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.... but not as much as Ranjan Badhuri implies in his article in

Ranjan writes about a game where liquidity pays:

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 problem with this argument is that investing is a different game from this one.  The game he describes is extremely path dependent, as the probability of outcomes after each step is very much changed by past outcomes.

If you want to make a financial argument regarding the investment performance of hedge funds - with or without lockups - then real financial data should be used in my opinion.

Interested in your thoughts,

Jonathan Starr Add to Google Posted on Sunday, December 23, 2007 4:58 PM Philosophy , Critique , Personal , Thought Experiments , Finance | Back to top

Comments on this post: Liquidity is Undervalued ...

# re: Liquidity is Undervalued ...
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I don't get how the odds are in your favor if 60% of the time you have to give up a dollar. Doesn't seem to be a winning situation at all. Unless I start with $0 and don't have to go into debt if I pick a black one. Then I can at least play until I get a white one and be up a buck. I just don't get it.
Left by Lorin Thwaits on Dec 23, 2007 9:37 PM

# re: Liquidity is Undervalued ...
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From Ranjan (in his post)

The best way to calculate the expected winnings from a given hat is to realize that it can be done so in a recursive nature. Consider, a hat with m black balls and n white balls. Suppose you pick a white ball, then you are left with m black balls and (n-1) white balls, and the decision of whether or not to play is determined by the expected winnings from this “new, smaller” hat. Indeed,

E (winnings from m black balls, n white balls) =
max { m/(m+n) [-1 + E(n,m-1)] + n/(m+n) [1 + E(n-1,m)] , 0 }

The above formula shows that we should calculate the expected winnings from the “small” hats and build our way up. This recursion lends itself well to a computer language, and can be done on excel in minutes.

Anyway, if you work it out in Excel, because you can choose to quit whenever you want to, and because the odds move in your favor after a loss, playing this game actually works out in your favor (although it is counterintuitive).

Left by Jonathan Starr on Dec 23, 2007 11:23 PM

# re: Liquidity is Undervalued ...
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I still think it's Vegas. I mean, after picking one black ball, you are still at a disadvantage with a 55% chance of picking black the next time. Only after picking two black balls does it become a break-even situation.

Nonetheless I agree that more people should have more liquid investments so as to avoid emergency debt. With double the cost of transportation for the past 6 months, here comes the recession. We need to each take careful assessment, and live within our means!
Left by Lorin Thwaits on Dec 25, 2007 6:39 AM

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