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Alternative views on extrapolated yield curves: a fundamental question remains unanswered

Tue, 03 Jul 2012 14:51:46 GMT

The valuation of ultra long-term cash flows is surely one of the most basic challenges faced by accountants and actuaries. Yet the resulting debate grinds on about how to extrapolate observable yield curves. At its heart is an absolutely fundamental choice. On the one hand, extrapolated prices could represent where we might truly expect to trade a promised cash flow. These prices will be uncomfortably volatile and will imply relatively high levels of solvency capital for insurance firms. Alternatively, extrapolated prices can be stabilized for the purposes of avoiding this variability. Unfortunately, prices produced by the two methods are quite different.

The estimation and extrapolation of market yield curves has gained the attention of insurance firms, accountants and regulators over the past few years as a consequence of a move towards a market-based approach to valuation. This basic valuation principle is embedded in IFRS/FASB rules for fair valuation (including insurance contracts) and a worldwide move by insurance regulators towards risk-based capital to support an economic balance sheet. Here we will discuss one fundamental question – the basic purpose of any extrapolation. There are two separate ways of thinking about extrapolation which turn out to be quite different.

View #1: Accountants and traders – the Traders’ yield curve

Consider the perspective of accountants and dealers. The FASB definition of fair value says:

“Fair value is the price that would be received to sell an asset or paid to transfer a liability in an orderly transaction  ... between market participants  ... under current market conditions.”

IASB/FASB anticipates using a range of market information and judgement to arrive at a valuation. Where prices are unavailable, valuations are to be based on expected values with risk adjustments. In order to give insight into these risk adjustments, consider the question of where a transaction would take place and ask yourself what factors would determine where you would be prepared to trade? The trader’s approach is to ask: firstly, how much of the resulting risk in my position can be hedged? Secondly, what is the cost of the hedge over the possible life of the position (itself often highly uncertain – especially if the hedge requires dynamic action)? Thirdly, how to adjust a price for the unhedgeable risk for which additional trading risk capital is required i.e. what is the necessary amount and required return on the trader’s risk capital. For a cash flow falling beyond the traded market, we could say:

  • The cost of the hedge will be closely linked to the availability of similar tradable bonds.
  • The risk charge is likely to be unstable. In stressed market conditions, the risk charge will probably rise in line with other risk capital costs.

This line of argument suggests that a fair value approach will produce volatile extrapolated prices. For anyone who must trade an asset or liability, these are the values that really matter and pretending otherwise could be costly. Let’s call the results produced by hedging and taking account of capital costs the traders’ yield curve. You might expect the extrapolated curves produced to contain flat forward curves where variability in traded rates is transferred to extrapolated maturities.

As an aside, you should note EIOPA’s view is that risk adjustments for unhedgeable market risk can be ignored – either because they are immaterial or just too difficult to calculate. 

View #2: Actuaries and insurance regulators – the Stabilized yield curve

Volatile market-based yield curves result in volatile insurance balance sheets and, given a short-term VaR capital measure, relatively high and volatile capital requirements. This volatility is seen as unhelpful by many in a long-term business where extrapolated cash flows are rarely traded. A consensus has emerged to stabilize the curve and methods essentially attempt to answer three questions:

  1. What is the limiting (“ultimate”) forward interest rate (UFR)?
  2. Which observable market prices should be fitted?
  3. What is the appropriate speed of convergence between observed rates and the ultimate rate?

The way these questions are answered could deliver curves that are indistinguishable from the trader’s curve. Alternatively, highly stable rates could be generated that bear little resemblance to the trader’s curve. For all three questions, there are quite different views. The discarding of market prices – due to their lack of liquidity – runs the risk of disconnecting liability values from markets and creating a disincentive to hedge – probably not the regulators’ intention nor in the long-term interests of shareholders and policyholders.

Where next?

So, is it possible to simultaneously stabilize the extrapolated curve whilst respecting market prices and the trader’s pricing models? I doubt it. The stability that regulators and firms seek simply is not consistent with a trader’s view of pricing dynamics.
Does this matter? In Europe at least, it seems a simple fact of life that the answers to these questions will now be determined by political compromise rather than cold, objective economic analysis. However, there is a fine balance here which now risks the creation of two sets of yield curves – one for accountants’ fair valuation which makes use of all reliable market information and an alternative which stabilizes for the purposes of regulatory valuation. That would be a disappointing outcome for the architects of Solvency II.
 

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