Table 3 Results on risk for the AR (1)-GARCH (1,1) process. The table reports the actual standard deviations of the simulated returns and their theoretical values for eight AR (1)-GARCH (1,1) processes with different parameters. The actual standard deviation of the simulated returns is denoted by σsimul, and its theoretical value is denoted by σg
From: How to compare market efficiency? The Sharpe ratio based on the ARMA-GARCH forecast
Group | (1) | (2) | (3) | (4) | (5) | (6) | (7) | (8) |
|---|---|---|---|---|---|---|---|---|
a1 | 0.1 | 0.1 | 0.1 | 0.1 | 0.1 | 0.1 | 0.1 | 0.1 |
φ | 0.0001 | 0.0001 | 0.0001 | 0.0001 | 0.0004 | 0.0004 | 0.0004 | 0.0004 |
α1 | 0.1 | 0.1 | 0.2 | 0.2 | 0.1 | 0.1 | 0.2 | 0.2 |
β1 | 0.1 | 0.2 | 0.1 | 0.2 | 0.1 | 0.2 | 0.1 | 0.2 |
σg | 0.0112 | 0.0120 | 0.0120 | 0.0129 | 0.0224 | 0.0239 | 0.0239 | 0.0259 |
σsimul | 0.0114 | 0.0120 | 0.0121 | 0.0127 | 0.0224 | 0.0236 | 0.0238 | 0.0262 |