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Euro-swapping to be optimised

Due to recent developments in supervision and accounting, insurance companies are inevitably entering into a world dominated by market values and economic risks. An important consequence of these developments is the worldwide trend towards liability-driven investment strategies. To make a proper evaluation of the returns of assets, they have to be benchmarked against the returns of liabilities. This liability benchmark needs to be liquid and must closely mirror the financial characteristics of the liabilities.

The extent to which the liability benchmark can mimic the liabilities is driven by the complexity of the liabilities and the availability of replicating products in financial markets. The mismatch between the liability benchmark and the actual liability portfolio is strongly dictated by the liquidity of long-term interest rate markets. For countries with a relatively small interest rate market in comparison with its life and pension insurance sector, the mismatch can be large. However, using a liability benchmark based on liquid foreign interest markets with high correlation to domestic interest rates might provide a solution.

In this paper, we will discuss the need to use a liability benchmark. The challenges of setting up such a benchmark in illiquid markets will be addressed by looking at the Swedish markets. We will show that the liquidity of Swedish markets is inadequate, but that the euro market can serve as an alternative.

In carrying out an insurance business, two decisions are of major importance:

1. Pricing of products. The level of the premiums in relation to the promised pension benefits should reflect all the costs of maintaining the product;

2. The strategic asset allocation. The aim of the strategic asset allocation is to generate high returns, while satisfying constraints, such as a minimum solvency level. Usually, the strategic asset allocation is determined by means of an asset-liability model (see Laster and Thorlacius, 2000).

In order to evaluate properly the effects of both decisions, a liability benchmark is a useful tool. A liability benchmark is a portfolio of liquid assets of which the returns have minimal mismatch with the returns on the portfolio of liabilities (see Ho, 2005). The way the liability benchmark is linked to the liability portfolio and strategic asset allocation is shown in Figure 1.

Figure 1 gives a split-up of the insurance structure into distinct steps. The first step is to create a replicating portfolio, or an exact replication of the financial liabilities in cash flows and optionalities, non-financial risks (eg, actuarial risks) are not included. Parts of the replicating portfolio might not be available in the financial markets at a reasonable cost.

The second step is to create the liability benchmark with available liquid instruments. The optimal liability benchmark has the lowest possible mismatch with the replicating portfolio. The magnitude of the mismatch, called basis risk, depends on both the structure of the replicating portfolio and the availability of financial products. Basis risk is intrinsic to the insurance business, due to factors such as the long-term character of liabilities and complex optionalities embedded in the insurance policies.

If desired, a financial institution could minimise its financial risk by investing in its liability benchmark. In practice, the strategic asset benchmark of insurance companies deviates substantially from their liability benchmark aiming at excess return in the long run. This strategic risk is absorbed by available capital. Finally, tactical deviations from the strategic benchmark are taken by asset managers.

The liability benchmark (LMB) is a useful tool to evaluate both assumptions and charges with respect to the pricing of products and the strategic asset allocation decision. The performance due to (commercial) pricing decision is measured by taking the difference of the performance of the liabilities and the liability benchmark. The performance of the strategic asset allocation decision is measured by taking the difference of the performance of the strategic asset allocation portfolio and the liability benchmark.

A consequence of this split is that positive and negative returns due to basis risk are included in the performance of the pricing decision. An example of the use of a liability benchmark in the context of performance measurement is shown in Exhibit 1.

An optimal liability benchmark is therefore vital for proper performance measurement and risk management in general. Using a non-liquid LBM will make the split between the pricing decision and the strategic asset allocation decision questionable. It will lead to a lower estimate of the basis risk and therefore to an underestimation of the required capital, thus leading to a distorted view on the pricing of the products. At the same time, it will also lead to a distorted view on the strategic asset allocation since (part of) the basis risk is now wrongfully allocated to this decision.

An insurance company with only euro-denominated liabilities is able to use a liability benchmark with relative low mismatch with the replicating portfolio, since the euro market is highly liquid, even for maturities up to 40 years. However, the Swedish interest rate market is limited in liquidity, especially in maturities longer than 10 years.1 This leads to a larger mismatch with the replicating portfolio when setting up a liability benchmark.

To elaborate on the challenges this illiquidity poses, we will analyse two different situations: an insurance company that is strictly euro based, and one that is strictly based in Swedish krona. Both companies have pension commitments to their policyholders up to 75 years. The present value of these liabilities is respectively SEK10bn and €1.06bn. In our analysis, we exclude embedded options and actuarial risks

First, we will consider the European company. The only risk in the replicating portfolio is interest rate risk. We determine the optimal liability benchmark by creating a position in cash and swaps with sensitivities to key interest rate buckets that exactly offset the sensitivities of the replicating portfolio. We constrain ourselves to using liquid swaps with a maturity up to 40 years to ensure that the optimal benchmark is investable.

The results of this approach can be seen in Figure 2. The figure shows the basis point value per interest rate bucket of the replicating portfolio and the liability benchmark. The replicating portfolio has negative sensitivities: when interest rates go up, the value of the replicating portfolio goes down and vice versa. Sensitivities are particularly large for interest rates between 10 and 30 years, consistent with the duration. The unhedgeable sensitivity to interest rates of over 40 years is taken into account in the amount of swaps that is used to hedge the 30-40 bucket, thus making the difference between the LBM and the replicating portfolio insensitive to parallel changes of the yield curve.2 However, in case of a steepening of the yield curve between the 40- and 60-year interest rates, a negative result will occur in the total position. This is the basis risk.

Now let's consider the Swedish company: its benchmark would ideally include Swedish interest rate products up to 75 years. However, Swedish krona swaps are liquid to 10 years only, and even then the maximum tradeable size is limited.

The limited availability of long-term interest rate products leaves two possibilities open for the liability benchmark. The first is to set up the liability benchmark with short-term Swedish products, the second is to look for alternative specifications using foreign interest rate markets. The instruments with the highest correlation with long-term Swedish interest rates will lead to the smallest mismatch risk. Apart from the euro market, foreign interest rate markets typically have too low a correlation to be effective.3 Looking at historical data of the 30-year Swedish swap rate, we see that both the correlation with the 10-year Swedish swap rate and the correlation with the 30-year euro swap rate is nearly the same, around 85%. Nevertheless, because of higher convexity, leading to higher effectivity when large interest rate changes occur, the 30-year euro swap will be a better match to the liabilities than the 10-year SEK swap. Moreover, since transaction costs for SEK swaps can be up to five times as high as in the euro market, we will concentrate on using long-term euro swaps.

 

ince the replicating portfolio and the products in the liability benchmark are now in different currencies, we can no longer evaluate the optimal liability benchmark by matching the sensitivities in interest rate buckets. Instead, we use a simulation model of European and Swedish interest rates. In each scenario, the value of the liability benchmark is compared with the value of the replicating portfolio. The liability benchmark is evaluated based on value-at-risk (VaR) measures (see Jorion, 1996) of the total loss of replicating portfolio and liability benchmark together. The model is calibrated by means of historical data over the past four years. The most important parameter that will determine the mismatch between the Swedish replicating portfolio and the European liability benchmark is the correlation between the European and Swedish long-term interest rates, approximately 85%.

Table 1 shows the VaR indicators for the foreign liability benchmark. A liability benchmark with no mismatch with the replicating portfolio will have an effectivity of 100%, meaning that the value of the liability benchmark changes always exactly in line with the replicating portfolio. For such a liability benchmark, the VaR of the replicating portfolio minus liability benchmark will be zero.

For the European company, the effectivity is over 97%. Such a high effectivity cannot be achieved for a foreign benchmark. For the liability benchmark shown here, effectivity amounts to approximately 47%. This means that the interest rate risk of the insurance company can be almost halved. It is seen that with a 1% probability, the loss due to
interest rate changes would be (more than) SEK3.9bn instead of SEK7.4bn.

We have taken as an example an all-euro liability benchmark because of the illiquidity of the Swedish swap market. However, for shorter maturities, the market is certainly more liquid. Setting up a benchmark that consists of shorter Swedish swaps or bonds and euro swaps for the higher maturities can increase effectivity of the benchmark to around 62%.

The worldwide trend of liability driven investing has lead to the insight that a liability benchmark is needed. Application of such a benchmark leads to a well-defined split in the risks and returns due to the pricing decisions and decisions about the strategic asset allocation.

The process of the construction of the liability benchmark can be seen as a two-step procedure. First, the liabilities are stripped from non-financial risks. Subsequently, they are translated into liquid products.

For life insurance companies, it is generally not possible to replicate the replicating portfolio fully with liquid products, because their liabilities are long term and often contain complex embedded options. Moreover, in relatively illiquid financial markets the basis risk is even larger. By using a benchmark that is (partly) defined with euro-denominated products, the liability benchmark can be optimised.

The use of a liability benchmark is essential in measuring basis risk, which is an indispensable ingredient for a proper theoretical pricing of products. Using a liability benchmark will enlarge awareness of and insight into the risks taken by the strategic asset allocation and will lead the
way to more efficient investment portfolios.

Notes

1 The size of the total outstanding notional in Swedish government bonds amounts to approximately €50bn. European governments have more than €5.000bn, or 100 times as much. The swap market shows similar differences: an outstanding notional of about €2.200bn in Swedish swap notional, against more than €50.000bn in European swap notional.

2 Convexity between replicating portfolio and liability benchmark may still differ and can be incorporated, but is not explicited here.

Convexity between replicating portfolio and liability benchmark may still differ and can be incorporated, but is not explicited here.

3 Based on a rule of thumb, hedge effectivity between two instruments depends on correlation through the formula: 1-√[2(1-_)]. An instrument with a correlation of 90% will lead to a hedge effectivity of approximately 55%. With a correlation of 50%, however, no hedge effectivity will be attained, while at correlations lower than 50%, total risk will even increase.

Based on a rule of thumb, hedge effectivity between two instruments depends on correlation through the formula: 1-√[2(1-_)]. An instrument with a correlation of 90% will lead to a hedge effectivity of approximately 55%. With a correlation of 50%, however, no hedge effectivity will be attained, while at correlations lower than 50%, total risk will even increase.

References

Ho, Thomas, ‘Asset/Liability Management and Enterprise Risk Management of an Insurer', Journal Of Investment Management, Vol 3, No 1 (2005)

Jorion, Philippe, ‘Value at risk: the new benchmark for controlling market risks', 1996, Irwin Professionals

Laster, D and E Thorlacius, ‘Asset-liability management for insurers', Swiss Re Sigma, 6, 2000.

The size of the total outstanding notional in Swedish government bonds amounts to approximately
The size of the total outstanding notional in Swedish government bonds amounts to approximately

Mark van Maaren, Jan-Willem Wijkmans are with Cardano Risk Management in Rotterdam

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