Advanced Statistics: Trend Trade for Life
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 | -0.013 | ||||
| SD | 0.090 | ||||
| Sharpe ratio (Glass type estimate) | -0.149 | ||||
| Sharpe ratio (Hedges UMVUE) | -0.146 | ||||
| df | 44.000 | ||||
| t | -0.288 | ||||
| p | 0.613 | ||||
| Lowerbound of 95% confidence interval for Sharpe Ratio | -1.160 | ||||
| Upperbound of 95% confidence interval for Sharpe Ratio | 0.865 | ||||
| Lowerbound of 95% CI (Gibbons, Hedeker & Davis approximation) | -1.159 | ||||
| Upperbound of 95% CI (Gibbons, Hedeker & Davis approximation) | 0.867 | ||||
| Statistics related to Sortino ratio | |||||
| Sortino ratio | -0.283 | ||||
| Upside Potential Ratio | 1.532 | ||||
| Upside part of mean | 0.072 | ||||
| Downside part of mean | -0.085 | ||||
| Upside SD | 0.075 | ||||
| Downside SD | 0.047 | ||||
| N nonnegative terms | 6.000 | ||||
| N negative terms | 39.000 | ||||
| Statistics related to linear regression on benchmark | |||||
| N of observations | 45.000 | ||||
| Mean of predictor | 0.438 | ||||
| Mean of criterion | -0.013 | ||||
| SD of predictor | 0.248 | ||||
| SD of criterion | 0.090 | ||||
| Covariance | -0.005 | ||||
| r | -0.217 | ||||
| b (slope, estimate of beta) | -0.078 | ||||
| a (intercept, estimate of alpha) | 0.021 | ||||
| Mean Square Error | 0.008 | ||||
| DF error | 43.000 | ||||
| t(b) | -1.457 | ||||
| p(b) | 0.924 | ||||
| t(a) | 0.409 | ||||
| p(a) | 0.342 | ||||
| Lowerbound of 95% confidence interval for beta | -0.187 | ||||
| Upperbound of 95% confidence interval for beta | 0.030 | ||||
| Lowerbound of 95% confidence interval for alpha | -0.083 | ||||
| Upperbound of 95% confidence interval for alpha | 0.125 | ||||
| Treynor index (mean / b) | 0.170 | ||||
| Jensen alpha (a) | 0.021 | ||||
| Ratio statistics of excess log return rates | |||||
| Statistics related to Sharpe ratio | |||||
| Mean | -0.017 | ||||
| SD | 0.087 | ||||
| Sharpe ratio (Glass type estimate) | -0.196 | ||||
| Sharpe ratio (Hedges UMVUE) | -0.192 | ||||
| df | 44.000 | ||||
| t | -0.379 | ||||
| p | 0.647 | ||||
| Lowerbound of 95% confidence interval for Sharpe Ratio | -1.208 | ||||
| Upperbound of 95% confidence interval for Sharpe Ratio | 0.818 | ||||
| Lowerbound of 95% CI (Gibbons, Hedeker & Davis approximation) | -1.205 | ||||
| Upperbound of 95% CI (Gibbons, Hedeker & Davis approximation) | 0.821 | ||||
| Statistics related to Sortino ratio | |||||
| Sortino ratio | -0.355 | ||||
| Upside Potential Ratio | 1.443 | ||||
| Upside part of mean | 0.069 | ||||
| Downside part of mean | -0.086 | ||||
| Upside SD | 0.072 | ||||
| Downside SD | 0.048 | ||||
| N nonnegative terms | 6.000 | ||||
| N negative terms | 39.000 | ||||
| Statistics related to linear regression on benchmark | |||||
| N of observations | 45.000 | ||||
| Mean of predictor | 0.402 | ||||
| Mean of criterion | -0.017 | ||||
| SD of predictor | 0.232 | ||||
| SD of criterion | 0.087 | ||||
| Covariance | -0.005 | ||||
| r | -0.226 | ||||
| b (slope, estimate of beta) | -0.084 | ||||
| a (intercept, estimate of alpha) | 0.017 | ||||
| Mean Square Error | 0.007 | ||||
| DF error | 43.000 | ||||
| t(b) | -1.520 | ||||
| p(b) | 0.932 | ||||
| t(a) | 0.341 | ||||
| p(a) | 0.367 | ||||
| Lowerbound of 95% confidence interval for beta | -0.197 | ||||
| Upperbound of 95% confidence interval for beta | 0.028 | ||||
| Lowerbound of 95% confidence interval for alpha | -0.083 | ||||
| Upperbound of 95% confidence interval for alpha | 0.117 | ||||
| Treynor index (mean / b) | 0.202 | ||||
| Jensen alpha (a) | 0.017 | ||||
| Risk estimates for a one-period unit investment (parametric) | |||||
| assuming log normal returns and losses (using central moments from Sharpe statistics) | |||||
| VaR(95%) | 0.042 | ||||
| Expected Shortfall on VaR | 0.052 | ||||
| assuming Pareto losses only (using partial moments from Sortino statistics) | |||||
| VaR(95%) | 0.023 | ||||
| Expected Shortfall on VaR | 0.040 | ||||
| ORDER STATISTICS | |||||
| Quartiles of return rates | |||||
| Number of observations | 45.000 | ||||
| Minimum | 0.941 | ||||
| Quartile 1 | 1.000 | ||||
| Median | 1.000 | ||||
| Quartile 3 | 1.000 | ||||
| Maximum | 1.118 | ||||
| Mean of quarter 1 | 0.985 | ||||
| Mean of quarter 2 | 1.000 | ||||
| Mean of quarter 3 | 1.000 | ||||
| Mean of quarter 4 | 1.027 | ||||
| Inter Quartile Range | 0.000 | ||||
| Number outliers low | 9.000 | ||||
| Percentage of outliers low | 0.200 | ||||
| Mean of outliers low | 0.980 | ||||
| Number of outliers high | 7.000 | ||||
| Percentage of outliers high | 0.156 | ||||
| Mean of outliers high | 1.042 | ||||
| Risk estimates for a one-period unit investment (based on Extreme Value Theory) | |||||
| Extreme Value Index (moments method) | -3.064 | ||||
| VaR(95%) (moments method) | 0.001 | ||||
| Expected Shortfall (moments method) | 0.001 | ||||
| Extreme Value Index (regression method) | -0.553 | ||||
| VaR(95%) (regression method) | 0.015 | ||||
| Expected Shortfall (regression method) | 0.020 | ||||
| DRAW DOWN STATISTICS | |||||
| Quartiles of draw downs | |||||
| Number of observations | 4.000 | ||||
| Minimum | 0.006 | ||||
| Quartile 1 | 0.011 | ||||
| Median | 0.021 | ||||
| Quartile 3 | 0.053 | ||||
| Maximum | 0.125 | ||||
| Mean of quarter 1 | 0.006 | ||||
| Mean of quarter 2 | 0.013 | ||||
| Mean of quarter 3 | 0.030 | ||||
| Mean of quarter 4 | 0.125 | ||||
| Inter Quartile Range | 0.042 | ||||
| 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 | 0.250 | ||||
| Mean of outliers high | 0.125 | ||||
| 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) | 0.028 | ||||
| Compounded annual return (geometric extrapolation) | 0.027 | ||||
| Calmar ratio (compounded annual return / max draw down) | 0.219 | ||||
| Compounded annual return / average of 25% largest draw downs | 0.219 | ||||
| Compounded annual return / Expected Shortfall lognormal | 0.528 | ||||
| ANALYSIS BASED ON DAILY VALUES, FULL HISTORY (Back) | |||||
| RATIO STATISTICS | |||||
| Ratio statistics of excess return rates | |||||
| Statistics related to Sharpe ratio | |||||
| Mean | -0.013 | ||||
| SD | 0.091 | ||||
| Sharpe ratio (Glass type estimate) | -0.144 | ||||
| Sharpe ratio (Hedges UMVUE) | -0.144 | ||||
| df | 988.000 | ||||
| t | -0.279 | ||||
| p | 0.610 | ||||
| Lowerbound of 95% confidence interval for Sharpe Ratio | -1.153 | ||||
| Upperbound of 95% confidence interval for Sharpe Ratio | 0.865 | ||||
| Lowerbound of 95% CI (Gibbons, Hedeker & Davis approximation) | -1.152 | ||||
| Upperbound of 95% CI (Gibbons, Hedeker & Davis approximation) | 0.865 | ||||
| Statistics related to Sortino ratio | |||||
| Sortino ratio | -0.207 | ||||
| Upside Potential Ratio | 4.356 | ||||
| Upside part of mean | 0.275 | ||||
| Downside part of mean | -0.288 | ||||
| Upside SD | 0.065 | ||||
| Downside SD | 0.063 | ||||
| N nonnegative terms | 172.000 | ||||
| N negative terms | 817.000 | ||||
| Statistics related to linear regression on benchmark | |||||
| N of observations | 989.000 | ||||
| Mean of predictor | 0.455 | ||||
| Mean of criterion | -0.013 | ||||
| SD of predictor | 0.308 | ||||
| SD of criterion | 0.091 | ||||
| Covariance | -0.005 | ||||
| r | -0.171 | ||||
| b (slope, estimate of beta) | -0.051 | ||||
| a (intercept, estimate of alpha) | 0.010 | ||||
| Mean Square Error | 0.008 | ||||
| DF error | 987.000 | ||||
| t(b) | -5.468 | ||||
| p(b) | 1.000 | ||||
| t(a) | 0.216 | ||||
| p(a) | 0.415 | ||||
| Lowerbound of 95% confidence interval for beta | -0.069 | ||||
| Upperbound of 95% confidence interval for beta | -0.033 | ||||
| Lowerbound of 95% confidence interval for alpha | -0.081 | ||||
| Upperbound of 95% confidence interval for alpha | 0.101 | ||||
| Treynor index (mean / b) | 0.258 | ||||
| Jensen alpha (a) | 0.010 | ||||
| Ratio statistics of excess log return rates | |||||
| Statistics related to Sharpe ratio | |||||
| Mean | -0.017 | ||||
| SD | 0.091 | ||||
| Sharpe ratio (Glass type estimate) | -0.189 | ||||
| Sharpe ratio (Hedges UMVUE) | -0.189 | ||||
| df | 988.000 | ||||
| t | -0.368 | ||||
| p | 0.643 | ||||
| Lowerbound of 95% confidence interval for Sharpe Ratio | -1.198 | ||||
| Upperbound of 95% confidence interval for Sharpe Ratio | 0.820 | ||||
| Lowerbound of 95% CI (Gibbons, Hedeker & Davis approximation) | -1.198 | ||||
| Upperbound of 95% CI (Gibbons, Hedeker & Davis approximation) | 0.820 | ||||
| Statistics related to Sortino ratio | |||||
| Sortino ratio | -0.269 | ||||
| Upside Potential Ratio | 4.270 | ||||
| Upside part of mean | 0.273 | ||||
| Downside part of mean | -0.290 | ||||
| Upside SD | 0.065 | ||||
| Downside SD | 0.064 | ||||
| N nonnegative terms | 172.000 | ||||
| N negative terms | 817.000 | ||||
| Statistics related to linear regression on benchmark | |||||
| N of observations | 989.000 | ||||
| Mean of predictor | 0.407 | ||||
| Mean of criterion | -0.017 | ||||
| SD of predictor | 0.308 | ||||
| SD of criterion | 0.091 | ||||
| Covariance | -0.005 | ||||
| r | -0.172 | ||||
| b (slope, estimate of beta) | -0.051 | ||||
| a (intercept, estimate of alpha) | 0.003 | ||||
| Mean Square Error | 0.008 | ||||
| DF error | 987.000 | ||||
| t(b) | -5.474 | ||||
| p(b) | 1.000 | ||||
| t(a) | 0.075 | ||||
| p(a) | 0.470 | ||||
| Lowerbound of 95% confidence interval for beta | -0.069 | ||||
| Upperbound of 95% confidence interval for beta | -0.033 | ||||
| Lowerbound of 95% confidence interval for alpha | -0.087 | ||||
| Upperbound of 95% confidence interval for alpha | 0.094 | ||||
| Treynor index (mean / b) | 0.339 | ||||
| Jensen alpha (a) | 0.003 | ||||
| Risk estimates for a one-period unit investment (parametric) | |||||
| assuming log normal returns and losses (using central moments from Sharpe statistics) | |||||
| VaR(95%) | 0.009 | ||||
| Expected Shortfall on VaR | 0.012 | ||||
| assuming Pareto losses only (using partial moments from Sortino statistics) | |||||
| VaR(95%) | 0.003 | ||||
| Expected Shortfall on VaR | 0.007 | ||||
| ORDER STATISTICS | |||||
| Quartiles of return rates | |||||
| Number of observations | 989.000 | ||||
| Minimum | 0.952 | ||||
| Quartile 1 | 1.000 | ||||
| Median | 1.000 | ||||
| Quartile 3 | 1.000 | ||||
| Maximum | 1.047 | ||||
| Mean of quarter 1 | 0.996 | ||||
| Mean of quarter 2 | 1.000 | ||||
| Mean of quarter 3 | 1.000 | ||||
| Mean of quarter 4 | 1.004 | ||||
| Inter Quartile Range | 0.000 | ||||
| Number outliers low | 137.000 | ||||
| Percentage of outliers low | 0.139 | ||||
| Mean of outliers low | 0.993 | ||||
| Number of outliers high | 176.000 | ||||
| Percentage of outliers high | 0.178 | ||||
| Mean of outliers high | 1.006 | ||||
| Risk estimates for a one-period unit investment (based on Extreme Value Theory) | |||||
| Extreme Value Index (moments method) | 0.148 | ||||
| VaR(95%) (moments method) | 0.002 | ||||
| Expected Shortfall (moments method) | 0.005 | ||||
| Extreme Value Index (regression method) | 0.146 | ||||
| VaR(95%) (regression method) | 0.004 | ||||
| Expected Shortfall (regression method) | 0.010 | ||||
| DRAW DOWN STATISTICS | |||||
| Quartiles of draw downs | |||||
| Number of observations | 6.000 | ||||
| Minimum | 0.002 | ||||
| Quartile 1 | 0.044 | ||||
| Median | 0.074 | ||||
| Quartile 3 | 0.109 | ||||
| Maximum | 0.135 | ||||
| Mean of quarter 1 | 0.022 | ||||
| Mean of quarter 2 | 0.050 | ||||
| Mean of quarter 3 | 0.097 | ||||
| Mean of quarter 4 | 0.124 | ||||
| Inter Quartile Range | 0.065 | ||||
| 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) | 0.028 | ||||
| Compounded annual return (geometric extrapolation) | 0.027 | ||||
| Calmar ratio (compounded annual return / max draw down) | 0.201 | ||||
| Compounded annual return / average of 25% largest draw downs | 0.219 | ||||
| Compounded annual return / Expected Shortfall lognormal | 2.346 | ||||
| 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 | 0.953 | ||||
| Mean of criterion | -0.044 | ||||
| SD of predictor | 0.482 | ||||
| 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 | 0.836 | ||||
| Mean of criterion | -0.044 | ||||
| SD of predictor | 0.482 | ||||
| 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) | -8749323841211024.000 | ||||
| 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) | -187262397776722532872341302542336.000 | ||||
| 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 | ||||