Advanced Statistics: Short-Term Stock Index Program (SPY)
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 | -0.035 | ||||
| SD | 0.019 | ||||
| Sharpe ratio (Glass type estimate) | -1.823 | ||||
| Sharpe ratio (Hedges UMVUE) | -1.806 | ||||
| df | 82.000 | ||||
| t | -4.794 | ||||
| p | 1.000 | ||||
| Lowerbound of 95% confidence interval for Sharpe Ratio | -2.614 | ||||
| Upperbound of 95% confidence interval for Sharpe Ratio | -1.022 | ||||
| Lowerbound of 95% CI (Gibbons, Hedeker & Davis approximation) | -2.601 | ||||
| Upperbound of 95% CI (Gibbons, Hedeker & Davis approximation) | -1.011 | ||||
| Statistics related to Sortino ratio | |||||
| Sortino ratio | -2.580 | ||||
| Upside Potential Ratio | 0.666 | ||||
| Upside part of mean | 0.009 | ||||
| Downside part of mean | -0.045 | ||||
| Upside SD | 0.017 | ||||
| Downside SD | 0.014 | ||||
| N nonnegative terms | 2.000 | ||||
| N negative terms | 81.000 | ||||
| Statistics related to linear regression on benchmark | |||||
| N of observations | 83.000 | ||||
| Mean of predictor | 0.237 | ||||
| Mean of criterion | -0.035 | ||||
| SD of predictor | 0.276 | ||||
| SD of criterion | 0.019 | ||||
| Covariance | 0.000 | ||||
| r | 0.007 | ||||
| b (slope, estimate of beta) | 0.001 | ||||
| a (intercept, estimate of alpha) | -0.036 | ||||
| Mean Square Error | 0.000 | ||||
| DF error | 81.000 | ||||
| t(b) | 0.067 | ||||
| p(b) | 0.473 | ||||
| t(a) | -4.639 | ||||
| p(a) | 1.000 | ||||
| Lowerbound of 95% confidence interval for beta | -0.015 | ||||
| Upperbound of 95% confidence interval for beta | 0.016 | ||||
| Lowerbound of 95% confidence interval for alpha | -0.051 | ||||
| Upperbound of 95% confidence interval for alpha | -0.020 | ||||
| Treynor index (mean / b) | -67.812 | ||||
| Jensen alpha (a) | -0.036 | ||||
| Ratio statistics of excess log return rates | |||||
| Statistics related to Sharpe ratio | |||||
| Mean | -0.036 | ||||
| SD | 0.019 | ||||
| Sharpe ratio (Glass type estimate) | -1.858 | ||||
| Sharpe ratio (Hedges UMVUE) | -1.841 | ||||
| df | 82.000 | ||||
| t | -4.886 | ||||
| p | 1.000 | ||||
| Lowerbound of 95% confidence interval for Sharpe Ratio | -2.651 | ||||
| Upperbound of 95% confidence interval for Sharpe Ratio | -1.056 | ||||
| Lowerbound of 95% CI (Gibbons, Hedeker & Davis approximation) | -2.638 | ||||
| Upperbound of 95% CI (Gibbons, Hedeker & Davis approximation) | -1.044 | ||||
| Statistics related to Sortino ratio | |||||
| Sortino ratio | -2.589 | ||||
| Upside Potential Ratio | 0.654 | ||||
| Upside part of mean | 0.009 | ||||
| Downside part of mean | -0.045 | ||||
| Upside SD | 0.017 | ||||
| Downside SD | 0.014 | ||||
| N nonnegative terms | 2.000 | ||||
| N negative terms | 81.000 | ||||
| Statistics related to linear regression on benchmark | |||||
| N of observations | 83.000 | ||||
| Mean of predictor | 0.197 | ||||
| Mean of criterion | -0.036 | ||||
| SD of predictor | 0.276 | ||||
| SD of criterion | 0.019 | ||||
| Covariance | 0.000 | ||||
| r | 0.013 | ||||
| b (slope, estimate of beta) | 0.001 | ||||
| a (intercept, estimate of alpha) | -0.036 | ||||
| Mean Square Error | 0.000 | ||||
| DF error | 81.000 | ||||
| t(b) | 0.114 | ||||
| p(b) | 0.455 | ||||
| t(a) | -4.779 | ||||
| p(a) | 1.000 | ||||
| Lowerbound of 95% confidence interval for beta | -0.014 | ||||
| Upperbound of 95% confidence interval for beta | 0.016 | ||||
| Lowerbound of 95% confidence interval for alpha | -0.051 | ||||
| Upperbound of 95% confidence interval for alpha | -0.021 | ||||
| Treynor index (mean / b) | -40.592 | ||||
| Jensen alpha (a) | -0.036 | ||||
| Risk estimates for a one-period unit investment (parametric) | |||||
| assuming log normal returns and losses (using central moments from Sharpe statistics) | |||||
| VaR(95%) | 0.012 | ||||
| Expected Shortfall on VaR | 0.014 | ||||
| assuming Pareto losses only (using partial moments from Sortino statistics) | |||||
| VaR(95%) | 0.005 | ||||
| Expected Shortfall on VaR | 0.005 | ||||
| ORDER STATISTICS | |||||
| Quartiles of return rates | |||||
| Number of observations | 83.000 | ||||
| Minimum | 0.989 | ||||
| Quartile 1 | 1.000 | ||||
| Median | 1.000 | ||||
| Quartile 3 | 1.000 | ||||
| Maximum | 1.036 | ||||
| Mean of quarter 1 | 0.999 | ||||
| Mean of quarter 2 | 1.000 | ||||
| Mean of quarter 3 | 1.000 | ||||
| Mean of quarter 4 | 1.003 | ||||
| Inter Quartile Range | 0.000 | ||||
| Number outliers low | 3.000 | ||||
| Percentage of outliers low | 0.036 | ||||
| Mean of outliers low | 0.996 | ||||
| Number of outliers high | 5.000 | ||||
| Percentage of outliers high | 0.060 | ||||
| Mean of outliers high | 1.015 | ||||
| Risk estimates for a one-period unit investment (based on Extreme Value Theory) | |||||
| Extreme Value Index (moments method) | -11.540 | ||||
| VaR(95%) (moments method) | -0.506 | ||||
| Expected Shortfall (moments method) | NA | ||||
| Extreme Value Index (regression method) | 1.439 | ||||
| VaR(95%) (regression method) | -0.001 | ||||
| Expected Shortfall (regression method) | NA | ||||
| DRAW DOWN STATISTICS | |||||
| Quartiles of draw downs | |||||
| Number of observations | 2.000 | ||||
| Minimum | 0.002 | ||||
| Quartile 1 | 0.004 | ||||
| Median | 0.007 | ||||
| Quartile 3 | 0.009 | ||||
| Maximum | 0.011 | ||||
| Mean of quarter 1 | 0.002 | ||||
| Mean of quarter 2 | NA | ||||
| Mean of quarter 3 | NA | ||||
| Mean of quarter 4 | 0.011 | ||||
| Inter Quartile Range | 0.005 | ||||
| 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) | 0.009 | ||||
| Compounded annual return (geometric extrapolation) | 0.008 | ||||
| Calmar ratio (compounded annual return / max draw down) | 0.750 | ||||
| Compounded annual return / average of 25% largest draw downs | 0.750 | ||||
| Compounded annual return / Expected Shortfall lognormal | 0.592 | ||||
| ANALYSIS BASED ON DAILY VALUES, FULL HISTORY (Back) | |||||
| RATIO STATISTICS | |||||
| Ratio statistics of excess return rates | |||||
| Statistics related to Sharpe ratio | |||||
| Mean | -0.034 | ||||
| SD | 0.060 | ||||
| Sharpe ratio (Glass type estimate) | -0.564 | ||||
| Sharpe ratio (Hedges UMVUE) | -0.564 | ||||
| df | 1812.000 | ||||
| t | -1.485 | ||||
| p | 0.517 | ||||
| Lowerbound of 95% confidence interval for Sharpe Ratio | -1.310 | ||||
| Upperbound of 95% confidence interval for Sharpe Ratio | 0.181 | ||||
| Lowerbound of 95% CI (Gibbons, Hedeker & Davis approximation) | -1.309 | ||||
| Upperbound of 95% CI (Gibbons, Hedeker & Davis approximation) | 0.181 | ||||
| Statistics related to Sortino ratio | |||||
| Sortino ratio | -0.823 | ||||
| Upside Potential Ratio | 1.226 | ||||
| Upside part of mean | 0.050 | ||||
| Downside part of mean | -0.084 | ||||
| Upside SD | 0.044 | ||||
| Downside SD | 0.041 | ||||
| N nonnegative terms | 43.000 | ||||
| N negative terms | 1770.000 | ||||
| Statistics related to linear regression on benchmark | |||||
| N of observations | 1813.000 | ||||
| Mean of predictor | 0.339 | ||||
| Mean of criterion | -0.034 | ||||
| SD of predictor | 0.533 | ||||
| SD of criterion | 0.060 | ||||
| Covariance | 0.004 | ||||
| r | 0.114 | ||||
| b (slope, estimate of beta) | 0.013 | ||||
| a (intercept, estimate of alpha) | -0.038 | ||||
| Mean Square Error | 0.004 | ||||
| DF error | 1811.000 | ||||
| t(b) | 4.886 | ||||
| p(b) | 0.428 | ||||
| t(a) | -1.685 | ||||
| p(a) | 0.525 | ||||
| Lowerbound of 95% confidence interval for beta | 0.008 | ||||
| Upperbound of 95% confidence interval for beta | 0.018 | ||||
| Lowerbound of 95% confidence interval for alpha | -0.083 | ||||
| Upperbound of 95% confidence interval for alpha | 0.006 | ||||
| Treynor index (mean / b) | -2.637 | ||||
| Jensen alpha (a) | -0.038 | ||||
| Ratio statistics of excess log return rates | |||||
| Statistics related to Sharpe ratio | |||||
| Mean | -0.036 | ||||
| SD | 0.060 | ||||
| Sharpe ratio (Glass type estimate) | -0.595 | ||||
| Sharpe ratio (Hedges UMVUE) | -0.594 | ||||
| df | 1812.000 | ||||
| t | -1.564 | ||||
| p | 0.518 | ||||
| Lowerbound of 95% confidence interval for Sharpe Ratio | -1.340 | ||||
| Upperbound of 95% confidence interval for Sharpe Ratio | 0.151 | ||||
| Lowerbound of 95% CI (Gibbons, Hedeker & Davis approximation) | -1.340 | ||||
| Upperbound of 95% CI (Gibbons, Hedeker & Davis approximation) | 0.151 | ||||
| Statistics related to Sortino ratio | |||||
| Sortino ratio | -0.844 | ||||
| Upside Potential Ratio | 1.172 | ||||
| Upside part of mean | 0.049 | ||||
| Downside part of mean | -0.085 | ||||
| Upside SD | 0.043 | ||||
| Downside SD | 0.042 | ||||
| N nonnegative terms | 43.000 | ||||
| N negative terms | 1770.000 | ||||
| Statistics related to linear regression on benchmark | |||||
| N of observations | 1813.000 | ||||
| Mean of predictor | 0.198 | ||||
| Mean of criterion | -0.036 | ||||
| SD of predictor | 0.530 | ||||
| SD of criterion | 0.060 | ||||
| Covariance | 0.004 | ||||
| r | 0.115 | ||||
| b (slope, estimate of beta) | 0.013 | ||||
| a (intercept, estimate of alpha) | -0.038 | ||||
| Mean Square Error | 0.004 | ||||
| DF error | 1811.000 | ||||
| t(b) | 4.919 | ||||
| p(b) | 0.427 | ||||
| t(a) | -1.687 | ||||
| p(a) | 0.525 | ||||
| Lowerbound of 95% confidence interval for beta | 0.008 | ||||
| Upperbound of 95% confidence interval for beta | 0.018 | ||||
| Lowerbound of 95% confidence interval for alpha | -0.083 | ||||
| Upperbound of 95% confidence interval for alpha | 0.006 | ||||
| Treynor index (mean / b) | -2.743 | ||||
| Jensen alpha (a) | -0.038 | ||||
| Risk estimates for a one-period unit investment (parametric) | |||||
| assuming log normal returns and losses (using central moments from Sharpe statistics) | |||||
| VaR(95%) | 0.006 | ||||
| Expected Shortfall on VaR | 0.008 | ||||
| assuming Pareto losses only (using partial moments from Sortino statistics) | |||||
| VaR(95%) | 0.001 | ||||
| Expected Shortfall on VaR | 0.002 | ||||
| ORDER STATISTICS | |||||
| Quartiles of return rates | |||||
| Number of observations | 1813.000 | ||||
| Minimum | 0.941 | ||||
| Quartile 1 | 1.000 | ||||
| Median | 1.000 | ||||
| Quartile 3 | 1.000 | ||||
| Maximum | 1.060 | ||||
| Mean of quarter 1 | 0.999 | ||||
| Mean of quarter 2 | 1.000 | ||||
| Mean of quarter 3 | 1.000 | ||||
| Mean of quarter 4 | 1.001 | ||||
| Inter Quartile Range | 0.000 | ||||
| Number outliers low | 42.000 | ||||
| Percentage of outliers low | 0.023 | ||||
| Mean of outliers low | 0.993 | ||||
| Number of outliers high | 59.000 | ||||
| Percentage of outliers high | 0.033 | ||||
| Mean of outliers high | 1.006 | ||||
| Risk estimates for a one-period unit investment (based on Extreme Value Theory) | |||||
| Extreme Value Index (moments method) | 1.221 | ||||
| VaR(95%) (moments method) | 0.000 | ||||
| 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 | 15.000 | ||||
| Minimum | 0.002 | ||||
| Quartile 1 | 0.002 | ||||
| Median | 0.002 | ||||
| Quartile 3 | 0.027 | ||||
| Maximum | 0.069 | ||||
| Mean of quarter 1 | 0.002 | ||||
| Mean of quarter 2 | 0.002 | ||||
| Mean of quarter 3 | 0.002 | ||||
| Mean of quarter 4 | 0.060 | ||||
| Inter Quartile Range | 0.025 | ||||
| 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 | 0.067 | ||||
| Mean of outliers high | 0.069 | ||||
| Risk estimates based on draw downs (based on Extreme Value Theory) | |||||
| Extreme Value Index (moments method) | -1.717 | ||||
| VaR(95%) (moments method) | 0.065 | ||||
| Expected Shortfall (moments method) | 0.066 | ||||
| Extreme Value Index (regression method) | -0.196 | ||||
| VaR(95%) (regression method) | 0.063 | ||||
| Expected Shortfall (regression method) | 0.068 | ||||
| COMBINED STATISTICS | |||||
| Annualized return (arithmetic extrapolation) | 0.009 | ||||
| Compounded annual return (geometric extrapolation) | 0.008 | ||||
| Calmar ratio (compounded annual return / max draw down) | 0.122 | ||||
| Compounded annual return / average of 25% largest draw downs | 0.141 | ||||
| Compounded annual return / Expected Shortfall lognormal | 1.092 | ||||
| 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 | 1.119 | ||||
| Mean of criterion | -0.044 | ||||
| SD of predictor | 0.505 | ||||
| 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 | 0.988 | ||||
| Mean of criterion | -0.044 | ||||
| SD of predictor | 0.512 | ||||
| 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) | -8737311210347733.000 | ||||
| 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) | 217074681322916667606960999235584.000 | ||||
| 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 | ||||