Advanced Statistics: Fletch
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 | -0.071 | ||||
| SD | 0.023 | ||||
| Sharpe ratio (Glass type estimate) | -3.123 | ||||
| Sharpe ratio (Hedges UMVUE) | -3.055 | ||||
| df | 35.000 | ||||
| t | -5.409 | ||||
| p | 1.000 | ||||
| Lowerbound of 95% confidence interval for Sharpe Ratio | -4.453 | ||||
| Upperbound of 95% confidence interval for Sharpe Ratio | -1.761 | ||||
| Lowerbound of 95% CI (Gibbons, Hedeker & Davis approximation) | -4.394 | ||||
| Upperbound of 95% CI (Gibbons, Hedeker & Davis approximation) | -1.716 | ||||
| Statistics related to Sortino ratio | |||||
| Sortino ratio | -2.337 | ||||
| Upside Potential Ratio | 0.000 | ||||
| Upside part of mean | 0.000 | ||||
| Downside part of mean | -0.071 | ||||
| Upside SD | 0.000 | ||||
| Downside SD | 0.031 | ||||
| N nonnegative terms | 0.000 | ||||
| N negative terms | 36.000 | ||||
| Statistics related to linear regression on benchmark | |||||
| N of observations | 36.000 | ||||
| Mean of predictor | 0.562 | ||||
| Mean of criterion | -0.071 | ||||
| SD of predictor | 0.351 | ||||
| SD of criterion | 0.023 | ||||
| Covariance | 0.001 | ||||
| r | 0.121 | ||||
| b (slope, estimate of beta) | 0.008 | ||||
| a (intercept, estimate of alpha) | -0.076 | ||||
| Mean Square Error | 0.001 | ||||
| DF error | 34.000 | ||||
| t(b) | 0.710 | ||||
| p(b) | 0.241 | ||||
| t(a) | -5.163 | ||||
| p(a) | 1.000 | ||||
| Lowerbound of 95% confidence interval for beta | -0.015 | ||||
| Upperbound of 95% confidence interval for beta | 0.030 | ||||
| Lowerbound of 95% confidence interval for alpha | -0.106 | ||||
| Upperbound of 95% confidence interval for alpha | -0.046 | ||||
| Treynor index (mean / b) | -9.069 | ||||
| Jensen alpha (a) | -0.076 | ||||
| Ratio statistics of excess log return rates | |||||
| Statistics related to Sharpe ratio | |||||
| Mean | -0.072 | ||||
| SD | 0.023 | ||||
| Sharpe ratio (Glass type estimate) | -3.094 | ||||
| Sharpe ratio (Hedges UMVUE) | -3.027 | ||||
| df | 35.000 | ||||
| t | -5.359 | ||||
| p | 1.000 | ||||
| Lowerbound of 95% confidence interval for Sharpe Ratio | -4.420 | ||||
| Upperbound of 95% confidence interval for Sharpe Ratio | -1.736 | ||||
| Lowerbound of 95% CI (Gibbons, Hedeker & Davis approximation) | -4.362 | ||||
| Upperbound of 95% CI (Gibbons, Hedeker & Davis approximation) | -1.692 | ||||
| Statistics related to Sortino ratio | |||||
| Sortino ratio | -2.326 | ||||
| Upside Potential Ratio | 0.000 | ||||
| Upside part of mean | 0.000 | ||||
| Downside part of mean | -0.072 | ||||
| Upside SD | 0.000 | ||||
| Downside SD | 0.031 | ||||
| N nonnegative terms | 0.000 | ||||
| N negative terms | 36.000 | ||||
| Statistics related to linear regression on benchmark | |||||
| N of observations | 36.000 | ||||
| Mean of predictor | 0.494 | ||||
| Mean of criterion | -0.072 | ||||
| SD of predictor | 0.332 | ||||
| SD of criterion | 0.023 | ||||
| Covariance | 0.001 | ||||
| r | 0.107 | ||||
| b (slope, estimate of beta) | 0.007 | ||||
| a (intercept, estimate of alpha) | -0.075 | ||||
| Mean Square Error | 0.001 | ||||
| DF error | 34.000 | ||||
| t(b) | 0.630 | ||||
| p(b) | 0.266 | ||||
| t(a) | -5.122 | ||||
| p(a) | 1.000 | ||||
| Lowerbound of 95% confidence interval for beta | -0.017 | ||||
| Upperbound of 95% confidence interval for beta | 0.032 | ||||
| Lowerbound of 95% confidence interval for alpha | -0.105 | ||||
| Upperbound of 95% confidence interval for alpha | -0.045 | ||||
| Treynor index (mean / b) | -9.567 | ||||
| Jensen alpha (a) | -0.075 | ||||
| Risk estimates for a one-period unit investment (parametric) | |||||
| assuming log normal returns and losses (using central moments from Sharpe statistics) | |||||
| VaR(95%) | 0.017 | ||||
| Expected Shortfall on VaR | 0.020 | ||||
| assuming Pareto losses only (using partial moments from Sortino statistics) | |||||
| VaR(95%) | 0.019 | ||||
| Expected Shortfall on VaR | 0.026 | ||||
| ORDER STATISTICS | |||||
| Quartiles of return rates | |||||
| Number of observations | 36.000 | ||||
| Minimum | 0.970 | ||||
| Quartile 1 | 1.000 | ||||
| Median | 1.000 | ||||
| Quartile 3 | 1.000 | ||||
| Maximum | 1.002 | ||||
| Mean of quarter 1 | 0.991 | ||||
| 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 | 6.000 | ||||
| Percentage of outliers low | 0.167 | ||||
| Mean of outliers low | 0.986 | ||||
| Number of outliers high | 1.000 | ||||
| Percentage of outliers high | 0.028 | ||||
| Mean of outliers high | 1.002 | ||||
| Risk estimates for a one-period unit investment (based on Extreme Value Theory) | |||||
| Extreme Value Index (moments method) | -24.751 | ||||
| VaR(95%) (moments method) | 0.002 | ||||
| Expected Shortfall (moments method) | 0.002 | ||||
| Extreme Value Index (regression method) | -0.361 | ||||
| VaR(95%) (regression method) | 0.015 | ||||
| Expected Shortfall (regression method) | 0.022 | ||||
| DRAW DOWN STATISTICS | |||||
| Quartiles of draw downs | |||||
| Number of observations | 1.000 | ||||
| Minimum | 0.080 | ||||
| Quartile 1 | 0.080 | ||||
| Median | 0.080 | ||||
| Quartile 3 | 0.080 | ||||
| Maximum | 0.080 | ||||
| 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) | -0.027 | ||||
| Compounded annual return (geometric extrapolation) | -0.027 | ||||
| Calmar ratio (compounded annual return / max draw down) | -0.343 | ||||
| Compounded annual return / average of 25% largest draw downs | NA | ||||
| Compounded annual return / Expected Shortfall lognormal | -1.393 | ||||
| ANALYSIS BASED ON DAILY VALUES, FULL HISTORY (Back) | |||||
| RATIO STATISTICS | |||||
| Ratio statistics of excess return rates | |||||
| Statistics related to Sharpe ratio | |||||
| Mean | -0.070 | ||||
| SD | 0.042 | ||||
| Sharpe ratio (Glass type estimate) | -1.698 | ||||
| Sharpe ratio (Hedges UMVUE) | -1.697 | ||||
| df | 794.000 | ||||
| t | -2.958 | ||||
| p | 0.998 | ||||
| Lowerbound of 95% confidence interval for Sharpe Ratio | -2.826 | ||||
| Upperbound of 95% confidence interval for Sharpe Ratio | -0.569 | ||||
| Lowerbound of 95% CI (Gibbons, Hedeker & Davis approximation) | -2.825 | ||||
| Upperbound of 95% CI (Gibbons, Hedeker & Davis approximation) | -0.568 | ||||
| Statistics related to Sortino ratio | |||||
| Sortino ratio | -2.149 | ||||
| Upside Potential Ratio | 2.532 | ||||
| Upside part of mean | 0.083 | ||||
| Downside part of mean | -0.154 | ||||
| Upside SD | 0.026 | ||||
| Downside SD | 0.033 | ||||
| N nonnegative terms | 52.000 | ||||
| N negative terms | 743.000 | ||||
| Statistics related to linear regression on benchmark | |||||
| N of observations | 795.000 | ||||
| Mean of predictor | 0.568 | ||||
| Mean of criterion | -0.070 | ||||
| SD of predictor | 0.337 | ||||
| SD of criterion | 0.042 | ||||
| Covariance | 0.000 | ||||
| r | 0.035 | ||||
| b (slope, estimate of beta) | 0.004 | ||||
| a (intercept, estimate of alpha) | -0.073 | ||||
| Mean Square Error | 0.002 | ||||
| DF error | 793.000 | ||||
| t(b) | 0.982 | ||||
| p(b) | 0.163 | ||||
| t(a) | -3.044 | ||||
| p(a) | 0.999 | ||||
| Lowerbound of 95% confidence interval for beta | -0.004 | ||||
| Upperbound of 95% confidence interval for beta | 0.013 | ||||
| Lowerbound of 95% confidence interval for alpha | -0.120 | ||||
| Upperbound of 95% confidence interval for alpha | -0.026 | ||||
| Treynor index (mean / b) | -16.450 | ||||
| Jensen alpha (a) | -0.073 | ||||
| Ratio statistics of excess log return rates | |||||
| Statistics related to Sharpe ratio | |||||
| Mean | -0.071 | ||||
| SD | 0.042 | ||||
| Sharpe ratio (Glass type estimate) | -1.716 | ||||
| Sharpe ratio (Hedges UMVUE) | -1.714 | ||||
| df | 794.000 | ||||
| t | -2.989 | ||||
| p | 0.999 | ||||
| Lowerbound of 95% confidence interval for Sharpe Ratio | -2.844 | ||||
| Upperbound of 95% confidence interval for Sharpe Ratio | -0.587 | ||||
| Lowerbound of 95% CI (Gibbons, Hedeker & Davis approximation) | -2.842 | ||||
| Upperbound of 95% CI (Gibbons, Hedeker & Davis approximation) | -0.586 | ||||
| Statistics related to Sortino ratio | |||||
| Sortino ratio | -2.162 | ||||
| Upside Potential Ratio | 2.506 | ||||
| Upside part of mean | 0.083 | ||||
| Downside part of mean | -0.154 | ||||
| Upside SD | 0.026 | ||||
| Downside SD | 0.033 | ||||
| N nonnegative terms | 52.000 | ||||
| N negative terms | 743.000 | ||||
| Statistics related to linear regression on benchmark | |||||
| N of observations | 795.000 | ||||
| Mean of predictor | 0.510 | ||||
| Mean of criterion | -0.071 | ||||
| SD of predictor | 0.341 | ||||
| SD of criterion | 0.042 | ||||
| Covariance | 0.000 | ||||
| r | 0.034 | ||||
| b (slope, estimate of beta) | 0.004 | ||||
| a (intercept, estimate of alpha) | -0.073 | ||||
| Mean Square Error | 0.002 | ||||
| DF error | 793.000 | ||||
| t(b) | 0.961 | ||||
| p(b) | 0.169 | ||||
| t(a) | -3.064 | ||||
| p(a) | 0.999 | ||||
| Lowerbound of 95% confidence interval for beta | -0.004 | ||||
| Upperbound of 95% confidence interval for beta | 0.013 | ||||
| Lowerbound of 95% confidence interval for alpha | -0.121 | ||||
| Upperbound of 95% confidence interval for alpha | -0.026 | ||||
| Treynor index (mean / b) | -17.164 | ||||
| Jensen alpha (a) | -0.073 | ||||
| Risk estimates for a one-period unit investment (parametric) | |||||
| assuming log normal returns and losses (using central moments from Sharpe statistics) | |||||
| VaR(95%) | 0.004 | ||||
| Expected Shortfall on VaR | 0.006 | ||||
| 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 | 795.000 | ||||
| Minimum | 0.978 | ||||
| Quartile 1 | 1.000 | ||||
| Median | 1.000 | ||||
| Quartile 3 | 1.000 | ||||
| Maximum | 1.017 | ||||
| Mean of quarter 1 | 0.998 | ||||
| Mean of quarter 2 | 1.000 | ||||
| Mean of quarter 3 | 1.000 | ||||
| Mean of quarter 4 | 1.001 | ||||
| Inter Quartile Range | 0.000 | ||||
| Number outliers low | 69.000 | ||||
| Percentage of outliers low | 0.087 | ||||
| Mean of outliers low | 0.995 | ||||
| Number of outliers high | 53.000 | ||||
| Percentage of outliers high | 0.067 | ||||
| Mean of outliers high | 1.005 | ||||
| Risk estimates for a one-period unit investment (based on Extreme Value Theory) | |||||
| Extreme Value Index (moments method) | -0.070 | ||||
| VaR(95%) (moments method) | 0.002 | ||||
| Expected Shortfall (moments method) | 0.003 | ||||
| Extreme Value Index (regression method) | 0.057 | ||||
| VaR(95%) (regression method) | 0.002 | ||||
| Expected Shortfall (regression method) | 0.005 | ||||
| DRAW DOWN STATISTICS | |||||
| Quartiles of draw downs | |||||
| Number of observations | 2.000 | ||||
| Minimum | 0.000 | ||||
| Quartile 1 | 0.025 | ||||
| Median | 0.050 | ||||
| Quartile 3 | 0.074 | ||||
| Maximum | 0.099 | ||||
| Mean of quarter 1 | 0.000 | ||||
| Mean of quarter 2 | NA | ||||
| Mean of quarter 3 | NA | ||||
| Mean of quarter 4 | 0.099 | ||||
| Inter Quartile Range | 0.050 | ||||
| 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) | -0.026 | ||||
| Compounded annual return (geometric extrapolation) | -0.027 | ||||
| Calmar ratio (compounded annual return / max draw down) | -0.272 | ||||
| Compounded annual return / average of 25% largest draw downs | -0.272 | ||||
| Compounded annual return / Expected Shortfall lognormal | -4.852 | ||||
| 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 | 1.013 | ||||
| Mean of criterion | -0.044 | ||||
| SD of predictor | 0.517 | ||||
| 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 | 0.881 | ||||
| Mean of criterion | -0.044 | ||||
| SD of predictor | 0.510 | ||||
| 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) | -8749795556451685.000 | ||||
| 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) | -240107231063553257834086764904448.000 | ||||
| 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 | ||||