Step 1. n = 1194 months; mean 0.96 percent; standard deviation 5.30 percent
Step 2. Months down more than five percent: 121 of 1194 = 10.13 percent
Step 3. The count test (bounds strictly outside):
        k   below obs   below pred   above obs   above pred   either obs   either pred
        1     145        189.4         119        189.4         264         378.9
        2      33         27.2          20         27.2          53          54.3
        3      11          1.6           6          1.6          17           3.2

Step 4. Normal quantiles from the series' mean and standard deviation, beside the empirical quantiles (book's rule, type 7):
        prob   normal   empirical
        0.001    -15.41    -23.66
        0.010    -11.36    -13.41
        0.050     -7.75     -7.55
        0.250     -2.61     -1.78
        0.500     +0.96     +1.34
        0.750     +4.53     +3.95
        0.950     +9.68     +7.71
        0.990    +13.29    +12.89
        0.999    +17.33    +36.47
        The fitted curve's one-in-1,200 lower quantile: -15.69 percent

Step 5. Lag-1 autocorrelation of returns 0.09; of squared returns 0.295; rolling 12-month standard deviation from 1.08 to 20.5 percent

Part B, R lane solution: SPY daily returns from the adjusted close series, n = 2765 days; mean +0.0564 percent; standard deviation 1.1208 percent
  Beyond 2 standard deviations: 126 days observed against 125.8 predicted
  Beyond 3 standard deviations: 39 days observed against 7.5 predicted
  Daily skewness (moment measure, Chapter 2's rule): -0.31
  For the record, on the unadjusted closes (price returns, dividends excluded): standard deviation 1.1250 percent; beyond two standard deviations 128 days; beyond three 36 days.

Chapter 3 lab complete.
