Vincent Milhau

Dynamic allocation decisions in the presence of funding ratio constraints

This paper introduces a continuous-time allocation model for an investor facing stochastic liability commitments indexed with respect to inflation. In the presence of funding ratio constraints, the optimal policy is shown to involve dynamic allocation strategies that are reminiscent of portfolio insurance strategies, extended to an asset–liability management (ALM) context. Empirical tests suggest that their benefits are relatively robust with respect to changes in the objective function and the introduction of various forms of market incompleteness. We also show that the introduction of maximum funding ratio targets would allow pension funds to decrease the cost of downside liability risk protection.

Towards Conditional Risk Parity -- Improving Risk Budgeting Techniques in Changing Economic Environments

Risk parity portfolios are traditionally constructed by choosing historical volatility as the risk measure. In an asset allocation context, this results in a substantial overweighting of bonds versus more volatile asset classes such as stocks: this is a concern in a low bond yield environment, since the presence of mean reversion in the yield implies that bonds are likely to perform poorly in the next future. In this article, we introduce three distinct risk parity strategies, explicitly designed to respond to changes in interest rate levels. Our results indicate that these strategies deliver higher returns when interest rates start to increase back to their long-term levels, and that the maximum Sharpe ratio portfolio, which also incorporates information on expected returns, is a less robust alternative.

Bond Portfolio Optimization in the Presence of Duration Constraints

Although there exists an abundant literature on the benefits and limits of scientific diversification in the equity universe, little is known about the out-of-sample performance of portfolio optimization models in the fixed-income universe. In this article, the authors address two key challenges that are specific to bond portfolio optimization, namely, the presence of duration constraints and the presence of no-arbitrage restrictions on risk parameter estimates, for which no equivalent exists in the equity universe. In an application to sovereign bonds in the eurozone, they find that the use of portfolio optimization techniques based on robust estimators for risk parameters generates an improvement in investor welfare compared with the use of ad hoc bond benchmarks such as equally weighted or cap-weighted portfolios. These results are robust with respect to changes in the number of constituents in the portfolio and the rebalancing period, and in the presence of duration or weight constraints.

Equity Portfolios with Improved Liability-Hedging Benefits

This article analyzes whether it is desirable and feasible for an investor endowed with liabilities to hold an equity portfolio with better liability-hedging properties than a broad cap-weighted index. From a theoretical standpoint, the authors show that liability-driven investors will generally benefit from reducing the tracking error of their performance portfolios with respect to liabilities, unless this comes at an exceedingly large loss of performance. The authors then empirically document the heterogeneity of interest-rate-hedging properties across the constituents of the S&P 500 universe, and they show that substantial welfare gains can be achieved by selecting low-volatility and high-dividend-yield stocks. These benefits are further enhanced if a minimum-variance weighting scheme is applied to the selected stocks.

A Reinterpretation of the Optimal Demand for Risky Assets in Fund Separation Theorems

In a continuous-time portfolio selection model with N risky assets and K state variables driving their risk and return parameters, we derive simple expressions for the allocation to each asset in the K + 1 risky funds of the (K + 2)-fund separation theorem. We show that the allocation to any given risky asset in each fund can be written in terms of the parameters of a regression of the excess returns of this asset on those of the N − 1 remaining assets. We also use these parameters to provide quantitative measures of the increase in Sharpe ratio of the speculative demand, or in the maximum correlation of each hedging demand with respect to the corresponding risk factor, associated with the introduction of a new asset in the investment universe. Finally, we show that in a multiperiod setting, an asset is “spanned” by others if and only if it improves neither the maximum Sharpe ratio of the speculative demand nor the maximum correlations of the hedging demands with the risk factors. This paper was accepted ...

Hedging Inflation-Linked Liabilities without Inflation-Linked Instruments through Long/Short Investments in Nominal Bonds

In the absence of inflation-linked bonds or inflation swaps, no perfect hedging strategy exists for inflation-linked liabilities, so nominal bonds are often used as substitute hedging instruments. This article provides a formal analysis of the problem of hedging inflation-linked liabilities with nominal bonds in the presence of real rate uncertainty as well as realized and expected inflation risks. Although a long-only position in nominal bonds will always have a negative exposure to unexpected inflation, the analysis suggests that long/short nominal bond portfolio strategies can in principle be designed to achieve a zero exposure to changes in unexpected inflation (required to hedge inflation-linked liabilities) while having a target exposure to changes in real rate equal to that of liabilities. The practical implementation of such long/short replication strategies, however, is not a straightforward task in the presence of parameter uncertainty. The authors explore several non-exclusive solutions to the estimation risk problem, including the use of conditional parameter estimation methodologies as well as the introduction of robust restrictions on input parameters or portfolio weights. These approaches lead to substantial improvements in out-of-sample hedging performance.

Exploiting Asset-Liability Management Concepts in Private Wealth Management

Asset and liability management (ALM) has traditionally been applied to banks, insurance companies and pension funds. In this chapter we will introduce a new application area of ALM: private wealth management. Over the past dec-ade, private wealth management has become a profitable business for banks and asset managers around the globe. According to the private banking and wealth management survey conducted by Euromoney (2008), global private banking assets rose to USD 7.6 trillion in 2008, from USD 3.3 trillion the year before. This increase is currently driving a growth in the wealth management market, creating greater opportunities for wealth advisors to leverage new tech-nology to acquire new clients and grow profits. As a result, competition among wealth advisory firms is increasing for new ways to improve existing client relationships and provide new tools to improve advisor effectiveness. While the private banking industry is, in general, relatively well equipped on the tax-planning side, with tools that can potentially allow private bankers to analyze the situation of high net worth individuals operating offshore or across mul-tiple tax jurisdictions, the software packages used on the financial simulation side typically suffer from significant limitations and cannot satisfy the needs of a sophisticated clientele.