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FIN 701 Lecture Notes - Lecture 13: Nominal Yield, Interest Rate Risk, Yield Curve

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skywombat72
13 Apr 2016
School
Ryerson University
Department
Finance
Course
FIN 701
Professor
Patricia Mc Graw

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Document Summary

Chapter #9: interest rate risk ii book value accounting: accounting method in which the assets and liabilities of the fi are recorded at historic values. Market value accounting: accounting method in which the assets and liabilities of the fi are revalued according to the current level of interest rates. Marking to market: valuing securities at their current market price. Example: suppose a loan with a 15% interest rate, with half repayment after a year, and the remaining at the end of the year. Duration is a more complete measure of asset"s or liability"s interest rate sensitivity than maturity because it takes into account time of arrival (or payment) of all cash flows and maturity. After that time, the fi earns a profit, or return, on the loan. When cash flows are limited to one payment at the end of the period with no intervening cash flows, duration equals maturity. Duration measures the average life of an asset or liability.

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Related Questions

The following market value (mark-to-market) balance sheet information is available for Duguay State Bank (amounts in $ thousands and duration in years):

Book Value Market Value

Assets Amount Amount Duration

T-bills $ 180 $ 180 0.50

Loans* 5,000 ______ _____

Total Assets 5,180 ______

Liabilities

Deposits 4,184 4,184 1.00

Total Liabilities 4,184 4,184

Equity 996 _______

Total Lia and NW 5,180 _______

*Since this is a simple bank, it has only one type of loan. The loan has a $5,000 book value (current outstanding principal), amortized loan with annual payments, an interest rate of 6 percent, and 20-years to maturity. Similar loans today would have an interest rate of 7 percent which is the market yield.

Using Excel, determine the market value and duration of the loan and fill in the blanks in the balance sheet above. Please include a copy of your Excel Spreadsheet with your completed exam. What is the average duration of all the assets?

Weighted Average Duration Assets:

b. What is the average duration of all the liabilities?

Weighted Average Duration Liabilities:

c. What is the leverage-adjusted duration gap? What is the interest rate risk exposure?

DG = DA - kDL =

d. What is the forecasted impact on the market value of equity caused by a relative upward shift in the entire yield curve of 1.5 percent [i.e., Dr/(1+r) = 0.0150]?

The market value of the equity will change by the following:

MVE = -DG * (A) * r/(1 + r) =

e. What variables are available to the financial institution to immunize the balance sheet? Taking one variable at a time, how much would each variable need to change to get DGAP equal to 0?

To immunize the institution for interest rate risk, the Leverage Adjusted DG needs to be zero:

DG = DA –kDL = 0

The choice is to make the duration of assets equal to:

DA =

or the duration of liabilities equal to:

DL =

Or some combination thereof.

The following market value (mark-to-market) balance sheet information is available for Delasho State Bank (amounts in $ thousands and duration in years):

Book Value Market Value

Assets Amount Amount Duration

T-bills $ 180 $ 180 0.50

Loans* 5,000 ______ _____

Total Assets 5,180 ______

Liabilities

Deposits 4,184 4,184 1.00

Total Liabilities 4,184 4,184

Equity 996 _______

Total Lia and NW 5,180 _______

*Since this is a simple bank, it has only one type of loan. The loan has a $5,000 book value (current outstanding principal), amortized loan with annual payments, an interest rate of 6 percent, and 20-years to maturity. Similar loans today would have an interest rate of 7 percent which is the market yield.

Using Excel, determine the market value and duration of the loan and fill in the blanks in the balance sheet above. Please include a copy of your Excel Spreadsheet with your completed exam. What is the average duration of all the assets?

Weighted Average Duration Assets:

b. What is the average duration of all the liabilities?

Weighted Average Duration Liabilities:

c. What is the leverage-adjusted duration gap? What is the interest rate risk exposure?

DG = DA - kDL =

d. What is the forecasted impact on the market value of equity caused by a relative upward shift in the entire yield curve of 1.5 percent [i.e., Dr/(1+r) = 0.0150]?

The market value of the equity will change by the following:

MVE = -DG * (A) * r/(1 + r) =

e. What variables are available to the financial institution to immunize the balance sheet? Taking one variable at a time, how much would each variable need to change to get DGAP equal to 0?

To immunize the institution for interest rate risk, the Leverage Adjusted DG needs to be zero:

DG = DA –kDL = 0

The choice is to make the duration of assets equal to:

DA =

or the duration of liabilities equal to:

DL =

Or some combination thereof.

Your client is a regional savings and loan institution. You have been hired to assess the client’s exposure to interest rate risk and advise on possible ways to reduce it. You have the following information on the S&L’s balance sheet: The total assets are mortgages and are worth $3,096.87M. The assets have a duration of 9.23 years. The liabilities are 5-year Certificates of Deposit (CDs) with a coupon rate of 8%, which we assume is paid annually (CDs are coupon bonds, so all coupon bond formulas apply to them). The total face value of the CDs that have been issued by your client is $2.5 billion. The yield curve is flat at 8%.

a) Compute the duration of the liabilities.

b) Compute the duration of the (net) market value of the bank.

c) Your recommendation to the client is to sell some of the mortgage portfolio and buy 1-year CDs (which pay an annual coupon rate of 8%) with the proceeds. How many dollars worth of the assets does your client have to sell to reduce the duration of the (net) market value of the bank to 0 (i.e., to achieve immunization)?