### Advanced Statistics: Green Dog

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 | 0.313 | ||||

SD | 0.678 | ||||

Sharpe ratio (Glass type estimate) | 0.462 | ||||

Sharpe ratio (Hedges UMVUE) | 0.452 | ||||

df | 37.000 | ||||

t | 0.821 | ||||

p | 0.208 | ||||

Lowerbound of 95% confidence interval for Sharpe Ratio | -0.648 | ||||

Upperbound of 95% confidence interval for Sharpe Ratio | 1.565 | ||||

Lowerbound of 95% CI (Gibbons, Hedeker & Davis approximation) | -0.654 | ||||

Upperbound of 95% CI (Gibbons, Hedeker & Davis approximation) | 1.558 | ||||

Statistics related to Sortino ratio | |||||

Sortino ratio | 0.803 | ||||

Upside Potential Ratio | 2.314 | ||||

Upside part of mean | 0.902 | ||||

Downside part of mean | -0.589 | ||||

Upside SD | 0.551 | ||||

Downside SD | 0.390 | ||||

N nonnegative terms | 18.000 | ||||

N negative terms | 20.000 | ||||

Statistics related to linear regression on benchmark | |||||

N of observations | 38.000 | ||||

Mean of predictor | 0.173 | ||||

Mean of criterion | 0.313 | ||||

SD of predictor | 0.135 | ||||

SD of criterion | 0.678 | ||||

Covariance | 0.018 | ||||

r | 0.198 | ||||

b (slope, estimate of beta) | 0.999 | ||||

a (intercept, estimate of alpha) | 0.140 | ||||

Mean Square Error | 0.454 | ||||

DF error | 36.000 | ||||

t(b) | 1.214 | ||||

p(b) | 0.116 | ||||

t(a) | 0.347 | ||||

p(a) | 0.365 | ||||

Lowerbound of 95% confidence interval for beta | -0.670 | ||||

Upperbound of 95% confidence interval for beta | 2.668 | ||||

Lowerbound of 95% confidence interval for alpha | -0.679 | ||||

Upperbound of 95% confidence interval for alpha | 0.960 | ||||

Treynor index (mean / b) | 0.313 | ||||

Jensen alpha (a) | 0.140 | ||||

Ratio statistics of excess log return rates | |||||

Statistics related to Sharpe ratio | |||||

Mean | 0.097 | ||||

SD | 0.663 | ||||

Sharpe ratio (Glass type estimate) | 0.147 | ||||

Sharpe ratio (Hedges UMVUE) | 0.144 | ||||

df | 37.000 | ||||

t | 0.262 | ||||

p | 0.398 | ||||

Lowerbound of 95% confidence interval for Sharpe Ratio | -0.956 | ||||

Upperbound of 95% confidence interval for Sharpe Ratio | 1.248 | ||||

Lowerbound of 95% CI (Gibbons, Hedeker & Davis approximation) | -0.958 | ||||

Upperbound of 95% CI (Gibbons, Hedeker & Davis approximation) | 1.246 | ||||

Statistics related to Sortino ratio | |||||

Sortino ratio | 0.207 | ||||

Upside Potential Ratio | 1.662 | ||||

Upside part of mean | 0.781 | ||||

Downside part of mean | -0.684 | ||||

Upside SD | 0.456 | ||||

Downside SD | 0.470 | ||||

N nonnegative terms | 18.000 | ||||

N negative terms | 20.000 | ||||

Statistics related to linear regression on benchmark | |||||

N of observations | 38.000 | ||||

Mean of predictor | 0.162 | ||||

Mean of criterion | 0.097 | ||||

SD of predictor | 0.134 | ||||

SD of criterion | 0.663 | ||||

Covariance | 0.018 | ||||

r | 0.203 | ||||

b (slope, estimate of beta) | 1.003 | ||||

a (intercept, estimate of alpha) | -0.065 | ||||

Mean Square Error | 0.433 | ||||

DF error | 36.000 | ||||

t(b) | 1.244 | ||||

p(b) | 0.111 | ||||

t(a) | -0.166 | ||||

p(a) | 0.566 | ||||

Lowerbound of 95% confidence interval for beta | -0.632 | ||||

Upperbound of 95% confidence interval for beta | 2.639 | ||||

Lowerbound of 95% confidence interval for alpha | -0.860 | ||||

Upperbound of 95% confidence interval for alpha | 0.730 | ||||

Treynor index (mean / b) | 0.097 | ||||

Jensen alpha (a) | -0.065 | ||||

Risk estimates for a one-period unit investment (parametric) | |||||

assuming log normal returns and losses (using central moments from Sharpe statistics) | |||||

VaR(95%) | 0.264 | ||||

Expected Shortfall on VaR | 0.319 | ||||

assuming Pareto losses only (using partial moments from Sortino statistics) | |||||

VaR(95%) | 0.116 | ||||

Expected Shortfall on VaR | 0.236 | ||||

ORDER STATISTICS | |||||

Quartiles of return rates | |||||

Number of observations | 38.000 | ||||

Minimum | 0.569 | ||||

Quartile 1 | 1.000 | ||||

Median | 1.000 | ||||

Quartile 3 | 1.094 | ||||

Maximum | 1.647 | ||||

Mean of quarter 1 | 0.821 | ||||

Mean of quarter 2 | 1.000 | ||||

Mean of quarter 3 | 1.034 | ||||

Mean of quarter 4 | 1.261 | ||||

Inter Quartile Range | 0.094 | ||||

Number outliers low | 6.000 | ||||

Percentage of outliers low | 0.158 | ||||

Mean of outliers low | 0.741 | ||||

Number of outliers high | 4.000 | ||||

Percentage of outliers high | 0.105 | ||||

Mean of outliers high | 1.442 | ||||

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) | -0.394 | ||||

VaR(95%) (regression method) | 0.254 | ||||

Expected Shortfall (regression method) | 0.333 | ||||

DRAW DOWN STATISTICS | |||||

Quartiles of draw downs | |||||

Number of observations | 2.000 | ||||

Minimum | 0.221 | ||||

Quartile 1 | 0.352 | ||||

Median | 0.483 | ||||

Quartile 3 | 0.613 | ||||

Maximum | 0.744 | ||||

Mean of quarter 1 | 0.221 | ||||

Mean of quarter 2 | NA | ||||

Mean of quarter 3 | NA | ||||

Mean of quarter 4 | 0.744 | ||||

Inter Quartile Range | 0.261 | ||||

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) | 0.178 | ||||

Compounded annual return (geometric extrapolation) | 0.152 | ||||

Calmar ratio (compounded annual return / max draw down) | 0.204 | ||||

Compounded annual return / average of 25% largest draw downs | 0.204 | ||||

Compounded annual return / Expected Shortfall lognormal | 0.476 | ||||

ANALYSIS BASED ON DAILY VALUES, FULL HISTORY (Back) | |||||

RATIO STATISTICS | |||||

Ratio statistics of excess return rates | |||||

Statistics related to Sharpe ratio | |||||

Mean | 0.244 | ||||

SD | 0.575 | ||||

Sharpe ratio (Glass type estimate) | 0.424 | ||||

Sharpe ratio (Hedges UMVUE) | 0.423 | ||||

df | 850.000 | ||||

t | 0.764 | ||||

p | 0.223 | ||||

Lowerbound of 95% confidence interval for Sharpe Ratio | -0.664 | ||||

Upperbound of 95% confidence interval for Sharpe Ratio | 1.511 | ||||

Lowerbound of 95% CI (Gibbons, Hedeker & Davis approximation) | -0.664 | ||||

Upperbound of 95% CI (Gibbons, Hedeker & Davis approximation) | 1.511 | ||||

Statistics related to Sortino ratio | |||||

Sortino ratio | 0.735 | ||||

Upside Potential Ratio | 6.244 | ||||

Upside part of mean | 2.070 | ||||

Downside part of mean | -1.826 | ||||

Upside SD | 0.470 | ||||

Downside SD | 0.331 | ||||

N nonnegative terms | 303.000 | ||||

N negative terms | 548.000 | ||||

Statistics related to linear regression on benchmark | |||||

N of observations | 851.000 | ||||

Mean of predictor | 0.188 | ||||

Mean of criterion | 0.244 | ||||

SD of predictor | 0.163 | ||||

SD of criterion | 0.575 | ||||

Covariance | 0.007 | ||||

r | 0.073 | ||||

b (slope, estimate of beta) | 0.258 | ||||

a (intercept, estimate of alpha) | 0.195 | ||||

Mean Square Error | 0.329 | ||||

DF error | 849.000 | ||||

t(b) | 2.130 | ||||

p(b) | 0.017 | ||||

t(a) | 0.611 | ||||

p(a) | 0.271 | ||||

Lowerbound of 95% confidence interval for beta | 0.020 | ||||

Upperbound of 95% confidence interval for beta | 0.495 | ||||

Lowerbound of 95% confidence interval for alpha | -0.432 | ||||

Upperbound of 95% confidence interval for alpha | 0.822 | ||||

Treynor index (mean / b) | 0.946 | ||||

Jensen alpha (a) | 0.195 | ||||

Ratio statistics of excess log return rates | |||||

Statistics related to Sharpe ratio | |||||

Mean | 0.094 | ||||

SD | 0.537 | ||||

Sharpe ratio (Glass type estimate) | 0.175 | ||||

Sharpe ratio (Hedges UMVUE) | 0.175 | ||||

df | 850.000 | ||||

t | 0.315 | ||||

p | 0.376 | ||||

Lowerbound of 95% confidence interval for Sharpe Ratio | -0.913 | ||||

Upperbound of 95% confidence interval for Sharpe Ratio | 1.262 | ||||

Lowerbound of 95% CI (Gibbons, Hedeker & Davis approximation) | -0.913 | ||||

Upperbound of 95% CI (Gibbons, Hedeker & Davis approximation) | 1.262 | ||||

Statistics related to Sortino ratio | |||||

Sortino ratio | 0.266 | ||||

Upside Potential Ratio | 5.605 | ||||

Upside part of mean | 1.979 | ||||

Downside part of mean | -1.886 | ||||

Upside SD | 0.405 | ||||

Downside SD | 0.353 | ||||

N nonnegative terms | 303.000 | ||||

N negative terms | 548.000 | ||||

Statistics related to linear regression on benchmark | |||||

N of observations | 851.000 | ||||

Mean of predictor | 0.175 | ||||

Mean of criterion | 0.094 | ||||

SD of predictor | 0.163 | ||||

SD of criterion | 0.537 | ||||

Covariance | 0.006 | ||||

r | 0.073 | ||||

b (slope, estimate of beta) | 0.241 | ||||

a (intercept, estimate of alpha) | 0.052 | ||||

Mean Square Error | 0.288 | ||||

DF error | 849.000 | ||||

t(b) | 2.137 | ||||

p(b) | 0.016 | ||||

t(a) | 0.174 | ||||

p(a) | 0.431 | ||||

Lowerbound of 95% confidence interval for beta | 0.020 | ||||

Upperbound of 95% confidence interval for beta | 0.462 | ||||

Lowerbound of 95% confidence interval for alpha | -0.533 | ||||

Upperbound of 95% confidence interval for alpha | 0.637 | ||||

Treynor index (mean / b) | 0.390 | ||||

Jensen alpha (a) | 0.052 | ||||

Risk estimates for a one-period unit investment (parametric) | |||||

assuming log normal returns and losses (using central moments from Sharpe statistics) | |||||

VaR(95%) | 0.053 | ||||

Expected Shortfall on VaR | 0.066 | ||||

assuming Pareto losses only (using partial moments from Sortino statistics) | |||||

VaR(95%) | 0.018 | ||||

Expected Shortfall on VaR | 0.040 | ||||

ORDER STATISTICS | |||||

Quartiles of return rates | |||||

Number of observations | 851.000 | ||||

Minimum | 0.743 | ||||

Quartile 1 | 0.997 | ||||

Median | 1.000 | ||||

Quartile 3 | 1.006 | ||||

Maximum | 1.591 | ||||

Mean of quarter 1 | 0.973 | ||||

Mean of quarter 2 | 1.000 | ||||

Mean of quarter 3 | 1.001 | ||||

Mean of quarter 4 | 1.030 | ||||

Inter Quartile Range | 0.010 | ||||

Number outliers low | 105.000 | ||||

Percentage of outliers low | 0.123 | ||||

Mean of outliers low | 0.954 | ||||

Number of outliers high | 104.000 | ||||

Percentage of outliers high | 0.122 | ||||

Mean of outliers high | 1.049 | ||||

Risk estimates for a one-period unit investment (based on Extreme Value Theory) | |||||

Extreme Value Index (moments method) | 0.553 | ||||

VaR(95%) (moments method) | 0.017 | ||||

Expected Shortfall (moments method) | 0.046 | ||||

Extreme Value Index (regression method) | 0.258 | ||||

VaR(95%) (regression method) | 0.026 | ||||

Expected Shortfall (regression method) | 0.048 | ||||

DRAW DOWN STATISTICS | |||||

Quartiles of draw downs | |||||

Number of observations | 27.000 | ||||

Minimum | 0.000 | ||||

Quartile 1 | 0.018 | ||||

Median | 0.029 | ||||

Quartile 3 | 0.050 | ||||

Maximum | 0.786 | ||||

Mean of quarter 1 | 0.007 | ||||

Mean of quarter 2 | 0.025 | ||||

Mean of quarter 3 | 0.040 | ||||

Mean of quarter 4 | 0.222 | ||||

Inter Quartile Range | 0.032 | ||||

Number outliers low | 0.000 | ||||

Percentage of outliers low | 0.000 | ||||

Mean of outliers low | NA | ||||

Number of outliers high | 3.000 | ||||

Percentage of outliers high | 0.111 | ||||

Mean of outliers high | 0.427 | ||||

Risk estimates based on draw downs (based on Extreme Value Theory) | |||||

Extreme Value Index (moments method) | 0.872 | ||||

VaR(95%) (moments method) | 0.227 | ||||

Expected Shortfall (moments method) | 1.880 | ||||

Extreme Value Index (regression method) | 1.631 | ||||

VaR(95%) (regression method) | 0.233 | ||||

Expected Shortfall (regression method) | NA | ||||

COMBINED STATISTICS | |||||

Annualized return (arithmetic extrapolation) | 0.174 | ||||

Compounded annual return (geometric extrapolation) | 0.148 | ||||

Calmar ratio (compounded annual return / max draw down) | 0.188 | ||||

Compounded annual return / average of 25% largest draw downs | 0.667 | ||||

Compounded annual return / Expected Shortfall lognormal | 2.248 | ||||

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) | -972.869 | ||||

Sharpe ratio (Hedges UMVUE) | -967.245 | ||||

df | 130.000 | ||||

t | -687.922 | ||||

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) | -1084.848 | ||||

Upperbound of 95% CI (Gibbons, Hedeker & Davis approximation) | -849.642 | ||||

Statistics related to Sortino ratio | |||||

Sortino ratio | -16.184 | ||||

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 | 0.411 | ||||

Mean of criterion | -0.044 | ||||

SD of predictor | 0.274 | ||||

SD of criterion | 0.000 | ||||

Covariance | 0.000 | ||||

r | 0.175 | ||||

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) | 2.018 | ||||

p(b) | 0.389 | ||||

t(a) | -693.204 | ||||

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) | -1523.594 | ||||

Jensen alpha (a) | -0.044 | ||||

Ratio statistics of excess log return rates | |||||

Statistics related to Sharpe ratio | |||||

Mean | -0.044 | ||||

SD | 0.000 | ||||

Sharpe ratio (Glass type estimate) | -972.803 | ||||

Sharpe ratio (Hedges UMVUE) | -967.179 | ||||

df | 130.000 | ||||

t | -687.875 | ||||

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) | -1084.774 | ||||

Upperbound of 95% CI (Gibbons, Hedeker & Davis approximation) | -849.584 | ||||

Statistics related to Sortino ratio | |||||

Sortino ratio | -16.184 | ||||

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 | 0.373 | ||||

Mean of criterion | -0.044 | ||||

SD of predictor | 0.276 | ||||

SD of criterion | 0.000 | ||||

Covariance | 0.000 | ||||

r | 0.171 | ||||

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) | 1.971 | ||||

p(b) | 0.392 | ||||

t(a) | -693.210 | ||||

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) | -1573.335 | ||||

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 | 1.000 | ||||

Percentage of outliers high | 0.008 | ||||

Mean of outliers high | 1.000 | ||||

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 | 0.368 |