Advanced Statistics: Old System
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 | 0.197 | ||||
| SD | 1.141 | ||||
| Sharpe ratio (Glass type estimate) | 0.173 | ||||
| Sharpe ratio (Hedges UMVUE) | 0.171 | ||||
| df | 97.000 | ||||
| t | 0.493 | ||||
| p | 0.311 | ||||
| Lowerbound of 95% confidence interval for Sharpe Ratio | -0.514 | ||||
| Upperbound of 95% confidence interval for Sharpe Ratio | 0.858 | ||||
| Lowerbound of 95% CI (Gibbons, Hedeker & Davis approximation) | -0.515 | ||||
| Upperbound of 95% CI (Gibbons, Hedeker & Davis approximation) | 0.858 | ||||
| Statistics related to Sortino ratio | |||||
| Sortino ratio | 0.977 | ||||
| Upside Potential Ratio | 2.058 | ||||
| Upside part of mean | 0.415 | ||||
| Downside part of mean | -0.218 | ||||
| Upside SD | 1.119 | ||||
| Downside SD | 0.202 | ||||
| N nonnegative terms | 2.000 | ||||
| N negative terms | 96.000 | ||||
| Statistics related to linear regression on benchmark | |||||
| N of observations | 98.000 | ||||
| Mean of predictor | 0.187 | ||||
| Mean of criterion | 0.197 | ||||
| SD of predictor | 0.271 | ||||
| SD of criterion | 1.141 | ||||
| Covariance | -0.061 | ||||
| r | -0.198 | ||||
| b (slope, estimate of beta) | -0.834 | ||||
| a (intercept, estimate of alpha) | 0.353 | ||||
| Mean Square Error | 1.264 | ||||
| DF error | 96.000 | ||||
| t(b) | -1.980 | ||||
| p(b) | 0.975 | ||||
| t(a) | 0.879 | ||||
| p(a) | 0.191 | ||||
| Lowerbound of 95% confidence interval for beta | -1.670 | ||||
| Upperbound of 95% confidence interval for beta | 0.002 | ||||
| Lowerbound of 95% confidence interval for alpha | -0.444 | ||||
| Upperbound of 95% confidence interval for alpha | 1.149 | ||||
| Treynor index (mean / b) | -0.236 | ||||
| Jensen alpha (a) | 0.353 | ||||
| Ratio statistics of excess log return rates | |||||
| Statistics related to Sharpe ratio | |||||
| Mean | -0.044 | ||||
| SD | 0.557 | ||||
| Sharpe ratio (Glass type estimate) | -0.079 | ||||
| Sharpe ratio (Hedges UMVUE) | -0.079 | ||||
| df | 97.000 | ||||
| t | -0.227 | ||||
| p | 0.590 | ||||
| Lowerbound of 95% confidence interval for Sharpe Ratio | -0.765 | ||||
| Upperbound of 95% confidence interval for Sharpe Ratio | 0.607 | ||||
| Lowerbound of 95% CI (Gibbons, Hedeker & Davis approximation) | -0.765 | ||||
| Upperbound of 95% CI (Gibbons, Hedeker & Davis approximation) | 0.607 | ||||
| Statistics related to Sortino ratio | |||||
| Sortino ratio | -0.192 | ||||
| Upside Potential Ratio | 0.856 | ||||
| Upside part of mean | 0.197 | ||||
| Downside part of mean | -0.242 | ||||
| Upside SD | 0.504 | ||||
| Downside SD | 0.231 | ||||
| N nonnegative terms | 2.000 | ||||
| N negative terms | 96.000 | ||||
| Statistics related to linear regression on benchmark | |||||
| N of observations | 98.000 | ||||
| Mean of predictor | 0.150 | ||||
| Mean of criterion | -0.044 | ||||
| SD of predictor | 0.264 | ||||
| SD of criterion | 0.557 | ||||
| Covariance | -0.027 | ||||
| r | -0.184 | ||||
| b (slope, estimate of beta) | -0.389 | ||||
| a (intercept, estimate of alpha) | 0.014 | ||||
| Mean Square Error | 0.303 | ||||
| DF error | 96.000 | ||||
| t(b) | -1.838 | ||||
| p(b) | 0.965 | ||||
| t(a) | 0.072 | ||||
| p(a) | 0.471 | ||||
| Lowerbound of 95% confidence interval for beta | -0.810 | ||||
| Upperbound of 95% confidence interval for beta | 0.031 | ||||
| Lowerbound of 95% confidence interval for alpha | -0.374 | ||||
| Upperbound of 95% confidence interval for alpha | 0.402 | ||||
| Treynor index (mean / b) | 0.114 | ||||
| Jensen alpha (a) | 0.014 | ||||
| Risk estimates for a one-period unit investment (parametric) | |||||
| assuming log normal returns and losses (using central moments from Sharpe statistics) | |||||
| VaR(95%) | 0.235 | ||||
| Expected Shortfall on VaR | 0.284 | ||||
| assuming Pareto losses only (using partial moments from Sortino statistics) | |||||
| VaR(95%) | 0.063 | ||||
| Expected Shortfall on VaR | 0.131 | ||||
| ORDER STATISTICS | |||||
| Quartiles of return rates | |||||
| Number of observations | 98.000 | ||||
| Minimum | 0.706 | ||||
| Quartile 1 | 1.000 | ||||
| Median | 1.000 | ||||
| Quartile 3 | 1.000 | ||||
| Maximum | 4.195 | ||||
| Mean of quarter 1 | 0.943 | ||||
| Mean of quarter 2 | 1.000 | ||||
| Mean of quarter 3 | 1.000 | ||||
| Mean of quarter 4 | 1.136 | ||||
| Inter Quartile Range | 0.000 | ||||
| Number outliers low | 8.000 | ||||
| Percentage of outliers low | 0.082 | ||||
| Mean of outliers low | 0.821 | ||||
| Number of outliers high | 3.000 | ||||
| Percentage of outliers high | 0.031 | ||||
| Mean of outliers high | 2.133 | ||||
| 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) | -0.689 | ||||
| VaR(95%) (regression method) | 0.072 | ||||
| Expected Shortfall (regression method) | 0.129 | ||||
| DRAW DOWN STATISTICS | |||||
| Quartiles of draw downs | |||||
| Number of observations | 1.000 | ||||
| Minimum | 0.762 | ||||
| Quartile 1 | 0.762 | ||||
| Median | 0.762 | ||||
| Quartile 3 | 0.762 | ||||
| Maximum | 0.762 | ||||
| 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) | -0.000 | ||||
| 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 | NA | ||||
| Compounded annual return / Expected Shortfall lognormal | -0.001 | ||||
| ANALYSIS BASED ON DAILY VALUES, FULL HISTORY (Back) | |||||
| RATIO STATISTICS | |||||
| Ratio statistics of excess return rates | |||||
| Statistics related to Sharpe ratio | |||||
| Mean | 1.608 | ||||
| SD | 2.628 | ||||
| Sharpe ratio (Glass type estimate) | 0.612 | ||||
| Sharpe ratio (Hedges UMVUE) | 0.612 | ||||
| df | 2148.000 | ||||
| t | 1.752 | ||||
| p | 0.040 | ||||
| Lowerbound of 95% confidence interval for Sharpe Ratio | -0.073 | ||||
| Upperbound of 95% confidence interval for Sharpe Ratio | 1.296 | ||||
| Lowerbound of 95% CI (Gibbons, Hedeker & Davis approximation) | -0.073 | ||||
| Upperbound of 95% CI (Gibbons, Hedeker & Davis approximation) | 1.296 | ||||
| Statistics related to Sortino ratio | |||||
| Sortino ratio | 2.410 | ||||
| Upside Potential Ratio | 4.141 | ||||
| Upside part of mean | 2.763 | ||||
| Downside part of mean | -1.155 | ||||
| Upside SD | 2.544 | ||||
| Downside SD | 0.667 | ||||
| N nonnegative terms | 64.000 | ||||
| N negative terms | 2085.000 | ||||
| Statistics related to linear regression on benchmark | |||||
| N of observations | 2149.000 | ||||
| Mean of predictor | 0.313 | ||||
| Mean of criterion | 1.608 | ||||
| SD of predictor | 0.554 | ||||
| SD of criterion | 2.628 | ||||
| Covariance | -0.444 | ||||
| r | -0.305 | ||||
| b (slope, estimate of beta) | -1.447 | ||||
| a (intercept, estimate of alpha) | 2.062 | ||||
| Mean Square Error | 6.270 | ||||
| DF error | 2147.000 | ||||
| t(b) | -14.831 | ||||
| p(b) | 1.000 | ||||
| t(a) | 2.357 | ||||
| p(a) | 0.009 | ||||
| Lowerbound of 95% confidence interval for beta | -1.639 | ||||
| Upperbound of 95% confidence interval for beta | -1.256 | ||||
| Lowerbound of 95% confidence interval for alpha | 0.346 | ||||
| Upperbound of 95% confidence interval for alpha | 3.778 | ||||
| Treynor index (mean / b) | -1.111 | ||||
| Jensen alpha (a) | 2.062 | ||||
| Ratio statistics of excess log return rates | |||||
| Statistics related to Sharpe ratio | |||||
| Mean | -0.044 | ||||
| SD | 1.660 | ||||
| Sharpe ratio (Glass type estimate) | -0.027 | ||||
| Sharpe ratio (Hedges UMVUE) | -0.027 | ||||
| df | 2148.000 | ||||
| t | -0.076 | ||||
| p | 0.530 | ||||
| Lowerbound of 95% confidence interval for Sharpe Ratio | -0.711 | ||||
| Upperbound of 95% confidence interval for Sharpe Ratio | 0.658 | ||||
| Lowerbound of 95% CI (Gibbons, Hedeker & Davis approximation) | -0.711 | ||||
| Upperbound of 95% CI (Gibbons, Hedeker & Davis approximation) | 0.658 | ||||
| Statistics related to Sortino ratio | |||||
| Sortino ratio | -0.040 | ||||
| Upside Potential Ratio | 1.385 | ||||
| Upside part of mean | 1.546 | ||||
| Downside part of mean | -1.590 | ||||
| Upside SD | 1.228 | ||||
| Downside SD | 1.116 | ||||
| N nonnegative terms | 64.000 | ||||
| N negative terms | 2085.000 | ||||
| Statistics related to linear regression on benchmark | |||||
| N of observations | 2149.000 | ||||
| Mean of predictor | 0.159 | ||||
| Mean of criterion | -0.044 | ||||
| SD of predictor | 0.557 | ||||
| SD of criterion | 1.660 | ||||
| Covariance | -0.332 | ||||
| r | -0.359 | ||||
| b (slope, estimate of beta) | -1.070 | ||||
| a (intercept, estimate of alpha) | 0.126 | ||||
| Mean Square Error | 2.401 | ||||
| DF error | 2147.000 | ||||
| t(b) | -17.839 | ||||
| p(b) | 1.000 | ||||
| t(a) | 0.233 | ||||
| p(a) | 0.408 | ||||
| Lowerbound of 95% confidence interval for beta | -1.187 | ||||
| Upperbound of 95% confidence interval for beta | -0.952 | ||||
| Lowerbound of 95% confidence interval for alpha | -0.935 | ||||
| Upperbound of 95% confidence interval for alpha | 1.187 | ||||
| Treynor index (mean / b) | 0.041 | ||||
| Jensen alpha (a) | 0.126 | ||||
| Risk estimates for a one-period unit investment (parametric) | |||||
| assuming log normal returns and losses (using central moments from Sharpe statistics) | |||||
| VaR(95%) | 0.155 | ||||
| Expected Shortfall on VaR | 0.190 | ||||
| assuming Pareto losses only (using partial moments from Sortino statistics) | |||||
| VaR(95%) | 0.015 | ||||
| Expected Shortfall on VaR | 0.034 | ||||
| ORDER STATISTICS | |||||
| Quartiles of return rates | |||||
| Number of observations | 2149.000 | ||||
| Minimum | 0.241 | ||||
| Quartile 1 | 1.000 | ||||
| Median | 1.000 | ||||
| Quartile 3 | 1.000 | ||||
| Maximum | 4.307 | ||||
| Mean of quarter 1 | 0.983 | ||||
| Mean of quarter 2 | 1.000 | ||||
| Mean of quarter 3 | 1.000 | ||||
| Mean of quarter 4 | 1.042 | ||||
| Inter Quartile Range | 0.000 | ||||
| Number outliers low | 86.000 | ||||
| Percentage of outliers low | 0.040 | ||||
| Mean of outliers low | 0.894 | ||||
| Number of outliers high | 65.000 | ||||
| Percentage of outliers high | 0.030 | ||||
| Mean of outliers high | 1.349 | ||||
| Risk estimates for a one-period unit investment (based on Extreme Value Theory) | |||||
| Extreme Value Index (moments method) | -0.013 | ||||
| VaR(95%) (moments method) | -0.000 | ||||
| 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 | 2.000 | ||||
| Minimum | 0.768 | ||||
| Quartile 1 | 0.770 | ||||
| Median | 0.771 | ||||
| Quartile 3 | 0.772 | ||||
| Maximum | 0.774 | ||||
| Mean of quarter 1 | 0.768 | ||||
| Mean of quarter 2 | NA | ||||
| Mean of quarter 3 | NA | ||||
| Mean of quarter 4 | 0.774 | ||||
| Inter Quartile Range | 0.003 | ||||
| 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 | -0.001 | ||||
| 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 | 0.964 | ||||
| Mean of criterion | -0.044 | ||||
| SD of predictor | 0.444 | ||||
| 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 | 0.864 | ||||
| Mean of criterion | -0.044 | ||||
| SD of predictor | 0.445 | ||||
| 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) | -8736647483214272.000 | ||||
| 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) | 87098803792532817393655037820928.000 | ||||
| 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 | ||||