The problem of duration matching assets to liabilities in a fiat 'money' system

The matching of asset cashflows to expected liability cashflows is an approach used by insurance companies and others when investing an asset portfolio. When the size and timing of the cashflows are identical, an entity is said to be ‘cashflow matched’.

If a person or company has a payment to be made in 60 days, it should be possible to purchase an asset that will give rise to a cashflow in 60 days that will satisfy the payment. A high quality bill of exchange would be ideal as the owner would earn the discount rate over the 60 days prior to payment.

If a person or company has a payment to be made in five years, it should be possible to purchase an asset that will give rise to cashflows that over those five years that will satisfy the payment. A high quality bond would be ideal as the owner would earn the interest rate over the five years prior to payment. It will be important that the quality of the asset is maintained throughout the five year term – for example it would be expected that a sinking fund would be established to satisfy the bond maturity payment.

It is, however, often too difficult to match the size and timing of assets cashflows to the expected liability cashflows. Instead, a portfolio of assets is chosen so that the payment profile closely resembles the liabilities. This is the typical approach used by insurance companies. It is known as ‘duration matching’ and the portfolio is said to be ‘immunised’ from interest rate risk.

It should be noted that so called ‘duration matching’ actually uses the modified duration of the portfolio and not the duration of the portfolio. The duration is the time value weighted payment schedule of a bond (‘D’) using the interest rate, but the concept of modified duration arises from the 1st order approximation of the Taylor series expansion for the change in the price of a bond for a change in interest rate. Modified duration can be derived from duration as D/(1+i) where i is the periodic interest rate.

The concept of convexity arises from the 2st order approximation of the Taylor Series expansion.

Modified duration and convexity are essentially short-hand expressions for how a bond portfolio changes in price for a change in interest rate. However, as the Taylor series expansion formula assumes a flat term structure of interest rates it has limitations in its usefulness.

More importantly, under a fiat ‘money’ system it can be shown that the concept of duration is distorted. The concept of duration only makes sense if an asset is self-liquidating - that is the asset cashflows arise from customer receipts following the provision of goods and/or services. If an asset relies upon refinancing its duration is only nominal.

For example, let’s consider a company that raises money through the issue of a bond to finance a seven year project. The project involves a two year pre-production period in order to develop the plant & equipment which will then allow for customer sales over the following five year period. The project is of high quality. The bond would have no payments in the first two years. Thereafter interest would be payable, with the principal repayment backed by a sinking fund. It would act similarly to a five year annuity deferred by two years. In this case, the bond is self-liquidating as product sales cover interest and the repayment of capital.

If, however, interest on the bond were to be paid in the first two years, during the pre-production prior to any customer sales, it would fail the self-liquidating test. For the first two years the asset owner would be receiving capital back, fraudulently displayed as ‘interest’.

If the company had issued a four year bond to finance the seven year project it would also fail the self-liquidating test. The bond would require refinancing after only two years of production. In this case the refinancing of the bond is similar to receiving interest prior to production. The asset owner would be receiving capital back despite the project not yet creating sufficient sales to return that capital. This distorts the concept of capital required to fund the deprecation of plant & equipment. It too would be fraudulent.

If you were to treat this four year bond as nominally described, you would calculate its duration at around 3.7 years. The project, however, has an average ‘duration’ of around 5.0 years, assuming equal production in years 3, 4, 5, 6 and 7. The four year bond has distorted the perceived duration of the asset! That is nominalism in action.

A bond issuer that issues a seven-year bond for a seven-year project is acting honestly.

In practice, the matching of assets to liabilities by insurance companies typically also tries to minimise ‘credit risk’. In a fiat ‘money’ system that is typically conceived as investing in ‘risk-free’ assets such as government, semi-government and other ‘high-quality’ bonds.

A government fiat bond is, however, not self-liquidating - so the concept of duration for a government bond becomes meaningless. Government bonds don’t provide funding for a project that will give rise to the provision of goods and/or services in demand. Instead, government bonds are used to fund government expenditures. They are perceived as ‘risk-free’ due to the income and wealth confiscation capacity of the government. More than likely, the government bond will be refinanced on maturity.

The nominal duration of a two year government bond is around 1.95 years. However, the repayment of principal is typically reliant on the government refinancing the bond. If the bond is continually rolled-over, the principal is never repaid. The 1.95 year duration is clearly bogus.

Equity on the other hand is typically viewed as a perpetuity with a long duration (circa 15-20 years) and one that is difficult to measure. The following text table shows an example of this type of thinking from Russell Research, James Gannon, June, 2010.

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Does equity have duration?  And if so, is it useful for LDI?

Issue: Many defined benefit pension plans are seeking to implement a liability-driven investing (LDI) hedging program by matching the durations and credit exposures of their asset portfolios to the durations and credit exposures of their liabilities. Do the behaviors of their equity portfolios help to this end?

Response: While equities can offer attractive long-term returns, possibly in excess of the liability interest cost, and therefore hope for increased plan funded status over the long term, their short-term behavior is so volatile as to offer no material benefit as a hedge for the duration of the defined benefit pension plan liabilities.

https://www.russell.com/au/assets/pdfs/insights/2010-june-Equity-Duration.pdf

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The perception of equity capital as a perpetuity derives from equity capital not having a contractual nominal maturity date for the repayment of principal. However, as we have shown previously it is the duration of the funded project which actually defines the duration of the asset.

The real duration of equity would become more apparent if company management progressively returned equity capital to investors throughout the equity funded project at a rate equivalent to depreciation. Equity capital would appear more accurately as a form of annuity. Additional equity capital could be raised for new projects.

In practice, instead of the clumsy process of returning and reissuing equity, any new equity capital requirements are netted off against the return of capital from existing projects. It is this explicit rolling of equity which often wrongly creates a perception that equity has a longer duration that its underlying projects.

While it is likely that equity funded projects are typically longer than debt funded projects this only relates to the length of projects which equity is used to fund.

In conclusion, in a fiat ‘money’ system the distortion of duration for bonds through nominalism creates a range of problems. In particular, it leads to an excessive focus on using bonds for the matching of liability cashflows. In a fiat ‘money’ system the bond market appears to provide a wide-range of assets for duration matching. It is, however, a deception as often there are no underlying projects to define the duration of the assets.

For the matching of liability cashflows a greater focus should be placed on finding suitable high-quality equity based projects that are self-liquidating as the real duration of equity is often not too long after all.

As first published in Course of the Exchange, Fekete Research, 2Q16