CACEIS NEWS 37

No. 37 - March 2014 - caceis news 3 products and services

Interview of Lionel Martellini, Professor of Finance, EDHEC Business School, and Scientific Director, of the EDHEC-Risk Institute regarding the first study carried out within the framework of the new research chair, sponsored by CACEIS

Why have you chosen to study asset allo- cation by means of risk factors rather than asset classes? Analysis of diversification in terms of risk factors has become a new paradigm. Its emergence has been supported by the high- lighting of the limitations of the convention- al approach, based on the supposed advan- tages of diversification between asset classes. First of all, it is worth recognising that a breakdown by asset classes is often arbitrary. For example, convertible bond yields are ex- posed not only to interest rate and credit risk, but also - due to the conversion option - to equity and volatility risk. As a result, treating these securities as if they belong to the bond class is debatable as a classification choice. Another limitation relates to the correlation of asset classes. An investor practising conven- tional diversification and allocating the same amount to different correlated assets may be under the illusion of managing a well-diversi- fied portfolio. In practice, however, their port- folio may be subject to high concentration of a small number of risk factors. For example, an investor holding 25% equi- ties, 25% corporate bonds, 25% speculative funds and 25% private equity would be very likely to be exposed to a dominant risk fac- tor. This reasoning applies to short-term and long-term investments. Are the advantages of diversifying invest- ments illusory? Although it is well known that diversifica- tion consists intuitively of not putting all of your eggs in one basket, it should be recog- nised that this is still a rather ambiguous for- mulation. As stated above, the conventional approach consists of saying that each basket is repre- sented by an asset class and that being well diversified consists of the investor spreading their eggs (money) across the largest pos- sible number of baskets (asset classes). This poses at least two problems. Firstly, reasoning in terms of correlated as- set classes is not satisfactory. It is hard to see what the advantage would be of putting your eggs in different baskets if these baskets are related to each other, which means that they could all collapse together. Furthermore, it seems important to take ac- count of the risk associated with each of these baskets. If we have two baskets, but the sec- ond is much more fragile than the first, equal allocation of the eggs between both baskets would not be appropriate. The desire for di- versification would inevitably result in trying to allocate different assets so that each has an equal contribution in terms of risk, rather than in purely monetary terms. It is only within a fictional context with decorrelated assets of the same risk that equally weighted allocation would result in all assets making an equal con- tribution to portfolio risk.

Are there any indicators that allow for cor- relations to be identified between asset classes in order to give a coherent overview of the risks? It should be noted that counting the number of baskets - whether represented by correlat- ed asset classes or decorrelated risk factors - is not as easy as it seems. For example, if an investor allocates 99% of their wealth to a particular asset class or risk factor, while the remaining 1% is allocated to 9 other as- set classes or risk factors, it would clearly be of little relevance to say that the number of constituents represented in the investor’s portfolio is equal to 10. The effective number in terms of risk assessment would be much lower, in this case just above 1. In order to give a more relevant measure- ment of the number of constituents in a portfolio, an indicator can be introduced, called effective number of constituents” or ENC, formally defined as the entropy of the weight distribution of the portfolio. This quantity tends towards 1 when the portfolio tends to be concentrated as a single asset, and takes on a value equal to the nominal number of constituents if the portfolio is equally weighted. Therefore, in the same way as duration is a more relevant measurement of the effective maturity of a bond than facial maturity, the effective number of constituents is a more relevant measurement of the number of bas- kets than the nominal number. The “effective number of bets” (ENB) is defined as the en- tropy of the distribution of contributions of a series of non-correlated risk factors repre- senting total portfolio risk. This means that a portfolio invested with equal weighting in very closely correlated assets - such as bonds from the same sover- eign issuer - will have a high ENC but a low ENB (well diversified in terms of allocation to portfolio constituents but highly concen- trated in terms of exposure to risk factors). ENB allows for more in-depth risk analysis than ENC. You have studied the performances over 55 years of 14 major international equity indi- ces (United States, Europe, Asia). How well diversified are they? Building up a stock market index on the ba- sis of weighting proportional to market capi- talisation poses a problem, as this system of weighting tends to create portfolios with a high concentration of investments in a rela- tively small number of stocks, precisely those with the largest capitalisations. Within a universe like the CAC 40, the FTSE 100 or the S&P 500, there are considerable differences in terms of size of capitalisation. These very marked differences imply that the smallest stocks in each universe receive just a very small allocation within the index. This concentration leads to a high opportunity cost in terms of diversification. By definition, poorly diversified portfolios contain excess

risk without remuneration, and in this re- spect do not represent effective benchmarks for investors looking for the best risk-reward profile. You dedicate another part of your study to analysis of the 10 largest pension fund portfolios in the world and the 1,000 larg- est US pension fund portfolios. What is the main conclusion of this? The main conclusion obtained from our study of the diversification of US pension funds is that there is a positive relationship between the effective number of bets and performance in downward markets. The most well diversified funds, within the sense of a higher effective number of bets, have tended to be more resilient to extreme mar- ket situations, such as that of autumn 2008. Although statistically significant, however, this is not a linear relationship. As can be expected, the pension funds performed best in 2008 are those that adopted an extremely concentrated portfolio, investing exclusively in risk-free assets. Furthermore, this relationship is much weaker when diversification is measured by the effective number of constituents, which confirms the idea that reasoning in terms of independent risk factors allows for a better assessment of the level of diversification of a portfolio. In your opinion, how could this study con- tribute to changes in measurement, perfor- mance attribution and risk reporting com- ponents? The study demonstrates the possibility of in- troducing new indicators to help to improve portfolios’ ex-ante risk analysis. Within this context, it seems that indicators such as the effective number of independent bets in a given portfolio allow asset manag- ers to make a better assessment of the degree of portfolio diversification and therefore the performance potential of their portfolios un- der different market conditions. The introduction of these indicators could be useful both within the context of inter-class allocation and within the context of an intra- class portfolio, such as an equity portfolio ■

“  The study demonstrates the possibility of introducing new

indicators to help to improve portfolios’

ex-ante risk analysis. ”