Advanced Statistics: Risk Off
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 | -0.082 | ||||
| SD | 0.426 | ||||
| Sharpe ratio (Glass type estimate) | -0.193 | ||||
| Sharpe ratio (Hedges UMVUE) | -0.189 | ||||
| df | 37.000 | ||||
| t | -0.343 | ||||
| p | 0.633 | ||||
| Lowerbound of 95% confidence interval for Sharpe Ratio | -1.294 | ||||
| Upperbound of 95% confidence interval for Sharpe Ratio | 0.911 | ||||
| Lowerbound of 95% CI (Gibbons, Hedeker & Davis approximation) | -1.291 | ||||
| Upperbound of 95% CI (Gibbons, Hedeker & Davis approximation) | 0.913 | ||||
| Statistics related to Sortino ratio | |||||
| Sortino ratio | -0.263 | ||||
| Upside Potential Ratio | 1.491 | ||||
| Upside part of mean | 0.465 | ||||
| Downside part of mean | -0.547 | ||||
| Upside SD | 0.283 | ||||
| Downside SD | 0.312 | ||||
| N nonnegative terms | 20.000 | ||||
| N negative terms | 18.000 | ||||
| Statistics related to linear regression on benchmark | |||||
| N of observations | 38.000 | ||||
| Mean of predictor | 0.542 | ||||
| Mean of criterion | -0.082 | ||||
| SD of predictor | 0.275 | ||||
| SD of criterion | 0.426 | ||||
| Covariance | -0.046 | ||||
| r | -0.391 | ||||
| b (slope, estimate of beta) | -0.607 | ||||
| a (intercept, estimate of alpha) | 0.247 | ||||
| Mean Square Error | 0.158 | ||||
| DF error | 36.000 | ||||
| t(b) | -2.550 | ||||
| p(b) | 0.992 | ||||
| t(a) | 0.957 | ||||
| p(a) | 0.172 | ||||
| Lowerbound of 95% confidence interval for beta | -1.089 | ||||
| Upperbound of 95% confidence interval for beta | -0.124 | ||||
| Lowerbound of 95% confidence interval for alpha | -0.276 | ||||
| Upperbound of 95% confidence interval for alpha | 0.770 | ||||
| Treynor index (mean / b) | 0.135 | ||||
| Jensen alpha (a) | 0.247 | ||||
| Ratio statistics of excess log return rates | |||||
| Statistics related to Sharpe ratio | |||||
| Mean | -0.175 | ||||
| SD | 0.443 | ||||
| Sharpe ratio (Glass type estimate) | -0.394 | ||||
| Sharpe ratio (Hedges UMVUE) | -0.386 | ||||
| df | 37.000 | ||||
| t | -0.702 | ||||
| p | 0.756 | ||||
| Lowerbound of 95% confidence interval for Sharpe Ratio | -1.497 | ||||
| Upperbound of 95% confidence interval for Sharpe Ratio | 0.713 | ||||
| Lowerbound of 95% CI (Gibbons, Hedeker & Davis approximation) | -1.491 | ||||
| Upperbound of 95% CI (Gibbons, Hedeker & Davis approximation) | 0.719 | ||||
| Statistics related to Sortino ratio | |||||
| Sortino ratio | -0.483 | ||||
| Upside Potential Ratio | 1.186 | ||||
| Upside part of mean | 0.430 | ||||
| Downside part of mean | -0.604 | ||||
| Upside SD | 0.250 | ||||
| Downside SD | 0.362 | ||||
| N nonnegative terms | 20.000 | ||||
| N negative terms | 18.000 | ||||
| Statistics related to linear regression on benchmark | |||||
| N of observations | 38.000 | ||||
| Mean of predictor | 0.497 | ||||
| Mean of criterion | -0.175 | ||||
| SD of predictor | 0.253 | ||||
| SD of criterion | 0.443 | ||||
| Covariance | -0.043 | ||||
| r | -0.385 | ||||
| b (slope, estimate of beta) | -0.674 | ||||
| a (intercept, estimate of alpha) | 0.160 | ||||
| Mean Square Error | 0.172 | ||||
| DF error | 36.000 | ||||
| t(b) | -2.504 | ||||
| p(b) | 0.992 | ||||
| t(a) | 0.596 | ||||
| p(a) | 0.277 | ||||
| Lowerbound of 95% confidence interval for beta | -1.221 | ||||
| Upperbound of 95% confidence interval for beta | -0.128 | ||||
| Lowerbound of 95% confidence interval for alpha | -0.385 | ||||
| Upperbound of 95% confidence interval for alpha | 0.705 | ||||
| Treynor index (mean / b) | 0.259 | ||||
| Jensen alpha (a) | 0.160 | ||||
| Risk estimates for a one-period unit investment (parametric) | |||||
| assuming log normal returns and losses (using central moments from Sharpe statistics) | |||||
| VaR(95%) | 0.201 | ||||
| Expected Shortfall on VaR | 0.242 | ||||
| assuming Pareto losses only (using partial moments from Sortino statistics) | |||||
| VaR(95%) | 0.102 | ||||
| Expected Shortfall on VaR | 0.197 | ||||
| ORDER STATISTICS | |||||
| Quartiles of return rates | |||||
| Number of observations | 38.000 | ||||
| Minimum | 0.633 | ||||
| Quartile 1 | 0.946 | ||||
| Median | 1.008 | ||||
| Quartile 3 | 1.054 | ||||
| Maximum | 1.392 | ||||
| Mean of quarter 1 | 0.861 | ||||
| Mean of quarter 2 | 0.970 | ||||
| Mean of quarter 3 | 1.025 | ||||
| Mean of quarter 4 | 1.131 | ||||
| Inter Quartile Range | 0.108 | ||||
| Number outliers low | 2.000 | ||||
| Percentage of outliers low | 0.053 | ||||
| Mean of outliers low | 0.708 | ||||
| Number of outliers high | 1.000 | ||||
| Percentage of outliers high | 0.026 | ||||
| Mean of outliers high | 1.392 | ||||
| Risk estimates for a one-period unit investment (based on Extreme Value Theory) | |||||
| Extreme Value Index (moments method) | 0.460 | ||||
| VaR(95%) (moments method) | 0.156 | ||||
| Expected Shortfall (moments method) | 0.322 | ||||
| Extreme Value Index (regression method) | 0.886 | ||||
| VaR(95%) (regression method) | 0.149 | ||||
| Expected Shortfall (regression method) | 1.104 | ||||
| DRAW DOWN STATISTICS | |||||
| Quartiles of draw downs | |||||
| Number of observations | 1.000 | ||||
| Minimum | 0.489 | ||||
| Quartile 1 | 0.489 | ||||
| Median | 0.489 | ||||
| Quartile 3 | 0.489 | ||||
| Maximum | 0.489 | ||||
| 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) | -0.107 | ||||
| Compounded annual return (geometric extrapolation) | -0.123 | ||||
| Calmar ratio (compounded annual return / max draw down) | -0.251 | ||||
| Compounded annual return / average of 25% largest draw downs | NA | ||||
| Compounded annual return / Expected Shortfall lognormal | -0.506 | ||||
| ANALYSIS BASED ON DAILY VALUES, FULL HISTORY (Back) | |||||
| RATIO STATISTICS | |||||
| Ratio statistics of excess return rates | |||||
| Statistics related to Sharpe ratio | |||||
| Mean | 0.025 | ||||
| SD | 0.672 | ||||
| Sharpe ratio (Glass type estimate) | 0.038 | ||||
| Sharpe ratio (Hedges UMVUE) | 0.038 | ||||
| df | 849.000 | ||||
| t | 0.068 | ||||
| p | 0.473 | ||||
| Lowerbound of 95% confidence interval for Sharpe Ratio | -1.051 | ||||
| Upperbound of 95% confidence interval for Sharpe Ratio | 1.126 | ||||
| Lowerbound of 95% CI (Gibbons, Hedeker & Davis approximation) | -1.051 | ||||
| Upperbound of 95% CI (Gibbons, Hedeker & Davis approximation) | 1.126 | ||||
| Statistics related to Sortino ratio | |||||
| Sortino ratio | 0.056 | ||||
| Upside Potential Ratio | 5.933 | ||||
| Upside part of mean | 2.668 | ||||
| Downside part of mean | -2.643 | ||||
| Upside SD | 0.499 | ||||
| Downside SD | 0.450 | ||||
| N nonnegative terms | 422.000 | ||||
| N negative terms | 428.000 | ||||
| Statistics related to linear regression on benchmark | |||||
| N of observations | 850.000 | ||||
| Mean of predictor | 0.585 | ||||
| Mean of criterion | 0.025 | ||||
| SD of predictor | 0.346 | ||||
| SD of criterion | 0.672 | ||||
| Covariance | -0.039 | ||||
| r | -0.169 | ||||
| b (slope, estimate of beta) | -0.327 | ||||
| a (intercept, estimate of alpha) | 0.217 | ||||
| Mean Square Error | 0.439 | ||||
| DF error | 848.000 | ||||
| t(b) | -4.980 | ||||
| p(b) | 1.000 | ||||
| t(a) | 0.586 | ||||
| p(a) | 0.279 | ||||
| Lowerbound of 95% confidence interval for beta | -0.456 | ||||
| Upperbound of 95% confidence interval for beta | -0.198 | ||||
| Lowerbound of 95% confidence interval for alpha | -0.509 | ||||
| Upperbound of 95% confidence interval for alpha | 0.943 | ||||
| Treynor index (mean / b) | -0.077 | ||||
| Jensen alpha (a) | 0.217 | ||||
| Ratio statistics of excess log return rates | |||||
| Statistics related to Sharpe ratio | |||||
| Mean | -0.197 | ||||
| SD | 0.667 | ||||
| Sharpe ratio (Glass type estimate) | -0.295 | ||||
| Sharpe ratio (Hedges UMVUE) | -0.295 | ||||
| df | 849.000 | ||||
| t | -0.532 | ||||
| p | 0.702 | ||||
| Lowerbound of 95% confidence interval for Sharpe Ratio | -1.383 | ||||
| Upperbound of 95% confidence interval for Sharpe Ratio | 0.793 | ||||
| Lowerbound of 95% CI (Gibbons, Hedeker & Davis approximation) | -1.383 | ||||
| Upperbound of 95% CI (Gibbons, Hedeker & Davis approximation) | 0.793 | ||||
| Statistics related to Sortino ratio | |||||
| Sortino ratio | -0.402 | ||||
| Upside Potential Ratio | 5.223 | ||||
| Upside part of mean | 2.559 | ||||
| Downside part of mean | -2.755 | ||||
| Upside SD | 0.452 | ||||
| Downside SD | 0.490 | ||||
| N nonnegative terms | 422.000 | ||||
| N negative terms | 428.000 | ||||
| Statistics related to linear regression on benchmark | |||||
| N of observations | 850.000 | ||||
| Mean of predictor | 0.526 | ||||
| Mean of criterion | -0.197 | ||||
| SD of predictor | 0.343 | ||||
| SD of criterion | 0.667 | ||||
| Covariance | -0.040 | ||||
| r | -0.173 | ||||
| b (slope, estimate of beta) | -0.335 | ||||
| a (intercept, estimate of alpha) | -0.021 | ||||
| Mean Square Error | 0.432 | ||||
| DF error | 848.000 | ||||
| t(b) | -5.105 | ||||
| p(b) | 1.000 | ||||
| t(a) | -0.056 | ||||
| p(a) | 0.522 | ||||
| Lowerbound of 95% confidence interval for beta | -0.464 | ||||
| Upperbound of 95% confidence interval for beta | -0.206 | ||||
| Lowerbound of 95% confidence interval for alpha | -0.740 | ||||
| Upperbound of 95% confidence interval for alpha | 0.699 | ||||
| Treynor index (mean / b) | 0.587 | ||||
| Jensen alpha (a) | -0.021 | ||||
| Risk estimates for a one-period unit investment (parametric) | |||||
| assuming log normal returns and losses (using central moments from Sharpe statistics) | |||||
| VaR(95%) | 0.066 | ||||
| Expected Shortfall on VaR | 0.082 | ||||
| assuming Pareto losses only (using partial moments from Sortino statistics) | |||||
| VaR(95%) | 0.023 | ||||
| Expected Shortfall on VaR | 0.050 | ||||
| ORDER STATISTICS | |||||
| Quartiles of return rates | |||||
| Number of observations | 850.000 | ||||
| Minimum | 0.738 | ||||
| Quartile 1 | 0.990 | ||||
| Median | 1.000 | ||||
| Quartile 3 | 1.010 | ||||
| Maximum | 1.428 | ||||
| Mean of quarter 1 | 0.964 | ||||
| Mean of quarter 2 | 0.996 | ||||
| Mean of quarter 3 | 1.004 | ||||
| Mean of quarter 4 | 1.037 | ||||
| Inter Quartile Range | 0.019 | ||||
| Number outliers low | 47.000 | ||||
| Percentage of outliers low | 0.055 | ||||
| Mean of outliers low | 0.906 | ||||
| Number of outliers high | 54.000 | ||||
| Percentage of outliers high | 0.064 | ||||
| Mean of outliers high | 1.089 | ||||
| Risk estimates for a one-period unit investment (based on Extreme Value Theory) | |||||
| Extreme Value Index (moments method) | 0.601 | ||||
| VaR(95%) (moments method) | 0.035 | ||||
| Expected Shortfall (moments method) | 0.098 | ||||
| Extreme Value Index (regression method) | 0.293 | ||||
| VaR(95%) (regression method) | 0.031 | ||||
| Expected Shortfall (regression method) | 0.054 | ||||
| DRAW DOWN STATISTICS | |||||
| Quartiles of draw downs | |||||
| Number of observations | 3.000 | ||||
| Minimum | 0.000 | ||||
| Quartile 1 | 0.001 | ||||
| Median | 0.003 | ||||
| Quartile 3 | 0.272 | ||||
| Maximum | 0.541 | ||||
| Mean of quarter 1 | 0.000 | ||||
| Mean of quarter 2 | 0.003 | ||||
| Mean of quarter 3 | NA | ||||
| Mean of quarter 4 | 0.541 | ||||
| Inter Quartile Range | 0.270 | ||||
| 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) | -0.120 | ||||
| Compounded annual return (geometric extrapolation) | -0.142 | ||||
| Calmar ratio (compounded annual return / max draw down) | -0.262 | ||||
| Compounded annual return / average of 25% largest draw downs | -0.262 | ||||
| Compounded annual return / Expected Shortfall lognormal | -1.726 | ||||
| ANALYSIS BASED ON DAILY VALUES, LAST 6 MONTHS (Back) | |||||
| RATIO STATISTICS | |||||
| Ratio statistics of excess return rates | |||||
| Statistics related to Sharpe ratio | |||||
| Mean | 0.169 | ||||
| SD | 0.802 | ||||
| Sharpe ratio (Glass type estimate) | 0.210 | ||||
| Sharpe ratio (Hedges UMVUE) | 0.209 | ||||
| df | 130.000 | ||||
| t | 0.149 | ||||
| p | 0.493 | ||||
| Lowerbound of 95% confidence interval for Sharpe Ratio | -2.562 | ||||
| Upperbound of 95% confidence interval for Sharpe Ratio | 2.982 | ||||
| Lowerbound of 95% CI (Gibbons, Hedeker & Davis approximation) | -2.563 | ||||
| Upperbound of 95% CI (Gibbons, Hedeker & Davis approximation) | 2.981 | ||||
| Statistics related to Sortino ratio | |||||
| Sortino ratio | 0.302 | ||||
| Upside Potential Ratio | 8.775 | ||||
| Upside part of mean | 4.896 | ||||
| Downside part of mean | -4.727 | ||||
| Upside SD | 0.572 | ||||
| Downside SD | 0.558 | ||||
| N nonnegative terms | 68.000 | ||||
| N negative terms | 63.000 | ||||
| Statistics related to linear regression on benchmark | |||||
| N of observations | 131.000 | ||||
| Mean of predictor | 1.059 | ||||
| Mean of criterion | 0.169 | ||||
| SD of predictor | 0.455 | ||||
| SD of criterion | 0.802 | ||||
| Covariance | -0.156 | ||||
| r | -0.428 | ||||
| b (slope, estimate of beta) | -0.754 | ||||
| a (intercept, estimate of alpha) | 0.968 | ||||
| Mean Square Error | 0.529 | ||||
| DF error | 129.000 | ||||
| t(b) | -5.377 | ||||
| p(b) | 0.764 | ||||
| t(a) | 0.931 | ||||
| p(a) | 0.448 | ||||
| Lowerbound of 95% confidence interval for beta | -1.032 | ||||
| Upperbound of 95% confidence interval for beta | -0.477 | ||||
| Lowerbound of 95% confidence interval for alpha | -1.089 | ||||
| Upperbound of 95% confidence interval for alpha | 3.024 | ||||
| Treynor index (mean / b) | -0.224 | ||||
| Jensen alpha (a) | 0.968 | ||||
| Ratio statistics of excess log return rates | |||||
| Statistics related to Sharpe ratio | |||||
| Mean | -0.150 | ||||
| SD | 0.802 | ||||
| Sharpe ratio (Glass type estimate) | -0.187 | ||||
| Sharpe ratio (Hedges UMVUE) | -0.186 | ||||
| df | 130.000 | ||||
| t | -0.132 | ||||
| p | 0.506 | ||||
| Lowerbound of 95% confidence interval for Sharpe Ratio | -2.959 | ||||
| Upperbound of 95% confidence interval for Sharpe Ratio | 2.585 | ||||
| Lowerbound of 95% CI (Gibbons, Hedeker & Davis approximation) | -2.958 | ||||
| Upperbound of 95% CI (Gibbons, Hedeker & Davis approximation) | 2.586 | ||||
| Statistics related to Sortino ratio | |||||
| Sortino ratio | -0.258 | ||||
| Upside Potential Ratio | 8.140 | ||||
| Upside part of mean | 4.741 | ||||
| Downside part of mean | -4.891 | ||||
| Upside SD | 0.547 | ||||
| Downside SD | 0.582 | ||||
| N nonnegative terms | 68.000 | ||||
| N negative terms | 63.000 | ||||
| Statistics related to linear regression on benchmark | |||||
| N of observations | 131.000 | ||||
| Mean of predictor | 0.954 | ||||
| Mean of criterion | -0.150 | ||||
| SD of predictor | 0.457 | ||||
| SD of criterion | 0.802 | ||||
| Covariance | -0.157 | ||||
| r | -0.427 | ||||
| b (slope, estimate of beta) | -0.748 | ||||
| a (intercept, estimate of alpha) | 0.564 | ||||
| Mean Square Error | 0.530 | ||||
| DF error | 129.000 | ||||
| t(b) | -5.362 | ||||
| p(b) | 0.763 | ||||
| t(a) | 0.543 | ||||
| p(a) | 0.470 | ||||
| Lowerbound of 95% confidence interval for beta | -1.025 | ||||
| Upperbound of 95% confidence interval for beta | -0.472 | ||||
| Lowerbound of 95% confidence interval for alpha | -1.490 | ||||
| Upperbound of 95% confidence interval for alpha | 2.618 | ||||
| Treynor index (mean / b) | 0.201 | ||||
| Jensen alpha (a) | 0.564 | ||||
| Risk estimates for a one-period unit investment (parametric) | |||||
| assuming log normal returns and losses (using central moments from Sharpe statistics) | |||||
| VaR(95%) | 0.079 | ||||
| Expected Shortfall on VaR | 0.097 | ||||
| assuming Pareto losses only (using partial moments from Sortino statistics) | |||||
| VaR(95%) | 0.041 | ||||
| Expected Shortfall on VaR | 0.077 | ||||
| ORDER STATISTICS | |||||
| Quartiles of return rates | |||||
| Number of observations | 131.000 | ||||
| Minimum | 0.877 | ||||
| Quartile 1 | 0.972 | ||||
| Median | 1.002 | ||||
| Quartile 3 | 1.029 | ||||
| Maximum | 1.168 | ||||
| Mean of quarter 1 | 0.938 | ||||
| Mean of quarter 2 | 0.990 | ||||
| Mean of quarter 3 | 1.014 | ||||
| Mean of quarter 4 | 1.061 | ||||
| Inter Quartile Range | 0.057 | ||||
| Number outliers low | 3.000 | ||||
| Percentage of outliers low | 0.023 | ||||
| Mean of outliers low | 0.882 | ||||
| Number of outliers high | 2.000 | ||||
| Percentage of outliers high | 0.015 | ||||
| Mean of outliers high | 1.154 | ||||
| Risk estimates for a one-period unit investment (based on Extreme Value Theory) | |||||
| Extreme Value Index (moments method) | -0.150 | ||||
| VaR(95%) (moments method) | 0.061 | ||||
| Expected Shortfall (moments method) | 0.077 | ||||
| Extreme Value Index (regression method) | -0.578 | ||||
| VaR(95%) (regression method) | 0.061 | ||||
| Expected Shortfall (regression method) | 0.069 | ||||
| DRAW DOWN STATISTICS | |||||
| Quartiles of draw downs | |||||
| Number of observations | 5.000 | ||||
| Minimum | 0.004 | ||||
| Quartile 1 | 0.008 | ||||
| Median | 0.020 | ||||
| Quartile 3 | 0.053 | ||||
| Maximum | 0.403 | ||||
| Mean of quarter 1 | 0.006 | ||||
| Mean of quarter 2 | 0.020 | ||||
| Mean of quarter 3 | 0.053 | ||||
| Mean of quarter 4 | 0.403 | ||||
| Inter Quartile Range | 0.045 | ||||
| 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 | 0.200 | ||||
| Mean of outliers high | 0.403 | ||||
| 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) | -0.103 | ||||
| Compounded annual return (geometric extrapolation) | -0.101 | ||||
| Calmar ratio (compounded annual return / max draw down) | -0.250 | ||||
| Compounded annual return / average of 25% largest draw downs | -0.250 | ||||
| Compounded annual return / Expected Shortfall lognormal | -1.032 | ||||