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The Actuary The magazine of the Institute & Faculty of Actuaries
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Financial Crisis: Liquid assets?

There has been a long-running discussion in actuarial circles as to whether any ‘liquidity’ component in corporate bond yields can justifiably be used to reduce the value placed on annuity liabilities. This argument has intensified since the start of the credit crisis.

This article argues that, while in current conditions, a liquidity premium can be part of the justification of a lower value for annuities, such a premium has generally been small, and has only become significant in recent stressed markets. Further, some of the arguments put forward in the past no longer stand up.

What is the argument?
An argument that has commonly been made runs as follows: ignoring mortality variation, annuity cash flows are relatively ‘illiquid’. A result of this is they can be matched by illiquid assets, which can then be held to maturity. This means that annuity writers can profit from the liquidity premium available in corporate bonds.

There are many issues to discuss here: is there a liquidity premium, are annuity liabilities ‘illiquid’ and, if so, does this mean that a different valuation should be put on them?

Is there a liquidity premium?
The idea that more liquid assets have a higher price than less liquid assets is well established. For example, highly liquid on-the-run government bonds trade at higher prices than otherwise identical off-the-run bonds. Closer to home, many studies have shown that the swap spread (the difference between the swap rate and the equivalent yield on government bonds) is sensitive to measures of government bond market liquidity. It is therefore well established, and not contentious, that relative liquidity is a driver of asset prices.

Is the liquidity premium in corporate bonds significant?
Most writers of annuities hold investment grade corporate bonds as a partial match for their liabilities. The match is only partial because these bonds are subject to default risk. At the same time, most market-consistent liability valuations are calculated using the swap rate as the ‘risk-free’ rate.

It is not possible to directly compare the yield on the two asset classes to determine any liquidity premium because of the difference in credit risk. Nor is it reasonable to simply deduct historic average default rates from the difference, because the market requires a risk premium for exposure to credit risk.

Attempts have been made to estimate the market cost of credit risk using so-called structural models, such as the Merton model and the Bank of England model. However, these models have proved unable to reflect the full range of risks a company faces and have been difficult to calibrate. Fortunately, the development of the credit default swap (CDS) market has largely solved this problem. It is important to note that structural models are essentially attempts to estimate the prices of CDS contracts from first principles. Differences in results between the two approaches reflect the fact that structural models aren’t perfect (in the same way that the original Black-Scholes option pricing formula doesn’t typically give the market value of equity options); it is unlikely they give any further insight.

However, the CDS market provides a directly observable market price for credit risk. We can simply deduct the CDS spread from the spread on a corporate bond portfolio to determine the possible liquidity premium. This comparison is shown in figure 1 (below).

Until the start of the credit crisis, it can be seen that this was no more than 10 basis points. This issue has been subject to rigorous academic study and, until very recently, the conclusions were always the same: there was very little spread.

The variation in this spread is sensitive to measures of bond market liquidity but, as the spread itself is so low, it was not really significant for the valuation of annuity liabilities. To put it another way, in normal times, any liquidity premium has been too small to worry about.

This has changed recently, and a gap has opened up that may be due to bond market liquidity, although it may be due to other factors as well. We shall return to this later.

Are annuities illiquid?
At the heart of the argument that annuity writers can benefit from any liquidity premium, is the claim that annuity cash flows are illiquid. This is true, to the extent that all insurance liabilities are illiquid, but it is not relevant.

Liquidity is, in practice, a purely asset-related attribute. Liquid assets can be traded in large volumes, as and when required, without having any significant impact on the market price. Less liquid assets can only be traded in smaller volumes, at longer notice, and with a greater impact on the market price.

In general, liabilities cannot be traded at all and, given there is not a market, do not have a market price. It is worth noting, however, that we would expect an illiquid liability, if it did trade, to have a higher value than a more liquid liability. Investors will want more money to take on a liability they can’t get rid of, than one they can.

The issue here is that ‘illiquid’ is being used as a synonym for ‘predictable’. The argument is really that annuity cash flows are predictable and, consequently, annuity writers do not need access to liquid assets because they can be certain of when they will need to realise them.

Does predictability matter?
Nomenclature matters. There are many cash flows outside of the insurance industry that are predictable and much theory over how to value them. Nowhere in this theory do we see mention of the valuation of predictable cash flows being linked to the liquidity of backing assets. Indeed, it is at the core of financial valuation theory that the value of a liability depends only upon the characteristics of that liability, not the assets held to back it.

A good example is the valuation of the fixed leg of an interest rate swap. The cash flows from such an instrument are entirely predictable since they are defined in the contract, and the swap counterparties have no right to change the terms of the swap.

The swap rate is therefore the minimum ‘no bells and whistles’ rate at which the market values fixed cash flows. The fixed leg of a swap is at least as predictable as annuity cash flows. This suggests that the swap rate should be the appropriate starting point for annuity liability valuation.

Of course, the swap rate is affected by the credit risk in LIBOR, but academic research still supports the use of a discount rate for fixed cash flows that is closer to the swap rate than any other traded instrument.

Are annuities unique?
The other side of the claim that annuities should be valued differently to other contracts is that they are unique: they are essentially the only way that it is possible to take advantage of any liquidity premium in corporate bonds. This argument is needed as, otherwise, market forces would eliminate any liquidity premium.

There is a well known trade, the ‘negative basis trade’, that is expressly designed to profit from any difference between the yield on corporate bonds (after buying CDS protection) and the swap rate. Under this trade, an arbitrageur would purchase a corporate bond, funded by borrowing in the repo market, buy CDS protection against credit risk and enter into an interest rate swap to hedge away interest rate risk. What is left is the ‘liquidity premium’. There are transaction costs to such trades, which is why there can be small differences between the bond and CDS markets, but such trades typically keep the markets in line.

It has been argued that only annuity writers, who raise large amounts of cash through their businesses, have the money to invest in, and hold, corporate bonds to maturity. Yet banks and other financial institutions raise many trillions of dollars in fixed liabilities, such as bonds, to fund their activities. The question arises as to why banks could take advantage of the liquidity premium in the same way that insurers issue annuities.

Valuing annuity liabilities today
We have argued that the value of annuity liabilities should not be affected by the type of assets that are held, that in normal times the liquidity premium in corporate bonds is small, and that there is no rationale to treat annuities as a special case. However, in current times there are reasons why annuity liabilities could be given a lower value than that achieved by discounting at the swap rate.

Firstly, from CDS prices we can see that the market’s view of the (risk-adjusted) probability of an insurance company defaulting on its obligations has increased, from single-digit basis points to the order of one hundred basis points over the last year. This is a change in the nature of the liabilities and, from an economic perspective, it would be reasonable to reflect this in the valuation of the liabilities. This is nothing to do with the liquidity of either the liabilities or the assets held, but a direct reflection of the ‘own credit risk’ in the liabilities.

Secondly, there seems to be a anomaly in the market at the moment, as shown in the later period in figure 1, with prices being such that it should be possible to make money through a negative basis trade, but arbitrageurs are not trading (and hence bringing markets into equilibrium). In such conditions, it is possible to construct several different replicating portfolios that are all essentially risk-free and which match annuity liabilities equally well – in essence, we have multiple risk-free rates – and it seems reasonable for firms to use the cheapest when valuing annuity liabilities.

In current markets, however, it may not be possible for such replicating portfolios to actually be constructed, and we would argue that, if it can’t be constructed, it can’t be used. At present, the cheapest replicating portfolio for annuity liabilities appears to be a mixture of corporate bonds and a CDS portfolio. It seems unlikely that a firm could actually purchase the bonds to build such a portfolio at current market prices today, but for annuity writers that already hold suitable bonds this is a viable valuation approach.

Even in these circumstances, the rationale for using such a portfolio is not that annuity liabilities are illiquid, or even predictable – the same arguments could hold for other liabilities. Nor is it that corporate bonds themselves have a significant liquidity premium – in normal times they do not. It is simply that at present, the market appears to be broken.
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David Dullaway is a principal of Towers Perrin in London. He specialises in the application of market-consistent valuation techniques to pricing, financial management and reporting, corporate valuation, and risk and capital management.
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Related features
This is one of three articles this month from the Actuarial Profession’s Global Financial Crisis Group. Elsewhere, Paul Stanworth and Adrian Lawrence consider why regulatory influences may lead to inconsistencies between the liquidity of firms’ assets and liabilities (www.the-actuary.org.uk/834564) and Paul Fulcher and Colin Wilson discuss the rationale for including liquidity premiums in the valuation of annuity business (www.the-actuary.org.uk/834588).
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