## Portfolio Immunization vs. Cash Flow Matching: An Overview

Whenever we talk about the asset-liability portfolio management (ALM) approach, the concepts of immunization and cash flow matching come into play. In portfolio management, immunization and cash flow matching are two types of dedication strategies.

When a portfolio is constructed with the purpose of funding specific future liabilities, there is a risk of the portfolio value not meeting the target value when the liabilities become due. Portfolio immunization is precisely the strategy to overcome and minimize this risk.

### Key Takeaways

- Portfolio immunization and cash flow matching are two types of dedication strategies to safeguard the funding of liabilities when due.
- Immunization aims to balance the opposing effects interest rates have on price return and reinvestment return of a coupon bond.
- A multiple liability immunization strategy pays off better when the interest rate shifts are not too arbitrary.
- Cash flow matching relies on the availability of securities with specific principals, coupons, and maturities to work efficiently.

## Portfolio Immunization

In simple terms, to immunize a portfolio, we have to match the duration of portfolio assets with the duration of future liabilities. To understand, let us look into the tradeoff between price risk and reinvestment risk in the context of a fixed-income portfolio. There is an inverse relationship between price risk (return) and reinvestment risk (return).

When interest rates increase, the price of a coupon bond falls, whereas the reinvestment return on the coupon rises. The aim of immunization is to establish a portfolio in which these two components of total return—price return and reinvestment return (coupons being constant)—exactly offset each other in case of a parallel interest rate shift once the portfolio is set up. This is achieved by matching the duration of the portfolio with that of the investment horizon of the future liability.

Let’s consider a two-year bond with a 6% coupon payable semi-annually that is selling at par value of $1,000, yielding 6%. The investor’s time horizon for such a bond is one year—that is, the duration of future liability.

The duration (see Macaulay Duration) of this bond is 1.91 years.

The amount needed after one year to fund this liability is:

** 1000 * (1 + 0.06 / 2) ^{2} = 1060.90**

Now let us consider three different scenarios involving variations of interest rates right after the bond is purchased. Scenario 1 corresponds to no change in rates, while in Scenario 2 and 3, there are rates of 8% and 4%, respectively.

To achieve an immunized 6% rate of return over the horizon period of one year, the duration of the bond or portfolio of bonds must be set at 1. When the durations are matched, the price return and reinvestment return offset each other so that there is no net change in total return.

In the case above, the duration of the bond was 1.91 as opposed to liability duration of 1.0 and hence the portfolio return (Column 6) varied with the interest rate shifts (Column 1). Therefore, it is crucial that the portfolio duration remain matched with the liability duration at all times as the first step to achieve immunization.

The above case is often called Classical Single-Period Immunization. However, when an investor has to fund a stream of future liabilities, this approach is extended to include several other conditions that must be satisfied to achieve a Multiple Liability Immunization.

Fong and Vasicek (1984) identified these conditions as follows:

- The present value of assets should equal the present value of liabilities. (See video:
*Understanding Net Present Value)* - The duration of the portfolio should equal that of liabilities.
- The range of durations of individual bonds in the portfolio must have a span that extends beyond the range of durations of individual liabilities, which means that the portfolio must contain individual bonds each with a duration less than that of the first liability and a duration greater than that of the last liability.

One should bear in mind that these conditions assure an immunized rate of return only in case of a parallel rate shift. If the interest rates shift in an arbitrary fashion, which is mostly the case in the real world, techniques such as optimization and linear programming may be used to construct a minimum-risk immunized portfolio.

## Cash Flow Matching

Cash flow matching is another dedication strategy but is relatively simple to understand. As noted above, there is a stream of liabilities to be funded at specified time intervals. To achieve this, a cash flow matching strategy makes use of cash flows from principal and coupon payments on various bonds that are chosen so that the total cash flows exactly match the liability amounts. This is best understood with an example.

The table above shows a liability stream for four years. To fund these liabilities with cash flow matching, we start with funding the last liability with a four-year $10,000 face-value bond with annual coupon payments of $1,000 (Row C4). The principal and coupon payments together satisfy the liability of $11,000 at year four.

Next, we look at the second to last liability, Liability 3 of $8,000, and fund it with a three-year $6,700 face-value bond with annual coupon payments of $300. Next, we look at Liability 2 of $9,000 and fund it with a two-year $7,000 face-value bond with annual coupon payments of $700. Finally, investing in a one-year zero-coupon bond with a face value of $3,000, we can fund Liability 1 of $5,000.

This, of course, is a simplified example, and there are several challenges in attempting to cash flow match a liability stream in the real world. First, the bonds with the required face values and coupon payments might not be available. Second, there might be excess funds available before a liability is due, and these excess funds must be reinvested at a conservative short-term rate. This leads to some reinvestment risk in a cash flow matching strategy. Again, linear programming techniques may be used to select a set of bonds in a given context to create a minimum reinvestment risk cash flow match.

## Special Considerations

In an ideal world in which one had access to all kinds of securities offering a full range of face values—coupons and maturities—a cash flow matching strategy would create a perfect match between the flow of cash and liabilities and completely eliminate any reinvestment risk or cash flow match risk. However, the ideal rarely exists in any real-world scenario, and so a cash flow matching strategy is hard to achieve without a significant tradeoff in terms of higher cash investment and excess cash balances being reinvested at very conservative rates.

In cash flow matching, cash flows must be available before a liability is due, whereas, in multiple immunizations, liabilities are funded from cash flows derived from portfolio rebalancing on the basis of dollar durations. In this respect, a multiple liability immunization strategy is generally superior to cash flow matching.

However, in specific cases where the liability amounts and cash flows can be reasonably matched over the time horizon without much reinvestment risk, a cash flow matching strategy may be favored for its simplicity. In some cases, it is even possible to combine the two strategies in what is called combination matching, where the portfolio assets and liabilities are not just duration-matched for the complete time horizon but also cash-flow matched for the initial few years.