**A Martini with Martellini**

*Consultant and journalist Pierre Saint-Laurent* covers **EDHEC’s Asset Management Days** in Geneva this week for All About Alpha. On Monday, he sat down with EDHEC’s Lionel Martellini to have a frank discussion about hedge fund replication in advance of Martellini’s much anticipated presentation on Tuesday.*

*Martellini, one of the top EDHEC researchers, is the co-author of a new study** on the topic (to be presented for the first time at the conference). Martellini is a member of the editorial board of The Journal of Portfolio Management and The Journal of Alternative Investments. His research on quantitative asset management and derivatives valuation has been published in leading journals and featured in major dailies such as The Financial Times and The Wall Street Journal.*

**Pierre Saint-Laurent (PSL): Professor Martellini, thank you for meeting with All About Alpha. In your words what exactly is hedge fund replication?**

Lionel Martellini: Hedge fund replication is a set of investment approaches that hold the promise of lower fees, greater transparency, and higher liquidity while accessing alternative risk premia. The delivery of so-called “alternative beta” allows us to maintain desirable distributional asymmetries with these added benefits. At least, that’s the objective.

There are two main approaches to HF replication. The first is factor-based replication, the second is payoff distribution replication.

**PSL: Can you please define them further?**

With proper specification of the factors, factor-based replication will produce a relatively accurate replication of the distributional features of hedge funds. Payoff distribution replication is a clever approach, championed by Harry Kat, which replicates the statistical properties of hedge funds through an option-like way of thinking about hedge fund payoffs.

**PSL: Let’s take these one at a time, starting with the factor-based approach.**

The factor-based approach is conceptually correct. That’s because the factors actually explain hedge fund behavior and allow an exact replication. The sum of the factors constitutes the â€˜recipe’ of hedge fund behavior and is therefore accurate. But here’s the catch: Model quality is poor because the factors are hard to identify. Our research models have produced low in-sample quality measures (e.g., 20-40% R-squared measures and other equivalent goodness-of-fit calculations). Out-of-sample calculations, however – those that really count – are catastrophic, with quality measures such as R squared tending for all practical purposes to zero.

**PSL: What seems to be the problem?**

The problem is that factor exposures are not stable over time. Why? I think there are two reasons. Firstly, managers rebalance tactically, so instability may be part of the process. Second, managing risk according to a risk budget will force the manager to change exposures when the risk budget is spent. This is because the manager is working to an absolute benchmark, in this case the risk budget. In a long-only portfolio, the manager manages to a moving target, a relative benchmark. By construction, this recalibrates to risk in tandem with the portfolio, thus â€˜absorbing’ the tactical risk change.

**PSL: So what can academics do to help solve this problem?**

LM: We’re working on it. One idea, amongst many we are pursuing, consists in analyzing option portfolios. The optionality tends to improve quality measures. The correct specification of a full set of explanatory factors is a very significant undertaking. This is clearly work in progress.

**PSL: This is not the end of the road for factor-based replication research, then. What about payoff distribution replication?**

As I said, this is a clever approach. Instead of the â€˜full-blown’, conceptually accurate factor-based approach, it consists of circumventing the specification issue by identifying payoffs as a function of a so-called â€˜reserve asset’. The cleverness comes in using optionality a la Fischer-Black and Merton (as an analogy, think of delta hedging) to dynamically calculate how much should be held in the reserve asset (the rest of the portfolio is held in the risk-free asset).

**PSL: Is this the way to go then?**

We have attempted to model payoff distribution replication with the available information from Kat’s publications, which are somewhat allusive. Our replications on long-term distributions – say, 10 years – seem relatively acceptable. On shorter timespans, though, the quality deteriorates significantly.

**PSL: Any thoughts on why this may be the case?**

I can comment on the work we’ve been doing on the topic. Using the S&P 500 index as the reserve asset (as Kat does), our replications underperform systematically and significantly, by approximately 500 bps per year. We’ve also noticed some significant performance differences between the results obtained using 1990-2000 data and those obtained using 1997-2007 data (and between the results obtained using 1997-2000 data and 2000-2007 data). These data sets are rather different from the point of view of equity market behavior.

Another important aspect of this approach is that it captures the second, third and fourth moments of the replicated distributions well. This makes it quite suitable for the design of structured products and for managing risk profiles. However, it does not do a good job on the first moment – the average return. This is an issue, as I think investors are likely to be concerned about the returns of their investments. This is the state of research as we understand it.

**PSL: What does this say to investors contemplating hedge fund replication for their portfolios?**

I would advise caution. I understand providers may hold proprietary models and information, which may be withheld for competitive reasons. However, academic research over several years has failed to identify modeling that reasonably identifies how to proceed with effective hedge fund replication. I believe that we may reach a point at which hedge fund replication will be an applicable alternative to traditional hedge fund investing. Clearly, my EDHEC colleagues and I are working hard towards that goal. But it is definitely a work in progress. Anyone considering hedge fund replication at this juncture needs, in my view, to kick the tires and check the oil. Hedge fund replication is a wonderful idea, but its implementation is not straightforward.

**PSL: Professor Martellini, thank you for your time.**

** Pierre Saint-Laurent, MSc, CFA, CAIA is president of AssetCounsel Inc., one of Canada’s top alternative investments consultancies with offices in Toronto and Montreal.*

***W. GÃ©hin, L. Martellini and J.-C. Meyfredi, research to be presented in the Emerging Alternatives to Hedge Funds session, EDHEC Asset Management Days, Geneva, Mar. 13, 2007.*

## 3 Comments

March 14, 2007 at 4:24 pm## pb273