Advanced Statistics: STC Mt. Shasta
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 | -0.082 | ||||
| SD | 0.112 | ||||
| Sharpe ratio (Glass type estimate) | -0.736 | ||||
| Sharpe ratio (Hedges UMVUE) | -0.729 | ||||
| df | 74.000 | ||||
| t | -1.841 | ||||
| p | 0.965 | ||||
| Lowerbound of 95% confidence interval for Sharpe Ratio | -1.527 | ||||
| Upperbound of 95% confidence interval for Sharpe Ratio | 0.059 | ||||
| Lowerbound of 95% CI (Gibbons, Hedeker & Davis approximation) | -1.522 | ||||
| Upperbound of 95% CI (Gibbons, Hedeker & Davis approximation) | 0.064 | ||||
| Statistics related to Sortino ratio | |||||
| Sortino ratio | -0.856 | ||||
| Upside Potential Ratio | 0.719 | ||||
| Upside part of mean | 0.069 | ||||
| Downside part of mean | -0.151 | ||||
| Upside SD | 0.060 | ||||
| Downside SD | 0.096 | ||||
| N nonnegative terms | 17.000 | ||||
| N negative terms | 58.000 | ||||
| Statistics related to linear regression on benchmark | |||||
| N of observations | 75.000 | ||||
| Mean of predictor | 0.228 | ||||
| Mean of criterion | -0.082 | ||||
| SD of predictor | 0.204 | ||||
| SD of criterion | 0.112 | ||||
| Covariance | 0.002 | ||||
| r | 0.067 | ||||
| b (slope, estimate of beta) | 0.037 | ||||
| a (intercept, estimate of alpha) | -0.091 | ||||
| Mean Square Error | 0.013 | ||||
| DF error | 73.000 | ||||
| t(b) | 0.577 | ||||
| p(b) | 0.283 | ||||
| t(a) | -1.921 | ||||
| p(a) | 0.971 | ||||
| Lowerbound of 95% confidence interval for beta | -0.090 | ||||
| Upperbound of 95% confidence interval for beta | 0.164 | ||||
| Lowerbound of 95% confidence interval for alpha | -0.185 | ||||
| Upperbound of 95% confidence interval for alpha | 0.003 | ||||
| Treynor index (mean / b) | -2.235 | ||||
| Jensen alpha (a) | -0.091 | ||||
| Ratio statistics of excess log return rates | |||||
| Statistics related to Sharpe ratio | |||||
| Mean | -0.089 | ||||
| SD | 0.115 | ||||
| Sharpe ratio (Glass type estimate) | -0.772 | ||||
| Sharpe ratio (Hedges UMVUE) | -0.764 | ||||
| df | 74.000 | ||||
| t | -1.931 | ||||
| p | 0.971 | ||||
| Lowerbound of 95% confidence interval for Sharpe Ratio | -1.564 | ||||
| Upperbound of 95% confidence interval for Sharpe Ratio | 0.024 | ||||
| Lowerbound of 95% CI (Gibbons, Hedeker & Davis approximation) | -1.558 | ||||
| Upperbound of 95% CI (Gibbons, Hedeker & Davis approximation) | 0.029 | ||||
| Statistics related to Sortino ratio | |||||
| Sortino ratio | -0.874 | ||||
| Upside Potential Ratio | 0.662 | ||||
| Upside part of mean | 0.067 | ||||
| Downside part of mean | -0.156 | ||||
| Upside SD | 0.058 | ||||
| Downside SD | 0.101 | ||||
| N nonnegative terms | 17.000 | ||||
| N negative terms | 58.000 | ||||
| Statistics related to linear regression on benchmark | |||||
| N of observations | 75.000 | ||||
| Mean of predictor | 0.206 | ||||
| Mean of criterion | -0.089 | ||||
| SD of predictor | 0.196 | ||||
| SD of criterion | 0.115 | ||||
| Covariance | 0.002 | ||||
| r | 0.072 | ||||
| b (slope, estimate of beta) | 0.042 | ||||
| a (intercept, estimate of alpha) | -0.097 | ||||
| Mean Square Error | 0.013 | ||||
| DF error | 73.000 | ||||
| t(b) | 0.615 | ||||
| p(b) | 0.270 | ||||
| t(a) | -2.018 | ||||
| p(a) | 0.976 | ||||
| Lowerbound of 95% confidence interval for beta | -0.094 | ||||
| Upperbound of 95% confidence interval for beta | 0.178 | ||||
| Lowerbound of 95% confidence interval for alpha | -0.193 | ||||
| Upperbound of 95% confidence interval for alpha | -0.001 | ||||
| Treynor index (mean / b) | -2.113 | ||||
| Jensen alpha (a) | -0.097 | ||||
| Risk estimates for a one-period unit investment (parametric) | |||||
| assuming log normal returns and losses (using central moments from Sharpe statistics) | |||||
| VaR(95%) | 0.060 | ||||
| Expected Shortfall on VaR | 0.073 | ||||
| assuming Pareto losses only (using partial moments from Sortino statistics) | |||||
| VaR(95%) | 0.038 | ||||
| Expected Shortfall on VaR | 0.072 | ||||
| ORDER STATISTICS | |||||
| Quartiles of return rates | |||||
| Number of observations | 75.000 | ||||
| Minimum | 0.851 | ||||
| Quartile 1 | 0.992 | ||||
| Median | 1.000 | ||||
| Quartile 3 | 1.003 | ||||
| Maximum | 1.107 | ||||
| Mean of quarter 1 | 0.963 | ||||
| Mean of quarter 2 | 0.998 | ||||
| Mean of quarter 3 | 1.000 | ||||
| Mean of quarter 4 | 1.026 | ||||
| Inter Quartile Range | 0.010 | ||||
| Number outliers low | 10.000 | ||||
| Percentage of outliers low | 0.133 | ||||
| Mean of outliers low | 0.943 | ||||
| Number of outliers high | 9.000 | ||||
| Percentage of outliers high | 0.120 | ||||
| Mean of outliers high | 1.046 | ||||
| Risk estimates for a one-period unit investment (based on Extreme Value Theory) | |||||
| Extreme Value Index (moments method) | 0.389 | ||||
| VaR(95%) (moments method) | 0.029 | ||||
| Expected Shortfall (moments method) | 0.059 | ||||
| Extreme Value Index (regression method) | 0.553 | ||||
| VaR(95%) (regression method) | 0.039 | ||||
| Expected Shortfall (regression method) | 0.104 | ||||
| DRAW DOWN STATISTICS | |||||
| Quartiles of draw downs | |||||
| Number of observations | 4.000 | ||||
| Minimum | 0.045 | ||||
| Quartile 1 | 0.046 | ||||
| Median | 0.059 | ||||
| Quartile 3 | 0.137 | ||||
| Maximum | 0.335 | ||||
| Mean of quarter 1 | 0.045 | ||||
| Mean of quarter 2 | 0.047 | ||||
| Mean of quarter 3 | 0.071 | ||||
| Mean of quarter 4 | 0.335 | ||||
| Inter Quartile Range | 0.091 | ||||
| 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 | 0.335 | ||||
| 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) | -0.039 | ||||
| Compounded annual return (geometric extrapolation) | -0.044 | ||||
| Calmar ratio (compounded annual return / max draw down) | -0.130 | ||||
| Compounded annual return / average of 25% largest draw downs | -0.130 | ||||
| Compounded annual return / Expected Shortfall lognormal | -0.599 | ||||
| ANALYSIS BASED ON DAILY VALUES, FULL HISTORY (Back) | |||||
| RATIO STATISTICS | |||||
| Ratio statistics of excess return rates | |||||
| Statistics related to Sharpe ratio | |||||
| Mean | -0.082 | ||||
| SD | 0.109 | ||||
| Sharpe ratio (Glass type estimate) | -0.756 | ||||
| Sharpe ratio (Hedges UMVUE) | -0.756 | ||||
| df | 1658.000 | ||||
| t | -1.903 | ||||
| p | 0.523 | ||||
| Lowerbound of 95% confidence interval for Sharpe Ratio | -1.536 | ||||
| Upperbound of 95% confidence interval for Sharpe Ratio | 0.023 | ||||
| Lowerbound of 95% CI (Gibbons, Hedeker & Davis approximation) | -1.535 | ||||
| Upperbound of 95% CI (Gibbons, Hedeker & Davis approximation) | 0.023 | ||||
| Statistics related to Sortino ratio | |||||
| Sortino ratio | -0.978 | ||||
| Upside Potential Ratio | 3.536 | ||||
| Upside part of mean | 0.297 | ||||
| Downside part of mean | -0.379 | ||||
| Upside SD | 0.069 | ||||
| Downside SD | 0.084 | ||||
| N nonnegative terms | 319.000 | ||||
| N negative terms | 1340.000 | ||||
| Statistics related to linear regression on benchmark | |||||
| N of observations | 1659.000 | ||||
| Mean of predictor | 0.261 | ||||
| Mean of criterion | -0.082 | ||||
| SD of predictor | 0.245 | ||||
| SD of criterion | 0.109 | ||||
| Covariance | 0.003 | ||||
| r | 0.119 | ||||
| b (slope, estimate of beta) | 0.053 | ||||
| a (intercept, estimate of alpha) | -0.096 | ||||
| Mean Square Error | 0.012 | ||||
| DF error | 1657.000 | ||||
| t(b) | 4.858 | ||||
| p(b) | 0.425 | ||||
| t(a) | -2.232 | ||||
| p(a) | 0.535 | ||||
| Lowerbound of 95% confidence interval for beta | 0.031 | ||||
| Upperbound of 95% confidence interval for beta | 0.074 | ||||
| Lowerbound of 95% confidence interval for alpha | -0.180 | ||||
| Upperbound of 95% confidence interval for alpha | -0.012 | ||||
| Treynor index (mean / b) | -1.563 | ||||
| Jensen alpha (a) | -0.096 | ||||
| Ratio statistics of excess log return rates | |||||
| Statistics related to Sharpe ratio | |||||
| Mean | -0.088 | ||||
| SD | 0.109 | ||||
| Sharpe ratio (Glass type estimate) | -0.806 | ||||
| Sharpe ratio (Hedges UMVUE) | -0.806 | ||||
| df | 1658.000 | ||||
| t | -2.029 | ||||
| p | 0.525 | ||||
| Lowerbound of 95% confidence interval for Sharpe Ratio | -1.586 | ||||
| Upperbound of 95% confidence interval for Sharpe Ratio | -0.027 | ||||
| Lowerbound of 95% CI (Gibbons, Hedeker & Davis approximation) | -1.585 | ||||
| Upperbound of 95% CI (Gibbons, Hedeker & Davis approximation) | -0.027 | ||||
| Statistics related to Sortino ratio | |||||
| Sortino ratio | -1.028 | ||||
| Upside Potential Ratio | 3.439 | ||||
| Upside part of mean | 0.295 | ||||
| Downside part of mean | -0.383 | ||||
| Upside SD | 0.068 | ||||
| Downside SD | 0.086 | ||||
| N nonnegative terms | 319.000 | ||||
| N negative terms | 1340.000 | ||||
| Statistics related to linear regression on benchmark | |||||
| N of observations | 1659.000 | ||||
| Mean of predictor | 0.231 | ||||
| Mean of criterion | -0.088 | ||||
| SD of predictor | 0.246 | ||||
| SD of criterion | 0.109 | ||||
| Covariance | 0.003 | ||||
| r | 0.122 | ||||
| b (slope, estimate of beta) | 0.054 | ||||
| a (intercept, estimate of alpha) | -0.101 | ||||
| Mean Square Error | 0.012 | ||||
| DF error | 1657.000 | ||||
| t(b) | 5.009 | ||||
| p(b) | 0.422 | ||||
| t(a) | -2.331 | ||||
| p(a) | 0.536 | ||||
| Lowerbound of 95% confidence interval for beta | 0.033 | ||||
| Upperbound of 95% confidence interval for beta | 0.075 | ||||
| Lowerbound of 95% confidence interval for alpha | -0.185 | ||||
| Upperbound of 95% confidence interval for alpha | -0.016 | ||||
| Treynor index (mean / b) | -1.624 | ||||
| Jensen alpha (a) | -0.101 | ||||
| Risk estimates for a one-period unit investment (parametric) | |||||
| assuming log normal returns and losses (using central moments from Sharpe statistics) | |||||
| VaR(95%) | 0.011 | ||||
| Expected Shortfall on VaR | 0.014 | ||||
| assuming Pareto losses only (using partial moments from Sortino statistics) | |||||
| VaR(95%) | 0.004 | ||||
| Expected Shortfall on VaR | 0.010 | ||||
| ORDER STATISTICS | |||||
| Quartiles of return rates | |||||
| Number of observations | 1659.000 | ||||
| Minimum | 0.929 | ||||
| Quartile 1 | 1.000 | ||||
| Median | 1.000 | ||||
| Quartile 3 | 1.000 | ||||
| Maximum | 1.067 | ||||
| Mean of quarter 1 | 0.995 | ||||
| Mean of quarter 2 | 1.000 | ||||
| Mean of quarter 3 | 1.000 | ||||
| Mean of quarter 4 | 1.005 | ||||
| Inter Quartile Range | 0.000 | ||||
| Number outliers low | 347.000 | ||||
| Percentage of outliers low | 0.209 | ||||
| Mean of outliers low | 0.994 | ||||
| Number of outliers high | 328.000 | ||||
| Percentage of outliers high | 0.198 | ||||
| Mean of outliers high | 1.006 | ||||
| Risk estimates for a one-period unit investment (based on Extreme Value Theory) | |||||
| Extreme Value Index (moments method) | 0.608 | ||||
| VaR(95%) (moments method) | 0.004 | ||||
| Expected Shortfall (moments method) | 0.012 | ||||
| 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 | 12.000 | ||||
| Minimum | 0.000 | ||||
| Quartile 1 | 0.008 | ||||
| Median | 0.012 | ||||
| Quartile 3 | 0.056 | ||||
| Maximum | 0.357 | ||||
| Mean of quarter 1 | 0.002 | ||||
| Mean of quarter 2 | 0.011 | ||||
| Mean of quarter 3 | 0.032 | ||||
| Mean of quarter 4 | 0.170 | ||||
| Inter Quartile Range | 0.048 | ||||
| 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 | 0.357 | ||||
| Risk estimates based on draw downs (based on Extreme Value Theory) | |||||
| Extreme Value Index (moments method) | 0.672 | ||||
| VaR(95%) (moments method) | 0.187 | ||||
| Expected Shortfall (moments method) | 0.614 | ||||
| Extreme Value Index (regression method) | 3.734 | ||||
| VaR(95%) (regression method) | 0.439 | ||||
| Expected Shortfall (regression method) | NA | ||||
| COMBINED STATISTICS | |||||
| Annualized return (arithmetic extrapolation) | -0.038 | ||||
| Compounded annual return (geometric extrapolation) | -0.043 | ||||
| Calmar ratio (compounded annual return / max draw down) | -0.121 | ||||
| Compounded annual return / average of 25% largest draw downs | -0.253 | ||||
| Compounded annual return / Expected Shortfall lognormal | -3.045 | ||||
| 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 | 1.308 | ||||
| Mean of criterion | -0.044 | ||||
| SD of predictor | 0.321 | ||||
| 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 | 1.254 | ||||
| Mean of criterion | -0.044 | ||||
| SD of predictor | 0.319 | ||||
| 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) | -8549392182198841.000 | ||||
| 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) | 118103821164464684845170323095552.000 | ||||
| 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 | ||||