Advanced Statistics: CTT
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 | -0.062 | ||||
| SD | 0.133 | ||||
| Sharpe ratio (Glass type estimate) | -0.467 | ||||
| Sharpe ratio (Hedges UMVUE) | -0.461 | ||||
| df | 57.000 | ||||
| t | -1.027 | ||||
| p | 0.846 | ||||
| Lowerbound of 95% confidence interval for Sharpe Ratio | -1.361 | ||||
| Upperbound of 95% confidence interval for Sharpe Ratio | 0.431 | ||||
| Lowerbound of 95% CI (Gibbons, Hedeker & Davis approximation) | -1.356 | ||||
| Upperbound of 95% CI (Gibbons, Hedeker & Davis approximation) | 0.435 | ||||
| Statistics related to Sortino ratio | |||||
| Sortino ratio | -0.558 | ||||
| Upside Potential Ratio | 0.546 | ||||
| Upside part of mean | 0.061 | ||||
| Downside part of mean | -0.123 | ||||
| Upside SD | 0.073 | ||||
| Downside SD | 0.111 | ||||
| N nonnegative terms | 6.000 | ||||
| N negative terms | 52.000 | ||||
| Statistics related to linear regression on benchmark | |||||
| N of observations | 58.000 | ||||
| Mean of predictor | 0.448 | ||||
| Mean of criterion | -0.062 | ||||
| SD of predictor | 0.245 | ||||
| SD of criterion | 0.133 | ||||
| Covariance | 0.004 | ||||
| r | 0.129 | ||||
| b (slope, estimate of beta) | 0.070 | ||||
| a (intercept, estimate of alpha) | -0.094 | ||||
| Mean Square Error | 0.018 | ||||
| DF error | 56.000 | ||||
| t(b) | 0.977 | ||||
| p(b) | 0.166 | ||||
| t(a) | -1.365 | ||||
| p(a) | 0.911 | ||||
| Lowerbound of 95% confidence interval for beta | -0.074 | ||||
| Upperbound of 95% confidence interval for beta | 0.214 | ||||
| Lowerbound of 95% confidence interval for alpha | -0.231 | ||||
| Upperbound of 95% confidence interval for alpha | 0.044 | ||||
| Treynor index (mean / b) | -0.885 | ||||
| Jensen alpha (a) | -0.094 | ||||
| Ratio statistics of excess log return rates | |||||
| Statistics related to Sharpe ratio | |||||
| Mean | -0.071 | ||||
| SD | 0.141 | ||||
| Sharpe ratio (Glass type estimate) | -0.508 | ||||
| Sharpe ratio (Hedges UMVUE) | -0.501 | ||||
| df | 57.000 | ||||
| t | -1.116 | ||||
| p | 0.865 | ||||
| Lowerbound of 95% confidence interval for Sharpe Ratio | -1.402 | ||||
| Upperbound of 95% confidence interval for Sharpe Ratio | 0.391 | ||||
| Lowerbound of 95% CI (Gibbons, Hedeker & Davis approximation) | -1.397 | ||||
| Upperbound of 95% CI (Gibbons, Hedeker & Davis approximation) | 0.395 | ||||
| Statistics related to Sortino ratio | |||||
| Sortino ratio | -0.581 | ||||
| Upside Potential Ratio | 0.472 | ||||
| Upside part of mean | 0.058 | ||||
| Downside part of mean | -0.129 | ||||
| Upside SD | 0.069 | ||||
| Downside SD | 0.123 | ||||
| N nonnegative terms | 6.000 | ||||
| N negative terms | 52.000 | ||||
| Statistics related to linear regression on benchmark | |||||
| N of observations | 58.000 | ||||
| Mean of predictor | 0.411 | ||||
| Mean of criterion | -0.071 | ||||
| SD of predictor | 0.236 | ||||
| SD of criterion | 0.141 | ||||
| Covariance | 0.005 | ||||
| r | 0.141 | ||||
| b (slope, estimate of beta) | 0.084 | ||||
| a (intercept, estimate of alpha) | -0.106 | ||||
| Mean Square Error | 0.020 | ||||
| DF error | 56.000 | ||||
| t(b) | 1.066 | ||||
| p(b) | 0.146 | ||||
| t(a) | -1.479 | ||||
| p(a) | 0.928 | ||||
| Lowerbound of 95% confidence interval for beta | -0.074 | ||||
| Upperbound of 95% confidence interval for beta | 0.242 | ||||
| Lowerbound of 95% confidence interval for alpha | -0.250 | ||||
| Upperbound of 95% confidence interval for alpha | 0.038 | ||||
| Treynor index (mean / b) | -0.849 | ||||
| Jensen alpha (a) | -0.106 | ||||
| Risk estimates for a one-period unit investment (parametric) | |||||
| assuming log normal returns and losses (using central moments from Sharpe statistics) | |||||
| VaR(95%) | 0.070 | ||||
| Expected Shortfall on VaR | 0.086 | ||||
| assuming Pareto losses only (using partial moments from Sortino statistics) | |||||
| VaR(95%) | 0.033 | ||||
| Expected Shortfall on VaR | 0.070 | ||||
| ORDER STATISTICS | |||||
| Quartiles of return rates | |||||
| Number of observations | 58.000 | ||||
| Minimum | 0.786 | ||||
| Quartile 1 | 1.000 | ||||
| Median | 1.000 | ||||
| Quartile 3 | 1.000 | ||||
| Maximum | 1.127 | ||||
| Mean of quarter 1 | 0.973 | ||||
| Mean of quarter 2 | 1.000 | ||||
| Mean of quarter 3 | 1.000 | ||||
| Mean of quarter 4 | 1.021 | ||||
| Inter Quartile Range | 0.000 | ||||
| Number outliers low | 9.000 | ||||
| Percentage of outliers low | 0.155 | ||||
| Mean of outliers low | 0.955 | ||||
| Number of outliers high | 9.000 | ||||
| Percentage of outliers high | 0.155 | ||||
| Mean of outliers high | 1.035 | ||||
| Risk estimates for a one-period unit investment (based on Extreme Value Theory) | |||||
| Extreme Value Index (moments method) | -2.975 | ||||
| VaR(95%) (moments method) | 0.002 | ||||
| Expected Shortfall (moments method) | 0.003 | ||||
| Extreme Value Index (regression method) | 0.396 | ||||
| VaR(95%) (regression method) | 0.039 | ||||
| Expected Shortfall (regression method) | 0.127 | ||||
| DRAW DOWN STATISTICS | |||||
| Quartiles of draw downs | |||||
| Number of observations | 2.000 | ||||
| Minimum | 0.033 | ||||
| Quartile 1 | 0.079 | ||||
| Median | 0.125 | ||||
| Quartile 3 | 0.171 | ||||
| Maximum | 0.217 | ||||
| Mean of quarter 1 | 0.033 | ||||
| Mean of quarter 2 | NA | ||||
| Mean of quarter 3 | NA | ||||
| Mean of quarter 4 | 0.217 | ||||
| Inter Quartile Range | 0.092 | ||||
| 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) | -0.125 | ||||
| Compounded annual return / average of 25% largest draw downs | -0.125 | ||||
| Compounded annual return / Expected Shortfall lognormal | -0.316 | ||||
| ANALYSIS BASED ON DAILY VALUES, FULL HISTORY (Back) | |||||
| RATIO STATISTICS | |||||
| Ratio statistics of excess return rates | |||||
| Statistics related to Sharpe ratio | |||||
| Mean | -0.055 | ||||
| SD | 0.178 | ||||
| Sharpe ratio (Glass type estimate) | -0.311 | ||||
| Sharpe ratio (Hedges UMVUE) | -0.311 | ||||
| df | 1270.000 | ||||
| t | -0.686 | ||||
| p | 0.510 | ||||
| Lowerbound of 95% confidence interval for Sharpe Ratio | -1.201 | ||||
| Upperbound of 95% confidence interval for Sharpe Ratio | 0.579 | ||||
| Lowerbound of 95% CI (Gibbons, Hedeker & Davis approximation) | -1.201 | ||||
| Upperbound of 95% CI (Gibbons, Hedeker & Davis approximation) | 0.579 | ||||
| Statistics related to Sortino ratio | |||||
| Sortino ratio | -0.436 | ||||
| Upside Potential Ratio | 3.080 | ||||
| Upside part of mean | 0.392 | ||||
| Downside part of mean | -0.448 | ||||
| Upside SD | 0.125 | ||||
| Downside SD | 0.127 | ||||
| N nonnegative terms | 128.000 | ||||
| N negative terms | 1143.000 | ||||
| Statistics related to linear regression on benchmark | |||||
| N of observations | 1271.000 | ||||
| Mean of predictor | 0.554 | ||||
| Mean of criterion | -0.055 | ||||
| SD of predictor | 0.512 | ||||
| SD of criterion | 0.178 | ||||
| Covariance | -0.004 | ||||
| r | -0.045 | ||||
| b (slope, estimate of beta) | -0.016 | ||||
| a (intercept, estimate of alpha) | -0.047 | ||||
| Mean Square Error | 0.032 | ||||
| DF error | 1269.000 | ||||
| t(b) | -1.612 | ||||
| p(b) | 0.529 | ||||
| t(a) | -0.577 | ||||
| p(a) | 0.510 | ||||
| Lowerbound of 95% confidence interval for beta | -0.035 | ||||
| Upperbound of 95% confidence interval for beta | 0.003 | ||||
| Lowerbound of 95% confidence interval for alpha | -0.206 | ||||
| Upperbound of 95% confidence interval for alpha | 0.112 | ||||
| Treynor index (mean / b) | 3.526 | ||||
| Jensen alpha (a) | -0.047 | ||||
| Ratio statistics of excess log return rates | |||||
| Statistics related to Sharpe ratio | |||||
| Mean | -0.071 | ||||
| SD | 0.178 | ||||
| Sharpe ratio (Glass type estimate) | -0.400 | ||||
| Sharpe ratio (Hedges UMVUE) | -0.400 | ||||
| df | 1270.000 | ||||
| t | -0.881 | ||||
| p | 0.512 | ||||
| Lowerbound of 95% confidence interval for Sharpe Ratio | -1.290 | ||||
| Upperbound of 95% confidence interval for Sharpe Ratio | 0.490 | ||||
| Lowerbound of 95% CI (Gibbons, Hedeker & Davis approximation) | -1.290 | ||||
| Upperbound of 95% CI (Gibbons, Hedeker & Davis approximation) | 0.490 | ||||
| Statistics related to Sortino ratio | |||||
| Sortino ratio | -0.545 | ||||
| Upside Potential Ratio | 2.940 | ||||
| Upside part of mean | 0.385 | ||||
| Downside part of mean | -0.456 | ||||
| Upside SD | 0.121 | ||||
| Downside SD | 0.131 | ||||
| N nonnegative terms | 128.000 | ||||
| N negative terms | 1143.000 | ||||
| Statistics related to linear regression on benchmark | |||||
| N of observations | 1271.000 | ||||
| Mean of predictor | 0.429 | ||||
| Mean of criterion | -0.071 | ||||
| SD of predictor | 0.496 | ||||
| SD of criterion | 0.178 | ||||
| Covariance | -0.004 | ||||
| r | -0.045 | ||||
| b (slope, estimate of beta) | -0.016 | ||||
| a (intercept, estimate of alpha) | -0.064 | ||||
| Mean Square Error | 0.032 | ||||
| DF error | 1269.000 | ||||
| t(b) | -1.592 | ||||
| p(b) | 0.528 | ||||
| t(a) | -0.796 | ||||
| p(a) | 0.514 | ||||
| Lowerbound of 95% confidence interval for beta | -0.036 | ||||
| Upperbound of 95% confidence interval for beta | 0.004 | ||||
| Lowerbound of 95% confidence interval for alpha | -0.223 | ||||
| Upperbound of 95% confidence interval for alpha | 0.094 | ||||
| Treynor index (mean / b) | 4.443 | ||||
| Jensen alpha (a) | -0.064 | ||||
| Risk estimates for a one-period unit investment (parametric) | |||||
| assuming log normal returns and losses (using central moments from Sharpe statistics) | |||||
| VaR(95%) | 0.018 | ||||
| Expected Shortfall on VaR | 0.023 | ||||
| assuming Pareto losses only (using partial moments from Sortino statistics) | |||||
| VaR(95%) | 0.006 | ||||
| Expected Shortfall on VaR | 0.012 | ||||
| ORDER STATISTICS | |||||
| Quartiles of return rates | |||||
| Number of observations | 1271.000 | ||||
| Minimum | 0.902 | ||||
| Quartile 1 | 1.000 | ||||
| Median | 1.000 | ||||
| Quartile 3 | 1.000 | ||||
| Maximum | 1.102 | ||||
| Mean of quarter 1 | 0.994 | ||||
| Mean of quarter 2 | 1.000 | ||||
| Mean of quarter 3 | 1.000 | ||||
| Mean of quarter 4 | 1.006 | ||||
| Inter Quartile Range | 0.000 | ||||
| Number outliers low | 105.000 | ||||
| Percentage of outliers low | 0.083 | ||||
| Mean of outliers low | 0.981 | ||||
| Number of outliers high | 129.000 | ||||
| Percentage of outliers high | 0.101 | ||||
| Mean of outliers high | 1.015 | ||||
| Risk estimates for a one-period unit investment (based on Extreme Value Theory) | |||||
| Extreme Value Index (moments method) | -4.966 | ||||
| VaR(95%) (moments method) | 0.002 | ||||
| Expected Shortfall (moments method) | 0.002 | ||||
| Extreme Value Index (regression method) | -0.247 | ||||
| VaR(95%) (regression method) | 0.004 | ||||
| Expected Shortfall (regression method) | 0.018 | ||||
| DRAW DOWN STATISTICS | |||||
| Quartiles of draw downs | |||||
| Number of observations | 7.000 | ||||
| Minimum | 0.008 | ||||
| Quartile 1 | 0.036 | ||||
| Median | 0.098 | ||||
| Quartile 3 | 0.118 | ||||
| Maximum | 0.253 | ||||
| Mean of quarter 1 | 0.013 | ||||
| Mean of quarter 2 | 0.076 | ||||
| Mean of quarter 3 | 0.103 | ||||
| Mean of quarter 4 | 0.193 | ||||
| Inter Quartile Range | 0.082 | ||||
| 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 | 0.143 | ||||
| Mean of outliers high | 0.253 | ||||
| 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) | -0.107 | ||||
| Compounded annual return / average of 25% largest draw downs | -0.140 | ||||
| Compounded annual return / Expected Shortfall lognormal | -1.186 | ||||
| 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 | 1.002 | ||||
| Mean of criterion | -0.044 | ||||
| SD of predictor | 0.504 | ||||
| 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 | 0.875 | ||||
| Mean of criterion | -0.044 | ||||
| SD of predictor | 0.502 | ||||
| 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) | -8748724916608439.000 | ||||
| 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) | -769027339976300193040518455754752.000 | ||||
| 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 | ||||