March 2015

EDHEC RESEARCH: A better balancing act

LevelLiability solutions can be enhanced by designing performance-seeking equity benchmarks with improved liability-hedging properties, Edhec-Risk Institute research for the Ontario Teachers’ Pension Plan shows. Asset-liability management (ALM) for pension funds has become relatively straightforward, in principle, within liability-driven investing (LDI).  When extended to ALM, modern portfolio theory and the fund separation theorem advocate that pension plans should implement a combination of a liability-hedging portfolio (LHP) invested in fixed-income securities and aiming to match the risk factors impacting the value of their liabilities, and a performance-seeking portfolio (PSP) aiming to efficiently harvest risk premia across and within risky asset classes, most importantly in global equity markets.  While this clear separation between the search for performance and the desire to hedge liabilities is perfectly intuitive and sensible in theory, it suffers from a number of limitations in terms of real-world implementation.  The main limitation is the presence of leverage constraints, which implies that most underfunded pension funds cannot use as much leverage as would be required to fully hedge their liabilities. In practice, pension funds end up investing all their assets in a zero- or low-leverage portfolio mostly containing stocks and bonds.  In this context, the question arises whether it would make sense for a pension fund to hold a customised equity portfolio with enhanced liability-hedging properties, rather than an off-the-shelf broad equity index.  Intuition suggests that a better alignment of the performance-seeking portfolio with respect to the liabilities would lead to an increased allocation to stocks for the same level of volatility of the funding ratio, which in turn would generate higher access to the equity risk premium. Recent research at Edhec-Risk Institute, backed by Ontario Teachers’ Pension Plan, assesses whether LDI solutions can be enhanced by the design of performance-seeking equity benchmarks with improved liability-hedging properties. We confirm this intuition and show that improving hedging characteristics of the performance portfolio generates welfare gains unless this improvement comes at an exceedingly large opportunity cost in terms of performance, a result that we call the fund interaction theorem.  While two competing effects exist in principle (a better alignment of the equity portfolio with the liabilities leads to a higher allocation to equities for the same ALM risk budget due to enhanced liability-friendliness, but it may also lead to a lower reward per dollar invested compared to a pure focus on performance), our empirical analysis actually suggests that the selection of stocks with above-average liability-hedging properties leads to both a higher degree of liability-friendliness (as expected) and also to better performance due to increased exposure to rewarded factor tilts. In this context, we find that very substantial increases in investor welfare would come from switching from a standard off-the-shelf cap-weighted equity benchmark to an equity benchmark designed to exhibit above-average liability hedging properties.  We consider two alternative approaches to the definition of liability-friendliness. The first one is based on cash-flow matching capability: under this definition, liability hedging is aimed at finding securities whose dividend payments match the pension payments as closely as possible. The stocks which are expected to display above-average liability-friendliness in terms of cash-flow matching capacity are those that generate large and stable dividend yields. The second definition is based on factor exposure matching. Since perfect cash-flow replication is typically difficult to achieve in practice, investors who need to hedge liabilities may choose instead to match the risk-factor exposures of their assets with those of their liabilities. The objective pursued in this case is to immunise the funding ratio against variations in the risk factors that impact liabilities, and the success is measured in terms of tracking error with the liability proxy.  In this setting, with a focus on risk-factor matching, a stock will be said to be liability-friendly if the tracking error of the stock returns with respect to the returns on the liability proxy is low.  Given the decomposition of the tracking error into two components – one that is related to the portfolio volatility and one that is related to the portfolio correlation with the liability proxy – a low tracking error can be achieved either if the volatility of the stock is low and/or if the correlation between the stock and the liability proxy is high.  Using data from the CRSP database from 1975-2012, we construct portfolios with stocks originating from the S&P 500 universe. We cast the analysis at the individual stock level. The portfolios are rebalanced every year in March. In the analysis, the liability proxy is computed as a constant maturity bond and its returns are computed using 15-year US Treasury yields.  The second step of the procedure establishes the
weights that are assigned to each stock. We start by considering equal weights (EW) for all stocks (no selection EW), so as to assess the benefits of the selection stage, and we additionally provide the results for the cap-weighted (CW) portfolio of all stocks (no selection CW), which is the commonly used benchmark. In order to compare the relative performance of the portfolios, we compute the following out-of-sample indicators – the tracking error and correlation with respect to the liabilities, volatility, average dividend yield, Sharpe ratio and annual turnover. 
We conclude that the various selection procedures deliver what they are designed for. The equally weighted portfolio of the 20% of stocks with the lowest volatilities has a tracking error of 14.6% with respect to our liability proxy, while the equally weighted portfolio of the 20% of stocks with the highest volatilities is almost twice as large. This improvement in tracking error emanates not only from lower portfolio volatility; it is also linked to a strong increase in correlation with the liabilities.  Hence, the selection of low-volatility stocks generates a positive 7.7% correlation with the liability proxy, while a selection of high-volatility stocks generates a negative correlation of -6.7%. This improvement can be traced to the fact that low-volatility stocks, which tend to be low-dividend-uncertainty stocks, are the stocks that tend to be the closest approximations to fixed-income securities.  In terms of correlations, the high-correlation selection ranks only second (though close to first), with a large turnover, suggesting that empirical correlations are highly unstable. We further observe that all selections increase the Sharpe ratio as well as the turnover, compared to both the EW and CW benchmarks, and the increased liability-friendliness of the portfolios is therefore not penalised by lower risk-adjusted performance. We also confirm that the selection on dividend yields generates a statistically and economically significant increase in this dimension with respect to the use of the standard S&P 500 index as a benchmark. Addressing the focus on liability-hedging through a double-sort procedure, starting with the 200 highest-dividend-yield (DY) stocks, selecting the 100 lowest-volatility stocks among them, and subsequently performing a minimum-variance optimisation, leads to further improvements in the liability-friendliness of the selected portfolios.  Hence, combining the double-sort selection procedure with the minimum-variance weighting scheme with norm constraints (MV-C), leads to improvements in all indicators with respect to the base case results, and reach the following attractive levels: 14.1% tracking error, 12.5% volatility, 8.2% correlation and 5.4% average dividend yield.  Measuring the impact on investor welfare
Due to the resulting improvement in liability-hedging benefits, liability-driven investors can allocate a higher fraction of their portfolios to equities without a corresponding increase in funding ratio volatility. For example, we find that a pension fund allocating 40% to equities on the basis of a CW equity benchmark can allocate as much as 53.3% to a minimum variance portfolio of selected stocks from the aforementioned double-sort procedure for the same volatility of the funding ratio. This substantial increase in equity allocation without a corresponding increase in ALM risk budgets confirms that the improvements in liability-friendliness are economically significant. The resulting increase in equity allocation for the same ALM risk budget, combined with an improved risk-adjusted performance of the dedicated equity benchmark with respect to the S&P 500 index, leads to an improvement in performance reaching 158 basis points annualised over the 1975-2012 sample period.  This improvement can be decomposed into a contribution emanating purely from the increase in equity allocation assuming no impact on performance (39 basis points) and a contribution emanating purely from the improved performance of the equity benchmark assuming no increase in allocation (119 basis points).  With the exception of the MV-C portfolio of all stocks, the reduction in the maximum drawdown reaches at least 10%
in absolute value, or 30% in relative value. 
Furthermore, we observe that even after controlling for the volatility, LDI strategies with liability friendly portfolios dominate those with the S&P 500 in terms of extreme risk measures (maximum funding ratio drawdown). Written by Guillaume Coqueret, Romain Deguest, Lionel Martellini and Vincent Milhau of the Edhec-Risk Institute ©2015 funds europe

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