The problem with adding ‘prudence’ to a discount rate is that it does nothing for the uncertainty of the ultimate benefits, but it raises costs in the meantime in a manner which simply cannot be justified. In the case we look at here, (a single fifty year liability), we have a 20% adjustment to the ultimate payment, and a 20% lowering of the discount rate and the results is that the present value of this obligation rises by 93%, I will repeat that, 93%.

This blog was prompted by a number of questions that arose from our publication of “Discount rates, defined benefit pensions schemes and their sponsors”, which is available here: Professional Articles – Long Finance . The questions all revolved around modification of a discount rate, such as credit risk or ‘prudence’.

The problem can most easily explained in terms of the compounded ‘prudence’ of UK DB pension schemes.  It can be illustrated stylistically – see figure 1. Suppose we have an obligation to make a single payment of £1,000, fifty years from now, and that the rate at which we acquired this obligation was 5% pa, then the result is the blue line shown – the evolution of the obligation over time. Note the vertical scale (value) is logarithmic. Now let us suppose that the £1000 was simply our best estimate of an uncertain payment, and that to be prudent we need to add 20% to this sum, raising the endpoint. Let us then suppose that we have a stupid rule which says that we must also be prudent with our discount rate, as we do with UK DB pension schemes, so we lower this from 5% to 4% and the result is the red line.

Figure 1 

Suppose we have an obligation to make a single payment of £1000 fifty years from now, and that the rate at which we acquired this obligation was 5% pa, then the result is the blue line shown. Note the scale is logarithmic. Now let us suppose that the £1000 was simply our best estimate of an uncertain payment, and that to be prudent we add 20% to this sum, raising the endpoint. Let us then suppose that we have a stupid rule which says that we must also be prudent with out discount rate, so we lower this from 5% to 4% and the result is the red line.

This raises an obvious question: why should we overfund so massively now? Figure 2 shows the funding correct funding level, as a green dashed line. It is everywhere 20% higher than the original.

Figure 2

The excess funding that this requirement to use a “prudent” discount rate in additional to prudence in the estimate of ultimate payments is shown as figure 3.  Note that the excess cost is linear in proportional (Prudent vs Correct) and distinctly non-linear in cost is monetary terms (excess cost).

The excess cost shown is the amount in excess of ‘correct’ which lies 20% above the original.

Figure 3

Finnegan

The problem with adding ‘prudence’ to a discount rate is that it does nothing for the uncertainty of the ultimate benefits, but it raises costs materially in the interim in a manner which simply cannot be rationalised. In this case, a single fifty year liability, we have a 20% adjustment to the ultimate payment, and a 20% lowering of the discount rate and the results is that the present value of this obligation rises by 93%, I will repeat that, 93%.