Lionel Martellini, Professor of Finance, EDHEC Business School and Scientific Director, EDHEC-Risk Institute
Vincent Milhau, Senior Research Engineer, EDHEC-Risk Institute

A recent surge in inflation uncertainty has further increased the need for investors to hedge against unexpected changes in price levels. Inflation hedging has in fact become a concern of critical importance for pension funds, given that pension payments are typically indexed with respect to consumer price or wage level indexes, but also for private investors, who consider inflation as a direct threat with respect to the protection of their purchasing power. In the face of an increasing need for inflation hedging, inflation-linked securities have been introduced, first by sovereign states. While a dominant fraction of inflation-linked debt is still issued by sovereign states, there has been recent interest amongst various state-owned agencies, municipalities but also corporations, in particular utility or financial-services companies, to issue inflation-linked bonds. In fact, the intuition suggests that if a firm's revenues tend to grow with inflation, then having some inflation-linked issuance can be a natural hedge.

In this context, it is perhaps surprising that some large corporations are still sitting on the sidelines, as they implement debt structure decisions involving no inflation-linked bonds. This situation may in part be explained by a common belief that debt management decisions should be governed by the desire to reduce the cost of debt financing. In particular, the standard argument suggests a corporation should seek to issue fixed (floating) debt if it anticipates an increase (a decrease) in interest rates and issue nominal (inflation-linked) bonds if it anticipates an increase (a decrease) in inflation. In this context, inflation-linked bonds would not seem attractive from the issuer's perspective since the cost of debt servicing would be expected to increase with inflation. This seemingly straightforward line of reasoning suffers, however, from one fatal flaw: the difference in fixed versus floating (versus real) rates merely reflects market expectations and a risk premium. In the end, the only non-trivial impact may come from the chief financial officer's active views if they deviate from the market views and the "raison d'être" of a corporation is hardly to make profits from trading in financial markets.

In a recent paper supported by Rothschild & Cie, we introduce a general framework for analysing debt management decisions by a corporation subject to default risk. We argue that the main motive behind debt management is not reducing the cost of debt financing, but instead hedging interest rate and inflation risk exposures. In fact, by matching the interest rate and inflation exposure of the liabilities to that of the assets, the managers of a firm can contribute to reducing the variability of the cash flows. This has a direct positive consequence in terms of decreasing the probability of default, and consequently decreasing the cost of equity and increasing equity value.

More specifically, we attempt to answer the following question: given an exogenous revenues process for a corporation, what is the optimal liability structure when the issuer faces various forms of debt instruments, including in particular, fixed-rate debt, floating-rate debt, and inflation-linked debt? In fact, this problem is the exact counterpart of the standard asset-liability management problem for a pension fund, where the liabilities are exogenously given while the allocation decision is to be optimised over.

To gain an intuitive understanding of why the presence of specific risk factors in asset returns matters, let us consider the problem of optimal issuance of inflation-indexed bonds by sovereign states, municipalities or corporations. Issuing inflation-indexed bonds leads to a reduction in the cost of debt since the issuing party is selling insurance against inflation and receives the associated premium. On the other hand, issuing inflation-linked bonds, as opposed to nominal bonds, increases the uncertainty in the financing costs because of heightened uncertainty in coupon payments. This is a cost-risk trade-off which is the counterpart from a pure liability management perspective of the return-risk trade-off in asset allocation decisions. Recognising the presence of the assets in place leads, however, to a somewhat more contrasted picture. Indeed, because revenues (tax revenues for states and municipalities, or operating cash-flows for corporations) are often positively related to changes in inflation, it is not necessarily the case that increases in inflation always lead to a decrease in net revenues for the issuer. In other words, while issuing inflation-indexed bonds leads to an increase in risk from a pure liability perspective, it is not necessarily more risky from a combined liability-asset management perspective. In this context, inflation-indexed debt would appear to dominate nominal debt both in terms of risk and return, and the optimal composition of a debt portfolio will be affected accordingly. In other words, the intuition suggests that the optimal debt structure should not so much emanate from a concern over minimising the cost of debt, but also involve hedging motives with respect to risk factors impacting the revenues of the firm.

Beyond these basic intuitions, it is fair to say that our formal understanding of liability allocation decisions by corporations (capital structure decisions and debt structure decisions) is relatively limited. In particular, relatively few quantitative insights are available about the optimal allocation to various classes of debt (fixed, floating, inflation-linked) by a corporation, and the cost associated with suboptimal debt management strategies. To formalise these intuitions, we consider a stylised debt management problem whereby three classes of debt can be issued by a firm: fixed-rate bonds, floating-rate bonds and inflation-linked (IL) bonds. In an attempt to increase shareholder wealth, the managers of the firm seek to immunise debt servicing with respect to the exposure to interest rate and inflation risk factors. In fact, what matters is not so much the variability of debt servicing as the volatility of the firm cash flows net of debt payments. Hence, decreasing the share of fixed-rate bonds increases uncertainty about debt servicing since interest payments on floating-rate and inflation-linked bonds are uncertain. On the other hand, this may lead to increases in the correlation between changes in liability and asset values provided that the correlation between asset value and interest rate or inflation is positive. In other words, issuing floating-rate bonds or inflation-linked bonds may increase risk from a pure debt management perspective, but decrease risk from an integrated asset-liability management perspective. From this trade-off emerges an optimal debt structure, and one can show that under (mild) simplifying assumptions, minimising the volatility of assets versus liabilities is equivalent to minimising the (risk-adjusted) default probability, which in turn is equivalent to maximising firm value.

Consistent with the hedging motive, we find that the optimal share of floating rate bonds increases with the correlation between changes in interest rates and changes in the revenues of the firm. Hence, a firm with positive (negative) correlation between its operating cash-flows (before interest expenses) and interest rates should maintain higher (lower) floating-rate debt to avoid the (bankruptcy) costs associated with situations with low cash-flows and high debt servicing. Similarly, the optimal share of inflation-linked bonds increases with the correlation between changes in inflation rates and changes in the revenues of the firm. Overall, we find that optimising the structure of debt leads to lower default probability, and therefore to higher firm value. One key conclusion that we obtain is that debt management decisions have a strong positive impact on firm value. Another key conclusion is that for reasonable parameter values, corporations should issue a non-zero share of inflation-linked bonds. We also find the opportunity costs associated with not issuing IL bonds to be substantial. From an implementation perspective, one could also use derivatives to adjust interest rate and inflation risk exposures, but derivatives would not be the natural approach for long horizons in the presence of counterparty risk.

Our analysis could be further extended in a number of useful directions. In particular, it would be useful to include other types of instruments, such as convertible bonds, preferred shares and other equity-linked structures in the liability mix, in addition to fixed-rate and floating-rate bonds. On a different note, it should be emphasised that our model, following previous literature, considers the liability allocation problem from the standpoint of the original owners of the firm, assumed to be risk-neutral with respect to the (diversifiable) source of uncertainty impacting the firm value. In practice, however, the managers of the firm, as opposed to the owners of the firm, are in charge of making corporate risk-management and liability allocation decisions. Academic research has documented the role of conflicts of interests and managerial incentives in the design of corporate debt structure programmes and incorporating the impact of these conflicts of interest would be of relevance.