Exam 9: Interest Rate Risk II

Rate Maturity Ask Change Ask yield 7.1250 Oct 15,2005 102:08 -1 5.9156 -What is the duration of the above Treasury note? Use the asked price to calculate the duration. Recall that Treasuries pay interest semiannually.

The greater is convexity, the more insurance a portfolio manager has against interest rate increases and the greater potential gain from rate decreases.

-What is the weighted average duration of the assets of the FI?

Attempts to satisfy the objectives of shareholders and regulators requires the bank to use the same duration match in the protection of net worth from interest rate risk.

Immunizing the balance sheet of an FI against interest rate risk requires that the leverage adjusted duration gap (D_A-kD_L) should be set to zero.

For given changes in interest rates, the change in the market value of net worth of an FI is equal to the difference between the changes in the market value of the assets and market value of the liabilities.

The value for duration describes the percentage increase in the price of an asset for a given increase in the required yield or interest rate.

The smaller the leverage adjusted duration gap, the more exposed the FI is to interest rate shocks.

The rate of change in duration values is less than the rate of change in maturity.

The shortcomings of this strategy are the following except

Immunizing the balance sheet to protect equity holders from the effects of interest rate risk occurs when

Convexity is a desirable effect to a portfolio manager because it is easy to measure and price.

Assets Amount Proportion Duration Prop. \times Dur 30-day T-bills 300 300\div1,730 0.1734 30+360 0.083 0.144442 90-day T-bills 550 550\div1.730 0.3179 90\div360 0.250 0.079475 2-year T-notes 700 700\div1,730 0.4046 720\div360 2.000 0.8092 180-day munis 180 180\div1,730 0.1041 180\div360 0.500 0.05205 Total \ 1,730 Weighted average duration of assets -What is the duration of the liabilities?

Duration normally is less than the maturity for a fixed income asset.

Matching the maturities of assets and liabilities is not a perfect method of immunizing the balance sheet because the timing of the cash flows is likely to differ between the assets and liabilities.

$1,000 face value, 9% annual coupon, 5 year maturity, 10% rate =962.09 =1,000 =10 =5 PMT =90 -Calculate the percentage change in this bond's price if interest rates on comparable risk securities increase to 11 percent. Use the duration valuation equation.

Macaulay's Duration $D = \frac { \sum _ { t = 1 } ^ { N } P V _ { t } \times t } { \sum _ { t = 1 } ^ { N } P _ { t } } = \frac { \left[ \frac { 8 } { ( 1.08 ) ^ { 1 } } \times 1 \right] + \left[ \frac { 8 + 100 } { ( 1.08 ) ^ { 2 } } \times 2 \right] } { 100 } = 1.9259 \text { years }$ -What is the duration of a 5-year par value zero coupon bond yielding 10 percent annually?

Duration considers the timing of all the cash flows of an asset by summing the product of the cash flows and the time of occurrence.

Duration is equal to maturity when at least some of the cash flows are received upon maturity of the asset.

Duration is the weighted-average present value of the cash flows using the timing of the cash flows as weights.