When a set of predetermined liabilities are given, the investor must construct a non-callable bond portfolio of homogeneous ratings by considering certain characteristics such as follows:
The bond portfolio cash flow must occur in such a way that at any time a liability matures, the cumulative bond portfolio cash-flow is comparatively larger than the cumulative cash-flow of liabilities.
The amount and maturity of both asset as well as liability cash flows must match to the possible extent.
With the first condition, the investor is assured that every liability will be funded in the future. The second condition will make sure that the exposure to term structure risk factors of assets and liabilities will match to the possible extent, thus limiting risk-taking on the net value of both assets as well as liabilities. However, this technique does not entail the risk of not being able to fund the liability system. This method can be implemented using minimal information on cash flows.
Let us assume that we have pricing information on bonds and we can adopt an operational way of implementing the second rule by minimizing the value of bond portfolio. Further, let us assume that a single liability of 100 will mature in 5 years. Let us also consider two zero-coupon bonds maturing in 4.5 and 4.9 years respectively. Now, the investor must invest either Rs.65.12 in the first discount bond or 62.69 in the second one in order to fund his liability. The significant point to be noted here is that if the investor is choosing the cheapest portfolio, he will be choosing the best cash-flow match also and thus the least risk. However, this minimization of the value of the bond portfolio can be applied only on bonds of same quality. Otherwise, it will pick up only bonds of lesser quality.
By using this procedure, the investor will have enough cash in advance to fund each liability. He may hold cash in certain time periods, such as the period between the time he receives it and the time he funds the liability. Thus, there is immense possibility of reinvesting this cash for a short period of time.
By considering the reinvestment possibility which is based on an assumption for the reinvestment rate for the cash, the procedure for minimizing the value of the bond can be refined further. At the same time, the investor also depends on the return he receives from the cash to fund the liabilities. Reinvestment risk can arise if the investor is unable to fully fund the liabilities when he actually reinvests at a lesser rate compared to assumed rate.
Finally, we can say that the minimization technique can be applied periodically to take advantage of the emergence of term structure in order to construct an even cheaper bond portfolio. To solve this problem, optimization methods such as linear programming can be used.