Advanced Statistics: Conservative Trader
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 | -0.050 | ||||
| SD | 0.007 | ||||
| Sharpe ratio (Glass type estimate) | -6.667 | ||||
| Sharpe ratio (Hedges UMVUE) | -6.527 | ||||
| df | 36.000 | ||||
| t | -11.707 | ||||
| p | 1.000 | ||||
| Lowerbound of 95% confidence interval for Sharpe Ratio | NA | ||||
| Upperbound of 95% confidence interval for Sharpe Ratio | -4.753 | ||||
| Lowerbound of 95% CI (Gibbons, Hedeker & Davis approximation) | -8.403 | ||||
| Upperbound of 95% CI (Gibbons, Hedeker & Davis approximation) | -4.651 | ||||
| Statistics related to Sortino ratio | |||||
| Sortino ratio | -3.083 | ||||
| Upside Potential Ratio | 0.000 | ||||
| Upside part of mean | 0.000 | ||||
| Downside part of mean | -0.050 | ||||
| Upside SD | 0.000 | ||||
| Downside SD | 0.016 | ||||
| N nonnegative terms | 0.000 | ||||
| N negative terms | 37.000 | ||||
| Statistics related to linear regression on benchmark | |||||
| N of observations | 37.000 | ||||
| Mean of predictor | 0.536 | ||||
| Mean of criterion | -0.050 | ||||
| SD of predictor | 0.227 | ||||
| SD of criterion | 0.007 | ||||
| Covariance | 0.000 | ||||
| r | 0.050 | ||||
| b (slope, estimate of beta) | 0.002 | ||||
| a (intercept, estimate of alpha) | -0.050 | ||||
| Mean Square Error | 0.000 | ||||
| DF error | 35.000 | ||||
| t(b) | 0.294 | ||||
| p(b) | 0.385 | ||||
| t(a) | -9.677 | ||||
| p(a) | 1.000 | ||||
| Lowerbound of 95% confidence interval for beta | -0.010 | ||||
| Upperbound of 95% confidence interval for beta | 0.013 | ||||
| Lowerbound of 95% confidence interval for alpha | -0.061 | ||||
| Upperbound of 95% confidence interval for alpha | -0.040 | ||||
| Treynor index (mean / b) | -30.476 | ||||
| Jensen alpha (a) | -0.050 | ||||
| Ratio statistics of excess log return rates | |||||
| Statistics related to Sharpe ratio | |||||
| Mean | -0.049 | ||||
| SD | 0.007 | ||||
| Sharpe ratio (Glass type estimate) | -6.621 | ||||
| Sharpe ratio (Hedges UMVUE) | -6.482 | ||||
| df | 36.000 | ||||
| t | -11.626 | ||||
| p | 1.000 | ||||
| Lowerbound of 95% confidence interval for Sharpe Ratio | NA | ||||
| Upperbound of 95% confidence interval for Sharpe Ratio | -4.716 | ||||
| Lowerbound of 95% CI (Gibbons, Hedeker & Davis approximation) | -8.349 | ||||
| Upperbound of 95% CI (Gibbons, Hedeker & Davis approximation) | -4.614 | ||||
| Statistics related to Sortino ratio | |||||
| Sortino ratio | -3.078 | ||||
| Upside Potential Ratio | 0.000 | ||||
| Upside part of mean | 0.000 | ||||
| Downside part of mean | -0.049 | ||||
| Upside SD | 0.000 | ||||
| Downside SD | 0.016 | ||||
| N nonnegative terms | 0.000 | ||||
| N negative terms | 37.000 | ||||
| Statistics related to linear regression on benchmark | |||||
| N of observations | 37.000 | ||||
| Mean of predictor | 0.500 | ||||
| Mean of criterion | -0.049 | ||||
| SD of predictor | 0.216 | ||||
| SD of criterion | 0.007 | ||||
| Covariance | 0.000 | ||||
| r | 0.044 | ||||
| b (slope, estimate of beta) | 0.002 | ||||
| a (intercept, estimate of alpha) | -0.050 | ||||
| Mean Square Error | 0.000 | ||||
| DF error | 35.000 | ||||
| t(b) | 0.259 | ||||
| p(b) | 0.399 | ||||
| t(a) | -9.646 | ||||
| p(a) | 1.000 | ||||
| Lowerbound of 95% confidence interval for beta | -0.010 | ||||
| Upperbound of 95% confidence interval for beta | 0.013 | ||||
| Lowerbound of 95% confidence interval for alpha | -0.061 | ||||
| Upperbound of 95% confidence interval for alpha | -0.040 | ||||
| Treynor index (mean / b) | -32.774 | ||||
| Jensen alpha (a) | -0.050 | ||||
| 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 | 0.009 | ||||
| assuming Pareto losses only (using partial moments from Sortino statistics) | |||||
| VaR(95%) | 0.007 | ||||
| Expected Shortfall on VaR | 0.007 | ||||
| ORDER STATISTICS | |||||
| Quartiles of return rates | |||||
| Number of observations | 37.000 | ||||
| Minimum | 0.988 | ||||
| Quartile 1 | 1.000 | ||||
| Median | 1.000 | ||||
| Quartile 3 | 1.000 | ||||
| Maximum | 1.000 | ||||
| Mean of quarter 1 | 0.998 | ||||
| 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 | 3.000 | ||||
| Percentage of outliers low | 0.081 | ||||
| Mean of outliers low | 0.994 | ||||
| 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) | -33.911 | ||||
| VaR(95%) (moments method) | 0.000 | ||||
| Expected Shortfall (moments method) | 0.000 | ||||
| Extreme Value Index (regression method) | -0.020 | ||||
| VaR(95%) (regression method) | 0.004 | ||||
| Expected Shortfall (regression method) | 0.012 | ||||
| DRAW DOWN STATISTICS | |||||
| Quartiles of draw downs | |||||
| Number of observations | 1.000 | ||||
| Minimum | 0.017 | ||||
| Quartile 1 | 0.017 | ||||
| Median | 0.017 | ||||
| Quartile 3 | 0.017 | ||||
| Maximum | 0.017 | ||||
| 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) | -0.005 | ||||
| Compounded annual return (geometric extrapolation) | -0.005 | ||||
| Calmar ratio (compounded annual return / max draw down) | -0.326 | ||||
| Compounded annual return / average of 25% largest draw downs | NA | ||||
| Compounded annual return / Expected Shortfall lognormal | -0.638 | ||||
| ANALYSIS BASED ON DAILY VALUES, FULL HISTORY (Back) | |||||
| RATIO STATISTICS | |||||
| Ratio statistics of excess return rates | |||||
| Statistics related to Sharpe ratio | |||||
| Mean | -0.049 | ||||
| SD | 0.035 | ||||
| Sharpe ratio (Glass type estimate) | -1.405 | ||||
| Sharpe ratio (Hedges UMVUE) | -1.403 | ||||
| df | 817.000 | ||||
| t | -2.482 | ||||
| p | 0.993 | ||||
| Lowerbound of 95% confidence interval for Sharpe Ratio | -2.516 | ||||
| Upperbound of 95% confidence interval for Sharpe Ratio | -0.293 | ||||
| Lowerbound of 95% CI (Gibbons, Hedeker & Davis approximation) | -2.515 | ||||
| Upperbound of 95% CI (Gibbons, Hedeker & Davis approximation) | -0.292 | ||||
| Statistics related to Sortino ratio | |||||
| Sortino ratio | -1.823 | ||||
| Upside Potential Ratio | 1.254 | ||||
| Upside part of mean | 0.034 | ||||
| Downside part of mean | -0.082 | ||||
| Upside SD | 0.022 | ||||
| Downside SD | 0.027 | ||||
| N nonnegative terms | 19.000 | ||||
| N negative terms | 799.000 | ||||
| Statistics related to linear regression on benchmark | |||||
| N of observations | 818.000 | ||||
| Mean of predictor | 0.593 | ||||
| Mean of criterion | -0.049 | ||||
| SD of predictor | 0.363 | ||||
| SD of criterion | 0.035 | ||||
| Covariance | -0.000 | ||||
| r | -0.003 | ||||
| b (slope, estimate of beta) | -0.000 | ||||
| a (intercept, estimate of alpha) | -0.049 | ||||
| Mean Square Error | 0.001 | ||||
| DF error | 816.000 | ||||
| t(b) | -0.074 | ||||
| p(b) | 0.530 | ||||
| t(a) | -2.460 | ||||
| p(a) | 0.993 | ||||
| Lowerbound of 95% confidence interval for beta | -0.007 | ||||
| Upperbound of 95% confidence interval for beta | 0.006 | ||||
| Lowerbound of 95% confidence interval for alpha | -0.087 | ||||
| Upperbound of 95% confidence interval for alpha | -0.010 | ||||
| Treynor index (mean / b) | 196.617 | ||||
| Jensen alpha (a) | -0.049 | ||||
| Ratio statistics of excess log return rates | |||||
| Statistics related to Sharpe ratio | |||||
| Mean | -0.049 | ||||
| SD | 0.035 | ||||
| Sharpe ratio (Glass type estimate) | -1.418 | ||||
| Sharpe ratio (Hedges UMVUE) | -1.416 | ||||
| df | 817.000 | ||||
| t | -2.505 | ||||
| p | 0.994 | ||||
| Lowerbound of 95% confidence interval for Sharpe Ratio | -2.529 | ||||
| Upperbound of 95% confidence interval for Sharpe Ratio | -0.306 | ||||
| Lowerbound of 95% CI (Gibbons, Hedeker & Davis approximation) | -2.528 | ||||
| Upperbound of 95% CI (Gibbons, Hedeker & Davis approximation) | -0.305 | ||||
| Statistics related to Sortino ratio | |||||
| Sortino ratio | -1.823 | ||||
| Upside Potential Ratio | 1.230 | ||||
| Upside part of mean | 0.033 | ||||
| Downside part of mean | -0.083 | ||||
| Upside SD | 0.022 | ||||
| Downside SD | 0.027 | ||||
| N nonnegative terms | 19.000 | ||||
| N negative terms | 799.000 | ||||
| Statistics related to linear regression on benchmark | |||||
| N of observations | 818.000 | ||||
| Mean of predictor | 0.527 | ||||
| Mean of criterion | -0.049 | ||||
| SD of predictor | 0.361 | ||||
| SD of criterion | 0.035 | ||||
| Covariance | -0.000 | ||||
| r | -0.003 | ||||
| b (slope, estimate of beta) | -0.000 | ||||
| a (intercept, estimate of alpha) | -0.049 | ||||
| Mean Square Error | 0.001 | ||||
| DF error | 816.000 | ||||
| t(b) | -0.078 | ||||
| p(b) | 0.531 | ||||
| t(a) | -2.486 | ||||
| p(a) | 0.993 | ||||
| Lowerbound of 95% confidence interval for beta | -0.007 | ||||
| Upperbound of 95% confidence interval for beta | 0.006 | ||||
| Lowerbound of 95% confidence interval for alpha | -0.088 | ||||
| Upperbound of 95% confidence interval for alpha | -0.010 | ||||
| Treynor index (mean / b) | 186.139 | ||||
| Jensen alpha (a) | -0.049 | ||||
| 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 | 0.005 | ||||
| assuming Pareto losses only (using partial moments from Sortino statistics) | |||||
| VaR(95%) | 0.001 | ||||
| Expected Shortfall on VaR | 0.002 | ||||
| ORDER STATISTICS | |||||
| Quartiles of return rates | |||||
| Number of observations | 818.000 | ||||
| Minimum | 0.968 | ||||
| Quartile 1 | 1.000 | ||||
| Median | 1.000 | ||||
| Quartile 3 | 1.000 | ||||
| Maximum | 1.026 | ||||
| Mean of quarter 1 | 0.999 | ||||
| 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 | 19.000 | ||||
| Percentage of outliers low | 0.023 | ||||
| Mean of outliers low | 0.994 | ||||
| Number of outliers high | 21.000 | ||||
| Percentage of outliers high | 0.026 | ||||
| Mean of outliers high | 1.005 | ||||
| Risk estimates for a one-period unit investment (based on Extreme Value Theory) | |||||
| Extreme Value Index (moments method) | -0.248 | ||||
| VaR(95%) (moments method) | -0.002 | ||||
| Expected Shortfall (moments method) | NA | ||||
| Extreme Value Index (regression method) | 0.322 | ||||
| VaR(95%) (regression method) | -0.004 | ||||
| Expected Shortfall (regression method) | NA | ||||
| DRAW DOWN STATISTICS | |||||
| Quartiles of draw downs | |||||
| Number of observations | 6.000 | ||||
| Minimum | 0.000 | ||||
| Quartile 1 | 0.001 | ||||
| Median | 0.003 | ||||
| Quartile 3 | 0.006 | ||||
| Maximum | 0.066 | ||||
| Mean of quarter 1 | 0.000 | ||||
| Mean of quarter 2 | 0.003 | ||||
| Mean of quarter 3 | 0.004 | ||||
| Mean of quarter 4 | 0.036 | ||||
| Inter Quartile Range | 0.005 | ||||
| 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 | 0.167 | ||||
| Mean of outliers high | 0.066 | ||||
| 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) | -0.005 | ||||
| Compounded annual return (geometric extrapolation) | -0.005 | ||||
| Calmar ratio (compounded annual return / max draw down) | -0.082 | ||||
| Compounded annual return / average of 25% largest draw downs | -0.148 | ||||
| Compounded annual return / Expected Shortfall lognormal | -1.165 | ||||
| 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 | 1.064 | ||||
| Mean of criterion | -0.044 | ||||
| SD of predictor | 0.503 | ||||
| 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 | 0.935 | ||||
| Mean of criterion | -0.044 | ||||
| SD of predictor | 0.509 | ||||
| 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) | -8743190759822265.000 | ||||
| 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) | 938597761694311998388010045407232.000 | ||||
| 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 | ||||