Options can mimic hedge fund returns: Andrew Lo

Even complex hedge fund strategies can be replicated.

So says Andrew W. Lo, Harris & Harris Group professor and director of the Massachusetts Institute of Technology Laboratory for Financial Engineering, Cambridge, Mass. Mr. Lo is working on a paper on constructing a buy-and-hold portfolio of options that he says will replicate the returns of hedge fund strategies, such as merger arbitrage funds, that produce non-normal returns.

For pension plans, such a portfolio would give them a way to produce hedge-fund-like returns without paying high hedge fund fees. For researchers and consultants, Mr. Lo's work would help solve an age-old problem: how to go about analyzing a hedge fund that produces uneven returns.

Traditionally, consultants and researchers analyze investment portfolios using the standard mean-variance approach, which looks at how much of the returns of an actively managed portfolio vary from the portfolio's average return. Additionally, they use linear regression analysis to produce an "R-squared," which shows how much of the return of an actively managed portfolio can be statistically explained by its benchmark. An R-squared of 50%, for example, means 50% of a portfolio's returns can be explained by the broad market. But in complex hedge fund strategies, such as merger and fixed-income arbitrage funds, neither of these analyses works because these funds typically produce a steady stream of positive returns with a small risk of blow-up.

James McKee, director of hedge fund research at Callan Associates Inc., San Francisco, said: "Analyzing hedge funds with non-linear return distributions has been a problem. I've heard people talk about it, but no one has reached a general consensus on how to solve it."

Mr. Lo, in a presentation at the CFA Institute's Risk Management Symposium in New York in February, underscored this problem by using a mock hedge fund that he called the perfect timing fund, which placed $1 in 1926 in the Standard & Poor's 500 index and switched that same dollar between the S&P 500 and Treasury bills at the moment when one index was up and the other was down. The perfect timing fund would have produced a little more than $23 billion today, while a passive investment in the S&P 500 would have produced $3,100. Despite the perfect timing fund's R-squared of 70% to the S&P 500, "this strategy can't be replicated using a linear regression model," said Mr. Lo.

Harry Kat, director of the Alternative Investment Research Centre at the City of London's Cass Business School, London, noted the problem. Mr. Kat recently researched using a dynamic trading strategy of options to produce hedge-fund-like returns. "Despite the fact that alternative investments are markedly different from traditional assets such as stocks and bonds, academia still insists on analyzing them using the same old toolbox, including factor models," said Mr. Kat. "The result is a lot of time wasted and a lot of incorrect conclusions all over the place. Are you really willing to attach any value to, and even base your investment decisions on, the alphas and betas derived from models that can only explain 10% to 20% of a fund's returns?"

Mr. Lo said his upcoming paper will show that hedge funds with non-linear returns can be replicated with passive portfolios of options and other derivative securities. "Harry Kat's research is quite striking, but the typical pension plan sponsor probably isn't set up to implement a dynamic trading strategy," Mr. Lo said in an interview. "We show that you can replicate the returns of certain types of non-linear hedge funds with a buy-and-hold portfolio of put and call options. This is much simpler and more practical for pension plans."

He acknowledged that not all strategies can be replicated in this way. For example, event-driven distressed hedge funds are particularly challenging, "but even a partial solution to the replication problem may be useful to passive investors," said Mr. Lo. He expects to complete his paper within the next few months.

Some hedge fund managers questioned how realistic it is to replicate complicated hedge fund strategies.

Cliff Asness, managing and founding principal at AQR Capital Management LLC, Greenwich, Conn., who has conducted research showing that a large portion of returns of the major hedge fund indexes actually come from the broad market, applauded Mr. Lo's efforts. "What Andrew is trying to do is get at what's the managers' ‘skill' vs. other things they do with regularity. … If people produce strategies that make money most of the time because they're taking a small risk of disaster, and over some period that disaster does not come, they look great. But it does not mean they're any good. It sounds like Andy is choosing an extreme to make a good point," Mr. Asness said in an interview.

Jeff Geller, director of hedge fund investments at Russell Investment Group, Tacoma, Wash., said: "What Andrew is getting at is that you can see a hedge fund that looks to be producing a smooth return pattern without necessarily realizing what the manager is doing to get those returns. You have to make sure you understand the risks that managers are taking."

Kent Clark, managing director and chief investment officer of hedge fund strategies at Goldman Sachs Asset Management, New York, added: "A potential challenge with replication is that managers change their strategies. For example, if you look at merger arbitrage index returns over the period from 2002 to 2004, they have more similarity to (corporate debt) trading strategies than true merger arbitrage."

Warun Kumar, co-founder and CEO of hedge fund of funds firm Sigma Investment Advisors LLC, New York, which focuses on tail-risk when putting together a portfolio of hedge funds, said he is not sure whether Mr. Lo's technique would work. "What Andrew is doing sounds great in theory. But in practice, with a merger arbitrage fund, for example, the options market for those companies involved in a merger may not be very liquid."