ALTERNATIVE VIEWPOINTS …powered by CAIA
As part of our on-going series of features written by holders of the Chartered Alternative Investment Analyst (CAIA) designation, we are pleased to bring you this piece by Ranjan Bhaduri, Ph.D., CFA, CAIA. Dr. Bhaduri is Vice President in the Graystone Research group at Morgan Stanley. Prior to this, he was with a multi-billion dollar capital management firm where he was involved in all aspects of its fund of hedge funds and structured finance business. He has also held advisory roles at the East-West Center, a leading think tank on the Asia-Pacific region and has taught finance and mathematics at several universities. He is the author of several articles on advanced risk management techniques and hedge fund issues and is a member of the American Mathematical Society, the Mathematical Association of America and the Global Association of Risk Professionals. Dr. Bhaduri also serves on the Advisory Council of the World Trade University.
Dr. Bhaduri has just returned from a speaking tour that took him from Chicago to London and Beijing where he addressed audiences on the role of liquidity in hedge fund returns.
By: Ranjan Bhaduri, special to AllAboutAlpha.com
The word liquidity gets bandied about quite a lot, but it is surprising how many portfolio managers take a naÃ¯ve approach to liquidity. It is well known that one should be compensated for investing in less liquid instruments (liquidity premium), but how much? What is the value of liquidity?
It is dangerous in merely trust one’s intuition on the value of liquidity. Consider the following one-person game:
The “Balls in the Hat Game”
The game consists of a hat that contains 6 black balls and 4 white balls. The player picks balls from the hat and gains $1 for each white ball, and loses $1 for each black ball. The selection is done without replacement. At the end of each pick, the player may choose to stop or continue. The player has the right to refuse to play (i.e. not pick any balls at all). Given these rules, and a hat containing 6 black balls and 4 white balls, would you play? (Why?)
Mathematically one can prove that there is a POSITIVE expected value (of 1/15) in playing this game, so one SHOULD play! The ability to stop any time is analogous to perfect liquidity (i.e. being able to pull out of an investment at any time without the action having an impact on the value of the investment). This value of liquidity helps overcome the imbalance between the black and white balls, and thus makes this game profitable. This is interesting from a behavioral finance point of view, since it seems to suggest that humans are wired such that they will tend to underestimate the value of liquidity.
The mathematics behind calculating the value of liquidity can be complex as there can be subtle nuances. Niall Whelan of Scotia Capital and I wrote a pair of papers coming out which tackles the above game in the asymptotic case (i.e. hats of infinite size) and connect the value of liquidity to option pricing. Niall is one of the best quants north of the South Pole and much of these papers were hammered out in an all-night bus ride that we were forced to take from NY to Toronto (our flight from La Guardia got cancelled but we both needed to be back in Toronto in the morning for important meetings).
Mistaking Illiquidity for Alpha
Consider the following:
- Hedge Fund A has a two-year lock-up with annual redemption and trades in illiquid instruments.
- Hedge Fund B has no lock-up with monthly redemption and trades in liquid instruments.
- Both have a five-year track year.
It is incorrect to merely compare the statistics (return, volatility, skew, kurtosis, omega, sharpe, etc.) of these two funds. Hedge Fund B allows the investor to get out of the investment sooner and this has a value that does not appear when one calculates the statistics. Due to the illiquidity and lock-up, Hedge Fund A should be furnishing a better statistical return. One needs to quantify the value of liquidity in order to make a fair statistical comparison. Otherwise, it really is comparing apples to oranges. Too many portfolio managers are mistaking the illiquidity of Hedge Fund A with alpha. Moreover, many portfolio managers are not getting paid enough to take on the illiquid assets.
While a hedge fund which trades in illiquid instruments is prudent to have more stringent redemption clauses (or else it will leave itself vulnerable to a liquidity mismatch), it is generally true that there are less hidden risks in hedge funds that trade more liquid instruments. Hedge funds that have the opposite type of liquidity mismatch (trade liquid instruments but have onerous redemption terms) often claim that they are trying to avoid hot money of fund of funds. However hedge fund managers always retain the right to refuse a potential investor, so that does not really wash. Furthermore, if they are truly trading liquid instruments, then it should not really make all that much difference if a client redeems. Finally, if they are delivering the risk-adjusted returns that they promised, then the probability of investors wanting to pull their money out is low. Bottom line is that if the redemption terms are more onerous, then one should expect a higher return.
Side pockets, gates, lock-ups, notice one really needs to understand the fine print in order to avoid being caught in a Hotel California situation (in reference to the famous Eagles song which contains the lyrics â€“ You can checkout any time you like, but you can never leave!). While qualitative due diligence is more important than quantitative, intuition is another word for laziness concerning matters of liquidity. Liquidity buckets and perhaps liquidity derivatives may be helpful techniques of portfolio management. Do not mistake illiquidity for alpha.
Bhaduri has also penned an in-depth article on this topic for upcoming issues of the Journal of Alternative Investments and Wilmott Magazine. This paper by Bhaduri covers some of the more complex mathematical dimensions of the topic, and these slides from his presentation to the 2007 Canadian Annual Derivatives Conference provide a good overview of the key themes he discusses above. The opinions expressed in this guest posting are those of the author and not necessarily those of AllAboutAlpha.com.
Ranjan Bhaduri can be reached at: firstname.lastname@example.org