Advanced Finance:

Consider the Hasbrouck vector autoregression: (36)-( * )*+[24] (**)+() (1) Here, rt is the stock return estimated as the movement in the quote midpoint between trade times t and t-1, and It is measured order flow. For example, if at time t = 2, a $20,000 trade came in and was classified as a sell trade, 12 = -20,000. Note that t is measured in trading time rather than calendar time units, i.e., indexing times at which trades occur. a) This is a single-lag vector autoregression, i.e., lags beyond the previous time period/trade are consid- ered irrelevant. Does this strike you as a sensible modelling choice? Should you include additional lags of both returns and order flow? If so, why? b) Once the VAR is estimated, Hasbrouck uses the coefficient estimates to compute the impulse response function of returns to order flow shocks. Assume that an order flow shock of $1 hits the system today (i.e., period 0), and assume that no other shocks hit the system. What is the return impulse response two periods after the shock hits (period 2)? Present an expression in terms of the coefficients given in equation (1) above. c) How can we use Hasbrouck's VAR and the associated impulse response to better understand the relationship between order flow shocks and stock returns? In particular, can we use this methodology to uncover whether order flow contains fundamental information relevant for pricing stocks? Discuss. Consider the Hasbrouck vector autoregression: (36)-( * )*+[24] (**)+() (1) Here, rt is the stock return estimated as the movement in the quote midpoint between trade times t and t-1, and It is measured order flow. For example, if at time t = 2, a $20,000 trade came in and was classified as a sell trade, 12 = -20,000. Note that t is measured in trading time rather than calendar time units, i.e., indexing times at which trades occur. a) This is a single-lag vector autoregression, i.e., lags beyond the previous time period/trade are consid- ered irrelevant. Does this strike you as a sensible modelling choice? Should you include additional lags of both returns and order flow? If so, why? b) Once the VAR is estimated, Hasbrouck uses the coefficient estimates to compute the impulse response function of returns to order flow shocks. Assume that an order flow shock of $1 hits the system today (i.e., period 0), and assume that no other shocks hit the system. What is the return impulse response two periods after the shock hits (period 2)? Present an expression in terms of the coefficients given in equation (1) above. c) How can we use Hasbrouck's VAR and the associated impulse response to better understand the relationship between order flow shocks and stock returns? In particular, can we use this methodology to uncover whether order flow contains fundamental information relevant for pricing stocks? Discuss