In explaining how a pension fund should transition to a liability-driven investment strategy, Duane Rocheleau, managing director of Northern Trust's global investment solutions team, writes in "Implementing LDI in Pension Plans," January 2007":

Question

1, Analyze and characterize the liabilities;
2, Quantify the relationship between the assets and liabilities;
3, Develop and implement appropriate investment strategies;
4, Monitor the account, rebalance the assets and liabilities mix and tweak the investment strategy as necessary."

Describe each of the above elements.

Answer 1

In terms of analyzing and characterizing the liabilities, the manager wants to know the amounts of cash flows and the timing of the cash flows that are owed pension fund recipients. This is needed to determine what kinds and proportion of funds to allocate to asset types. For example, a diversified mix of asset types with a significant commitment to one type of assets might then be judged to offer the highest probability of building assets, containing costs and meeting the plan's obligations.

In terms of quantifying the relation between the assets and liabilities, the manager wants to be able to match the cash flows from the assets with those of the liabilities so that pension fund recipients will be paid in full and on time. To understand this problem and the need to quantify, consider duration. We can note that for many pension plans, the duration of the liabilities is quite long ranging from twelve years on up to even over twenty years. The duration provides an estimate of how the liability will change as a result of a one percent parallel shift in the yield curve. A plan with a liability duration of ten years could expect to see liabilities grow by approximately ten percent if interest rates dropped by one percent. Over periods of time, interest rates have dropped by far more than one percent for a number of consecutive years. In light of this, it becomes important that we match the duration for assets and liabilities.

In regards to developing and implementing appropriate investment strategies, there are two strategies to choose from: multi-period immunization and cash flow matching.

A multi-period immunization strategy is one in which a portfolio is created that will be capable of satisfying more than one predetermined future liability regardless if interest rates change. Even if there is a parallel shift in the yield curve, it has been demonstrated that matching the duration of the portfolio to the duration of the liabilities is not a sufficient condition to immunize a portfolio seeking to satisfy a liability stream. Instead, it is necessary to decompose the portfolio payment stream in such a way that each liability is immunized by one of the component streams. The key to understanding this approach is recognizing that the payment stream on the portfolio, not the portfolio itself, must be decomposed in this manner. There may be no actual bonds that would give the component payment stream.

A cash flow matching strategy is used to construct a portfolio that will fund a schedule of liabilities from a portfolio's cash flows, with the portfolio's value diminishing to zero after payment of the last liability. This strategy can be summarized as follows. A bond is selected with a maturity that matches the last liability stream. An amount of principal plus final coupon equal to the amount of the last liability stream is then invested in this bond. The remaining elements of the liability stream are then reduced by the coupon payments on this bond, and another bond is chosen for the new, reduced amount of the next-to-last liability. Going backward in time, this cash flow matching process is continued until all liabilities have been matched by the payment of the securities in the portfolio.

In regards to further action (monitoring, rebalancing, and tweaking) on the investment strategy as necessary, we can note that action is required because the market yield will fluctuate over the investment horizon. As a result, the duration of the portfolio will change (and change by more than that caused simply by the passage of time). In the face of changing yields, a portfolio can maintain immunization by rebalancing so that its duration is equal to the duration of the liability's remaining time. For example, if the liability is initially five years, the initial portfolio assets should have a duration of five years. After a year, the duration for the liabilities and assets will change and it is unlikely they will be matched. This is because duration depends on the remaining time to maturity and the new level of yields, and there is no reason why the change in these two values should change the duration by the exact amount of time. Thus, the portfolio must be rebalanced.

A question we can pose is: How often should the portfolio be rebalanced to adjust its duration? On the one hand, the more frequent rebalancing increases transactions costs, thereby reducing the likelihood of achieving the target yield. On the other hand, less frequent rebalancing will result in the duration wandering from the target duration, which will also reduce the likelihood of achieving the target yield. Thus, the portfolio manager faces a trade-off: some transaction costs must be accepted to prevent the duration from wandering too far from its target, but some maladjustment in the duration must be accepted or transaction costs will become prohibitively high.