Advanced Statistics: JV Long/Short Equity
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 | 0.381 | ||||
| SD | 0.368 | ||||
| Sharpe ratio (Glass type estimate) | 1.036 | ||||
| Sharpe ratio (Hedges UMVUE) | 1.026 | ||||
| df | 75.000 | ||||
| t | 2.608 | ||||
| p | 0.005 | ||||
| Lowerbound of 95% confidence interval for Sharpe Ratio | 0.237 | ||||
| Upperbound of 95% confidence interval for Sharpe Ratio | 1.829 | ||||
| Lowerbound of 95% CI (Gibbons, Hedeker & Davis approximation) | 0.230 | ||||
| Upperbound of 95% CI (Gibbons, Hedeker & Davis approximation) | 1.822 | ||||
| Statistics related to Sortino ratio | |||||
| Sortino ratio | 2.800 | ||||
| Upside Potential Ratio | 4.431 | ||||
| Upside part of mean | 0.603 | ||||
| Downside part of mean | -0.222 | ||||
| Upside SD | 0.356 | ||||
| Downside SD | 0.136 | ||||
| N nonnegative terms | 47.000 | ||||
| N negative terms | 29.000 | ||||
| Statistics related to linear regression on benchmark | |||||
| N of observations | 76.000 | ||||
| Mean of predictor | 0.267 | ||||
| Mean of criterion | 0.381 | ||||
| SD of predictor | 0.233 | ||||
| SD of criterion | 0.368 | ||||
| Covariance | 0.023 | ||||
| r | 0.267 | ||||
| b (slope, estimate of beta) | 0.421 | ||||
| a (intercept, estimate of alpha) | 0.268 | ||||
| Mean Square Error | 0.127 | ||||
| DF error | 74.000 | ||||
| t(b) | 2.388 | ||||
| p(b) | 0.010 | ||||
| t(a) | 1.798 | ||||
| p(a) | 0.038 | ||||
| Lowerbound of 95% confidence interval for beta | 0.070 | ||||
| Upperbound of 95% confidence interval for beta | 0.773 | ||||
| Lowerbound of 95% confidence interval for alpha | -0.029 | ||||
| Upperbound of 95% confidence interval for alpha | 0.566 | ||||
| Treynor index (mean / b) | 0.905 | ||||
| Jensen alpha (a) | 0.268 | ||||
| Ratio statistics of excess log return rates | |||||
| Statistics related to Sharpe ratio | |||||
| Mean | 0.317 | ||||
| SD | 0.333 | ||||
| Sharpe ratio (Glass type estimate) | 0.953 | ||||
| Sharpe ratio (Hedges UMVUE) | 0.943 | ||||
| df | 75.000 | ||||
| t | 2.398 | ||||
| p | 0.009 | ||||
| Lowerbound of 95% confidence interval for Sharpe Ratio | 0.156 | ||||
| Upperbound of 95% confidence interval for Sharpe Ratio | 1.743 | ||||
| Lowerbound of 95% CI (Gibbons, Hedeker & Davis approximation) | 0.150 | ||||
| Upperbound of 95% CI (Gibbons, Hedeker & Davis approximation) | 1.737 | ||||
| Statistics related to Sortino ratio | |||||
| Sortino ratio | 2.175 | ||||
| Upside Potential Ratio | 3.761 | ||||
| Upside part of mean | 0.548 | ||||
| Downside part of mean | -0.231 | ||||
| Upside SD | 0.310 | ||||
| Downside SD | 0.146 | ||||
| N nonnegative terms | 47.000 | ||||
| N negative terms | 29.000 | ||||
| Statistics related to linear regression on benchmark | |||||
| N of observations | 76.000 | ||||
| Mean of predictor | 0.238 | ||||
| Mean of criterion | 0.317 | ||||
| SD of predictor | 0.223 | ||||
| SD of criterion | 0.333 | ||||
| Covariance | 0.019 | ||||
| r | 0.254 | ||||
| b (slope, estimate of beta) | 0.378 | ||||
| a (intercept, estimate of alpha) | 0.227 | ||||
| Mean Square Error | 0.105 | ||||
| DF error | 74.000 | ||||
| t(b) | 2.256 | ||||
| p(b) | 0.014 | ||||
| t(a) | 1.682 | ||||
| p(a) | 0.048 | ||||
| Lowerbound of 95% confidence interval for beta | 0.044 | ||||
| Upperbound of 95% confidence interval for beta | 0.712 | ||||
| Lowerbound of 95% confidence interval for alpha | -0.042 | ||||
| Upperbound of 95% confidence interval for alpha | 0.495 | ||||
| Treynor index (mean / b) | 0.838 | ||||
| Jensen alpha (a) | 0.227 | ||||
| Risk estimates for a one-period unit investment (parametric) | |||||
| assuming log normal returns and losses (using central moments from Sharpe statistics) | |||||
| VaR(95%) | 0.123 | ||||
| Expected Shortfall on VaR | 0.157 | ||||
| assuming Pareto losses only (using partial moments from Sortino statistics) | |||||
| VaR(95%) | 0.035 | ||||
| Expected Shortfall on VaR | 0.074 | ||||
| ORDER STATISTICS | |||||
| Quartiles of return rates | |||||
| Number of observations | 76.000 | ||||
| Minimum | 0.787 | ||||
| Quartile 1 | 0.977 | ||||
| Median | 1.017 | ||||
| Quartile 3 | 1.061 | ||||
| Maximum | 1.450 | ||||
| Mean of quarter 1 | 0.939 | ||||
| Mean of quarter 2 | 0.998 | ||||
| Mean of quarter 3 | 1.036 | ||||
| Mean of quarter 4 | 1.169 | ||||
| Inter Quartile Range | 0.084 | ||||
| Number outliers low | 1.000 | ||||
| Percentage of outliers low | 0.013 | ||||
| Mean of outliers low | 0.787 | ||||
| Number of outliers high | 6.000 | ||||
| Percentage of outliers high | 0.079 | ||||
| Mean of outliers high | 1.309 | ||||
| Risk estimates for a one-period unit investment (based on Extreme Value Theory) | |||||
| Extreme Value Index (moments method) | 0.039 | ||||
| VaR(95%) (moments method) | 0.057 | ||||
| Expected Shortfall (moments method) | 0.079 | ||||
| Extreme Value Index (regression method) | 0.281 | ||||
| VaR(95%) (regression method) | 0.067 | ||||
| Expected Shortfall (regression method) | 0.111 | ||||
| DRAW DOWN STATISTICS | |||||
| Quartiles of draw downs | |||||
| Number of observations | 14.000 | ||||
| Minimum | 0.003 | ||||
| Quartile 1 | 0.024 | ||||
| Median | 0.045 | ||||
| Quartile 3 | 0.069 | ||||
| Maximum | 0.213 | ||||
| Mean of quarter 1 | 0.015 | ||||
| Mean of quarter 2 | 0.036 | ||||
| Mean of quarter 3 | 0.055 | ||||
| Mean of quarter 4 | 0.158 | ||||
| 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 | 3.000 | ||||
| Percentage of outliers high | 0.214 | ||||
| Mean of outliers high | 0.187 | ||||
| Risk estimates based on draw downs (based on Extreme Value Theory) | |||||
| Extreme Value Index (moments method) | -19.119 | ||||
| VaR(95%) (moments method) | 0.142 | ||||
| Expected Shortfall (moments method) | 0.142 | ||||
| Extreme Value Index (regression method) | -2.476 | ||||
| VaR(95%) (regression method) | 0.269 | ||||
| Expected Shortfall (regression method) | 0.272 | ||||
| COMBINED STATISTICS | |||||
| Annualized return (arithmetic extrapolation) | 1.395 | ||||
| Compounded annual return (geometric extrapolation) | 0.435 | ||||
| Calmar ratio (compounded annual return / max draw down) | 2.040 | ||||
| Compounded annual return / average of 25% largest draw downs | 2.752 | ||||
| Compounded annual return / Expected Shortfall lognormal | 2.765 | ||||
| ANALYSIS BASED ON DAILY VALUES, FULL HISTORY (Back) | |||||
| RATIO STATISTICS | |||||
| Ratio statistics of excess return rates | |||||
| Statistics related to Sharpe ratio | |||||
| Mean | 0.339 | ||||
| SD | 0.291 | ||||
| Sharpe ratio (Glass type estimate) | 1.167 | ||||
| Sharpe ratio (Hedges UMVUE) | 1.166 | ||||
| df | 1667.000 | ||||
| t | 2.944 | ||||
| p | 0.454 | ||||
| Lowerbound of 95% confidence interval for Sharpe Ratio | 0.389 | ||||
| Upperbound of 95% confidence interval for Sharpe Ratio | 1.944 | ||||
| Lowerbound of 95% CI (Gibbons, Hedeker & Davis approximation) | 0.388 | ||||
| Upperbound of 95% CI (Gibbons, Hedeker & Davis approximation) | 1.944 | ||||
| Statistics related to Sortino ratio | |||||
| Sortino ratio | 1.959 | ||||
| Upside Potential Ratio | 8.417 | ||||
| Upside part of mean | 1.457 | ||||
| Downside part of mean | -1.118 | ||||
| Upside SD | 0.234 | ||||
| Downside SD | 0.173 | ||||
| N nonnegative terms | 830.000 | ||||
| N negative terms | 838.000 | ||||
| Statistics related to linear regression on benchmark | |||||
| N of observations | 1668.000 | ||||
| Mean of predictor | 0.268 | ||||
| Mean of criterion | 0.339 | ||||
| SD of predictor | 0.260 | ||||
| SD of criterion | 0.291 | ||||
| Covariance | 0.021 | ||||
| r | 0.285 | ||||
| b (slope, estimate of beta) | 0.319 | ||||
| a (intercept, estimate of alpha) | 0.254 | ||||
| Mean Square Error | 0.078 | ||||
| DF error | 1666.000 | ||||
| t(b) | 12.122 | ||||
| p(b) | 0.358 | ||||
| t(a) | 2.291 | ||||
| p(a) | 0.472 | ||||
| Lowerbound of 95% confidence interval for beta | 0.267 | ||||
| Upperbound of 95% confidence interval for beta | 0.370 | ||||
| Lowerbound of 95% confidence interval for alpha | 0.037 | ||||
| Upperbound of 95% confidence interval for alpha | 0.471 | ||||
| Treynor index (mean / b) | 1.064 | ||||
| Jensen alpha (a) | 0.254 | ||||
| Ratio statistics of excess log return rates | |||||
| Statistics related to Sharpe ratio | |||||
| Mean | 0.297 | ||||
| SD | 0.286 | ||||
| Sharpe ratio (Glass type estimate) | 1.039 | ||||
| Sharpe ratio (Hedges UMVUE) | 1.039 | ||||
| df | 1667.000 | ||||
| t | 2.622 | ||||
| p | 0.459 | ||||
| Lowerbound of 95% confidence interval for Sharpe Ratio | 0.262 | ||||
| Upperbound of 95% confidence interval for Sharpe Ratio | 1.817 | ||||
| Lowerbound of 95% CI (Gibbons, Hedeker & Davis approximation) | 0.261 | ||||
| Upperbound of 95% CI (Gibbons, Hedeker & Davis approximation) | 1.816 | ||||
| Statistics related to Sortino ratio | |||||
| Sortino ratio | 1.673 | ||||
| Upside Potential Ratio | 8.044 | ||||
| Upside part of mean | 1.430 | ||||
| Downside part of mean | -1.133 | ||||
| Upside SD | 0.225 | ||||
| Downside SD | 0.178 | ||||
| N nonnegative terms | 830.000 | ||||
| N negative terms | 838.000 | ||||
| Statistics related to linear regression on benchmark | |||||
| N of observations | 1668.000 | ||||
| Mean of predictor | 0.234 | ||||
| Mean of criterion | 0.297 | ||||
| SD of predictor | 0.261 | ||||
| SD of criterion | 0.286 | ||||
| Covariance | 0.022 | ||||
| r | 0.291 | ||||
| b (slope, estimate of beta) | 0.319 | ||||
| a (intercept, estimate of alpha) | 0.223 | ||||
| Mean Square Error | 0.075 | ||||
| DF error | 1666.000 | ||||
| t(b) | 12.430 | ||||
| p(b) | 0.354 | ||||
| t(a) | 2.048 | ||||
| p(a) | 0.475 | ||||
| Lowerbound of 95% confidence interval for beta | 0.269 | ||||
| Upperbound of 95% confidence interval for beta | 0.370 | ||||
| Lowerbound of 95% confidence interval for alpha | 0.009 | ||||
| Upperbound of 95% confidence interval for alpha | 0.436 | ||||
| Treynor index (mean / b) | 0.931 | ||||
| Jensen alpha (a) | 0.223 | ||||
| Risk estimates for a one-period unit investment (parametric) | |||||
| assuming log normal returns and losses (using central moments from Sharpe statistics) | |||||
| VaR(95%) | 0.028 | ||||
| Expected Shortfall on VaR | 0.035 | ||||
| assuming Pareto losses only (using partial moments from Sortino statistics) | |||||
| VaR(95%) | 0.010 | ||||
| Expected Shortfall on VaR | 0.021 | ||||
| ORDER STATISTICS | |||||
| Quartiles of return rates | |||||
| Number of observations | 1668.000 | ||||
| Minimum | 0.876 | ||||
| Quartile 1 | 0.995 | ||||
| Median | 1.000 | ||||
| Quartile 3 | 1.006 | ||||
| Maximum | 1.207 | ||||
| Mean of quarter 1 | 0.985 | ||||
| Mean of quarter 2 | 0.999 | ||||
| Mean of quarter 3 | 1.003 | ||||
| Mean of quarter 4 | 1.020 | ||||
| Inter Quartile Range | 0.011 | ||||
| Number outliers low | 74.000 | ||||
| Percentage of outliers low | 0.044 | ||||
| Mean of outliers low | 0.960 | ||||
| Number of outliers high | 99.000 | ||||
| Percentage of outliers high | 0.059 | ||||
| Mean of outliers high | 1.045 | ||||
| Risk estimates for a one-period unit investment (based on Extreme Value Theory) | |||||
| Extreme Value Index (moments method) | 0.460 | ||||
| VaR(95%) (moments method) | 0.015 | ||||
| Expected Shortfall (moments method) | 0.031 | ||||
| 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 | 78.000 | ||||
| Minimum | 0.000 | ||||
| Quartile 1 | 0.005 | ||||
| Median | 0.020 | ||||
| Quartile 3 | 0.042 | ||||
| Maximum | 0.293 | ||||
| Mean of quarter 1 | 0.002 | ||||
| Mean of quarter 2 | 0.013 | ||||
| Mean of quarter 3 | 0.032 | ||||
| Mean of quarter 4 | 0.111 | ||||
| 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 | 10.000 | ||||
| Percentage of outliers high | 0.128 | ||||
| Mean of outliers high | 0.162 | ||||
| Risk estimates based on draw downs (based on Extreme Value Theory) | |||||
| Extreme Value Index (moments method) | 0.148 | ||||
| VaR(95%) (moments method) | 0.106 | ||||
| Expected Shortfall (moments method) | 0.159 | ||||
| Extreme Value Index (regression method) | 0.066 | ||||
| VaR(95%) (regression method) | 0.133 | ||||
| Expected Shortfall (regression method) | 0.196 | ||||
| COMBINED STATISTICS | |||||
| Annualized return (arithmetic extrapolation) | 1.224 | ||||
| Compounded annual return (geometric extrapolation) | 0.407 | ||||
| Calmar ratio (compounded annual return / max draw down) | 1.388 | ||||
| Compounded annual return / average of 25% largest draw downs | 3.652 | ||||
| Compounded annual return / Expected Shortfall lognormal | 11.729 | ||||
| ANALYSIS BASED ON DAILY VALUES, LAST 6 MONTHS (Back) | |||||
| RATIO STATISTICS | |||||
| Ratio statistics of excess return rates | |||||
| Statistics related to Sharpe ratio | |||||
| Mean | 1.011 | ||||
| SD | 0.507 | ||||
| Sharpe ratio (Glass type estimate) | 1.994 | ||||
| Sharpe ratio (Hedges UMVUE) | 1.983 | ||||
| df | 130.000 | ||||
| t | 1.410 | ||||
| p | 0.439 | ||||
| Lowerbound of 95% confidence interval for Sharpe Ratio | -0.792 | ||||
| Upperbound of 95% confidence interval for Sharpe Ratio | 4.773 | ||||
| Lowerbound of 95% CI (Gibbons, Hedeker & Davis approximation) | -0.800 | ||||
| Upperbound of 95% CI (Gibbons, Hedeker & Davis approximation) | 4.765 | ||||
| Statistics related to Sortino ratio | |||||
| Sortino ratio | 3.283 | ||||
| Upside Potential Ratio | 11.408 | ||||
| Upside part of mean | 3.514 | ||||
| Downside part of mean | -2.503 | ||||
| Upside SD | 0.405 | ||||
| Downside SD | 0.308 | ||||
| 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 | 1.312 | ||||
| Mean of criterion | 1.011 | ||||
| SD of predictor | 0.498 | ||||
| SD of criterion | 0.507 | ||||
| Covariance | 0.118 | ||||
| r | 0.466 | ||||
| b (slope, estimate of beta) | 0.474 | ||||
| a (intercept, estimate of alpha) | 0.390 | ||||
| Mean Square Error | 0.203 | ||||
| DF error | 129.000 | ||||
| t(b) | 5.974 | ||||
| p(b) | 0.215 | ||||
| t(a) | 0.604 | ||||
| p(a) | 0.466 | ||||
| Lowerbound of 95% confidence interval for beta | 0.317 | ||||
| Upperbound of 95% confidence interval for beta | 0.631 | ||||
| Lowerbound of 95% confidence interval for alpha | -0.888 | ||||
| Upperbound of 95% confidence interval for alpha | 1.667 | ||||
| Treynor index (mean / b) | 2.134 | ||||
| Jensen alpha (a) | 0.390 | ||||
| Ratio statistics of excess log return rates | |||||
| Statistics related to Sharpe ratio | |||||
| Mean | 0.884 | ||||
| SD | 0.502 | ||||
| Sharpe ratio (Glass type estimate) | 1.761 | ||||
| Sharpe ratio (Hedges UMVUE) | 1.751 | ||||
| df | 130.000 | ||||
| t | 1.246 | ||||
| p | 0.446 | ||||
| Lowerbound of 95% confidence interval for Sharpe Ratio | -1.022 | ||||
| Upperbound of 95% confidence interval for Sharpe Ratio | 4.538 | ||||
| Lowerbound of 95% CI (Gibbons, Hedeker & Davis approximation) | -1.029 | ||||
| Upperbound of 95% CI (Gibbons, Hedeker & Davis approximation) | 4.531 | ||||
| Statistics related to Sortino ratio | |||||
| Sortino ratio | 2.799 | ||||
| Upside Potential Ratio | 10.880 | ||||
| Upside part of mean | 3.436 | ||||
| Downside part of mean | -2.552 | ||||
| Upside SD | 0.391 | ||||
| Downside SD | 0.316 | ||||
| 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 | 1.184 | ||||
| Mean of criterion | 0.884 | ||||
| SD of predictor | 0.502 | ||||
| SD of criterion | 0.502 | ||||
| Covariance | 0.119 | ||||
| r | 0.474 | ||||
| b (slope, estimate of beta) | 0.473 | ||||
| a (intercept, estimate of alpha) | 0.323 | ||||
| Mean Square Error | 0.197 | ||||
| DF error | 129.000 | ||||
| t(b) | 6.112 | ||||
| p(b) | 0.210 | ||||
| t(a) | 0.510 | ||||
| p(a) | 0.471 | ||||
| Lowerbound of 95% confidence interval for beta | 0.320 | ||||
| Upperbound of 95% confidence interval for beta | 0.627 | ||||
| Lowerbound of 95% confidence interval for alpha | -0.931 | ||||
| Upperbound of 95% confidence interval for alpha | 1.577 | ||||
| Treynor index (mean / b) | 1.867 | ||||
| Jensen alpha (a) | 0.323 | ||||
| Risk estimates for a one-period unit investment (parametric) | |||||
| assuming log normal returns and losses (using central moments from Sharpe statistics) | |||||
| VaR(95%) | 0.046 | ||||
| Expected Shortfall on VaR | 0.059 | ||||
| assuming Pareto losses only (using partial moments from Sortino statistics) | |||||
| VaR(95%) | 0.022 | ||||
| Expected Shortfall on VaR | 0.042 | ||||
| ORDER STATISTICS | |||||
| Quartiles of return rates | |||||
| Number of observations | 131.000 | ||||
| Minimum | 0.924 | ||||
| Quartile 1 | 0.987 | ||||
| Median | 1.002 | ||||
| Quartile 3 | 1.021 | ||||
| Maximum | 1.142 | ||||
| Mean of quarter 1 | 0.967 | ||||
| Mean of quarter 2 | 0.996 | ||||
| Mean of quarter 3 | 1.012 | ||||
| Mean of quarter 4 | 1.042 | ||||
| Inter Quartile Range | 0.035 | ||||
| Number outliers low | 1.000 | ||||
| Percentage of outliers low | 0.008 | ||||
| Mean of outliers low | 0.924 | ||||
| Number of outliers high | 3.000 | ||||
| Percentage of outliers high | 0.023 | ||||
| Mean of outliers high | 1.103 | ||||
| Risk estimates for a one-period unit investment (based on Extreme Value Theory) | |||||
| Extreme Value Index (moments method) | 0.016 | ||||
| VaR(95%) (moments method) | 0.031 | ||||
| Expected Shortfall (moments method) | 0.042 | ||||
| Extreme Value Index (regression method) | -0.148 | ||||
| VaR(95%) (regression method) | 0.034 | ||||
| Expected Shortfall (regression method) | 0.044 | ||||
| DRAW DOWN STATISTICS | |||||
| Quartiles of draw downs | |||||
| Number of observations | 10.000 | ||||
| Minimum | 0.006 | ||||
| Quartile 1 | 0.014 | ||||
| Median | 0.035 | ||||
| Quartile 3 | 0.110 | ||||
| Maximum | 0.157 | ||||
| Mean of quarter 1 | 0.009 | ||||
| Mean of quarter 2 | 0.028 | ||||
| Mean of quarter 3 | 0.042 | ||||
| Mean of quarter 4 | 0.147 | ||||
| Inter Quartile Range | 0.096 | ||||
| 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) | -80.591 | ||||
| VaR(95%) (moments method) | 0.153 | ||||
| Expected Shortfall (moments method) | NA | ||||
| Extreme Value Index (regression method) | -3.425 | ||||
| VaR(95%) (regression method) | 0.182 | ||||
| Expected Shortfall (regression method) | 0.182 | ||||
| COMBINED STATISTICS | |||||
| Annualized return (arithmetic extrapolation) | 1.181 | ||||
| Compounded annual return (geometric extrapolation) | 1.529 | ||||
| Calmar ratio (compounded annual return / max draw down) | 9.767 | ||||
| Compounded annual return / average of 25% largest draw downs | 10.436 | ||||
| Compounded annual return / Expected Shortfall lognormal | 26.044 | ||||