5. The following table presents sample daily historical price data for a stock whose returns are given in the third column.

Time Pricet Returnt 0 30.000 N.A.

1 30.125 0.00417 2 30.250 0.00415 3 30.125 20.00413 4 32.000 0.06224 5 34.000 0.06250 6 31.000 20.08824 7 32.000 0.03226 8 30.500 20.04688 9 30.750 0.00820 10 30.875 0.00407 11 31.000 0.00405 12 30.875 20.00403 13 31.000 0.00405 14 31.125 0.00403 15 30.250 20.02811 16 33.000 0.09091 17 30.000 20.09091 18 35.125 0.17083 19 33.000 20.06050 20 32.125 20.02652 21 32.250 0.00389 22 32.375 0.00388 23 32.125 20.00772 24 32.250 0.00389 25 34.250 0.06202 26 36.375 0.06204 27 38.500 0.05842 28 34.375 20.10714 29 33.875 20.01455 30 33.625 20.00738

a. Based on a traditional sample estimator, calculate a daily variance estimator for this stock.

b. Assume that returns follow a Brownian motion process (at least that stock returns are uncorrelated over time) and that there are 30 trading days per month. What would be the monthly variance for this stock?

c. What would be the Parkinson extreme value estimated daily returns variance for this stock?