 In the domain of bond management, another passive strategy is the immunization strategy. In immunization strategy, actions are taken to mitigate the risk of interest rate changes on the bond portfolio. So in these strategies, the bond portfolio have no effect of riskiness of the interest rate changes. So immunization is a way to mitigate interest rate risk used by financial institutions like banks, pension funds and insurance companies. We know that there is a natural mismatch between bank assets and its liabilities, maturities because the bank has short-term and low-duration deposits which are the bank's liabilities. On the other hand, the bank has interest rate sensitive long-term advances which are treated as the bank's assets. Now the rising interest rates may erode the bank's net worth. This means the value of the bank assets may go down substantially. On the other hand, the value of the liabilities may go up substantially. Fall in interest rates may grow speedily the liabilities than the assets of pension funds that is also with the pension fund like the case of bank. Immunization requires deep understanding of duration and convexity of a bond portfolio by the portfolio manager. Immunize portfolio by matching the interest rate risk of assets and liabilities. Now how to do it? We need to first match the duration of the assets and liabilities, then we need to determine the price risk and reinvestment risk because these two cancel out for small interest rate changes. So the lesson here is that the value of assets will track the value of liabilities whether the interest rate falls or it gets a rise. To understand this we have an example where an insurance company issues a $10,000 investment contract for five years maturity at 8% guaranteed interest rate. So the payment in five years would be equal to $10,000 multiplied by 1.085 that comes to $14,693.28. Suppose the company chooses to fund this obligation with same amount of 8% annual coupon bond selling at the par value with the maturity of six years. Now we see that the obligation has a maturity of five years where is the investment plan has the maturity of six years. If the market interest rate stays at 8% the obligation has been fully funded. Now how these data will work? We have a table that shows the terminal value of a bond portfolio after five years assuming that we reinvest all of the proceeds. Now if we see on the left panel of the screen we see the rate used by 8% then the if the rate falls to 7% or if the rate increases to 9%. So we have three scenarios where the one is the scenario of 8% other is the scenario with 7% that is fall in the rate and the third scenario is 9% that is increase in the rate. You see that at 8% the accumulated funds from the bonds grow equal to the same value of obligation that is $14,693.28 because we have reinvested the coupon income of $800 at 8%. So we reinvested all of our coupon bonds and this way the bond will sell for par value that is the $10,000. This is because that the coupon interest rate is equal to the market interest rate and that is 10%. Now come to the second scenario where the interest rate falls to 7%. If it falls to 7% we see that now the fund will grow to $14,694.05. So in this way the fund is providing a little surplus of $0.77 what will happen if interest rate increases to 9% and we see that with the increase to 9% the fund grows to $14,696.02. Again the fund is giving a small surplus of $2.74. So how duration matching balances can be there? We see that these balances between accumulated value of the coupon payments and the sale value of the bond that is the price risk. So we need to have a balance between the reinvestment rate risk and the price risk and if interest rate falls the coupons grow less than the base case but the bond's higher value offsets this and if interest rate rise the bond value will also rise because the coupon more than makeup for the loss but because of the reinvested at the higher rate. So how rebalancing can be done for the immunized portfolio? We see on the right side of the screen where we can see that the solid line in below that is the curved line that represents the bonds accumulated value of the interest rate remains at 8%. But what about the dashed curved line in black color? That shows value if the interest rate increases. Initially there is a capital loss but eventually it is offset by the new faster growth rate of the reinvested fund and at the 5 year horizon date it is equal to the bonds duration. The two effects just cancel leaving the company able to satisfy its obligation at the accumulated proceeds from the bond. So what is cash flow matching and the dedication strategy? By cash flow matching it is the automatically immunize the portfolio from the interest rate risk because cash flows from the bonds and the obligations exactly offset each other. Cash flow matching is also sometimes called as the dedicating strategy. Here a manager selects either zero or coupon bonds with the total cash flows in each period that matches a series of obligations. Once for all approach to eliminate interest rate risk and that approach is used in this dedication strategy because once the cash flows are matched there is no need for rebalancing the cash flows.