EWMA. The table below reports the daily log-returns of the S&P 500 index over 22 consecutive business days. Also reported are the daily estimates of the EWMA volatilities using two constant decay factors, ₁ and ₂ . We use the standard dating convention: the volatility _t+1 reported for Day t + 1 are calculated using the information available on Day t .

Day Daily Ret (%) A B C D E F G H I J K 1.6946 0.2258 0.0030 -2.7377 -0.2132 -1.3845 -0.9885 -0.5416 1.6445 -2.9982 -2.3704 -5.2976 -22.8997 5.1954 8.7089 -3.9995 -0.0121 -8.6418 2.3957 0.0386 4.8079 2.8276 EWMA Volatility (%) with decay li with decay 12 1.0133 0.9741 1.0665 1.0032 1.0355 0.9888 1.0040 0.9739 1.1820 1.0700 1.1472 1.0545 1.1628 1.0658 1.1531 1.0636 1.1258 1.0517 1.1635 1.0743 1.3460 1.1786 1.4284 1.2313 1.8978 1.5207 5.9033 4.2397 5.8633 4.2715 6.0717 4.4692 5.9677 4.4558 5.7859 4.3885 5.9958 4.5740 5.8426 4.5239 5.6647 4.4555 5.6169 4.4665 S T U V (a) Which day was Day M (at least what was the month and year)? (b) Which number is larger, l1 and 12 ? Explain in words without calculations. (c) Using the data reported in the table to calculate li. Day Daily Ret (%) A B C D E F G H I J K 1.6946 0.2258 0.0030 -2.7377 -0.2132 -1.3845 -0.9885 -0.5416 1.6445 -2.9982 -2.3704 -5.2976 -22.8997 5.1954 8.7089 -3.9995 -0.0121 -8.6418 2.3957 0.0386 4.8079 2.8276 EWMA Volatility (%) with decay li with decay 12 1.0133 0.9741 1.0665 1.0032 1.0355 0.9888 1.0040 0.9739 1.1820 1.0700 1.1472 1.0545 1.1628 1.0658 1.1531 1.0636 1.1258 1.0517 1.1635 1.0743 1.3460 1.1786 1.4284 1.2313 1.8978 1.5207 5.9033 4.2397 5.8633 4.2715 6.0717 4.4692 5.9677 4.4558 5.7859 4.3885 5.9958 4.5740 5.8426 4.5239 5.6647 4.4555 5.6169 4.4665 S T U V (a) Which day was Day M (at least what was the month and year)? (b) Which number is larger, l1 and 12 ? Explain in words without calculations. (c) Using the data reported in the table to calculate li