Please determine the sensitivity of the following bond to very small changes in the yields (e.g. for the case of duration neutral hedging)! We have a bond, with the following properties. Face value: 100 Coupon: 8% each year Coupon payment: quarterly Maturity: 10 years Issue date: September 30th, 2023 Current date: December 1st, 2023 Current dirty price on the market: 103.877 Accrued interest calculation: linearly, equal months are assumed (30/360) The yield curve is flat (we have constant ' r ' on all maturities) HINTS: First, make sure you understand the difference between the clean price and the dirty price. In addition, we have a special feature here, since the price is not been set to a complete period (the coupon payment is due quarterly and we are between September 30th and December 31st). Somehow you would need to shift the cashflows to their regular periods (with the general logic of the DCF method). a) What is the clean price of this bond? b) What is the Macaluay Duration of this bond? How can you interpret this measure for your portfolio manager? c) What is the modified duration of this bond? What is the difference of this compared to the previous one, and what does it mean in terms of sensitivity to market yields? Which one should used together with convexity, when you need to recalculate the price of the bond for the case of a large yield movements? Please help your PM to evaluate the sensitivity of your bond to relatively large interest rate (or yield) movements on the market! We have the same bond and assumptions as in the previous exercise. Using its parameters, please answer the following questions: a) What is the convexity measure of this bond? (as this is a discrete case, please do not use continuous case formulas) b) How would affect a 5 percentage point ( 500 basis points) increase in yields the bond price? (What is "delta P and what is the new P?) c) What would be the difference in question b), if the initial yield ( r ) would be - 500 basis point lower; - 500 basis point higher