Asset and Liability Management

Please show your work. All problems are worth 10 points each.

1. A $1,000 six-year bond has an 8 percent coupon, is selling at par, and contracts to make annual payments of interest. The duration of this bond is 4.99 years. What will be the new price if interest rates increase to 8.5 percent?

**YTM =8%**

**CHANGE IN INTEREST RATE = 0.5% (8.5%-8%) = INCREASE OF 0.5%**

**%CHANGE IN PRICE OF BOND = -DURATION/(1+YTM) X CHANGE IN RATE = -4.99/(1+0.08) X 0.5% = -2.310%**

**SO THERE WILL A DECREASE OF 2.310% IN PRICE OF BOND**

**NEW BOND PRICE = 1000 – (1000 X 2.310%) = 1000 – 23.10 = 976.90**

**The new price will be 976.90.**

2. TD Bank has the following assets and liabilities as of year-end. All assets and liabilities are currently priced at par and pay interest annually. a. What is the change in the value of its assets if all interest rates decrease by 1 percent?

b. What is the change in the value of its liabilities if all interest rates decrease by 1 percent?

c. What is the effect on the value of the FI’s equity if interest rates decrease by 1 percent?

A. Approximately $2.29 million

**Need the process**

B：

**PV=61,603,807 FV=60,000,000 I=6 N=3 PMT=60,000,000 x 0.07=4,200,000**

**Decrease by 1 percent,**

**PV=31,298,843 PV=30,000,000 i=5 n=5 PMT=30,000,000 x0.06=1,800,000**

**△L=(61,603,807-60,000,000)+(31,298,843-30,000,000)**

**=$2,902,650.**

**It will increase about 2.906 million.**

C:

Loss of $0.6048 million

**Need the process**

3. An FI purchases at par value a $100,000 Treasury bond paying 10 percent interest with a 7.5 year duration. If interest rates rise by 4 percent, calculate the bond’s new value.

**MD= 7.5/1.05=7.143**

**Dollar Durtion=MD x P=7.143 x 100,000= 714,300**

**Change Price= 714,300 x 0.04= -28,572**

**New Price= 100,000 – 28,572= $71,428**

4. Consider a one-year maturity, $100,000 face value bond that pays a 6 percent fixed coupon annually. If the bond is selling at par, what is the percentage price change for the bond if interest rates increase 50 basis points from 6 percent?

**Change in YTM =0.5**

**K = N**

**Bond Price =∑ [(Coupon)/ (1 + YTM) ^k] + Par value/(1 + YTM)^N**

**K =1**

**Bond Price =∑ [(6*100000/100)/ (1 + 6.5/100) ^k] + 100000/ (1 + 6.5/100) ^1**

**Bond Price = 99530.52**

**%age change in price = (New Price-Old price) *100/old price**

**%age change in price = (99530.52-100000) *100/100000**

**= -0.47%**

**The percentage price change will be -0.47%**

5. The balance sheet of MassMutual Insurance shows the following fixed and rate sensitive assets and liabilities. a. What is the repricing gap for the FI?

b. What will be the FI’s net interest income at year-end if interest rates do not change?

c. Suppose short-term interest rates increase by 1 percent. Calculate the change in net interest income after the interest rate increase.

**A:**

REPRICING GAP = RATE SENSITIVE ASSETS – RATE SENSITIVE LIABILITIES

REPRICING GAP = 35,000,000 – 40,000,000 = – 5,000,000

The repricing gap for the FI is- $5,000,000

B:

6 .Consider a five-year, 8 percent annual coupon bond selling at par of $1,000. a. What is the duration of this bond?

b. If interest rates increase by 20 basis points, what is the approximate change in the market price using the duration approximation?

A: | ||||

YEAR | Cash flows | PVIF at 8% | PV at 8% | PV*Year/1000 |

1 | 80 | 0.92593 | 74.07 | 0.07 |

2 | 80 | 0.85734 | 68.59 | 0.14 |

3 | 80 | 0.79383 | 63.51 | 0.19 |

4 | 80 | 0.73503 | 58.80 | 0.24 |

5 | 1080 | 0.68058 | 735.03 | 3.68 |

1000.00 | 4.31 |

Therefore, the duration of this bond will be 4.31 years.

B:

Modified duration = Macaulay duration/(1+YTM)

=4.31/(1+0.08)

=3.99271

Modified duration prediction=-3.99*0.002*1000=-7.99

%age change in bond price=-7.99/1000=-0.8%

New bond price=1000-7.99=992.01

The

7. HSBC has the following assets and liabilities as of year-end. All assets and liabilities are currently priced at par and pay interest annually. a. What is the weighted average maturity of the assets of the FI?

b. What is the weighted average maturity of the liabilities of the FI?

c. What is the FI’s maturity gap?

8. Eastern Bank Investments has the following assets and liabilities on its balance sheet. The two-year Treasury notes are zero coupon assets. Interest payments on all other assets and liabilities occur at maturity. Assume 360 days in a year. a. What is the duration of the assets?

b. What is the duration of the liabilities?

c. What is the leverage-adjusted duration gap?

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