Advanced Statistics: Canada Market Timing
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 | 0.111 | ||||
| SD | 0.217 | ||||
| Sharpe ratio (Glass type estimate) | 0.509 | ||||
| Sharpe ratio (Hedges UMVUE) | 0.502 | ||||
| df | 59.000 | ||||
| t | 1.137 | ||||
| p | 0.130 | ||||
| Lowerbound of 95% confidence interval for Sharpe Ratio | -0.375 | ||||
| Upperbound of 95% confidence interval for Sharpe Ratio | 1.388 | ||||
| Lowerbound of 95% CI (Gibbons, Hedeker & Davis approximation) | -0.379 | ||||
| Upperbound of 95% CI (Gibbons, Hedeker & Davis approximation) | 1.383 | ||||
| Statistics related to Sortino ratio | |||||
| Sortino ratio | 1.125 | ||||
| Upside Potential Ratio | 2.686 | ||||
| Upside part of mean | 0.264 | ||||
| Downside part of mean | -0.153 | ||||
| Upside SD | 0.194 | ||||
| Downside SD | 0.098 | ||||
| N nonnegative terms | 13.000 | ||||
| N negative terms | 47.000 | ||||
| Statistics related to linear regression on benchmark | |||||
| N of observations | 60.000 | ||||
| Mean of predictor | 0.417 | ||||
| Mean of criterion | 0.111 | ||||
| SD of predictor | 0.245 | ||||
| SD of criterion | 0.217 | ||||
| Covariance | 0.012 | ||||
| r | 0.231 | ||||
| b (slope, estimate of beta) | 0.204 | ||||
| a (intercept, estimate of alpha) | 0.025 | ||||
| Mean Square Error | 0.045 | ||||
| DF error | 58.000 | ||||
| t(b) | 1.806 | ||||
| p(b) | 0.038 | ||||
| t(a) | 0.238 | ||||
| p(a) | 0.407 | ||||
| Lowerbound of 95% confidence interval for beta | -0.022 | ||||
| Upperbound of 95% confidence interval for beta | 0.431 | ||||
| Lowerbound of 95% confidence interval for alpha | -0.188 | ||||
| Upperbound of 95% confidence interval for alpha | 0.238 | ||||
| Treynor index (mean / b) | 0.541 | ||||
| Jensen alpha (a) | 0.025 | ||||
| Ratio statistics of excess log return rates | |||||
| Statistics related to Sharpe ratio | |||||
| Mean | 0.088 | ||||
| SD | 0.206 | ||||
| Sharpe ratio (Glass type estimate) | 0.428 | ||||
| Sharpe ratio (Hedges UMVUE) | 0.422 | ||||
| df | 59.000 | ||||
| t | 0.956 | ||||
| p | 0.171 | ||||
| Lowerbound of 95% confidence interval for Sharpe Ratio | -0.454 | ||||
| Upperbound of 95% confidence interval for Sharpe Ratio | 1.306 | ||||
| Lowerbound of 95% CI (Gibbons, Hedeker & Davis approximation) | -0.458 | ||||
| Upperbound of 95% CI (Gibbons, Hedeker & Davis approximation) | 1.302 | ||||
| Statistics related to Sortino ratio | |||||
| Sortino ratio | 0.863 | ||||
| Upside Potential Ratio | 2.409 | ||||
| Upside part of mean | 0.246 | ||||
| Downside part of mean | -0.158 | ||||
| Upside SD | 0.179 | ||||
| Downside SD | 0.102 | ||||
| N nonnegative terms | 13.000 | ||||
| N negative terms | 47.000 | ||||
| Statistics related to linear regression on benchmark | |||||
| N of observations | 60.000 | ||||
| Mean of predictor | 0.381 | ||||
| Mean of criterion | 0.088 | ||||
| SD of predictor | 0.234 | ||||
| SD of criterion | 0.206 | ||||
| Covariance | 0.012 | ||||
| r | 0.254 | ||||
| b (slope, estimate of beta) | 0.224 | ||||
| a (intercept, estimate of alpha) | 0.003 | ||||
| Mean Square Error | 0.040 | ||||
| DF error | 58.000 | ||||
| t(b) | 1.999 | ||||
| p(b) | 0.025 | ||||
| t(a) | 0.029 | ||||
| p(a) | 0.488 | ||||
| Lowerbound of 95% confidence interval for beta | -0.000 | ||||
| Upperbound of 95% confidence interval for beta | 0.448 | ||||
| Lowerbound of 95% confidence interval for alpha | -0.196 | ||||
| Upperbound of 95% confidence interval for alpha | 0.202 | ||||
| Treynor index (mean / b) | 0.394 | ||||
| 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%) | 0.087 | ||||
| Expected Shortfall on VaR | 0.109 | ||||
| assuming Pareto losses only (using partial moments from Sortino statistics) | |||||
| VaR(95%) | 0.038 | ||||
| Expected Shortfall on VaR | 0.074 | ||||
| ORDER STATISTICS | |||||
| Quartiles of return rates | |||||
| Number of observations | 60.000 | ||||
| Minimum | 0.896 | ||||
| Quartile 1 | 1.000 | ||||
| Median | 1.000 | ||||
| Quartile 3 | 1.000 | ||||
| Maximum | 1.232 | ||||
| Mean of quarter 1 | 0.960 | ||||
| Mean of quarter 2 | 1.000 | ||||
| Mean of quarter 3 | 1.000 | ||||
| Mean of quarter 4 | 1.091 | ||||
| Inter Quartile Range | 0.000 | ||||
| Number outliers low | 10.000 | ||||
| Percentage of outliers low | 0.167 | ||||
| Mean of outliers low | 0.941 | ||||
| Number of outliers high | 13.000 | ||||
| Percentage of outliers high | 0.217 | ||||
| Mean of outliers high | 1.105 | ||||
| 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) | -1.013 | ||||
| VaR(95%) (regression method) | 0.065 | ||||
| Expected Shortfall (regression method) | 0.078 | ||||
| DRAW DOWN STATISTICS | |||||
| Quartiles of draw downs | |||||
| Number of observations | 7.000 | ||||
| Minimum | 0.007 | ||||
| Quartile 1 | 0.041 | ||||
| Median | 0.083 | ||||
| Quartile 3 | 0.123 | ||||
| Maximum | 0.161 | ||||
| Mean of quarter 1 | 0.020 | ||||
| Mean of quarter 2 | 0.066 | ||||
| Mean of quarter 3 | 0.104 | ||||
| Mean of quarter 4 | 0.152 | ||||
| Inter Quartile Range | 0.082 | ||||
| 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) | 0.187 | ||||
| Compounded annual return (geometric extrapolation) | 0.141 | ||||
| Calmar ratio (compounded annual return / max draw down) | 0.878 | ||||
| Compounded annual return / average of 25% largest draw downs | 0.930 | ||||
| Compounded annual return / Expected Shortfall lognormal | 1.299 | ||||
| ANALYSIS BASED ON DAILY VALUES, FULL HISTORY (Back) | |||||
| RATIO STATISTICS | |||||
| Ratio statistics of excess return rates | |||||
| Statistics related to Sharpe ratio | |||||
| Mean | 0.196 | ||||
| SD | 0.470 | ||||
| Sharpe ratio (Glass type estimate) | 0.416 | ||||
| Sharpe ratio (Hedges UMVUE) | 0.415 | ||||
| df | 1329.000 | ||||
| t | 0.937 | ||||
| p | 0.484 | ||||
| Lowerbound of 95% confidence interval for Sharpe Ratio | -0.454 | ||||
| Upperbound of 95% confidence interval for Sharpe Ratio | 1.286 | ||||
| Lowerbound of 95% CI (Gibbons, Hedeker & Davis approximation) | -0.455 | ||||
| Upperbound of 95% CI (Gibbons, Hedeker & Davis approximation) | 1.286 | ||||
| Statistics related to Sortino ratio | |||||
| Sortino ratio | 0.635 | ||||
| Upside Potential Ratio | 4.572 | ||||
| Upside part of mean | 1.409 | ||||
| Downside part of mean | -1.214 | ||||
| Upside SD | 0.355 | ||||
| Downside SD | 0.308 | ||||
| N nonnegative terms | 267.000 | ||||
| N negative terms | 1063.000 | ||||
| Statistics related to linear regression on benchmark | |||||
| N of observations | 1330.000 | ||||
| Mean of predictor | 0.467 | ||||
| Mean of criterion | 0.196 | ||||
| SD of predictor | 0.373 | ||||
| SD of criterion | 0.470 | ||||
| Covariance | 0.079 | ||||
| r | 0.449 | ||||
| b (slope, estimate of beta) | 0.566 | ||||
| a (intercept, estimate of alpha) | -0.069 | ||||
| Mean Square Error | 0.177 | ||||
| DF error | 1328.000 | ||||
| t(b) | 18.293 | ||||
| p(b) | 0.276 | ||||
| t(a) | -0.366 | ||||
| p(a) | 0.505 | ||||
| Lowerbound of 95% confidence interval for beta | 0.505 | ||||
| Upperbound of 95% confidence interval for beta | 0.627 | ||||
| Lowerbound of 95% confidence interval for alpha | -0.436 | ||||
| Upperbound of 95% confidence interval for alpha | 0.299 | ||||
| Treynor index (mean / b) | 0.346 | ||||
| Jensen alpha (a) | -0.069 | ||||
| Ratio statistics of excess log return rates | |||||
| Statistics related to Sharpe ratio | |||||
| Mean | 0.086 | ||||
| SD | 0.468 | ||||
| Sharpe ratio (Glass type estimate) | 0.184 | ||||
| Sharpe ratio (Hedges UMVUE) | 0.184 | ||||
| df | 1329.000 | ||||
| t | 0.415 | ||||
| p | 0.493 | ||||
| Lowerbound of 95% confidence interval for Sharpe Ratio | -0.686 | ||||
| Upperbound of 95% confidence interval for Sharpe Ratio | 1.054 | ||||
| Lowerbound of 95% CI (Gibbons, Hedeker & Davis approximation) | -0.686 | ||||
| Upperbound of 95% CI (Gibbons, Hedeker & Davis approximation) | 1.054 | ||||
| Statistics related to Sortino ratio | |||||
| Sortino ratio | 0.259 | ||||
| Upside Potential Ratio | 4.057 | ||||
| Upside part of mean | 1.352 | ||||
| Downside part of mean | -1.266 | ||||
| Upside SD | 0.328 | ||||
| Downside SD | 0.333 | ||||
| N nonnegative terms | 267.000 | ||||
| N negative terms | 1063.000 | ||||
| Statistics related to linear regression on benchmark | |||||
| N of observations | 1330.000 | ||||
| Mean of predictor | 0.394 | ||||
| Mean of criterion | 0.086 | ||||
| SD of predictor | 0.385 | ||||
| SD of criterion | 0.468 | ||||
| Covariance | 0.078 | ||||
| r | 0.435 | ||||
| b (slope, estimate of beta) | 0.529 | ||||
| a (intercept, estimate of alpha) | -0.122 | ||||
| Mean Square Error | 0.177 | ||||
| DF error | 1328.000 | ||||
| t(b) | 17.616 | ||||
| p(b) | 0.282 | ||||
| t(a) | -0.651 | ||||
| p(a) | 0.509 | ||||
| Lowerbound of 95% confidence interval for beta | 0.470 | ||||
| Upperbound of 95% confidence interval for beta | 0.587 | ||||
| Lowerbound of 95% confidence interval for alpha | -0.490 | ||||
| Upperbound of 95% confidence interval for alpha | 0.246 | ||||
| Treynor index (mean / b) | 0.163 | ||||
| Jensen alpha (a) | -0.122 | ||||
| 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 | 0.057 | ||||
| assuming Pareto losses only (using partial moments from Sortino statistics) | |||||
| VaR(95%) | 0.014 | ||||
| Expected Shortfall on VaR | 0.031 | ||||
| ORDER STATISTICS | |||||
| Quartiles of return rates | |||||
| Number of observations | 1330.000 | ||||
| Minimum | 0.728 | ||||
| Quartile 1 | 1.000 | ||||
| Median | 1.000 | ||||
| Quartile 3 | 1.000 | ||||
| Maximum | 1.310 | ||||
| Mean of quarter 1 | 0.982 | ||||
| Mean of quarter 2 | 1.000 | ||||
| Mean of quarter 3 | 1.000 | ||||
| Mean of quarter 4 | 1.022 | ||||
| Inter Quartile Range | 0.000 | ||||
| Number outliers low | 212.000 | ||||
| Percentage of outliers low | 0.159 | ||||
| Mean of outliers low | 0.972 | ||||
| Number of outliers high | 268.000 | ||||
| Percentage of outliers high | 0.202 | ||||
| Mean of outliers high | 1.027 | ||||
| Risk estimates for a one-period unit investment (based on Extreme Value Theory) | |||||
| Extreme Value Index (moments method) | 0.342 | ||||
| VaR(95%) (moments method) | 0.005 | ||||
| Expected Shortfall (moments method) | 0.011 | ||||
| Extreme Value Index (regression method) | 0.380 | ||||
| VaR(95%) (regression method) | 0.015 | ||||
| Expected Shortfall (regression method) | 0.041 | ||||
| DRAW DOWN STATISTICS | |||||
| Quartiles of draw downs | |||||
| Number of observations | 34.000 | ||||
| Minimum | 0.001 | ||||
| Quartile 1 | 0.016 | ||||
| Median | 0.067 | ||||
| Quartile 3 | 0.148 | ||||
| Maximum | 0.272 | ||||
| Mean of quarter 1 | 0.006 | ||||
| Mean of quarter 2 | 0.035 | ||||
| Mean of quarter 3 | 0.104 | ||||
| Mean of quarter 4 | 0.191 | ||||
| Inter Quartile Range | 0.131 | ||||
| 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) | -0.354 | ||||
| VaR(95%) (moments method) | 0.212 | ||||
| Expected Shortfall (moments method) | 0.235 | ||||
| Extreme Value Index (regression method) | -0.085 | ||||
| VaR(95%) (regression method) | 0.220 | ||||
| Expected Shortfall (regression method) | 0.257 | ||||
| COMBINED STATISTICS | |||||
| Annualized return (arithmetic extrapolation) | 0.185 | ||||
| Compounded annual return (geometric extrapolation) | 0.139 | ||||
| Calmar ratio (compounded annual return / max draw down) | 0.511 | ||||
| Compounded annual return / average of 25% largest draw downs | 0.727 | ||||
| Compounded annual return / Expected Shortfall lognormal | 2.419 | ||||
| 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 | 1.352 | ||||
| Mean of criterion | -0.044 | ||||
| SD of predictor | 0.353 | ||||
| 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 | 1.286 | ||||
| Mean of criterion | -0.044 | ||||
| SD of predictor | 0.354 | ||||
| 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) | -8584416804913799.000 | ||||
| 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) | -61611467112681197980102296600576.000 | ||||
| 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 | ||||