08 Oct 2019 On the Solvency II Risk Margin

Opening talk for IFoA Sessional Meeting on Risk Margin paper, 7th October 2019

Thank you for the opportunity to open this evening’s discussion of the Risk Margin Working Party’s paper. On behalf of all of us here this evening, I would like to extend my thanks and congratulations to the Working Party for producing this excellent and much-needed paper.

The paper provides a comprehensive study of Solvency II’s Risk Margin – the background behind its development; the questions that surround its calibration; the many practical matters that arise in its implementation; some potential solutions to those issues; some alternatives to the cost-of-capital approach; as well as current industry perspectives on how to manage the Risk Margin’s financial consequences. This is all presented in a highly accessible and concise way whilst being balanced, rigorous and objective. I strongly commend it to anyone who wishes to have a clear picture of the current state of play on this topic.

The paper provides us with an excellent platform for an informed discussion of the Risk Margin topic this evening. In the spirit of stimulating discussion, I will now offer a few thoughts on the Risk Margin topic that were prompted by my reading the paper.

Cost of capital methodology as a conceptually elegant Risk Margin solution

My personal view is that the cost of capital methodology provides a coherent and insightful way of modelling the market-consistent valuation of an insurance contract that generates promised cashflows that have non-hedgeable uncertainty.

In such circumstances, any financially secure entity must hold capital in excess of the best estimate liabilities to support those risks over the lifetime of the contract. That capital has a cost that therefore must be reflected in the exit value of the contract. This cost is the Risk Margin. This concept fits so naturally into the 1-year market-consistent VaR framework of Solvency II that, even if starting with a blank piece of Risk Margin paper, I think the cost-of-capital approach would be the preferred methodology. The alternative approaches to the Risk Margin that were explored in Section 7 of the Working Party paper such as the run-off percentile approach and other ways of determining a margin over the best estimate offer reasonable approaches to measuring risk. But none of them coherently fit into the idea of a 1-year VaR and its requisite need for an exit value measure in the way that the cost-of-capital method does.

So, I would argue that the cost of capital methodology is a conceptually elegant solution to Solvency II’s question of how to treat un-hedgeable risks in liability valuation. But it is also a highly abstract way of empirically estimating a current exit value for an insurance contract. There is a risk, when making use of such an abstraction to deliver a real-world insight, and especially when using it to determine the quantitative value of a real-world quantity to four or more significant figures, that the logic of the abstract model is mis-applied. I believe the Solvency II implementation of the cost of capital method is open to this charge, and the result is that the Solvency II Risk Margin is generally materially larger than it ought to be. There are a couple of key areas in the SII implementation where I believe these errors have occurred. In the interests of time this evening, I will focus on one in particular, and that is the calibration of the cost of capital rate.

Non-hedgeable risks

But before I do that, I will first touch on another difficult topic that arises in the context of the Risk Margin – how do we determine what risks should be reflected in the Risk Margin? Put another way, what do we mean by ‘non-hedgeable risks’?

Longevity risk provides an interesting, and of course topical, example. The Working Party paper notes that a deep and efficient market for longevity risk transfer exists and is used regularly by insurers to transfer their longevity risk to reinsurers. But they also note that the pricing of such transactions is not in the public domain. This is a significant barrier to the use of these prices in the direct estimation of current exit values. Such a use, however, arguably has some parallels with the use of illiquid OTC derivative prices in liability valuation, it certainly would seem to be only a difference of degree in transparency rather than a difference in kind. Nonetheless, only some of the non-hedgeable risks that insurers undertake will be readily accepted by a reinsurer. As a result, the need for some form of abstract modelling approach to the assessment of the Risk Margin seems unavoidable. But as I will argue below, I think a correctly implemented cost of capital calculation would reconcile much more closely with anecdotal estimates of reinsurance pricing than current Risk Margins do.

It may also be noted that in Solvency II it has been determined that some significant forms of financial market risk exposure on EU insurers’ balance sheets do not trade in deep, liquid and transparent markets. Whilst, at the same time, it has also been determined that the capital that must therefore follow from at least partially bearing those risks should not be included in the calculation of the Risk Margin.

The 30-year risk-free Euro interest rate is an interesting example. In the apparent absence of reliable market prices for the 30-year rate, Solvency II uses best estimate assumptions to build the Euro yield curve out beyond 20 years. But no risk margin is held for the cost of the capital that must presumably be held for the substantial residual risks that arise in the absence of such hedging instruments. What is the difference between longevity risk and long interest rate risk here? In both cases I think we are saying there is a market for risk transfer; but its pricing is not transparent; so we must use best-estimate rather than market-derived assumptions to value the liabilities. But in one case an insurer must also hold a Risk Margin and in the other case the insurer does not.

Calibrating the cost of capital rate

Moving on to my critique of Solvency II’s cost of capital methodology. I believe the choice of 6% as the cost of capital rate is a significant technical error. As the Working Party paper notes, this assumption can be traced back to a 2006 paper related to the Swiss Solvency Test. I think most actuaries who have read that paper will agree with the Working Party’s description of the paper’s justification of the 6% parameter as superficial. And yet it has stuck. And since then, EIOPA has sought to justify this choice of parameter with reference to a historical estimate of the equity risk premium. And others have then argued that it would be more appropriate to instead consider a forward-looking estimate of the equity risk premium. It is also been suggested that, as the insurance sector typically has a beta greater than 1, the applicable risk premium should be greater than the overall equity market risk premium.

But the economic theory underlying the cost of capital method has nothing to do with the equity risk premium. As in any other market-consistent valuation, the size of the risk premium is irrelevant. The economic logic behind the cost of capital methodology is that the cost is there to compensate shareholders for their capital being tied up on the reference entity’s balance sheet rather than sitting in their own account. To the extent that the capital is exposed to equity risk, the equity risk premium will be both expected and required. In the valuation of the cost of supplying the future capital, we must allow for the earnings that the capital is expected to generate, as well as the risk premium that should be incorporated into the total cost of that capital. The equity risk premium cancels out.

But, the theoretical argument for the irrelevance of the equity risk premium in the context of the reference entity can be made even simpler and more direct. The reference entity, as explicitly defined in the Solvency II regulations, is a hypothetical entity with some very specific properties. It does not have any other business on its balance sheet other than the business it will acquire from the insurance firm. The reference entity will hedge any and all financial market risk exposures that it acquires through obtaining the insurance firm’s business. By design, the reference entity unambiguously has, from its explicit characterisation in the Solvency II regulations, a zero-beta balance sheet. It looks nothing like a typical European insurance company, and nothing like the index of corporations that has been referred to in the EIOPA calibration of the cost of capital parameter. The only compensation required by the shareholders of the reference entity is for the frictional costs incurred in tying up their capital on this balance sheet rather than holding it directly.

The frictional cost of capital is not a new idea in economics. Conventionally, there are three components identified as the key components of this cost. These are: the cost of double taxation, agency costs, and the costs of financial distress. Briefly taking these in turn:

The double taxation effect can be estimated as the marginal corporate tax rate multiplied by the risk-free rate. This provides a rationale for the cost of capital rate having a link to the risk-free rate, and today’s low rate environment implies this component of the cost is very small.

Agency costs refer to the cost to the shareholder that arises from the firm’s management doing things with shareholder capital that are not in shareholders’ interests. This is an unusual example of where the regulator might be the friend of the shareholder. Compared with other corporations, insurance company managers are extremely constrained in what they can do with the capital shareholders have provided to fund prudential solvency levels. Conceptually, and we are inevitably dealing in the currency of the conceptual when dealing with a cost of capital methodology, this cost should therefore also be very small.

The third component conventionally identified for the frictional cost of capital is the cost of financial distress. This relates to the idea that, in the event of bankruptcy or near bankruptcy of the firm, there are a range of costs incurred that all capital providers share the burden of. Again, for a highly regulated and financially secure insurance firm, this risk of bankruptcy and its associated costs will be lower than that of the typical corporation.

Typical estimates of the frictional cost of capital of a typical firm in the economics literature usually vary between 2% and 4.5% (see, for example, the CRO Forum publication back in 2008). I believe, for the reasons I have outlined above, that the frictional cost of capital for a UK insurance firm today should be at the very low end of this spectrum. I would therefore contend that halving the cost of capital rate from 6% to 3% could be viewed as quite prudent, and a case for a 2% or even lower assumption could reasonably be made. Clearly, a 3% assumption would halve the Risk Margin. The calculations provided in Section 3 of the Working Party’s paper show that such an assumption would reconcile much better with current reinsurance pricing than the assumed rate of 6%.

I hope these brief thoughts may be useful in opening this evening’s discussion of the Working Party paper and its topic of the Solvency II Risk Margin. There are many interesting and important topics that the Working Party has raised in their paper that I have not commented upon: does we need a Risk Margin at all? Can it result in the double-counting of risks? Does it result in a prudential solvency system that requires too much capital, with the inevitable harmful consequences for consumer costs and choices? What should the UK do with the Risk Margin following its departure from the EU; how does it fit with ICS and Solvency II equivalence. And so on. But that’s enough from me, and I look forward to now hearing the thoughts and comments of others. Thank you.