MERCHANDISER Diversification Not Sufficient for Managing Risk
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 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 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 optimization problem – combine risky assets in such a way as to minimize 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 capitalization. In the past forty 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 to be 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, i.e., slope or Sharpe Ratio. Critical inputs for the quality of
16 December 2010
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 indexTM 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 trade-off 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.
It is often mistakenly believed that
diversification can also provide explicit protection from extreme risks
LHPs can be designed in various ways. Cash-
flow 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
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