Step 2: Understanding the relationship between an LDI strategy’s tracking error and the plan’s liabilities
Once plan sponsors have decided to start to de-risk, the allocation to LDI and its role in matching the liabilities can be confusing. First, it’s important to understand how the pension plan’s liabilities are calculated. An actuary begins by projecting what the benefit payment stream will look like over a given period of time. The actuary then calculates the present value of these future cash flows by discounting the benefit payment stream against a yield curve of high-quality corporate bonds (Chart 1). Because the discount rate ties the benefit payment stream to the performance of interest rates, the plan’s liabilities respond accordingly: when rates go down, liabilities go up, and vice versa.
The sensitivity of an asset to the movement of interest rates is known as the duration. For example, having a duration of “10” means that for every 1% change in interest rates, the asset value will change by 10%. In an LDI strategy, duration looks at the benefit payment streams and calculates the sensitivity of each stream to the discount rates. It makes sense that a benefit payment that is further in the future will be more sensitive to a change in interest rates. This calculation would be fairly simple if there were only one payment stream; however, a pension plan has many payment streams, all with different durations. The effective duration of a pension plan is a combination of all of these benefit payments discounted back to the present. To do this efficiently, the present value sensitivities are aggregated into key-rate duration buckets.
Let’s look at an example of how liabilities and
durations are calculated. In Chart 2, the pension plan is 100% funded and uses a 100% Core Fixed-Income LDI implementation. Core Fixed Income has a duration
of roughly four years, and the plan has a duration of around 13 years. In this
example, you can see that Core Fixed Income provides good coverage and closely
matches the liability in the early years, but there are significant gaps
beginning with year seven. As a result, the plan has an effective hedge of
32.8% and a funded-ratio volatility of 9.4%. This means that the 100%-funded
plan, with all of its assets invested in Core Fixed Income, has an
unpredictable and fairly volatile funded ratio of between 82.2%
and 112% on an annual basis.
Some plan sponsors try to address this mismatch by buying long-duration bonds, such as the Barclays Capital Long Government Credit Index or the Barclays Capital Long Corporate Index. As can be seen in Chart 3, adding long bonds would indeed improve the duration match, as the current liability duration is 13.4 years and the effective asset duration is 12.5 years, giving an effective hedge of 93.3%. But you can also see in this example that there are some mismatches, especially near the long end. This type of implementation is based upon public market benchmarks, not the unique benefit payment stream of the pension. If the money manager buys bonds that differ from the public market index, there will be tracking error, which will either yield alpha or lead to loss relative to the public market benchmark. The challenge is that the true benchmark is the pension plan’s distribution of key-rate durations, not the public market benchmark.
An effective LDI implementation would fill the remaining gaps. An overlay of U.S. Treasury STRIPS or interest rate swaps can help to create coverage across the entire curve as a result of their liquidity. In Chart 4, an overlay of STRIPS more closely matches the effective duration and also reduces funded-ratio volatility and the range in the funded-ratio confidence interval.
As you may have noticed in Chart 4, a diverse fixed-income strategy, coupled with an overlay of STRIPS, still does not guarantee a perfect hedge. In tough markets, the sample pension plan has a 92.8% funded ratio, but it’s only 103.9% in good times. So while a customized LDI implementation goes a long way to reduce the risk and volatility of the pension plan, there are still risks that remain due to the construction methodology of the liabilities discussed earlier. This is commonly known as “basis risk,” or the difference between what is used to build the discount rate and what is used in the LDI implementation.
The match to the liabilities is imperfect, and there has been a lot of research as to why the tracking error and benchmarking to the liability are likewise imperfect. So at best, the goal should be to understand the major factors impacting the tracking to the liabilities, and investments should be made so as to best minimize that risk. Plan sponsors should be cognizant that this mismatch is not solely dependent upon the liability, but due to the correlation and impact of the nonmatching portfolio as well.
