Why would I care about the present value of my liabilities?

Alex White - Redington

Alex White

Managing Director, ALM
(Friday, Aug, 18, 2017)
|   19 mins

10 second summary

Managing a pension fund’s assets against its liabilities is fundamental in driving the investment and risk policies (highlighted further by TPR guidance March 2017). As interest rates have fallen over the last 2 decades, the mark-to-market, present value (PV) approach of calculating a liability value has been criticized by some for ascribing greater present values to liabilities, and therefore making pensions seem unaffordable1. Here we review the philosophy behind it, and remind ourselves of some the key rationale and reasons behind it – concluding that these remain valid. While we find it has weaknesses, and that other lenses can provide a helpful perspective in certain situations, we believe it has enough advantages to be the best starting point for running a scheme.


Pension liabilities are hard to value. The present values you get by discounting using market rates can move dramatically over a short period, mostly because of interest rates. This is quite counter-intuitive – why should a long term estimate be so variable? This is one reason why some- such as the 300 club- argue against managing pension funds by discounting liabilities at market-derived interest rates. Discussions around pension fund investment often assume a context of managing assets against a present value of liabilities, yet not everyone accepts it. It’s worth taking a step back and reminding ourselves of the theoretical underpinning of this approach, why it is useful, and where potential limitations may arise.

So what now/next steps

If you are a pension fund trustee, are you clear on the reasons behind the approach taken to managing the scheme’s assets and the implications for the investment and risk management policies? These are tricky issues and to some extent philosophical in nature. We know trustee boards and stakeholders often struggle to generate consensus in these areas. This can make it hard to move forward with important decisions. We hope this article can help make the picture a little clearer.

Key Insights

  • The point of valuing a fund is to test whether there are enough assets
  • Bond prices are the market values of future income streams
  • Buyout prices depend on mark-to-market present values. If buyout prices are important to you, then so are PV’s.
  • Actions with regard to interest rates are a key consequence of a present value framework. But the same decisions may be reached through other lenses.
  • A present value approach isn’t necessarily the same as a mark-to-market approach, but a present value framework makes a mark-to-market approach possible.
  • Present value and mark-to-market approaches are more robust to getting assumptions or decisions wrong, as if a scheme needs to sell or rebalance it has to do so at market prices.

The goal of a DB pension fund

The goal of a pension fund, and of the trustees that oversee them, is to pay pensions. If the pensions get paid, the fund succeeded; if they don’t, it failed. The question is then how to manage to that target.

How to manage a DB pension fund

Intuitively, a scheme might look for assets that provide the cashflows needed to pay the pensions. Before worrying about valuing either assets or liabilities, one might argue that the scheme just needs to have enough assets to pay each pension payment as it falls due. This makes sense in theory, but it quickly becomes quite complicated to measure. After all, how do you know whether your assets are enough or not?

Do you have enough assets? The Present Value approach

This is where the approach of discounting at market rates evolved (in this paper, we refer to this as the balance sheet approach). To find out if you have enough assets, you value both your assets and your liabilities consistently, and see which is bigger. You know you need to meet a certain payment stream (your liabilities), so you want to know how much money you would need to buy that stream of payments. You then compare this to the value you could get by selling your portfolio. In this context, the liability PV is really a shorthand for the cost of future payments.

This is a simplification, and there are lots of complications. For example, your asset value may not be that certain as illiquid assets may be hard to value, and the sale price might depend on how long you had to sell them. However, the principle is still there. Assets can be valued at their prices in the market. Liabilities are streams of payments. Streams of payments can also be valued in the markets, as that is what bonds are. Therefore, you can use bond pricing to price liabilities in a way that is consistent with your assets.

So what are the pros and cons?

You could run a pension fund without valuing the liabilities. To do this, you could make assumptions about future returns and then project your assets forward accordingly. We can think of this as The Direct Projection approach.

It is increasingly a matter of philosophical debate in the DB pensions community whether a Direct Projection approach might be an appropriate way to manage a scheme. We believe that a key question is the effect that a particular approach has on the key decisions facing the scheme’s trustees. Often, different approaches should lead to the same decisions. And at the end of a scheme’s life they should also converge.

For example, suppose you have a scheme which is fully funded on a gilts flat basis. This means if you discount your liabilities at gilt rates, you get a liability value equal to the value of your assets. Put another way, if your assets grow at gilt interest rates, they will meet the liabilities. This means you need to invest in assets which will earn gilt rates (or better) to meet the liabilities. That means you have enough assets to fund your liabilities simply by buying gilts (and index linked gilts). If this was the case, then in either approach, investing everything in gilts would be justified. But there may well be differences along the way.

We caveat that this is a simplification. The liabilities will have inflation-linkage, but pensioner inflation will be floored at zero (unlike the inflation in linkers), and liabilities will have longevity risk as well. In practice this could motivate keeping a small holding in risky assets, or entering more complicated hedging programmes. However, the principle still holds. If you only need to earn gilt rates to meet your objectives, however low they are, then gilts are a good investment.

Legal/Regulatory Requirements

The regulatory framework is set up around a present value approach, in a number of ways, and this influences behaviour. Firstly, the PPF levy is charged based on a present value perspective. Secondly, the scheme specific funding regime is set up around funding to meet the present value of liabilities calculated using a suitably-chosen discount rate. Thirdly, buyout pricing is driven by a present value/mark-to-market approach. If a sponsor fails and the scheme has to do a partial buyout, the benefits the trustees can secure will depend on the buyout price available from providers in the market at that point in time. Insurers’ pricing of liabilities is driven by discounting at market rates, and this is likely to remain the case in the future. Adopting the same approach to managing the scheme is likely to be a more effective way to manage against the risk of a partial buyout. Therefore, if the sponsor covenant is particularly weak and buyout is a real risk, that gives a clear rationale for managing according to a balance-sheet and mark-to-market approach. This is because if you have to do a partial or full buyout, you want to manage against buyout prices.

These are all important factors. However, this piece aims to go deeper into the philosophy behind the present value approach, constructing the rationale from first principles and assessing whether it remains relevant.

What decisions does it make you take?

To address a key point up front – the only important consequences of any approach to pension scheme management are the actions taken as a result of it.  That said, the way you define which decisions are riskier than others is likely to affect which decisions you make. That’s why it matters.

In a direct projection framework, there’s no reason to look at your liability PV. After all, the actual payments due do not change with changes in long term interest rates. However, what does happen is the cost of income streams moves up or down, and it becomes harder or easier to meet the liabilities with the same amount of assets.

Let’s look at a simplified example which attempts to illustrate how the position of a pension fund changes when interest rates move:

Say I have £100 and need to make a payment of £105 next year. If one-year gilt rates are 5%, this is easy- I can buy a one-year gilt. If one-year rates are 0.5%, then I will have to take some risk to deliver a return of 5% and meet my liability, as the return I need is now significantly in excess of the risk free rate available. I am in a materially different position if rates are 5% or 0.5%, even if everything else is the same.

A fundamental underpinning of much of finance theory since the 1960’s (and possibly earlier) is the decomposition of the expected returns on an asset or portfolio as the risk free rate, plus a return to compensate the investor for the risk being taken.2

The effect of interest rates on a scheme’s position may become clear through lenses other than a PV approach, but it is a lot clearer when you look at a scheme through a present value lens. And in the last decade, a fund’s decisions with respect to interest rate exposures have generally had a significantly bigger effect than any other decisions they might have made, as falls in interest rates have made it harder to meet fixed benefit payments in the future.

For a continuation of the discussion on these points see this paper: Is It Too Late to Hedge

Present Values and Mark-to-Market

There is a subtle point about the present value approach which is worth clarifying up front. It is entirely possible to value liabilities based on discount rates that are not determined by the market. When we consider the present value approach, it is worth separating the decision to value the liabilities at all from the decision to use a market-based discount rate. The next two sections highlight the operational advantages of using a liability value at all, while the subsequent sections focus on using market discount rates specifically.

Key Questions – in the following section we take the approach of posing the following questions of a present value approach to test the appropriateness.

  1. Does a present value approach make things clearer?
  2. Does a present value approach make decision making easier?
  3. Is the present value approach enough – what happens as a closed scheme runs down?
  4. Is the present value approach helpful for setting contributions?
  5. What if I’m wrong?
  6. Doesn’t this just make me buy bonds, when equities do better long-term?

Does a present value approach make things clearer?

A present value approach reduces the problem of running a pension fund to simple metrics that say whether the fund is on track or not. Take a scheme that is fully funded on a gilts flat basis. Again, this means that the scheme would invest solely in gilts and earn enough to pay the liabilities. From either perspective, a 100% allocation to gilts would be a valid portfolio.  However, it might be easier to see this on a present value basis. On a direct projection basis, you would see a stream of asset cashflows and a stream of liability cashflows which roughly offset each other. On a present value basis, you could see your assets and liabilities as just two numbers.

Direct projection is arguably a more intuitive way of thinking about managing a fund, but it can be operationally difficult and may not easily lead to a clear decision making process. One big advantage of the present value approach is that funding levels are relatively simple to understand, whereas vectors of somewhat offsetting cashflows are not. This isn’t a deep-rooted, philosophical proposition on why one approach is economically superior. The point is simply that a message conveyed by 2 numbers is probably clearer than the same message conveyed by a big table of numbers. Practically, this means that the present value approach can help simplify some of the issues that arise when running a pension scheme.

Does a present value approach make things clearer? YES – by summarising a scheme’s position into a single ratio.

Does a present value approach make decision making easier?

The point about clarity may be easier to see with an example. As an example, we look at setting triggers for changing the asset allocation.

When managing a pension fund (or anything else) it is often helpful to think about the end goal. If you have a pension fund that is 100% funded on gilts flat, you only need to earn the same returns as gilts, so you may choose a portfolio of just 100% in gilts. If you wanted to hold 100% in gilts when your scheme was 100% funded, it would be perverse not to have a significant holding at 99% funded- your allocations at 99% funded and 100% funded should be similar. It follows that if you are 99% funded, you will want to hold a large allocation to gilts. It is then fairly easy to setup a trigger framework and increase your gilt allocation when the funding level improves.

On a direct projection basis you might also have a large gilt holding, but it’s less obvious what measure you might use to judge when to de-risk or re-risk. It’s hard to see what such metrics might be. While it is fine in theory to manage a fund this way, if you can’t tell whether it’s working or not you’re unlikely to be able to manage it successfully.

In a previous piece we showed two hopefully uncontroversial results: that funding level is strongly linked to probability of paying pensions, and that the optimal strategy to meet pensions varies a lot for different funding levels. This means that looking at the funding level gives you useful, clear information about your scheme.

Does a present value approach make decision making easier? YES – it provides a framework for triggers to change the asset allocation.

From this we can see the operational advantages of having a liability value, but we haven’t yet considered whether the discount rate should be market-based. This is the focus for the remaining sections.

Is the present value approach enough – what happens as a closed scheme runs down?

Most pension funds are now closed to new accrual. Eventually, all the members will die and there will be no more pensions to pay. As a scheme approaches its end, there will be a “run-off period”, where the scheme becomes smaller through time. At this point, the cashflows needed to pay pensioners can be relatively large.

It is common for businesses with reasonably strong present values to hit real financial difficulty just from cashflow timings, and this will be familiar to anyone who’s had to pay a big expense before payday. This is a disadvantage of a present value approach, and anyone using one also has to be aware of and manage these risks. To be clear, just looking at the present value is not enough information to run a pension scheme, as schemes must also consider liquidity requirements. However, this doesn’t mean abandoning the present value approach, it just means it needs to be complemented with measures of liquidity risk.

To highlight this point, we consider two schemes with the same assets, funding level and discount rate (75% on gilts + 50). One scheme is much older than the other, and is running down its liability profile. As a base case, the young scheme might be paying 2% of its assets every year, while the old scheme pays 6%. If assets fall 20%, the young scheme would still only be paying around 2% of its assets, while the older scheme would be paying more than 7%. This means that the older scheme should, all ese being equal, have less ability to recover from losses. Here, the present value approach is not enough on its own.

Figure 1 – cashflow requirements for immature and mature schemes

Figure 1 – cashflow requirements for immature and mature schemes


Is the present value approach enough when as a closed scheme runs down? NO – it needs to be complemented by other metrics

Is the present value approach helpful for setting contributions?

A pension fund is there to pay pensions, and the sponsor is a backstop. Sometimes things go wrong and the fund will need contributions from the sponsor. This is a difficult point, and it is not straightforward to know how much will be needed.

With a direct projection approach, the answer will be sensitive to expected return assumptions. With a present value approach, the answer will be sensitive to the discount rate used. Both are vulnerable to using poorly chosen assumptions.

Neither works perfectly, and both rely on uncertain assumptions. The question then becomes whether adopting a present value approach makes this process more or less resistant to error. Broadly speaking, the present value approach has an edge here as there are clear reference points against which to benchmark your discount rate, which aren’t as clear for expected returns. It is therefore probably easier to ensure contribution rates are adequate if you use a present value approach.

Is the present value approach helpful for setting contributions? YES – discounting liabilities and comparing to assets gives a workable framework for setting required contributions. The choice of discount rate becomes a focal point.

What if I’m wrong?

Perhaps the biggest advantage of the present value approach is that it is robust to being wrong. This comes from the market value of assets and liabilities being the preferred measure.  At some point, under either framework, you will have to sell assets. This could happen if your liabilities change, if your cashflow assumptions change (e.g. dividend rates are cut), or if you’re running down a mature fund. When you do sell assets, it doesn’t matter how much cashflow those assets might have produced; all you will get for them is market value.

And if that isn’t enough, and it means you can no longer pay pensions, then you’ve failed.

If that seems brutal, it’s because it is. Even if you’re right and the market is undervaluing your assets, the market will not care. In a quote commonly attributed to Keynes, “the markets can remain irrational longer than you can remain solvent”. If you manage to a present value approach you can sell assets and change your allocation without destroying your strategy. This makes your strategy a lot more robust.

This is an example of a more general point made by Smith (1996)3. If we pursue a management framework that does not use market value as the preferred measure, at some point we are bound to run into a “fault line” where we are required to reconcile a quantity with a market value. Or, we may create an arbitrage where there is a possibility to choose between two approaches selectively.

Does the PV approach help you if you are wrong? YES – by discounting at market values the PV management approach ensures that the scheme remains robust to transactions and rebalancing (which occur at market values).

Doesn’t this just make me buy bonds, when equities do better long-term?

One of the big objections to a present value approach is that it encourages schemes to buy bonds, even though equity performance has been better over the long term. After all, as a long-term investor, why wouldn’t you just buy the best performing assets?

The answer is a bit subtler, and may be best explained by analogy. First though, it is vital to remember that the ultimate risk is not assets under-performing; it is being unable to pay pensioners. If assets do badly, but the scheme pays its pensioners, it has succeeded. If the assets do well but the scheme can’t pay its pensioners, it has failed. This means the risk-return trade-off is not just the risks and returns of the assets, but the risks and returns of the assets against the liabilities.

Now, the analogy.

Suppose, instead of paying normal pensions, I had to pay every retiree a lump of gold when they retired. Over the long-term, I would expect equities to outperform gold. But there would be a risk there. My least-risk position would be to hold a lot of gold. I might choose to take risk against that position. If I think gold prices are high and equities are cheap, I might take that risk and expect to earn money from it. But my risk would not be that equities do badly on their own, but that they do badly relative to gold prices. If I take this bet and equities go up 10%, but gold goes up 20%, then I am worse off because I have to pay pensioners in gold.

Similarly, if I have to pay pensioners in houses, my risk-free asset is houses, and the risk I run is that my assets underperform house prices. Since I pay each retiree with a stream of future payments, my risk-free asset is a stream of future payments, i.e. a bond.

This doesn’t mean you must only buy bonds. For most schemes that’s not practical. What it does mean is your risk is not that your assets under-perform, but that they underperform bonds. If I have to pay pensioners in houses, I might take a view that houses are currently overpriced and will fall in value, and so I might reduce my exposure to property. But my least-risk position – relative to my liabilities – would still be to hold property. Similarly, my least-risk position as a pension fund is to hold bonds (this was established in an academic framework by a number of papers in the late 1990’s)4.

Does the PV approach force you to buy bonds? NO, not necessarily, but the reference point for asset allocation is a bond portfolio.


In conclusion, it could be possible to manage a pension fund without reference to a present value of liabilities. In the end, different approaches should converge to lead you to the same decisions. However, the present value approach has a lot of practical advantages, helping with clarity and decision making. Crucially, it is much more robust if you need to adjust your strategy. Relying exclusively on this one perspective could lead to poor cashflow management; ignoring it can lead to the liabilities becoming unaffordable, and mean the pension scheme ultimately fails to pay its pensioners.

The liability PV can be a volatile number. However, all it really means is the cost today of a stream of payments. From this perspective, the liability PV doesn’t matter in and of itself; what matters is the cost of future payment streams. The liability PV is just an effective shorthand for the cost of the specific payment stream you need. It’s not an abstract and meaningless number; it’s the cost of a stream of cashflows. And when interest rates are lower it is harder to meet cashflow streams. With this view of a PV, the decision to hedge interest rates is generally a lot easier.

1. Eg http://www.standard.co.uk/business/anthony-hilton-our-mad-approach-to-pensionfund-deficits-a3344816.html ↩
2. Sharpe (1964): Capital Asset Prices: A Theory of Market Equilibrium Under Conditions of Risk↩
3. SMITH, A.D.(1996). How actuaries can use financial economics. BAJ 2, part V, 1057-1193.↩
4. See for example “The Financial Theory of Defined Benefit Pension Schemes” Exley, Mehta & Smith 1997 http://citeseerx.ist.psu.edu/viewdoc/download?doi= ↩


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