Advanced Statistics: Test 1 (closed)
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 | -0.028 | ||||
| SD | 0.186 | ||||
| Sharpe ratio (Glass type estimate) | -0.151 | ||||
| Sharpe ratio (Hedges UMVUE) | -0.150 | ||||
| df | 95.000 | ||||
| t | -0.427 | ||||
| p | 0.665 | ||||
| Lowerbound of 95% confidence interval for Sharpe Ratio | -0.844 | ||||
| Upperbound of 95% confidence interval for Sharpe Ratio | 0.543 | ||||
| Lowerbound of 95% CI (Gibbons, Hedeker & Davis approximation) | -0.843 | ||||
| Upperbound of 95% CI (Gibbons, Hedeker & Davis approximation) | 0.544 | ||||
| Statistics related to Sortino ratio | |||||
| Sortino ratio | -0.258 | ||||
| Upside Potential Ratio | 0.783 | ||||
| Upside part of mean | 0.085 | ||||
| Downside part of mean | -0.113 | ||||
| Upside SD | 0.150 | ||||
| Downside SD | 0.109 | ||||
| N nonnegative terms | 5.000 | ||||
| N negative terms | 91.000 | ||||
| Statistics related to linear regression on benchmark | |||||
| N of observations | 96.000 | ||||
| Mean of predictor | 0.181 | ||||
| Mean of criterion | -0.028 | ||||
| SD of predictor | 0.244 | ||||
| SD of criterion | 0.186 | ||||
| Covariance | -0.000 | ||||
| r | -0.005 | ||||
| b (slope, estimate of beta) | -0.004 | ||||
| a (intercept, estimate of alpha) | -0.027 | ||||
| Mean Square Error | 0.035 | ||||
| DF error | 94.000 | ||||
| t(b) | -0.045 | ||||
| p(b) | 0.518 | ||||
| t(a) | -0.405 | ||||
| p(a) | 0.657 | ||||
| Lowerbound of 95% confidence interval for beta | -0.160 | ||||
| Upperbound of 95% confidence interval for beta | 0.153 | ||||
| Lowerbound of 95% confidence interval for alpha | -0.162 | ||||
| Upperbound of 95% confidence interval for alpha | 0.107 | ||||
| Treynor index (mean / b) | 7.898 | ||||
| Jensen alpha (a) | -0.027 | ||||
| Ratio statistics of excess log return rates | |||||
| Statistics related to Sharpe ratio | |||||
| Mean | -0.044 | ||||
| SD | 0.178 | ||||
| Sharpe ratio (Glass type estimate) | -0.248 | ||||
| Sharpe ratio (Hedges UMVUE) | -0.246 | ||||
| df | 95.000 | ||||
| t | -0.701 | ||||
| p | 0.757 | ||||
| Lowerbound of 95% confidence interval for Sharpe Ratio | -0.941 | ||||
| Upperbound of 95% confidence interval for Sharpe Ratio | 0.447 | ||||
| Lowerbound of 95% CI (Gibbons, Hedeker & Davis approximation) | -0.940 | ||||
| Upperbound of 95% CI (Gibbons, Hedeker & Davis approximation) | 0.448 | ||||
| Statistics related to Sortino ratio | |||||
| Sortino ratio | -0.363 | ||||
| Upside Potential Ratio | 0.625 | ||||
| Upside part of mean | 0.076 | ||||
| Downside part of mean | -0.120 | ||||
| Upside SD | 0.129 | ||||
| Downside SD | 0.121 | ||||
| N nonnegative terms | 5.000 | ||||
| N negative terms | 91.000 | ||||
| Statistics related to linear regression on benchmark | |||||
| N of observations | 96.000 | ||||
| Mean of predictor | 0.151 | ||||
| Mean of criterion | -0.044 | ||||
| SD of predictor | 0.242 | ||||
| SD of criterion | 0.178 | ||||
| Covariance | -0.000 | ||||
| r | -0.008 | ||||
| b (slope, estimate of beta) | -0.006 | ||||
| a (intercept, estimate of alpha) | -0.043 | ||||
| Mean Square Error | 0.032 | ||||
| DF error | 94.000 | ||||
| t(b) | -0.082 | ||||
| p(b) | 0.533 | ||||
| t(a) | -0.671 | ||||
| p(a) | 0.748 | ||||
| Lowerbound of 95% confidence interval for beta | -0.157 | ||||
| Upperbound of 95% confidence interval for beta | 0.144 | ||||
| Lowerbound of 95% confidence interval for alpha | -0.170 | ||||
| Upperbound of 95% confidence interval for alpha | 0.084 | ||||
| Treynor index (mean / b) | 7.100 | ||||
| Jensen alpha (a) | -0.043 | ||||
| Risk estimates for a one-period unit investment (parametric) | |||||
| assuming log normal returns and losses (using central moments from Sharpe statistics) | |||||
| VaR(95%) | 0.084 | ||||
| Expected Shortfall on VaR | 0.103 | ||||
| assuming Pareto losses only (using partial moments from Sortino statistics) | |||||
| VaR(95%) | 0.032 | ||||
| Expected Shortfall on VaR | 0.067 | ||||
| ORDER STATISTICS | |||||
| Quartiles of return rates | |||||
| Number of observations | 96.000 | ||||
| Minimum | 0.753 | ||||
| Quartile 1 | 1.000 | ||||
| Median | 1.000 | ||||
| Quartile 3 | 1.000 | ||||
| Maximum | 1.391 | ||||
| Mean of quarter 1 | 0.976 | ||||
| Mean of quarter 2 | 1.000 | ||||
| Mean of quarter 3 | 1.000 | ||||
| Mean of quarter 4 | 1.029 | ||||
| Inter Quartile Range | 0.000 | ||||
| Number outliers low | 7.000 | ||||
| Percentage of outliers low | 0.073 | ||||
| Mean of outliers low | 0.918 | ||||
| Number of outliers high | 9.000 | ||||
| Percentage of outliers high | 0.094 | ||||
| Mean of outliers high | 1.078 | ||||
| Risk estimates for a one-period unit investment (based on Extreme Value Theory) | |||||
| Extreme Value Index (moments method) | -149.000 | ||||
| VaR(95%) (moments method) | 0.000 | ||||
| Expected Shortfall (moments method) | 0.000 | ||||
| Extreme Value Index (regression method) | -0.076 | ||||
| VaR(95%) (regression method) | 0.020 | ||||
| Expected Shortfall (regression method) | 0.104 | ||||
| DRAW DOWN STATISTICS | |||||
| Quartiles of draw downs | |||||
| Number of observations | 2.000 | ||||
| Minimum | 0.086 | ||||
| Quartile 1 | 0.141 | ||||
| Median | 0.196 | ||||
| Quartile 3 | 0.250 | ||||
| Maximum | 0.305 | ||||
| Mean of quarter 1 | 0.086 | ||||
| Mean of quarter 2 | NA | ||||
| Mean of quarter 3 | NA | ||||
| Mean of quarter 4 | 0.305 | ||||
| Inter Quartile Range | 0.109 | ||||
| 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) | 0.000 | ||||
| Compounded annual return (geometric extrapolation) | 0.000 | ||||
| Calmar ratio (compounded annual return / max draw down) | 0.000 | ||||
| Compounded annual return / average of 25% largest draw downs | 0.000 | ||||
| Compounded annual return / Expected Shortfall lognormal | 0.000 | ||||
| ANALYSIS BASED ON DAILY VALUES, FULL HISTORY (Back) | |||||
| RATIO STATISTICS | |||||
| Ratio statistics of excess return rates | |||||
| Statistics related to Sharpe ratio | |||||
| Mean | 0.011 | ||||
| SD | 0.342 | ||||
| Sharpe ratio (Glass type estimate) | 0.033 | ||||
| Sharpe ratio (Hedges UMVUE) | 0.033 | ||||
| df | 2103.000 | ||||
| t | 0.095 | ||||
| p | 0.462 | ||||
| Lowerbound of 95% confidence interval for Sharpe Ratio | -0.658 | ||||
| Upperbound of 95% confidence interval for Sharpe Ratio | 0.725 | ||||
| Lowerbound of 95% CI (Gibbons, Hedeker & Davis approximation) | -0.658 | ||||
| Upperbound of 95% CI (Gibbons, Hedeker & Davis approximation) | 0.725 | ||||
| Statistics related to Sortino ratio | |||||
| Sortino ratio | 0.057 | ||||
| Upside Potential Ratio | 2.008 | ||||
| Upside part of mean | 0.405 | ||||
| Downside part of mean | -0.393 | ||||
| Upside SD | 0.276 | ||||
| Downside SD | 0.202 | ||||
| N nonnegative terms | 79.000 | ||||
| N negative terms | 2025.000 | ||||
| Statistics related to linear regression on benchmark | |||||
| N of observations | 2104.000 | ||||
| Mean of predictor | 0.297 | ||||
| Mean of criterion | 0.011 | ||||
| SD of predictor | 0.529 | ||||
| SD of criterion | 0.342 | ||||
| Covariance | -0.038 | ||||
| r | -0.210 | ||||
| b (slope, estimate of beta) | -0.136 | ||||
| a (intercept, estimate of alpha) | 0.052 | ||||
| Mean Square Error | 0.112 | ||||
| DF error | 2102.000 | ||||
| t(b) | -9.837 | ||||
| p(b) | 1.000 | ||||
| t(a) | 0.438 | ||||
| p(a) | 0.331 | ||||
| Lowerbound of 95% confidence interval for beta | -0.163 | ||||
| Upperbound of 95% confidence interval for beta | -0.109 | ||||
| Lowerbound of 95% confidence interval for alpha | -0.180 | ||||
| Upperbound of 95% confidence interval for alpha | 0.283 | ||||
| Treynor index (mean / b) | -0.084 | ||||
| Jensen alpha (a) | 0.052 | ||||
| Ratio statistics of excess log return rates | |||||
| Statistics related to Sharpe ratio | |||||
| Mean | -0.044 | ||||
| SD | 0.331 | ||||
| Sharpe ratio (Glass type estimate) | -0.133 | ||||
| Sharpe ratio (Hedges UMVUE) | -0.133 | ||||
| df | 2103.000 | ||||
| t | -0.376 | ||||
| p | 0.647 | ||||
| Lowerbound of 95% confidence interval for Sharpe Ratio | -0.824 | ||||
| Upperbound of 95% confidence interval for Sharpe Ratio | 0.559 | ||||
| Lowerbound of 95% CI (Gibbons, Hedeker & Davis approximation) | -0.824 | ||||
| Upperbound of 95% CI (Gibbons, Hedeker & Davis approximation) | 0.559 | ||||
| Statistics related to Sortino ratio | |||||
| Sortino ratio | -0.192 | ||||
| Upside Potential Ratio | 1.625 | ||||
| Upside part of mean | 0.373 | ||||
| Downside part of mean | -0.417 | ||||
| Upside SD | 0.239 | ||||
| Downside SD | 0.230 | ||||
| N nonnegative terms | 79.000 | ||||
| N negative terms | 2025.000 | ||||
| Statistics related to linear regression on benchmark | |||||
| N of observations | 2104.000 | ||||
| Mean of predictor | 0.156 | ||||
| Mean of criterion | -0.044 | ||||
| SD of predictor | 0.533 | ||||
| SD of criterion | 0.331 | ||||
| Covariance | -0.038 | ||||
| r | -0.213 | ||||
| b (slope, estimate of beta) | -0.133 | ||||
| a (intercept, estimate of alpha) | -0.023 | ||||
| Mean Square Error | 0.105 | ||||
| DF error | 2102.000 | ||||
| t(b) | -10.009 | ||||
| p(b) | 1.000 | ||||
| t(a) | -0.204 | ||||
| p(a) | 0.581 | ||||
| Lowerbound of 95% confidence interval for beta | -0.159 | ||||
| Upperbound of 95% confidence interval for beta | -0.107 | ||||
| Lowerbound of 95% confidence interval for alpha | -0.247 | ||||
| Upperbound of 95% confidence interval for alpha | 0.201 | ||||
| Treynor index (mean / b) | 0.332 | ||||
| Jensen alpha (a) | -0.023 | ||||
| Risk estimates for a one-period unit investment (parametric) | |||||
| assuming log normal returns and losses (using central moments from Sharpe statistics) | |||||
| VaR(95%) | 0.033 | ||||
| Expected Shortfall on VaR | 0.041 | ||||
| assuming Pareto losses only (using partial moments from Sortino statistics) | |||||
| VaR(95%) | 0.005 | ||||
| Expected Shortfall on VaR | 0.012 | ||||
| ORDER STATISTICS | |||||
| Quartiles of return rates | |||||
| Number of observations | 2104.000 | ||||
| Minimum | 0.658 | ||||
| Quartile 1 | 1.000 | ||||
| Median | 1.000 | ||||
| Quartile 3 | 1.000 | ||||
| Maximum | 1.493 | ||||
| Mean of quarter 1 | 0.995 | ||||
| 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 | 123.000 | ||||
| Percentage of outliers low | 0.058 | ||||
| Mean of outliers low | 0.977 | ||||
| Number of outliers high | 108.000 | ||||
| Percentage of outliers high | 0.051 | ||||
| Mean of outliers high | 1.030 | ||||
| Risk estimates for a one-period unit investment (based on Extreme Value Theory) | |||||
| Extreme Value Index (moments method) | 0.636 | ||||
| VaR(95%) (moments method) | 0.000 | ||||
| Expected Shortfall (moments method) | 0.005 | ||||
| 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 | 7.000 | ||||
| Minimum | 0.006 | ||||
| Quartile 1 | 0.015 | ||||
| Median | 0.042 | ||||
| Quartile 3 | 0.163 | ||||
| Maximum | 0.358 | ||||
| Mean of quarter 1 | 0.008 | ||||
| Mean of quarter 2 | 0.031 | ||||
| Mean of quarter 3 | 0.068 | ||||
| Mean of quarter 4 | 0.308 | ||||
| Inter Quartile Range | 0.148 | ||||
| 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) | 0.000 | ||||
| Compounded annual return (geometric extrapolation) | 0.000 | ||||
| Calmar ratio (compounded annual return / max draw down) | 0.000 | ||||
| Compounded annual return / average of 25% largest draw downs | 0.000 | ||||
| Compounded annual return / Expected Shortfall lognormal | 0.000 | ||||
| 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 | 1.050 | ||||
| Mean of criterion | -0.044 | ||||
| SD of predictor | 0.480 | ||||
| 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 | 0.932 | ||||
| Mean of criterion | -0.044 | ||||
| SD of predictor | 0.486 | ||||
| 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) | -8738196960914607.000 | ||||
| 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) | 214299494035335651347773593223168.000 | ||||
| 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 | ||||