Advanced Statistics: Tradestreaming Hedge Fund Guru Portfolio
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 | 0.300 | ||||
| SD | 0.270 | ||||
| Sharpe ratio (Glass type estimate) | 1.111 | ||||
| Sharpe ratio (Hedges UMVUE) | 1.097 | ||||
| df | 60.000 | ||||
| t | 2.505 | ||||
| p | 0.007 | ||||
| Lowerbound of 95% confidence interval for Sharpe Ratio | 0.215 | ||||
| Upperbound of 95% confidence interval for Sharpe Ratio | 1.998 | ||||
| Lowerbound of 95% CI (Gibbons, Hedeker & Davis approximation) | 0.206 | ||||
| Upperbound of 95% CI (Gibbons, Hedeker & Davis approximation) | 1.988 | ||||
| Statistics related to Sortino ratio | |||||
| Sortino ratio | 2.288 | ||||
| Upside Potential Ratio | 3.483 | ||||
| Upside part of mean | 0.457 | ||||
| Downside part of mean | -0.157 | ||||
| Upside SD | 0.249 | ||||
| Downside SD | 0.131 | ||||
| N nonnegative terms | 41.000 | ||||
| N negative terms | 20.000 | ||||
| Statistics related to linear regression on benchmark | |||||
| N of observations | 61.000 | ||||
| Mean of predictor | 0.306 | ||||
| Mean of criterion | 0.300 | ||||
| SD of predictor | 0.254 | ||||
| SD of criterion | 0.270 | ||||
| Covariance | 0.058 | ||||
| r | 0.849 | ||||
| b (slope, estimate of beta) | 0.904 | ||||
| a (intercept, estimate of alpha) | 0.023 | ||||
| Mean Square Error | 0.021 | ||||
| DF error | 59.000 | ||||
| t(b) | 12.365 | ||||
| p(b) | -0.000 | ||||
| t(a) | 0.344 | ||||
| p(a) | 0.366 | ||||
| Lowerbound of 95% confidence interval for beta | 0.757 | ||||
| Upperbound of 95% confidence interval for beta | 1.050 | ||||
| Lowerbound of 95% confidence interval for alpha | -0.112 | ||||
| Upperbound of 95% confidence interval for alpha | 0.158 | ||||
| Treynor index (mean / b) | 0.332 | ||||
| Jensen alpha (a) | 0.023 | ||||
| Ratio statistics of excess log return rates | |||||
| Statistics related to Sharpe ratio | |||||
| Mean | 0.262 | ||||
| SD | 0.259 | ||||
| Sharpe ratio (Glass type estimate) | 1.012 | ||||
| Sharpe ratio (Hedges UMVUE) | 1.000 | ||||
| df | 60.000 | ||||
| t | 2.282 | ||||
| p | 0.013 | ||||
| Lowerbound of 95% confidence interval for Sharpe Ratio | 0.120 | ||||
| Upperbound of 95% confidence interval for Sharpe Ratio | 1.896 | ||||
| Lowerbound of 95% CI (Gibbons, Hedeker & Davis approximation) | 0.112 | ||||
| Upperbound of 95% CI (Gibbons, Hedeker & Davis approximation) | 1.887 | ||||
| Statistics related to Sortino ratio | |||||
| Sortino ratio | 1.797 | ||||
| Upside Potential Ratio | 2.935 | ||||
| Upside part of mean | 0.428 | ||||
| Downside part of mean | -0.166 | ||||
| Upside SD | 0.225 | ||||
| Downside SD | 0.146 | ||||
| N nonnegative terms | 41.000 | ||||
| N negative terms | 20.000 | ||||
| Statistics related to linear regression on benchmark | |||||
| N of observations | 61.000 | ||||
| Mean of predictor | 0.273 | ||||
| Mean of criterion | 0.262 | ||||
| SD of predictor | 0.235 | ||||
| SD of criterion | 0.259 | ||||
| Covariance | 0.051 | ||||
| r | 0.838 | ||||
| b (slope, estimate of beta) | 0.923 | ||||
| a (intercept, estimate of alpha) | 0.010 | ||||
| Mean Square Error | 0.020 | ||||
| DF error | 59.000 | ||||
| t(b) | 11.813 | ||||
| p(b) | -0.000 | ||||
| t(a) | 0.147 | ||||
| p(a) | 0.442 | ||||
| Lowerbound of 95% confidence interval for beta | 0.767 | ||||
| Upperbound of 95% confidence interval for beta | 1.080 | ||||
| Lowerbound of 95% confidence interval for alpha | -0.124 | ||||
| Upperbound of 95% confidence interval for alpha | 0.143 | ||||
| Treynor index (mean / b) | 0.284 | ||||
| Jensen alpha (a) | 0.010 | ||||
| Risk estimates for a one-period unit investment (parametric) | |||||
| assuming log normal returns and losses (using central moments from Sharpe statistics) | |||||
| VaR(95%) | 0.096 | ||||
| Expected Shortfall on VaR | 0.124 | ||||
| assuming Pareto losses only (using partial moments from Sortino statistics) | |||||
| VaR(95%) | 0.022 | ||||
| Expected Shortfall on VaR | 0.051 | ||||
| ORDER STATISTICS | |||||
| Quartiles of return rates | |||||
| Number of observations | 61.000 | ||||
| Minimum | 0.754 | ||||
| Quartile 1 | 0.997 | ||||
| Median | 1.021 | ||||
| Quartile 3 | 1.048 | ||||
| Maximum | 1.352 | ||||
| Mean of quarter 1 | 0.955 | ||||
| Mean of quarter 2 | 1.012 | ||||
| Mean of quarter 3 | 1.036 | ||||
| Mean of quarter 4 | 1.117 | ||||
| Inter Quartile Range | 0.051 | ||||
| Number outliers low | 1.000 | ||||
| Percentage of outliers low | 0.016 | ||||
| Mean of outliers low | 0.754 | ||||
| Number of outliers high | 4.000 | ||||
| Percentage of outliers high | 0.066 | ||||
| Mean of outliers high | 1.236 | ||||
| Risk estimates for a one-period unit investment (based on Extreme Value Theory) | |||||
| Extreme Value Index (moments method) | -1.681 | ||||
| VaR(95%) (moments method) | 0.013 | ||||
| Expected Shortfall (moments method) | 0.014 | ||||
| Extreme Value Index (regression method) | 0.193 | ||||
| VaR(95%) (regression method) | 0.039 | ||||
| Expected Shortfall (regression method) | 0.072 | ||||
| DRAW DOWN STATISTICS | |||||
| Quartiles of draw downs | |||||
| Number of observations | 12.000 | ||||
| Minimum | 0.001 | ||||
| Quartile 1 | 0.015 | ||||
| Median | 0.033 | ||||
| Quartile 3 | 0.062 | ||||
| Maximum | 0.246 | ||||
| Mean of quarter 1 | 0.005 | ||||
| Mean of quarter 2 | 0.022 | ||||
| Mean of quarter 3 | 0.047 | ||||
| Mean of quarter 4 | 0.139 | ||||
| Inter Quartile Range | 0.047 | ||||
| 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 | 0.083 | ||||
| Mean of outliers high | 0.246 | ||||
| Risk estimates based on draw downs (based on Extreme Value Theory) | |||||
| Extreme Value Index (moments method) | -0.091 | ||||
| VaR(95%) (moments method) | 0.141 | ||||
| Expected Shortfall (moments method) | 0.190 | ||||
| Extreme Value Index (regression method) | 1.563 | ||||
| VaR(95%) (regression method) | 0.242 | ||||
| Expected Shortfall (regression method) | NA | ||||
| COMBINED STATISTICS | |||||
| Annualized return (arithmetic extrapolation) | 0.736 | ||||
| Compounded annual return (geometric extrapolation) | 0.358 | ||||
| Calmar ratio (compounded annual return / max draw down) | 1.457 | ||||
| Compounded annual return / average of 25% largest draw downs | 2.582 | ||||
| Compounded annual return / Expected Shortfall lognormal | 2.897 | ||||
| ANALYSIS BASED ON DAILY VALUES, FULL HISTORY (Back) | |||||
| RATIO STATISTICS | |||||
| Ratio statistics of excess return rates | |||||
| Statistics related to Sharpe ratio | |||||
| Mean | 0.307 | ||||
| SD | 0.308 | ||||
| Sharpe ratio (Glass type estimate) | 0.995 | ||||
| Sharpe ratio (Hedges UMVUE) | 0.994 | ||||
| df | 1341.000 | ||||
| t | 2.252 | ||||
| p | 0.461 | ||||
| Lowerbound of 95% confidence interval for Sharpe Ratio | 0.128 | ||||
| Upperbound of 95% confidence interval for Sharpe Ratio | 1.862 | ||||
| Lowerbound of 95% CI (Gibbons, Hedeker & Davis approximation) | 0.128 | ||||
| Upperbound of 95% CI (Gibbons, Hedeker & Davis approximation) | 1.861 | ||||
| Statistics related to Sortino ratio | |||||
| Sortino ratio | 1.515 | ||||
| Upside Potential Ratio | 7.453 | ||||
| Upside part of mean | 1.510 | ||||
| Downside part of mean | -1.203 | ||||
| Upside SD | 0.233 | ||||
| Downside SD | 0.203 | ||||
| N nonnegative terms | 739.000 | ||||
| N negative terms | 603.000 | ||||
| Statistics related to linear regression on benchmark | |||||
| N of observations | 1342.000 | ||||
| Mean of predictor | 0.315 | ||||
| Mean of criterion | 0.307 | ||||
| SD of predictor | 0.259 | ||||
| SD of criterion | 0.308 | ||||
| Covariance | 0.058 | ||||
| r | 0.731 | ||||
| b (slope, estimate of beta) | 0.871 | ||||
| a (intercept, estimate of alpha) | 0.033 | ||||
| Mean Square Error | 0.044 | ||||
| DF error | 1340.000 | ||||
| t(b) | 39.264 | ||||
| p(b) | 0.134 | ||||
| t(a) | 0.351 | ||||
| p(a) | 0.495 | ||||
| Lowerbound of 95% confidence interval for beta | 0.828 | ||||
| Upperbound of 95% confidence interval for beta | 0.915 | ||||
| Lowerbound of 95% confidence interval for alpha | -0.150 | ||||
| Upperbound of 95% confidence interval for alpha | 0.216 | ||||
| Treynor index (mean / b) | 0.352 | ||||
| Jensen alpha (a) | 0.033 | ||||
| Ratio statistics of excess log return rates | |||||
| Statistics related to Sharpe ratio | |||||
| Mean | 0.260 | ||||
| SD | 0.306 | ||||
| Sharpe ratio (Glass type estimate) | 0.849 | ||||
| Sharpe ratio (Hedges UMVUE) | 0.848 | ||||
| df | 1341.000 | ||||
| t | 1.921 | ||||
| p | 0.467 | ||||
| Lowerbound of 95% confidence interval for Sharpe Ratio | -0.018 | ||||
| Upperbound of 95% confidence interval for Sharpe Ratio | 1.715 | ||||
| Lowerbound of 95% CI (Gibbons, Hedeker & Davis approximation) | -0.018 | ||||
| Upperbound of 95% CI (Gibbons, Hedeker & Davis approximation) | 1.715 | ||||
| Statistics related to Sortino ratio | |||||
| Sortino ratio | 1.235 | ||||
| Upside Potential Ratio | 7.056 | ||||
| Upside part of mean | 1.484 | ||||
| Downside part of mean | -1.224 | ||||
| Upside SD | 0.223 | ||||
| Downside SD | 0.210 | ||||
| N nonnegative terms | 739.000 | ||||
| N negative terms | 603.000 | ||||
| Statistics related to linear regression on benchmark | |||||
| N of observations | 1342.000 | ||||
| Mean of predictor | 0.281 | ||||
| Mean of criterion | 0.260 | ||||
| SD of predictor | 0.257 | ||||
| SD of criterion | 0.306 | ||||
| Covariance | 0.057 | ||||
| r | 0.732 | ||||
| b (slope, estimate of beta) | 0.871 | ||||
| a (intercept, estimate of alpha) | 0.015 | ||||
| Mean Square Error | 0.044 | ||||
| DF error | 1340.000 | ||||
| t(b) | 39.275 | ||||
| p(b) | 0.134 | ||||
| t(a) | 0.158 | ||||
| p(a) | 0.498 | ||||
| Lowerbound of 95% confidence interval for beta | 0.828 | ||||
| Upperbound of 95% confidence interval for beta | 0.915 | ||||
| Lowerbound of 95% confidence interval for alpha | -0.167 | ||||
| Upperbound of 95% confidence interval for alpha | 0.196 | ||||
| Treynor index (mean / b) | 0.298 | ||||
| Jensen alpha (a) | 0.015 | ||||
| Risk estimates for a one-period unit investment (parametric) | |||||
| assuming log normal returns and losses (using central moments from Sharpe statistics) | |||||
| VaR(95%) | 0.030 | ||||
| Expected Shortfall on VaR | 0.037 | ||||
| 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 | 1342.000 | ||||
| Minimum | 0.852 | ||||
| Quartile 1 | 0.995 | ||||
| Median | 1.001 | ||||
| Quartile 3 | 1.007 | ||||
| Maximum | 1.225 | ||||
| Mean of quarter 1 | 0.983 | ||||
| Mean of quarter 2 | 0.999 | ||||
| Mean of quarter 3 | 1.004 | ||||
| Mean of quarter 4 | 1.019 | ||||
| Inter Quartile Range | 0.012 | ||||
| Number outliers low | 57.000 | ||||
| Percentage of outliers low | 0.042 | ||||
| Mean of outliers low | 0.953 | ||||
| Number of outliers high | 62.000 | ||||
| Percentage of outliers high | 0.046 | ||||
| Mean of outliers high | 1.050 | ||||
| Risk estimates for a one-period unit investment (based on Extreme Value Theory) | |||||
| Extreme Value Index (moments method) | 0.475 | ||||
| VaR(95%) (moments method) | 0.015 | ||||
| Expected Shortfall (moments method) | 0.034 | ||||
| Extreme Value Index (regression method) | 0.390 | ||||
| VaR(95%) (regression method) | 0.014 | ||||
| Expected Shortfall (regression method) | 0.026 | ||||
| DRAW DOWN STATISTICS | |||||
| Quartiles of draw downs | |||||
| Number of observations | 82.000 | ||||
| Minimum | 0.001 | ||||
| Quartile 1 | 0.006 | ||||
| Median | 0.015 | ||||
| Quartile 3 | 0.039 | ||||
| Maximum | 0.390 | ||||
| Mean of quarter 1 | 0.003 | ||||
| Mean of quarter 2 | 0.011 | ||||
| Mean of quarter 3 | 0.026 | ||||
| Mean of quarter 4 | 0.113 | ||||
| Inter Quartile Range | 0.033 | ||||
| Number outliers low | 0.000 | ||||
| Percentage of outliers low | 0.000 | ||||
| Mean of outliers low | NA | ||||
| Number of outliers high | 8.000 | ||||
| Percentage of outliers high | 0.098 | ||||
| Mean of outliers high | 0.215 | ||||
| Risk estimates based on draw downs (based on Extreme Value Theory) | |||||
| Extreme Value Index (moments method) | 0.713 | ||||
| VaR(95%) (moments method) | 0.132 | ||||
| Expected Shortfall (moments method) | 0.468 | ||||
| Extreme Value Index (regression method) | 1.209 | ||||
| VaR(95%) (regression method) | 0.093 | ||||
| Expected Shortfall (regression method) | NA | ||||
| COMBINED STATISTICS | |||||
| Annualized return (arithmetic extrapolation) | 0.730 | ||||
| Compounded annual return (geometric extrapolation) | 0.355 | ||||
| Calmar ratio (compounded annual return / max draw down) | 0.910 | ||||
| Compounded annual return / average of 25% largest draw downs | 3.134 | ||||
| Compounded annual return / Expected Shortfall lognormal | 9.525 | ||||
| ANALYSIS BASED ON DAILY VALUES, LAST 6 MONTHS (Back) | |||||
| RATIO STATISTICS | |||||
| Ratio statistics of excess return rates | |||||
| Statistics related to Sharpe ratio | |||||
| Mean | 1.048 | ||||
| SD | 0.693 | ||||
| Sharpe ratio (Glass type estimate) | 1.512 | ||||
| Sharpe ratio (Hedges UMVUE) | 1.503 | ||||
| df | 130.000 | ||||
| t | 1.069 | ||||
| p | 0.453 | ||||
| Lowerbound of 95% confidence interval for Sharpe Ratio | -1.269 | ||||
| Upperbound of 95% confidence interval for Sharpe Ratio | 4.287 | ||||
| Lowerbound of 95% CI (Gibbons, Hedeker & Davis approximation) | -1.275 | ||||
| Upperbound of 95% CI (Gibbons, Hedeker & Davis approximation) | 4.281 | ||||
| Statistics related to Sortino ratio | |||||
| Sortino ratio | 2.603 | ||||
| Upside Potential Ratio | 10.066 | ||||
| Upside part of mean | 4.051 | ||||
| Downside part of mean | -3.003 | ||||
| Upside SD | 0.564 | ||||
| Downside SD | 0.402 | ||||
| N nonnegative terms | 69.000 | ||||
| N negative terms | 62.000 | ||||
| Statistics related to linear regression on benchmark | |||||
| N of observations | 131.000 | ||||
| Mean of predictor | 1.577 | ||||
| Mean of criterion | 1.048 | ||||
| SD of predictor | 0.578 | ||||
| SD of criterion | 0.693 | ||||
| Covariance | 0.306 | ||||
| r | 0.765 | ||||
| b (slope, estimate of beta) | 0.916 | ||||
| a (intercept, estimate of alpha) | -0.397 | ||||
| Mean Square Error | 0.201 | ||||
| DF error | 129.000 | ||||
| t(b) | 13.475 | ||||
| p(b) | 0.066 | ||||
| t(a) | -0.618 | ||||
| p(a) | 0.535 | ||||
| Lowerbound of 95% confidence interval for beta | 0.782 | ||||
| Upperbound of 95% confidence interval for beta | 1.051 | ||||
| Lowerbound of 95% confidence interval for alpha | -1.669 | ||||
| Upperbound of 95% confidence interval for alpha | 0.875 | ||||
| Treynor index (mean / b) | 1.143 | ||||
| Jensen alpha (a) | -0.397 | ||||
| Ratio statistics of excess log return rates | |||||
| Statistics related to Sharpe ratio | |||||
| Mean | 0.816 | ||||
| SD | 0.675 | ||||
| Sharpe ratio (Glass type estimate) | 1.208 | ||||
| Sharpe ratio (Hedges UMVUE) | 1.201 | ||||
| df | 130.000 | ||||
| t | 0.854 | ||||
| p | 0.463 | ||||
| Lowerbound of 95% confidence interval for Sharpe Ratio | -1.570 | ||||
| Upperbound of 95% confidence interval for Sharpe Ratio | 3.981 | ||||
| Lowerbound of 95% CI (Gibbons, Hedeker & Davis approximation) | -1.575 | ||||
| Upperbound of 95% CI (Gibbons, Hedeker & Davis approximation) | 3.977 | ||||
| Statistics related to Sortino ratio | |||||
| Sortino ratio | 1.944 | ||||
| Upside Potential Ratio | 9.301 | ||||
| Upside part of mean | 3.905 | ||||
| Downside part of mean | -3.089 | ||||
| Upside SD | 0.528 | ||||
| Downside SD | 0.420 | ||||
| N nonnegative terms | 69.000 | ||||
| N negative terms | 62.000 | ||||
| Statistics related to linear regression on benchmark | |||||
| N of observations | 131.000 | ||||
| Mean of predictor | 1.410 | ||||
| Mean of criterion | 0.816 | ||||
| SD of predictor | 0.569 | ||||
| SD of criterion | 0.675 | ||||
| Covariance | 0.295 | ||||
| r | 0.766 | ||||
| b (slope, estimate of beta) | 0.909 | ||||
| a (intercept, estimate of alpha) | -0.465 | ||||
| Mean Square Error | 0.190 | ||||
| DF error | 129.000 | ||||
| t(b) | 13.540 | ||||
| p(b) | 0.065 | ||||
| t(a) | -0.747 | ||||
| p(a) | 0.542 | ||||
| Lowerbound of 95% confidence interval for beta | 0.776 | ||||
| Upperbound of 95% confidence interval for beta | 1.042 | ||||
| Lowerbound of 95% confidence interval for alpha | -1.699 | ||||
| Upperbound of 95% confidence interval for alpha | 0.768 | ||||
| Treynor index (mean / b) | 0.898 | ||||
| Jensen alpha (a) | -0.465 | ||||
| Risk estimates for a one-period unit investment (parametric) | |||||
| assuming log normal returns and losses (using central moments from Sharpe statistics) | |||||
| VaR(95%) | 0.063 | ||||
| Expected Shortfall on VaR | 0.080 | ||||
| assuming Pareto losses only (using partial moments from Sortino statistics) | |||||
| VaR(95%) | 0.025 | ||||
| Expected Shortfall on VaR | 0.051 | ||||
| ORDER STATISTICS | |||||
| Quartiles of return rates | |||||
| Number of observations | 131.000 | ||||
| Minimum | 0.879 | ||||
| Quartile 1 | 0.985 | ||||
| Median | 1.002 | ||||
| Quartile 3 | 1.019 | ||||
| Maximum | 1.225 | ||||
| Mean of quarter 1 | 0.960 | ||||
| Mean of quarter 2 | 0.995 | ||||
| Mean of quarter 3 | 1.009 | ||||
| Mean of quarter 4 | 1.053 | ||||
| Inter Quartile Range | 0.035 | ||||
| Number outliers low | 5.000 | ||||
| Percentage of outliers low | 0.038 | ||||
| Mean of outliers low | 0.901 | ||||
| Number of outliers high | 5.000 | ||||
| Percentage of outliers high | 0.038 | ||||
| Mean of outliers high | 1.131 | ||||
| Risk estimates for a one-period unit investment (based on Extreme Value Theory) | |||||
| Extreme Value Index (moments method) | 0.235 | ||||
| VaR(95%) (moments method) | 0.039 | ||||
| Expected Shortfall (moments method) | 0.062 | ||||
| Extreme Value Index (regression method) | 0.206 | ||||
| VaR(95%) (regression method) | 0.037 | ||||
| Expected Shortfall (regression method) | 0.056 | ||||
| DRAW DOWN STATISTICS | |||||
| Quartiles of draw downs | |||||
| Number of observations | 14.000 | ||||
| Minimum | 0.009 | ||||
| Quartile 1 | 0.021 | ||||
| Median | 0.028 | ||||
| Quartile 3 | 0.054 | ||||
| Maximum | 0.390 | ||||
| Mean of quarter 1 | 0.014 | ||||
| Mean of quarter 2 | 0.025 | ||||
| Mean of quarter 3 | 0.035 | ||||
| Mean of quarter 4 | 0.184 | ||||
| Inter Quartile Range | 0.033 | ||||
| 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 | 0.226 | ||||
| Risk estimates based on draw downs (based on Extreme Value Theory) | |||||
| Extreme Value Index (moments method) | -0.956 | ||||
| VaR(95%) (moments method) | 0.166 | ||||
| Expected Shortfall (moments method) | 0.183 | ||||
| Extreme Value Index (regression method) | 0.328 | ||||
| VaR(95%) (regression method) | 0.344 | ||||
| Expected Shortfall (regression method) | 0.675 | ||||
| COMBINED STATISTICS | |||||
| Annualized return (arithmetic extrapolation) | 1.075 | ||||
| Compounded annual return (geometric extrapolation) | 1.363 | ||||
| Calmar ratio (compounded annual return / max draw down) | 3.495 | ||||
| Compounded annual return / average of 25% largest draw downs | 7.414 | ||||
| Compounded annual return / Expected Shortfall lognormal | 17.146 | ||||