Theme 1: Duration differences and hedging performance In Chapter 2, the concept surrounding duration is explained In order to derive the latter,

the interest rate acts as a crucial input variable. Seeing as this figure deviates when comparing the replicating part and the pension liability itself, the duration differs as well. Thus, the two valuation methods each have a varying interest rate sensitivity.

Figure 6.1 on the next page shows the duration movements associated with the pension obligation cash flows, calculated by applying the four distinct interest rate curves. The graph is accompanied by Table 6.1, which shows the average durations. These have been derived for various periods of time, whereas the whole period is again the entire backtesting time span (between 2005 and 2014).

Table 6.1: Average durations

In essence, it is not about the values themselves but instead, the focus lies on the comparison between not averaging and averaging. Despite the fact that the period that is shown, 2012 and 2013, depicts relatively stable interest rate developments (i.e. there have been no extreme scenarios), the difference resulting from not applying or applying an averaging feature is still clearly visible.

Furthermore, it can be derived that the difference in duration between using the Basic curve + UFR or the DNB curve is smaller than amongst applying the Basic curve or the Average Basic curve. This is also highlighted by the red line, which represents the variation between the two. However, for this analysis and the overall goal of the chapter, these comparisons are of less worth. The focus within this theme lies on the mismatch in which interest rate developments are absorbed at the asset and the liability side of the balance sheet. In essence, this all comes down to a two-fold comparison with the duration based on market valuation, which is always applicable to the asset side. Concrete:

1) Basic curve (=considered the market curve) versus Average Basic curve. 2) Basic curve (=considered the market curve) versus DNB Curve.

In Table 6.2, the absolute differences in average duration are shown for these two comparisons. With it, it can be concluded that applying an Ultimate Forward Rate (which is the case for the DNB curve) does not result in less duration mismatch. On the contrary;

The four different term structures

Time period BC AVG BC BC + UFR DNB

Whole period 18,107 18,071 17,651 17,629

Last two years 19,535 19,555 18,710 18,722

Last year 19,332 19,382 18,592 18,640

Last three months 19,117 19,117 18,407 18,426

Figure 6.1: The duration movements belonging to the liability cash flows, discounted with the different interest rate term structures. The colour palette can be found in Table 3.1.

Table 6.2: Average differences in duration between assets and liabilities

Absolute differences with durations, based on the market interest rates

Time period AVG BC DNB

Whole period 0,233 0,549

Last two years 0,174 0,813

Last year 0,135 0,692

Last three months 0,115 0,691

using the UFR has only increased the absolute difference in duration between the replicating portfolio and the pension liability. The fact that this larger mismatch did not lead to a more volatile coverage ratio in the previous chapter is the result of the actual difference being exactly the same as the absolute difference (for nearly the entire period). The UFR with its, at least up until now, resulting higher interest rate, leads to structurally lower pension obligations and consequently, durations. As a result, the variation in duration is always positive, when applying the UFR.

The averaging feature however, might work both ways. This methodology resulted in a higher, as well as a lower provision in past periods. In practice, this means that sometimes, the duration’s value is bigger while at other times, it is smaller when compared to that of the replicating portfolio. Consequently, whenever non-absolute deviations are considered, the average differences are much smaller. As can be seen in Table 6.3, it centers closely around zero, which contrasts the absolute variation illustrated by Table 6.2.

Table 6.3: Raw average duration mismatches

A different discounting factor results in a different duration. Consequently, a perfect hedge of the targeted strategic replication percentage that is based on covering X% of the total pension liability is no longer feasible. Taking the realistic scenario discussed in the previous chapter as the primary example, the actual replication percentage is shown in Figure 6.2. In essence, the graph represents the percentage of the pension liability that is truly covered. The table below details the maximum and the average absolute deviations from the targeted replication (60%) that are tied to various periods of time.

Table 6.4: Deviations from targeted replication

As can be seen from the table, the differences can amount to considerable figures, with the center of attention being the maximum deviation of 32.38%. For this particular instance, almost 80% (60*1.3238=79.43) of the pension liability was covered by the replicating

Raw differences with durations, based on the market interest rates

Time period AVG BC DNB

Whole period 0,036 0,478

Last two years -0,020 0,813

Last year -0,050 0,692

Last three months 0,000 0,691

Last month 0,110 0,801

Absolute deviations from the targeted 60% hedging percentage

Time period Maximum Average

Whole period 32,38% 3,53%

Last two years 18,10% 4,25%

Last year 8,35% 2,88%

Last three months 5,58% 3,48%

Figure 6.2: Actual replication percentage belonging to the targeted rate of 60% between 2010 and 2013

portfolio. Of course, the variations can go the other way as well, leading to an actual replication percentage that lies (well) below the targeted level of 60%. Table 6.4 depicts the deviations as a percentage of the targeted rate. This is done in order to ensure that the information is still relevant when another replication percentage is chosen.

As expected, the selected replication method also affects the coverage ratio, illustrated by Figure 6.3. A randomly chosen period shows the distinct differences between on one hand using an exact replication of the liability cash flows, versus applying the duration/liquid method on the other. Furthermore, within the latter replication method, a distinction is made between monthly- and quarterly rebalancing. The graph shows that, with duration replication, only parallel shifts are taken into consideration. With it, we have a perfect link with the next theme.