
| Expected Shortfall (regression method) | 0.301 | ||||
| COMBINED STATISTICS | |||||
| Annualized return (arithmetic extrapolation) | 0.011 | ||||
| Compounded annual return (geometric extrapolation) | 0.011 | ||||
| Calmar ratio (compounded annual return / max draw down) | 0.039 | ||||
| Compounded annual return / average of 25% largest draw downs | 0.039 | ||||
| Compounded annual return / Expected Shortfall lognormal | 0.163 | ||||
| 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 | 1.121 | ||||
| Mean of criterion | -0.044 | ||||
| SD of predictor | 0.508 | ||||
| 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 | 0.989 | ||||
| Mean of criterion | -0.044 | ||||
| SD of predictor | 0.513 | ||||
| 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) | -8737550239341698.000 | ||||
| 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) | 173707936598704034183159432085504.000 | ||||
| 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 | ||||