February 2014

EDHEC: Attractive additions

PastryWith high levels of demand for corporate bonds, the Edhec-Risk Institute considers why these assets are good for both performance-seeking and liability-hedging portfolios. International accounting standards, which recommend that pension obligations be valued on the basis of a discount rate equal to the market yield on AA-rated bonds, say the most straightforward way for pension funds to match liability payments is to build a portfolio of long-dated, investment grade corporate bonds. In practice, pension funds and other institutions are actually showing an increasing appetite for corporate bonds, not only for their liability-hedging benefits, but also for their performance benefits related to the presence of a credit risk premium, which is imperfectly correlated with the equity risk premium. Recent research conducted as part of an Edhec-Risk Institute research chair – The case for corporate bonds: issuers’ and investors’ perspectives – supported by Rothschild & Cie, provides a formal analysis of the benefits of corporate bonds in investors’ portfolios, distinguishing between the impact of introducing them in performance-seeking portfolios (PSPs) and the impact of introducing them in liability-hedging portfolios (LHPs). From a formal standpoint, our analysis is cast within the context of the liability-driven investing (LDI) paradigm, a disciplined investment framework that advocates splitting an investor’s wealth between a dedicated LHP and a common PSP. While the LDI paradigm implies that investor welfare should depend on how good each building block is at delivering what it has been designed for (namely, hedging benefits for the LHP and risk-adjusted performance benefits for the PSP), intuition suggests that the interaction between performance and hedging motives should also play an important role. We analyse this effect and show that investor welfare can be improved by the design of performance-seeking portfolios with improved liability-hedging properties, or conversely by the design of liability-hedging portfolios with improved performance properties. A FUND THEOREM
To see this, we first introduce a formal decomposition of investor welfare in terms of performance and hedging benefits, and show that a residual term remains, which can be interpreted as a cross-effect emanating from the interaction between performance and hedging motives. This result, which we call the “fund interaction theorem”, is important in that it shows that investor welfare indeed includes contributions from the PSP and the LHP, but also cross-contributions related to the hedging potential of the PSP. When negative, the cross-contribution signals the presence of a conflict between the performance and hedging motives, such as a short position required for performance purposes and a long position required for hedging purposes. This cross-contribution can be substantial for some parameter values, and sometimes equal or superior in magnitude to the performance and hedging contributions. The practical implications of the fund interaction theorem is that investors will in general benefit from improving hedging characteristics of the PSP, unless this improvement is associated with an exceedingly large decrease in Sharpe ratio. In the end, the net impact will be positive or negative depending on the relative strength of the following two competing effects. On the one hand, the PSP with improved hedging benefits can represent a higher fraction of the investor’s portfolio for a given risk budget; on the other hand, the PSP with improved hedging properties may have lower performance: hence the trade-off is between an increase in performance due to a higher allocation to risky assets, and a decrease in risk-adjusted performance due to a lower reward for each dollar invested. In an empirical analysis, we find that corporate bonds are particularly well-suited to improving the PSP/LHP interaction, given that they have well-controlled interest rate risk exposure while providing access to an equity-like risk premium. These two properties make them natural candidates for inclusion in the performance portfolio, where the primary focus is on achieving a high expected return, and where a high correlation with liabilities helps to align performance and hedging motives, and also in the liability-hedging portfolio, where the primary focus is on interest rate risk hedging, and where the presence of a credit risk premium also contributes to aligning performance and hedging motives more effectively than what is allowed by sovereign bonds. As recalled above, if liabilities are discounted at the risk-free rate plus a spread, corporate bonds may actually hedge liability risk better than sovereign bonds do, precisely because they include a credit spread component that evolves in line with the discount rate on liabilities. POSITIVE IMPACT
Our research provides an empirical analysis of the sources of added-value of corporate bonds for institutional investors. For reasonable parameter values, we have found corporate bonds to be attractive additions to investors’ portfolios. On the one hand, introducing them in PSPs typically generates positive benefits from an asset liability management perspective since it will lead to substantial improvements in hedging benefits, which come at the cost of a less-than-proportional reduction in performance compared to equity-dominated portfolios. Introducing corporate bonds in LHPs has also been found to generate a positive impact on investor welfare since it leads to improvements in both hedging and performance benefits, especially for investors facing liabilities discounted using a credit spread adjustment. In this context, one may want to assess whether a particular proportion of corporate bonds in each portfolio would lead to the highest level of welfare gains. The answer to this question is of course that the optimal allocation to corporate bonds should maximise the Sharpe ratio within the PSP, and the (squared) correlation with the liabilities within the LHP. In fact, the fund interaction theorem and the fund separation theorem are not mutually inconsistent; the fund interaction theorem complements the fund separation theorem by emphasising the benefits of having, if and when possible, an alignment, as opposed to a conflict, between the performance and hedging motives. Our analysis can be extended in many possible directions. First of all, it would be useful to draw a distinction between investment grade bonds and high yield bonds, given that the risk/return, as well as factor exposure characteristics of these two segments of the corporate bond market, are clearly distinct. Also, one could consider corporate bond benchmarks with various numbers of constituents so as to assess the impact of credit risk diversification on the results in the paper. Finally, the interaction analysis in our research could usefully be extended to other types of securities, including, for example, equities. In particular, a large cross-sectional variation exists in the interest rate exposure of various segments of the equity markets, and some sectors or types of stocks have been found to have a duration that is substantially higher than the duration of a well-diversified equity portfolio.
If an equity benchmark can be constructed with a substantially enhanced interest rate risk exposure, without a significant cost in terms of Sharpe ratio, then the analysis in our research suggests that using this benchmark as opposed to a standard market index may lead to improvement in welfare for an investor facing liabilities. More generally, there are at least two reasons investors would find it optimal to invest in any asset class. First, the asset class under consideration can be useful if it provides access to excess performance with respect to cash (speculative demand for risky assets that generate an exposure to rewarded sources of risk). Second, it can also be useful if it provides hedging benefits (intertemporal hedging demands for risky assets that can be used to immunise wealth levels with respect to risk factors that impact the value of liabilities and the opportunity set). Clearly, these motives are not mutually exclusive; for example, bonds are useful ingredients in the speculative component of investors’ portfolios, where they bring excess performance with respect to cash and diversification benefits with respect to equities, and they are also useful in the hedging component of liability-driven long-term investors’ portfolios, where they allow for protection against unexpected changes in interest rates. The analysis in our research suggests that not only are the two motives not mutually exclusive, but also that these two motives interact, and their interaction is a key driver of the ability for investors to achieve attractive funding objectives from an asset-liability management perspective. This is an edited version of an article by Lionel Martellini, professor of finance, Edhec Business School, and scientific director, Edhec-Risk Institute, and Vincent Milhau, deputy scientific director, Edhec-Risk Institute. ©2014 funds europe

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