By Victor Haghani and James White¹
ESTIMATED READING TIME: 8 min.

Well, so what? Some economist called you irrational. Why should you care? You should care because this is exactly the kind of irrationality that will allow me to take all your money. … When an economist calls you irrational, it almost always means that if you follow through on your stated preferences, a sufficiently clever opponent can take all your money, leaving you smiling along the way.
    – Steven Landsburg, Can You Outsmart an Economist? (2018)

The above quote is describing what economists call a “money pump,” which is a process that extracts money from a person with weird or inconsistent preferences and transfers it to the pumper in a nearly sure way. No one in their right mind would want to be subject to a money pump, yet the target would find himself going through it making decisions which individually matched his preferences, but collectively were inconsistent or unrealistic. If he played long enough, he’d be guaranteed to lose all his money, while at each decision point making a choice he’d be quite happy with.

In this note, we’re going to explore the question of whether investors who allocate their wealth primarily by extrapolating past returns into the future can be money pumped. Both survey-based and anecdotal evidence suggest that extrapolative – aka “return-chasing” – behavior is widespread among investors, especially in assets and strategies where the absence of future cash-flows leaves little choice but to base decisions on historical performance.

To answer this question, let’s create an imaginary world with a market for just one risky asset, which we’ll call “AirShares”. We’ll assume that one unit of AirShares exists, its price is $100, it generates no cash flows, and it’s very risky, with annual volatility of 50%.

There are three investors:

• First, there’s Mr. X: our main subject of interest who decides how much AirShares to own based on his estimate of its expected return.² Mr. X comes up with this estimate by calculating AirShares’ return over the past year. He’s an extrapolator because he forms his expected return beliefs by extrapolating past returns into the future.
• The other two market participants we’ll call Ms. Ping and Mr. Pong. They’re very astute and would love nothing more than cranking a money pump. They don’t form their expected return for AirShares from historical returns, nor from its prospective cash-flows (since it doesn’t have any) – rather, they make their trading decisions based on their understanding of Mr. X’s behavior.

Let’s start the situation off with a few more assumptions:

• AirShares had a 25% return over the past year.
• Mr. X has $200 of savings, and given a 25% expected return, he wants to allocate 50% of his wealth to AirShares.³ So he owns all the outstanding amount of AirShares (1 share), at the current price of $100/share, and his portfolio is right where he wants it to be.
• Ping and Pong each start with $25 of wealth.

How might things play out from here? Well, Ping and Pong could come up with a fun game: they’ll flip a coin, and if it comes up heads, Ping will make a market in AirShares no more than $10 wide, and Pong will commit to either buy or sell 0.01 shares at Ping’s posted market. If it comes up tails, their roles will be reversed. Maybe if questioned by the authorities on what they’re doing, they’d respond by saying they’re just looking for some action or just practicing their business of market making.

Let’s say the coin comes up heads, and Ping will either buy at $95 or sell at $105. Pong then decides to sell 0.01 shares at 95 (leaving Pong short 0.01 shares, and Ping long 0.01 shares).

What happens next is that Mr. X sees that AirShares just traded at $95. He calculates the one-year realized return is now 18.75%, down from 25%. As a good extrapolator, he updates his expected return to 18.75%. He now wants to have just 37.5% of his wealth in AirShares, so he’ll need to sell 0.23 shares at $95 to get there. Ping and Pong oblige, and they’re not too worried about how much of the trade each does because they’re looking forward to many more trades where this one came from.

Now Ping and Pong keep playing their fun game. They flip again – let’s say it comes up tails and now Ping sells 0.01 shares at 100. Of course, Mr. X sees the new price of $100, and updates his expectation for AirShares’ future return back to 25%, the new one-year historical return. He again wants to have 50% of his wealth in AirShares. He’ll need to buy 0.225 shares from Ping and Pong, and they both independently and willingly sell those shares to him.

So, where are we left? At this point, Mr. X’s portfolio is worth $198.85, which is $1.15 or 0.58% less than his starting wealth despite the price of AirShares being back at its starting point. After 1,000 rounds of the above “fun”, Ping and Pong will have virtually all (99.7% to be exact) of Mr. X’s money – ouch! But sadly for Ping and Pong, with Mr. X out of money, they run out of profitable trading strategies unless more investors like Mr. X enter the market.

This is what a money pump looks like: bleeding wealth while acting consistently with your preferences every step along the way. It’ll take a while, but eventually Ping and Pong will have all of Mr. X’s wealth – and every trade Mr. X did, he did with a smile. Mr. X makes every decision rationally based on his model, yet Ping and Pong systematically extract his wealth by exploiting his extrapolative behavior.

Perhaps the most commonly-encountered money pump in the real world involves people who behave as “risk-seekers.” This allows them to be money-pumped by offering them many small gambles with a negative edge – e.g. Vegas casinos and online sports betting – which will extract whatever wealth they’ve committed to these activities over time. Our hypothetical case is a bit different, as Mr. X can still be money-pumped even if he’s invested in an asset with a positive expected return all the while.

If anyone asks them, Ping and Pong might honestly say they weren’t conscious of doing anything wrong – they could have built complex trading models that just happened upon this magical money machine. And there are lots of interesting and hard-to-detect variations to the game that Ping and Pong can play, which we needn’t go into here since this is just an imaginary exercise.

Or is it? Here’s an interesting recent case brought by the U.S. Justice Department:

Gotbit Consulting LLC (Gotbit), a financial services firm known in the cryptocurrency industry as a “market maker,” was sentenced yesterday in federal court in Boston for criminal charges relating to Gotbit’s fraudulent manipulation of cryptocurrency trading volume on behalf of client cryptocurrency companies.
…Gotbit was a well-known “market maker” in the cryptocurrency industry. Between 2018 and 2024, Gotbit provided market manipulation services to create artificial trading volume for multiple cryptocurrency companies.
…Gotbit is the third market maker to resolve criminal charges relating to wash trading in the cryptocurrency industry.

… and a recent Bloomberg article by Muyao Shen reports:

Rug pulls. Sniping. Trading “cabals.” The niche world of memecoins on the Solana blockchain is rife with danger for those unfamiliar with the machinations that cause token prices to suddenly surge and then crash…
Influencers often connect with creators through what crypto traders call “cabals”…These groups often are deeply involved in creating and allegedly manipulating prices of various memecoins to exploit retail investors.

Even if you found our imaginary marketplace far-fetched, we hope you found this an entertaining and intriguing thought experiment for considering the merits of extrapolating future returns from past returns in the presence of sharp market participants like Ping and Pong. If this story makes you worried about being like Mr. X, here’s a question you might want to ask yourself: Would you own your current portfolio of assets, scaled as you have them, if everything you own had worse historic returns than the things you don’t own?

Of course, this is a made-up example. For it to be realistic, we’d need a very volatile asset which doesn’t have cash-flows – and even if such assets and marketplaces were common, attentive regulators would never allow Ping and Pong to play their game.

Indeed, SEC Chair Atkins seemed to have Ping and Pong in his sights in a CNBC interview on October 22nd, saying he’s on the lookout for “indicia” of “hanky-panky”:

What we’re concerned about is manipulative behavior. We have stopped trading on eight foreign companies on NASDAQ that showed indicia of manipulative behavior — ramp and dump, we call it – and so those have been shut down. So we are monitoring the market for the behavior that indicates, you know, hanky-panky going on in the marketplace.

So nothing to worry about here, right?

Further Reading and References

• Barberis, N., Greenwood, R., Jin, L., and Shleifer, A. (2015). “X-CAPM: An extrapolative capital asset pricing model.” Journal of Financial Economics.
• De Grauwe, P. (1993). Exchange Rate Theory: Chaotic Models of Foreign Exchange Markets. Blackwell.
• DeLong, B., Shleifer, A., Summers, L. and Waldmann, R. (1990a). “Noise Trader Risk in Financial Markets.” Journal of Political Economy.
• DeLong, B., Shleifer, A., Summers, L., Waldmann, R. (1990b). “Positive feedback investment strategies and destabilizing rational speculation.” Journal of Finance.
• Gabaix, X., & Koijen, R. (2021). “In Search of the Origins of Financial Fluctuations: The Inelastic Markets Hypothesis.” NBER and SSRN.
• Grinold, R. and Kahn, R. (1994). Active Portfolio Management: A Quantitative Approach for Producing Superior Returns and Controlling Risk. McGraw Hill.
• Haghani, V. and White, J. (2025). “The Impact of U.S. Stock Buybacks: Theorey vs Practice.” SSRN.
• Haghani, V. and White, J. (2024). “Leverage It or Leave It? Making Sense of Turbo-charged ETFs.” SSRN.
• Perold, A. and Sharpe, W. (1988). “Dynamic Strategies for Asset Allocation.” Financial Analysts Journal.
• Shleifer, A., and Summers, L. (1990). “The noise trader approach to finance.” The Journal of Economic Perspectives.

1. This is not an offer or solicitation to invest, nor are we tax experts and nothing herein should be construed as tax advice. Past returns are not indicative of future performance.
   Thank you to Rich Dewey, Larry Hilibrand, John Karubian, Marlin Risinger, Jeff Rosenbluth and Mike Popov (Vic’s excellent and patient ping-pong coach) for their helpful comments.
   
2. His full calculation can also involve the risk of AirShares and his personal degree of risk aversion. We’ll assume these are both constant, so expected return is the only thing potentially moving around.
   
3. He could rely on the Merton share to decide his optimal allocation – which, in this case, would yield \(\frac{25\%}{(2 \cdot 50\%^2)}\) for \(\gamma\) = coefficient of constant relative risk-aversion = 2.