Advanced Statistics: RichDaddy
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 | -0.025 | ||||
| SD | 0.031 | ||||
| Sharpe ratio (Glass type estimate) | -0.824 | ||||
| Sharpe ratio (Hedges UMVUE) | -0.805 | ||||
| df | 32.000 | ||||
| t | -1.367 | ||||
| p | 0.909 | ||||
| Lowerbound of 95% confidence interval for Sharpe Ratio | -2.017 | ||||
| Upperbound of 95% confidence interval for Sharpe Ratio | 0.381 | ||||
| Lowerbound of 95% CI (Gibbons, Hedeker & Davis approximation) | -2.003 | ||||
| Upperbound of 95% CI (Gibbons, Hedeker & Davis approximation) | 0.393 | ||||
| Statistics related to Sortino ratio | |||||
| Sortino ratio | -2.032 | ||||
| Upside Potential Ratio | 1.380 | ||||
| Upside part of mean | 0.017 | ||||
| Downside part of mean | -0.043 | ||||
| Upside SD | 0.029 | ||||
| Downside SD | 0.013 | ||||
| N nonnegative terms | 1.000 | ||||
| N negative terms | 32.000 | ||||
| Statistics related to linear regression on benchmark | |||||
| N of observations | 33.000 | ||||
| Mean of predictor | 0.556 | ||||
| Mean of criterion | -0.025 | ||||
| SD of predictor | 0.284 | ||||
| SD of criterion | 0.031 | ||||
| Covariance | -0.000 | ||||
| r | -0.050 | ||||
| b (slope, estimate of beta) | -0.005 | ||||
| a (intercept, estimate of alpha) | -0.022 | ||||
| Mean Square Error | 0.001 | ||||
| DF error | 31.000 | ||||
| t(b) | -0.277 | ||||
| p(b) | 0.608 | ||||
| t(a) | -1.031 | ||||
| p(a) | 0.845 | ||||
| Lowerbound of 95% confidence interval for beta | -0.045 | ||||
| Upperbound of 95% confidence interval for beta | 0.034 | ||||
| Lowerbound of 95% confidence interval for alpha | -0.067 | ||||
| Upperbound of 95% confidence interval for alpha | 0.022 | ||||
| Treynor index (mean / b) | 4.716 | ||||
| Jensen alpha (a) | -0.022 | ||||
| Ratio statistics of excess log return rates | |||||
| Statistics related to Sharpe ratio | |||||
| Mean | -0.026 | ||||
| SD | 0.030 | ||||
| Sharpe ratio (Glass type estimate) | -0.858 | ||||
| Sharpe ratio (Hedges UMVUE) | -0.838 | ||||
| df | 32.000 | ||||
| t | -1.423 | ||||
| p | 0.918 | ||||
| Lowerbound of 95% confidence interval for Sharpe Ratio | -2.052 | ||||
| Upperbound of 95% confidence interval for Sharpe Ratio | 0.349 | ||||
| Lowerbound of 95% CI (Gibbons, Hedeker & Davis approximation) | -2.037 | ||||
| Upperbound of 95% CI (Gibbons, Hedeker & Davis approximation) | 0.362 | ||||
| Statistics related to Sortino ratio | |||||
| Sortino ratio | -2.066 | ||||
| Upside Potential Ratio | 1.345 | ||||
| Upside part of mean | 0.017 | ||||
| Downside part of mean | -0.043 | ||||
| Upside SD | 0.028 | ||||
| Downside SD | 0.013 | ||||
| N nonnegative terms | 1.000 | ||||
| N negative terms | 32.000 | ||||
| Statistics related to linear regression on benchmark | |||||
| N of observations | 33.000 | ||||
| Mean of predictor | 0.506 | ||||
| Mean of criterion | -0.026 | ||||
| SD of predictor | 0.268 | ||||
| SD of criterion | 0.030 | ||||
| Covariance | -0.000 | ||||
| r | -0.044 | ||||
| b (slope, estimate of beta) | -0.005 | ||||
| a (intercept, estimate of alpha) | -0.023 | ||||
| Mean Square Error | 0.001 | ||||
| DF error | 31.000 | ||||
| t(b) | -0.244 | ||||
| p(b) | 0.596 | ||||
| t(a) | -1.109 | ||||
| p(a) | 0.862 | ||||
| Lowerbound of 95% confidence interval for beta | -0.046 | ||||
| Upperbound of 95% confidence interval for beta | 0.036 | ||||
| Lowerbound of 95% confidence interval for alpha | -0.066 | ||||
| Upperbound of 95% confidence interval for alpha | 0.020 | ||||
| Treynor index (mean / b) | 5.257 | ||||
| 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%) | 0.016 | ||||
| Expected Shortfall on VaR | 0.020 | ||||
| assuming Pareto losses only (using partial moments from Sortino statistics) | |||||
| VaR(95%) | 0.004 | ||||
| Expected Shortfall on VaR | 0.004 | ||||
| ORDER STATISTICS | |||||
| Quartiles of return rates | |||||
| Number of observations | 33.000 | ||||
| Minimum | 1.000 | ||||
| Quartile 1 | 1.000 | ||||
| Median | 1.000 | ||||
| Quartile 3 | 1.000 | ||||
| Maximum | 1.051 | ||||
| Mean of quarter 1 | 1.000 | ||||
| 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 | 0.000 | ||||
| Percentage of outliers low | 0.000 | ||||
| Mean of outliers low | NA | ||||
| Number of outliers high | 1.000 | ||||
| Percentage of outliers high | 0.030 | ||||
| Mean of outliers high | 1.051 | ||||
| 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) | 0.019 | ||||
| Compounded annual return (geometric extrapolation) | 0.018 | ||||
| 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 | 0.922 | ||||
| ANALYSIS BASED ON DAILY VALUES, FULL HISTORY (Back) | |||||
| RATIO STATISTICS | |||||
| Ratio statistics of excess return rates | |||||
| Statistics related to Sharpe ratio | |||||
| Mean | -0.026 | ||||
| SD | 0.027 | ||||
| Sharpe ratio (Glass type estimate) | -0.972 | ||||
| Sharpe ratio (Hedges UMVUE) | -0.971 | ||||
| df | 738.000 | ||||
| t | -1.632 | ||||
| p | 0.948 | ||||
| Lowerbound of 95% confidence interval for Sharpe Ratio | -2.139 | ||||
| Upperbound of 95% confidence interval for Sharpe Ratio | 0.197 | ||||
| Lowerbound of 95% CI (Gibbons, Hedeker & Davis approximation) | -2.139 | ||||
| Upperbound of 95% CI (Gibbons, Hedeker & Davis approximation) | 0.198 | ||||
| Statistics related to Sortino ratio | |||||
| Sortino ratio | -3.000 | ||||
| Upside Potential Ratio | 2.996 | ||||
| Upside part of mean | 0.026 | ||||
| Downside part of mean | -0.052 | ||||
| Upside SD | 0.025 | ||||
| Downside SD | 0.009 | ||||
| N nonnegative terms | 5.000 | ||||
| N negative terms | 734.000 | ||||
| Statistics related to linear regression on benchmark | |||||
| N of observations | 739.000 | ||||
| Mean of predictor | 0.620 | ||||
| Mean of criterion | -0.026 | ||||
| SD of predictor | 0.332 | ||||
| SD of criterion | 0.027 | ||||
| Covariance | 0.000 | ||||
| r | 0.029 | ||||
| b (slope, estimate of beta) | 0.002 | ||||
| a (intercept, estimate of alpha) | -0.027 | ||||
| Mean Square Error | 0.001 | ||||
| DF error | 737.000 | ||||
| t(b) | 0.788 | ||||
| p(b) | 0.216 | ||||
| t(a) | -1.711 | ||||
| p(a) | 0.956 | ||||
| Lowerbound of 95% confidence interval for beta | -0.003 | ||||
| Upperbound of 95% confidence interval for beta | 0.008 | ||||
| Lowerbound of 95% confidence interval for alpha | -0.059 | ||||
| Upperbound of 95% confidence interval for alpha | 0.004 | ||||
| Treynor index (mean / b) | -11.134 | ||||
| Jensen alpha (a) | -0.027 | ||||
| Ratio statistics of excess log return rates | |||||
| Statistics related to Sharpe ratio | |||||
| Mean | -0.026 | ||||
| SD | 0.026 | ||||
| Sharpe ratio (Glass type estimate) | -0.997 | ||||
| Sharpe ratio (Hedges UMVUE) | -0.996 | ||||
| df | 738.000 | ||||
| t | -1.674 | ||||
| p | 0.953 | ||||
| Lowerbound of 95% confidence interval for Sharpe Ratio | -2.164 | ||||
| Upperbound of 95% confidence interval for Sharpe Ratio | 0.172 | ||||
| Lowerbound of 95% CI (Gibbons, Hedeker & Davis approximation) | -2.164 | ||||
| Upperbound of 95% CI (Gibbons, Hedeker & Davis approximation) | 0.173 | ||||
| Statistics related to Sortino ratio | |||||
| Sortino ratio | -3.029 | ||||
| Upside Potential Ratio | 2.947 | ||||
| Upside part of mean | 0.026 | ||||
| Downside part of mean | -0.052 | ||||
| Upside SD | 0.025 | ||||
| Downside SD | 0.009 | ||||
| N nonnegative terms | 5.000 | ||||
| N negative terms | 734.000 | ||||
| Statistics related to linear regression on benchmark | |||||
| N of observations | 739.000 | ||||
| Mean of predictor | 0.564 | ||||
| Mean of criterion | -0.026 | ||||
| SD of predictor | 0.335 | ||||
| SD of criterion | 0.026 | ||||
| Covariance | 0.000 | ||||
| r | 0.029 | ||||
| b (slope, estimate of beta) | 0.002 | ||||
| a (intercept, estimate of alpha) | -0.028 | ||||
| Mean Square Error | 0.001 | ||||
| DF error | 737.000 | ||||
| t(b) | 0.790 | ||||
| p(b) | 0.215 | ||||
| t(a) | -1.746 | ||||
| p(a) | 0.959 | ||||
| Lowerbound of 95% confidence interval for beta | -0.003 | ||||
| Upperbound of 95% confidence interval for beta | 0.008 | ||||
| Lowerbound of 95% confidence interval for alpha | -0.059 | ||||
| Upperbound of 95% confidence interval for alpha | 0.003 | ||||
| Treynor index (mean / b) | -11.465 | ||||
| Jensen alpha (a) | -0.028 | ||||
| Risk estimates for a one-period unit investment (parametric) | |||||
| assuming log normal returns and losses (using central moments from Sharpe statistics) | |||||
| VaR(95%) | 0.003 | ||||
| Expected Shortfall on VaR | 0.003 | ||||
| assuming Pareto losses only (using partial moments from Sortino statistics) | |||||
| VaR(95%) | 0.001 | ||||
| Expected Shortfall on VaR | 0.001 | ||||
| ORDER STATISTICS | |||||
| Quartiles of return rates | |||||
| Number of observations | 739.000 | ||||
| Minimum | 0.990 | ||||
| Quartile 1 | 1.000 | ||||
| Median | 1.000 | ||||
| Quartile 3 | 1.000 | ||||
| Maximum | 1.030 | ||||
| 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 | 4.000 | ||||
| Percentage of outliers low | 0.005 | ||||
| Mean of outliers low | 0.994 | ||||
| Number of outliers high | 5.000 | ||||
| Percentage of outliers high | 0.007 | ||||
| Mean of outliers high | 1.015 | ||||
| Risk estimates for a one-period unit investment (based on Extreme Value Theory) | |||||
| Extreme Value Index (moments method) | -15.088 | ||||
| VaR(95%) (moments method) | -51647253005012.695 | ||||
| Expected Shortfall (moments method) | NA | ||||
| Extreme Value Index (regression method) | -1.401 | ||||
| VaR(95%) (regression method) | -0.258 | ||||
| Expected Shortfall (regression method) | NA | ||||
| DRAW DOWN STATISTICS | |||||
| Quartiles of draw downs | |||||
| Number of observations | 1.000 | ||||
| Minimum | 0.023 | ||||
| Quartile 1 | 0.023 | ||||
| Median | 0.023 | ||||
| Quartile 3 | 0.023 | ||||
| Maximum | 0.023 | ||||
| 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) | 0.018 | ||||
| Compounded annual return (geometric extrapolation) | 0.018 | ||||
| Calmar ratio (compounded annual return / max draw down) | 0.784 | ||||
| Compounded annual return / average of 25% largest draw downs | NA | ||||
| Compounded annual return / Expected Shortfall lognormal | 5.169 | ||||
| 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 | 1.133 | ||||
| Mean of criterion | -0.044 | ||||
| SD of predictor | 0.511 | ||||
| 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 | 1.001 | ||||
| Mean of criterion | -0.044 | ||||
| SD of predictor | 0.513 | ||||
| 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) | -8736035520663620.000 | ||||
| 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) | -238439751156381954178969205997568.000 | ||||
| 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 | ||||