In our previous articles, we explained the principle of using an efficient frontier framework to assess the contribution of capital protected structured products in the context of a portfolio. Today, we apply these ideas specifically to pension funds.

The liabilities of a defined benefit pension scheme can be described as a series of future cash flows to be paid out. These cash flows are not guaranteed and depend on a certain number of factors or future events – the most important being mortality. A big mortality shock will considerably reduce the liabilities of the scheme, while the probable increase in life expectancy will increase the predicted cash flows. Since mortality risk is not related to the market, it cannot be hedged with financial products. However, other risk factors are highly market-related and do affect pension funds.

Firstly, the liabilities are obviously highly linked to interest rates as they determine the discount factors that will be applied to the future cash flows, and the increase in the pensions is sometimes linked to the long-term or short-term rate. Secondly, inflation has to be considered. In most defined benefit pension schemes, the annual increase of the defined pension is linked to inflation, which implies that the value of the liabilities is highly dependent on future levels of inflation. Finally, liabilities are linked to the market through more complex phenomena such as final salary evolution. The principle of a defined benefit pension fund is that it guarantees a pension equal to a certain proportion of the final salary (or final salaries) of the employee. The modelling of the average salary has always been a controversial issue in economics and finance, but we can say without taking too much risk that it is linked with inflation, interest rate and domestic and international growth. The exact form of this dependency is very hard to determine, and some empirical hypotheses have to be made.

Asset liability management

Pension schemes’ liabilities are highly dependent on market conditions, which renders it possible to optimise the portfolio’s asset allocation in order to match assets with liabilities effectively. This is called asset liability management.

Now that we have established how the fund liabilities behave, we can model the asset allocation. In our example, we look at an underfunded pension fund, our aim being to optimise the asset allocation. We simultaneously simulate the assets and the liabilities and calculate the funding ratio for a specific time horizon.

We are now back to the problem that we had last month. We have a distribution of results (last month, the result was the return of the portfolio, this month the result is the final funding ratio) and we want to optimise the shape of our distribution with regard to the initial asset allocation. If an important part of the portfolio is invested in fixed income products like standard bonds or inflation-linked bonds, the average return of the portfolio will be relatively small and we will find it hard to restore an acceptable funding ratio. Although, since the distribution of the funding ratios will not be volatile, high losses will also not be incurred. To the contrary, if the portfolio is mainly invested in stocks, we will benefit from the risk premium and our average funding ratio will be much more acceptable, as the diagram illustrates. The distribution, however, will be very volatile and the worst cases will pose a significant risk.

Again we will need indicators to optimise our portfolio and to quantify the risk/return profile of the pension scheme. By maximising the average of the funding ratio and keeping the risk level under control (which will be done by choosing a maximum conditional value at risk level), the pension fund manager will choose a target for his funding ratio at maturity. This framework will provide the optimal portfolio to attain this target while minimising the risks.

In this context, structured products prove their optimality. With their asymmetric payoffs, they have two features that make them very attractive: they provide exposure to the upside of the stock markets and therefore have a risk premium, and at the same time they can also provide full capital protection consequently carrying less risk than stocks. As a result, structured products have a significant impact on the efficiency of the portfolio. For a given funding ratio target, the use of structured products decreases the risk significantly and for a maximum level of risk, they increase the target funding ratio.

In our next two instalments, we will examine a practical example of portfolio optimisation using a structured product.

Wojtek Nabialek is head of structuring and new products group at BNP Paribas London.

In association with BNP Paribas.

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