Effectively Mitigating Interest Rate Risk Across Multiple Liabilities

Cash Flow Matching

Cash flow matching is a safe and straightforward strategy. It entails purchasing a zero-coupon bond with an amount equal to each liability's due date. Alternatively, coupon-bearing bonds can be used for cash flow matching. The principle or face value of these bonds becomes due at maturity, allowing for a theoretical match with the liability in terms of timing and size to immunize it. Coupons received before the maturity date can be reinvested or used to offset earlier liabilities partially.

Duration Matching

Duration matching is a flexible approach for funding multiple liabilities. It commonly employs money-matching duration but can also use Macaulay duration. The following rules, similar to immunizing a single liability, are important when immunizing multiple liabilities:

1. The initial portfolio market value equals the present value of liabilities.
2. Portfolio and liability basis point values match.
3. Asset convexity should be nearly equal to, but exceed liability convexity.
4. Regularly rebalance the portfolio to maintain the BPV match as times and yields change (while considering the tradeoff between higher transaction costs from frequent rebalancing versus the risk of allowing durations to drift apart).

Derivatives Overlay

A derivatives overlay involves using Treasury futures to adjust the exposure of specific fixed-income instruments in a portfolio, avoiding the need to sell the underlying securities directly. This method is often quicker and more cost-effective. In the United States, various Treasury futures contracts are available based on the 30-year bond, 10, 5, and 2-year Treasury notes, each representing $100,000 par value of the underlying security, also known as the cheapest to deliver (“CTD”) bond.

The formula to calculate the basis point value (BPV) of futures contracts required for purchase or sale is:

$$ \text{Futures BPV} =\frac {\text{BPV}_{(CTD)} }{ \text{CF}_{(CTD)} } $$

This formula helps determine the number of futures contracts to be bought or sold to achieve the desired change in BPV exposure. Remember that negative values indicate selling futures contracts, while positive values indicate the need for purchases:

$$ {\#}_{\text{Futures}} = \frac {(\text{Liability BPV} – \text{Current Portfolio BPV}) }{ \text{Futures BPV}} $$

Contingent Immunization

Contingent immunization is a hybrid strategy blending active and passive management. It requires a significant surplus before implementation. The goal is to maintain a surplus to fund liabilities while seeking excess returns actively. If the surplus grows, it benefits portfolio owners. If it shrinks, active management pauses, and the portfolio is immunized to cover future liabilities. Active management options include:

1. Entire portfolio in long stock or equity options contracts.
2. Long stock or equity options for the surplus, with the rest immunized (a more conservative approach).
3. Active bond management based on interest rate views.

Contingent immunization has some liquidity risk. If the surplus shrinks and the whole portfolio is in equities, quick selling may be needed to prevent a negative surplus. Short futures and options contracts carry unlimited loss potential, exposing the portfolio to significant downside risk.

Question

Which of the following is least likely consistent with the rules for immunizing multiple liabilities in a portfolio?

1. Initial portfolio market value equals the present value of liabilities
2. Portfolio and liability basis point values match
3. Liability convexity should be nearly equal to but should exceed asset convexity

Solution

The correct answer is C.

C is the least likely consistent. This is because asset convexity should be nearly equal to but exceed liability convexity. Convexity acts as a cushion, allowing assets to decline in value slightly slower than liabilities and also permitting assets to grow somewhat faster than liabilities. This ensures the portfolio remains adequately funded to meet its obligations.

A is incorrect. This statement is consistent with the rules for immunizing multiple liabilities. When setting up an immunization strategy, the initial portfolio market value should indeed equal the present value of the liabilities to ensure that the assets are sufficient to cover the obligations.

B is incorrect. This statement is also consistent with the rules for immunizing multiple liabilities. The basis point values, which represent the sensitivity of the portfolio and liabilities to changes in interest rates, should match as closely as possible to minimize interest rate risk.

Reading 20: Liability-driven and Index-based Strategies

Los 20 (c) Compare strategies for a single liability and for multiple liabilities, including alternative means of implementation