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The Actuary The magazine of the Institute & Faculty of Actuaries

Adding alpha to LDI

A large number of UK pension plans
face funding shortfalls, which are
being exacerbated by rising lia-
bility costs. Portable alpha strategies, which ‘port’ the added value or ‘alpha’ generated by one asset onto a benchmark asset to generate additional investment returns, can provide a solution to this dilemma.
In order to test the efficacy of these strategies, it is necessary to develop a control portfolio that provides a realistic representation of the position of many UK pension funds today and then test the possible impact of a portable alpha structure.

Control portfolio
The liability-replicating portfolio described in table 1 contains mostly inflation-linked exposure, with a modified duration of about 18.7 years. The aggregation of assets and liabilities gives the surplus view, which implies a mark to market valuation of assets and liabilities:
surplus return = asset return 1/(funding ratio) x liability return,
where the funding ratio is the assets to liabilities ratio; initially a value of one is assumed.
The correlation matrix shown in table 2 and some risk-return figures over the period from January 2000 to January 2006 describe these assets and liabilities. Performance is in GBP or converted to GBP.
Given the equity allocation, the funding ratio of this pension scheme probably suffered in the early 2000s and it would probably still be under-funded like the majority of its peers. Risk could be reduced by replacing (parts of) the equity exposure with an allocation to gilts or index linked securities, but that would leave the pension fund looking for additional income sources to improve its funding ratio, preferably without having to require further funding from the plan sponsor.

Portable alpha
A portable alpha structure can provide that additional funding by using swaps to gain exposure to a benchmark asset and investing the free capital thus generated in a portfolio designed to provide consistent alpha. In this example, a highly diversified fund of hedge funds is used as the alpha provider while the benchmark is accessed via a swap. The benchmark could be a longer-term interest rate or any major index such as the FTSE All Share or FTSE UK Gilt Index. The swap is structured for the investor to pay LIBOR and receive the benchmark.
The composition of the hedge fund portfolio (HF portfolio) is of paramount importance, as it needs to consistently outperform the overall cost of the swap, ie LIBOR plus a spread. This spread includes three items: the actual cost of the swap (for major indices this should be at most a few basis points), administrative fees to service the portable alpha structure and the cost of a stand-by credit line for improved cash management in case of swap payments. The latter two items contain partly fixed costs so larger transactions tend to have lower percentage costs.
The combined performance of the benchmark and the ported alpha is summarised as follows:
Portable alpha solution = Benchmark
+ (HF portfolio LIBOR Spread),
where the benchmark, HF portfolio, and LIBOR are the respective return series. The spread includes the costs described above. As long as the HF portfolio outperforms the cost of the swap, ie LIBOR plus a spread, the investor will receive the return of the benchmark plus any outperformance.
Selecting an appropriate benchmark to match the liability-replicating portfolio makes this solution attractive for liability-driven investors. In its simplest form, this benchmark is a longer-term interest rate, which means that the portable alpha solution combines an interest rate swap and a HF portfolio, the latter enhancing the performance through an additional source of income. Hence, this product is called an ‘enhanced LDI solution’.

Inflation protection
A portable alpha solution will improve returns by generating additional income, but does not ensure effective protection against inflation. Owing to the growth of the swap market, such inflation protection can be achieved by combining an interest rate swap (receive fix) and an inflation swap (pay fix). Hence, the buyer will pay a fixed rate (3% say) and receive longer-term inflation protection. Furthermore, a spread can be locked in between the fixed legs of the two swaps, which is effectively the real yield at the time of investment. To ensure that the maturity of these swaps remains within the desired range close to the liability replicating portfolio’s duration, the swaps need to be rolled over periodically, once a year say.
Including the inflation protection in the summary formula, it can be seen that
Enhanced LDI solution =
Benchmark + (HF portfolio LIBOR Spread)
+ (Inflation PayFix + Lock in)
where Inflation is the ‘return series’ of inflation, PayFix the fixed leg to be paid in the inflation swap, and Lock in is the spread between the fixed legs of the two swaps.
The enhanced LDI solution offers inflation protection and is expected to generate a real rate of return. As such, the Enhanced LDI solution could potentially replace parts of the equity allocation within a pension portfolio, with a lower level of surplus volatility.

Computing the return series
Return series for the benchmark and the hedge fund portfolio have been collected since the early 1990s and are generally fairly easy to obtain. However, inflation swap data has been collected only fairly recently and covers too short a period of time for the purpose of this analysis. A way around this data problem is to use an inflation-linked bond index as the benchmark; ie including the inflation protection in the benchmark:
Enhanced LDI solution =
Inflation-linked bond benchmark
+ (HF portfolio LIBOR Spread)
In this analysis, the Barclays index-linked gilts over 15 years are used as the inflation linked bond benchmark (available since January 2000). Because of its long-dated bonds, this benchmark’s duration is close to the liability-replicating portfolio. The HFRI Fund of Funds Market Defensive index serves as the HF portfolio . Finally, a spread of 50 bps (costs for swap, servicing, and stand-by credit line) is assumed. As the hedge fund index is in USD, it has been hedged to GBP through Libor 3mth differential:
ReturnGBP = ReturnUSD Libor 3mthUSD
+ Libor 3mthGBP
Table 3 summarises the risk-return characteristics of the various instruments over the period January 2000 to January 2006.
It is now possible to show the impact of applying an enhanced LDI solution to the control portfolio introduced above (Portfolio X): changes in risk-return characteristics are material when looking at the surplus view and the funding ratio projection.

Surplus view
Table 3 shows how the risk-return profile of the control portfolio changes when the enhanced LDI approach is applied to a single asset class (bonds or equities) or parts of the portfolio.
As can be seen, replacing any part of the portfolio with the enhanced LDI solution has a positive impact on the risk-return characteristics of the surplus. For a given level of replacement (eg 35%), reducing the equity allocation has the largest impact on the risk-return characteristics of the portfolio. These improvements result from a benchmark that better matches the liability-replicating portfolio and the additional return from the hedge fund portfolio ‘ported’ onto the benchmark.

Funding ratio projection
Another way to look at the impact of adding the enhanced LDI solution is to compare the funding ratio projection for the initial portfolio with a portfolio containing the enhanced LDI solution. For each of these portfolios, 100,000 monthly surplus return series have been simulated over ten years. The resulting cumulative funding ratio series all start with a funding ratio of one and cover a cone-shaped zone. To mitigate the impact of simulation outliers, the ‘inner’ 95 percentiles have been considered. See Otruba, Quesada, and Scholz (2006) for a full description of the methodology.
Figures 2 and 3 overleaf show the impact of allocating 35% of the portfolio to the enhanced LDI solution. It is possible either to replace equities or bonds, or to proportionally reduce a portion of the portfolio. In any case, the impact on the funding ratio is positive: the mean funding ratio is improved and the downside risk of the portfolio is reduced.
Replacing equities improves the mean funding ratio significantly. Furthermore, this replacement considerably reduces the dispersion of the funding ratio paths. As a result, the upside potential exceeds the levels of the initial portfolio, but with a much reduced downside risk over time.
Replacing bonds has a less pronounced effect than replacing equities and essentially results in an improved mean funding ratio, while the dispersion increases slightly, mainly because of a stronger upside.

The risk-return characteristic changes illustrated through the funding ratio projections are consistent with the changes observed in the surplus view. They suggest that replacing parts of the control portfolio have a material impact. Replacing equities shows more pronounced effects than replacing bonds. c