22 Aug 2023 4 min read

Looking to r-star for inspiration: revisiting DB scheme hedge ratios

By John Southall

With real yields having risen sharply in the past 18 months, trustees of defined benefit (DB) schemes could arguably now be more cautious about under-hedging rates and inflation risks.


In early 2022 Safwan Mir and I set out a potential framework for trustees to integrate active views into their hedging decision in a blog post called Market-based hedging triggers in a rising rate environment. The article implied that a material under-hedging of rates and inflation risks could make sense for some DB schemes. This was based on real yields being much lower than central bankers’ estimates of neutral real rates.

While we believe the fundamental framework remains valid, the world has since changed! In this blog post we update our analysis to reflect three key factors:

  • Real yields on index-linked gilts are now at a level that felt almost inconceivable at the start of 2022
  • The stock-bond correlation may have increased, at least in the short term
  • Bond yields may now be more volatile, with potentially much more room to fall. This increases the riskiness of unhedged liabilities[1]

This is shown below:


On the other hand, estimates of r-star – the ‘neutral’ or ‘natural’ long-term real interest rate[2] for developed markets don’t appear to have changed[3]. A recent paper by John Williams, President of the Federal Reserve Bank of New York , estimated that r-star at the end of 2022 was close to the levels estimated directly before the pandemic, hovering around 0.5%.

This matters because r-star can be used as a guide to whether real yields are potentially attractive or not.  In our previous blog post we didn’t say that investors should use r-star to make hedging decisions – with active decisions there’s always a risk of neglecting other important factors – but we provided it as an example of how views could be formed.

What are the potential implications for hedging?

Qualitatively, factor (1) encourages higher hedge ratios as bond exposure appears ‘cheaper’. However, factor (2) implies schemes may get more ‘implicit’ hedging from growth assets and so need less ‘explicit’ hedging from liability-driven investment (LDI).  Lastly, factor (3) encourages smaller tilts away from 100%, since taking a view has become riskier; this leads to smaller over- and under-hedges.

Estimating any of these changes precisely is impossible – all the quantities involved are difficult to estimate (particularly the stock-bond correlation) and some are scheme-specific. However, the illustration below indicates the potential impacts according to our modelling for a scheme targeting cash + 1.0% per annum from diversified growth assets:


The key point is that, unsurprisingly, under-hedging looks like a much less attractive proposition than 18 months ago – the ‘ideal’ explicit hedge rises from 69% to 93%. You don’t reach 100% because of the implicit hedging from growth assets held.

As a side note, excess return targets and growth asset allocations have likely reduced for many schemes since last year. Such schemes may consequently have less implicit hedging. They may also have a reduced risk appetite so their tilts to reflect a view are likely to be commensurately smaller. This results in a scaled-down under-hedge[4].

Under-hedging would now appear to be less justified

Notwithstanding the timing of our previous blog post, formulating an active view on interest rates can be challenging, and track records for predicting the direction of yields are generally poor. As such there is a debate to be had about whether this is something trustees should consider at all.

However, under a reasonable approach for doing so – looking to r-star for inspiration – we’ve seen that this potential justification for substantial under-hedges appears to have evaporated over the past 18 months.



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[1] Albeit higher yields have a slight offsetting effect because they reduce scheme duration

[2] The real interest rate which supports the economy at full employment and maximum output while keeping inflation constant.

[3] Although MPC member Megan Greene did write a piece in the FT, outlining her thoughts about why r-star might have risen.

[4] As an example, a scheme targeting half the excess return, so cash + 0.5% has an ideal explicit under-hedge of half that in the cash + 1.0% example (namely 3.6% rather than 7.2%). This is because both the implicit hedge and the tilt to allow for the active view are halved.

John Southall

Head of Solutions Research

John works on financial modelling, investment strategy development and thought leadership. He also gets involved in bespoke strategy work. John used to work as a pensions consultant before joining LGIM in 2011. He has a PhD in dynamical systems and is a qualified actuary.

John Southall