Solutions to Further Problems
Risk Management and Financial Institutions
Second Edition
John C. Hull
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Chapter 1: Introduction
1.15. The impact of investing w1 in the first investment and w2 = 1 – w1 in the second investment is shown in the table below. The range of possible risk-return trade-offs is shown in figure below. w1 w2 ?P ?P 0.0 1.0 12% 20% 0.2 0.8 11.2% 17.05% 0.4 0.6 10.4% 14.69% 0.6 0.4 9.6% 13.22% 0.8 0.2 8.8% 12.97% 1.0 0.0 8.0% 14.00%
1.16. In this case the efficient frontier is as shown in the figure below. The standard deviation of returns corresponding to an expected return of 10% is 9%. The standard deviation of returns corresponding to an expected return of 20% is 39%.
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1.17.
(a) The bank can be 99% certain that profit will better than 0.8?2.33×2 or –3.85% of assets. It therefore needs equity equal to 3.85% of assets to be 99% certain that it will have a positive equity at the year end.
(b) The bank can be 99.9% certain that profit will be greater than 0.8 ? 3.09 × 2 or –5.38% of assets. It therefore needs equity equal to 5.38% of assets to be 99.9% certain that it will have a positive equity at the year end.
1.18. When the expected return on the market is ?30% the expected return on a portfolio with a beta of 0.2 is
0.05 + 0.2 × (?0.30 ? 0.05) = ?0.02
or –2%. The actual return of –10% is worse than the expected return. The portfolio manager has achieved an alpha of –8%!
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Chapter 2: Banks
2.15. There is a 99.9% chance that the profit will not be worse than 0.6 ? 3.090 × 2.0 = ?$5.58 million. Regulators will require $0.58 million of additional capital.
2.16. Deposit insurance makes depositors less concerned about the financial health of a bank. As a result, banks may be able to take more risk without being in danger of losing deposits. This is an example of moral hazard. (The existence of the insurance changes the behavior of the parties involved with the result that the expected payout on the insurance contract is higher.) Regulatory requirements that banks keep sufficient capital for the risks they are taking reduce their incentive to take risks. One approach (used in the US) to avoiding the moral hazard
problem is to make the premiums that banks have to pay for deposit insurance dependent on an assessment of the risks they are taking.
2.17. When ranked from lowest to highest the bidders are G, D, E and F, A, C, H, and B.
Individuals G, D, E, and F bid for 170, 000 shares in total. Individual A bid for a further 60,000 shares. The price paid by the investors is therefore the price bid by A (i.e., $50). Individuals G, D, E, and F get the whole amount of the shares they bid for. Individual A gets 40,000 shares. 2.18. If it succeeds in selling all 10 million shares in a best efforts arrangement, its fee will be $2 million. If it is able to sell the shares for $10.20, this will also be its profit in a firm commitment arrangement. The decision is likely to hinge on a) an estimate of the probability of selling the shares for more than $10.20 and b) the investment banks appetite for risk. For example, if the bank is 95% certain that it will be able to sell the shares for more than $10.20, it is likely to choose a firm commitment. But if assesses the probability of this to be only 50% or 60% it is likely to choose a best efforts arrangement.
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风险管理与金融机构-约翰-第二版-答案
