Duration Matching as a Risk Management Strategy—Rating: Poor
By Edward J. Freeman
Risk Management, June 2023
Duration matching is a risk management strategy, commonly used in the insurance industry, where the duration (price sensitivity to a yield curve movement) of an asset portfolio is adjusted to be made equal to the duration of the liability. This is done under that assumption that doing so eliminates interest risk. To put it another way, when asset duration matches liability duration, it is assumed that the assets form a hedge against the liability.
However, this approach has flaws. In this essay, I note some key failures of duration matching and offer a potential alternative. Broadly speaking, duration matching is a poor strategy since the basic assumptions of the method are not met, there is no dollar measure of risk, and risk mitigation is not derivative.
Asset and Liability Price Variance
Typically, to manage a portfolio of liabilities in the insurance industry, a dedicated portfolio of assets is allocated to a set of liabilities and the amount is set equal to either the statutory liability value or net GAAP liability value. The combination of a group of assets and liabilities is commonly called a segment. In either case (stat or GAAP), in a segment, the market price of assets is unequal to the fair value/price of the liability. To properly hedge a liability, the price movement of both assets and liabilities must match under market movements. If the durations of assets and liabilities are equal but the prices aren’t, then the hedge will be ineffective.
Moreover, since the strategy often assumes elimination of the risk by definition then the determination of the liability price is often given short shrift. Determining the liability price is a hard problem but there is plenty of guidance in both GAAP and IRFS. With a poor measure of liability price, the hedge will be ineffective.
Interest Rate Movements—Not Parallel
The modern definition of duration assumed a small, parallel movement of the yield curve to allow the theory to progress. However, it is unrealistic as we know that the short end of the yield curve is far more volatile than the long end.
As a corollary, duration matching ignores changes in Treasury yield slope and curvature. Slope is critical since high short rates can cause surrenders of contracts due to more attractive market rates. Curvature is critical since many asset portfolios are bar-belled for duration. Illiquid (higher yielding) assets often have lower duration than the liability, and overall duration is managed with the purchase of public bonds with durations longer than the liability.
The industry has attempted to resolve both issues with the use of key rate or partial durations (price sensitivity to a yield movement at only one point on the yield curve) but, in my experience, the mismatch limits for key rate variances are high and of low value. Limit breaches are often ignored, or limits increased so the problem goes away, neither of which is ideal risk management.
Convexity Ignored
Due to embedded options, the convexity (change in duration due to a yield curve movement) of many liabilities can be extremely high and unstable. It is generally impossible to hedge the liability convexity, so variances to assets are ignored. Using only the first order in a Taylor expansion (duration matching) assumes that the second order and higher terms are de minimis. To put it mildly, this assumption is often incorrect. Partial convexities exist but involve pencils and a seriously high tower. They are not used.
Unreachable Liability Duration
Many new insurance contracts can have durations that exceed 70. This often causes the duration of an open block of business to approach or exceed 20. To get this kind of overall asset duration, Treasury strips with durations of 30 are required. However, to support the liability minimum guarantees, companies need higher yields than Treasuries provide. Low yields guarantee losses, so the usual response is to run the portfolio with higher yields and shorter duration. This may be appropriate since the purchase of higher yielding assets replace a guaranteed loss with an uncertain risk (duration mismatch). The duration matching strategy doesn’t allow for this type of risk mitigation.
Risk at the Legal Entity Level
One statutory requirement is that, in extremis, all assets of a legal entity must be used to satisfy all liabilities. This means that, while segmentation of assets and liabilities is useful for income measurement, for risk management purposes it is somewhat of a fiction. Unavoidable risk positions in a segment, such as mentioned above, may be offset within other segments. If one segment has assets with a lower duration than the liability’s, then risk may be offset by running another segment with an asset duration higher than the liability’s. If your duration matching strategy forces you to duration match the second segment, then the overall strategy may be risk-taking rather than risk-reducing.
Not a Dollar Measure
Given the above, even if a company is duration matched, risk is not zero. The strategy doesn’t generate a dollar value to define the magnitude of the risk. Some companies have expanded the concept to “dollar duration,” which is the product of price, duration, and a 1 bps movement. This does help, marginally, but many issues noted above (e.g., convexity) remain.
Inappropriate Definition of Risk
The focus of financial economics is the consistency of market prices. Financial economic risk measures using small, instantaneous shocks (like duration), assume the change in price is the key risk measure. However, neither the horizon nor the measure may be important in an insurance company where income and capital adequacy get far more press. The goal of risk management in an insurance company is to manage the probability of insolvency, not price arbitrage. Insurance companies live in the real world and need to answer the question, “We are in the business of taking risk but how often will we lose $x of capital?” Owners and management think in real dollars in real time. If the method can’t answer the real-world dollar question, then it’s deficient.
Implication
So, what is the inevitable result of the above? Despite all the work, a company doesn’t really know how much risk it has. Asset liability management (ALM), as frequently structured, is seen as something that a company needs to do but it rarely drives better earnings. ALM becomes a compliance exercise and seen as a drag on earnings. Duration matching has an implicit assumption of risk elimination, which, aside from being ineffective, is neither possible nor desirable since insurance companies are in the business of taking and managing risk. Insurance companies routinely accept the interest risk of contracts with maturity dates 100 years hence.
Potential Solution—Real-World Analysis
For risk management to add value, measurement must expand to include real-world measures that speak to risk as perceived by the owners of the business. A defined strategic asset allocation, considering all market and credit risks, will have an expected level and volatility of earnings and capital growth over a defined horizon. An alternate mix of assets might improve expected earnings but at the cost of a higher volatility. Management may not have an opinion on whether a duration mismatch of 0.25 or 0.50 is preferable across numerous segments and legal entities but they will certainly pay attention if you state, with a change in assets, that the company should expect another $x of annual earnings but also to lose $y of capital one year in 20.
I plan to explain in more detail how such a structure might work but the objective of this essay is to raise the awareness of the deficiencies in duration matching and to start thinking of better ways to manage the risk.
Essay Credits
As I wrote this essay, ChatGPT from OpenAI, was all over the headlines. So, I decided to test drive the model, because why not? The first warning was that it had significant jargon, which was to be expected. I did my best to remove lingo and any TLAs (three letter acronyms) to make it more legible. It also made the essay a little more structured and polite. For example, I had mentioned that the assumption of parallel movements in interest rates was “nonsense” and it recommended “unrealistic,” which, upon reflection, I agreed and accepted. For a technical essay, this style change seems appropriate. It did not attempt to change any of my arguments, which is not to say they are valid but likely just not within its training. It also suggested adding case studies, but I did not follow that advice since I believe the faults of the method are clear enough. Further, I did not want to point blame or weakness at particular companies since duration matching is industry wide. As a last note, I also gave the paper to several friends, both in risk and not, and their suggestions were far more useful. This too has been noted by others about ChatGPT; it is remarkable but still in its infancy.
Edward J. Freeman, FSA, is a principal of PVAJ Actuarial & Risk Services and can be contacted at Edward.freeman@outlook.com.