Liability-Relative Asset Allocation

Liability-relative approaches first view the cash flows of the sponsoring organization in question and then attempt to build a portfolio of securities that will satisfy these payments as they come due. This is in contrast to the popular asset-only approach in which investors begin thinking about the portfolio of assets and use techniques like MVO to create an optimal asset allocation.

Approaches to liability-relative asset allocation include:

• Surplus optimization.
• Hedging/return-seeking portfolios approach.
• Integrated asset-liability approach.

Surplus Optimization

Surplus Optimization involves MVO applied to surplus returns:

$$ \text{Surplus return} = \frac {\text{Change in total assets} – \text{Change in total liabilities}}{\text{Initial total assets}} $$

The idea with a surplus return is first to satisfy the liabilities and then to view the excess asset value through the lens of MVO, seeking to come up with an optimal asset allocation that will give the best risk-adjusted return. The utility-maximization calculation applies here:

$$ (U_m )= E(R_m )- 0.005 \times \lambda \times Var_m $$

Where:

\(U_m\) = Utility.

\(E(R_m )\)= Expected surplus return.

\(Var_m\) = Variance of the surplus return.

\(\lambda\) = Portfolio risk-aversion parameter.

Hedging/Return-Seeking Portfolios (Two Portfolio-approach)

This method is remarkably similar to surplus optimization. The difference lies in the flexibility to ‘choose’ a surplus amount or change the size of the optimizing portion of the investments in the two-portfolio approach.

A hedging/return-seeking portfolios approach assigns assets to one of two portfolios. The objective of the hedging portfolio (first portfolio) is to hedge the investor’s liability stream. Any remaining funds are invested in the return-seeking portfolio (second portfolio).

Various modifications to this approach include only partially funding the hedging portfolio so that more can be allocated to the riskier return-seeking portfolio and later increasing the allocation to the hedging portfolio as the surplus increases. This approach is more aggressive. While it can be thought of as fail-proof in many ways, certain portfolio risks, such as natural disasters, are not always easy to capture with this approach and should be accounted for in other ways.

Formation of Hedging Portfolio

Hedging portfolios must include assets whose returns are driven by the same factor(s) that drive liabilities’ returns. The assets and liabilities will likely become inconsistent, even if they start with equal values. A good example is promising (cash outflows) that depend on inflation in the future. A hedging portfolio in this situation would typically include index-linked (inflation-linked) Treasury bonds, again cash-matched or immunized to the extent possible.

Hedging portfolios (securities) with active markets have a present value equal to the market value of their assets. As a result, the asset valuation date must coincide with the liability valuation date. The appraised value is used when there are no market values.

The discount rate assumption complicates forming the hedging portfolio, as does finding assets driven by the same factors as liabilities. It may be necessary to use instruments beyond nominal bonds in hedging a liability cash flow that is driven by a factor such as inflation (perhaps interest rate swaps, inflation-linked bonds, and real assets). The hedge may not be fully achieved in many applications if the driving factors are non-marketable (e.g., economic growth).

The discount rate for cash flows related to non-market factors depends on regulations and tradition. High discount rates lead to high funding ratios and lower contributions from the sponsoring organization, while low discount rates lead to lower funding ratios and higher contributions. Regulators set the guidelines, rules, and penalties for determining contribution policy.

Valuation of liability cash flows is complicated due to the inability to purchase a security with positive cash flows equal to the liability cash flows. However, uncertain liabilities can be made more confident through the law of large numbers, such as in the case of life insurance companies. This allows for the valuation of liabilities using the present value of expected cash flows based on a low-risk premium in the discount rate. However, applying the law of large numbers can be limited, and averages do not eliminate longevity risk.

Constraints

It is not always possible to use the basic two-portfolio approach. Creating a fully hedging portfolio is impossible without positive cash flow or contributions, for example, if the funding ratio is below 1. To improve the funding ratio, the sponsor can either increase contributions to generate a positive surplus or use conditional strategies like glide path rules.

Weather-related losses pose another problem when a true hedging portfolio is not available. A partial hedge of the portfolio may exist in these situations, but the investor is exposed to “basis risk” due to imperfect hedges. An investor may also arrange a contract with someone who will take on the liability risk that cannot be hedged for a fee, such as through an insurance policy.

The Integrated Asset-Liability Approach

An integrated asset-liability approach integrates and jointly optimizes asset and liability decisions. Rather than making a one-time, up-front static choice about asset allocation, this approach allows for continual adjustments.

Some institutions with high leverage may face risks such as interest rate risk. As their large portfolios of assets decline in value and/or liabilities, increase with often the same movements, more sophisticated tools such as scenario analysis can allow for adjustments to be made on an ongoing basis to both sides of the balance sheet.

The Three Liability-Related Asset Allocation Approaches and Their Characteristics

$$ \begin{array}{l|l|l}
{\textbf{Surplus} \\ \textbf{Optimization}} & {\textbf{Hedging/Return-Seeking} \\ \textbf{Portfolios}} & {\textbf{Integrated Asset–} \\ \textbf{Liability Portfolios}} \\ \hline
\text{Simplicity} & \text{Simplicity} & \text{Increased complexity} \\ \hline
\text{Linear correlation} & {\text{Linear or non-linear } \\ \text{correlation}} & {\text{Linear or non-linear} \\ \text{correlation}} \\ \hline
\text{All levels of risk} & \text{Conservative level of risk} & \text{All levels of risk} \\ \hline
\text{Any funded ratio} & { \text{Positive funded ratio for basic} \\ \text{approach}} & \text{Any funded ratio} \\ \hline
\text{Single period} & \text{Single period} & \text{Multiple periods}
 \end{array} $$

Question

Which of the following risks would most likely be effectively hedged by a two-portfolio approach?

1. Accounts payable for a cellphone retailer.
2. Fire hazard for an auto parts manufacturer.
3. Rainfall for a tree farm.

Solution

The correct answer is A:

Accounts payable can likely be well-timed, which lends them to being hedged via a two-portfolio approach.

B and C are incorrect. The risk from a fire or lack of rainfall for a farm is not likely to be handled by tradable financial products, limiting its use in a hedging portfolio. These situations would likely call for insurance products.

Reading 5: Principles of Asset Allocation

Los 5 (k) Discuss approaches to liability-relative asset allocation