Fantastic elastic

Think tanks such as the Adam Smith Institute have recently argued that retirees with assets worth more than £1 million shouldn’t be entitled to a state pension, with the payment instead being means-tested. So have various others as a way for governments to keep costs under control. We believe there’s a significant risk of this happening in the UK within the next few decades.

This possibility makes saving for retirement less attractive. But what are the implications for investment strategy?

The charts below, based on a model (key assumptions at the end of the blog), illustrate the findings of our research into this question. Our first graph assumes the current tax regime only, with no means-testing:

By construction, in the absence of income tax or means-testing, the proportion held in equity in the modelling is always 50%; this forms a benchmark, against which we can see the relative impact. The results suggest investors should hold slightly more in equity (typically an additional 5% their assets) than if there were no income tax.  

For our next set of results, we suppose means-testing of the state pension is introduced on top. Just for illustration, we’ve assumed every extra £1 of gross income (including the full state pension) above £30,270 you must pay back 50p of an assumed £10,000 state pension. This leads to an effective marginal tax rate of 70% (20% plus 50%) for gross incomes between £30,270 and £50,270.

To the left, we find those with small projected pensions should also hold slightly more equity, but it gets more interesting as we move up the income scale.

In the middle, there’s heavy de-risking but only for investors who are both near the cusp of means testing and close to retirement (within five years). Finally, to the right, the model suggests investing substantially more aggressively[1], with the lines that dipped the most also rebounding the strongest.

Many members are to the left of these charts, around a minimum-to-moderate PLSA living standard, so the implications for them are relatively limited. However, we expect many others will be targeting moderate or comfortable standards in the future[2].

What’s driving these results?

You may be wondering why on earth we get such results. We believe there are two key factors at play:

Asymmetry

Means-testing and progressive income tax introduce an asymmetry to payoffs. Investors receive a smaller portion of the upside relative to the downside risk. This disincentivises risk taking, particularly when the investor is close to retirement and near the cusp of means testing. But further from retirement it’s unlikely you’ll end up on this cusp, so it doesn’t matter as much.

Elasticity

Elasticity is a key concept in economics – it tells you how sensitive the percentage change in one quantity is to the percentage change in another. The elasticity of net income to gross income turns out to be crucial. For example, if the elasticity is 0.5 then percentage changes in net income are only 50% as sensitive to investment returns[3]. This means that to get the same effective exposure the investor needs to double their allocation to risky assets. The charts below show the relationship between gross and net income for the two examples above, and how elasticity varies as a result:

Elasticity dips modestly below 1 with no means-testing but the fall is much greater in the presence of means-testing, requiring higher risk allocations to get the same effective exposure.

Don’t buy the dip

The dip is the most striking aspect of our second chart above, reflecting asymmetry considerations. However, for investors who aren’t close to retirement it distracts from a more important story. That story is that normally taking more risk can make sense, because of the substantially reduced elasticity that tax and means testing introduce.

DC glidepaths are a complicated business. I often find myself arguing in favour of more cautious strategies, but it’s interesting to find some factors pointing in the other direction.

Key assumptions

The model is calibrated so that the investor would hold 50% equity in the absence of means-testing (or tax) and 50% in riskless assets. For simplicity we consider only these two assets. This was achieved by using a power utility function with risk aversion parameter 4.5

Equity returns are assumed to follow a lognormal distribution. The mean log return is 3.9% pa over risk free with 15% pa volatility

Projections are single premium over the period to retirement – we deliberately neglect contributions (human capital) to focus on the effects of means testing and income tax

[1] Although the effect dies away for very large incomes (not shown)

[2] We can’t rule out other possibilities either – means testing could kick in at a lower level – who knows what future governments will do? Projected incomes are also highly sensitive to the level of real interest rates. If real interest rates rise further, this could easily shift the future retirees to the right.

[3] Note that a flat tax rate of 50% (and no means-testing) would not actually mean the elasticity is 0.5. In fact, the elasticity would be 1 in that case, because although a 1% rise in gross income causes net income to increase half as much in pound terms, the percentage increase in net income is also 1%. On the other hand, changes in the rate that marginal increases in income are lost (either via taxation or lost state pension), do impact elasticity.