Aurora Borealis
1 January 2015 CFA Institute Journal Review

Tail Risk in Pension Funds: An Analysis Using ARCH Models and Bilinear Processes (Digest Summary)

  1. Michal Szudejko

Smoothing in defined benefit pension funds influences the level of tail risk in the form of rare but large losses. Fund managers assume intertemporally and countercyclically certain measures aimed at limiting the volatility of cash flow requirements from fund sponsors. The author finds that pension dynamics may exhibit tail risk and be subject to bursts in volatility. The smoothing measures may adversely affect both the security of benefits to future retirees and the valuation of firms that introduce corporate pension plans.

What’s Inside?

The author investigates the extent to which pension funding rules and practices embed smoothing and countercyclical mechanisms. In his opinion, such mechanisms may increase the tail risk in the distribution of pension plan results. The smoothing mechanisms in question include, among other methods, longer loss amortization and asset value averaging. These methods were used in the aftermath of the 2008 financial crisis when discrepancies between the values of pension assets and liabilities grew at a fast pace, increasing pressure on cash flow requirements from fund sponsors.

The depicted risk carries an increased probability of rare but extreme losses when the natural hedge provided by pension fund assets does not fully cover the volatility of its liabilities. Subsequently, this risk may adversely affect the security of employee benefits and the valuation of firms that introduce corporate pension plans.

How Is This Research Useful to Practitioners?

The author discusses an important aspect of risk management in financial institutions related to tail risk. Using stochastic simulation, he reveals that the distributions of the loss, unfunded liability, and supplementary contributions to the fund exhibit skewness, leptokurtosis, and heavy tails. This risk pattern is present when the cash flows in the pension funds are deferred and smoothed. Smoothing pension fund cash flows may lead to the deferral and accumulation of problems that, in turn, may affect pension plan value with multiplied strength.

A key suggestion to policymakers is to limit the extent of allowable smoothing in pension funds’ cash flow management and reporting. In particular, the author’s work is a call to the EU governing bodies to apply the Solvency II Directive’s capital adequacy standard to pension funds. Regardless of actual policy changes, this research should also be of interest to fund managers because it increases their awareness of the interpretation of “smoothed” results. The fact is that information carried in these smoothed figures may not be complete from a risk assessment perspective. The implications presented by the author could also provide interesting insight into the management of companies running pension plans—as well as to such companies’ investors on the impact of pension plans on company valuation.

How Did the Author Conduct This Research?

The author uses a simulation based on a plausible set of parameters to model how the smoothing mechanisms embedded in pension fund management practice may increase the risk of extreme losses. The underlying rationale is backed by the assumption of limited marketability of pension fund liabilities, which means that it is not possible to achieve a full hedge with pension fund assets. Instead, fund managers attempt to achieve an “optimal” hedge, which may in time prove not to be enough and thus the pension plan will lose value. Fund managers usually seek to carry these losses over time. Other methods to limit the volatility of cash flows required from fund sponsors include averaging in liability discount rates, asset values, and the choice of valuation parameters. But all these techniques may camouflage the emergence of real funding problems that can accumulate over time and lead to severe losses.

The author shows that these losses follow a nonlinear dynamic process that he analyzes using Markov chain theory and bilinear stochastic process theory. The key finding is that tail risk that transpires from the leptokurtic distribution of pension losses as well as Pareto-like slow decay in the distribution tails appears when pension cash flows are deferred and smoothed.

The author’s research is backed and preceded by a rich literature on the subject that emerged following the recent global financial crisis as well as literature on pension plan accounting, pension plan funding, and the impact of the crisis on pension plan assets and liabilities.

Abstractor’s Viewpoint

The article is a good addition to the subject literature. Using quantitative analysis, the author depicts a process that should be of interest to a broad group of stakeholders, including policymakers, company and fund managers, and future retirees. Pension plan stakeholders may not be fully informed about the risk pattern that results from smoothing and deferral that a given pension plan carries. Considering this possibility, I believe the author’s research is very important and that the issue in question requires careful yet increased consideration from all interested parties.

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