Advanced Statistics: PIPPROFIT.COM
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 | -0.029 | ||||
| SD | 0.097 | ||||
| Sharpe ratio (Glass type estimate) | -0.299 | ||||
| Sharpe ratio (Hedges UMVUE) | -0.295 | ||||
| df | 67.000 | ||||
| t | -0.711 | ||||
| p | 0.760 | ||||
| Lowerbound of 95% confidence interval for Sharpe Ratio | -1.123 | ||||
| Upperbound of 95% confidence interval for Sharpe Ratio | 0.527 | ||||
| Lowerbound of 95% CI (Gibbons, Hedeker & Davis approximation) | -1.120 | ||||
| Upperbound of 95% CI (Gibbons, Hedeker & Davis approximation) | 0.529 | ||||
| Statistics related to Sortino ratio | |||||
| Sortino ratio | -0.364 | ||||
| Upside Potential Ratio | 1.156 | ||||
| Upside part of mean | 0.092 | ||||
| Downside part of mean | -0.122 | ||||
| Upside SD | 0.055 | ||||
| Downside SD | 0.080 | ||||
| N nonnegative terms | 36.000 | ||||
| N negative terms | 32.000 | ||||
| Statistics related to linear regression on benchmark | |||||
| N of observations | 68.000 | ||||
| Mean of predictor | 0.282 | ||||
| Mean of criterion | -0.029 | ||||
| SD of predictor | 0.267 | ||||
| SD of criterion | 0.097 | ||||
| Covariance | 0.003 | ||||
| r | 0.120 | ||||
| b (slope, estimate of beta) | 0.044 | ||||
| a (intercept, estimate of alpha) | -0.041 | ||||
| Mean Square Error | 0.009 | ||||
| DF error | 66.000 | ||||
| t(b) | 0.982 | ||||
| p(b) | 0.165 | ||||
| t(a) | -0.968 | ||||
| p(a) | 0.832 | ||||
| Lowerbound of 95% confidence interval for beta | -0.045 | ||||
| Upperbound of 95% confidence interval for beta | 0.133 | ||||
| Lowerbound of 95% confidence interval for alpha | -0.127 | ||||
| Upperbound of 95% confidence interval for alpha | 0.044 | ||||
| Treynor index (mean / b) | -0.666 | ||||
| Jensen alpha (a) | -0.041 | ||||
| Ratio statistics of excess log return rates | |||||
| Statistics related to Sharpe ratio | |||||
| Mean | -0.034 | ||||
| SD | 0.099 | ||||
| Sharpe ratio (Glass type estimate) | -0.340 | ||||
| Sharpe ratio (Hedges UMVUE) | -0.336 | ||||
| df | 67.000 | ||||
| t | -0.810 | ||||
| p | 0.789 | ||||
| Lowerbound of 95% confidence interval for Sharpe Ratio | -1.164 | ||||
| Upperbound of 95% confidence interval for Sharpe Ratio | 0.487 | ||||
| Lowerbound of 95% CI (Gibbons, Hedeker & Davis approximation) | -1.162 | ||||
| Upperbound of 95% CI (Gibbons, Hedeker & Davis approximation) | 0.489 | ||||
| Statistics related to Sortino ratio | |||||
| Sortino ratio | -0.404 | ||||
| Upside Potential Ratio | 1.083 | ||||
| Upside part of mean | 0.091 | ||||
| Downside part of mean | -0.125 | ||||
| Upside SD | 0.053 | ||||
| Downside SD | 0.084 | ||||
| N nonnegative terms | 36.000 | ||||
| N negative terms | 32.000 | ||||
| Statistics related to linear regression on benchmark | |||||
| N of observations | 68.000 | ||||
| Mean of predictor | 0.243 | ||||
| Mean of criterion | -0.034 | ||||
| SD of predictor | 0.267 | ||||
| SD of criterion | 0.099 | ||||
| Covariance | 0.003 | ||||
| r | 0.115 | ||||
| b (slope, estimate of beta) | 0.043 | ||||
| a (intercept, estimate of alpha) | -0.044 | ||||
| Mean Square Error | 0.010 | ||||
| DF error | 66.000 | ||||
| t(b) | 0.941 | ||||
| p(b) | 0.175 | ||||
| t(a) | -1.023 | ||||
| p(a) | 0.845 | ||||
| Lowerbound of 95% confidence interval for beta | -0.048 | ||||
| Upperbound of 95% confidence interval for beta | 0.134 | ||||
| Lowerbound of 95% confidence interval for alpha | -0.131 | ||||
| Upperbound of 95% confidence interval for alpha | 0.042 | ||||
| Treynor index (mean / b) | -0.789 | ||||
| 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%) | 0.049 | ||||
| Expected Shortfall on VaR | 0.060 | ||||
| assuming Pareto losses only (using partial moments from Sortino statistics) | |||||
| VaR(95%) | 0.022 | ||||
| Expected Shortfall on VaR | 0.046 | ||||
| ORDER STATISTICS | |||||
| Quartiles of return rates | |||||
| Number of observations | 68.000 | ||||
| Minimum | 0.867 | ||||
| Quartile 1 | 0.991 | ||||
| Median | 1.004 | ||||
| Quartile 3 | 1.017 | ||||
| Maximum | 1.097 | ||||
| Mean of quarter 1 | 0.969 | ||||
| Mean of quarter 2 | 0.998 | ||||
| Mean of quarter 3 | 1.010 | ||||
| Mean of quarter 4 | 1.028 | ||||
| Inter Quartile Range | 0.026 | ||||
| Number outliers low | 3.000 | ||||
| Percentage of outliers low | 0.044 | ||||
| Mean of outliers low | 0.913 | ||||
| Number of outliers high | 1.000 | ||||
| Percentage of outliers high | 0.015 | ||||
| Mean of outliers high | 1.097 | ||||
| Risk estimates for a one-period unit investment (based on Extreme Value Theory) | |||||
| Extreme Value Index (moments method) | 0.293 | ||||
| VaR(95%) (moments method) | 0.028 | ||||
| Expected Shortfall (moments method) | 0.049 | ||||
| Extreme Value Index (regression method) | 0.647 | ||||
| VaR(95%) (regression method) | 0.022 | ||||
| Expected Shortfall (regression method) | 0.057 | ||||
| DRAW DOWN STATISTICS | |||||
| Quartiles of draw downs | |||||
| Number of observations | 2.000 | ||||
| Minimum | 0.100 | ||||
| Quartile 1 | 0.108 | ||||
| Median | 0.117 | ||||
| Quartile 3 | 0.125 | ||||
| Maximum | 0.133 | ||||
| Mean of quarter 1 | 0.100 | ||||
| Mean of quarter 2 | NA | ||||
| Mean of quarter 3 | NA | ||||
| Mean of quarter 4 | 0.133 | ||||
| Inter Quartile Range | 0.016 | ||||
| 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) | 0.010 | ||||
| Compounded annual return (geometric extrapolation) | 0.010 | ||||
| Calmar ratio (compounded annual return / max draw down) | 0.077 | ||||
| Compounded annual return / average of 25% largest draw downs | 0.077 | ||||
| Compounded annual return / Expected Shortfall lognormal | 0.171 | ||||
| ANALYSIS BASED ON DAILY VALUES, FULL HISTORY (Back) | |||||
| RATIO STATISTICS | |||||
| Ratio statistics of excess return rates | |||||
| Statistics related to Sharpe ratio | |||||
| Mean | -0.002 | ||||
| SD | 0.252 | ||||
| Sharpe ratio (Glass type estimate) | -0.008 | ||||
| Sharpe ratio (Hedges UMVUE) | -0.008 | ||||
| df | 1498.000 | ||||
| t | -0.019 | ||||
| p | 0.500 | ||||
| Lowerbound of 95% confidence interval for Sharpe Ratio | -0.827 | ||||
| Upperbound of 95% confidence interval for Sharpe Ratio | 0.812 | ||||
| Lowerbound of 95% CI (Gibbons, Hedeker & Davis approximation) | -0.827 | ||||
| Upperbound of 95% CI (Gibbons, Hedeker & Davis approximation) | 0.812 | ||||
| Statistics related to Sortino ratio | |||||
| Sortino ratio | -0.011 | ||||
| Upside Potential Ratio | 3.795 | ||||
| Upside part of mean | 0.653 | ||||
| Downside part of mean | -0.655 | ||||
| Upside SD | 0.184 | ||||
| Downside SD | 0.172 | ||||
| N nonnegative terms | 681.000 | ||||
| N negative terms | 818.000 | ||||
| Statistics related to linear regression on benchmark | |||||
| N of observations | 1499.000 | ||||
| Mean of predictor | 0.408 | ||||
| Mean of criterion | -0.002 | ||||
| SD of predictor | 0.548 | ||||
| SD of criterion | 0.252 | ||||
| Covariance | -0.026 | ||||
| r | -0.186 | ||||
| b (slope, estimate of beta) | -0.086 | ||||
| a (intercept, estimate of alpha) | 0.033 | ||||
| Mean Square Error | 0.061 | ||||
| DF error | 1497.000 | ||||
| t(b) | -7.326 | ||||
| p(b) | 0.618 | ||||
| t(a) | 0.318 | ||||
| p(a) | 0.495 | ||||
| Lowerbound of 95% confidence interval for beta | -0.109 | ||||
| Upperbound of 95% confidence interval for beta | -0.063 | ||||
| Lowerbound of 95% confidence interval for alpha | -0.170 | ||||
| Upperbound of 95% confidence interval for alpha | 0.236 | ||||
| Treynor index (mean / b) | 0.023 | ||||
| Jensen alpha (a) | 0.033 | ||||
| Ratio statistics of excess log return rates | |||||
| Statistics related to Sharpe ratio | |||||
| Mean | -0.034 | ||||
| SD | 0.254 | ||||
| Sharpe ratio (Glass type estimate) | -0.133 | ||||
| Sharpe ratio (Hedges UMVUE) | -0.133 | ||||
| df | 1498.000 | ||||
| t | -0.319 | ||||
| p | 0.504 | ||||
| Lowerbound of 95% confidence interval for Sharpe Ratio | -0.953 | ||||
| Upperbound of 95% confidence interval for Sharpe Ratio | 0.686 | ||||
| Lowerbound of 95% CI (Gibbons, Hedeker & Davis approximation) | -0.953 | ||||
| Upperbound of 95% CI (Gibbons, Hedeker & Davis approximation) | 0.686 | ||||
| Statistics related to Sortino ratio | |||||
| Sortino ratio | -0.180 | ||||
| Upside Potential Ratio | 3.380 | ||||
| Upside part of mean | 0.637 | ||||
| Downside part of mean | -0.671 | ||||
| Upside SD | 0.170 | ||||
| Downside SD | 0.189 | ||||
| N nonnegative terms | 681.000 | ||||
| N negative terms | 818.000 | ||||
| Statistics related to linear regression on benchmark | |||||
| N of observations | 1499.000 | ||||
| Mean of predictor | 0.261 | ||||
| Mean of criterion | -0.034 | ||||
| SD of predictor | 0.543 | ||||
| SD of criterion | 0.254 | ||||
| Covariance | -0.026 | ||||
| r | -0.187 | ||||
| b (slope, estimate of beta) | -0.088 | ||||
| a (intercept, estimate of alpha) | -0.011 | ||||
| Mean Square Error | 0.062 | ||||
| DF error | 1497.000 | ||||
| t(b) | -7.375 | ||||
| p(b) | 0.619 | ||||
| t(a) | -0.106 | ||||
| p(a) | 0.502 | ||||
| Lowerbound of 95% confidence interval for beta | -0.111 | ||||
| Upperbound of 95% confidence interval for beta | -0.064 | ||||
| Lowerbound of 95% confidence interval for alpha | -0.216 | ||||
| Upperbound of 95% confidence interval for alpha | 0.194 | ||||
| Treynor index (mean / b) | 0.387 | ||||
| Jensen alpha (a) | -0.011 | ||||
| Risk estimates for a one-period unit investment (parametric) | |||||
| assuming log normal returns and losses (using central moments from Sharpe statistics) | |||||
| VaR(95%) | 0.026 | ||||
| Expected Shortfall on VaR | 0.032 | ||||
| assuming Pareto losses only (using partial moments from Sortino statistics) | |||||
| VaR(95%) | 0.006 | ||||
| Expected Shortfall on VaR | 0.014 | ||||
| ORDER STATISTICS | |||||
| Quartiles of return rates | |||||
| Number of observations | 1499.000 | ||||
| Minimum | 0.768 | ||||
| Quartile 1 | 0.998 | ||||
| Median | 1.000 | ||||
| Quartile 3 | 1.002 | ||||
| Maximum | 1.265 | ||||
| Mean of quarter 1 | 0.992 | ||||
| Mean of quarter 2 | 0.999 | ||||
| Mean of quarter 3 | 1.001 | ||||
| Mean of quarter 4 | 1.009 | ||||
| Inter Quartile Range | 0.005 | ||||
| Number outliers low | 58.000 | ||||
| Percentage of outliers low | 0.039 | ||||
| Mean of outliers low | 0.971 | ||||
| Number of outliers high | 73.000 | ||||
| Percentage of outliers high | 0.049 | ||||
| Mean of outliers high | 1.028 | ||||
| Risk estimates for a one-period unit investment (based on Extreme Value Theory) | |||||
| Extreme Value Index (moments method) | 0.648 | ||||
| VaR(95%) (moments method) | 0.008 | ||||
| Expected Shortfall (moments method) | 0.024 | ||||
| Extreme Value Index (regression method) | 0.607 | ||||
| VaR(95%) (regression method) | 0.006 | ||||
| Expected Shortfall (regression method) | 0.014 | ||||
| DRAW DOWN STATISTICS | |||||
| Quartiles of draw downs | |||||
| Number of observations | 9.000 | ||||
| Minimum | 0.000 | ||||
| Quartile 1 | 0.005 | ||||
| Median | 0.007 | ||||
| Quartile 3 | 0.013 | ||||
| Maximum | 0.325 | ||||
| Mean of quarter 1 | 0.002 | ||||
| Mean of quarter 2 | 0.007 | ||||
| Mean of quarter 3 | 0.011 | ||||
| Mean of quarter 4 | 0.233 | ||||
| Inter Quartile Range | 0.008 | ||||
| Number outliers low | 0.000 | ||||
| Percentage of outliers low | 0.000 | ||||
| Mean of outliers low | NA | ||||
| Number of outliers high | 2.000 | ||||
| Percentage of outliers high | 0.222 | ||||
| Mean of outliers high | 0.233 | ||||
| Risk estimates based on draw downs (based on Extreme Value Theory) | |||||
| Extreme Value Index (moments method) | -19.818 | ||||
| VaR(95%) (moments method) | 0.051 | ||||
| Expected Shortfall (moments method) | 0.051 | ||||
| Extreme Value Index (regression method) | -0.497 | ||||
| VaR(95%) (regression method) | 0.388 | ||||
| Expected Shortfall (regression method) | 0.474 | ||||
| COMBINED STATISTICS | |||||
| Annualized return (arithmetic extrapolation) | 0.010 | ||||
| Compounded annual return (geometric extrapolation) | 0.010 | ||||
| Calmar ratio (compounded annual return / max draw down) | 0.031 | ||||
| Compounded annual return / average of 25% largest draw downs | 0.043 | ||||
| Compounded annual return / Expected Shortfall lognormal | 0.318 | ||||
| ANALYSIS BASED ON DAILY VALUES, LAST 6 MONTHS (Back) | |||||
| RATIO STATISTICS | |||||
| Ratio statistics of excess return rates | |||||
| Statistics related to Sharpe ratio | |||||
| Mean | 0.073 | ||||
| SD | 0.096 | ||||
| Sharpe ratio (Glass type estimate) | 0.765 | ||||
| Sharpe ratio (Hedges UMVUE) | 0.760 | ||||
| df | 130.000 | ||||
| t | 0.541 | ||||
| p | 0.476 | ||||
| Lowerbound of 95% confidence interval for Sharpe Ratio | -2.010 | ||||
| Upperbound of 95% confidence interval for Sharpe Ratio | 3.537 | ||||
| Lowerbound of 95% CI (Gibbons, Hedeker & Davis approximation) | -2.013 | ||||
| Upperbound of 95% CI (Gibbons, Hedeker & Davis approximation) | 3.534 | ||||
| Statistics related to Sortino ratio | |||||
| Sortino ratio | 1.281 | ||||
| Upside Potential Ratio | 9.724 | ||||
| Upside part of mean | 0.556 | ||||
| Downside part of mean | -0.483 | ||||
| Upside SD | 0.076 | ||||
| Downside SD | 0.057 | ||||
| N nonnegative terms | 50.000 | ||||
| N negative terms | 81.000 | ||||
| Statistics related to linear regression on benchmark | |||||
| N of observations | 131.000 | ||||
| Mean of predictor | 1.258 | ||||
| Mean of criterion | 0.073 | ||||
| SD of predictor | 0.494 | ||||
| SD of criterion | 0.096 | ||||
| Covariance | 0.013 | ||||
| r | 0.266 | ||||
| b (slope, estimate of beta) | 0.051 | ||||
| a (intercept, estimate of alpha) | 0.008 | ||||
| Mean Square Error | 0.009 | ||||
| DF error | 129.000 | ||||
| t(b) | 3.131 | ||||
| p(b) | 0.333 | ||||
| t(a) | 0.064 | ||||
| p(a) | 0.496 | ||||
| Lowerbound of 95% confidence interval for beta | 0.019 | ||||
| Upperbound of 95% confidence interval for beta | 0.084 | ||||
| Lowerbound of 95% confidence interval for alpha | -0.254 | ||||
| Upperbound of 95% confidence interval for alpha | 0.271 | ||||
| Treynor index (mean / b) | 1.423 | ||||
| Jensen alpha (a) | 0.008 | ||||
| Ratio statistics of excess log return rates | |||||
| Statistics related to Sharpe ratio | |||||
| Mean | 0.069 | ||||
| SD | 0.095 | ||||
| Sharpe ratio (Glass type estimate) | 0.719 | ||||
| Sharpe ratio (Hedges UMVUE) | 0.715 | ||||
| df | 130.000 | ||||
| t | 0.509 | ||||
| p | 0.478 | ||||
| Lowerbound of 95% confidence interval for Sharpe Ratio | -2.055 | ||||
| Upperbound of 95% confidence interval for Sharpe Ratio | 3.491 | ||||
| Lowerbound of 95% CI (Gibbons, Hedeker & Davis approximation) | -2.058 | ||||
| Upperbound of 95% CI (Gibbons, Hedeker & Davis approximation) | 3.488 | ||||
| Statistics related to Sortino ratio | |||||
| Sortino ratio | 1.195 | ||||
| Upside Potential Ratio | 9.618 | ||||
| Upside part of mean | 0.553 | ||||
| Downside part of mean | -0.484 | ||||
| Upside SD | 0.076 | ||||
| Downside SD | 0.057 | ||||
| N nonnegative terms | 50.000 | ||||
| N negative terms | 81.000 | ||||
| Statistics related to linear regression on benchmark | |||||
| N of observations | 131.000 | ||||
| Mean of predictor | 1.133 | ||||
| Mean of criterion | 0.069 | ||||
| SD of predictor | 0.499 | ||||
| SD of criterion | 0.095 | ||||
| Covariance | 0.012 | ||||
| r | 0.260 | ||||
| b (slope, estimate of beta) | 0.050 | ||||
| a (intercept, estimate of alpha) | 0.012 | ||||
| Mean Square Error | 0.009 | ||||
| DF error | 129.000 | ||||
| t(b) | 3.058 | ||||
| p(b) | 0.336 | ||||
| t(a) | 0.093 | ||||
| p(a) | 0.495 | ||||
| Lowerbound of 95% confidence interval for beta | 0.018 | ||||
| Upperbound of 95% confidence interval for beta | 0.082 | ||||
| Lowerbound of 95% confidence interval for alpha | -0.249 | ||||
| Upperbound of 95% confidence interval for alpha | 0.274 | ||||
| Treynor index (mean / b) | 1.379 | ||||
| Jensen alpha (a) | 0.012 | ||||
| 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%) | 0.005 | ||||
| Expected Shortfall on VaR | 0.009 | ||||
| ORDER STATISTICS | |||||
| Quartiles of return rates | |||||
| Number of observations | 131.000 | ||||
| Minimum | 0.978 | ||||
| Quartile 1 | 0.997 | ||||
| Median | 1.000 | ||||
| Quartile 3 | 1.003 | ||||
| Maximum | 1.026 | ||||
| Mean of quarter 1 | 0.994 | ||||
| Mean of quarter 2 | 0.999 | ||||
| Mean of quarter 3 | 1.001 | ||||
| Mean of quarter 4 | 1.008 | ||||
| Inter Quartile Range | 0.006 | ||||
| Number outliers low | 1.000 | ||||
| Percentage of outliers low | 0.008 | ||||
| Mean of outliers low | 0.978 | ||||
| Number of outliers high | 6.000 | ||||
| Percentage of outliers high | 0.046 | ||||
| Mean of outliers high | 1.017 | ||||
| Risk estimates for a one-period unit investment (based on Extreme Value Theory) | |||||
| Extreme Value Index (moments method) | 0.133 | ||||
| VaR(95%) (moments method) | 0.006 | ||||
| Expected Shortfall (moments method) | 0.008 | ||||
| Extreme Value Index (regression method) | 0.270 | ||||
| VaR(95%) (regression method) | 0.005 | ||||
| Expected Shortfall (regression method) | 0.007 | ||||
| DRAW DOWN STATISTICS | |||||
| Quartiles of draw downs | |||||
| Number of observations | 8.000 | ||||
| Minimum | 0.001 | ||||
| Quartile 1 | 0.007 | ||||
| Median | 0.011 | ||||
| Quartile 3 | 0.026 | ||||
| Maximum | 0.038 | ||||
| Mean of quarter 1 | 0.003 | ||||
| Mean of quarter 2 | 0.009 | ||||
| Mean of quarter 3 | 0.017 | ||||
| Mean of quarter 4 | 0.036 | ||||
| Inter Quartile Range | 0.019 | ||||
| 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) | 0.116 | ||||
| Compounded annual return (geometric extrapolation) | 0.119 | ||||
| Calmar ratio (compounded annual return / max draw down) | 3.170 | ||||
| Compounded annual return / average of 25% largest draw downs | 3.288 | ||||
| Compounded annual return / Expected Shortfall lognormal | 10.083 | ||||