**How well do Wtp interest rate risk models perform?**

The pension fund sector in Europe does not have an overarching European legislation yet. This means that every country has its own regulation and its own risk models. For example, in the Netherlands new national pension fund regulation (Wtp – Wet toekomst pensioenen) was recently introduced in July 2023.

The interest risk models under this regulation are based on scenario-sets that are provided by the Dutch Central Bank (DNB – De Nederlandsche Bank) with projections 100 years into the future. These scenario-sets are based on the assumptions and parameters as published by the Commissie Parameters 2022.

For the transfer of pension capital from an old (FTK) pension fund to a new (Wtp) pension fund the so-called **‘risk-neutral’ Q simulation set** is to be used.

After transition a so-called **‘market-consistent’ P simulation set** is to be used to report 5% and 95% VaR scenario’s to pension clients. This P simulation contains a risk-premium that is based both on market information and on ECB and CPB (Centraal Planbureau) inflation objectives.

As these simulation-sets have only been published since the start of 2023, it is not yet possible to make statements about the historical performance of these models.

However, we can make some statements about the usefulness of these models. We do this by calculating the risk on the 10 year risk-free interest rate using the Wtp models and comparing it to theSolvency II standard formula model and to market expectations as obtained from the forward curve.

**Wtp Q simulation**

First we compare the new risk-neutral Wtp Q model with the Solvency II Standard model (revised 2020 version):

For a one-year ahead projection, we observe that the Wtp Q model is slightly more conservative than the Solvency II standard formula model. As Wtp Q makes projections multiple years into the future while SII only gives us a one-year ahead projection we compare Wtp Q with an ‘extended’ Solvency II standard formula model which is scaled using IID normality assumption. Of course this assumption does not fully hold, but comparing such an extended model to Wtp Q helps us to make statements about the underlying process and distribution of Wtp Q. For a 10-years maturity interest rate Wtp Q has a wider risk range than the extended Solvency II standard formula. This shows us that the distribution of Wtp Q is drawn from a distribution with a higher standard deviation and/or that more autocorrelation between subsequent years is available. For short maturities on the other hand we see that the Wtp Q risk range is much narrower than the extended Solvency II projection. This shows us that there is much more mean reversion present for the short term maturities under Wtp Q.

When we compare the expected Wtp Q rate (VaR 50% scenario) with the forward curve we see that the current long term market expectation as given by the forward curve is almost 2% lower than the expected value from Wtp Q.

Aging population and lower productivity are often cited as drivers that bring interest rates down, while fiscal stimulus policies would act in the opposite direction. Research suggests that for many countries the effects of the downward pressures have been larger than the upward pressures (see:IMF blog article about historical drivers of natural rates). These drivers might indicate why the market expects a lower long-term interest rate than what we have historically experienced and what would be obtained by the risk neutral Wtp Q model.

**Wtp P simulation**

When we look at the Wtp P model we see that the 50% scenario tracks the forward curve pretty well after year 5, which indeed seems to suggest that Wtp P is much more ‘market-consistent’ than Wtp Q.

However, for the first 5 years it does not align at all with the market expectation from the forward curve. Wtp P even projects that the interest rate would be 2% lower than the market expectation based on the 10-year forward for June 2024. This seems quite unrealistic given the current stillhigh core-inflation. Therefore it appears that the model parameters are selected assuming quick reversion of interest revert to ECB inflation objectives. This might in itself be a good objective for central banks, but if reality is different then it is not so appropriate for decision making.

The upper and lower risk percentiles of Wtp P show a relatively narrow band around the 50% scenario. It is not so clear if these are extracted from market information or also influenced by central bank objectives. What we do note though is that they do not seem to align with the historical reality of a variety of macro-economic scenario’s that we have observed over the last century (see also next article on BASE and REGIME-BASED models).

**Conclusion**

Overall, we can conclude that, at least for the 10 year maturity interest rate, there are quite some differences between statistical reality, market expectations and central bank objectives.

The **Wtp Q** model provides wider risk estimations than an extended Solvency II model. As we noted in the previous article thatSolvency II did not always perform that well in the last 20 years, this might indicate that Wtp Q would be more appropriate to capture the risks. However, we also note that Wtp Q does not align well with the long term market expectations.

The **Wtp P** risk model, which is supposed to be market consistent, does indeed align much more with the current long-term market expectations. However, it does not align well with the short-term market expectations. This seems to be influenced by central bank’s objectives. In addition, we noted narrow risk estimates that do not align well with the statistical reality of ever changing macro-economic conditions (see also article on BASE an REGIME-BASED models). We saw in earlier validations of the Solvency II model that these changes happen quite fast, we would therefore be careful to rely too much on this model for (investment) decisions.

Can other models help us to make better decisions? Let’s explore some models that can adapt easier to changing regimes in the following articles.