The passive interest rate risk management

Both cash flow matching and immunization of duration gap between asset and liability are the defensive risk management methods. Their aim is evading interest rate risk, but they evade the loss from risk meanwhile they also give up the profit from risk.

7.2.2.1 Cash flow matching

The cash flow matching also called dedicating a portfolio; this is an alternative to multi-period immunization in which the manager matches the maturity of each element in the liability stream, working backward from the last liability to assure all required cash flows.⁵⁸ The cash flow matching is an effective, but largely impractical means of eliminating interest rate risk. If a portfolio has a positive fixed cash flow at some time t, its market value will increase or decrease inversely with changes in the

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spot interest rate for maturity t. If the portfolio has a negative fixed cash flow at time t, its market value will increase or decrease in tandem with changes in that spot rate.

Stated simply, interest rate risk arises from either positive or negative net future cash flows. The concept of cash matching is to eliminate interest rate risk by eliminating all net future cash flows. A portfolio is cash matched if

• every future cash inflow is balanced with an offsetting cash outflow on the same date, and

• every future cash outflow is balanced with an offsetting cash inflow on the same date.

The net cash flow for every date in the future is then 0.⁵⁹

But the requests of cash flow match are really strict which lead the high transaction costs. Moreover, it is not always possible to match all cash flows individually.

Especially in the life insurance company, it is difficult to find assets with maturities s long as those of certain liabilities. Furthermore, the net profitability of any institution attempting to hedge all cash flows one by one and having to buy the options to hedge those sold to policyholders would probably be negative (Vincent 2005).

7.2.2.2 Immunization of the duration gap

The method of immunization is a method that though adjusting the duration of the asset and liability to achieve their match. This match is also the match of interest rate sensitivity of asset and liability which can induce the same change of asset and liability value along with the interest rate fluctuation. If the duration of asset is too long and the life insurance company anticipates that the interest rate will goes up, to avoid the negative effects on the net value of capital, the company need to shorten the duration of asset, such as it can purchase the short-term or floating interest rate assets.

Otherwise, if the duration of asset is really short and the life insurance company anticipates that the interest rate will fall down, it should purchase the long-term assets

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or carry through long-term investment to prolong the duration of asset.

In the former part of this paper, we introduce some models to realize the measure of duration and immunization. Here we will base on the models to give out some detail instruments of asset and liability management to avoid the interest rate risk.

From the formula of duration we know that if the future cash flow is larger the duration is smaller, the maturity is longer the duration is longer. Because the duration of liability in a life insurance company is really longer than the duration of asset, normally the duration gap is negative, unless the profit of investment outclasses the future liability outgo which can counteract the negative increment of duration to lead the duration gap is positive. But it is hard to achieve this aim because of the limited financial market of China and the low-grade management in the life insurance companies. Generally speaking, the duration gap of the life insurance company in China is negative. In this situation, if the interest rate falls down the increase of liability will exceed the increase of asset to lead the negative net profit. If the interest rate goes up the decrease of liability will exceed the decrease of asset to lead the positive net profit. However, the existence of embedded options will countervail such positive profit. The more importance is, because of the substitute character of financial products, the policyholders will purchase other investment products while the interest rate increases. This will induce the shrink of insurance product market.

Nowadays, all the life insurance companies contest each other to occupy the market share; it is hard to tolerance the shrink of the market. Considering the situation of China, we can start from deflating the DG to prevent interest rate risk.

Along with time passing, the matched asset and liability will have the new DG;

meanwhile the company will have the new interest rate sensitivity cash, thus the company need to rebalance the asset and liability to reduce the DG. The longer the period of rebalance, the management cost is fewer, and also the reliability of the immunization is lower.

In the duration analysis, to give a basic of calculation, we assume the yield curve is flat which means the change of long-term interest rate has the linear relation with the change of short-term interest rate. Actually, they have different fluctuation; the long-term fluctuating rate is less than the short-term. They can not always keep the linear relation sometimes they will change in the opposite side. Even the immunization applies a convenient method of interest rate management; it still has some limitations due to the assumptions.