Advanced Statistics: Rainier
Advanced Statistics module contributed by Jules Ellis, C2 Member. Jules has written a very helpful guide for these statistics. | |||||
| |||||
| ANALYSIS BASED ON MONTHLY VALUES, FULL HISTORY (Back) | |||||
| RATIO STATISTICS | |||||
| Ratio statistics of excess return rates | |||||
| Statistics related to Sharpe ratio | |||||
| Mean | -0.000 | ||||
| SD | 0.232 | ||||
| Sharpe ratio (Glass type estimate) | -0.001 | ||||
| Sharpe ratio (Hedges UMVUE) | -0.001 | ||||
| df | 79.000 | ||||
| t | -0.002 | ||||
| p | 0.501 | ||||
| Lowerbound of 95% confidence interval for Sharpe Ratio | -0.760 | ||||
| Upperbound of 95% confidence interval for Sharpe Ratio | 0.758 | ||||
| Lowerbound of 95% CI (Gibbons, Hedeker & Davis approximation) | -0.760 | ||||
| Upperbound of 95% CI (Gibbons, Hedeker & Davis approximation) | 0.758 | ||||
| Statistics related to Sortino ratio | |||||
| Sortino ratio | -0.001 | ||||
| Upside Potential Ratio | 0.706 | ||||
| Upside part of mean | 0.145 | ||||
| Downside part of mean | -0.145 | ||||
| Upside SD | 0.104 | ||||
| Downside SD | 0.205 | ||||
| N nonnegative terms | 32.000 | ||||
| N negative terms | 48.000 | ||||
| Statistics related to linear regression on benchmark | |||||
| N of observations | 80.000 | ||||
| Mean of predictor | 0.242 | ||||
| Mean of criterion | -0.000 | ||||
| SD of predictor | 0.284 | ||||
| SD of criterion | 0.232 | ||||
| Covariance | 0.026 | ||||
| r | 0.400 | ||||
| b (slope, estimate of beta) | 0.327 | ||||
| a (intercept, estimate of alpha) | -0.079 | ||||
| Mean Square Error | 0.046 | ||||
| DF error | 78.000 | ||||
| t(b) | 3.859 | ||||
| p(b) | 0.000 | ||||
| t(a) | -0.929 | ||||
| p(a) | 0.822 | ||||
| Lowerbound of 95% confidence interval for beta | 0.158 | ||||
| Upperbound of 95% confidence interval for beta | 0.495 | ||||
| Lowerbound of 95% confidence interval for alpha | -0.249 | ||||
| Upperbound of 95% confidence interval for alpha | 0.091 | ||||
| Treynor index (mean / b) | -0.000 | ||||
| Jensen alpha (a) | -0.079 | ||||
| Ratio statistics of excess log return rates | |||||
| Statistics related to Sharpe ratio | |||||
| Mean | -0.036 | ||||
| SD | 0.295 | ||||
| Sharpe ratio (Glass type estimate) | -0.123 | ||||
| Sharpe ratio (Hedges UMVUE) | -0.122 | ||||
| df | 79.000 | ||||
| t | -0.318 | ||||
| p | 0.624 | ||||
| Lowerbound of 95% confidence interval for Sharpe Ratio | -0.882 | ||||
| Upperbound of 95% confidence interval for Sharpe Ratio | 0.637 | ||||
| Lowerbound of 95% CI (Gibbons, Hedeker & Davis approximation) | -0.881 | ||||
| Upperbound of 95% CI (Gibbons, Hedeker & Davis approximation) | 0.637 | ||||
| Statistics related to Sortino ratio | |||||
| Sortino ratio | -0.131 | ||||
| Upside Potential Ratio | 0.503 | ||||
| Upside part of mean | 0.139 | ||||
| Downside part of mean | -0.176 | ||||
| Upside SD | 0.097 | ||||
| Downside SD | 0.277 | ||||
| N nonnegative terms | 32.000 | ||||
| N negative terms | 48.000 | ||||
| Statistics related to linear regression on benchmark | |||||
| N of observations | 80.000 | ||||
| Mean of predictor | 0.198 | ||||
| Mean of criterion | -0.036 | ||||
| SD of predictor | 0.291 | ||||
| SD of criterion | 0.295 | ||||
| Covariance | 0.047 | ||||
| r | 0.543 | ||||
| b (slope, estimate of beta) | 0.551 | ||||
| a (intercept, estimate of alpha) | -0.146 | ||||
| Mean Square Error | 0.062 | ||||
| DF error | 78.000 | ||||
| t(b) | 5.714 | ||||
| p(b) | 0.000 | ||||
| t(a) | -1.478 | ||||
| p(a) | 0.928 | ||||
| Lowerbound of 95% confidence interval for beta | 0.359 | ||||
| Upperbound of 95% confidence interval for beta | 0.743 | ||||
| Lowerbound of 95% confidence interval for alpha | -0.342 | ||||
| Upperbound of 95% confidence interval for alpha | 0.051 | ||||
| Treynor index (mean / b) | -0.066 | ||||
| Jensen alpha (a) | -0.146 | ||||
| Risk estimates for a one-period unit investment (parametric) | |||||
| assuming log normal returns and losses (using central moments from Sharpe statistics) | |||||
| VaR(95%) | 0.133 | ||||
| Expected Shortfall on VaR | 0.163 | ||||
| assuming Pareto losses only (using partial moments from Sortino statistics) | |||||
| VaR(95%) | 0.030 | ||||
| Expected Shortfall on VaR | 0.070 | ||||
| ORDER STATISTICS | |||||
| Quartiles of return rates | |||||
| Number of observations | 80.000 | ||||
| Minimum | 0.503 | ||||
| Quartile 1 | 1.000 | ||||
| Median | 1.000 | ||||
| Quartile 3 | 1.019 | ||||
| Maximum | 1.216 | ||||
| Mean of quarter 1 | 0.960 | ||||
| Mean of quarter 2 | 1.000 | ||||
| Mean of quarter 3 | 1.007 | ||||
| Mean of quarter 4 | 1.047 | ||||
| Inter Quartile Range | 0.019 | ||||
| Number outliers low | 3.000 | ||||
| Percentage of outliers low | 0.037 | ||||
| Mean of outliers low | 0.769 | ||||
| Number of outliers high | 6.000 | ||||
| Percentage of outliers high | 0.075 | ||||
| Mean of outliers high | 1.085 | ||||
| Risk estimates for a one-period unit investment (based on Extreme Value Theory) | |||||
| Extreme Value Index (moments method) | 1.493 | ||||
| VaR(95%) (moments method) | 0.009 | ||||
| Expected Shortfall (moments method) | NA | ||||
| Extreme Value Index (regression method) | 1.367 | ||||
| VaR(95%) (regression method) | 0.025 | ||||
| Expected Shortfall (regression method) | NA | ||||
| DRAW DOWN STATISTICS | |||||
| Quartiles of draw downs | |||||
| Number of observations | 4.000 | ||||
| Minimum | 0.002 | ||||
| Quartile 1 | 0.007 | ||||
| Median | 0.087 | ||||
| Quartile 3 | 0.249 | ||||
| Maximum | 0.497 | ||||
| Mean of quarter 1 | 0.002 | ||||
| Mean of quarter 2 | 0.008 | ||||
| Mean of quarter 3 | 0.166 | ||||
| Mean of quarter 4 | 0.497 | ||||
| Inter Quartile Range | 0.242 | ||||
| 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) | 0.008 | ||||
| Compounded annual return (geometric extrapolation) | 0.008 | ||||
| Calmar ratio (compounded annual return / max draw down) | 0.016 | ||||
| Compounded annual return / average of 25% largest draw downs | 0.016 | ||||
| Compounded annual return / Expected Shortfall lognormal | 0.047 | ||||
| ANALYSIS BASED ON DAILY VALUES, FULL HISTORY (Back) | |||||
| RATIO STATISTICS | |||||
| Ratio statistics of excess return rates | |||||
| Statistics related to Sharpe ratio | |||||
| Mean | 0.015 | ||||
| SD | 0.286 | ||||
| Sharpe ratio (Glass type estimate) | 0.054 | ||||
| Sharpe ratio (Hedges UMVUE) | 0.054 | ||||
| df | 1757.000 | ||||
| t | 0.140 | ||||
| p | 0.498 | ||||
| Lowerbound of 95% confidence interval for Sharpe Ratio | -0.703 | ||||
| Upperbound of 95% confidence interval for Sharpe Ratio | 0.811 | ||||
| Lowerbound of 95% CI (Gibbons, Hedeker & Davis approximation) | -0.703 | ||||
| Upperbound of 95% CI (Gibbons, Hedeker & Davis approximation) | 0.811 | ||||
| Statistics related to Sortino ratio | |||||
| Sortino ratio | 0.063 | ||||
| Upside Potential Ratio | 1.965 | ||||
| Upside part of mean | 0.478 | ||||
| Downside part of mean | -0.462 | ||||
| Upside SD | 0.151 | ||||
| Downside SD | 0.243 | ||||
| N nonnegative terms | 441.000 | ||||
| N negative terms | 1317.000 | ||||
| Statistics related to linear regression on benchmark | |||||
| N of observations | 1758.000 | ||||
| Mean of predictor | 0.261 | ||||
| Mean of criterion | 0.015 | ||||
| SD of predictor | 0.350 | ||||
| SD of criterion | 0.286 | ||||
| Covariance | 0.050 | ||||
| r | 0.495 | ||||
| b (slope, estimate of beta) | 0.405 | ||||
| a (intercept, estimate of alpha) | -0.090 | ||||
| Mean Square Error | 0.062 | ||||
| DF error | 1756.000 | ||||
| t(b) | 23.876 | ||||
| p(b) | 0.252 | ||||
| t(a) | -0.937 | ||||
| p(a) | 0.511 | ||||
| Lowerbound of 95% confidence interval for beta | 0.372 | ||||
| Upperbound of 95% confidence interval for beta | 0.438 | ||||
| Lowerbound of 95% confidence interval for alpha | -0.279 | ||||
| Upperbound of 95% confidence interval for alpha | 0.099 | ||||
| Treynor index (mean / b) | 0.038 | ||||
| Jensen alpha (a) | -0.090 | ||||
| Ratio statistics of excess log return rates | |||||
| Statistics related to Sharpe ratio | |||||
| Mean | -0.036 | ||||
| SD | 0.345 | ||||
| Sharpe ratio (Glass type estimate) | -0.106 | ||||
| Sharpe ratio (Hedges UMVUE) | -0.105 | ||||
| df | 1757.000 | ||||
| t | -0.273 | ||||
| p | 0.504 | ||||
| Lowerbound of 95% confidence interval for Sharpe Ratio | -0.862 | ||||
| Upperbound of 95% confidence interval for Sharpe Ratio | 0.651 | ||||
| Lowerbound of 95% CI (Gibbons, Hedeker & Davis approximation) | -0.862 | ||||
| Upperbound of 95% CI (Gibbons, Hedeker & Davis approximation) | 0.651 | ||||
| Statistics related to Sortino ratio | |||||
| Sortino ratio | -0.116 | ||||
| Upside Potential Ratio | 1.490 | ||||
| Upside part of mean | 0.467 | ||||
| Downside part of mean | -0.503 | ||||
| Upside SD | 0.143 | ||||
| Downside SD | 0.314 | ||||
| N nonnegative terms | 441.000 | ||||
| N negative terms | 1317.000 | ||||
| Statistics related to linear regression on benchmark | |||||
| N of observations | 1758.000 | ||||
| Mean of predictor | 0.195 | ||||
| Mean of criterion | -0.036 | ||||
| SD of predictor | 0.372 | ||||
| SD of criterion | 0.345 | ||||
| Covariance | 0.073 | ||||
| r | 0.567 | ||||
| b (slope, estimate of beta) | 0.526 | ||||
| a (intercept, estimate of alpha) | -0.139 | ||||
| Mean Square Error | 0.081 | ||||
| DF error | 1756.000 | ||||
| t(b) | 28.852 | ||||
| p(b) | 0.216 | ||||
| t(a) | -1.265 | ||||
| p(a) | 0.515 | ||||
| Lowerbound of 95% confidence interval for beta | 0.490 | ||||
| Upperbound of 95% confidence interval for beta | 0.562 | ||||
| Lowerbound of 95% confidence interval for alpha | -0.354 | ||||
| Upperbound of 95% confidence interval for alpha | 0.076 | ||||
| Treynor index (mean / b) | -0.069 | ||||
| Jensen alpha (a) | -0.139 | ||||
| Risk estimates for a one-period unit investment (parametric) | |||||
| assuming log normal returns and losses (using central moments from Sharpe statistics) | |||||
| VaR(95%) | 0.035 | ||||
| Expected Shortfall on VaR | 0.043 | ||||
| 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 | 1758.000 | ||||
| Minimum | 0.494 | ||||
| Quartile 1 | 1.000 | ||||
| Median | 1.000 | ||||
| Quartile 3 | 1.000 | ||||
| Maximum | 1.221 | ||||
| Mean of quarter 1 | 0.993 | ||||
| Mean of quarter 2 | 1.000 | ||||
| Mean of quarter 3 | 1.000 | ||||
| Mean of quarter 4 | 1.007 | ||||
| Inter Quartile Range | 0.000 | ||||
| Number outliers low | 231.000 | ||||
| Percentage of outliers low | 0.131 | ||||
| Mean of outliers low | 0.988 | ||||
| Number of outliers high | 388.000 | ||||
| Percentage of outliers high | 0.221 | ||||
| Mean of outliers high | 1.008 | ||||
| Risk estimates for a one-period unit investment (based on Extreme Value Theory) | |||||
| Extreme Value Index (moments method) | 1.206 | ||||
| VaR(95%) (moments method) | 0.003 | ||||
| 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 | 9.000 | ||||
| Minimum | 0.000 | ||||
| Quartile 1 | 0.002 | ||||
| Median | 0.030 | ||||
| Quartile 3 | 0.057 | ||||
| Maximum | 0.528 | ||||
| Mean of quarter 1 | 0.001 | ||||
| Mean of quarter 2 | 0.021 | ||||
| Mean of quarter 3 | 0.047 | ||||
| Mean of quarter 4 | 0.379 | ||||
| Inter Quartile Range | 0.055 | ||||
| Number outliers low | 0.000 | ||||
| Percentage of outliers low | 0.000 | ||||
| Mean of outliers low | NA | ||||
| Number of outliers high | 2.000 | ||||
| Percentage of outliers high | 0.222 | ||||
| Mean of outliers high | 0.379 | ||||
| Risk estimates based on draw downs (based on Extreme Value Theory) | |||||
| Extreme Value Index (moments method) | -7.173 | ||||
| VaR(95%) (moments method) | 0.174 | ||||
| Expected Shortfall (moments method) | 0.174 | ||||
| Extreme Value Index (regression method) | -0.210 | ||||
| VaR(95%) (regression method) | 0.618 | ||||
| Expected Shortfall (regression method) | 0.832 | ||||
| COMBINED STATISTICS | |||||
| Annualized return (arithmetic extrapolation) | 0.008 | ||||
| Compounded annual return (geometric extrapolation) | 0.008 | ||||
| Calmar ratio (compounded annual return / max draw down) | 0.015 | ||||
| Compounded annual return / average of 25% largest draw downs | 0.020 | ||||
| Compounded annual return / Expected Shortfall lognormal | 0.178 | ||||
| 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 | 0.866 | ||||
| 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 | 0.748 | ||||
| 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) | -8759994867571836.000 | ||||
| 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) | -130778313627179652050159323316224.000 | ||||
| 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 | ||||