Advanced Statistics: Azymuth Capital Group
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 | -0.136 | ||||
| SD | 0.245 | ||||
| Sharpe ratio (Glass type estimate) | -0.554 | ||||
| Sharpe ratio (Hedges UMVUE) | -0.549 | ||||
| df | 79.000 | ||||
| t | -1.431 | ||||
| p | 0.922 | ||||
| Lowerbound of 95% confidence interval for Sharpe Ratio | -1.316 | ||||
| Upperbound of 95% confidence interval for Sharpe Ratio | 0.212 | ||||
| Lowerbound of 95% CI (Gibbons, Hedeker & Davis approximation) | -1.313 | ||||
| Upperbound of 95% CI (Gibbons, Hedeker & Davis approximation) | 0.215 | ||||
| Statistics related to Sortino ratio | |||||
| Sortino ratio | -0.634 | ||||
| Upside Potential Ratio | 0.662 | ||||
| Upside part of mean | 0.141 | ||||
| Downside part of mean | -0.277 | ||||
| Upside SD | 0.122 | ||||
| Downside SD | 0.214 | ||||
| N nonnegative terms | 21.000 | ||||
| N negative terms | 59.000 | ||||
| Statistics related to linear regression on benchmark | |||||
| N of observations | 80.000 | ||||
| Mean of predictor | 0.238 | ||||
| Mean of criterion | -0.136 | ||||
| SD of predictor | 0.224 | ||||
| SD of criterion | 0.245 | ||||
| Covariance | 0.014 | ||||
| r | 0.254 | ||||
| b (slope, estimate of beta) | 0.277 | ||||
| a (intercept, estimate of alpha) | -0.202 | ||||
| Mean Square Error | 0.057 | ||||
| DF error | 78.000 | ||||
| t(b) | 2.317 | ||||
| p(b) | 0.012 | ||||
| t(a) | -2.088 | ||||
| p(a) | 0.980 | ||||
| Lowerbound of 95% confidence interval for beta | 0.039 | ||||
| Upperbound of 95% confidence interval for beta | 0.516 | ||||
| Lowerbound of 95% confidence interval for alpha | -0.394 | ||||
| Upperbound of 95% confidence interval for alpha | -0.009 | ||||
| Treynor index (mean / b) | -0.489 | ||||
| Jensen alpha (a) | -0.202 | ||||
| Ratio statistics of excess log return rates | |||||
| Statistics related to Sharpe ratio | |||||
| Mean | -0.171 | ||||
| SD | 0.277 | ||||
| Sharpe ratio (Glass type estimate) | -0.616 | ||||
| Sharpe ratio (Hedges UMVUE) | -0.611 | ||||
| df | 79.000 | ||||
| t | -1.592 | ||||
| p | 0.942 | ||||
| Lowerbound of 95% confidence interval for Sharpe Ratio | -1.380 | ||||
| Upperbound of 95% confidence interval for Sharpe Ratio | 0.151 | ||||
| Lowerbound of 95% CI (Gibbons, Hedeker & Davis approximation) | -1.376 | ||||
| Upperbound of 95% CI (Gibbons, Hedeker & Davis approximation) | 0.154 | ||||
| Statistics related to Sortino ratio | |||||
| Sortino ratio | -0.670 | ||||
| Upside Potential Ratio | 0.526 | ||||
| Upside part of mean | 0.134 | ||||
| Downside part of mean | -0.305 | ||||
| Upside SD | 0.115 | ||||
| Downside SD | 0.255 | ||||
| N nonnegative terms | 21.000 | ||||
| N negative terms | 59.000 | ||||
| Statistics related to linear regression on benchmark | |||||
| N of observations | 80.000 | ||||
| Mean of predictor | 0.210 | ||||
| Mean of criterion | -0.171 | ||||
| SD of predictor | 0.230 | ||||
| SD of criterion | 0.277 | ||||
| Covariance | 0.015 | ||||
| r | 0.234 | ||||
| b (slope, estimate of beta) | 0.282 | ||||
| a (intercept, estimate of alpha) | -0.230 | ||||
| Mean Square Error | 0.073 | ||||
| DF error | 78.000 | ||||
| t(b) | 2.125 | ||||
| p(b) | 0.018 | ||||
| t(a) | -2.117 | ||||
| p(a) | 0.981 | ||||
| Lowerbound of 95% confidence interval for beta | 0.018 | ||||
| Upperbound of 95% confidence interval for beta | 0.546 | ||||
| Lowerbound of 95% confidence interval for alpha | -0.446 | ||||
| Upperbound of 95% confidence interval for alpha | -0.014 | ||||
| Treynor index (mean / b) | -0.605 | ||||
| Jensen alpha (a) | -0.230 | ||||
| Risk estimates for a one-period unit investment (parametric) | |||||
| assuming log normal returns and losses (using central moments from Sharpe statistics) | |||||
| VaR(95%) | 0.136 | ||||
| Expected Shortfall on VaR | 0.164 | ||||
| assuming Pareto losses only (using partial moments from Sortino statistics) | |||||
| VaR(95%) | 0.067 | ||||
| Expected Shortfall on VaR | 0.138 | ||||
| ORDER STATISTICS | |||||
| Quartiles of return rates | |||||
| Number of observations | 80.000 | ||||
| Minimum | 0.593 | ||||
| Quartile 1 | 0.994 | ||||
| Median | 1.000 | ||||
| Quartile 3 | 1.005 | ||||
| Maximum | 1.168 | ||||
| Mean of quarter 1 | 0.919 | ||||
| Mean of quarter 2 | 0.999 | ||||
| Mean of quarter 3 | 1.001 | ||||
| Mean of quarter 4 | 1.051 | ||||
| Inter Quartile Range | 0.010 | ||||
| Number outliers low | 16.000 | ||||
| Percentage of outliers low | 0.200 | ||||
| Mean of outliers low | 0.902 | ||||
| Number of outliers high | 10.000 | ||||
| Percentage of outliers high | 0.125 | ||||
| Mean of outliers high | 1.092 | ||||
| Risk estimates for a one-period unit investment (based on Extreme Value Theory) | |||||
| Extreme Value Index (moments method) | 0.298 | ||||
| VaR(95%) (moments method) | 0.039 | ||||
| Expected Shortfall (moments method) | 0.074 | ||||
| Extreme Value Index (regression method) | 0.209 | ||||
| VaR(95%) (regression method) | 0.099 | ||||
| Expected Shortfall (regression method) | 0.184 | ||||
| DRAW DOWN STATISTICS | |||||
| Quartiles of draw downs | |||||
| Number of observations | 1.000 | ||||
| Minimum | 0.588 | ||||
| Quartile 1 | 0.588 | ||||
| Median | 0.588 | ||||
| Quartile 3 | 0.588 | ||||
| Maximum | 0.588 | ||||
| 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) | -0.085 | ||||
| Compounded annual return (geometric extrapolation) | -0.119 | ||||
| Calmar ratio (compounded annual return / max draw down) | -0.202 | ||||
| Compounded annual return / average of 25% largest draw downs | NA | ||||
| Compounded annual return / Expected Shortfall lognormal | -0.727 | ||||
| ANALYSIS BASED ON DAILY VALUES, FULL HISTORY (Back) | |||||
| RATIO STATISTICS | |||||
| Ratio statistics of excess return rates | |||||
| Statistics related to Sharpe ratio | |||||
| Mean | -0.132 | ||||
| SD | 0.270 | ||||
| Sharpe ratio (Glass type estimate) | -0.489 | ||||
| Sharpe ratio (Hedges UMVUE) | -0.489 | ||||
| df | 1747.000 | ||||
| t | -1.263 | ||||
| p | 0.519 | ||||
| Lowerbound of 95% confidence interval for Sharpe Ratio | -1.248 | ||||
| Upperbound of 95% confidence interval for Sharpe Ratio | 0.270 | ||||
| Lowerbound of 95% CI (Gibbons, Hedeker & Davis approximation) | -1.248 | ||||
| Upperbound of 95% CI (Gibbons, Hedeker & Davis approximation) | 0.270 | ||||
| Statistics related to Sortino ratio | |||||
| Sortino ratio | -0.635 | ||||
| Upside Potential Ratio | 2.923 | ||||
| Upside part of mean | 0.608 | ||||
| Downside part of mean | -0.740 | ||||
| Upside SD | 0.172 | ||||
| Downside SD | 0.208 | ||||
| N nonnegative terms | 488.000 | ||||
| N negative terms | 1260.000 | ||||
| Statistics related to linear regression on benchmark | |||||
| N of observations | 1748.000 | ||||
| Mean of predictor | 0.241 | ||||
| Mean of criterion | -0.132 | ||||
| SD of predictor | 0.237 | ||||
| SD of criterion | 0.270 | ||||
| Covariance | 0.008 | ||||
| r | 0.130 | ||||
| b (slope, estimate of beta) | 0.148 | ||||
| a (intercept, estimate of alpha) | -0.168 | ||||
| Mean Square Error | 0.072 | ||||
| DF error | 1746.000 | ||||
| t(b) | 5.471 | ||||
| p(b) | 0.435 | ||||
| t(a) | -1.614 | ||||
| p(a) | 0.519 | ||||
| Lowerbound of 95% confidence interval for beta | 0.095 | ||||
| Upperbound of 95% confidence interval for beta | 0.201 | ||||
| Lowerbound of 95% confidence interval for alpha | -0.371 | ||||
| Upperbound of 95% confidence interval for alpha | 0.036 | ||||
| Treynor index (mean / b) | -0.893 | ||||
| Jensen alpha (a) | -0.168 | ||||
| Ratio statistics of excess log return rates | |||||
| Statistics related to Sharpe ratio | |||||
| Mean | -0.171 | ||||
| SD | 0.283 | ||||
| Sharpe ratio (Glass type estimate) | -0.602 | ||||
| Sharpe ratio (Hedges UMVUE) | -0.602 | ||||
| df | 1747.000 | ||||
| t | -1.555 | ||||
| p | 0.524 | ||||
| Lowerbound of 95% confidence interval for Sharpe Ratio | -1.361 | ||||
| Upperbound of 95% confidence interval for Sharpe Ratio | 0.157 | ||||
| Lowerbound of 95% CI (Gibbons, Hedeker & Davis approximation) | -1.361 | ||||
| Upperbound of 95% CI (Gibbons, Hedeker & Davis approximation) | 0.157 | ||||
| Statistics related to Sortino ratio | |||||
| Sortino ratio | -0.730 | ||||
| Upside Potential Ratio | 2.544 | ||||
| Upside part of mean | 0.594 | ||||
| Downside part of mean | -0.765 | ||||
| Upside SD | 0.160 | ||||
| Downside SD | 0.234 | ||||
| N nonnegative terms | 488.000 | ||||
| N negative terms | 1260.000 | ||||
| Statistics related to linear regression on benchmark | |||||
| N of observations | 1748.000 | ||||
| Mean of predictor | 0.213 | ||||
| Mean of criterion | -0.171 | ||||
| SD of predictor | 0.238 | ||||
| SD of criterion | 0.283 | ||||
| Covariance | 0.008 | ||||
| r | 0.126 | ||||
| b (slope, estimate of beta) | 0.149 | ||||
| a (intercept, estimate of alpha) | -0.202 | ||||
| Mean Square Error | 0.079 | ||||
| DF error | 1746.000 | ||||
| t(b) | 5.289 | ||||
| p(b) | 0.437 | ||||
| t(a) | -1.856 | ||||
| p(a) | 0.522 | ||||
| Lowerbound of 95% confidence interval for beta | 0.094 | ||||
| Upperbound of 95% confidence interval for beta | 0.205 | ||||
| Lowerbound of 95% confidence interval for alpha | -0.416 | ||||
| Upperbound of 95% confidence interval for alpha | 0.012 | ||||
| Treynor index (mean / b) | -1.142 | ||||
| Jensen alpha (a) | -0.202 | ||||
| Risk estimates for a one-period unit investment (parametric) | |||||
| assuming log normal returns and losses (using central moments from Sharpe statistics) | |||||
| VaR(95%) | 0.029 | ||||
| Expected Shortfall on VaR | 0.036 | ||||
| assuming Pareto losses only (using partial moments from Sortino statistics) | |||||
| VaR(95%) | 0.008 | ||||
| Expected Shortfall on VaR | 0.018 | ||||
| ORDER STATISTICS | |||||
| Quartiles of return rates | |||||
| Number of observations | 1748.000 | ||||
| Minimum | 0.653 | ||||
| Quartile 1 | 0.999 | ||||
| Median | 1.000 | ||||
| Quartile 3 | 1.001 | ||||
| Maximum | 1.284 | ||||
| Mean of quarter 1 | 0.989 | ||||
| Mean of quarter 2 | 1.000 | ||||
| Mean of quarter 3 | 1.000 | ||||
| Mean of quarter 4 | 1.009 | ||||
| Inter Quartile Range | 0.002 | ||||
| Number outliers low | 260.000 | ||||
| Percentage of outliers low | 0.149 | ||||
| Mean of outliers low | 0.983 | ||||
| Number of outliers high | 261.000 | ||||
| Percentage of outliers high | 0.149 | ||||
| Mean of outliers high | 1.014 | ||||
| Risk estimates for a one-period unit investment (based on Extreme Value Theory) | |||||
| Extreme Value Index (moments method) | 0.937 | ||||
| VaR(95%) (moments method) | 0.007 | ||||
| Expected Shortfall (moments method) | 0.122 | ||||
| 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 | 3.000 | ||||
| Minimum | 0.000 | ||||
| Quartile 1 | 0.005 | ||||
| Median | 0.010 | ||||
| Quartile 3 | 0.307 | ||||
| Maximum | 0.603 | ||||
| Mean of quarter 1 | 0.000 | ||||
| Mean of quarter 2 | 0.010 | ||||
| Mean of quarter 3 | NA | ||||
| Mean of quarter 4 | 0.603 | ||||
| Inter Quartile Range | 0.301 | ||||
| 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) | -0.085 | ||||
| Compounded annual return (geometric extrapolation) | -0.119 | ||||
| Calmar ratio (compounded annual return / max draw down) | -0.197 | ||||
| Compounded annual return / average of 25% largest draw downs | -0.197 | ||||
| Compounded annual return / Expected Shortfall lognormal | -3.296 | ||||
| ANALYSIS BASED ON DAILY VALUES, LAST 6 MONTHS (Back) | |||||
| RATIO STATISTICS | |||||
| Ratio statistics of excess return rates | |||||
| Statistics related to Sharpe ratio | |||||
| Mean | -0.049 | ||||
| SD | 0.131 | ||||
| Sharpe ratio (Glass type estimate) | -0.375 | ||||
| Sharpe ratio (Hedges UMVUE) | -0.373 | ||||
| df | 130.000 | ||||
| t | -0.265 | ||||
| p | 0.512 | ||||
| Lowerbound of 95% confidence interval for Sharpe Ratio | -3.147 | ||||
| Upperbound of 95% confidence interval for Sharpe Ratio | 2.398 | ||||
| Lowerbound of 95% CI (Gibbons, Hedeker & Davis approximation) | -3.145 | ||||
| Upperbound of 95% CI (Gibbons, Hedeker & Davis approximation) | 2.399 | ||||
| Statistics related to Sortino ratio | |||||
| Sortino ratio | -0.493 | ||||
| Upside Potential Ratio | 5.179 | ||||
| Upside part of mean | 0.518 | ||||
| Downside part of mean | -0.568 | ||||
| Upside SD | 0.084 | ||||
| Downside SD | 0.100 | ||||
| N nonnegative terms | 31.000 | ||||
| N negative terms | 100.000 | ||||
| Statistics related to linear regression on benchmark | |||||
| N of observations | 131.000 | ||||
| Mean of predictor | 1.422 | ||||
| Mean of criterion | -0.049 | ||||
| SD of predictor | 0.442 | ||||
| SD of criterion | 0.131 | ||||
| Covariance | 0.005 | ||||
| r | 0.087 | ||||
| b (slope, estimate of beta) | 0.026 | ||||
| a (intercept, estimate of alpha) | -0.086 | ||||
| Mean Square Error | 0.017 | ||||
| DF error | 129.000 | ||||
| t(b) | 0.989 | ||||
| p(b) | 0.445 | ||||
| t(a) | -0.454 | ||||
| p(a) | 0.525 | ||||
| Lowerbound of 95% confidence interval for beta | -0.026 | ||||
| Upperbound of 95% confidence interval for beta | 0.077 | ||||
| Lowerbound of 95% confidence interval for alpha | -0.461 | ||||
| Upperbound of 95% confidence interval for alpha | 0.289 | ||||
| Treynor index (mean / b) | -1.912 | ||||
| Jensen alpha (a) | -0.086 | ||||
| Ratio statistics of excess log return rates | |||||
| Statistics related to Sharpe ratio | |||||
| Mean | -0.058 | ||||
| SD | 0.132 | ||||
| Sharpe ratio (Glass type estimate) | -0.439 | ||||
| Sharpe ratio (Hedges UMVUE) | -0.436 | ||||
| df | 130.000 | ||||
| t | -0.310 | ||||
| p | 0.514 | ||||
| Lowerbound of 95% confidence interval for Sharpe Ratio | -3.211 | ||||
| Upperbound of 95% confidence interval for Sharpe Ratio | 2.334 | ||||
| Lowerbound of 95% CI (Gibbons, Hedeker & Davis approximation) | -3.209 | ||||
| Upperbound of 95% CI (Gibbons, Hedeker & Davis approximation) | 2.336 | ||||
| Statistics related to Sortino ratio | |||||
| Sortino ratio | -0.571 | ||||
| Upside Potential Ratio | 5.073 | ||||
| Upside part of mean | 0.515 | ||||
| Downside part of mean | -0.573 | ||||
| Upside SD | 0.084 | ||||
| Downside SD | 0.101 | ||||
| N nonnegative terms | 31.000 | ||||
| N negative terms | 100.000 | ||||
| Statistics related to linear regression on benchmark | |||||
| N of observations | 131.000 | ||||
| Mean of predictor | 1.322 | ||||
| Mean of criterion | -0.058 | ||||
| SD of predictor | 0.439 | ||||
| SD of criterion | 0.132 | ||||
| Covariance | 0.005 | ||||
| r | 0.092 | ||||
| b (slope, estimate of beta) | 0.028 | ||||
| a (intercept, estimate of alpha) | -0.094 | ||||
| Mean Square Error | 0.017 | ||||
| DF error | 129.000 | ||||
| t(b) | 1.046 | ||||
| p(b) | 0.442 | ||||
| t(a) | -0.497 | ||||
| p(a) | 0.528 | ||||
| Lowerbound of 95% confidence interval for beta | -0.025 | ||||
| Upperbound of 95% confidence interval for beta | 0.080 | ||||
| Lowerbound of 95% confidence interval for alpha | -0.470 | ||||
| Upperbound of 95% confidence interval for alpha | 0.281 | ||||
| Treynor index (mean / b) | -2.102 | ||||
| Jensen alpha (a) | -0.094 | ||||
| Risk estimates for a one-period unit investment (parametric) | |||||
| assuming log normal returns and losses (using central moments from Sharpe statistics) | |||||
| VaR(95%) | 0.014 | ||||
| Expected Shortfall on VaR | 0.017 | ||||
| assuming Pareto losses only (using partial moments from Sortino statistics) | |||||
| VaR(95%) | 0.006 | ||||
| Expected Shortfall on VaR | 0.013 | ||||
| ORDER STATISTICS | |||||
| Quartiles of return rates | |||||
| Number of observations | 131.000 | ||||
| Minimum | 0.959 | ||||
| Quartile 1 | 1.000 | ||||
| Median | 1.000 | ||||
| Quartile 3 | 1.000 | ||||
| Maximum | 1.033 | ||||
| Mean of quarter 1 | 0.992 | ||||
| Mean of quarter 2 | 1.000 | ||||
| Mean of quarter 3 | 1.000 | ||||
| Mean of quarter 4 | 1.008 | ||||
| Inter Quartile Range | 0.000 | ||||
| Number outliers low | 27.000 | ||||
| Percentage of outliers low | 0.206 | ||||
| Mean of outliers low | 0.990 | ||||
| Number of outliers high | 31.000 | ||||
| Percentage of outliers high | 0.237 | ||||
| Mean of outliers high | 1.009 | ||||
| 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 | 2.000 | ||||
| Minimum | 0.004 | ||||
| Quartile 1 | 0.022 | ||||
| Median | 0.040 | ||||
| Quartile 3 | 0.059 | ||||
| Maximum | 0.077 | ||||
| Mean of quarter 1 | 0.004 | ||||
| Mean of quarter 2 | NA | ||||
| Mean of quarter 3 | NA | ||||
| Mean of quarter 4 | 0.077 | ||||
| Inter Quartile Range | 0.037 | ||||
| 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) | -0.014 | ||||
| Compounded annual return (geometric extrapolation) | -0.014 | ||||
| Calmar ratio (compounded annual return / max draw down) | -0.180 | ||||
| Compounded annual return / average of 25% largest draw downs | -0.180 | ||||
| Compounded annual return / Expected Shortfall lognormal | -0.818 | ||||