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You are a consultant to XY Corporation. The firm seeks your advice for the elaboration of a hedging strategy against interest rate risk. Four years from now, XY will need to make a bullet payment of £10,000 and wonders how to invest cash available today to fund that future outflow. Suppose there are two liquid bonds in the market: Bond A: Face value- £100, current price- £100, annual coupon of 5, remaining life -3 vears Bond B: Face value life5 vears £100, current price £78.35, no coupon payments, remaining Assume all debt considered in this exercise has the same level of defaultrisk. The benchmark yield curve for fixed-income investments of the same riskiness is flat at a level of 5% p.a. (a) Calculate the Macaulay Duration for bond A. Explain the difference to the duration of a zero-coupon bond of the same maturity. (b) Calculate the Modified Duration for bond A. Based on this metric, what's the price change resulting from an increase in yield of 0.1%? What about an increase of 10% and how meaningful is such an estimate of the implied price change? Hint: You can assess the latter point by calculating the exact price change. For this, leave the duration aside and simply look at the price impact in the present value computation resulting from a yield increase. (c) Calculate the Macaulay Duration of bond B. (d) Form a portfolio of bonds A and B by matching the Macaulay Duration of the portfolio with the Macaulay Duration of the liability mentioned above. How many units of each bond would need to be bought or sold? To what extent would such a strategy indeed immunize XY?
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