How Factor Investing Can Help Liability-Driven Investors

by Vincent Milhau, Research Director, EDHEC-Risk Institute

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Investment practices in institutional asset management have been profoundly impacted by the rise of two new paradigms: factor investing and liability-driven investing. Interestingly, both of these approaches have conceptual justifications in financial theory, an encouraging sign that the famous “gap between theory and practice” is not as wide as it once appeared. The recent study published by EDHEC-Risk Institute with the support of Amundi as part of the “ETF, Indexing and Smart Beta Investment Strategies” research chair aims to establish a series of connections, between factor investing and liability-driven investing.


Vincent Milhau EDHEC Risk Research Director


Liability-driven investing and factor investing have conceptual justifications in financial theory.


Liability-driven investing has its theoretical justification in the fund separation theorems derived from the portfolio optimization models introduced by Harry Markowitz, William F. Sharpe and Robert C. Merton (all awarded the Nobel Prize in economics), which show that the optimal trade-off between risk and return is achieved by combining a “performance-seeking portfolio” (PSP) and a “minimum risk portfolio”. In the presence of liabilities, to minimize risk means to minimize the tracking error with respect to liabilities, so the second building block is the liability-hedging portfolio (LHP). This investment principle is conceptually cleaner than the “policy portfolio” approach, which has long been dominant and attempts to find a portfolio that accomplishes both goals at the same time.

The factor investing paradigm recommends that allocation decisions be expressed in terms of risk factors, as opposed to standard asset class decompositions. It is also related to advances in financial economics, specifically the work of Eugene F. Fama (another Nobel Prize winning economist) and Kenneth R. French on empirical asset pricing. It is widely admitted that certain passive equity strategies that select stocks based on given observable characteristics such as low size, high book-to-market ratio or high past year return yield greater average returns than a standard cap-weighted index, and this has been a key driver of investors’ interest in equity indices providing exposure to selected factors. However, the notion of factor is not limited to passive strategies with expected performance above the expected market return. In particular, a factor can also be a “common risk factor”, which affects the returns of multiple securities within a given class, or even the returns of several asset classes. The market factor for equities and the level of interest rates for bonds are two examples.

In liability-driven investing, both definitions of factors are relevant, but they do not apply to the same steps of the process. Factors with a historically robust and economically justified risk premium are clearly good candidates for inclusion in the PSP, where they are expected to improve long-term performance and the risk-return profile, as summarized in the Sharpe ratio, with respect to portfolios traditionally used as benchmarks, like a broad cap-weighted equity index. It is important to emphasize, however, that factor investing is not a free lunch, since the enhanced returns take a long horizon to materialize and because shortfall risk is still present in the short run. As an illustration, our empirical tests show that an equally weighted portfolio of the six traditional US equity factors (size, value, momentum, volatility, investment and profitability) earns on average 11.21% per year between 1972 and 2016, which is well beyond the 10.09% earned by the cap-weighted index, but its maximum drawdown of 52.14% is barely lower than the 53.78% posted by the benchmark.


Factor-matching techniques would be helpful in individual money management, e.g. to help individuals prepare for retirement.


For the construction of the LHP, one should instead look for the risk factors that explain changes in the present value of liabilities over time. Because this present value is calculated by discounting future promised payments, any factor that determines the level or shape of the yield curve is a risk factor for liabilities. This property is exploited in the traditional techniques by which the factor exposures of the hedging portfolio are matched with those of liabilities, like duration and convexity hedging. EDHEC-Risk Institute’s position, which has been affirmed since the beginning of its research on goal-based investing in 2015, is that these methods, which are routinely employed in institutional money management, notably at pension funds, would also be helpful in individual money management to construct portfolios that ensure the achievement of certain goals. In the aforementioned study, we give a specific example by considering a working person who wants to secure replacement income for future retirement. A cash account, which is regarded by many individuals as the safest investment option, actually leaves them with large uncertainty over the amount of income that they will eventually receive, while a fixed-income portfolio with a properly adjusted duration enables them to know exactly how much income their savings will produce.


By choosing a performance-seeking portfolio better aligned with their liabilities, investors can expect higher long-term returns.


The last step of the liability-investing process is the choice of allocation to the PSP and the LHP. Again, fund separation theorems provide useful guidelines by showing that it should be a function of the tolerance for uncertainty and the tolerance for loss, with more risk-averse investors allocating a larger share of their assets to the LHP. This rule should be complemented by another, which says that the risk of the whole asset portfolio with respect to liabilities decreases with the relative risk of the PSP with respect to liabilities. Therefore, investors who choose a PSP with lower tracking error or less drawdown risk relative to liabilities are able to allocate more to this building block without increasing the relative risk of their asset portfolio. The point is that by increasing the weight of the PSP in their assets, they can expect higher long-term returns, and they can do so without facing higher risk. Overall, the recent work conducted at EDHEC-Risk Institute shows that liability-driven investors will benefit from adopting a factor perspective for the construction of their building blocks and the allocation to these components.