3. Interest-Rate Risk Management. As chief financial officer (CFO) of TSTR ("Too Small 100 To Rescue") Bank, a small neighborhood bank, one of your primary tasks is the management of its interest rate exposure. You are currently trying to convince your board, composed of neighborhood worthies, to measure and manage your institution's interest rate risk by using mathematical relations between fixed-income prices and yields.

(a) State a formula which relates changes in fixed-income price to interest-rate variability (i.e., changes in yields) using at least one if not two different measures of yield sensitivity. Illustrate how bond prices are related to yields on the basis of this formula and a diagram. Why or why not is this approach valid?

(b) The modified duration and convexity of a high-grade corporate bond in TSTR's investment portfolio are 5.6 years and 34.9, respectively. By what dollar amounts would you expect its price to change for a 60 bpts rise or fall in interest rates given that the current bond's price is $91.65?

(c) At a meeting of TSTR Bank's board you propose to change current A&L management practices focusing more on interest-rate risk. Formulate an appropriate objective in terms of a measure of interest-rate sensitivity. One of your board members, a retired S&L executive, claims that your approach to interest-rate exposure measurement and management is fundamentally flawed. What problems might she referring to? Do you agree with her assessment?

(d) Currently, the average duration of your loan portfolio is 3 years whereas the average duration of your various fixed income liabilities (deposits and bonds) is 1.5 years. Propose a strategy to neutralize the effect of interest-rate changes on your balance sheet which is (in million USD) as follows:

TSTR Bank Assets Liabilities Loan portfolio 100 Equity 11 Cash and cash equivalent 10 Deposits, bonds 99 Total 110 Total 110