Advanced Statistics: STP 100
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 | -0.053 | ||||
| SD | 0.019 | ||||
| Sharpe ratio (Glass type estimate) | -2.725 | ||||
| Sharpe ratio (Hedges UMVUE) | -2.690 | ||||
| df | 59.000 | ||||
| t | -6.093 | ||||
| p | 1.000 | ||||
| Lowerbound of 95% confidence interval for Sharpe Ratio | -3.721 | ||||
| Upperbound of 95% confidence interval for Sharpe Ratio | -1.712 | ||||
| Lowerbound of 95% CI (Gibbons, Hedeker & Davis approximation) | -3.692 | ||||
| Upperbound of 95% CI (Gibbons, Hedeker & Davis approximation) | -1.688 | ||||
| Statistics related to Sortino ratio | |||||
| Sortino ratio | -2.309 | ||||
| Upside Potential Ratio | 0.173 | ||||
| Upside part of mean | 0.004 | ||||
| Downside part of mean | -0.057 | ||||
| Upside SD | 0.009 | ||||
| Downside SD | 0.023 | ||||
| N nonnegative terms | 1.000 | ||||
| N negative terms | 59.000 | ||||
| Statistics related to linear regression on benchmark | |||||
| N of observations | 60.000 | ||||
| Mean of predictor | 0.379 | ||||
| Mean of criterion | -0.053 | ||||
| SD of predictor | 0.266 | ||||
| SD of criterion | 0.019 | ||||
| Covariance | 0.000 | ||||
| r | 0.009 | ||||
| b (slope, estimate of beta) | 0.001 | ||||
| a (intercept, estimate of alpha) | -0.053 | ||||
| Mean Square Error | 0.000 | ||||
| DF error | 58.000 | ||||
| t(b) | 0.065 | ||||
| p(b) | 0.474 | ||||
| t(a) | -5.606 | ||||
| p(a) | 1.000 | ||||
| Lowerbound of 95% confidence interval for beta | -0.018 | ||||
| Upperbound of 95% confidence interval for beta | 0.020 | ||||
| Lowerbound of 95% confidence interval for alpha | -0.072 | ||||
| Upperbound of 95% confidence interval for alpha | -0.034 | ||||
| Treynor index (mean / b) | -84.537 | ||||
| Jensen alpha (a) | -0.053 | ||||
| Ratio statistics of excess log return rates | |||||
| Statistics related to Sharpe ratio | |||||
| Mean | -0.053 | ||||
| SD | 0.019 | ||||
| Sharpe ratio (Glass type estimate) | -2.719 | ||||
| Sharpe ratio (Hedges UMVUE) | -2.684 | ||||
| df | 59.000 | ||||
| t | -6.079 | ||||
| p | 1.000 | ||||
| Lowerbound of 95% confidence interval for Sharpe Ratio | -3.714 | ||||
| Upperbound of 95% confidence interval for Sharpe Ratio | -1.706 | ||||
| Lowerbound of 95% CI (Gibbons, Hedeker & Davis approximation) | -3.685 | ||||
| Upperbound of 95% CI (Gibbons, Hedeker & Davis approximation) | -1.683 | ||||
| Statistics related to Sortino ratio | |||||
| Sortino ratio | -2.300 | ||||
| Upside Potential Ratio | 0.170 | ||||
| Upside part of mean | 0.004 | ||||
| Downside part of mean | -0.057 | ||||
| Upside SD | 0.009 | ||||
| Downside SD | 0.023 | ||||
| N nonnegative terms | 1.000 | ||||
| N negative terms | 59.000 | ||||
| Statistics related to linear regression on benchmark | |||||
| N of observations | 60.000 | ||||
| Mean of predictor | 0.340 | ||||
| Mean of criterion | -0.053 | ||||
| SD of predictor | 0.253 | ||||
| SD of criterion | 0.019 | ||||
| Covariance | 0.000 | ||||
| r | 0.005 | ||||
| b (slope, estimate of beta) | 0.000 | ||||
| a (intercept, estimate of alpha) | -0.053 | ||||
| Mean Square Error | 0.000 | ||||
| DF error | 58.000 | ||||
| t(b) | 0.036 | ||||
| p(b) | 0.486 | ||||
| t(a) | -5.626 | ||||
| p(a) | 1.000 | ||||
| Lowerbound of 95% confidence interval for beta | -0.020 | ||||
| Upperbound of 95% confidence interval for beta | 0.021 | ||||
| Lowerbound of 95% confidence interval for alpha | -0.072 | ||||
| Upperbound of 95% confidence interval for alpha | -0.034 | ||||
| Treynor index (mean / b) | -144.372 | ||||
| Jensen alpha (a) | -0.053 | ||||
| Risk estimates for a one-period unit investment (parametric) | |||||
| assuming log normal returns and losses (using central moments from Sharpe statistics) | |||||
| VaR(95%) | 0.014 | ||||
| Expected Shortfall on VaR | 0.016 | ||||
| assuming Pareto losses only (using partial moments from Sortino statistics) | |||||
| VaR(95%) | 0.014 | ||||
| Expected Shortfall on VaR | 0.018 | ||||
| ORDER STATISTICS | |||||
| Quartiles of return rates | |||||
| Number of observations | 60.000 | ||||
| Minimum | 0.975 | ||||
| Quartile 1 | 1.000 | ||||
| Median | 1.000 | ||||
| Quartile 3 | 1.000 | ||||
| Maximum | 1.023 | ||||
| Mean of quarter 1 | 0.996 | ||||
| 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 | 7.000 | ||||
| Percentage of outliers low | 0.117 | ||||
| Mean of outliers low | 0.990 | ||||
| Number of outliers high | 2.000 | ||||
| Percentage of outliers high | 0.033 | ||||
| Mean of outliers high | 1.012 | ||||
| Risk estimates for a one-period unit investment (based on Extreme Value Theory) | |||||
| Extreme Value Index (moments method) | -27.546 | ||||
| VaR(95%) (moments method) | 0.001 | ||||
| Expected Shortfall (moments method) | 0.001 | ||||
| Extreme Value Index (regression method) | -1.237 | ||||
| VaR(95%) (regression method) | 0.011 | ||||
| Expected Shortfall (regression method) | 0.018 | ||||
| DRAW DOWN STATISTICS | |||||
| Quartiles of draw downs | |||||
| Number of observations | 1.000 | ||||
| Minimum | 0.057 | ||||
| Quartile 1 | 0.057 | ||||
| Median | 0.057 | ||||
| Quartile 3 | 0.057 | ||||
| Maximum | 0.057 | ||||
| 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) | -0.009 | ||||
| Compounded annual return (geometric extrapolation) | -0.009 | ||||
| Calmar ratio (compounded annual return / max draw down) | -0.154 | ||||
| Compounded annual return / average of 25% largest draw downs | NA | ||||
| Compounded annual return / Expected Shortfall lognormal | -0.552 | ||||
| ANALYSIS BASED ON DAILY VALUES, FULL HISTORY (Back) | |||||
| RATIO STATISTICS | |||||
| Ratio statistics of excess return rates | |||||
| Statistics related to Sharpe ratio | |||||
| Mean | -0.050 | ||||
| SD | 0.069 | ||||
| Sharpe ratio (Glass type estimate) | -0.732 | ||||
| Sharpe ratio (Hedges UMVUE) | -0.731 | ||||
| df | 1314.000 | ||||
| t | -1.640 | ||||
| p | 0.523 | ||||
| Lowerbound of 95% confidence interval for Sharpe Ratio | -1.607 | ||||
| Upperbound of 95% confidence interval for Sharpe Ratio | 0.144 | ||||
| Lowerbound of 95% CI (Gibbons, Hedeker & Davis approximation) | -1.607 | ||||
| Upperbound of 95% CI (Gibbons, Hedeker & Davis approximation) | 0.144 | ||||
| Statistics related to Sortino ratio | |||||
| Sortino ratio | -1.045 | ||||
| Upside Potential Ratio | 1.867 | ||||
| Upside part of mean | 0.090 | ||||
| Downside part of mean | -0.140 | ||||
| Upside SD | 0.049 | ||||
| Downside SD | 0.048 | ||||
| N nonnegative terms | 49.000 | ||||
| N negative terms | 1266.000 | ||||
| Statistics related to linear regression on benchmark | |||||
| N of observations | 1315.000 | ||||
| Mean of predictor | 0.411 | ||||
| Mean of criterion | -0.050 | ||||
| SD of predictor | 0.307 | ||||
| SD of criterion | 0.069 | ||||
| Covariance | -0.003 | ||||
| r | -0.135 | ||||
| b (slope, estimate of beta) | -0.030 | ||||
| a (intercept, estimate of alpha) | -0.038 | ||||
| Mean Square Error | 0.005 | ||||
| DF error | 1313.000 | ||||
| t(b) | -4.952 | ||||
| p(b) | 0.586 | ||||
| t(a) | -1.240 | ||||
| p(a) | 0.522 | ||||
| Lowerbound of 95% confidence interval for beta | -0.042 | ||||
| Upperbound of 95% confidence interval for beta | -0.018 | ||||
| Lowerbound of 95% confidence interval for alpha | -0.098 | ||||
| Upperbound of 95% confidence interval for alpha | 0.022 | ||||
| Treynor index (mean / b) | 1.658 | ||||
| Jensen alpha (a) | -0.038 | ||||
| Ratio statistics of excess log return rates | |||||
| Statistics related to Sharpe ratio | |||||
| Mean | -0.053 | ||||
| SD | 0.069 | ||||
| Sharpe ratio (Glass type estimate) | -0.767 | ||||
| Sharpe ratio (Hedges UMVUE) | -0.766 | ||||
| df | 1314.000 | ||||
| t | -1.718 | ||||
| p | 0.524 | ||||
| Lowerbound of 95% confidence interval for Sharpe Ratio | -1.642 | ||||
| Upperbound of 95% confidence interval for Sharpe Ratio | 0.109 | ||||
| Lowerbound of 95% CI (Gibbons, Hedeker & Davis approximation) | -1.642 | ||||
| Upperbound of 95% CI (Gibbons, Hedeker & Davis approximation) | 0.109 | ||||
| Statistics related to Sortino ratio | |||||
| Sortino ratio | -1.072 | ||||
| Upside Potential Ratio | 1.805 | ||||
| Upside part of mean | 0.089 | ||||
| Downside part of mean | -0.142 | ||||
| Upside SD | 0.048 | ||||
| Downside SD | 0.049 | ||||
| N nonnegative terms | 49.000 | ||||
| N negative terms | 1266.000 | ||||
| Statistics related to linear regression on benchmark | |||||
| N of observations | 1315.000 | ||||
| Mean of predictor | 0.363 | ||||
| Mean of criterion | -0.053 | ||||
| SD of predictor | 0.308 | ||||
| SD of criterion | 0.069 | ||||
| Covariance | -0.003 | ||||
| r | -0.135 | ||||
| b (slope, estimate of beta) | -0.030 | ||||
| a (intercept, estimate of alpha) | -0.042 | ||||
| Mean Square Error | 0.005 | ||||
| DF error | 1313.000 | ||||
| t(b) | -4.934 | ||||
| p(b) | 0.586 | ||||
| t(a) | -1.370 | ||||
| p(a) | 0.524 | ||||
| Lowerbound of 95% confidence interval for beta | -0.042 | ||||
| Upperbound of 95% confidence interval for beta | -0.018 | ||||
| Lowerbound of 95% confidence interval for alpha | -0.102 | ||||
| Upperbound of 95% confidence interval for alpha | 0.018 | ||||
| Treynor index (mean / b) | 1.753 | ||||
| Jensen alpha (a) | -0.042 | ||||
| Risk estimates for a one-period unit investment (parametric) | |||||
| assuming log normal returns and losses (using central moments from Sharpe statistics) | |||||
| VaR(95%) | 0.007 | ||||
| Expected Shortfall on VaR | 0.009 | ||||
| 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 | 1315.000 | ||||
| Minimum | 0.933 | ||||
| Quartile 1 | 1.000 | ||||
| Median | 1.000 | ||||
| Quartile 3 | 1.000 | ||||
| Maximum | 1.072 | ||||
| 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 | 79.000 | ||||
| Percentage of outliers low | 0.060 | ||||
| Mean of outliers low | 0.994 | ||||
| Number of outliers high | 71.000 | ||||
| Percentage of outliers high | 0.054 | ||||
| Mean of outliers high | 1.007 | ||||
| Risk estimates for a one-period unit investment (based on Extreme Value Theory) | |||||
| Extreme Value Index (moments method) | 0.383 | ||||
| VaR(95%) (moments method) | 0.000 | ||||
| Expected Shortfall (moments method) | 0.002 | ||||
| Extreme Value Index (regression method) | 0.528 | ||||
| VaR(95%) (regression method) | 0.000 | ||||
| Expected Shortfall (regression method) | 0.005 | ||||
| DRAW DOWN STATISTICS | |||||
| Quartiles of draw downs | |||||
| Number of observations | 3.000 | ||||
| Minimum | 0.004 | ||||
| Quartile 1 | 0.007 | ||||
| Median | 0.010 | ||||
| Quartile 3 | 0.042 | ||||
| Maximum | 0.075 | ||||
| Mean of quarter 1 | 0.004 | ||||
| Mean of quarter 2 | 0.010 | ||||
| Mean of quarter 3 | NA | ||||
| Mean of quarter 4 | 0.075 | ||||
| Inter Quartile Range | 0.035 | ||||
| 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) | -0.009 | ||||
| Compounded annual return (geometric extrapolation) | -0.009 | ||||
| Calmar ratio (compounded annual return / max draw down) | -0.117 | ||||
| Compounded annual return / average of 25% largest draw downs | -0.117 | ||||
| Compounded annual return / Expected Shortfall lognormal | -0.976 | ||||
| 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 | 1.037 | ||||
| Mean of criterion | -0.044 | ||||
| SD of predictor | 0.433 | ||||
| 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 | 0.941 | ||||
| Mean of criterion | -0.044 | ||||
| SD of predictor | 0.436 | ||||
| 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) | -8721927186598228.000 | ||||
| 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) | -183855317733261353826316210667520.000 | ||||
| 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 | ||||