You are considering investing in a hedge fund. Before you make the decision of investing in the hedge fund, you need to do some research about it and here are some key questions you are trying to address:

b. Hedge funds may also have some high-frequency trading. Using the trade at 3:13:07 as the kth trade, calculate Huang and Stoll (1996)s realized spread.

Stock ID Date [L] ABCDE.PA ABCDE.PA ABCDE.PA ABCDE.PA ABCDE.PA ABCDE.PA ABCDE.PA ABCDE.PA ABCDE.PA ABCDE.PA ABCDE.PA ABCDE.PA ABCDE.PA 2-Jan-18 2-Jan-18 2-Jan-18 2-Jan-18 2-Jan-18 2-Jan-18 2-Jan-18 2-Jan-18 2-Jan-18 2-Jan-18 2-Jan-18 2-Jan-18 2-Jan-18 Time[L] Type 3:03:25 PM Quote 3:07:46 PM Quote 3:10:21 PM Quote 3:13:07 PM Trade 3:13:07 PM Quote 3:13:07 PM Quote 3:13:07 PM Quote 3:13:25 PM Quote 3:13:27 PM Quote 3:13:29 PM Quote 3:13:30 PM Quote 3:13:32 PM Quote 3:18:07 PM Trade Price 0.07 0.06 Volume 70573 13852 Bid Price 0.06 0.06 0.06 0.06 0.06 0.06 0.06 0.06 0.06 0.06 0.06 Ask Price 0.07 0.07 0.07 0.07 0.07 0.07 0.07 0.07 0.07 0.07 0.07 Realized Spread (TAQ)k = { 2. (ln(Pk) ln(Pk+5)) 2. (In(Pk+5) - In(P)) when the kth trade is a buy when the kth trade is a sell, (2) Stock ID Date [L] ABCDE.PA ABCDE.PA ABCDE.PA ABCDE.PA ABCDE.PA ABCDE.PA ABCDE.PA ABCDE.PA ABCDE.PA ABCDE.PA ABCDE.PA ABCDE.PA ABCDE.PA 2-Jan-18 2-Jan-18 2-Jan-18 2-Jan-18 2-Jan-18 2-Jan-18 2-Jan-18 2-Jan-18 2-Jan-18 2-Jan-18 2-Jan-18 2-Jan-18 2-Jan-18 Time[L] Type 3:03:25 PM Quote 3:07:46 PM Quote 3:10:21 PM Quote 3:13:07 PM Trade 3:13:07 PM Quote 3:13:07 PM Quote 3:13:07 PM Quote 3:13:25 PM Quote 3:13:27 PM Quote 3:13:29 PM Quote 3:13:30 PM Quote 3:13:32 PM Quote 3:18:07 PM Trade Price 0.07 0.06 Volume 70573 13852 Bid Price 0.06 0.06 0.06 0.06 0.06 0.06 0.06 0.06 0.06 0.06 0.06 Ask Price 0.07 0.07 0.07 0.07 0.07 0.07 0.07 0.07 0.07 0.07 0.07 Realized Spread (TAQ)k = { 2. (ln(Pk) ln(Pk+5)) 2. (In(Pk+5) - In(P)) when the kth trade is a buy when the kth trade is a sell, (2)