A financial institution wishes to unwind a position of 120 million shares in a stock over 8 days. The dollar bidoffer spread as a function of daily trading volume, q, is a + bcq where a = 0.25, b = 0.15, and c = 0.08 and q is measured in millions. The standard deviation of the stock price change per day is $1.25. a) What is the optimal strategy that minimizes the 95% confidence level for the costs? Hint: use excel solver to identify the optimal trading strategy for the financial institution. (6 marks) b) What is the average time the institution waits before selling? (3 marks) c) How does the average time from part b) change as the confidence level changes to 99% and 99.99%? (3 marks) d) Explain how liquidity black holes occur. How can algorithmic trading lead to liquidity black holes? (6 marks)