An investor makes the decision to purchase 10,000 shares of BHP based on a price of $11 per share. Accordingly, the investor's broker makes the following trades over one trading day:

Time	Buy/Sell	Price	Volume
10:01:00	Buy	$12.17	1,000
12:01:00	Buy	$12.60	1,000
12:02:00	Buy	$16.36	6,000
13:07:00	Buy	$12.39	1,000
14:54:00	Buy	$12.99	1,000

The stock closed at a price of $13.30. The broker charges a commission of $0.01 per share, including all explicit fees.

Calculate the broker's hypothetical portfolio cost, hypothetical profits, actual portfolio cost, actual profits and implementation shortfall. Show all working.

1: Apply the implementation shortfall method to categorise the trader's costs into the commission, delay, price impact and opportunity cost components. Show all working.

2: Provide a qualitative justification for you categorisation in the previous question.

3: Now, assume that the market VWAP on this trading day was $12.80. Calculate the broker's total execution cost and execution cost per share. Show all working.

4: Did the broker over or under perform relative to the VWAP benchmark?

5: Explain how ex-ante risk measures differ from ex-post risk measures. Provide an example of both. Use your own words.

6. Describe how to implement a pairs trading strategy by providing an example. What are the risks associated with implementing a pairs trading strategy? Use your own words.