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.

**DOING WHAT THEY'RE SUPPOSED TO**

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**