3. Interest-Rate Risk Management. As chief financial officer (CFO) of The California 100+20 Widows \& Orphans Insurance Company ("C-WOIC"), one of your primary tasks is the management of your company's interest rate exposure. Following best industry practices, you are currently trying to convince your board to move beyond traditional approaches to interest-rate risk and actively manage your institution's rate exposure by relying less on external consultants but instead implement models based on tried and tested mathematical relations between fixed-income prices and yields (rates). 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 C-WOIC's in- vestment 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? 3. Interest-Rate Risk Management. As chief financial officer (CFO) of The California 100+20 Widows \& Orphans Insurance Company ("C-WOIC"), one of your primary tasks is the management of your company's interest rate exposure. Following best industry practices, you are currently trying to convince your board to move beyond traditional approaches to interest-rate risk and actively manage your institution's rate exposure by relying less on external consultants but instead implement models based on tried and tested mathematical relations between fixed-income prices and yields (rates). 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 C-WOIC's in- vestment 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