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# FIN 446 Income Tax and Estate Planning: Market Conditions

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## Questions:

Q1) Write a function that will take Bid and ask price in dollars, and

c) Write test code to test a) and b)

Q2) write a function that will compute the cost of liquidation during normal times for one posi- tion namely: 1 s?. Where s is the proportional bid-ask spread and ? is the total investment in the position. Such a function will take three inputs (investment, bid, and ask). Please call the func- tion in Q1-b in this function to compute s. Also write the test code so that you can test the function.

Q2) to solve problem in page number (540-541) Suppose that a nancial institution has bought 10 million shares of one company and 50 million ounces of a commodity. The shares are bid \$89.5, o er \$90.5. The commodity is bid \$15, o er \$15.1. The mid-market value of the position in the shares is 90 Ö 10 = \$900 million. The mid-market value of the position in the commodity is 15.05 Ö 50 = \$752.50 million. The proportional bid o er spread for the shares is 1/90 or 0.01111. The proportional bid o er spread for the commodity is 0.1/15.05 or 0.006645. The cost of liquidation in a normal market is: Please note that you have to call the function in

Q4) Under Stressed market conditions, we assume that s ? N(?,?). and for one position the liquidation is given by 1 (? + ??)?. Here ? is the z score of the con dence level (say 99%) It is 2 given by the function ? = qnorm(0.99). This function should take the following inputs: {mean, standard_deviation, con dence_interval, total investment} and return the liquidation cost under stressed condition. Q5)Use the function written in Q4) to compute Suppose that in Example 24.1 the mean and standard deviation for the bid o er spread for the shares are \$1.0 and \$2.0, respectively.

Suppose further that the mean and standard deviation for the bid o er spread for the commodity are both \$0.1. The mean and standard deviation for the proportional bid o er spread for the shares are 0.01111 and 0.02222, respectively. The mean and standard deviation for the proportional bid o er spread for the commodity are both 0.006645. Assuming the spreads are normally distributed, the cost of liquidation that we are 99% con dent will not be exceeded is: Please note that you have to call the function in Q4) multiple times and add the returns.

### FIN 446 Income Tax and Estate Planning

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