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Capital Markets Homework Assignment for Class Session 4 Preparation for Monday, November 11th,
2002 Topic: Bond Price Volatility and Managing Interest
Rate Risk
Preparatory Readings:
F&I,
Chapter 21 CMImmunization101.xls
(CP) and on TUCK STREAMS 1.
Suppose
the U.S. Treasury issued $1,000 million face value, 7.5%, 30-year bonds
on January 15, 1996 (issue and settlement date). Coupon interest is paid semi-anually
with the face value payable in 30 years (1/15/2026).
At a purchase price of $94 for each $100 of face value on
1/15/96, the yield maturity is 8.032%. Assume that on January 15th
(on the day you bought the bond, but later in the day after you
purchased it) interest rates shift at every maturity. a)
First,
consider an upward shift of 100 basis points (+1.00 % to 9.032%).
What is the new price of the bond? b)
Given
the shift in a), what was the percentage price change of the bond? c)
Now,
consider a downward shift of 100 basis points (-1.00% to 7.032%)
instead. What is the new
price of the bond? d)
Given
the shift in c), what was the percentage price change of the bond? 2.
Calculate
the Macaulay duration and the Modified duration of the Treasury strip
maturing on August 15, 2006 as of Jan 15, 1998.
Assume the yield is 6.39%. 3.
Calculate
the durations (Macaulay and Modified) of the 8% Treasury note maturing
on January 15, 2002 as of January 15, 1997.
Assume the yield is 6.0%., For this problem you can use
equal-length semi-annual periods, although you may have learned by now
that it is not exactly correct in the Treasury market (where actual days to each payment date are used).
What problems might you anticipate if you had calculated the
durations as of Jan. 10th or Jan. 20th? 4.
Suppose
the liabilities of an insurance company consist of an annual
end-of-the-year cash outflow (for pension obligations) of $100 for each
of the next 5 years. To
fund these obligations over the next five years, the insurance company
can make investments in two bonds that pay annual (end-of-the-year)
coupon interest. These bonds include a one-year bond with a 6 percent coupon
and a four-year bond with an 8 percent coupon.
Both bonds have a face value of $100.
The interest rate (yield) is currently 10 percent for all
maturities. a)
Calculate
the present value of the liability. b)
Calculate
the duration of the liability. c)
Calculate
the duration of each of the bonds (assets). d)
The
company desires to immunize its liability against interest rate
fluctuations. To do this,
the firm needs to set the Macaulay duration of its liabilities
equal to the Macaulay duration of its assets.
Given the durations of the assets (bonds) and the liability
above, how much of each bond does the firm need to buy to immunize the
liability? e)
Later
in the same day that you purchased the two bonds, the interest rate
falls to 9.5%. Recalculate
the value of the assets and the liability after this drop.
Is the liability immunized?
Why or why not? Suppose
the interest rate had risen to 10.5% (from the original 10%).
Recalculate the value of the assets and liability after this
rise. Is the liability
immunized? Why or why not? f)
Why
would the insurance company
want to immunize its liability? What
risk would the insurance company have incurred if it had not immunized
the liability? |
