QUESTION 1 Financial Institution XY has assets of $1 million Invested in a 30-year, 10 percent annual coupon. Treasury b

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QUESTION 1 Financial Institution XY has assets of $1 million
Invested in a 30-year, 10 percent annual coupon. Treasury bond
selling at par.
The duration of this bond has been estimated at 9.94
years.
The assets are financed with equity and a $900.000, year, annual
coupon bond selling at par with duration 1.8975
a.What is the leverage-adjusted duration gap?
What risk is the Fl facing? Explain
b. What is the impact on equity value if the relative change in
market interest rates is a decrease of 20 basis points? NOTE, The
relative change in Interest rates is a ΔR/(I+R)
c Using the information calculated in parts (a) and (b), what
can be said about the desired duration gap for a financial
institution if interest rates are expected to increase or
decrease.
d. Verify your answer to part (c) by calculating the change in the
market value of equity assuming that the relative change in all
market interest rates is an increase of 30 basis points.
e. What would the duration of the assets need to be to immunize
the equity from changes in market interest rates?
f. The Fl wants to bedge its interest rate risk exposure
using bond futures. Suppose the current futures price quote is $95
per $100 of face value for the benchmark 20-year, bond underlying
the nearby futures contract, the minimum contract size is $100,000,
and the duration of the deliverable bond is 9 years.
i. How can futures be used to hedge the risk faced by the
FI?
ii. Calculate number of futures contracts to be used to
fully hedge the balancesheet
g. What is the meaning of the basis risk adjustment ratio?
Calculate the number futures contracts should have been used using
the 20-year bond contracts if the ratio were b = 1.32. Calculate
the optimal hedge ratio in this case and explain its meaning