This is quasi - modified duration

It is possible to extend the process of immunization to the term structure framework. A portfolio of bonds designed to fund a stream of obligations can be immunized against a parallel shift in the spot rate curve by matching both the present values and the quasi-modified durations of the bonds and the obligations. Consider the following stream of obligations, in dollars, over the next 8 years as shown in the table below below: Year 1 2 3 4 5 6 7 8 100 200 300 400 500 600 700 800 You are given the spot rate curve is as follows: Year Spot 1 2 3 4 5 6 7 8 9 10 11 12 7.67 8.27 8.81 9.31 9.75 10.16 10.52 10.85 11.15 11.42 11.67 11.89 Find a portfolio, consisting of the two bonds below, that has the same present value as the obligation stream and is immunized against an additive shift in the spot rate curve: Bond 1 is a 12-year 6% annual coupon bond Bond 2 is a 5-year 10% annual coupon bond Both bonds have a face value of $100. How many units of Bond 2 should be held in the immunized portfolio? It is possible to extend the process of immunization to the term structure framework. A portfolio of bonds designed to fund a stream of obligations can be immunized against a parallel shift in the spot rate curve by matching both the present values and the quasi-modified durations of the bonds and the obligations. Consider the following stream of obligations, in dollars, over the next 8 years as shown in the table below below: Year 1 2 3 4 5 6 7 8 100 200 300 400 500 600 700 800 You are given the spot rate curve is as follows: Year Spot 1 2 3 4 5 6 7 8 9 10 11 12 7.67 8.27 8.81 9.31 9.75 10.16 10.52 10.85 11.15 11.42 11.67 11.89 Find a portfolio, consisting of the two bonds below, that has the same present value as the obligation stream and is immunized against an additive shift in the spot rate curve: Bond 1 is a 12-year 6% annual coupon bond Bond 2 is a 5-year 10% annual coupon bond Both bonds have a face value of $100. How many units of Bond 2 should be held in the immunized portfolio