Diversification alone is not enough to manage downside risk, rather academic research in dynamic portfolio theory suggests the three complementary techniques of diversification, hedging, and insurance can be used together to design customised investment solutions, that ultimately separate assets into performance seeking portfolios and liability hedging portfolios, according to EDHEC’s Felix Goltz and Stoyan Stoyanov.

The global financial crisis has shifted the attention of all investors to risk. A survey of the practices of European pension funds conducted by EDHEC-Risk Institute^{1} highlights three great challenges — gaining additional access to performance through optimal diversification, improving the hedge of the stream of liabilities, and respecting the minimum funding ratio constraint by insuring downside risk away.

The essence of diversification is captured by the proverb: “Do not put all your eggs in one basket”. In portfolio construction, the proverbial insights were given a scientific basis by Harry Markowitz (1952). In a landmark paper which gave birth to modern portfolio theory, Markowitz introduced variance as a proxy for risk and formulated a portfolio construction technique by means of an optimisation problem — combine risky assets in such a way as to minimise variance at each level of expected return.

The resulting set of portfolios enjoys the full benefits of diversification and describes the efficient frontier. In the presence of a risk free asset, Tobin (1958) argued that risk-averse investors should hold portfolios of only two funds — the risk-free asset and a fund of risky assets which is itself an efficient portfolio.

The degree of risk aversion influences only the relative weight of the two funds, not their composition; the implication for portfolio construction is that lower-risk portfolios are best obtained by increasing the weight of the risk-free asset rather than by re-optimizing the fund of risky assets.

In the presence of a risk-free asset, investors choose portfolios along a linear efficient frontier called the capital market line (CML) that has the highest possible slope, or risk-return ratio. The CML identifies geometrically the fund of risky assets as the point of tangency with the efficient frontier of the risky assets, also known as the tangency portfolio, indicating that it has the best risk-return ratio of all other risky portfolios.

Under a series of strong assumptions, Sharpe (1964) used Tobin’s two-fund separation theorem to develop the capital asset pricing model (CAPM), suggesting that the tangency portfolio is the market portfolio that consists of all existing assets weighted by market capitalisation.

In the past 40 years, passive investment approaches crucial for institutional investors have been developed on the presumption that a cap-weighted portfolio of stocks was a good proxy for the elusive market portfolio and an efficient means of allocating capital.

Since the assumptions behind CAPM have been found empirically incorrect, using a cap-weighted index is not, in practice, theoretically justifiable. Furthermore, empirical studies demonstrate that commercially available equity indices do not provide an efficient risk/reward profile and are heavily concentrated portfolios. In other words, they are far less efficient than the tangency portfolio.

A practical approach to building a proxy for the tangency portfolio is to solve for the portfolio of risky assets yielding the highest risk-adjusted return, ie, slope or Sharpe ratio. Critical inputs for the quality of the proxy, however, are the risk and the expected return parameters.

Going back to the roots of modern portfolio theory, Amenc et al (2010b) suggest solutions to these challenges and develop an approach for efficient index construction that shows that it generates significantly higher out-of-sample Sharpe ratios than those of the corresponding cap-weighted indices.

Diversification allows investors to obtain the best risk/return tradeoff in normal market conditions. It is often mistakenly believed that diversification can also provide explicit protection from extreme risks if, rather than variance, a downside risk measure is used.

Although diversification may make extreme portfolio losses less likely, it does not provide a guarantee that such losses will not occur. The reason is that the correlation of assets tends to spike in market crashes, making diversification inefficient. Nonetheless, two other methods, hedging and insurance, can be used to manage downside risk.

While diversification is used to construct portfolios achieving the highest risk-adjusted returns, hedging is done to shed risk that cannot be diversified away. In fact, the theory of optimal asset/liability management (ALM) indicates that efficient capital allocation involves two portfolios — a performance-seeking portfolio (PSP) constructed through diversification, and a liability-hedging portfolio (LHP) used to deal with the variability of the stream of liabilities arising from different sources, mainly interest rates and inflation^{2}.

LHPs can be designed in various ways. Cashflow matching is a popular technique that, through investments in suitable bonds, attempts to ensure a perfect static match between the cash flows from the portfolio of assets and the commitments in the liabilities. Although the technique is simple, a big problem is finding bonds with the proper duration, a major challenge above all in the corporate bond sector.

Approaches to hedging inflation include investing in cash instruments such as Treasury inflation-protected securities (TIPS) or derivatives such as inflation swaps. A problem with this approach is the very low real performance of inflation-protected securities; for this reason, other asset classes have also been considered. Although research is ongoing, empirical studies indicate that stocks, commodities, and real estate can offer protection from inflation at lower cost.

From an ALM perspective, hedging is done to protect long-term liability needs. It can also reduce downside risk — the equity risk in an equity portfolio, for example, can be reduced trivially by increasing the weight of the cash component, leading to a limited downside risk but also to limited upside potential.

The right approach to limiting downside risk while maintaining access to the upside potential is risk-controlled investing (RCI), a form of insurance. Like any other form of insurance, it comes at a certain cost.

Dynamic asset allocation theory suggests that downside risk constraints, or asset value floors, can be implemented through an optimal state-dependent weighting of the PSP component depending on the size of the risk budget. In this way, risk exposure can be adjusted in an optimal manner, allowing at the same time the highest possible exposure to the upside potential of the PSP component within the imposed risk constraints.

The framework is flexible and can accommodate such floors as capital guarantees, maximum drawdowns, and rolling performance floors. The floor can also be benchmark-relative, indicating that the LHP can be adopted as a benchmark. In this way, risk-controlled investing can be done in an ALM context and provide a guarantee that the value of the assets will remain above a multiple of the value of the liabilities at any time until the horizon.

As mentioned above, diversification alone is not an appropriate means of controlling downside risk.

However, well-diversified portfolios are a crucial ingredient in such insurance strategies because an attractive risk/reward ratio makes it possible to lower the cost of insurance.

Broadly speaking, investment management concerns optimal expenditure of risk budgets. To this end, diversification, hedging, and insurance represent three complementary rather than competing techniques. Diversification can be used to achieve efficient risk-adjusted returns, specific risk factors such as interest rate and inflation can be neutralised through hedging and, finally, insurance can be used to implement downside constraints. Academic research in dynamic portfolio theory suggests the three techniques can be used together to design customized investment solutions.

Felix Goltz is head of applied research at EDHEC-Risk Institute, and Stoyan Stoyanov is head of research at EDHEC Risk Institute Asia.

**Footnotes**

- EDHEC Survey of the Asset and Liability Management Practices of European Pension Funds, EDHEC-Risk Institute, June 2010.
- See Amenc
*et al.*(2010a).

**References**

- Amenc, N, F. Goltz, L. Martellini and V. Milhau (2010a), “New Frontiers in Benchmarking and Liability-Driven Investing,” EDHEC-Risk Institute Publication.
- Amenc, N., F. Goltz, L. Martellini, and P. Retkowsky (2010b), “Efficient Indexation: An Alternative to Cap-Weighted Indices,” EDHEC-Risk Institute Publication.
- Markowitz, H. M. (1952), “Portfolio Selection”,
*Journal of Finance*7, (1), 77-91. - Sharpe, W. F. (1964), “Capital Asset Prices: A Theory of Market Equilibrium under Conditions of Risk,”
*Journal of Finance*19 (September): 425-42. - Tobin, James (1958), “Liquidity Preference as Behavior towards Risk,”
*Review of Economic Studies*, 25, 65–86.