Module 5 Interest rate risk management

Transcription

1 Module 5 Interest rate risk management 1 Module 5 Interest rate risk management Self-assessment question 5.1 Revision questions 1, 2, 3 from Valentine et al., chapter 14. Questions 1, 4 & 6; Quantitative problems 3, 5, 9, 10 & 15 from Mishkin & Eakins, chapter 23. Question 2; Quantitative problems 5, 6, 7, 10 & 21 from Mishkin & Eakins, chapter 24. Revision questions 1. Consider: a 10-year bond with a face value of $ and semi-annual coupon of $40 000; and a two-year bond with a face value of $ and semi-annual coupon of $ The 10-year yield is 8.25% p.a. and the two-year yield is 8.75% p.a. We buy year bonds and 40 2-year bonds. a. What is the average duration of the bond portfolio? b. Suggest a liability that we can issue to finance this holding and immunise ourselves against interest rate risk. c. What are the problems with this hedge? Answer: The price of bond (a) at 8.25% p.a. (4.125% per half-year) is found as follows: 1 V V The price of the bond is: P $ $ $ If the market interest rate increases by one basis point to 8.26% p.a., the price is calculated as follows: 1 V V

2 2 FIN8202 Financial markets and instruments Therefore, P $ $ $ The PVBP is ($ $ ) = $ We can use the duration approximation on page 367 to calculate the duration of this bond D That is, D = half-years The price of bond (b) at 8.75% p.a. (4.375% per half-year) is found as follows: 1 V V Therefore, P $ $ $ When the market interest rate increases to 8.76% p.a. (4.38% per half-year, the price is calculated as follows: 1 V V Then, P $ $ $ Therefore, PVBP = $90.42.

3 Module 5 Interest rate risk management 3 We can calculate the duration of this security from: D Therefore, D = 3.74 half-years i. 20 bonds of type (a) = 20 $ = $ bonds of type (b) = 40 $ = $ Total value of portfolio = $ Proportionofbond(a) Proportionofbond(b) Note that these weights are based on market values and not on face values. ii. Average duration of assets =( )+( ) = = 4.42 years. iii. We can set DGAP = 0 by funding our assets by issuing a zero-coupon bond with: iv. The problems with this hedge are:

4 4 FIN8202 Financial markets and instruments 2. Year Cash Flow ($) a. The four year interest rate is 5.40% p.a. What is the price of the security? b. What is the duration of this security? c. If we held the security as an asset, what liability should we issue to hedge ourselves against interest rate risk? What are the problems with this hedge? Answer: a. The price of the security is given by: $1 0$2 0$3 0$4 0 P $ $ $ $ b. The price of the security at 5.41% p.a. is given by: $1 0$2 0$3 0$4 0 P $ $ $ $ $ Therefore, PV BP = $ $ The duration of the security can be obtained from: D Therefore D = 2.95 years. c. We could hedge our interest rate exposure by issuing a zero-coupon bond with: a. face value $ ; and

5 Module 5 Interest rate risk management 5 b. term and duration equal to 2.95 years. d. The problems with the hedge are: i. The portfolio is only protected against a parallel shift in the yield curve. Specifically, it is only protected if the three- and four-year interest rates change by the same amount. ii. The hedge is instantaneous and it erodes over time. This means that the hedge must be rebalanced frequently. For example, consider what happens after one year. The price of the bond is then: $200$300$400 P $ $ $ $ At 5.41%, the price of the security is: $200$300$400 P $ $ $ $ Therefore, PVBP = $ $ The duration of the security is given by: D Therefore D = 2.19 years. The duration of the zero-coupon bond a year later would be 1.95 years. The DGAP would then be: DGAP = = 0.24 years. This problem arises because, as time passes, different securities have a different rate of change of duration. A zero-coupon bond loses one year off its duration for every year that passes, whereas other bonds lose a smaller amount. Also, a change in interest rates has a different impact on the durations of different securities. Therefore, the hedge will need to be rebalanced after a change in interest rates. iii. The hedge is accurate only for small interest rate changes.

6 6 FIN8202 Financial markets and instruments 3. We hold the following portfolio. Assets $m Liabilities/Capital $m Will the capital of this portfolio be reduced or increased by an increase in interest rates? Answer: Average duration of assets = ½ ½ 0.25 Average duration of liabiliti es = ½ 3 + ½ 1.9 DGA P = / That is, an increase in interest rates will increase the capital of the portfolio.

7 Module 5 Interest rate risk management 7 Answers to end-of-chapter questions Mishkin & Eakins, chapter Yes. By warning borrowers that they will not be able to get future loans if they engage in risky activities, borrowers will be less likely to engage in these activities in order to have access to loans in the future. 4. To reduce adverse selection, a banker needs to screen out bad credit risks by learning as much as possible about potential borrowers. Similarly, to minimize moral hazard, the banker must continually monitor borrowers to see that they are complying with restrictive loan covenants. Hence it pays for the banker to by nosy. 6. False. Although diversification is a desirable strategy for a bank, it may still make sense for a bank to specialize in certain types of lending. For example, a bank may have developed expertise in screening and monitoring a particular kind of loan, thereby improving its ability to handle problems of adverse selection and moral hazard. Quantitative problems Mishkin & Eakins, chapter 23 Quantitative problems 4, 5, 9, 10 & The value of a $100,000 fixed-rate, 30-year mortgage falls to $89,537 when interest rates move from 5% to 6%. What is the approximate duration of the mortgage? Solution: P i 1iP Duration,orDuration P 1i ip Duration 10.98years Calculate the duration of a commercial loan. The face value of the loan is $2,000,000. It requires simple interest yearly, with an APR of 8%. The loan is due in four years. The current market rate for such loans is 8%. Solution: The annual interest is 0.08 $2,000,000 = $160, This loan has a duration of 3.57 years.

8 8 FIN8202 Financial markets and instruments 9. The following financial statement is for the current year. From the past, you know that 10% of fixed-rate mortgages prepay each year. You also estimate that 10% of checkable deposits and 20% of savings accounts are rate sensitive. Second National Bank What is the current Income GAP for Second National Bank? What will happen to the bank s current net interest income if rates fall by 75 basis points? Solution: RSA RSL = 6 M + 7 M + ( M) M = $15.8 million = ( M) M + ( M) + 15 M + 22 M + 5 M + 12 M = $62.6 million GAP = $15.8 million $62.6 million GAP = $46.8 million ΔI = $46.8 million ( ) = +$351,000

9 Module 5 Interest rate risk management Chicago Avenue Bank has the following assets: Asset Value Duration (in years) What is Chicago Avenue Bank s asset portfolio duration? Solution: Total assets = $155 M Asset duration = 0.55 (100/155) (40/155) (15/155) = 1.53 years. 15. The following financial statement is for the current year: Second National Bank Calculate the duration gap for the bank.

10 10 FIN8202 Financial markets and instruments Solution: DUR a = ( ) + ( ) + ( ) + ( ) + ( ) + ( ) + ( ) + ( ) DUR a = By the same technique, using total liabilities of $95,000,000: DUR L DURDUR gap a DUR / A

11 Module 5 Interest rate risk management 11 Answers to end-of-chapter questions Mishkin & Eakins, chapter 24 Question 2. It would swap interest on $5 million of variable-rate assets for the interest on $5 million of fixed-rate assets, thereby eliminating its income GAP. Quantitative problems Mishkin & Eakins, chapter 24. Quantitative problems 5, 6, 7, 10 & You would buy a $100 million worth, i.e contracts of long-term bond futures contracts with an expiration date of one year in the future. This means that you would be entitled to delivery of the long-term bonds at today s price so that the current rate would be locked in. 6. You would buy $100 million worth (1000 contracts) of the call long-term bond option with a delivery date of one year in the future and with a strike price that corresponds to a yield of 8%. This means that you would have the option to buy the long bond with the 8% interest rate, thereby making sure that you can earn the 8%. The disadvantage of the options contract is that you have to pay a premium that you would not have to pay with a futures contract. The advantage of the options contract is that if the interest rate rises and the bond price falls during the next year, you do not have to exercise the option and so will be able to earn a higher rate than 8% when the funds come in next year, whereas with the futures contract, you have to take delivery of the bond and will only earn 8%. 7. The put option is out of the money because you would not want to take the option to sell the futures at $95 when the price at expiration is $120. Since the premium is $4,000 and you did not exercise the contract, your loss on the contract is $4, It would swap interest on $42 million of fixed-rate assets for the interest on $42 million of variable-rate assets, thereby eliminating its income gap. 21. Springer Country Bank has assets totalling $180 million with a duration of 5 years, and liabilities totalling $160 million with a duration of 2 years. Bank management expects interest rates to fall from 9% to 8.25% shortly. A T-bond futures contract is available for hedging. Its duration is 6.5 years and is currently priced at How many contracts does Springer need to hedge against the expected rate change? Assume each contract is has a face value of $1,000,000. Solution: $180 million 5 = ($160 million 2) + (TB 6.5) Since the current price is $991,562.50, this requires 90 contracts. They should take a short position.