Q1. In the textbook example 6.5, what is your hedging position in bond B if yo 1.35 + 0.85yA + et = a Example 6.5 A portfolio manager invests a nominal amount of $50,000,000 in a bond A whose gross price (in % of the nominal amount) and modified duration are, respectively, 93.274 and 8.319. He fears a rate increase and wants to protect his investment. Suppose that the hedging instrument is a bond B whose gross price (in % of the nominal amount) and modified duration are, respectively, 105.264 and 7.04. Its nominal amount is $1,000 We suppose that changes in yields are not equal and that the relationship between the yield to maturity of bond A denoted by ya and the yield to maturity of bond B denoted by yb is equal to Aya - 1.18 x AyB 3 Because of cointegration and nonstationarity of the series, it is better to consider a linear relationship in variations rather than in level. We should write DR = adR: +b+ 192 Fixed Income Securities For example, a 10-bp move of the yield y will be accompanied by a 1.18 x 10 bps = 11.8 bps change in the yield ya. We find the number n of units of bond B that the investor has to sell as given by the following ratio 8.319 x 93.274 x 50,000,000 x 1.18 = 61,777.6 7.04 x 105.264 x 1,000 The investor has to sell 61,778 units of bond B. n =