Factor-Based Liability Hedge Solutions

Liability Hedge Fixed Income Solutions created using Factor Sensitivity Matching are based on the fundamental notion that interest rate term structure can be decomposed into the underlying Factors and a portfolio of bonds can be chosen such that its sensitivity to changes in such Factors is the same as the sensitivity of pension liability to changes in these Factors. One of the statistical techniques used to extract the underlying Factors from the interest rate term structure is Principal Component Analysis.

Estimation of Factors

Initially, these Factors are not known, since they are not observable in the market place, i.e. they are not tradable Factors, but it is assumed that they represent linear combinations of the underlying spot rates of the interest rate term structure. Principal Component Analysis is a statistical technique used to identify and evaluate Factors by maximizing their co-variability with the underlying interest rates.

High Levels of t-statistic
The resulting Factors have very high statistical significance as shown by high levels of t-statistic (much greater than 2) in the following table for all maturities and for all three Factors.
High Levels of R^2
These Factors also explain great majority of interest rate variation as shown by very high levels of R^2 statistic (98%-99%) in the table for all three Factors combined (“L+S+C” column), when monthly changes of interest rates in selected maturities (1,5,10,…,30 years) are regressed against changes in Factors.
Ortho-gonal Factors
These Factors are also designed to be independent of each other, i.e. they are orthogonal Factors, which is a good property, since there would be no need to model and hedge co-variability among Factors.
High Explanato-ry power
As shown in the table in “L+S+C” column, three Factors already have significantly high explanatory power of interest rate term structure as measured by very high R^2 , and therefore there is no benefit in estimating additional Factors.

Time Series of Factors

Once these three Factors are identified and estimated, it is necessary to determine their economic interpretation, since they were not known in advance as they are not tradable and not otherwise observable.
As shown in the following chart, where the time series of the estimated three Factors are presented, it is very difficult to provide economic intuition behind three Factors by just looking at their respective time series plots.

Economic Interpretation of Factors

Therefore, when it comes to Principal Component Factors representing interest rate term structure, the most appropriate way to interpret Factors is to look at and examine sensitivities of the underlying interest rate term structure to such Factors as shown on the following chart:

Level Factor
First Factor is interpreted as Level Factor, since sensitivities of changes in spot rates to changes in this Factor are relatively uniform across all maturities. Shifts in this Factor will change general Level of the entire yield curve by about the same amount across all maturities.
Slope Factor
Second Factor is interpreted as Slope Factor, since sensitivities of changes in spot rates to changes in this Factor are positive at the short-term maturities and negative at the long-term maturities (i.e. opposite sign). Shifts in this Factor will change general slope of the yield curve term structure.
Curvature Factor
Third Factor is interpreted as Curvature Factor, since sensitivities of changes in spot rates to changes in this Factor are negative at the short-term and long-term maturities and positive at the mid-term maturities. Shifts in this Factor will change general curvature of the yield curve term structure.

Factor Sensitivity Match vs Other Strategies: Efficient Frontier

Benefits of Factor Sensitivity Matching strategy are better understood and appreciated when its results are compared to those of other strategies. The following chart presents a plot of Risk and Return for several Liability Hedge strategies, such as Duration Matching, Duration/Convexity Matching, Key Rate Duration Matching, and Full Cash Flow Matching as compared to Factor Sensitivity Matching strategy. Risk and Return on the Efficient Frontier are based on pension plan’s Funded Status (Liability minus Bond portfolio invested in a given strategy), where Risk is measured as the expected downside of Funded Status in the worst 5% scenarios, and Return is measured as the expected level of Funded Status. Efficient Frontier is interpreted as follows:

Highest Risk Return
Highest Risk and Return strategies are located in the upper-right corner of the Efficient Frontier, represented by Duration Matching strategy which is the least restrictive strategy leading to greater Risk and Return. Duration Matching is very similar to matching one Key Rate or one Factor (Level) as shown on the chart.
Key Rates Added
As more Key Rates are added to the hedging strategy, asset-liability mismatch is decreasing, leading to lower Risk and Return, and as a result, moving in the lower-left direction on the Efficient Frontier.
Lowest Risk Return
The lowest asset-liability mismatch is when all Key Rates are hedged, which is equivalent to Full Cash Flow Matching, as shown on the opposite side of the Efficient Frontier in the lower-left corner. However, additional Key Rates require more bonds to be purchased leading to extra transaction costs and illiquidity costs that would magnify Risk measured as the downside of the Funded Status.

Superiority of the Factor Sensitivity Matching Strategies is shown by the fact that these strategies are located off the Efficient Frontier in the upper-left corner. This position implies that as compared to other matching strategies, Factor Sensitivity Matching provides greater Return for the same level of Risk or smaller Risk for the same level of Return.

Factor Sensitivity Match vs Other Strategies: Stochastic Projections

Another way to see superiority of Factor Sensitivity Matching Strategies as compared to other strategies is to look at the stochastic projections of Funded Status over time based for all strategies and compare them to each other. The results are presented in the following chart:

Duration Matching
Duration Matching strategy (or Duration plus Convexity matching) has the greatest Risk/downside and upside potential, which is consistent with its position on the Efficient Frontier as having greatest Risk and Return expectations.
Key Rates Matching
As we add more and more Key Rate Durations matched, expected Surplus, downside Risk and upside potentials become smaller and smaller, which is consistent with their respective positions on the Efficient Frontier chart analyzed above.
Factor Sensitivity Matching
Factor Sensitivity Matching Strategy, on the other hand, has a very different range of Surpluses, with greater expected Surplus (mid-point), smaller downside Risk and greater upside potential. This is again consistent with its position off the Efficient Frontier by providing superior risk adjusted returns.

In general, Factor Sensitivity Matching Strategy provides asset-liability mismatch protection equivalent to 10-15 Key Rate buckets, but using much fewer bonds, since it is a much less restrictive strategy, leading to superior Risk and Return measures.

Sequential De-Risking Solutions

Since various Liability Hedge strategies have very different Risk and Return profiles, they can be deployed sequentially under different circumstances or triggers, and packaged as part of Sequential De-Risking Solutions as follows:

Low Funding Ratios
When pension plan’s Funding Ratio is low (60%-70% or below), the primary objective is to improve funding levels by earning extra yield while controlling Risk. As a result, Duration Matching strategy is more appropriate in this case, which provides greatest Return and Risk while still reducing asset-liability mismatch.
Funding Ratios Increase
As Funding Ratios increase, strategies with lower Risk and Return profiles should be implemented automatically, by gradually increasing the number of Key Rates Matched or implementing Factor Sensitivity Matching strategies.
Fully Funded Plans
When pension plan is more than fully funded on the US GAAP basis (usually 105%-110%), Cash Flow Matching strategy is implemented to lock in Funded Status gains and prepare for Annuitization as part of the pension plans’ de-risking “End-Game”.

As pension plans’ funding levels improved over time and many pension plans embarked on the de-risking path, Liability Hedge asset class became one of the most dominant asset classes in many pension portfolios, requiring much greater attention and sophistication. Given the recent advances in the fixed income quantitative research, a Liability Hedge strategy based on hedging liability’s sensitivity to Factors embedded in the interest rate term structure proved to provide superior Risk/Return characteristics as compared to the traditional strategies. Such Factor Sensitivity Matching strategies effectively hedge against non-parallel yield curve shifts as 10-15 Key Rate buckets would but with much fewer bonds leading to greater cost efficiency and greater protection of asset-liability matching.