ECOM055 – Risk Management For Banking
Problem Set 6
Based on Book Chapter 9 银行业风险管理课业代写
9.15.
Prove (a) that the definitions of duration in equations (9.1) and (9.3) are the same when y is continuously compounded and (b) that when y is compounded m times per year they are the same if the right-hand side of equation (9.3) is divided by 1 + y/m.
9.16.
Suppose that a bank has $10 billion of one-year loans and $30 billion of five-year loans. These are financed by $35 billion of one-year deposits and $5 billion of five-year deposits.
The bank has equity totaling $2 billion and its return on equity is currently 12%. Estimate what change in interest rates next year would lead to the bank’s return on equity being reduced to zero. Assume that the bank is subject to a tax rate of 30%.
9.17.
Portfolio A consists of a one-year zero-coupon bond with a face value of $2,000 and a 10-year zero-coupon bond with a face value of $6,000. Portfolio B consists of a 5.95-year zero-coupon bond with a face value of $5,000. The current yield on all bonds is 10% per annum (continuously compounded).
(a) Show that both portfolios have the same duration.
(b) Show that the percentage changes in the values of the two portfolios for a 0.1% per annum increase in yields are the same.
(c) What are the percentage changes in the values of the two portfolios for a 5% per annum increase in yields?
9.18.
What are the convexities of the portfolios in Problem 9.17? To what extent does (a) duration and (b) convexity explain the difference between the percentage changes calculated in part (c) of Problem 9.17?
9.19. 银行业风险管理课业代写
When the partial durations are as in Table 9.5, estimate the effect of a shift in the yield curve where the 10-year rate stays the same, the one-year rate moves up by 9e, and the
movements in intermediate rates are calculated by interpolation between 9e and 0. How could your answer be calculated from the results for the rotation calculated in Section 9.6?
9.20. (Optional)
Suppose that the change in a portfolio value for a one-basis-point shift in the 1-year, 2- year, 3-year, 4-year, 5-year, 7-year, 10-year, and 30-year rates are (in $ millions) +5, – 3, –1, +2, +5, +7, +8, and +1, respectively. Estimate the delta of the portfolio with respect to the first three factors in Table 9.6. Quantify the relative importance of the three factors for this portfolio.
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