four-day returns of stock x: (-.3, .3, -.3, .3) -> MAD = 0; four-day returns of stock y: (-.5, .5, -.5, .5) -> MAD = 0.

The A in MAD stands for 'absolute', so no, the MAD for those two stocks is .3 and .5 respectively - versus standard deviations of 0.35 and 0.58.

No, it's the median absolute deviation. Absolute deviation is the absolute difference between an average and a data point. So (-.3, .3, -.3, .3) -> MAD = 0.3; (-.5, .5, -.5, .5) -> MAD = 0.5.

You have calculated the mean. This is only the first step in calculating the MAD (mean absolute deviation). You then need to take the absolute value of the difference (deviation) of each datapoint from this mean - for your x you get (.3, .3, .3, .3) and for your y (.5, .5, .5, .5). Finally you take the mean of these absolute deviations to get MAD(x)=0.3 and MAD(x)=0.5.

nope. look at what the "A" in MAD stands for.